Answer:
-A person can be 95% confident that the mean drive through service time lies between 177.6 seconds and 181.0 seconds.
Step-by-step explanation:
- Confidence level is the degree of certainty we have on a particular statistic.
-The 95% confidence interval means that we are 95% confident that the mean drive through service time is lies between 177.6 seconds and 181.0 minutes.
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 428428 gram setting. It is believed that the machine is underfilling or overfilling the bags. A 7171 bag sample had a mean of 433433 grams with a variance of 441441. Assume the population is normally distributed. A level of significance of 0.010.01 will be used. Specify the type of hypothesis test.
Answer:
z-test
Step-by-step explanation:
-A z-test is a test used to determine the difference in two population means of known variances.
-The sample size has to be large enough, [tex]n\geq 30[/tex](n=71).
-And, the population must follow a normal distribution.
-Since our sample meets all the above conditions, the hypothesis test used is a z-test
Ten years ago, college students spent an average of 120 hours per semester on extra-curricular activities. A researcher believes that now college students spend less time on extra-curricular activities than they did ten years ago. A simple random sample of 100 college students found that in the past year the average number of hours spent per semester in extracurricular activities was 107 hours with a standard deviation of 45 hours. If we are testing at a significance level of 0.05, based on the p-value, what is your conclusion?
Answer:
We conclude that the college students spend less time on extra-curricular activities than they did ten years ago.
Step-by-step explanation:
We are given that Ten years ago, college students spent an average of 120 hours per semester on extra-curricular activities.
A simple random sample of 100 college students found that in the past year the average number of hours spent per semester in extracurricular activities was 107 hours with a standard deviation of 45 hours.
Let [tex]\mu[/tex] = average time spent on extra-curricular activities.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 120 hours {means that the college students spend more or equal time on extra-curricular activities than they did ten years ago}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 120 hours {means that the college students spend less time on extra-curricular activities than they did ten years ago}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average number of hours spent per semester = 107 hrs
s = sample standard deviation = 45 hours
n = sample of college students = 100
So, test statistics = [tex]\frac{107-120}{\frac{45}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= -2.889
The value of t test statistics is -2.889.
Now, the P-value of the test statistics is given by following formula;
P-value = P( [tex]t_9_9[/tex] < -2.889) = 0.00314
Since, the P-value is less than the level of significance as 0.05 > 0.00314, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the college students spend less time on extra-curricular activities than they did ten years ago.
A piece of wire 26 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area?
Answer:
For the maximize the total area, the all wire i.e. 26 m should be used for the square.
Step-by-step explanation:
Length of the wire = 26 m
Let Amount of wire cut for square = x
Amount of wire cut for triangle = 26 - x
Side of the square = [tex]\frac{x}{4}[/tex]
Area of the square = [tex]\frac{x^{2} }{16}[/tex] ------ (1)
Side of the triangle is given by
[tex]a = \frac{26 - x}{3}[/tex]
Side of the triangle is [tex]a = \frac{26 - x}{3}[/tex]
Area of the triangle is given by
[tex]A = \frac{\sqrt{3} }{4} a^{2}[/tex]
Area of the triangle is
[tex]A =\frac{\sqrt{3} }{36} (26 - x)^{2}[/tex] ------- (2)
Now the total area = Area of square + Area of triangle
The total area = [tex]\frac{x^{2} }{16} + \frac{\sqrt{3} }{36} (26 - x)^{2}[/tex] ------- (3)
Differentiate above equation with respect to x we get
[tex]A' = \frac{x}{8} - \frac{\sqrt{3} }{18} (26 - x)[/tex]
Take [tex]A' = 0[/tex]
[tex]\frac{x}{8} - \frac{\sqrt{3} }{18} (26 - x) = 0[/tex] ------- (4)
By solving the above equation we get
x = 11.31 m
Again take [tex]A''[/tex] by differentiating equation (4)
[tex]\frac{x}{8} + \frac{\sqrt{3} }{18} (26)[/tex]
Which is greater than zero. so the value x = 11.31 m gives the area minimum.
Thus for the maximize the total area, the all wire i.e. 26 m should be used for the square.
In a test of hypothesis, the null hypothesis is that the population proportion is equal to .58 and the alternative hypothesis is that the population proportion is greater than .58. Suppose we make the test at the 2.5% significance level. A sample of 1200 elements selected from this population produces a sample proportion of .62. What is the value of the test statistic, z?
