Answer:6
Step-by-step explanation:
Let digit be r=abc
if tens digit of [tex]\frac{r}{10}[/tex] is 3.2
i.e. [tex]\frac{r}{10}[/tex] is written as ab.c
so tens digit is a=3
If the hundreds digit of 10r is 6
i.e. 10r is written as abc0
its hundreds digit is b=6
thus tens digit of abc is b=6
To find the tens digit of the integer r, we use the information that the hundreds digit of 10r is 6, indicating that the tens digit of r is also 6.
Explanation:The question is asking to determine the tens digit of a positive integer r. To solve this, we need to analyze the given facts separately:
The tens digit of r/10 is 3. If we divide the integer r by 10 and find that its tens digit is 3, this implies that in the original number r, the ones digit was 3.The hundreds digit of 10r is 6. By multiplying r by 10, we essentially shift each digit one place to the left, meaning the tens digit of r becomes the hundreds digit of 10r. Therefore, if the hundreds digit of 10r is 6, the tens digit of r is also 6.From statement 2 alone, we can determine that the tens digit of the positive integer r is 6.
A backyard is 40.5 feet long and 25 feet wide. In order to install a pool, the yard needs to be reduced by a scale of 1/3. What is the area of the reduced yard?
Answer:The area of the reduced backyard is 112.5 square feet
Step-by-step explanation:
The initial length of the backyard is 40.5 feet long.
The initial width of the backyard is 25 feet wide.
In order to install a pool, the yard needs to be reduced by a scale of 1/3. This means that the new length of the backyard is would be
40.5 × 1/3 = 40.5/3 feet lonng
The new width of the backyard would be
25 × 1/3 = 25/3 feet wide
The backyard is rectangular in shape. Area of a rectangle is length × width. The area of the reduced backyard becomes
40.5/3 × 25/3 = 1012.5/9 = 112.5 square feet
Answer:
112.5 square feet... edg2020
Imagine a pond. In it sits one lilypad, which reproduces once a day. Each of its offspring also reproduces once a day, doubling the number of lily pads in the pond every day. If the pond is full of lily pads on the 30th day, on what day is it half-full of lily pads
Answer: On the 29th day
Step-by-step explanation:
According to this problem, no lilypad dies and the lilypads always reproduce, so we can apply the following reasoning.
On the first day there is only 1 lilypad in the pond. On the second day, the lilypad from the first reproduces, so there are 2 lilypads. On day 3, the 2 lilypads from the second day reproduce, so there are 2×2=4 lilypads. Similarly, on day 4 there are 8 lilypads. Following this pattern, on day 30 there are 2×N lilypads, where N is the number of lilypads on day 29.
The pond is full on the 30th day, when there are 2×N lilypads, so it is half-full when it has N lilypads, that is, on the 29th day. Actually, there are [tex]2^{30} [/tex] lilypads on the 30th, and [tex]2^{29}[/tex] lilypads on the 29th. This can be deduced multiplying succesively by 2.
The number of events is 29, the number of trials is 298, the claimed population proportion is 0.10, and the significance level is 0.05. Use technology to identify the test statistic for this hypothesis test, rounding to two decimal places.
Answer:
[tex]z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155[/tex]
[tex]p_v =2*P(Z<-0.155)=0.877[/tex]
And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .
Step-by-step explanation:
1) Data given and notation
n=298 represent the random sample taken
X=29 represent the events claimed
[tex]\hat p=\frac{29}{298}=0.0973[/tex] estimated proportion
[tex]p_o=0.1[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the proportion is 0.1 or no.:
Null hypothesis:[tex]p=0.1[/tex]
Alternative hypothesis:[tex]p \neq 0.1[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.0973 -0.1}{\sqrt{\frac{0.1(1-0.1)}{298}}}=-0.155[/tex]
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(Z<-0.155)=0.877[/tex]
And we can use excel to find the p value like this: "=2*NORM.DIST(-0.155;0;1;TRUE)"
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is not significantly different from 0.1 .
