John Calipari, head basketball coach for the national champion University of Kentucky Wildcats, is the highest paid coach in college basketball with an annual salary of million (USA Today, March 29, 2012). The following sample shows the head basketball coach's salary for a sample of schools playing NCAA Division basketball. Salary data are in millions of dollars.
University Coach's Salary University Coach's Salary
Indian 2.2 Syracuse 1.5
Xavier .5 Murry State .2
Texas 2.4 Florida State 1.1
Connecticut 2.7 South Dekota State .1
West Virginia 2.0 Vermont .2
A. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division 1 basketball (to 2 decimal).
B. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches (to 4 decimals).
C. what is the 95% confidence interval for the population variance (to 2 decimals)?
D. what is the 95% confidence interval for the population standard deviation (to 2 decimals)?

Solution,

Radius=2 m

Area =pi r^2

= 3.142*(2)^2

=12.568 m^2

hope it helps

Good luck on your assignment

Answer:

2880

Step-by-step explanation:

Consider the 5 boys to be 1 group.  The boys and 3 girls can be arranged in 4! ways.

Within the group, the boys can be arranged 5! ways.

The total number of permutations is therefore:

4! × 5! = 2880

Answer:

[tex]=\left(x+4\right)\left(x-9\right)[/tex]

Step-by-step explanation:

[tex]x^2-5x-36\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(x^2+4x\right)+\left(-9x-36\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+4x\mathrm{:\quad }x\left(x+4\right)\\\mathrm{Factor\:out\:}-9\mathrm{\:from\:}-9x-36\mathrm{:\quad }-9\left(x+4\right)\\=x\left(x+4\right)-9\left(x+4\right)\\\mathrm{Factor\:out\:common\:term\:}x+4\\=\left(x+4\right)\left(x-9\right)[/tex]

Answer:

In a relation h(x) = y, the values of x are the domain and the values of y are the range.

Here the domain is:

D = {-6, -1, 7}

The range is:

R = {-9, 0 , 9}

Now, a relation f(x) = y is a function only if for every x in the domain we have only and only one value in the range.

Here we can see that for the value -1 in the domain we have two different values in the range:

(-1, 0) and (-1, 9)

So this can not be a function.

(If you want to take the variable as y, you also have that the value y = 0 leads to two different values in x, so this cant be a function either)

Answer:

a) C. The population must be normally distributed.

b) P(x < 65.8) = 0.8159

c) P(x > 64.2) = 0.3015

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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

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 = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22[/tex]

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me

n < 30, so the distribution of the population must be normal.

The correct answer is:

C. The population must be normally distributed.

(b) Assuming the normal model can be used, determine P(x < 65.8).

This is the pvalue of Z when X = 65.8. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{65.8 - 62}{4.22}[/tex]

[tex]Z = 0.9[/tex]

[tex]Z = 0.9[/tex] has a pvalue of 0.8159.

So

P(x < 65.8) = 0.8159

(c) Assuming the normal model can be used, determine P(x > 64.2).

This is 1 subtracted by the pvalue of Z when X = 64.2. So

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

[tex]Z = \frac{64.2 - 62}{4.22}[/tex]

[tex]Z = 0.52[/tex]

[tex]Z = 0.52[/tex] has a pvalue of 0.6985.

1 - 0.6985 = 0.3015

So

P(x > 64.2) = 0.3015

Answer: The volume of the​ sculpture is 141.84 cubic-feet

Step-by-step explanation: Please see the attachments below

Answer:

the volume of the box is increasing

dV = +310,000 ft^3/s

Step-by-step explanation:

Volume of a rectangular box with side a,b and c can be expressed as;

V = abc

The change in volume dV can be expressed as;

dV = d(abc)/da + d(abc)/db + d(abc)/dc

dV = bc.da + ac.db + ab.dc ......1

Given:

a= 150 feet,

b= 80 feet, and

c= 50 feet

ais increasing at 100 feet/sec,bis decreasing 20 feet/sec, andcisincreasing at 5 feet/sec

da = +100 feet/s

db = -20 feet/s

dc = +5 feet/s

Substituting the values into the equation 1;

dV = (80×50×+100) + (150×50×-20) + (150×80×+5)

dV = +400000 - 150000 + 60000 ft^3/s

dV = +310,000 ft^3/s

Since dV is positive, the volume of the box is increasing at that instant.