Answer:
z statistic = 2.82
Step-by-step explanation:
Sample size = 1200
Null hypothesis, [tex]H_{0}[/tex]: p = 0.58
Alternative hypothesis, [tex]H_{a}[/tex]: p > 0.58
From the null and alternative hypothesis, we can derive that Hypothesized proportion, [tex]p_{0}[/tex] = 0.58 = 58%
Significance level = 2.5% = 0.025
Sample proportion, [tex]p_{1}[/tex] = 0.62 = 62%
Test statistic, z:
[tex]z_{statistic} = \frac{p_{1} -p_{0} }{\sqrt{\frac{p_{0}( 1 -p_{0} )}{n} } }[/tex]
[tex]z_{statistic} = \frac{0.62-0.58}{\sqrt{\frac{0.58(1-0.58)}{1200} } }[/tex]
[tex]z statistic =\frac{0.04}{\sqrt{0.000203} }[/tex] [tex]= \frac{0.04}{0.0142}[/tex]
[tex]z statistic = 2.82[/tex]
The value of the test statistic 'z' for the given hypothesis test is approximately 5.65, calculated using the provided sample proportion, hypothesized population proportion, and sample size.
The question asks for the calculation of the test statistic 'z' for a hypothesis test where the null hypothesis states that the population proportion is equal to .58 and the alternative hypothesis says that the population proportion is greater than .58. This is tested at a 2.5% significance level with a sample size of 1200 and sample proportion of .62.
To calculate the test statistic z, use the formula:
z = (p' - p) / √(p(1 - p)/n)
where:
p' is the sample proportion (0.62)p is the hypothesized population proportion (0.58)n is the sample size (1200)Now, plug in the values:
z = (0.62 - 0.58) / √(0.58(1 - 0.58)/1200)
z ≈ 5.65
This is the value of the test statistic z for conducting the hypothesis test.
An architect was asked to build a special staircase in a new building. The staircase will be built like a helix that rotates around the outside of a cylindrical waterfall. Because it is a helix, the beginning of the staircase begins at a point directly above the position where the staircase ends at the bottom base of the column. Describe how to find the length of the staircase if the cylinder it surrounds is 30 m in height and has a radius of 12 m
Answer:
[tex]\Delta s \approx 754.579\,m[/tex] (See explanation below).
Step-by-step explanation:
Each floor has a height of 3 meters. Then, the number of floors of the cylinder is:
[tex]n = \frac{30\,m}{3\,m}[/tex]
[tex]n = 10\,floors[/tex]
Let consider that spiral makes a revolution per floor. Then, the parametric equations of the spiral are:
[tex]x = r\cdot \cos \theta[/tex]
[tex]y = r\cdot \sin \theta[/tex]
[tex]z = \Delta h \cdot \frac{\theta}{2\pi}[/tex]
Length of the staircase can be modelled by using the formula for arc length:
[tex]\Delta s = \int\limits^{20\pi}_{0} {\sqrt{\left(\frac{dx}{d\theta} \right) ^{2}+\left(\frac{dy}{d\theta} \right)^{2}+\left(\frac{dz}{d\theta}\right)^{2}}} \, d\theta[/tex]
[tex]\Delta s = \int\limits^{20\pi}_{0} {\sqrt{\left(-r\cdot \sin \theta\right)^{2}+\left(r\cdot \cos \theta\right)^{2}+\left(\frac{\Delta h}{2\pi} \right)^{2}} } \, d\theta[/tex]
[tex]\Delta s = \int\limits^{20\pi}_{0} {\sqrt{r^{2}+\frac{(\Delta h)^{2}}{4\pi^{2}} }} \, d\theta[/tex]
[tex]\Delta s = \sqrt{(12\,m)^{2}+\frac{(3\,m)^{2}}{4\pi^{2}} } \cdot (20\pi-0)[/tex]
[tex]\Delta s \approx 754.579\,m[/tex]
Fluoxetine, a generic anti-depressant, claims to have, on average, at least 20 milligrams of active ingredient. An independent lab tests a random sample of 80 tablets and finds the mean content of active ingredient in this sample is 18.7 milligrams with a standard deviation of 5 milligrams. If the lab doesn't believe the manufacturer's claim, what is the approximate p-value for the suitable test
Answer:
[tex]t=\frac{18.7-20}{\frac{5}{\sqrt{80}}}=-2.326[/tex]
[tex]df=n-1=80-1=79[/tex]
[tex]p_v =P(t_{(79)}<-2.326)=0.0113[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=18.7[/tex] represent the sample mean for the content of active ingredient
[tex]s=5[/tex] represent the sample standard deviation for the sample
[tex]n=80[/tex] sample size
[tex]\mu_o =20[/tex] represent the value that we want to test
t would represent the statistic
[tex]p_v[/tex] represent the p value for the test
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean for the active agent is at least 20 mg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 20[/tex]
Alternative hypothesis:[tex]\mu < 20[/tex]
The statistic would be:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Now we can calculate the statistic:
[tex]t=\frac{18.7-20}{\frac{5}{\sqrt{80}}}=-2.326[/tex]
P value
The degrees of freedom are calculated like this:
[tex]df=n-1=80-1=79[/tex]
Since is a one left tailed test the p value would be:
[tex]p_v =P(t_{(79)}<-2.326)=0.0113[/tex]
Option (e) 0.0113 is correct. The approximate p-value for the lab's one-sample t-test on fluoxetine is 0.0113.
