Suppose a geyser has a mean time between irruption’s of 75 minutes. If the interval of time between the eruption is normally distributed with a standard deviation 20 minutes, answer the following questions. (A) What is the probability that a randomly selected Time interval between irruption’s is longer than 84 minutes? (B) what is the probability that a random sample of 13 time intervals between irruption‘s has a mean longer than 84 minutes? (C) what is the probability that a random sample of 20 time intervals between irruption‘s has a mean longer than 84 minutes? (D) what effect does increasing the sample size have on the probability? Provide an exclamation for this result. Choose the correct answer below. (E) what might you conclude if a random sample of 20 time intervals between irruption‘s has a mean longer than 84 minutes? Choose the best answer below. I’m not entirely certain about my answer for a bit I am completely and utterly lost on the other questions... please help.

Answer:

[29 over 2 divided by 5 over 4] = 29/2 ÷ 5/4 (A)

[29 over 2 times 4 over 5] = 29/2 × 4/5 (C)

Step-by-step explanation:

The total amount of water a tank can hold is 14 and one and one-half gallons = 14½

We are to determine the number of 1/4 gallon buckets of water that can be used to fill the tank.

To find this, we would divide 14½ by 1¼ = 14½ ÷ 1¼

Convert 14½ and 1¼ to improper fraction

14½ = [(14×2)+1]/2 = 29/2

1¼ = [(1×4)+1]/4 = 5/4

14½ ÷ 1¼ =29/2 ÷ 5/4

Then we find the inverse of ¼ to convert the division to multiplication

= 29/2 × 4/5 = 116/10

= 11.6

14½ ÷ ¼ = 11.6

Therefore 11.6 gallons of ¼ buckets of water can be used to fill the tank.

But the two expressions that could be used to represent this scenario to get the answer from the options = 29/2 ÷ 5/4 (A)

[29 over 2 divided by 5 over 4]

29/2 × 4/5 (C)

[29 over 2 times 4 over 5]

Answer:

I believe it is A and C.

Answer:

P-value = 0.0367

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the percentage of residents who favor construction is significantly over 42%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.42\\\\H_a:\pi>0.42[/tex]

The sample has a size n=900.

The sample proportion is p=0.45.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.42*0.58}{900}}\\\\\\ \sigma_p=\sqrt{0.000271}=0.016[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.45-0.42-0.5/900}{0.016}=\dfrac{0.029}{0.016}=1.79[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>1.79)=0.0367[/tex]

Answer:

53/28

Step-by-step explanation:

100 g jam

Blackberry / sugar= 53/28

Answer:

Solution,

Amount of sugar=100-(19+53)

=100-72

=28 gram

Ratio of blackberries to sugar=53/28

=53:28

Hope this helps..

Good luck on your assignment..

Answer:

Step-by-step explanation:

A trapezoid and two rectangulars are in the  opening form of the geometric shapes and you should calculate their surface areas seperately which is:

Answer:

Total surface area  = 3744 cm^2

Step-by-step explanation:

All linear measurements are in cm

Surface area of BOTH bases

Ab = 2*  (12+29)*24/2

= 984

Circumference of base

Cb = (25+12+26+29)

= 92

Height of prism

H = 30  (given)

Surface area of sides of prism

As= Cb*H

= 2760

Total Surface area of Prism

A = Ab + As

= 984 + 2760

= 3744 cm^2

Answer:

[tex]r \approx 2.41\%[/tex]

Step-by-step explanation:

The computation of the approximate new interest rate is shown below:

As we know that there are four quarters in a year so

The new equation is

[tex]A = 250(1 + r)^{4t}[/tex]

Now to determine the value of interest rate,i.e r, so place this to the first equation.

So,

[tex]250(1.1)^{t} = 250(1 + r)^{4t}[/tex]

[tex]1.1^{t} = (1 + r)^{4t}[/tex]

1.1 = (1 + r)^4

[tex]\sqrt[4]{1.1} = 1 + r[/tex]

[tex]r = -1 + \sqrt[4]{1.1}[/tex]

[tex]r \approx 0.0241[/tex]

[tex]r \approx 2.41\%[/tex]

We simply applied the above formula so that the interest rate could come

Answer: graphing calculator!

Step-by-step explanation: if you’re looking for the square root of a # that isn’t a perfect square (ie. sqrt4, sqrt 36) then you have to use a calculator for that. however the idea behind square roots is just a # multiplied by itself to give the original #. just ask yourself “what can i multiply by itself to get the original number”. hope that helped !

Answer:

By multiplying the number by its power 2.

E.g= 4^2

Answer:

v = Δs/Δt

Step-by-step explanation:

Velocity is equal to the displacement/distance (delta symbol s) over the change of time (delta symbol t).

Answer:

(3,2)

(-9,-6)

Step-by-step explanation:

Given that the graph is a direct variation.

