Isaac is a professional swimmer who trains, in part, by running. She would like to
estimate the average number of miles she runs in each week. For a random sample
of 20 weeks, the mean is
x
= 17.5 miles with standard deviation s = 3.8 miles. Find
a 99% confidence interval for the population mean number of weekly miles Isaac runs.
(a) 15.01 to 19.99 miles (b) 15.07 to 19.93 miles
(c) 15.34 to 19.66 miles (d) 15.31 to 19.69 miles
(e) 15.08 to 19.92 miles

The answer is B..........

Answer:

B. 1

Step-by-step explanation:

If it was more than one it wouldn't be a triangle.

Answer:

b) -2/5

Step-by-step explanation:

b is -2/5 because its negative and goes down at a rate of 0.4 or 2/5

a , ummmm IDK that, sorry

Brainliest, crown to me

Answer:

14

Step-by-step explanation:

Answer:

Which of these factors will affect the friction on a road

Step-by-step explanation:

Answer:

6.68% probability that the mean weight is below 68.5g.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]

Probability that the mean weight is below 68.5g:

This is 1 subtracted by the pvalue of Z when X = 68.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{68.5 - 70}{1}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

6.68% probability that the mean weight is below 68.5g.

Answer:

P(x ∠ 68.5) = 0.07

Step-by-step explanation:

Got it right on khan.

Before Andrei adds the marbles to the glass tank, the glass tank was empty. This means that the volume of the empty tank is when n = 0 and the volume is 32 liters.

Given that:

[tex]W = 32 - 0.05n[/tex]

A linear function is represented as:

[tex]y = b + mx[/tex]

Where

[tex]b \to[/tex] y intercept

Literally, the y intercept is the initial value of the function.

In this function, the y intercept means the initial volume of the glass tank before filling it with marbles.

Compare [tex]y = b + mx[/tex] and [tex]W = 32 - 0.05n[/tex]

[tex]b = 32[/tex]

This means that the volume of the glass tank is 32 liters.

Read more about linear functions at:

https://brainly.com/question/21107621

Answer:

0.05

Step-by-step explanation:

Answer:

if the 5 numbers are different, the maximum difference is 64

Step-by-step explanation:

We have 5 positive (different) integers, a, b, c, d and e (suppose that are ordered from least to largest, so a is the smallest and b is the largest.

The mean will be:

M = (a + b + c + d + e)/5 = 15.

Now, if we want to find the largest difference between a and e, then we must first select the first 4 numbers as the smallest numbers possible, this is:

a = 1, b = 2, c = 3 and d = 4

M = (1 + 2 + 3 + 4 + d)/5 = 15

M = (10 + d)/5 = 15

10 + d = 15*5 = 75

d = 75 - 10 = 65

then the difference between a and d is = 65 - 1 = 64.

Now, if we take any of the first 4 numbers a little bit bigger, then we will see that the value of d must be smaller, and the difference between d and a will be smaller.

Answer:

For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]

Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:

[tex] z_{\alpha/2}= \pm 1.62015[/tex]

And we can use the following excel code for example:

"=NORM.INV(0.0526,0,1)"

Step-by-step explanation:

For this case we know that the confidence level is 89.48% or 0.8948 and the significance would be: [tex] \alpha=1-0.8948 = 0.1052[/tex] and the value of [tex]\alpha/2 =0.0526[/tex]

Now we need to find a quantile in the normal standard distribution who accumulate 0.0526 of the area on each tail of the normal standard distribution and we got:

[tex] z_{\alpha/2}= \pm 1.62015[/tex]

And we can use the following excel code for example:

"=NORM.INV(0.0526,0,1)"

Answer:

C.

Step-by-step explanation:

1/2r = 2π/Cb

Answer: -6m-n+3

Step-by-step explanation:

The answer is -6m-n+3 because -3

times 2m is -6m and -n stays the same its outside of the parenthesis

and lastly -3 times -1 is positive 3

so answer maches up with the last one

the answer is -6m-n+3

Hope this helps :)

Answer:

-6m-n+3

Step-by-step explanation:

-3 x 2 is -6m (n stays same)

-3 x -1 is whole or positive 3

put it together and u get -6m-n+3

hope this helps

Answer:

x = -8 or x = 3

Step-by-step explanation:

To factor ax² + bx + c, use AC method.

a times c is 1 × -24 = -24.

Factors of ac (-24) that add up to b (5) are 8 and -3.

Divide by a and reduce: 8/1 and -3/1.

Therefore, the factors are x + 8 and x − 3.

x² + 5x − 24 = 0

(x + 8) (x − 3) = 0

x = -8 or 3

Answer:

a) 5/9

b) 1/3

Step-by-step explanation:

a) P(Die A or Die B) = P(red and red with Die A) + P(red and red with Die B)

                               = 4/6 × 4/6 +  2/6×2/6

                               = 5/9

b)  P(Die A or Die B) = P(red and red and red with Die A) + P(red and red and red with die B)

                           = 4/6×4/6×4/6 + 2/6×2/6×2/6

                          = 1/3

Step-by-step explanation:

45.50

Converting decimal

45.50 x 100 = 4550

Answer:

Step-by-step explanation:

Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.