To determine the approximate p-value for the lab's test on fluoxetine, we can use a one-sample t-test. Here's a step-by-step explanation:
Null Hypothesis (H₀): The mean content of the active ingredient is at least 20 milligrams (μ ≥ 20 mg).Alternative Hypothesis (Hₐ): The mean content of the active ingredient is less than 20 milligrams (μ < 20 mg).Calculate the test statistic using the formula:(bar{x} - μ) / (s/√n)
where bar{x} is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Substituting the values:bar{x} = 18.7, μ = 20, s = 5, n = 80
t = (18.7 - 20) / (5/√80)
t = -1.3 / (5/8.944)
t = -1.3 / 0.559
t = -2.325
Using a t-distribution table or calculator, we find the p-value for t = -2.325 with (n - 1) = 79 degrees of freedom. The approximate p-value is 0.0113.Therefore, the correct answer is e. 0.0113.
Complete question:
Fluoxetine, a generic anti-depressant, claims to have, on average, at least 20 milligrams of active ingredient. An independent lab tests a random sample of 80 tablets and finds the mean content of active ingredient in this sample is 18.7 milligrams with a standard deviation of 5 milligrams. If the lab doesn't believe the manufacturer's claim, what is the approximate p-value for the suitable test?
a. 0.0226
b. 0.4885
c. 0.5115
d. 0.15
e. 0.0113
True or False: The megaspore that develops into the megagametophyte leaves the flower when it
reaches maturity
Answer: gang in la
Step-by-step explanation:
Which shapes can the shaded area be divided into to find the area?
O
a rectangle and a triangle
a rectangle and a square
a trapezoid and a rectangle
a trapezoid and two triangles
Answer:
A rectangle and a triangle
Step-by-step explanation:
The design of a concrete mix requires 2,314 lb/yd3 of gravel having a moisture content of 3.5% and absorption of 4.2%, and 899 lb/yd3 of sand having a moisture content of 5.7% and absorption of 1.4%, and 244 lb/yd3 of free water. What is the weight of the mixing water per cubic yard that should be used at the job site?
Answer:
Weight of mixing water=224.541 lb
Step-by-step explanation:
Taking 1 cubic yard of concrete
Mass of gravel = 2314 lb
Moisture content = 3.5% Absorption 4.2%
Extra water needed = (4.2-3.5)*2314/100= 16.198 lb
Mass of sand= 899 lb
Moisture content = 5.7% Absorption =1.4%
Water released = (5.7-1.4)*899/100= 38.657 lb
Free water = 244 lb
Weight of mixing water = free water + extra water needed-water released = 244+16.198-38.657=224.541 lb
Weight of mixing water=224.541 lb
Suppose that 650 lb of coffee are sold when the price is $4 per pound, and 400 lb are sold at $8 per pound. a. List the data points (use price as the independent variable). b. Find the slope of the line joining the points.
Answer:
a. (4, 650), (8, 400)
b. -62.5
Step-by-step explanation:
a......................
Data points are (4, 650) and (8, 400) since price is independent variable and weight of coffee is dependent
b......................
Slope = (y2-y1)/(x2-x1)
Slope = (400 - 650)/(8-4) = -250/4 = - 62.5
The data points representing the price and quantity of coffee sold are ($4, 650) and ($8, 400). The slope of the line connecting these points, which shows the relationship between price and quantity, is -62.5.
Explanation:This question is about mathematical calculations used in economics, specifically related to pricing and demand. Let's turn these scenarios into data points, with price ($4 and $8) as the independent variable and quantity (650 lbs and 400 lbs) as the dependent variable. So, your data points are ($4, 650) and ($8, 400).