The equation of variation is:

[tex]x=ky[/tex]

Since point (6, 4) is on the graph

[tex]6=4k\\\\k=\dfrac64[/tex]

Therefore, the equation connecting x and y is:

[tex]x=\dfrac64y[/tex]

[tex]\text{When y=2},x=\dfrac64 \times 2 =3\\\\\text{When y =}-6,x=\dfrac64 \times -6 =-9\\\\\text{When y =}8,x=\dfrac64 \times 8 =12\\\\\text{When y =}-3,x=\dfrac64 \times -3 =-4.5[/tex]

Therefore, the points that are also on the graph are:

(3,2) and  (-9,-6)

Answer:

(-9, -6) and (3, 2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's organise our information :

we want to khow the value of x that gives us : (1/2)x²+2x+3=x+7

Now the trick is to write this expression as a quadratic equation with zero at one side :

Now let's solve this equation :

Δ=1²-4*(1/2)*(-4)

 = 9

So we have two solutions :

So the solutions are -4 and 2

Answer:

∠CED

or

∠DEC

its the same thing

Step-by-step explanation:

E is the angle

Answer:

36 cups

3/12 = 9/c

Step-by-step explanation

3 ÷ 12 = .25

each cup = 25 cents

9 ÷ .25 = 36

Marco sold 36 cups of lemonade.

3/12 = 9/c

Answer:

36 cups

Step-by-step explanation:

We can set up a proportion:

12/3=c/9

Cross multiply.

12*9=3*c

108=3c

Divide both sides by 3.

c=36

The error that the proportion Kaycee set up was

cups/price=price/cups

This is not proportionate.

Possible proportions include:

cups/price=cups/price

price/cups=price/cups

cups/cups=price/price

price/price=cups/cups

Answer:

see explanation

Step-by-step explanation:

Given that y is inversely proportional to x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion

(a)

To find k use the condition when y = 7 , x = 9, that is

7 = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )

63 = k

y = [tex]\frac{63}{x}[/tex] ← equation of proportion

(b)

When x = 21, then

y = [tex]\frac{63}{21}[/tex] = 3

Answer:

3: 2

Step-by-step explanation:

game Apps: education apps:

3: 2

Answer:

99.86%

Step-by-step explanation:

What we have here is a binomial distribution, let x be the baby number among 8 births.

Binomial (n = 8, p = 0.559)

We want to find, P (X ≥ 1)

P (X ≥ 1)    = 1 - P (X <1)

P (X ≥ 1)  = 1 - P (X = 0)

P (X = 0)   = 8C0 * (0.559) ^ 0 * (1 - 0.559) ^ (8-0)]

8C0 = 8! / (0! * (8-0)!) = 1

replacing we have:

P (X = 0)   = 1 * 1 * 0.0014

P (X = 0)  = 0.0014

P (X ≥ 1))  = 1 - 0.001 4

P (X ≥ 1) = 0.9986

Therefore the probability is 99.86%

Answer:

2

Step-by-step explanation:

I would have to say it is two bc Everitt had 30% where Desery had 20%.

Answer:

solution,

Highest score=9

lowest score=1

now,

range= highest score-lowest score

=9-1

=8

Hope this helps...

Answer:

8

Step-by-step explanation:

The range of the sequence is the largest number - the smallest number.

The largest number is 9.

The smallest number is 1.

9 - 1

= 8

The range of the sequence is 8.

Answer:c

Step-by-step explanation:

hyp=6[tex]\sqrt{2}[/tex]

adj=6

hyp:adj=6[tex]\sqrt{2}[/tex]  :2

hyp:adj=[tex]\frac{6\sqrt{2} }{6} \\[/tex]

[tex]=\frac{\sqrt{2} }{1} \\hyp:adj=\sqrt{2} :1[/tex]

Answer:

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]

And replacing we got

[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]    

[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]    

For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]

[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]    

[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X¿ 17.5[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

s¿4.2 represent the sample standard deviation

n¿65 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=65-1=64[/tex]

Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value would be [tex]t_{\alpha/2}=1.669[/tex]

And replacing we got

[tex]17.5-1.669\frac{4.2}{\sqrt{65}}=16.63[/tex]    

[tex]17.5+1.669\frac{4.2}{\sqrt{65}}=18.37[/tex]    

For the 95% confidence the critical value is [tex]t_{\alpha/2}=1.998[/tex]

[tex]17.5-1.998\frac{4.2}{\sqrt{65}}=16.46[/tex]    

[tex]17.5+1.998\frac{4.2}{\sqrt{65}}=18.54[/tex]    

Answer:

Hope it helps you :)

And i hope you understand  

For store 1, it can be placed on 16 sites. Store 2 can be placed on 15 sites( since store 1 is already on site 1). Store 3 can be placed on 14 sites and so on until store 5 which has 12 sites.

Therefore the number of way is

C= 16*15*14*13*12

c=524,160 possibilities

Answer:

The answer is 1/27

Step-by-step explanation:

According to the rules of indices

a^-b can be written as 1/a^b

So 3^- 3 can be written as 1/3³

And

1/3³ = 1/27

Hope this helps you

Answer: 20 cm

If quadrilaterals WXYZ and BADC are congruent, then their corresponding sides are congruent.

Given that

WX≅DC,

XY≅BC,

you can state that

YZ≅AB,

WZ≅AD.

If AD = 4 cm and AB = 6 cm, then WZ = 4 cm and YZ = 6 cm. Opposite rectangle sides are congruent, then XY = 4 cm and WX = 6 cm.

The perimeter of WXYZ is

P = WX + XY + YZ + WZ = 6 + 4 + 6 + 4 = 20 cm.

Answer:

Test statistic t = 3.12

P-value = 0.001

As the P-value (0.001) 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 the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year (Gina's claim).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=55000\\\\H_a:\mu> 55000[/tex]

The significance level is 0.05.

The sample has a size n=61.

The sample mean is M=56500.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3750.

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

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3750}{\sqrt{61}}=480.138[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{56500-55000}{480.138}=\dfrac{1500}{480.138}=3.12[/tex]

The degrees of freedom for this sample size are:

df=n-1=61-1=60

This test is a right-tailed test, with 60 degrees of freedom and t=3.12, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>3.12)=0.001[/tex]

As the P-value (0.001) 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 the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.

Answer:Domain is x and range is y.For ex:-4 is domain and -7 is range.

Step-by-step explanatioFeel pleasure to help u:

Domain ( -4, 5) Range ( -7, 6)

The Domain includes the numbers between the least and the greatest x-values.

The range includes the numbers between the lowest and the highest y-values.

Answer:

A)x=2pi/3 and x=-2pi/3

Step-by-step explanation:

The function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values where the tan(a) has vertical asymptotes.

we know that tan(a) has vertical asymptotes in [tex]a=\frac{\pi }{2}[/tex] and  [tex]a=\frac{-\pi }{2}[/tex], if we made [tex]a=\frac{3x}{4}[/tex] and solve for x, we get:

for [tex]a=\frac{\pi }{2}[/tex]

[tex]\frac{\pi }{2} =\frac{3x}{4}\\x = \frac{2\pi }{3}[/tex]

for [tex]a=\frac{-\pi }{2}[/tex]

[tex]\frac{-\pi }{2} =\frac{3x}{4}\\x = \frac{-2\pi }{3}[/tex]

Finally, the function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values x=2pi/3 and x=-2pi/3

Answer:

A

Step-by-step explanation:

Answer:0.0081  or 0.81%

Step-by-step explanation:

The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, where

C5 3=  5!/3/2=4*5/2=10

p is the probability that one randomly selected calculator is defective= 10%=0.1

q is the probability that one randomly selected calculator is non-defective.

q=1-p=1-0.1=0.9

So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081

Answer:

She is saving 10 cents per pound

Step-by-step explanation:

First, we need to find how much she would pay without the sale:

12.5(1.8) = 22.5

Now, we can calculate how much she saved:

22.5 - 21.25 = 1.25

To find how much she's saving per pound, we divide the difference by the number of pounds:

1.25/12.5 = 0.1

She is saving 10 cents per pound

Answer:

A

Step-by-step explanation:

I took the test and got it right

Answer:b

Step-by-step explanation:

Answer:

828

Step-by-step explanation:

Missing leg of triangle:

√15²-12²= √225-144=√81=9

Triangle faces= 2*1/2*12*9= 108

Base= 20*9= 180

Front face= 20*15= 300

Back face= 20*12= 240

Total= 108+180+300+240= 828

Second choice

Answer:

fg t f h 10

Step-by-step explanation:

Answer:

a)0.654

b)-0.34

Step-by-step explanation:

a)2 3 4 5 6 7

[tex]\mu = 4[/tex]

[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{2+3+4+5+6+7}{6}\\Mean =4.5[/tex]

Standard deviation [tex]=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]

Standard deviation [tex]=\sqrt{\frac{(2-4.5)^2+(3-4.5)^2+(4-4.5)^2+(5-4.5)^2+(6-4.5)^2+(7-4.5)^2}{6-1}}=1.87[/tex]

[tex]t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\\t=\frac{4.5-4}{\frac{1.87}{\sqrt{6}}}\\t=0.654[/tex]

Df = n-1 = 6-1 = 5

Assume α=0.05

So[tex]t_{(\alpha,df)}=t_{0.05,5}=2.57[/tex]

So, t critical = 2.57

So, t calculated < t critical

b)1 2 2 5 5 7

[tex]\mu = 4 \\Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{1+2+2+5+5+7}{6}\\Mean =3.67[/tex]

Standard deviation =[tex]\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]

Standard deviation =[tex]\sqrt{\frac{(1-3.67)^2+(2-3.67)^2+(2-3.67)^2+(5-3.67)^2+(5-3.67)^2+(7-3.67)^2}{6-1}}=2.338[/tex]

[tex]t=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}t=\frac{3.67-4}{\frac{2.338}{\sqrt{6}}}t=-0.34[/tex]

Df = n-1 = 6-1 = 5

Assume α=0.05

So, [tex]t_{(\alpha,df)}=t_{0.05,5}=2.57[/tex]

So, t critical = 2.57

So, t calculated < t critical