We can do the test also in R with the following code:
> prop.test(29,298,p=0.1,alternative = c("two.sided"),conf.level = 1-0.05,correct = FALSE)
A triangular piece of land has one of its angle equal to 90°.The area of this land is 330sq m.If one side adjacent to the right angle is 11m what are the lengths of the other two sides
Answer:
60 m, 61 m
Step-by-step explanation:
If "a" and "b" represent the lengths of the sides adjacent to the right angle, the area is ...
area = (1/2)ab
Filling in the given information, we can find the other side to be ...
330 m² = (1/2)(11 m)b
60 m = b . . . . . . divide by the coefficient of b
Then the remaining side can be found from the Pythagorean theorem:
c² = a² + b² = 11² + 60² = 3721
c = √3721 = 61 . . . meters
The lengths of the other two sides are 60 m and 61 m.
1.
A rectangular swimming pool is represented by x as the width and one less than twice the width as the length. If the area of the swimming pool is given by 28 sq. ft., which equation could be used to model the area of the swimming pool?
A) 28 = 2x - 1•x
B) 28x = 2x - 1
C) 28 = (2x - 1) + (x)
D) 28 = (2x - 1)(x)
Answer:
C. 28 = (2x - 1)(x)
Step-by-step explanation:
There is a rectangular swimming pool.
Width of swimming pool is x
Length is one less than twice the width
Area of the swimming pool is 28 sq ft.
To Find : Equation could be used to model the area of the swimming pool.
Solution:
Since we are given that Length is one less than twice the width.
And width is x (given)
So, length = 2x-1
Area of the swimming pool is 28 sq ft.
Now ,
Formula of area of rectangle : Length*Width
⇒28= (2x-1)(x)
So, equation used to model the area of the swimming pool: 28= (2x-1)(x)
Hence Option c is correct.
Answer:
28=(2x-1)(x)
Step-by-step explanation:
The swimming pool is rectangular in shape.
Hence the area of it is given by:
l * w
where l = length of the rectangular swimming pool
w = width of the rectangular swimming pool
In this question it is given:
width = w = x
length = l = 2x - 1
Area = 28 sq.ft
Hence:
Area = l * w = (2x-1)(x)
28 = (2x-1)(x)
Sam plans to walk his dog a distance of 1 mile he walks 3/8 of a mile and stops to get a bottle of water then he walks 1/8 of a mile more and stops to say hello to a friend how far does Sam still have to walk his dog
1/2 of a mile.
Step-by-step explanation:
He has already gone 4/8 of a mile (3/8 + 1/8) and he needs to go 8/8 of a mile. 8/8 - 4/8 = 4/8. You can simplify that to 1/2.
Answer:
1/2 a mile.
Step-by-step explanation:
He wants to walk 1 mile.
Distance left = 1 - 3/8 - 1/8
= 8/8 - 3/8 - 1/8
= 8/8 - 4/8
= 4/8
= 1/2 a mile.
90% of adult females have height h (in feet) that satisfies the inequality h-5.350.21≤2.PEO8u1R7JRMqpfyKkyBAiu7m2VSa2P1jS2VeRvrV (SLO #2) Solve the inequality. Show your work. Interpret the meaning of your answer to part (a) in the context of this problem. Based on your answer to part (b), would it be unusual to encounter a female who was 5'9" tall? Explain.
Answer:
4.93 =< h =< 5.77
a) 90% woman (most of them) are within the height of 4.93 and 5.77 ft
b) not unusual since it is within the range
Note: for this answer, I'll use the following symbols:
=< as less or equal
=> as more or equal
Step-by-step explanation:
The inequality is
Abs[(h-5.35)/0.21)] = < 2
The absolute value sign will causes the value in the abs() bracket to be zero, whether the value is positive or negative
In other word, (h - 5.35)/0.21 could actually be a negative or positive
We consider both possibility
If it's positive: (h - 5.35)/0.21 =< 2
If it's negative: (h - 5.35)/0.21 => -2
Note that if we consider it as negative, the inequality sign change because at negative value, the order of magnitude is inverted to positive values.
