Answer:
The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].
Alyssa purchased 4 Americana chickens and 8 Delaware chickens.
Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.
Step-by-step explanation:
Given:
Let the number of Americana chickens be 'x'.
Let the number of Delaware chickens be 'y'.
Number of chickens purchased = 12
Now we know that;
Number of chickens purchased is equal to sum of the number of Americana chickens and the number of Delaware chickens.
framing in equation form we get;
[tex]x+y =12 \ \ \ \ equation\ 1[/tex]
Also Given:
Cost of Americana chickens = $3.75
Cost of Delaware chickens = $2.50
Total amount spent = $35
Now we know that;
Total amount spent is equal to sum of the number of Americana chickens multiplied by Cost of Americana chickens and the number of Delaware chickens multiplied Cost of Delaware chickens.
framing in equation form we get;
[tex]3.75x+2.5y =35 \ \ \ \ equation\ 2[/tex]
Hence The System of equation to determine the number of chickens purchased is [tex]\left \{ {{x+y =12} \atop {3.75x+2.5y =35}} \right.[/tex].
Now to find the number of each type of chickens she purchased we will solve the above equation.
First we will multiply equation 1 with 2.5 we get;
[tex]2.5(x+y)=12\times2.5\\\\2.5x.+2.5y = 30 \ \ \ \ equation \ 3[/tex]
Now we will subtract equation 3 from equation 2 we get;
[tex]3.75x+2.5y-(2.5x+2.5y)=35-30\\\\3.75x+2.5y-2.5x-2.5y=5\\\\1.25x=5[/tex]
Now Dividing both side by 1.25 we get;
[tex]\frac{1.25x}{1.25}=\frac{5}{1.25}\\\\x= 4[/tex]
Now we will substitute the value of 'x' in equation 1 we get;
[tex]x+y=12\\\\4+y=12\\\\y=12-4 = 8[/tex]
Hence Alyssa purchased 4 Americana chickens and 8 Delaware chickens.
Now Given:
Number of eggs laid by American chicken per day = 2 eggs
Number of eggs laid by Delaware chicken per day = 1 egg
Cost of 12 eggs = $2.5
Total number of days = 7
Now first we will find the Total number of eggs laid by both the chickens.
Total number of eggs laid per day = [tex]4\times2 + 8\times 1= 8 +8 =16\ eggs[/tex]
Total number of eggs laid in week = [tex]16\times7= 112[/tex] eggs
12 eggs = $2.5
112 eggs = Cost of 112 eggs.
By cross multiplication we get;
Cost of 112 eggs = [tex]\frac{2.5 \times 112}{12} = \$23.33[/tex]
Hence Alyssa will expect to make $23.33 at the end of first week with her 12 chickens.
The system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased are as follows;
A + D = 12
3.75A + 2.50D = 35
Alyssa purchased 4 Americans chicken and 8 Delaware chickens.
She is expected to take in $22.5 at the end of the first week with her 12 chickens.
number of Americana chickens = A
number of Delaware chickens = D
Therefore,
A + D = 12
3.75A + 2.50D = 35
A = 12 - D
3.75(12 - D) + 2.50D = 35
45 - 3.75D + 2.50D = 35
-1.25D = -10
D = -10 / -1.25
D = 8
A = 12 - 8 = 4
A = 4
Therefore, Alyssa bought 4 Americans chickens and 8 Delaware chickens.
Each American chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day.
She only sells the egg in full dozen for $2.50.
The amount of money she expects to take in at the end of the first week with her 12 chickens is calculated as follows.
1 week = 7 days
Number of American chicken eggs(first week) = 7 × 4 × 2 = 56 eggs
Number of Delaware chicken eggs(first week) = 1 × 7 × 8 = 56 eggs
Total eggs = 56 + 56 = 112 eggs.
She can only sell full dozen of eggs. Therefore,
112 / 12 = 9.333
1 dozen = $2.50
9 dozen =
cross multiply
Amount made from the eggs = 9 × 2.50 = $22.5
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The following data show the distances (in miles) from the homes of off-campus statistics students to the college. Create a stem plot using the data. 0.5; 0.7; 1.1; 1.2; 1.2; 1.3; 1.3; 1.5; 1.5; 1.7; 1.7; 1.8; 1.9; 2.0; 2.2; 2.5; 2.6; 2.8; 2.8; 2.8; 3.5; 3.8; 4.4; 4.8; 4.9; 5.2; 5.5; 5.7; 5.8; 8.0 Which are the outliers?
Answer:
See the plot below.
For this case we can consider as an outlier the value 8.0 since is far away from the other points
Step-by-step explanation:
For this case we can create the stem plot like this:
Stem Leaf
0 | 5 7
1 | 1 2 2 3 3 5 5 7 7 8 9
2 | 0 2 5 6 8 8 8
3 | 5 8
4 | 4 8 9
5 | 2 5 7 8
6 |
7 |
8 | 0
Notation : "1 |1 means 1.1 for example and 3|5 means 3.5"
By definition an outlier is "an observation that lies an abnormal distance from other values in a random sample from a population"
For this case we can consider as an outlier the value 8.0 since is far away from the other points
Determine the 6-day simple moving averages for the ten consecutive day closing prices.
