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

[tex]\displaystyle\bf\\AB=\sqrt{\Big(-6-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AB=\sqrt{\Big(-6+2\Big)^2+\Big(4+7\Big)^2}\\\\AB=\sqrt{\Big(-4\Big)^2+\Big(11\Big)^2}\\\\AB=\sqrt{16+121}\\\\\boxed{\bf AB=\sqrt{137}}[/tex]

.

[tex]\displaystyle\bf\\BC=\sqrt{\Big(-2-(-6)\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(-2+6\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(4\Big)^2+\Big(3\Big)^2}\\\\BC=\sqrt{16+9}\\\\BC=\sqrt{25}\\\\\boxed{\bf BC=5}[/tex]

.

[tex]\displaystyle\bf\\CD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(2+2\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(4\Big)^2+\Big(-3\Big)^2}\\\\CD=\sqrt{16+9}\\\\CD=\sqrt{25}\\\\\boxed{\bf CD=5}[/tex]

.

[tex]\displaystyle\bf\\AD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AD=\sqrt{\Big(2+2\Big)^2+\Big(4+7\Big)^2}\\\\AD=\sqrt{\Big(4\Big)^2+\Big(11\Big)^2}\\\\AD=\sqrt{16+121}\\\\\boxed{\bf AD=\sqrt{137}}[/tex]

.

[tex]\displaystyle\bf\\P=AB+BC+CD+AD=\sqrt{137}+5+5+\sqrt{137}\\\\\boxed{\bf P=10+2\sqrt{137}}[/tex]

The length of the side d would be 77/18.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or

[tex]\dfrac{a}{b}[/tex]

If triangles DEF and NPQ are similar, then

7/9 = d/ (11/2)

By cross multiply

9d = 7 x 11/2

d = 77/2 ÷ 9

d = 77/18

Thus, The length of the side d would be 77/18.

Learn more about ratios here:

brainly.com/question/186659

#SPJ2

Answer:

d. 10th  e. 26th

Step-by-step explanation:

22-12=10

12+14=26

Answer:

a) P(6) = 0.0097

b) P(More than 3) = 0.1611

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not. Questions are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A student takes a multiple-choice test that has 11 questions.

This means that [tex]n = 11[/tex]

Each question has five choices.

This means that [tex]p = \frac{1}{5} = 0.2[/tex]

(a) Find P (6)

This is P(X = 6).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{11,6}.(0.2)^{6}.(0.8)^{5} = 0.0097[/tex]

P(6) = 0.0097

(b) Find P (More than 3).

Either P is 3 or less, or it is more than three. The sum of the probabilities of these outcomes is 1. So

[tex]P(X \leq 3) + P(X > 3) = 1[/tex]

We want P(X > 3). So

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{11,0}.(0.2)^{0}.(0.8)^{11} = 0.0859[/tex]

[tex]P(X = 1) = C_{11,1}.(0.2)^{1}.(0.8)^{10} = 0.2362[/tex]

[tex]P(X = 2) = C_{11,2}.(0.2)^{2}.(0.8)^{9} = 0.2953[/tex]

[tex]P(X = 3) = C_{11,3}.(0.2)^{3}.(0.8)^{8} = 0.2215[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0859 + 0.2362 + 0.2953 + 0.2215 = 0.8389[/tex]

Then

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8389 = 0.1611[/tex]

P(More than 3) = 0.1611

Answer: 0.401294

Step-by-step explanation:

z=x-μ/σ

z=20-22/8

z=-0.25

the probability for this z-score is 0.401294.

Answer:

c. results in either of two directions can lead to rejection of the null hypothesis.

Step-by-step explanation:

A two tailed test is performed when we want to test if there is statistically significant difference from the null state. That means that if the statistic value is significantly higher or significantly lower, we will reject the null hypothesis. Both tails have rejection areas.

Answer:

Step-by-step explanation:

There's no plot, but I can give you this: Median is better with a large outlier, while mean is better for symmetry. Therefore, the correct answer would be either the first or fourth. Ofc, we can't see the plot so that's all I can give you.