To find the slope of the line connecting these points, use the slope formula. The slope(m) is equal to the difference in the y-values divided by the difference in the x-values. So, m = (400-650) / (8-4) = -250/4 = -62.5.
Thus, the slope of the line connecting these two points, representing the relationship between the price and quantity of coffee sold, is -62.5.
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PLEASE HELP ASAP geometry question 100 MAJOR POINTS!!!
Answer:
7
Step-by-step explanation:
The surface area is the lateral area plus the base area. The base area is 9*5=45. Since there are two bases, its 90. Subtract that from 286 to get the lateral surface area, which is 196. The lateral surface area is the base perimeter*height. The base perimeter is 9+9+5+5= 28. 196/28=height. The height is 7
Answer:
Height= 7in
Step-by-step explanation:
Use the surface area formula and pulg in.
2(wl)(hl)(hw)=286
divide by 2 to get it to the other side.
143=45+9h+5h
subtract 45 and divide by 14 (9+5)
the height is 7
Mass of Weight(C)
eight
A restaurant buys 9 pounds of truffles. Suppose truffles cost $168 per ounce.
How much would the restaurant pay for the truffles?
a $1,512
b $2,688
c $12,096
d $24,192
I need the answer now plz
The restaurant pay $24,192 for 9 pounds of truffles.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A restaurant buys 9 pounds of truffles.
as, 1 pound = 16 ounce
So, the restaurant buys
= 16 x 9
= 144 ounce of truffles.
If truffles cost $168 per ounce.
So, the cost for 9 pounds ruffles is
= 144 x 168
= $ 24,192
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A recreation center is offering special prices on its pool passes and gym memberships for the summer. On the first day of the offering, a family paid $96 for 4 pool passes and 2 gym memberships. Later that day, an individualbought apool pass for herself, a pool pass for a friend,and 1
This mathematics question from middle school algebra asks to solve a system of equations to find the price of pool passes and gym memberships at a recreation center. The problem is partially incomplete due to a cutoff in the additional information needed to set up the second equation. Consequently, we cannot provide a final answer without this information.
Explanation:The question involves a linear system of equations, which is a topic in algebra within the field of mathematics. The problem presents a scenario where a family purchases a combination of pool passes and gym memberships for a total cost, and another individual purchases a different combination of the same items for a different total cost. To solve, we set up two equations based on the given information.
Step-by-step solution:
Let the price of one pool pass be p dollars and the price of one gym membership be g dollars.According to the given information, 4p + 2g = $96.Unfortunately, the rest of the question seems to be cutoff. To proceed further, we would need the additional information about the second combination of purchases that the individual makes.If complete information were provided, we would use the additional information to set up a second equation and solve the system of equations either by substitution or elimination method to find the values of p and g.Without the full information, this question is incomplete, and thus we cannot provide a final answer.
n a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2472 subjects randomly selected from an online group involved with ears. 1022 surveys were returned. Construct a 99% confidence interval for the proportion of returned surveys.
Answer:
0.3876<p<0.4389
Step-by-step explanation:
-Given [tex]n=2472, \ x=1022 , \ CI=0.99[/tex]
-We calculate the proportion of surveys returned:
[tex]\hat p=\frac{1022}{2472}\\\\=0.4134[/tex]
For a 99% confidence interval:
[tex]z_{\alpha/2}=2.576[/tex]
#The margin of error is calculated as;
[tex]ME=z_{0.005}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=2.576\times \sqrt{\frac{0.4134(1-0.4134)}{2472}}\\\\=0.0255[/tex]
The confidence interval are then:
[tex]CI=\hat p\pm ME\\\\=0.4134\pm 0.0255\\\\=[0.3876,0.4389][/tex]
Hence, the confidence interval is 0.3876<p<0.4389
Consider the exponential function
g(x)=190,000•1.03x, which models the value of Evie’s house, where x represents the number of years since she purchased the house.
What is the value of Evie’s house after 5 years rounded to the nearest dollar?
Answer:
$220262
Step-by-step explanation:
We are given that an exponential function
[tex]g(x)=190000\cdot(1.03)^x[/tex]
Where x=Number of years
We have to find the value of Evie's house after 5 years .
Substitute the values in the given function
[tex]g(5)=190000\cdot(1.03)^5[/tex]
[tex]g(5)=220262.07[/tex]
[tex]g(5)\approx 220262[/tex]
Hence, the value of Evie's house after 5 years=$220262
Uni made a model of a 1970 Ford Mustang using a scale of .5 inches = 9 in. If the actual car is 15 ft long, how long is the model car?