97.70, 97.70, 98, 98.45, 99, 99.68, 101, 101.50, 100, 100.56
1 ; 2 ; 3 ; 4 ; 5
Answer:
40.112
Step-by-step explanation:
A rectangular prism made of wood has a length of 10 centimeters, a width of 8 centimeters, and a height of 12 centimeters. A rectangular hole with a length of 2 centimeters and a width of 3 centimeters is cut through the prism as shown. What is the volume of the resulting figure? A. 882 cubic centimeters B. 888 cubic centimeters C. 960 cubic centimeters D. 1,032 cubic centimeters
Answer:888 cubic centimeters
Step-by-step explanation:
The formula for determining the volume of a rectangular prism is expressed as
Volume = length × height × width
Length = 10 centimeters
Width = 8 centimeters
Height = 12 centimeters
Therefore, the volume of the rectangular prism would be
10 × 8 × 12 = 960 centimeters³
A rectangular hole with a length of 2 centimeters and a width of 3 centimeters is cut through the prism. The height of the hole would also be 12 centimeters.
Therefore, the volume of the rectangular hole would be
2 × 3 ×12 = 72 cm³
the volume of the resulting figure would be
960 - 72 = 888 cm³
In a research report, Richard H. Weindruch of the UCLA Medical School claims that mice with an average life span of 32 months will live to be about 40 months old when 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ < 40 if 64 mice that are placed on this diet have an average life of 38 months with a standard deviation of 5.8 months? Use a P-value in your conclusion.
Answer:
The average life of the mice that are placed on this diet is less than 40 months.
Step-by-step explanation:
Consider the provided information.
When 40% of the calories in their diet are replaced by vitamins and protein. Is there any reason to believe that μ < 40.
The null and alternative hypothesis are:
[tex]H_0:\mu=40\\H_a:\mu<40[/tex]
64 mice that are placed on this diet have an average life is 38 months with a standard deviation of 5.8 months.
Therefore, [tex]n = 64, \bar x=38\ and\ \sigma=5.8[/tex]
Use the formula: [tex]z=\dfrac{\bar x-\mu}{\frac{\sigma}{\sqrt{n} }}[/tex]
Substitute the respective values in the above formula.
[tex]z=\dfrac{38-40}{\frac{5.8}{\sqrt{64} }}[/tex]
[tex]z=-\dfrac{2}{\frac{5.8}{8}}\approx-2.76[/tex]
Now using the table [tex]P(Z<z)=0.029[/tex]
The p value is smaller than 0.05 so reject the null hypothesis.
Therefore, the average life of the mice that are placed on this diet is less than 40 months.
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.38°F and a standard deviation of 0.48°F. Using the empirical rule, find each approximate percentage below.
a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 97.05°F and 99.57°F?
b. What is the approximate percentage of healthy adults with body temperatures between 97.89°F and 98.73°F?
Answer:
a) The problem says that this represent the values within 3 deviations from the mean and using the empirical rule we know that on this case we have 68% of the data on this interval.
b) For this case we can use the z score formula again:
[tex] z_1= \frac{98.73-98.38}{0.48}=0.729[/tex]
[tex] z_2= \frac{97.89-98.38}{0.48}=-1.020[/tex]
For this case we want this probability:
[tex] P(97.89<X<98.73) =P(-1.02<Z<0.729)= P(Z<0.729)-P(Z<-1.02)=0.767-0.154= 0.613[/tex]
So the approximate percentage of temperatures between 97.89F and 98.73F is 61.3%
Step-by-step explanation:
The empirical rule, also referred to as "the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)". The empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).
For this case we know that the body temperatures for a group of heatlhy adults represented with the random variable X follows this distribution:
[tex] X \sim N(\mu =98.38F, \sigma=0.48 F)[/tex]
Part a
For this case we can use the z score formula to measure how many deviations we are within the mean, given by:
[tex] z=\frac{x-\mu}{\sigma}[/tex]
If we find the z score for the values given we got:
[tex] z_1= \frac{99.57-98.38}{0.48}=2.479[/tex]
[tex] z_2= \frac{97.05-98.38}{0.48}=-2.771[/tex]
The problem says that this represent the values within 3 deviations from the mean and using the empirical rule we know that on this case we have 68% of the data on this interval.