Answer:

A

Step-by-step explanation:

Calculate the products in the multiple choice and see if any equal the product in the problem.

Hence as the products calculated in choice A equal that in the problem;the answer is A

Answer: No 1 is 91.14 km who else could help with the rest of the solution for number 1, 2 & 3.

Answer:

Step-by-step explanation:

1) Vertical stretch is accomplished by multiplying the function value by the stretch factor. When |x| is stretched by a factor of 2, the stretched function is ...

  g(x) = 2|x|

__

2) Reflection over the x-axis means each y-value is replaced by its opposite. This is accomplished by multiplying the function value by -1.

  g(x) = -2|x|

__

3) As you know from when you plot a point on a graph, shifting it down 3 units subtracts 3 from the y-value.

  g(x) = -2|x| -3

__

4) A right-shift by k units means the argument of the function is replaced by x-k. We want a right shift of 1 unit, so ...

  g(x) = -2|x -1| -3

Answer:

Step-by-step explanation:

For focus-to-vertex distance "p", the equation of a parabola with vertex (h, k) can be written as ...

  y = 1/(4p)(x -h)^2 +k

Comparing this to your equation, we see that ...

  1/(4p) = 1

  h = -2

  k = -3

Solving for p, we find ...

  1/(4p) = 1

  1/4 = p . . . . . multiply by p

The parabola opens upward, so this means the focus is 1/4 unit above the vertex, and the directrix is 1/4 unit below the vertex.

Answer:

The focus is at (–2,–212) and the directrix is at y = –312.

Step-by-step explanation:

Find the focus and directrix of the parabola y=12(x+2)2−3.

got the answer right in the test.

Answer:

Step-by-step explanation:

Let X denote the dimension of the part after grinding

X has normal distribution with standard deviation [tex]\sigma=0.002 in[/tex]

Let the mean of X be denoted by [tex]\mu[/tex]

there is an upper specification of 3.150 in. on a dimension of a certain part after grinding.

We desire to have no more than 3% of the parts fail to meet specifications.

We have to find the maximum [tex]\mu[/tex] such that can be used if this 3% requirement is to be meet

[tex]\Rightarrow P(\frac{X- \mu}{\sigma} <\frac{3.15- \mu}{\sigma} )\leq 0.03\\\\ \Rightarrow P(Z <\frac{3.15- \mu}{\sigma} )\leq 0.03\\\\ \Rightarrow P(Z <\frac{3.15- \mu}{0.002} )\leq 0.03[/tex]

We know from the Standard normal tables that

[tex]P(Z\leq -1.87)=0.0307\\\\P(Z\leq -1.88)=0.0300\\\\P(Z\leq -1.89)=0.0293[/tex]

So, the value of Z consistent with the required condition is approximately -1.88

Thus we have

[tex]\frac{3.15- \mu}{0.002} =-1.88\\\\\Rrightarrow \mu =1.88\times0.002+3.15\\\\=3.15[/tex]

Answer:

Option (3)

Step-by-step explanation:

A stone has been thrown off towards the ground from a height [tex]h_{0}[/tex] = 18 feet

Initial speed of the stone 'u' = 4.5 feet per second

Since height 'h' of a projectile at any moment 't' will be represented by the function,

h(t) = ut - [tex]\frac{1}{2}(g)(t)^2[/tex] + [tex]h_{0}[/tex]

h(t) = 4.5t - [tex]\frac{1}{2}(32)t^2[/tex]+ 18 [ g = 32 feet per second square]

h(t) = 4.5t - 16t² + 18

h(t) =-16t² + 4.5t + 18

Therefore, Option (3) will be the answer.

The number of houses are 180, and the number of flats are 100.

It is given that the number of houses and the number of flats ratio is 9:5 the number of flats and the number of bungalows ratio is 10:3.

It is required to find the number of houses in the village if the number of bungalows is 30.

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The ratio of the number of houses and the number of flats:

= 9:5   and

The ratio of the number of flats and the number of bungalows :

=10:3

It means we can write the ratio of the number of houses and the number of flats = 18:10

And the ratio of the number of:

Houses : Flats : Bungalows = 18:10:3

But the number of bungalows are 30.

Then the ratios are:

180:100:30

Thus, the number of houses are 180, and the number of flats are 100.

Learn more about the fraction here:

brainly.com/question/1301963

Answer:

[tex]V=122.5in^3[/tex]

Step-by-step explanation:

The volume of a right circular cone is given by:

[tex]V=\frac{\pi r^2h}{3}[/tex]

where r is the radius of the circle and h is the height of the cone, and [tex]\pi[/tex] is a constant [tex]\pi=3.1416[/tex].

According to the problem the height is:

[tex]h=8.1 in[/tex]

and we don't have the radius but we have the diameter, which is useful to find it. We just divide the diameter by 2 to find the radius:

[tex]r=\frac{d}{2}=\frac{7.6in}{3}=3.8in[/tex]

Now, we can find the volume by substituting all the known values:

[tex]V=\frac{\pi r^2h}{3}[/tex]

[tex]V=\frac{(3.1416)(3.8in)^2(8.1in)}{3} \\\\V=\frac{(3.1416)(14.44in^2)(8.1in)}{3} \\\\V=\frac{367.454in^3}{3} \\\\V=122.485[/tex]

Rounding the volume to the nearest tenth of cubic inch we get:

[tex]V=122.5in^3[/tex]

Answer:

a) The velocity at which the water leaves the gun = 37.66 m/s

b) The volume rate of flow = (1.183 × 10⁻⁴) m³/s

c) The water hits the ground 18.64 m from the point where the water gun was shot.

Step-by-step explanation:

a) Using Bernoulli's equation, an equation that is based on the conservation of energy.

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

The two levels we are considering is just inside the water reservoir and just outside it.

ρgh is an extension of potential energy and since the two levels are at the same height,

ρgh₁ = ρgh₂

Bernoulli's equation becomes

P₁ + ½ρv₁² = P₂ + ½ρv₂²

P₁ = Pressure inside the water reservoir = 8 atm = 8 × 101325 = 810,600 Pa

ρ = density of water = 1000 kg/m³

v₁ = velocity iof f water in the reservoir = 0 m/s

P₂ = Pressure outside the water reservoir = atmospheric pressure = 1 atm = 1 × 101325 = 101,325 Pa

v₂ = velocity outside the reservoir = ?

810,600 + 0 = 101,325 + 0.5×1000×v₂²

500v₂² = 810,600 - 101,325 = 709,275

v₂² = (709,275/500) = 1,418.55

v₂ = √(1418.55) = 37.66 m/s

b) Volumetric flowrate is given as

Q = Av

A = Cross sectional Area of the channel of flow = πr² = π×(0.001)² = 0.0000031416 m²

v = velocity = 37.66 m/s

Q = 0.0000031416 × 37.66 = 0.0001183123 m³/s = (1.183 × 10⁻⁴) m³/s

c) If the height of gun above the ground is 1.2 m. Where does the water hit the ground?

The range of trajectory motion is given as

R = vT

v = horizontal component of the velocity = 37.66 m/s

T = time of flight = ?

But time of flight is given as

T = √(2H/g) (Since the initial vertical component of the velocity = 0 m/s

H = 1.2 m

g = acceleration due to gravity = 9.8 m/s²

T = √(2×1.2/9.8) = 0.495 s

Range = vT = 37.66 × 0.495 = 18.64 m

Hope this Helps!!!

She will receive a lot more money because she is already retired from work already and will win as bit more money

Answer:

156 minutes

Step-by-step explanation:

So we need to create an equation to represent how Frank's phone company bills him

So the phone company charges an $8 monthly fee, so this value remains constant and will be our "y-intercept"

They then charge $0.06 for every minute he talks, this will be our "slope"

Combining everything into an equation, we have: y = 0.06x + 8

Now since we were given Franks phone bill total and want to figure out how many minutes he used, we just need to solve the equation for x and plug in our known y value

Frank used up a total of 156 minutes

Complete Question:

Ellen is opening. Cookie shop eat a local middle school . She randomly surveys students to determine The types of cookies they would buy at the cookie shop the results of the surveys are below based on the survey. Which statement is not true?

