Answer:
Step-by-step explanation:
Given
Circle has radius [tex]r=5 in.[/tex]
Area of the sector is given by
[tex]A_s=\frac{\theta }{2\pi }\times \pi r^2[/tex]
if [tex]A_s[/tex] is one-sixth of area of circle then
[tex]A_s=\frac{\pi r^2}{6}[/tex]
[tex]\frac{\pi r^2}{6}=\frac{\theta }{2\pi }\times \pi r^2[/tex]
[tex]\theta =\frac{2\pi }{6}=\frac{\pi }{3}\ radian[/tex]
If [tex]A_s[/tex] is one-fourth of area of circle then
[tex]A_s=\frac{\pi r^2}{4}[/tex]
[tex]\theta =\frac{2\pi }{4}[/tex]
[tex]\theta =\frac{\pi }{2}[/tex]
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]
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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A dealership purchased a car and a truck and then sold them both. The purchasing cost of the truck was $8,000 greater than the purchasing cost of the car, and the selling price of the truck was $12,000 greater than the selling price of the car. The profit that the dealership made on the car was equal to 20 percent of its purchasing cost, and the profit that the dealership made on the truck was equal to 30 percent of its purchasing cost. If x is the purchasing cost, in dollars, of the car, then x satisfies which of the following equations? (Note: Profit equals selling price minus purchasing cost.)
A. 0.3x+8,000=0.2x+12,0000.3x+8,000=0.2x+12,000
B. 1.3x+8,000=1.2x+12,0001.3x+8,000=1.2x+12,000
C. 0.3(x+8,000)=0.2x+12,0000.3(x+8,000)=0.2x+12,000
D. 1.3(x+8,000)=1.2x+12,0001.3(x+8,000)=1.2x+12,000
E. 1.3(x+8,000)+12,000=1.2x
Answer:
the answer is option C. 0.3(x+8,000)=0.2x+12,000
Step-by-step explanation:
Assume;
Purchase cost of car = x
Purchase cost of truck = y = 8000 + x
Selling price of truck = a =12000+b
Selling price of car = b
Since profit for truck is 30%, therefore;
a = 30%*y
a = (30/100)*y
a = 0.3y
Since profit for car is 20%, therefore;
b = 20%*x
b = (20/100)*x
b = 0.2x
Now take;
A = 0.3y
12000 + b = 0.3 (8000+x)
12000 + 0.2x = 0.3(8000+x)
OR
0.3(8000+x) = 0.2x +12000
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)
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.
Ben earns $9 per hour for each delivery he makes. He wants to make more than $155 in 8 hours .What is the least number of deliverys he must make to reach his goal
Question is Incomplete,Complete question is given Below.
Ben earns $9 per hour and $6 for each delivery he makes. he wants to earn more than $155 in an 8-hour workday. what is the least number of deliveries he must make to reach his goal?
Answer:
Ben must make at least 14 Deliveries to achieve his goal.
Step-by-step explanation:
Hourly Rate = $9 per hour
Cost of each Delivery = $6
Number of hours to be worked = 8 hours.
Money needs to be earned =$155
we need to find the number of deliveries he must make to reach his goal.
Solution :
Let number of deliveries be 'x'.
Now we can say that Hourly rate multiplied by number of hours of work plus Cost of each delivery multiplied by number of deliveries should be greater than or equal to Money needs to be earned.
Framing in equation form we get;
[tex]9\times8+6x\geq 155[/tex]
Solving the equation we get;
[tex]72+6x\geq 155[/tex]
Subtracting both side by 72 using Subtraction property of Inequality we get;
[tex]72+6x-72\geq 155-72\\\\6x\geq 83[/tex]
Now Dividing both side by 6 using Division Property we get;
[tex]\frac{6x}{6} \geq \frac{83}{6} \\\\x\geq 13.83[/tex]
Hence Ben must make at least 14 Deliveries to achieve his goal.
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.
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 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
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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:
Lena wants to put the monkey stickers in all album. She says she will use more pages if she puts 5 stickers on a page instead of 10 stickers on a page. Is she correct
Answer:
She is absolutely correct!
Step-by-step explanation:
Let the total no. of stickers with Lena be x.
If she sticks 5 stickers per page, the number of pages she will use=[tex]\frac{x}{5}[/tex]
If she sticks 10 stickers per page, the number of pages she will use=[tex]\frac{x}{10}[/tex]
We all know, that the smaller the denominator the larger the number.
Therefore, [tex]\frac{x}{5} >\frac{x}{10}[/tex]
Condition being that x is a positive quantity which it automatically is.
So, Lena is right in her reasoning that she will use more no. of pages.
Yes, Lena is correct because placing a smaller number of stickers per page (5 instead of 10) will indeed result in the use of more pages overall, as this reduces the stickers-to-page ratio.
Explanation:The question is asking if Lena will use more pages for her stickers if she places 5 stickers on a page instead of 10. We are working with a simple division concept here. When you have a fixed number of items (stickers, in this case) and you use fewer items per group (or page), you will end up with more groups (or pages).
If Lena puts 5 stickers on each page as opposed to 10 stickers on a page, she will indeed need more pages because she’s placing fewer stickers on each page. For instance, if she has 20 stickers: with 5 stickers per page, she will need 4 pages (20 stickers / 5 stickers per page = 4 pages). On the other hand, with 10 stickers per page, she will only need 2 pages (20 stickers / 10 stickers per page = 2 pages). Therefore, placing fewer stickers on a page results in more pages being used.
An architect is planning several stone spheres of different sizes into the landscaping of a public park, and workers who will be applying the finish to the exterior of the spheres need to know the surface area of each sphere. The finishing process costs $92 per square meter. The surface area of a sphere is equal to 4(pi)r2 where r is the radius of the sphere.
How much would it cost to finish a sphere with a 5.50-meter circumference and a 7.85-meter circumference?
a) $900
b) $1200
c) $1800
d) $2800
e) $3200
f) $4500
Answer:
the answer is closest to option d) $2800
Step-by-step explanation:
Assume,
Cost per square meter = y = 92$
Step 1:
For Sphere 1:
Circumference = C1 = 5.5 m
Formula for Circumference is;
C = 6.2832(R)
Where R = radius of sphere
Therefore for radius;
C1 = 6.2832(R1)
5.5 = 6.2832(R1)
R1 = 5.5/6.2832
R1 = 0.87 m
Formula for Area;
A1 = 4π(R1)²
Since,
π = 3.14
Therefore;
A1 = 4*3.14*(0.87)²
A1 = 9.51 m²
Cost of finishing for sphere 1 will be;
X1 = 92*A1
X1 = 92*9.51
X1 = $875
Step 2:
For Sphere 2:
Circumference = C2 = 7.85 m
Formula for Circumference is;
C = 6.2832(R)
Where R = radius of sphere
Therefore for radius;
C2 = 6.2832(R2)
7.85 = 6.2832(R2)
R2 = 7.85/6.2832
R2 = 1.25 m
Formula for Area;
A1 = 4π(R2)²
Since,
π = 3.14
Therefore;
A1 = 4*3.14*(1.25)²
A1 = 19.63 m²
Cost of finishing for sphere 1 will be;
X2 = 92*A2
X2 = 92*19.63
X2 = $1,806
Step 3:
Now for total cost;
X = X1 + X2
X = 875 + 1806
X = $2,681
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:
Which type of correlation is suggested by the scatter plot?
A) positive correlation
B) negative correlation
C) equal correlation
D) no correlation
Answer:D no correlation
Step-by-step explanation:because if you were to draw a straight line, it wouldn’t be near all of the lines
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.
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.
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.
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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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:
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
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]
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.
Sunny side library has three times as many books as creek side library. The libraries have an average of 3,840 books. How many books does Sunnyside library have?
Answer:
2880
Step-by-step explanation:
Sunnyside has 3 of every 4 books, so has ...
(3/4)(3840) = 2880 . . . books
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:
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.
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.
A manufacturer of bedding wants to do quality control on its 400-thread-count sheets. The thread count varies normally with a mean thread count μ = 400 and a standard deviation σ = 8. A quality control researcher randomly selects 16 sheets and finds that the mean thread count for the sample is 395.2. We want to determine if these data provide enough evidence to conclude that the mean thread count is significantly different from the target level. One-sample z-test of μ = 400 vs. μ ≠ 400 Assumed standard deviation = 8 n = 16 Mean = 395.2 z-value = −2.4 Two-tailed p-value = 0.0164 95% confidence interval: (396.0801, 403.9199) Which of the following represents the correct conclusion we can make on the basis of the output (and at the usual significance level of 0.05)?
Answer:
[tex]z=\frac{395.2-400}{\frac{8}{\sqrt{16}}}=-2.4[/tex]
[tex]p_v =2*P(Z<-2.4)=0.0164[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly different from 400.
[tex]395.2-1.96\frac{8}{\sqrt{16}}=391.28[/tex]
[tex]395.2+1.96\frac{8}{\sqrt{16}}=399.12[/tex]
So on this case the 95% confidence interval would be given by (391.28;399.12)
Since the confidence interval not contains the value of 400 we can conclude that the true mean is different from 400 at 5% of significance.
Step-by-step explanation:
1) Data given and notation
[tex]\bar X=395.2[/tex] represent the sample mean
[tex]\sigma=8[/tex] represent the population standard deviation
[tex]n=16[/tex] sample size
[tex]\mu_o =7.3[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
2) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean pressure is different from 400, the system of hypothesis are :
Null hypothesis:[tex]\mu = 400[/tex]
Alternative hypothesis:[tex]\mu \neq 400[/tex]
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
3) Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z=\frac{395.2-400}{\frac{8}{\sqrt{16}}}=-2.4[/tex]
4) P-value
Since is a two sided test the p value would given by:
[tex]p_v =2*P(Z<-2.4)=0.0164[/tex]
5) Conclusion
If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly different from 400.
6) Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]
Now we have everything in order to replace into formula (1):
[tex]395.2-1.96\frac{8}{\sqrt{16}}=391.28[/tex]
[tex]395.2+1.96\frac{8}{\sqrt{16}}=399.12[/tex]
So on this case the 95% confidence interval would be given by (391.28;399.12)
Since the confidence interval not contains the value of 400 we can conclude that the true mean is different from 400 at 5% of significance.
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.
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.
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