Part b
For this case we can use the z score formula again:
[tex] z_1= \frac{98.73-98.38}{0.48}=0.729[/tex]
[tex] z_2= \frac{97.89-98.38}{0.48}=-1.020[/tex]
For this case we want this probability:
[tex] P(97.89<X<98.73) =P(-1.02<Z<0.729)= P(Z<0.729)-P(Z<-1.02)=0.767-0.154= 0.613[/tex]
So the approximate percentage of temperatures between 97.89F and 98.73F is 61.3%
The circular blade on a saw has a diameter of 6.25 inches and rotates at 4500 revolutions per minute. (a) Find the angular speed of the blade in radians per minute. (Round your answer to three decimal places.)
Answer:angular speed=471.429rad/sec
Step-by-step explanation:
One revolution is :
2×pi×radians
Then 4500 revolution will be:
2×pi×4500rad= 9000pi rad
1minutes = 60seconds
So the angular speed is :
=(9000×pi rad) / minutes
=9000×(22/7)rad /60seconds
=471.42857143 rad/sec
=471.429rad/sec to 3 d.p
The angular speed of the blade is [tex]471[/tex] radian per minute.
In one revolution, angle made is [tex]2\pi[/tex] radian.
In 4500 revolutions = [tex]2\pi *4500=9000\pi[/tex] radian.
We know that ,
1 hour = 60 minute.
Angular speed = [tex]\frac{9000\pi radian}{60minute} =\frac{9000*3.14}{60}=471radian/minute[/tex]
Therefore, the angular speed of the blade is [tex]471[/tex] radian per minute.
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Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals 500 comma x equals 150 comma 95 % confidencen=500, x=150, 95% confidence nothingless than
Answer:
(0.2599,0.3401)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 500
x = 150
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{150}{500} = 0.3[/tex]
Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96[/tex]
Putting the values, we get:
[tex]0.3\pm 1.96\sqrt{\dfrac{0.3(1-0.3)}{500}} = 0.3 \pm 0.0401 =(0.2599,0.3401)[/tex]
The 95% confidence interval is (0.2599,0.3401).
Find the sides of a triangle if two of its sides are equal, the third side is 1 1 3 cm longer than the others, and its perimeter is 5 2 5 cm.
Answer: [tex]137\dfrac{1}{3}\ cm,\ 137\dfrac{1}{3}\ cm,\ 250\dfrac{1}{3}\ cm[/tex]
Step-by-step explanation:
Let x be the equal sides of the triangle .
The , the third side would be x+113 cm.
The perimeter is the sum of all sides of a triangle.
So , The perimeter of triangle would be x+x+(x+113)= 3x+113 --------(1)
Since , it is given that the perimeter of triangle is 525. -----(2)
So from (1) and (2) , we have
[tex]3x+113=525\\\\ 3x=525-113=412\\\\ x=\dfrac{412}{3}=137\dfrac{1}{3}[/tex]
Then, third side = [tex]137\dfrac{1}{3}+113=250\dfrac{1}{3}\ cm[/tex]
Hence , the sides of a triangle are:[tex]137\dfrac{1}{3}\ cm,\ 137\dfrac{1}{3}\ cm,\ 250\dfrac{1}{3}\ cm[/tex]
Answer: 1 16/45, 1 16/45, 2 31/45
Step-by-step explanation:
Say x is the equal side of the triangle.
The third side would be x+113 cm.
The perimeter is the sum of all sides of a triangle.
So, the perimeter of the triangle would be x+x+(x+113)= 3x+113
Since the triangle's perimeter is 5 2/5, 3x + 1 1/3 = 5 2/5.
1 1/3 is 1 5/15. 5 2/5 is 5 6/15. 5 6/15 - 1 5/15 = 4 1/15.
This means 3x = 4 1/15.
4 1/15 = 61/15
3x = 61/15
To make 3x into x, you can multiply it by 1/3.
3x*1/3 is x. 61/15*1/3 = 61/45.
x = 1 16/45 because 61/45 = 1 16/45.
The longer side is x + 1 1/3 so you have to add 1 1/3 to 1 16/45 which is
2 31/45.
So, the sides are 1 16/45, 1 16/45 and 2 31,45.
Write a polynomial function of least degree with integral coefficients that has the given zeros
Answer:
[tex]x^{4}[/tex] + 3x² - 4
Step-by-step explanation:
Note that complex zeros occur in conjugate pairs
If 2i is a zero then - 2i is a zero
The zeros are x = 1, x = - 1, x = 2i, x = - 2i, thus the factors are
(x - 1), (x + 1), (x - 2i) and (x + 2i)
The polynomial is expressed as the product of the factors, thus
f(x) = (x - 1)(x + 1)(x - 2i)(x + 2i) ← expanding in pairs
= (x² - 1)(x² - 4i²) → i² = - 1
= (x² - 1)(x² + 4) ← distribute
= [tex]x^{4}[/tex] + 4x² - x² - 4
= [tex]x^{4}[/tex] + 3x² - 4
The most fundamental unit of computing is the ______, which is represented as an on (1) or off (0) value.
Answer:
Byte
Step-by-step explanation:
We use byte to represent 1 and 0 in computing..
The most basic unit of computing is the 'bit', which can be represented as either 1 (on) or 0 (off). This binary information is used in digital circuits to perform tasks in computing devices. The use of bits was crucial to the development of modern computing.
Explanation:The most fundamental unit of computing is the bit, which is represented as an on (1) or off (0) value. In digital circuits found in modern devices, transistors behave like switches that can be either on or off, encoding information in a binary code of ones and zeros. These bits are utilised to perform a variety of tasks like data manipulation and transmission of signals. Over time, scientists have found ways to amplify the computing capacity of bits by integrating vast collections of transistors on single silicon wafers, creating the integrated circuits (IC), which is foundational to the modern digital computer revolution.
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A food truck operator is parked in a lot at the corner of two streets. She wants to be equidistant from both streets. Should she park her truck on a perpendicular bisector, and angle bisector, a median, or an altitude
Answer:
Angle bisector
Step-by-step explanation:
Given that a food truck operator is parked in a lot at the corner of two streets. She wants to be equidistant from both streets.
We have to find out where she should park her truck on a perpendicular bisector, and angle bisector, a median, or an altitude
We know the perpendicular bisector is the locus of points equidistant form two points.
But here two streets can be treated as straight lines only.
The angle bisector of two lines will have all the points on the bisector.
Median is not applicable since here no triangle is there neither altitude
So right answer is angle bisector.
She should park her truck on the angle bisector of angle formed by intersection of two roads.
The cost of an adult ticket to a football game was 1.75. The cost of a student ticket 1.25. The number of student tickets sold was twice the number of adult tickets. The total income from the sale of tickets was 850. How many tickets of each type were sold?
ANSWER: Adult tickets: 200 Student tickets:400
STEP-BY-STEP EXPLANATION:
n = number of adult tickets sold
2n = number of student tickets sold
2n(1.25) + n(1.75) = $850
2.50n + 1.75n = $850
4.25n = $850
n = 200
2n= 2 × 200= 400
In this section we use r to denote the value of the linear correlation coefficient. Why do we refer to this correlation coofficient as being linear?
A. The term linear refers to a straight line, and r measures the fraction of the points the best line passes trough.
B. The term linear refers to a straight line that passes through the average values of the paired data, and r measures how well a scatterplot fits a straight-line pattem
C. The term linear refers to a straight line, and r measures how well a scatterplot fits a straight-line pattern
D. The term linear refers to the straight line that passes through the greatost number of points, and r meansures the fraction of the points the line passes through
Answer:
C. The term linear refers to a straight line, and r measures how well a scatter plot fits a straight-line pattern
Step-by-step explanation:
In statistics, when two variables are being investigated, the location of the co-ordinates on a rectangular co-ordinates ystem is called a scatter diagram.
The amount of linear correlation between two variables is expressed by a coefficient of correlation, given the symbol r. This is defined in terms of the deviations of the co-ordinates of two variables from their mean values and is given by the product-moment formula
For linear correlation, if points are plotted on a graph and all the points lie on a straight line, then perfect linear correlation is said to exist. When a straight line having a positive gradient can reasonably be drawn through points on a graph positive or direct linear correlation exists.
Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between z = − 1.6 z=-1.6 and z = 1.6 z=1.6 standard deviations of the mean (or within 1.6 standard deviations of the mean). What percent of the data points will fall in that range?
Answer:
89.04% of the data points will fall in the given range of z = − 1.6 and z = 1.6
Step-by-step explanation:
We are given a normally distributed data.
We have to find the percentage of data that lies within the range z = − 1.6 and z= 1.6
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
[tex]P(-1.6 \leq z \leq 1.6)\\= P(z \leq 1.6) - P(z \leq -1.6)\\\text{Calculating the value from standard normal table}\\= 0.9452 - 0.0548 = 0.8904= 89.04\%[/tex]
89.04% of the data points will fall in the given range of z = − 1.6 and z= 1.6
Final answer:
Approximately 89.04% of data points fall within 1.6 standard deviations of the mean in a normally distributed set, calculated using the empirical rule and Z-table for the standard normal distribution.
Explanation:
To find the percentage of data points that fall between z-scores of -1.6 and 1.6, we use the properties of the standard normal distribution. Based on the empirical rule (also known as the 68-95-99.7 rule), we know that approximately 68% of data points lie within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean in a normal distribution.
Since our z-scores are between -1 and 2, we will look at the percentages for these intervals. Typically, a z-score of 1.6 would correspond to a value between the percentages for 1 and 2 standard deviations from the mean. Using a Z-table or standard normal distribution curve calculator, we find that a z-score of 1.6 gives us approximately 0.4452 (or 44.52%) to the left of the z-score and 0.4452 to the right. Therefore, the total area between -1.6 and 1.6 is 2 × 0.4452, which is approximately 0.8904 (or 89.04%). Thus, approximately 89.04% of the data points will fall within 1.6 standard deviations from the mean in a normally distributed data set.
Candy has been saving her pocket money she began the month with 25 and ended with 75 she said the end of the month mount was 250 of her original amount
Which would best display the following data if you wanted to display the numbers which are outliers as well as the mean? [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]
Stem and Leaf plot would be the best choice to display the given data if we want to display the numbers which are outliers as well as the mean.
Hence option C is correct.
Given, representation of outliers and mean.
Data: [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32]
Stem and Leaf plot would be the best choice to display the given data if we want to display the numbers which are outliers as well as the mean.
Therefore option C is correct.
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Options for question :
1) Pie Graph
2) Bar Graph
3) Stem and Leaf Plot
4) Line Chart
5) Venn Diagram
A box and whisker plot is the best choice to display data including outliers and the mean in mathematics. It clearly shows the median, quartiles, and outliers. The mean can be depicted as an additional point.
Explanation:In the field of mathematics, to display the data with outliers and the mean, a box and whisker plot is the most suitable graph. This type of graph can highlight outliers and also show the mean. For instance, our given data [4, 1, 3, 10, 18, 12, 9, 4, 15, 16, 32] when plotted on a box and whisker plot would display the median (the line inside the box), the quartiles (the ends of the box), and outliers (points outside the whiskers). The mean can additionally be added as a separate point on the plot.
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Right triangle ABC is similar to triangle XYZ. If the length of side AB is 20.8 units, the length of side BC is 36.4 units, and the length of side YZ is 7 units, what is the length of side XY?
Answer:
XY is 4 units.
Step-by-step explanation:
We are given the following in the question:
Right triangle ABC is similar to triangle XYZ.
AB = 20.8 units
BC = 36.4 units
YZ = 7 units
We have to find the length of side XY.
Since the given triangles are similar, they have the following property:
The ratio of corresponding sides of similar triangles are equal.
We can write,
[tex]\displaystyle\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]
Putting the given values, we have,
[tex]\displaystyle\frac{AB}{XY}=\frac{BC}{YZ}\\\\\frac{20.8}{XY}=\frac{36.4}{7}\\\\XY = \frac{20.8\times 7}{36.4} =4 \text{ units}[/tex]
Thus, the length of XY is 4 units.
A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?(A) [tex]\sqrt{3}[/tex] : 1
(B) 1 : 1
(C) [tex]\frac{1}{2}[/tex] : 1
(D) [tex]\sqrt{2}[/tex] : 1
(E) 2 : 1
Answer:B
Step-by-step explanation:
Given
Right circular cone is inscribed in a hemisphere so that the base of the cone coincides with base of hemisphere
Height of cone is equal to radius of hemisphere
so ratio of the height of cone to the radius of the hemisphere is 1:1
Fernando works between 12 and 25 hours each week. The function t, where t(x) = 9.50x represents the amount of money Fernando earns given the number of hours, x, he works. Which statement best represents the domain of this function for any given week?
Answer:
Step-by-step explanation:
The function t, where t(x) = 9.50x represents the amount of money Fernando earns given the number of hours, x, that he works.
The domain of a function are the set of possible values of x, the independent variable that satisfies the function.
Fernando works between 12 and 25 hours each week. It means that the statement that best represents the domain of this function for any given week would be
12 ≤ x ≤ 25
The statement that best represents the domain of this function for any given week would be 12 ≤ x ≤ 25.
What is a function?The function is a type of relation, or rule, that maps one input to a specific single output.
Fernando works between 12 and 25 hours each week.
The function t, where t(x) = 9.50x represents the amount of money Fernando earns given the number of hours, x, he works.
The domain is the set of values x for which the given function is defined.
Or The independent variable that satisfies the function.
The statement that best represents the domain of this function for any given week would be 12 ≤ x ≤ 25.
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Nai earns $7 per hour mowing her neighbor's lawns. She also earned $14 far hauling away bags of recyclables for some neighbor's. Priya babysits her neighbor's children. Shw earns $8.40 per hour. Priya and Nai have agreed to go to the movies the weekends after they have earned the same amount of money for the same number of work hours How much money do they each have to work before they go to the movies?
9514 1404 393
Answer:
each has to work 5 hours and earn $42
Step-by-step explanation:
Let m and h represent hours Nai spends mowing and hauling, respectively. Then (m+h) will be the number of hours Priya spends babysitting. In order for their earnings to be equal, we must have ...
7m +14h = 8.40(m+h)
5.60h = 1.40m . . . . . . . . subtract 7m+8.40h
m = 4h . . . . . . . . . . . . . . divide by 1.40
Then the total number of hours worked by either person is ...
m + h = (4h) +h = 5h
If only whole numbers of hours are worked, then the smallest number of hours that will make earnings equal is 5h, with h=1, or 5 hours. In that time, each will earn 5×$8.40 = $42.
Each must work 5 hours and earn $42 before they go to the movies.
__
Nai will work 4 hours mowing and 1 hour hauling.
Priya and Nai have to work 0 hours before they go to the movies.
Explanation:To find out how much money Priya and Nai each have to work before they go to the movies, we need to set up an equation. Let x represent the number of work hours for both Priya and Nai. Nai earns $7 per hour, so her earnings in x hours would be 7x dollars. Priya earns $8.40 per hour, so her earnings in x hours would be 8.40x dollars. Since they want to earn the same amount, we can set up the equation:
7x = 8.40x
To solve for x, we can subtract 7x from both sides of the equation:
0.40x = 0
Now, divide both sides of the equation by 0.40 to solve for x:
x = 0 / 0.40
x = 0
Therefore, both Priya and Nai have to work 0 hours before they go to the movies. This means they have already earned the same amount of money.
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Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through left parenthesis negative 5 comma 5 right parenthesis(−5,5) and parallel to the line whose equation is 6 x minus 5 y minus 9 equals 0
Answer:
The answer to your question is below
Step-by-step explanation:
Data
P (-5, 5)
Parallel to 6x - 5y - 9 = 0
Process
1.- Find the equation of the line
6x - 5y = 9
-5y = -6x + 9
y = -6/-5 x + 9/-5
y = 6/5 x - 9/5
slope = 6/5, as the lines are parallels, the slope is the same.
2.- Get the equation of the new line
y - y1 = m(x - x1)
y - 5 = 6/5 (x + 5)
y - 5 = 6/5x + 6
y = 6/5x + 6 + 5
y = 6/5x + 11 Point-slope form
5y - 25 = 6(x + 5)
5y - 25 = 6x + 30
6x - 5y + 30 + 25 = 0
6x - 5y + 55 = 0 General form
The equation of the line that passes through (-5,5) and is parallel to 6x - 5y - 9 = 0 can be written in point-slope form as y - 5 = (6/5)(x + 5) and in general form as -6x + 5y - 55 = 0.
Explanation:To write an equation for the line that passes through the point (-5,5) and is parallel to the line 6x - 5y - 9 = 0, we first need to find the slope of the given line. By rewriting the equation in slope-intercept form (y = mx + b), we can identify the slope (m). The equation 6x - 5y - 9 = 0 can be rewritten as y = (6/5)x + 9/5, so the slope of the line is 6/5. Since parallel lines have the same slope, the slope of our new line is also 6/5.
Next, we use the point-slope form of the equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line (here (-5,5)) and m is the slope. Substituting these values into the equation gives us y - 5 = (6/5)(x + 5).
To express this in general form (Ax + By + C = 0), we rearrange the equation: multiply both sides by 5 to clear the fraction, resulting in 5(y - 5) = 6(x + 5), which simplifies to 5y - 25 = 6x + 30. Rearranging gives -6x + 5y - 55 = 0.
Bobby Borrowed 24,000 from two different banks to start a business One Bank charge the equivalent of 4% simple interest in the other charge 5.5% interest if the total interest after 1 year was $990 determine the amount borrowed from each Bank
Answer:he borrowed $22000 from bank 1.
He borrowed $2000 from bank 2
Step-by-step explanation:
Let x represent the amount of money that he borrowed from bank 1.
Let y represent the amount of money that he borrowed from bank 2.
Bobby Borrowed 24,000 from two different banks to start a business. This means that
x + y = 24000
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time
Considering the money borrowed from bank 1,
P = x
R = 4%
T = 1
I = (x × 4 × 1)/100 = 0.04x
Considering the money borrowed from bank 2,
P = y
R = 5.5%
T = 1
I = (y × 5.5 × 1)/100 = 0.055y
if the total interest after 1 year was $990, it means that
0.04x + 0.055y = 990 - - - - - -1
Substituting x = 24000 - y into equation 1, it becomes
0.04(24000 - y) + 0.055y = 990
960 - 0.04y + 0.055y = 990
- 0.04y + 0.055y = 990 - 960
0.015y = 30
y = 30/0.015 = $2000
Substituting y = 2000 into
x = 24000 - y, it becomes
x = 24000 - 2000
x = 22000
HFM & PST
What is the perimeter of HFM
Enter the answer in the box.
Answer:
50.75 units
Step-by-step explanation:
In this problem
Triangles HFM and PST are similar
we know that that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
step 1
Find the scale factor
Let
z ----> the scale factor
[tex]z=\frac{HF}{PS}[/tex]
substitute the given values
[tex]z=\frac{14}{8}=1.75[/tex]
step 2
Find the perimeter of triangle PST
[tex]P=8+9+12=29\ units[/tex]
step 3
Find the perimeter of triangle HFM
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
so
The perimeter of triangle HFM is equal to the perimeter of triangle PST multiplied by the scale factor
so
[tex]29(1.75)=50.75\ units[/tex]
In one month, Rama and Siham ran for a total of 670 minutes. If Rama spent 60 fewer minutes running than Siham did, for how many minutes did Siham run?