A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

B) 22½% of the students surveyed would buy a sugar cookie.

C) If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.

D) Half of the students prefer chocolate chips or oatmeal raisin cookies.

(Table showing the results of her survey is in the attachment below)

Answer:

A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

Step-by-step Explanation:

STEP 1:

In order to ascertain which of the statements given in the options that is NOT TRUE, let's express the given number of students that would buy the different types of cookies in their PROPORTIONS AND PERCENTAGES in the survey result.

Thus:

Type of Cookie==> no of students => Proportion (no of students of a cookie type ÷ total no of students) => % (each proportion for a cookie type)

Chocolate Chip==> 25 => 0.3125 (25÷80) => 31.25% (0.3125 × 100)

Oatmeal Raisin==> 15 => 0.1875 (15÷850) => 18.75% (0.1875 × 100)

Peanut Butter== 22 => 0.275 (22÷80) => 27.5% (0.275 × 100)

Sugar ==> 18 => 0.225 (18÷80) => 22.5% (0.225 × 100)

STEP 2:

Next step is to consider each statement given in the question to see if they are true or not.

==>OPTION A: If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.

To find out if this is true, multiply the proportion of students who would be buy a sugar cookie (0.255) by 160 = 0.255 × 160 = 36.

If 160 buy a cookie, approximately 36 students would buy a sugar.

Option A IS NOT TRUE.

OPTION B: 22½% of the students surveyed would buy a sugar cookie.

From our calculation in STEP 2, we have:

Sugar ==> 18 => 0.225 (18÷80) => 22.5% (0.225 × 100).

Option B is TRUE. 22.5% of the students would go for sugar cookie.

OPTION C: If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.

Number of students that would buy the peanut butter if 240 students were to get a cookie = proportion of students that opt for peanut butter cookie in the survey (0.275) × 240 = 0.275 × 240 = 66.

Option C is TRUE.

OPTION D: D) Half of the students prefer chocolate chips or oatmeal raisin cookies.

Proportion of students who prefer chocolate chips or oatmeal raisin cookies = 0.3125 + 0.1785 = 0.491

This is approximately 0.5 = ½ of the total number of students.

Option D is TRUE.

Therefore, we can conclude that the statement, "A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie" is NOT TRUE.

Answer:

[tex] y = 5x[/tex]

And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:

[tex] y_f = 5(2x) = 10x[/tex]

And if we find the ratio between the two equations we got:

[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]

So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2

Step-by-step explanation:

For this case we have this equation given:

[tex] y = 5x[/tex]

And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:

[tex] y_f = 5(2x) = 10x[/tex]

And if we find the ratio between the two equations we got:

[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]

So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2

Answer:

B and A

Step-by-step explanation:

So based on the facts given, we know that b and a both have the same abasolute value. It does not matter whether a or b is negative or positive.

Answer:

Step-by-step explanation:

a) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 451

x = 1.5/100 × 451 = 7

p = 7/451 = 0.02

q = 1 - 0.02 = 0.98

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.97 = 0.1

α/2 = 0.01/2 = 0.03

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.03 = 0.97

The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17

Therefore, the 97% confidence interval is

0.02 ± 2.17√(0.02)(0.98)/451

= 0.02 ± 0.014

b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.

P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.

The distribution that should be used is the normal distribution

Answer:

The probability that the next customer will request mid-grade gas and fill the tank is 0.1800

Step-by-step explanation:

In order to calculate the probability that the next customer will request mid-grade gas and fill the tank we would have to make the following calculation:

probability that the next customer will request mid-grade gas and fill the tank= percentage of the people using mid-grade gas* percentage of the people using mid-grade gas that fill their tanks

probability that the next customer will request mid-grade gas and fill the tank=  30%*60%

probability that the next customer will request mid-grade gas and fill the tank= 0.1800

The probability that the next customer will request mid-grade gas and fill the tank is 0.1800

Answer:

b

Step-by-step explanation:

In a parralel graph, the slopes would always be the same. The intercept in the answer is 2, showing that the coordinate points are (0,2)

Hope this helps!:)

Answer:

B) y = 2x + 2

Step-by-step explanation:

Firstly, you have to know that parallel lines have congruent slopes. That means that the slope of this line will be 2.

Next, make a point slope form of the equation:

y - y1 = m(x - x1)

y - 2 = 2(x - 0)

y - 2 = 2x - 0

Now, we can make it into slope intercept form.

y - 2 = 2x

y = 2x + 2

Hope this helps :)

Answer:

Step-by-step explanation:

Expansion of a 2×2 determinant requires 2 multiplications. Expansion of an n×n determinant multiplies each of the n elements of a row or column by its (n-1)×(n-1) cofactor determinant. Then the number of multiplies is ...

  mpy[n] = n·mp[n-1]

  mpy[2] = 2

So, ...

  mpy[n] = n! . . . n ≥ 2

__

If each multiplication takes 1 nanosecond, then a 10×10 matrix requires ...

  10! × 10^-9 s ≈ 0.0036288 s ≈ 0.004 s . . . for 10×10

Then the larger matrices take ...

  n=15, 15! × 10^-9 ≈ 1307.67 s ≈ 21.8 min

  n=20, 20! × 10^-9 ≈ 2.4329×10^9 s ≈ 77.09 years

  n=25, 25! × 10^-9 ≈ 1.55112×10^16 s ≈ 4.915×10^8 years

_____

For the shorter time periods (less than 100 years), we use 365.25 days per year.

For the longer time periods (more than 400 years), we use 365.2425 days per year.

Answer:

option 2

Step-by-step explanation:

4^2=16/8=2.  4^2=16/16=1.  2-1=1

Answer:

Yes, they are consistent.

A 99​% confidence interval is consistent with a​ two-sided test with significance level alpha=0.01 because if a​ two-sided test with this significance level does not reject the null​ hypothesis, then the confidence interval does contains the value in the null hypothesis.

Step-by-step explanation:

Yes, they are consistent.

A 99​% confidence interval is consistent with a​ two-sided test with significance level alpha=0.01 because if a​ two-sided test with this significance level does not reject the null​ hypothesis, then the confidence interval does contains the value in the null hypothesis.

The critical values of the confidence level are equivalent to the critical values in the hypothesis test. In the case that the conclusion of the test is to not reject the null hypothesis, the test statistic falls within the acceptance region: its value is within the critical values of the two-sided test.

Then, it is also within the critical values of the confidence interval and the sample mean (or other measure) will be within the confidence interval bounds.

Answer:

Step-by-step explanation:

The general form representing limit of a function is expressed as shown below;

[tex]\lim_{h \to a} f(h)[/tex] where a is the value that h will take and use in the function f(h). It can be expressed in words as limit of function f as h tends to a. Comparing the genaral form of the limit to the limit given in question [tex]\lim_{h \to 0} \frac{\sqrt{9+h} - 3}{h}[/tex], it can be seen that a = 0 and f(h) = [tex]\frac{\sqrt{9+h} - 3}{h}[/tex]

Taking the limit of the function

[tex]\lim_{h \to 0} \frac{\sqrt{9+h} -3}{h}\\= \frac{\sqrt{9+0}-3 }{0}\\= \frac{0}{0}(indeterminate)[/tex]

Applying l'hopital rule

[tex]\lim_{h \to 0} \frac{\frac{d}{dh} (\sqrt{9+h} - 3)} {\frac{d}{dh} (h)}\\= \lim_{h \to 0} \frac{1}{2} (9+h)^{-1/2} /1\\=\frac{1}{2} (9+0)^{-1/2}\\= \frac{1}{2} * \frac{1}{\sqrt{9} } \\= 1/2 * 1/3\\= 1/6[/tex]

Answer:

the answer is 64 .

Step-by-step explanation:

basically i just divided 48 by 2.4 and got 20 .. so that means that 20 has to be the multiplied factor so i just multiplied 3.2 by 20 and got 64.