Hope that helped,

-sirswagger21

Answer:

676

Step-by-step explanation:

lxw

14x35

4x24

6x15

676

Answer:

B.   1 over 8

Step-by-step explanation:

To determine the probability of the spinner landing on 5, we need to first know what probability is,

probability = required outcome/all possible outcome

since the spinner is divided into 8 equal sections and each section contains number from 1-8, this implies there are total of 64 numbers on the spinner.  This implies that all possible outcome = 64

In each section there is 5, since there are 8 sections on the spinner, the number of 5's on the spinner are 8.

This implies that the required outcome = 8

but

probability = required outcome/all possible outcome

probability (of the spinner landing on 5) = 8/64    =1/8

Answer:

b

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

In the attached file

Answer:

24

Step-by-step explanation:

That would be:

(3/8)(30)

---------------

(15/16)(1/2)

This can be reduced in various ways.  First, divide that 30 by 15, obtaining:

   6/8

-----------

   1/32

Now invert the divisor (1/32) and multiply:

(6/8)(32/1)

This reduces to 6*4, or 24.

Answer:

ln 4

Step-by-step explanation:

plus(+) will become times and minus(-)will become divide. Combine all together as all are in terms of ln

ln (2x8)/4

=ln 4

Answer: In 4

Step-by-step explanation: edge 2021

Answer:

y=-3x-2

Step-by-step explanation:

There is enough information to make a point-slope form equation that which we can convert into slope-intercept form.

Point-slope form is: [tex]y-y_1=m(x-x_1)[/tex]

We are given the slope of -3 and the point of (1,-5).

[tex]y-y_1=m(x-x_1)\rightarrow y+5=-3(x-1)[/tex]

Convert into Slope-Intercept Form:

[tex]y+5=-3(x-1)\\y+5-5=-3(x-1)-5\\\boxed{y=-3x-2}[/tex]

Answer:

[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]  

Now we can claculate the p value with this formula:

[tex]p_v =P(z<-1.42)=0.0778[/tex]  

If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.

Step-by-step explanation:

Information to given

n=735 represent the random sample taken

X=203 represent the number of people who have their prostate regularly examined

[tex]\hat p=\frac{203}{735}=0.276[/tex] estimated proportion of people who have their prostate regularly examined  

[tex]p_o=0.3[/tex] is the value to verify

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true proportion is less than 0.3, the ystem of hypothesis are.:  

Null hypothesis:[tex]p \geq 0.3[/tex]  

Alternative hypothesis:[tex]p < 0.3[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]  

Now we can claculate the p value with this formula:

[tex]p_v =P(z<-1.42)=0.0778[/tex]  

If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.

Step-by-step explanation:

Total gum balls = 22 + 18 + 10 + 23 = 73

Probability of red gum = 22/73

Answer:144 sweets

Step-by-step explanation:

Answer:

21-25 = 4

26-30 = 3

Step-by-step explanation:

16-20 (4)= 17 17 17 18

21-25 (4)= 21 22 24 25

26-30 (3)= 26 27

30

31-35 (3)= 32 35 35

36-40 (5)= 36 37 37 38 39

41-45 (2)= 41 42

Answer:

3/11 divided by 3/11 is 1

9/10 divided by 3/5 is 1 1/2 (1.5)

Step-by-step explanation:

Answer:

1

1.5

Step-by-step explanation:

3/11 ÷ 3/11 = 1

9/10 ÷ 3/5 = 3/2 ≈ 1.5

Answer:

1. Diverges

2. Converges

3. Diverges

Step-by-step explanation:

Solution:-

Limit comparison test:

- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ). Then the following three conditions are applicable for the limit:

                          Lim ( n-> ∞ )   [tex][ \frac{a_n}{b_n} ][/tex]  = c

Where,

1) If c is finite: 0 < c < 1, then both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] either converges or diverges.

2) If c = 0, then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges.