Answer:
Siham ran for 305 minutes
Step-by-step explanation:
Let
Siham Ran for time = X
Siham Ran for time = X-60
According to given condition
X + (X-60) = 670
X + X - 60 = 670
2X = 670-60
2X = 610
X = 610/2
X = 305
So Siham ran for 305 minutes only
Fat cat starts at 9 am and goes at 75 yards per minute then skinny cat starts at 9:02 am and goes at 100 yards per minute. How long does it take for skinny cat to catch up to fat cat?
Answer:
It would take skinny cat 6 mins to reach fat cat.
Step-by-step explanation:
Given:
Speed of Fat cat = 75 yd/min
Speed of skinny cat = 100 yd/min
We need to find the time taken by skinny cat to reach fat cat.
Let the distance covered by both be 'd'.
Also let the time taken by Fat cat to cover distance 'd' be 't' mins.
Now we know that skinny cat started 2 mins later so time taken by Skinny cat will be [tex]t-2 \ mins[/tex].
Now we know that;
Distance is equal to speed times time.
framing in equation form we get;
Distance cover by fat cat = [tex]75t[/tex]
Distance cover by skinny cat = [tex]100(t-2) =100t-200[/tex]
Both distance have to made same since we need to find the time required more to reach the other cat.
[tex]100t-200=75t[/tex]
Combining like terms we get;
[tex]100t-75t=200\\\\25t =200[/tex]
Dividing both side by 25 we get;
[tex]\frac{25t}{25}=\frac{200}{25}\\\\t = 8\ mins[/tex]
Time taken by skinny cat = [tex]t-2 =8-2=6 \ mins[/tex]
Hence it would take skinny cat 6 mins to reach fat cat.
Skinny Cat catches up to Fat Cat 6 minutes after starting at 9:02 am, which is at 9:08 am. This is calculated by determining the head start that Fat Cat has and the faster pace at which Skinny Cat moves.
We are presented with a problem where two cats, one named Fat Cat and the other Skinny Cat, start at different times and move at different speeds. Fat Cat starts at 9:00 am moving at 75 yards per minute, and Skinny Cat starts at 9:02 am moving at 100 yards per minute. The question is to find out how long it takes for Skinny Cat to catch up to Fat Cat.
Calculate the head start Fat Cat has by finding out how much distance they cover before Skinny Cat starts. Since Fat Cat starts at 9:00 am and Skinny Cat starts at 9:02 am, there is a 2-minute difference. In 2 minutes, Fat Cat travels 75 yards/minute × 2 minutes = 150 yards.Next, determine the speed difference between the two cats. Skinny Cat is moving at 100 yards per minute, and Fat Cat is moving at 75 yards per minute. The difference in speed is 100 yards/minute - 75 yards/minute = 25 yards/minute.Finally, calculate the time taken for Skinny Cat to catch up. Since Skinny Cat is going 25 yards per minute faster than Fat Cat, you would divide the head start by the speed difference: 150 yards / 25 yards/minute = 6 minutes.So, Skinny Cat will catch up to Fat Cat 6 minutes after starting at 9:02 am, which is at 9:08 am.
A survey of 500 farmers showed that of the farmers, 121 grew only wheat, 113 grew only corn, 90 grew only oats, 199 grew wheat, 60 grew wheat and corn, 57 grew wheat and oats, and 182 grew corn. Determine the number of farmers who a) grew at least one of the three. b) grew all three, c) did not grow any of the three, d) grew exactly two of the three
Answer:
Step-by-step explanation:
Let x represent the number of farmers that grew all three crops.
Let y represent the number of farmers that grew corn and oat.
The Venn diagram representing the scenario is shown in the attached photo.
W represents the subset for wheat
C represents the subset for corn
O represents the subset for oat
199 grew wheat. It means that
121 + 57 - x + x + 60 - x = 199
238 - x = 199
x = 238 - 199
x = 39
182 grew corn. It means that
113 + 60 - x + x + y - x = 182
173 + y - x = 182
y = 182 - 173 + 39
y = 48
a) the number of farmers who grew at least one of the three would be
121 + 113 + 90 + 57 - x + 48 - x + 60 - x + x
= 121 + 113 + 90 + 57 - 39 + 48 - 39 + 60 - 39 + 39 = 411
b) the number of farmers that grew all three would be
x = 39
c) the number of farmers who did not grow any of the three would be
500 - 411 = 89
d) the number of farmers who grew exactly two of the three would be
60 - x + 57 - x + 48 - x
= 60 - 39 + 57 - 39 + 48 - 39
= 21 + 18 + 9
= 48
The number of farmers who grew at least one of the crops is 328, all three is not stated, none of the three is 172 and exactly two of them is 117.
Explanation:To solve this problem, we have to understand Venn Diagrams and set theory. When adding up counts for different categories, it is important to not double count any item.