Answer:
The model car is 10 inches long
Step-by-step explanation:
To solve this question, we use conversion of units
Feet to inches.
Each feet has 12 inches.
The car is 15ft long.
So the car has 15*12 = 180 inches.
.5 inches = 9 in.
Rule of three
.5 inches - 9 inches
x inches - 180 inches
[tex]9x = 180*0.5[/tex]
[tex]9x = 90[/tex]
[tex]x = \frac{90}{9}[/tex]
[tex]x = 10[/tex]
The model car is 10 inches long
To find the length of Uni's model car, we convert the actual car's length to inches, set up a proportion with the given scale, and cross-multiply to solve for the model car's length, resulting in a model that is 10 inches long.
The subject matter of the question is related to scale models, which falls under the field of Mathematics. To solve this problem, we need to find the length of the model car based on the given scale and the actual length of the car.
The scale given is 0.5 inches = 9 inches. Firstly, we need to convert the actual length of the car from feet to inches, so we can work in the same units. There are 12 inches in a foot, so a 15 feet long car is 15 x 12 inches long, which is 180 inches. Now, we need to set up a proportion to find the length of the model car:
Actual car length (inch) : Model car length (inch) = Actual scale (inch) : Model scale (inch) 180 inches (actual car length) : x inches (model car length) = 9 inches (actual scale) : 0.5 inches (model scale)
By cross-multiplying, we get:
(180 inches x 0.5 inches) = (x inches x 9 inches)
Dividing both sides by 9 inches, we get:
x inches = (180 inches x 0.5 inches) / 9 inches
So, the length of the model car is:
x inches = 10 inches.
Therefore, Uni's model car is 10 inches long.
Find the midpoint of A and B where A has coordinates (2, 4)
and B has coordinates (-3, -9).
Answer:
(-0.5,-2.5)
Step-by-step explanation:
(x1 + x2) / 2 = x midpoint
(y1 + y2) / 2 = y midpoint
x)
2 + -3 = 5
5 / 2 = -0.5
y)
4 + -9 = -5
-5 / 2 = -2.5
= (-0.5, -2.5)
The midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)
What is Coordinate Geometry?A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
We have to find the midpoint of A and B where A has coordinates (2, 4)
and B has coordinates (-3, -9).
Midpoint = (2-3/2, 4-9/2)
=(-1/2, -5/2)
Hence, the midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)
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The table shows the results of a poll of 200 randomly selected juniors and seniors who were asked if they attended prom. Find the probability of each of the events.
juniors seniors
yes 28 97
no 56 19
Express your answer as a fraction, using the backslash. Example: 17 would be written as 1/7.
a) P (a junior who did not attend prom)
b) P (did not attend prom | senior)
c) P (junior | attended prom)
Answer:
(a)[tex]\frac{7}{25}[/tex]
(b)[tex]\frac{19}{116}[/tex]
(c)[tex]\frac{28}{125}[/tex]
Step-by-step explanation:
Number of juniors who attended prom,n(J)=28
Number of seniors who attended prom,n(S)=97
Total of those who attended prom=125Number of juniors who did not attend prom,n(J')=56
Number of seniors who did not attend prom,n(S')=19
Total of those who attended prom=75Total Number of students=200(a) P (a junior who did not attend prom)
[tex]P(J')=\frac{56}{200}= \frac{7}{25}[/tex]
(b)
[tex]P(Senior)=\frac{116}{200}[/tex]
[tex]P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}[/tex]
(c)P (junior | attended prom)
[tex]P(Senior)=\frac{84}{200}[/tex]
[tex]P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}[/tex]
Answer:
A. P = 7/25
B. P = 19/116
C. P = 28/125
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly this way:
Juniors Seniors Totals
Yes 28 97 125
No 56 19 75
Totals 84 116 200
2. Find the probability of each of the events.
Let's recall that the formula of probability is:
P = Number of favorable outcomes/Total number of possible outcomes
A. P (a junior who did not attend prom)
P = Juniors who did not attend prom/Total number of students surveyed
P = 56/200
P = 7/25 (Diving by 8 numerator and denominator)
B. P (did not attend prom | senior)
P = Seniors who did not attend prom/Total number of seniors surveyed
P = 19/116
C. P (junior | attended prom)
P = Juniors who attend prom/Total number of students attended prom
P = 28/125
The equation can be used to determine the number of centimeters, y, in a given number of inches, x. The equation was used to fill in the table below. Inches in Centimeters Number of Inches Number of Centimeters 2 5.08 10 25.4 63.5 40 101.6 What value is missing from the table?