Thus , the parameter of the exponential distribution is calculated as,

μ = 6

[tex]\frac{1}{\lambda} =6[/tex]

[tex]\lambda = \frac{1}{6}[/tex]

a) The required probability is

[tex]P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}[/tex]

= 0.513

Hence, the probability that a randomly selected car battery will last more than four years is 0.513

b) The variance of the battery span is calculated as

[tex]\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36[/tex]

The 95% percentile [tex]x_{a=0.05}[/tex] (α = 5%) of the battery span is calculated

[tex]x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years[/tex]

c)  

Let [tex]X_r[/tex] denote the remaining life time of a car battery

i)the probability the battery will last an additional five years is calculated below

[tex]P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346[/tex]

ii) The average time that the battery is expected to last is calculated

[tex]E(X_r)=\frac{1}{\lambda} \\\\=6[/tex]

Answer:

15 baskets

Step-by-step explanation:

Answer:

a) Level of significance α=0.05

Two-tailed test, with null and alternative hypothesis:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

b) Student's t distribution. We assume equal variances for both populations, independent sampled values and populations normally distributed.

Test statistic t=-2.4

c) P-value = 0.018

d) Rejection of the null hypothesis.

The data is statistically significant.

e) There is evidence to conclude there is significant difference in average off-schedule times between the bus lines. The difference we see in the samples seems not due to pure chance.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that there is a significant difference in average off-schedule times for this bus lines.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

The significance level is 0.05.

The sample 1 (bus line A), of size n1=51 has a mean of 53 and a standard deviation of 17.

The sample 2 (bus line B), of size n2=60 has a mean of 60 and a standard deviation of 13.

The difference between sample means is Md=-7.

[tex]M_d=M_1-M_2=53-60=-7[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{17^2}{51}+\dfrac{13^2}{60}}\\\\\\s_{M_d}=\sqrt{5.667+2.817}=\sqrt{8.483}=2.913[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-7-0}{2.913}=\dfrac{-7}{2.913}=-2.4[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-1=51+60-2=109[/tex]

This test is a two-tailed test, with 109 degrees of freedom and t=-2.4, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t<-2.4)=0.018[/tex]

As the P-value (0.018) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant difference in average off-schedule times for this bus lines.

Answer: No.

Step-by-step explanation:

I guess that here we have the statement:

If the sum of two numbers is odd----> can their quotient be an odd number?

first, for n an integer number, we have that:

an odd number can be written as 2n + 1

an even number can be written as 2n.

The sum of two numbers is only odd if one of them is odd and the other even.

Then we have a number that is 2n and other that is 2k + 1, for n and k integer numbers.

Now, let's see if the quotient can also be an odd number.

One way to think this is:

There is an odd number such that when we multiply it by another odd number, the result is an even number?

no, and i can prove it as:

let 2k + 1 be an odd number, and 2j + 1 other.

the product is:

(2k + 1)*(2j + 1) = 2*(2*k*j + k + j) + 1

and as k and j are integers, also does 2*k*j + k + j, so:

2*(2*k*j + k + j) + 1 is an odd number.

This says that the product of two odd numbers is always odd, then we never can have that the quotient between an even number and an odd number is odd.

Answer:

x^3-6x^2-4x-8

Step-by-step explanation:

First you would multiply (x-2) by itself (x-2) to get

x^2-2x-2x+4

then you would combine like terms

x^2-4x+4

Then you would multiply that by x-2

(x^2-4x+4)(x-2)

x^3-2x^2-4x^2-8x+4x-8

then you combine like terms

x^3-6x^2-4x-8

Answer:

8 hours

Step-by-step explanation:

Solve with a proportion

[tex]\frac{12}{5}[/tex] = [tex]\frac{19.20}{x}[/tex]

Multiply 5 by 1.6 to get x

5 x 1.6 = 8

Answer:

B. Average of the data set

Step-by-step explanation:

The mean is defined as the average of a data set and it's formula is

Mean = [tex]\frac{sum of observations}{number of observations}[/tex]

Answer:

P = 0.5207

Step-by-step explanation:

First, we have three options: Just the first card is a diamond or an ace, Just the second card is a diamond or an ace and both cards are diamonds or aces.

Additionally, there are 16 cards that are diamond or aces in a standard deck of 52 cards (13 diamonds and 3 aces that are not diamonds). It means that there are 36 cards that are not diamond or aces (52 - 16 = 36).