The number of farmers who grew at least one of three crops (wheat, corn, oats) can be determined by the sum of all the individual and intersection categories. However, we subtract the counts that have been mentioned twice.
a) At least one: (121 wheat only + 113 corn only + 90 oats only + 199 wheat + 60 wheat&corn + 57 wheat&oats + 182 corn) - (2*(60 wheat&corn) + 2*(57 wheat&oats) + 2*(182 corn&-)) = 328
b) All three: There is no clear information about farmers growing all three crops. We may assume it to be 0, as it is not stated.
c) None of three: The survey includes 500 farmers, if 328 grow at least one crop, then the number of farmers that did not grow any of the three is 500 - 328 = 172
d) Exactly two: 60 grew wheat and corn, 57 grew wheat and oats. Hence 117 farmers grew exactly two of the three crops.
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You have $11.50 to buy boxes of crackers for a party. A box of crackers costs $2.30. Which inequality represents the number x of boxes of crackers you can buy?
STEP-BY-STEP EXPLANATION:
Let be x the number of boxeds of crackers you can buy
If each box has a cost of $2.30 and you have $11.50
we can represent this into this equation
2.30x= 11.50
x=[tex]\frac{11.50}{2.30}[/tex]
x=5
You can buy 5 boxes of crackers
The position of a particle on the x-axis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for e ≤ t ≤ 2e?
Answer:
[tex]V_{avg} = \frac{ln2}{e} = 0.255fts^{-1}[/tex]
Step-by-step explanation:
The question asks for the average velocity and not the instantaneous velocity (which would have meant to differentiate). So, the right formula is
[tex]V_{avg} = \frac{s(t_{2}) - s(t_{1} ) }{t_{2} -t_{1} } =[/tex]
From the question, [tex]t_{1}[/tex] corresponds to e seconds and [tex]t_{2}[/tex] corresponds to 2e seconds. So, we have
[tex]V_{avg} = \frac{ln(2e) - ln(e)}{2e - e}[/tex]
One of the laws of logarithms says that
[tex]ln(\frac{a}{b} )= ln(a) - ln(b). \\\\ Therefore, ln(2e) - ln(e) = ln(\frac{2e}{e} ) = ln(2)[/tex]
[tex]V_{avg} = \frac{ln(2)}{e} = 0.2550fts^{-1}[/tex] ≅ [tex]0.255fts^{-1}[/tex]
If n denotes a number to the left of 0 on the number line such that the square of n is less than [tex]\small \frac{1}{100}[/tex], then the reciprocal of n must be _________.
The reciprocal of n must be less than –10
Solution:
Given n denotes a number to the left of 0 means n < 0.
Square of n is less than [tex]\frac{1}{100}[/tex] means [tex]n^2<\frac{1}{100}[/tex].
Therefore, we have [tex]n<0[/tex] and [tex]n^2<\frac{1}{100}[/tex].
⇒ [tex]n^2<\frac{1}{100}[/tex]
Taking square root on both sides, we get
⇒ [tex]n<\± \frac{1}{10}[/tex]
⇒[tex]\frac{-1}{10}<n<\frac{1}{10}[/tex]
⇒ But we know that n < 0, so [tex]n<\frac{1}{10}[/tex] false.
It should be [tex]\frac{-1}{10}<n[/tex].
To equal the expression, multiply both sides of the equation by –10n.
⇒ [tex]-\frac{1}{10} \times\frac{-10}{n}>n \times\frac{-10}{n}[/tex] (symbol < changed to > when multiply by minus)
⇒ [tex]\frac{1}{n}>-10[/tex]
Hence, the reciprocal of n must be less than –10.
In a production process, the diameter measures of manufactured o-ring gaskets are known to be normally distributed with a mean diameter of 80 mm and a standard deviation of 3 mm. Any o-ring measuring 75 mm or less in diameter is defective and cannot be used. Using Excel, determine the percent or proportion of defective o-rings that will be produced.
Answer:
DIRECT WAY EXCEL
"=NORM.DIST(75,80,3,TRUE)"
And we got: [tex] P(X\leq 75)= 0.04779[/tex]
OTHER WAY
[tex]P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z<-1.67)[/tex]
And we can find this probability using the normal standard table or excel:
[tex]P(Z<-1.67)=0.04779[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the diameter of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(80,3)[/tex]
Where [tex]\mu=80[/tex] and [tex]\sigma=3[/tex]
And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:
[tex] P(X\leq 75)[/tex]
One way to do this in excel is with the following formula:
"=NORM.DIST(75,80,3,TRUE)"
And we got: [tex] P(X\leq 75)= 0.04779[/tex]
And the other way is use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X\leq 75)=P(\frac{X-\mu}{\sigma}\leq \frac{75-\mu}{\sigma})=P(Z\leq \frac{75-80}{3})=P(Z<-1.67)[/tex]
And we can find this probability using the normal standard table or excel:
[tex]P(Z<-1.67)=0.04779[/tex]