3) If c = ∞ or undefined, then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges.

a) The given series ∑[tex]a_n[/tex] is:

                   (n = 1) ∑^∞  [tex][ \frac{n^2+1}{2n^3-1} ][/tex]

- We will make an educated guess on the comparative series  ∑[tex]b_n[/tex] by the following procedure.

                  (n = 1) ∑^∞   [tex][ \frac{n^2( 1 + \frac{1}{n^2} )}{n^3 ( 2 - \frac{1}{n^2} ) } ] = [ \frac{( 1 + \frac{1}{n^2} )}{n( 2 - \frac{1}{n^2} ) } ][/tex]

- Apply the limit ( n - > ∞ ):

                 (n = 1) ∑^∞  [tex][ \frac{1}{2n}][/tex]    .... The comparative series ( ∑[tex]b_n[/tex] )

- Both series  ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.

- Compute the limit:

                 Lim ( n-> ∞ )  [tex][ \frac{n^2 + 1}{2n^3 - 1} * 2n ] = [ \frac{2n^3 + 2n}{2n^3 - 1} ][/tex]

                 Lim ( n-> ∞ )    [tex][ \frac{2n^3 ( 1 + \frac{1}{n^2} ) }{2n^3 ( 1 - \frac{1}{2n^3} ) } ] = [ \frac{ 1 + \frac{1}{n^2} }{ 1 - \frac{1}{2n^3} } ][/tex]

- Apply the limit ( n - > ∞ ):

                Lim ( n-> ∞ )  [tex][ \frac{a_n}{b_n} ][/tex]  = [tex][ \frac{1 + 0}{1 + 0} ][/tex] = 1   ... Finite

- So from first condition both series either converge or diverge.

- We check for ∑[tex]b_n[/tex] convergence or divergence.

- The ∑[tex]b_n[/tex] = ( 1 / 2n ) resembles harmonic series ∑ ( 1 / n ) which diverges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 1 ≤ 1. Hence, ∑

- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also diverges.

Answer: Diverges    

b)          

The given series ∑[tex]a_n[/tex] is:

                   (n = 1) ∑^∞  [tex][ \frac{n}{n^\frac{5}{2} +5} ][/tex]

- We will make an educated guess on the comparative series  ∑[tex]b_n[/tex] by the following procedure.

                  (n = 1) ∑^∞   [tex][ \frac{n( 1 )}{n ( n^\frac{3}{2} + \frac{5}{n} ) } ] = [\frac{1}{( n^\frac{3}{2} + \frac{5}{n} )} ][/tex]

- Apply the limit ( n - > ∞ ) in the denominator for  ( 5 / n ), only the dominant term n^(3/2) is left:

                  (n = 1) ∑^∞    [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )

- Both series  ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.

- Compute the limit:

                 Lim ( n-> ∞ )   [tex][ \frac{n}{n^\frac{5}{2} +5} * n^\frac{3}{2} ] = [ \frac{n^\frac{5}{2}}{n^\frac{5}{2} +5} ][/tex]

                 Lim ( n-> ∞ )    [tex][ \frac{n^\frac{5}{2}}{n^\frac{5}{2} ( 1 + \frac{5}{n^\frac{5}{2}}) } ] = [ \frac{1}{1 + \frac{5}{n^\frac{5}{2}} } ][/tex]

- Apply the limit ( n - > ∞ ):

                Lim ( n-> ∞ )  [tex][ \frac{a_n}{b_n} ][/tex]  = [tex][\frac{1}{1 + 0}][/tex] = 1   ... Finite

- So from first condition both series either converge or diverge.

- We check for ∑[tex]b_n[/tex] convergence or divergence.

- The ∑[tex]b_n[/tex] = ( [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] ) converges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 3/2 > 1. Hence, ∑

- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also converges.

Answer: converges

Comparison Test:-  

- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ).

-Then the following conditions are applied:

1 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) < 0 , then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges

2 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≤ 0 , then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges

c) The given series ∑[tex]a_n[/tex] is:

                   (n = 1) ∑^∞ [tex][ \frac{4 + 3^2}{2^n} ][/tex]

- We will make an educated guess on the comparative series  ∑[tex]b_n[/tex] by the following procedure.