Answer:
25 Inches
Step-by-step explanation:
Given the table:
[tex]\left|\begin{array}{c|c|c|c|c}\text{Number of Inches}&2&10&&40\\\text{Number of Centimeters}&5.08&25.04&63.5&101.6\end{array}\right|[/tex]
We want to determine the missing value on the table.
Let the missing value be x.
1 inch = 2.54 cm
x inch = 63.5
Expressing the above as a ratio
[tex]\dfrac{1}{x}=\dfrac{2.54}{63.5} \\$Cross Multiply$\\2.54x=63.5\\$Divide both sides by 2.54$\\x=25 \:Inches[/tex]
Therefore, the missing value is 25.
Answer:
25 Inches
Step-by-step explanation:
hope this helps :))
The Movie Haven is planning to order new medium-size popcorn containers. It has a choice of four different containers. It costs the company $0.02 per cubic inch of popcorn to fill a container. The company does not want the new container to cost more than $3.00 to fill. Which container should the company use? Use 3.14 for Pi.
Answer:
the answer is container c
b=11.14in2
12in
Step-by-step explanation:
Answer:
Answer is C
Step-by-step explanation:
A woman is emptying her aquarium at a steady rate with a small pump. The water pumped to a 12-in.-diameter cylindrical bucket, and its depth is increasing at the rate of 4.0 in. per minute. Find the rate at which the aquarium water level is dropping if the aquarium measures 24 in. (wide) × 36 in. (long) × 18 in. (high).
Answer:
Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.
Step-by-step explanation:
Given that,
The diameter of cylindrical bucket = 12 in.
Depth is increasing at the rate of = 4.0 in per minutes.
i.e [tex]\frac{dh_1}{dt}=4[/tex]
[tex]h_1[/tex] is depth of the bucket.
The volume of the bucket is V = [tex]\pi r^2 h[/tex]
[tex]=\pi \times 6^2\itimes h_1[/tex]
[tex]\therefore V=36\pi h_1[/tex]
Differentiating with respect yo t,
[tex]\frac{dV}{dt}=36\pi \frac{dh_1}{dt}[/tex]
Putting [tex]\frac{dh_1}{dt}=4[/tex]
[tex]\therefore\frac{dV}{dt}=36\pi\times 4[/tex]
The rate of volume change of the bucket = The rate of volume change of the aquarium .
Given that,The aquarium measures 24 in × 36 in × 18 in.
When the water pumped out from the aquarium, the depth of the aquarium only changed.
Consider h be height of the aquarium.
The volume of the aquarium is V= ( 24× 36 ×h)
V= 24× 36 ×h
Differentiating with respect to t
[tex]\frac{dV}{dt}=24\times 36 \times \frac{dh}{dt}[/tex]
Putting [tex]\frac{dV}{dt}=36\pi\times 4[/tex]
[tex]36\pi\times 4= 24\times 36\times \frac{dh}{dt}[/tex]
[tex]\Rightarrow \frac{dh}{dt}=\frac{36\pi \times 4}{24\times 36}[/tex]
[tex]\Rightarrow \frac{dh}{dt}=\frac{11}{21}[/tex]
Therefore the rate at which water level is dropping is [tex]\frac{11}{21}[/tex] in per minute.
To find the rate at which the aquarium water level is dropping, calculate the volume of water being pumped into the bucket per minute and the volume of the aquarium. Then, divide the volume of water by the volume of the aquarium to find the rate.
Explanation:To find the rate at which the aquarium water level is dropping, we first need to determine the flow rate of water being pumped into the cylindrical bucket.
Now, let's find the rate at which the aquarium water level is dropping:
By calculating the above expression, you can find the rate at which the aquarium water level is dropping.
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The water level in the aquarium is dropping at an average rate of π/6 inches per minute. This is obtained by relating the volumes and their rates of change in both the bucket and the aquarium.
Explanation:The subject of this question is calculus, specifically, related rates. The situation describes two rates: one at which the depth of water in the bucket is increasing, and one at which the water level in the aquarium is dropping - a classic related rates problem.
To comprehend this, let us calculate the volume rates of each one: the bucket and the aquarium. The bucket is referred as cylindrical with a radius of 6 inches (half of 12 inches). The volume of a cylinder is V = πr²h. The depth or height, h, is increasing at the rate of 4 inches per minute, so dh/dt = 4 in/min. The rate at which the volume has been changing, dV/dt = πr²dh/dt = π * (6 in)² * 4 in/min = 144π in³/min.
The aquarium is a rectangular prism, thus its volume can be calculated by V = l*w*h. Therefore, the rate at which the water level is dropping is dV/dt / (l*w) which equals 144π in³/min divided by the area of the aquarium (24in*36in = 864 in²), which gives dh/dt = 144π / 864, which reduces to dh/dt = π/6 in/min downwards. Hence, the water level in the aquarium is dropping at π/6 in/min on an average.
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What is 1/3x1/3x1/3[/tex]?
Answer:
i believe the answer is 1/27
Step-by-step explanation:
you take the fractions and multiply them all together.
1x1x1 equals 1
and 3x3x3 equals 27
meaning the answer is 1/27 :)
To calculate 1/3 x 1/3 x 1/3, you're effectively cubing 1/3, which results in (1/3)^3 or 1^3/3^3, simplifying to 1/27.
Explanation:The student is asking about the multiplication of fractions and exponentiation rules in algebra. To solve 1/3 x 1/3 x 1/3, you multiply the fractions normally. When multiplying identical fractions, we simply raise the fraction to the power of the number of times it is being multiplied by itself. So 1/3 x 1/3 x 1/3 is equivalent to (1/3)^3. When you raise a fraction to an exponent, you raise both the numerator and the denominator to that power. Therefore, (1/3)^3 equals 1^3/3^3, which simplifies to 1/27.
The example given with 3².35 relates to the rules of exponents, which state that when multiplying exponential terms with the same base, you can add the exponents (x^p x x^q = x^(p+q)). For the concept of cubing of exponentials, you would cube the base and multiply the existing exponent by 3 to execute the operation effectively.
There are 3 paper clips and 5 erasers in a paper stack. If 2 items are drawn at random without replacement what is the probability that one draw a paper clip and then an eraser?
Answer:
15/56
Step-by-step explanation:
Total = 8
3/8 × 5/7
15/56
M/PF Research, Inc. lists the average monthly apartment rent in some of the most expensive apartment rental locations in the United States. According to their report, the average cost of renting an apartment in Minneapolis is $951. Suppose that the standard deviation of the cost of renting an apartment in Minneapolis is $96 and that apartment rents in Minneapolis are normally distributed. If a Minneapolis apartment is randomly selected, what is the probability that the price is:
Step-by-step explanation:
a) $1,000 or more?
As the data is usually distributed, using the 3-step approach to solve the problem: draw the image (I'm not going to do it here), locate the z-point, and identify the region on the graph.
(1000-951)/96 = .5104 = 0.51 = Z, so area = 1 -0.6950 = 0.3050
b) Between $900 and $1,100?
(900-951)/96 = -0.53 = Z, and (1100-951)/96 = 1.55 = Z So area = 0.9394 - 0.2981 = 0.6413
c) Between $825 and $925?
(825-951)/96 = -1.31 = Z, and (925-951)/96 = -0.27 = Z So area = 0.3936 - 0.0951 = 0.2985
d) Less than $700?
(700-951)/96 = -2.61 = Z, so area = 0.0045
The percentage increase in apartment supply is 30%, and the price sensitivity or price elasticity of supply is 3.90, indicating a relatively elastic supply to price changes.
Explanation:The question deals with the concept of price elasticity of supply, which measures the responsiveness of the quantity supplied to a change in price. To determine the percentage increase in apartment supply, we calculate the change in quantity supplied, divide it by the original quantity supplied, and then multiply by 100 to convert to a percentage:
The original quantity supplied was 10,000 units, and the new quantity supplied is 13,000 units. So the change in quantity supplied is 13,000 - 10,000 = 3,000 units.
The percentage increase in supply is (3,000 units / 10,000 units) × 100% = 30%
Next, we calculate the price sensitivity, also known as price elasticity of supply, using the formula:
Price Elasticity of Supply (Es) = (% Change in Quantity Supplied) / (% Change in Price)
The price increased from $650 to $700, which is an increase of $700 - $650 = $50. The percentage change in price is ($50 / $650) × 100% = 7.69%
Then the price elasticity of supply is 30% / 7.69% = 3.90, indicating that the supply is relatively elastic.
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The minimum length L of a highway sag curve can be computed by where θ 1 is the downhill grade in degrees (θ 1 < 0°), θ 2 is the uphill grade in degrees (θ 2 > 0°), S is the safe stopping distance for a given speed limit, h is the height of the headlights, and α is the alignment of the headlights in degrees. Compute L for a 55-mph speed limit, where and Round your answer to the nearest foot.
Answer:
The answer to the nearest foot is = 15 feet
Step-by-step explanation:
Solution
The first set taken is to Compute L for a 55-mph speed limit
Given that
L =(θ2 -θ1)/200 (h +S Tan ∝) =
= ( u + 5) 336²/200 (1.9 +336 tan 0.7°)
= 9° (336)²/200 (1.9 +336 tan 0.7°) = 14.7652094
= 15 feet { 9° = 9*π/180 = π/20}
Note: Kindly find an attached image for the complete question given and answered
what is the equation of the horizontal line that passes through ( 2 -2 )
Answer:
y = -2
Step-by-step explanation:
The equation of a horizontal line is ...
y = constant
In order to make it go through a point with a y-coordinate of -2, the value of the constant must be -2.
Your line is y = -2.
( WILL MARK BRAINLIEST IF CORRECT)
Jalil plays hockey. When Jalil takes a shot on goal, the probability that he scores is . If Jalil takes 80 shots on goal in a season, how many times can he expect to score a goal?
Answer:
60
Step-by-step explanation:
1/2 of 80 is 40.1/4 is 20.40 plus 20 equals 60.
Answer:
80x
Step-by-step explanation:
The probability is needed for this, so I put it as x.
If it was .25, he could expect to score 20 times.
If 8(x) is the inverse of f(x) and f(x) = 4x + 12 what is g(x) ?
g(x) = 12x + 4
g(x) = x-12
g(x) = x-3
g(x) - x-3
Answer:
(y-12)/4
Step-by-step explanation:
If g(x) is the inverse of f(x)
and f(x) = 4x + 12
f⁻¹(x) = g(x)
let f(x) be represented as y
f(x) = y
y = 4x + 12
subtract 12 from both sides
y-12= 4x
divide both sides by 4
(y-12)/4 = x
so f ⁻¹ (y)= (y-12)/4 so g(x) = (x-12)/4
Can someone please answer these for me?!
Answer:
base : 9
three points : (1,0), (9,1), (81,2)
domain : x>0
range : all real number
asymptote : x=0
Answer:
x=0
Step-by-step explanation:
I need to write a 5-paragraph eassy, so please help me it is base on an article name "Schools in Maryland Allow Elementary Students to Carry Cellphones, by Amanda Lenhart, The Washington Post" here are some pic. I just need help writing two paragraph. I already have my Introduction, Body Paragraph #1 and my Body paragraph #2 just need my Body paragraph #3 and my Conclusion I will give brainlis and 30 pnt.
Prompt:
Write an argumentative essay answering the questions: Should students be allowed to carry cellphones on campus? You must support your claim with evidence from the text. You may also use relevant examples from your own experience, observations, and other readings.
Directions:
Before you begin, read the text below, which presents information about the advantages and disadvantages of carrying a cell phone at school. Use the Student Writing Checklist on the back of this page to plan and write a multi-paragraph essay that addresses the prompt. Use your own words, except when quoting directly from the text.
PLEASE DONT WAST THEM
The Highway Safety Department wants to study the driving habits of individuals. A sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour. Round to 4 decimal places. 1.Calculate a 90% confidence interval for the true mean speed of all cars on this particular stretch of highway
Answer:
90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].
Step-by-step explanation:
We are given that a sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour.
Firstly, the pivotal quantity for 90% confidence interval for the true mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average speed of cars = 70.7 miles per hour
s = sample standard deviation = 6.3 miles per hour
n = sample of cars = 37
[tex]\mu[/tex] = true mean speed
Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.
So, 90% confidence interval for the true mean, [tex]\mu[/tex] is ;
P(-1.688 < [tex]t_3_6[/tex] < 1.688) = 0.90 {As the critical value of t at 36 degree of
freedom are -1.688 & 1.688 with P = 5%}
P(-1.688 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.688) = 0.90
P( [tex]-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
P( [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90
90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]70.7-1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] , [tex]70.7+1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] ]
= [68.9517 miles per hour , 72.4483 miles per hour]
Therefore, 90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].
The interpretation of the above interval is that we are 90% confident that the true mean speed of all cars will lie between 68.9517 miles per hour and 72.4483 miles per hour.