So, the probability that just the first card is a diamond or an ace is calculated as:

[tex]P_1=\frac{16}{52}*\frac{36}{52}=0.2130[/tex]

At the same way, the probability that just the second card is a diamond or an ace is:

[tex]P_2=\frac{36}{52}*\frac{16}{52}=0.2130[/tex]

Finally, the probability that both cards are diamonds or aces is:

[tex]P_3=\frac{16}{52}*\frac{16}{52}=0.0947[/tex]

Therefore, the probability that at least one of the cards is a diamond or an ace is:

[tex]P=P_1+P_2+P_3\\P=0.2130+0.2130+0.0947\\P=0.5207[/tex]

Answer:

She can answer, after performing the hypothesis test, that there is not enough evidence to support the claim that the city firefighters salary is significantly lower than the national average.

Step-by-step explanation:

She can statistically test the claim of the firefighters to see if it has statistical evidence.

This is a hypothesis test for the population mean.

The claim is that the city firefighters salary is significantly lower than the national average.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=38202\\\\H_a:\mu< 38202[/tex]

The significance level is 0.1.  Is less conservative than 0.05, for example, so if there is little evidence, the null hypothesis with be rejected.

The sample has a size n=27.

The sample mean is M=38073.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=575.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{575}{\sqrt{27}}=110.659[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{38073-38202}{110.659}=\dfrac{-129}{110.659}=-1.17[/tex]

The degrees of freedom for this sample size are:

df=n-1=27-1=26

This test is a left-tailed test, with 26 degrees of freedom and t=-1.17, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.17)=0.127[/tex]

As the P-value (0.127) is bigger than the significance level (0.1), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the city firefighters salary is significantly lower than the national average.

Answer:

Step-by-step explanation:

0.00039 hm

Answer:

0.00039 hm is ur answer....

3.9 cm to 0.00039 hm...

Mark me as Brainlist...

Answer:

I think it is 288.6 ft. Lol hope this helps

Step-by-step explanation:

The image of the ramp with dimensions is missing, so i have attached it.

Answer:

680 in² of wood is needed.

Step-by-step explanation:

The way to find how much wood would be needed by devon would be to find the total surface area of the ramp.

From the attached image,

Let's find the area of the 2 triangles first;

A1 = 2(½bh) = bh = 15 x 8 = 120 in²

Area of the slant rectangular portion;

A2 = 17 x 14 = 238 in²

Area of the base;

A3 = 15 × 14 = 210 in²

Area of vertical rectangle;

A4 = 8 × 14 = 112 in²

Total Surface Area = A1 + A2 + A3 + A4 = 120 + 238 + 210 + 112 = 680 in²

Answer:

A. The causal connection is valid. Students who spend more time and effort studying will be able to memorize more​ information, so their test grades will be higher.

Step-by-step Explanation:

The causal connection between the test grades of students and the amount of time and effort spent the students spend in studying and preparing for the test appears to be valid. This is valid because students who spend more time and effort studying would most likely be able to memorize more information of which they are most likely to come by in the test they take. Invariably, they'd be able to easily recall what they've memorize and give the right answers to the questions they are asked in the test, and this definitely will earn them higher test grades.

Answer:

16

Step-by-step explanation:

There are three possible equations: the first is used for inputs (x-values) in between negative infinity and -7, the second for inputs in between -7 and 2, and the third for inputs in between 2 and infinity. 7 is in between 2 and infinity so the third equation is applicable.

[tex]g(x)=(x+1)(x-5)[/tex]

[tex]g(7)=(7+1)(7-5)[/tex] Plug in the values

[tex]g(7)=(8)(2)[/tex] Simplify

[tex]g(7)=16[/tex]

The image of the stem-and-leaf plots is in the attachment.

Answer: (a) 31 years; (b) 59 years; (c) 56 years

Step-by-step explanation: Steam and leaf is a table that shows the digits of the data value split into a "stem", which represents the first digit, and a "leaf", which is the last digit.

For example, the first row of the table in the attachment, indicate a "stem" 2 and the first number of a "leaf" is 1, so the actress has 21 years.

(a) According to the table, the youngest actor to win an Oscar has a "stem" 3 and the first "leaf" from the right is 1, so the actor has 31 years.

(b) The oldest actress is 80 and the youngest is 21, so difference is:

80 - 21 = 59

The difference is 59 years.

(c) The oldest age shared by 2 actors is 56 years.

Answer: The new price of  the car is $41856

Step-by-step explanation:

So we know the the original price as 43,600 which is 100% and is being dropped by 4%  so you would have to subtract 4% from a 100% and multiply it by the original price.

100% - 4% = 96%

Now 96% of the original price is the new price.

96% * 43,600= ?

0.96 * 43,600 = 41856

easy claps!!

Answer: 30=2x+4 and there are 17 girls in the class.

Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.

It's BASIC prealgebra so you should probably practice bit more with linear equations!

Answer:

The expected value of the random variable with the given probability distribution = 12 .52

Step-by-step explanation:

Given data

 x    :   0         1            5       10     1000

p(x)  :  0.33  0.32   0.24     0.10    0.01

The expected value of the given random variable of given probability distribution

E(X)  =  ∑ x p ( X = x)

E(X)  =  0 × 0.33 + 1 × 0.32 + 5 × 0.24 + 10× 0.10 + 1000×0.01

E (X)  =  12.52