Let's consider the positive first:
(h-5.35)/0.21 =< 2
h =< 2*0.21 +5.35
h =< 5.77
And then the negative
(h - 5.35)/0.21 => -2
h => -2*0.21 + 5.35
h => 4.93
From both calculation we can see that the range value of h is
4.93 =< h =< 5.77
a) this means that 90% of woman height is between 4.93 to 5.77 feet
b) 5'99'' = 5.75 ft
The height is within the range found from this calculation. So it's not that unusual.
Answer:
?
Step-by-step explanation:
A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 85 pounds. The truck is transporting 50 large boxes and 65 small boxes. If the truck is carrying a total of 4625 pounds in boxes, how much does each type of box weigh? Note that the ALEKS graphing calculator can be used to make computations easier
Answer:
Large box weighs 60 pounds and small box weighs 25 pounds
Step-by-step explanation:
Let x be the weight of large box and y be the weight of small box
The combined weight of a large box and a small box is 85 pounds.
[tex]x+y= 85[/tex]
[tex]y= 85-x[/tex]
The truck is transporting 50 large boxes and 65 small boxes. If the truck is carrying a total of 4625 pounds in boxes
[tex]50x+65y= 4625[/tex]
Solve for x and y using both equations
[tex]y= 85-x[/tex]
[tex]50x+65(85-x)= 4625[/tex]
[tex]50x+5525-65x= 4625[/tex]
[tex]-15x+5525= 4625[/tex]
[tex]-15x= 4625-5525[/tex]
[tex]-15x=-900[/tex]
Divide both sides by -15
x=60
[tex]y= 85-x=85-60=25[/tex]
Large box weighs 60 pounds and small box weighs 25 pounds
If r and s are positive integers, each greater than 1, and if 11(s-1) =13(r-1), what is the least possible value of (r+s)?
Answer:
The least value of (r+s) is (12+14)=26
Step-by-step explanation:
Well, first let us solve equation of 11(s-1)=13(r-1), which results in 11s-11=13r-13. Hence, 11s+2=13r. It is stated that r and s both are integers and greater than 1.
To make sure that r and s are integers, the least value of s must be equal to 14 (s=14) then the least value of r becomes 12 (r=12).
Finally, the least value of (r+s) is (12+14)=26.
WILL GIVE BRAINLIEST! PLUS 20 PTS! ALGEBRA 1!
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Suppose U= { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } is the universal set and G= {1,2,3,4,5,6,7}
What is G?
A. {1,2,3,4,5,6,7,8,9,10}
B. {1,2,3,4,5,6,7,}
C. Cannot be determined
D. {8,9,10}
Answer:
i believe its B
Step-by-step explanation:
Answer:
The answer is 8,9,10
Step-by-step explanation:
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 87 degrees occurs at 6 PM and the average temperature for the day is 70 degrees. Find the temperature, to the nearest degree, at 11 AM.
Answer:
6554 degres
Step-by-step explanation:
he physical plant at the main campus of a large state university receives daily requests to replace florescent light-bulbs. The distribution of the number of daily requests is Normally distributed with a mean of 47 and a standard deviation of 10. Using the Empirical Rule, what is the approximate percentage of light-bulb replacement requests numbering between 47 and 57?
Answer:
47.75 %
Step-by-step explanation:
It is a very well known issue that in Standard Normal Distribution porcentages of all values fall according to:
μ + σ will contain a 68.3 %
μ + 2σ will contain a 95.5 %
μ + 3σ will contain a 99.7 %
However it is extremely importan to understand that the quantities above mentioned are distributed simmetrically at both sides of the mean, that is, the intervals are:
[ μ - 0,5σ ; μ + 0,5σ ]
[ μ - 1σ ; μ + 1σ ]
[ μ - 1.5σ ; μ + 1.5σ ]
So we have to take that fact into account when applying the empirical rule. Then
With mean μ = 47 and σ = 10 is equal to say
values between 47 and 57 ( μ + σ ) we are talking about the second interval, but just half of it.