                  (n = 1) ∑^∞ [tex][ \frac{3^n ( \frac{4}{3^n} + 1 )}{2^n} ][/tex]

- Apply the limit ( n - > ∞ ) in the numerator for  ( 4 / 3^n ), only the dominant terms ( 3^n ) and ( 2^n ) are left:  

                 (n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex]   ... The comparative series ( ∑[tex]b_n[/tex] )

- Compute the difference between sequences ( [tex]a_n[/tex] - [tex]b_n[/tex] ):

                 [tex]a_n - b_n = \frac{4 + 3^n}{2^n} - [ \frac{3^n}{2^n} ] \\\\a_n - b_n = \frac{4 }{2^n} \geq 0[/tex], for all values of ( n )

- Check for divergence of the comparative series ( ∑[tex]b_n[/tex] ), using divergence test:

               ∑[tex]b_n[/tex] = (n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex]  diverges

- The first condition is applied when  ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≥ 0, then ∑diverges only if ∑[tex]b_n[/tex] diverges.

Answer: Diverges

Answer:

d = 48 h

Step-by-step explanation:

Lamar's distance traveled is directly proportional to the number of hours be drove.

So distance (d) ∝ hours (h)

Lamar traveled 288 miles in 6 hours

Since d ∝ h

then d = kh    [ where k is the proportionality constant ]

if     288 = k × 6

k =  =288/48

Therefore, equation will be d = 48 h will be the equation

Answer:

One plane has a speed of 450 km/h and the other has a speed of 900 km/h.

Step-by-step explanation:

I am going to say that:

The speed of the first plane is x.

The speed of the second plane is y.

One plane is flying at twice the speed of the other.

I will say that y = 2x. We could also say that x = 2y.

Two airplanes leave an airport at the same time, flying in the same direction

They fly in the same direction, so their relative speed(difference) at the end of each hour is y - x = 2x - x = x.

If after 4 hours they are 1800 km apart, find the speed of each plane

After 1 hour, they will be x km apart. After 4, 1800. So

1 hour - x km apart

4 hours - 1800 km apart

4x = 1800

x = 1800/4

x = 450

2x = 2*450 = 900

One plane has a speed of 450 km/h and the other has a speed of 900 km/h.

Answer:

  Exponential; $376.32

Step-by-step explanation:

Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.

The same would be true for the second month, so the overall multiplier for the two months is ...

  (1.12)(1.12) = 1.12^2 = 1.2544

This makes the food bill for the second month amount to ...

  1.2544 × $300 = $376.32

_____

As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.

If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.

Answer:

Height of the Dom is 112.18 m.

Step-by-step explanation:

The tallest church tower in the Netherlands is the Dom Tower in Utrecht. The angle of elevation to the top of the tower is 77° when 25.9 m from the base. It is required to find the height of the Dom Tower. Let its height is h. So, using trigonometric formula to find it as :

[tex]\tan\theta=\dfrac{h}{b}\\\\\tan(77)=\dfrac{h}{25.9}\\\\h=\tan(77)\times 25.9\\\\h=112.18\ m[/tex]

So, the height of the Dom is 112.18 m.

Answer:

14

Step-by-step explanation:

Answer:

Which of these factors will affect the friction on a road

Step-by-step explanation:

Answer:

1.54

Margin of error M.E = 1.54

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-M.E

Where M.E = margin of error

M.E = zr/√n

Given that

Standard deviation r = 1.93

Number of samples n = 6

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

M.E = (1.96×1.93/√6) = 1.544321633166

M.E = 1.54 (to 2 decimal place)

Margin of error M.E = 1.54

Answer:

y= 1/5x + 12/5

Step-by-step explanation:

Parallel line to this has same slope and passes through the point (-2, 2)

The required equation in slope- intercept form is:

Answer:

4 can be divided by 1 and 2

6 can be divided by 1 and 2

12 is wrong because it can be divided by 1,2, and 4 so it has 6 factors instead of 4

Step-by-step explanation:

Answer:

g(X)=3(2^x)

Step-by-step explanation: