1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
user100 [1]
3 years ago
11

You run at a steady rate of 7 minutes per mile in a cross country race. You finish after 21 minutes in fourth place. How long is

the race
Mathematics
1 answer:
Genrish500 [490]3 years ago
3 0
The race is 3 miles.
21 minutes divided by 7mph (miles per hour)= 3 miles
You might be interested in
Reliance on solid biomass fuel for cooking and heating exposes many children from developing countries to high levels of indoor
castortr0y [4]

Answer:

A) 95% confidence interval for the population mean PEF for children in biomass households = (3.214, 3.386)

95% confidence interval for the population mean PEF for children in LPG households

= (4.125, 4.375)

Simultaneous confidence interval for both = (3.214, 4.375)

B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.

C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.375)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Step-by-step explanation:

A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.

Finding the critical value from the z-tables,

Significance level for 95% confidence interval

= (100% - 95%)/2 = 2.5% = 0.025

z (0.025) = 1.960 (from the z-tables)

For the children in the biomass households

Sample mean = 3.30

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.20

N = sample size = 755

σₓ = (1.20/√755) = 0.0436724715 = 0.04367

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 3.30 ± (1.960 × 0.04367)

CI = 3.30 ± 0.085598

95% CI = (3.214402, 3.385598)

95% Confidence interval = (3.214, 3.386)

For the children in the LPG households

Sample mean = 4.25

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation of the sample = 1.75

N = sample size = 750

σₓ = (1.75/√750) = 0.063900965 = 0.063901

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 4.25 ± (1.960 × 0.063901)

CI = 4.25 ± 0.125246

95% CI = (4.12475404, 4.37524596)

95% Confidence interval = (4.125, 4.375)

Simultaneous confidence interval for both = (3.214, 4.375)

B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.

The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.

Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂

The null hypothesis is

H₀: μ ≥ 0 or μ₁ ≥ μ₂

The alternative hypothesis is

Hₐ: μ < 0 or μ₁ < μ₂

Test statistic for 2 sample mean data is given as

Test statistic = (μ₂ - μ₁)/σ

σ = √[(s₂²/n₂) + (s₁²/n₁)]

μ₁ = 3.30

n₁ = 755

s₁ = 1.20

μ₂ = 4.25

n₂ = 750

s₂ = 1.75

σ = √[(1.20²/755) + (1.75²/750)] = 0.07740

z = (3.30 - 4.25) ÷ 0.07740 = -12.27

checking the tables for the p-value of this z-statistic

Significance level = 0.01

The hypothesis test uses a one-tailed condition because we're testing in only one direction.

p-value (for z = -12.27, at 0.01 significance level, with a one tailed condition) = < 0.000000001

The interpretation of p-values is that

When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.

Significance level = 0.01

p-value = 0.000000001

0.000000001 < 0.01

Hence,

p-value < significance level

This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.

C) For FEY for biomass households,

Sample mean = 2.3 L/s

Standard error of the mean = σₓ = (σ/√N)

σ = standard deviation = 0.5

N = sample size = 755

σₓ = (0.5/√755) = 0.0182

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 2.30 ± (1.960 × 0.0182)

CI = 2.30 ± 0.03567

95% CI = (2.264, 2.336)

Simultaneous confidence interval for both = (2.264, 4.375)

This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).

Hope this Helps!!!

6 0
2 years ago
An insurance company sells automobile liability and collision insurance. Let X denote the percentage of liability policies that
qaws [65]

Answer:

-764.28

Step-by-step explanation:

Given the joint cumulative distribution of X and Y as

F(x,y) = \frac{xy(x+y)}{2000000}\ \ \ \, \ 0\leq x100, 0\leq y\leq 100

#First find F_x and probability distribution function ,f_x(x):

F_x(x)=F(x,100)\\\\\\=\frac{100x(x+100)}{2000000}\\\\\\\\=\frac{100x^2+10000x}{2000000}\\\\\\=>f_x(x)=\frac{x}{10000}+\frac{1}{200}

#Have determined the probability distribution unction ,f_x(x), we calculate the Expectation of the random variable X:

E(X)=\int\limits^{100}_0 \frac{x^2}{10000}+\frac{x}{200}  dx \\\\\\\\=|\frac{x^3}{30000}+\frac{x^2}{400}|\limits^{100}_0\\\\=58.33\\\\

#We then calculate E(X^2):

E(X^2)=\int\limits^{100}_0 \frac{x^3}{10000}+\frac{x^2}{200}\ dx\\\\=\frac{x^4}{40000}+\frac{x^3}{600}|\limits^{100}_0=4166.67\\\\Var(X)=E(X^2)-(E(X))^2=4166.67-58.33^2\\\\Var(X)=764.28

Hence, the Var(X) is 764.28  

4 0
3 years ago
-1/2(10x + 2) - 7 = -x - 4
xxTIMURxx [149]
The answer would be -1. ☺️
7 0
3 years ago
Read 2 more answers
Which of the following statements is NOT equivalent to the statement, 'There exists either a
irina [24]
Computer Scientist lol I need 20 characters
8 0
3 years ago
I need to know the quotient of this problem heeellllllppppp!!!!
olga nikolaevna [1]
The only way to do this is by long division of polynomials.  That's because the quadratic doesn't factor with real numbers and you can't cancel out from numerator to denominator.  Set up your problem with the x-squared term inside the division box and the x + 6 outside.  It's quite impossible to demonstrate long division in this forum, so your answer is going to be x-7 R3.  I do suggest you learn this, though, as it is very important as you advance in your math classes in school.
8 0
3 years ago
Other questions:
  • Please help me thank you
    5·2 answers
  • Jake, Andy, and Damon caught 78 pounds of large mouth bass. Jake caught 22 pounds. Andy caught at least 30 pounds, but no greate
    6·1 answer
  • Which congruency statement is it ?
    6·1 answer
  • 5. One Saturday, you want to put in 3 volunteer hours at the food bank. You need to be the for dinner
    6·1 answer
  • Solve for x <br> 6(x-1) =9(x+2)
    9·1 answer
  • Here is the region of integration of the integral Integral from negative 6 to 6 Integral from x squared to 36 Integral from 0 to
    6·1 answer
  • NEED ANSWER ASAP <br> MARKING BRAINLIEST
    11·1 answer
  • I need help with this question, i am having troubling solving it.
    10·1 answer
  • There are cars, trucks, and motorcycles in our company parking lot. The ratio of cars to trucks to motorcycles is $4:3:2.$ If th
    12·1 answer
  • For each graph below, state whether it represents a function.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!