Then the approximate porcentage of light-bulb replacement requests is
95.5 /2 = 47.75 %
Roni wants to write an equation to represent a proportional relationship that has a constant of proportionality equal to 7/25. She writes the equation y = x + 7/25. What error is Roni making?
Answer:
Roni did not make use of the equation for a proportional relationship.
Step-by-step explanation:
For some constant of proportionality k, y is proportional to x if x and y satisfy the equation ...
y = kx
Roni knows k=7/25, but she did not use this equation. She added instead of multiplying, so did not end with an equation expressing a proportional relation.
___
y = (7/25)x
Identify the sampling technique used.
At a local community college, five statistics classes are randomly selected out of 20 and all of the students from each class are interviewed.
A) cluster
B) stratified
C) systematic
D) random
E) convenience
Answer:
Random
Step-by-step explanation:
The sampling technique used in this scenario is A) cluster sampling.
Cluster sampling is a method where the population is divided into clusters or groups, and a random sample of these clusters is selected for analysis.
In this case, the population consists of 20 statistics classes at the local community college.
Instead of selecting individual students, the clusters (classes) are randomly selected.
Once the clusters are chosen, all the students from each selected class are interviewed.
This approach is different from other sampling techniques because it focuses on sampling groups rather than individuals within the population.
Hence, the most appropriate sampling technique in this scenario is cluster sampling (option A), where the classes were randomly selected as clusters, and all the students within each selected class were interviewed.
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Owen has enough materials to build up to 10 birdhouses in shop class. Each birdhouse needs 12 square feet of wood. The function W(b) = 12b represents the total amount of wood that Owen would need to build b birdhouses. What domain and range are reasonable for the function?
A.
D: 0 ≤ b ≤ 120
R: 0 ≤ W(b) ≤ 10
B.
D: 10 ≤ b ≤ 12
R: 0 ≤ W(b) ≤ 120
C.
D: 0 ≤ b ≤ 10
R: 12 ≤ W(b) ≤ 120
D.
D: 0 ≤ b ≤ 10
R: 0 ≤ W(b) ≤ 120
Answer:
D. D: 0 ≤ b ≤ 10; R: 0 ≤ W(b) ≤ 120
Step-by-step explanation:
The problem statement tells you Owen can build up to 10 birdhouses, and that b represents that number. Then 0 ≤ b ≤ 10 is the domain described by the problem statement.
It also tells you that W(b) = 12b, so filling in values from 0 to 10 gives a range from 0 to 120: 0 ≤ W(b) ≤ 120.
These observations match choice D.
The domain and range for the function W(b) = 12b are D: 0 ≤ b ≤ 10 and R: 0 ≤ W(b) ≤ 120 respectively. The option D is correct.
The function W(b) = 12b represents the total amount of wood needed to build b birdhouses, where each birdhouse requires 12 square feet of wood. Since Owen can build up to 10 birdhouses, the domain of the function (which represents the number of birdhouses Owen can build) is 0 ≤ b ≤ 10.
For the range of the function, which represents the total amount of wood in square feet, if Owen builds no birdhouses (b = 0) he needs no wood (0 square feet), and if he builds the maximum of 10 birdhouses (b = 10), he would need 120 square feet of wood which is calculated as W(10) = 12 * 10. Therefore, the range of his function would be 0 ≤ W(b) ≤ 120. The appropriate domain and range for the function are D: 0 ≤ b ≤ 10 and R: 0 ≤ W(b) ≤ 120, which corresponds to option D.
Can anyone help me with this geometry problem?
Answer:
H. 13
Step-by-step explanation:
Make use of the Pythagorean theorem twice. The first time, use it to find TS. The second time, use it to find QR.
TS² + RT² = RS²
TS² = RS² -RT² = 64 -48 = 16 . . . . subtract RT², fill in numbers
TS = 4 . . . . . take the square root
Now, QT = QS -TS = 15 -4 = 11, so ...
QR² = QT² +RT²
QR² = 11² +(4√3)² = 121 +48 = 169
QR = √169 = 13
The length of QR is 13.
There are 4 red marbles and 8 green marbles in a box. If Emma randomly selects a marble from the box, what is the probability of her selecting a red marble?
Answer:
The probability of a successful event is the ratio of the number of successful events to the total number of events. In this case, a successful event is selecting a red marble from the box. The total number of events is the total number of marbles in the box:
Red marbles/Total number of marbles
4/12 divide
=1/3
The probability of her selecting a red marble is 1/3
How to determine the probability?The distribution of the marbles is given as:
Red = 4
Green = 8
The probability of selecting a red marble is:
P(Red) =Red/Total
So, we have:
P(Red) = 4/(4 + 8)
Evaluate
P(Red) = 1/3
Hence, the probability of her selecting a red marble is 1/3
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The area of a rectangular banquet call is 7400 ft.². The length of one side of the hall is 82 feet. Explain how you can use compatible numbers to activate the width of the hall
Answer:
Compatible width of rectangular banquet hall could be 90 feet approximately.
Step-by-step explanation:
Given
Area of a rectangular banquet hall = 7400 square feet
Length of rectangular banquet hall = 82 feet
We need to calculate width of the rectangular banquet hall.
Now Area of rectangle is equal to length times width.
Framing in equation form we get;
[tex]Area\ of \ Rectangle= length \times width[/tex]
Substituting the given values we get;
[tex]82 \times width = 7400\\\\width = \frac{7400}{82} = 90.2439[/tex]
Now by definition of Compatible numbers which state that:
"Compatible numbers are the numbers that are easy to add, subtract, multiply, or divide mentally. Compatible numbers are close in value to the actual numbers that make estimating the answer and computing problems easier."
Now By Using width as 90 feet and length as 82 feet we get area as 7380 sq ft. which is closet to actual area which is 7400 sq ft.
Hence we can say compatible width could be 90 feet approximately.
The width of the rectangular drawing is one third the length plus 3 inches. What is the perimeter of the drawing. Write and evaluate an expression to solve the problem
Answer:
Step-by-step explanation:
One hat company makes and sells two types of hats. The Bradley hat requires 4 yards of leather. The karli hat requires 6 yards of leather. If the company used 100 yards of leather to make 19 hats, how many of each type did the company make
Answer:
The Company made 6 Bradley hats and 12 Karli hats.
Step-by-step explanation:
Given,
Total Amount of leather = 100 yards
Total number of hats = 19
Solution,
Let the number of Bradley hat be x.
And also let the number of Karli hat be y.
Total number of hats = 19
[tex]\therefore x+y=19\ \ \ \ \ equation\ 1[/tex]
Now, Bradly hats requires 4 yards and Karli hats requires 6 yards of leather.
So framing the above sentence in equation form, we get;
[tex]4x+6y=100\ \ \ \ \ equation\ 2[/tex]
Now, multiplying equation 1 by 4, we get;
[tex]4(x+y)=19\times4\\\\4x+4y=76\ \ \ \ \ equation\ 3[/tex]
Now we subtract equation 3 from equation 2, we get;
[tex](4x+6y)-(4x+6y)=100-76\\\\4x+6y-4x-4y=24\\\\2y=24\\\\y=\frac{24}{2}=12[/tex]
[tex]y=12[/tex]
On substituting the value of y in equation 1, we get the value of x.
[tex]x+y=19\\\\x+12=19\\\\x=19-12=6[/tex]
Hence The Company made 6 Bradley hats and 12 Karli hats.
Solve the system by substitution.
2.5x-3y=-13
3.25x-y=-14
Solving the given system of equations involves rearranging one equation to solve for a variable, substituting this into the other equation to find the value of one variable, and then substituting this value back into the rearranged equation to find the value of the other variable.
Explanation:To solve a system of equations by substitution, we first solve one of the equations for one variable and then substitute this expression into the other equation. Looking at the two given equations, the second equation, 3.25x - y = -14, is easier to solve for y (because the coefficient before y is -1). So, we'll start with that:
Rearrange the second equation: y = 3.25x + 14.Substitute this newly formed equation in place of 'y' in the first equation: 2.5x - 3(3.25x + 14) = -13.Simplify this equation to find the 'x' value.Substitute this 'x' value back into the newly formed equation (step 1) to get the 'y' value.This step-by-step process will give the solution to the system by substitution.
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The continuously compounded return of Mordice Corporation shares for the period August 1 to August 15 is closest to:__________
Answer:
The continuously compounded return of Mordice Corporation shares for the period August 1 to August 15 is closest to:______6.90%
Step-by-step explanation:
The question is incomplete. This is the complete version
The weekly closing prices of mordice corporation shares are as follows;
Date. Closing price
Ist August. 112
8 August 160
15 August. 120
Solution
The continuous compounded return of mordice corporation shares can be calculated by taking the natural log change
In(120/112)*100= 6.89% which is closest to 6.90%
Reese went cycling in the morning .The ratio of her distance in miles to the length of time in minutes was 15:60 tease concluded that she rode at an average speed of 4 miles per minute is she correct or not ?
Answer:
No, she is not correct as her speed is 0.25 miles per minute.
Step-by-step explanation:
Given:
Ratio of distance to time taken is 15 : 60.
Distance is in miles and length of time is in minutes.
We know that, average speed is given as the ratio of the distance traveled and the length of the time taken.
So, the ratio above is nothing but the average speed of Reese for cycling.
Thus, average speed of Reese is given as:
[tex]\textrm{Average speed}=\frac{Distance}{Time}\\\\\textrm{Average speed}=\frac{15}{60}\ miles\ per\ min\\\\\textrm{Average speed}=\frac{1}{4} = 0.25\ miles\ per\ min[/tex]
Therefore, the average speed of Reese is 0.25 miles per minute which is not equal to the one mentioned by Reese as 4 miles per minute.
So, Reese conclusion of her average speed is incorrect. It's not 4 but the reciprocal of 4 which is 0.25 miles per minute.
Find the slope using the formula LaTeX: \frac{y_2-y_1}{x_2-x_1}y2−y1x2−x1 (9, 10) and (7, 2)
Final answer:
The slope of the line passing through the points (9, 10) and (7, 2) is 4.
Explanation:
The slope of a line is a measure of how steep the line is and can be calculated using the formula slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two different points on the line.
Given two points (9, 10) and (7, 2), we can calculate the slope by subtracting the y-coordinate of the first point from the y-coordinate of the second point, and then dividing that number by the result of subtracting the x-coordinate of the first point from the x-coordinate of the second point.
So, the slope would be calculated as follows:
Slope = (10 - 2) / (9 - 7)
Slope = 8 / 2
Slope = 4
Therefore, the slope of the line passing through the points (9, 10) and (7, 2) is 4. This means there is a rise of 4 on the vertical axis for every increase of 1 on the horizontal axis.
Manufacture wants to enlarger it's floor area 1.5 times that of the current facility. The current facility is 260 ft by 140 ft. The manufacture wants to increase each dimension the same amount.
Answer:
New dimensions of the floor is approximately 301.25 ft by 181.25 ft
Step-by-step explanation:
The question is incomplete. The complete question should be:
Manufacture wants to enlarger it's floor area 1.5 times that of the current facility. The current facility is 260 ft by 140 ft. The manufacture wants to increase each dimension the same amount. Write the dimensions of the new floor.
Given:
Length of floor = 260 ft
Width of floor = 140 ft
The floor area is increased 1.5 times.
To find the new dimensions of the floor.
Solution:
Original area of the floor = [tex]length\times width= 260\times 140=36400\ ft^2[/tex]
New area = [tex]1.5\times Original\ Area = 1.5\times 36,400=54,600\ ft^2[/tex]
Let the length and width be increased by [tex]x[/tex] ft.
Thus, new length = [tex](260+x)\ ft[/tex]
New width = [tex](140+x)\ ft[/tex]
Area of the new floor can be given as:
⇒ [tex]new\ length\times new\ width[/tex]
⇒ [tex](260+x)(140+x)[/tex]
Multiplying using distribution.
⇒ [tex]x^2+260x+140x+36400[/tex]
⇒ [tex]x^2+400x+36400[/tex]
Thus we can equate this with new area to get the equation to find [tex]x[/tex]
[tex]x^2+400x+36400=54600[/tex]
subtracting both sides by 54600.
[tex]x^2+400x+36400-54600=54600-54600[/tex]
[tex]x^2+400x+18200=0[/tex]
Using quadratic formula:
For a quadratic equation [tex]ax^2+bx+c=0[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
For the equation [tex]x^2+400x-18200=0[/tex]
[tex]x=\frac{-400\pm\sqrt{(400)^2-4(1)(-18200)}}{2(1)}[/tex]
[tex]x=\frac{-400\pm\sqrt{232800)}}{2}[/tex]
[tex]x=\frac{-400\pm482.49}{2}[/tex]
[tex]x=\frac{-400+482.49}{2} \ and\ x= \frac{-400-482.49}{2}[/tex]
∴ [tex]x\approx 41.25 \ and\ x\approx-441.25[/tex]
Since length is being increased, so we take [tex]x\approx41.25[/tex]
New dimensions are:
New length [tex]\approx 260\ ft + 41.25\ ft =301.25\ ft[/tex]
New width [tex]\approx 140\ ft + 41.25\ ft =181.25\ ft[/tex]
The boundary lines for the system of inequalities is given in the graph.
y ≥ 2x − 3
y ≤ −x + 2
Which region represents the solution to the system of inequalities?
A) region A
B) region B
C) region C
D) region D
Last year , the eagles soccer team win 40% of the games they played. If the eagles won 12 games last year, what is the total number of the games that the eagles played?
Answer:
The total number of the games that the eagles played is 12
Step-by-step explanation:
Given:
The eagles soccer team win 40% of the games
Number games won last year = 12
To Find:
Total number of the games that the eagles played = ?
Solution:
Let the total number of games eagles played be X
Then
according to the question,
40% of X = 12
[tex]\frac{40}{100} \times X = 12[/tex]
[tex]X = 12 \times \frac{100}{40}[/tex]
[tex]X = \frac{1200}{40}[/tex]
X = 30
The Eagles played a total of 30 games last year.
Explanation:To find the total number of games that the Eagles played last year, we can set up a proportion using the information given. Since the Eagles won 40% of their games, we can say that 40% is equal to 12 games. Let x be the total number of games played. The proportion would be: 40/100 = 12/x. Cross multiplying gives us 40x = 1200. Dividing both sides by 40, we find that x = 30. Therefore, the Eagles played a total of 30 games last year.
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Given:
R, S, T are midpoints of , , and .
If the perimeter (distance around) of ABC is 20, then the perimeter of RST is
Answer:
[tex]10[/tex]
Step-by-step explanation:
Given that [tex]R,S,T[/tex] are mid points of the sides of the triangle [tex]ABC[/tex]
Perimeter of [tex]\Delta ABC=AB+AC+BC=20[/tex]
In the [tex]\Delta ARS\ and\ \Delta ABC[/tex]
[tex]\frac{AR}{AB}=\frac{1}{2} \ \ (as\ R\ is\ mid\ point\ of\ AB)[/tex]
[tex]\frac{AS}{AC}=\frac{1}{2} \ \ (as\ S\ is\ mid\ point\ of\ AC)[/tex]
[tex]\angle A=\angle A[/tex]
from [tex]SAS[/tex] these two triangles are similar
Hence
[tex]\frac{RS}{BC}=\frac{AR}{AB}=\frac{AS}{AC}=\frac{1}{2}[/tex]
[tex]RS=\frac{BC}{2}[/tex]
Similarly [tex]RT=\frac{AC}{2}\ and\ ST=\frac{AB}{2}[/tex]
[tex]Perimeter\ of \ \Delta RST=RS+ST+RT\\\\=\frac{BC}{2}+\frac{AR}{2}+\frac{AC}{2} \\\\=\frac{AB+AC+BC}{2}\\\\=\frac{20}{2}\\\\ =10[/tex]
You are analyzing the allele frequencies for fur color in a population of squirrels where black fur is dominant to red fur. As part of your research, you collect the following data:
Total individuals: 1,000
Red fur individuals: 216
What is the value of p2 in this population? Include up to 3 decimal places in your answer.
Answer:
0.784
Step-by-step explanation:
Given that you are analyzing the allele frequencies for fur color in a population of squirrels where black fur is dominant to red fur.
As part of your research, you collect the following data:
Total individuals: 1,000
Red fur individuals: 216
So black fur individuals = [tex]1000-216\\=784[/tex]
p2 = proportion of black fur individuals to total individuals
= [tex]\frac{784}{1000} \\=0.784[/tex]
Final answer:
The value of p2 in the population of squirrels is calculated using the homozygous recessive genotype for red fur (q2), which is found to be 0.216. We find q by taking the square root of q2 and then calculate p as 1 - q. The value of p2 is then p squared, resulting in approximately 0.286.
Explanation:
To determine the value of p2 in the population of squirrels for the trait of fur color, we first need to understand that red fur individuals represent the homozygous recessive genotype, which is indicated by q2 in Hardy-Weinberg equations. Since the total number of red fur individuals is given as 216 out of 1,000, we can calculate q2 by dividing the number of red fur individuals by the total number of individuals, which is 216/1000 = 0.216. To find the value of q, we need to take the square root of q2, so q = sqrt(0.216). Then, according to the Hardy-Weinberg principle, we know p + q = 1. Thus, we can calculate p by subtracting q from 1. Finally, to find p2, we just square the value of p.
The calculations are as follows:
Find q2: 216/1000 = 0.216.Find q: sqrt(0.216) (around 0.465).Find p: 1 - 0.465 (which is approximately 0.535).Find p2: (0.535)2 (which is approximately 0.286).Thus, the value of p2 in this population is approximately 0.286.
Suppose that we know that a=5cm, b=5cm, and angle A=53o in a certain triangle. According to the Law of Sines,a) angle B must have an approximate measure of 48 degreesb) angle B must be obtusec) there are two triangles which meet the criteriad) there is exactly one triangle which meets the criteria
Answer:
B = 53°
C = 74°
The correct option for Suppose that we know that a=5cm, b=5cm, and angle A=53o in a certain triangle. According to the Law of Sines D. There is exactly one triangle that meets the criteria.
Given:
a = 5, b = 5, A = 53°
⇒ a/sin A = b/sin B ⇒ Sin B = Sin A
⇒ B = A (or) 180-A
⇒ B = 53° (or) 127°
B = 53°:
C = 180-A-B = 0 (not possible)
⇒ B = 53°, C = 74° ⇒ C = (Sin C) (b/sin B) ≅ 6.02 cm
In which cases, can we use the law of sines?
Generally, the law of sines is used to solve the triangle, when we know two angles and one side or two angles and one included side. It means that the law of sines can be used when we have ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria.
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