The grades in a statistics course for a particular semester were as follows:
Grade ABCDF f 14 18 32 20 16
Test the hypothesis, at the 0.05 level of significance, that the distribution of grades is uniform. (Test that each grade is equally likely) Round your solutions to 3 decimal places where necessary.
Test Statistic =
Critical Value =

Answer:

Step-by-step explanation:

I'm from the UK and I'm not familiar with a two column proof, but the following proves the converse.

Draw 2 right angled triangles with the 2 legs = a and b in each case and the longest side = c in one triangle and f in the other.

By Pythagoras a^2 + b^2 = c^2   (Given)

Also in the other triangle a^2 + b^2 = f^2,  if it is right-angled.

Therefore a^2 = f^2 and a = f.

So the 2 triangles are congruent by SSS.

So m < C  in one triangle = m < F  ( the angles opposite the hypotenuse)

Therefore the second triangle is right angled .

This completes the proof.

Answer:

The 100 trees closest to a ranger station are assessed for damage.

Step-by-step explanation:

Convenience samples are samples taken from only around the focal point.

Option B is correct, The 100 trees closest to a ranger station are assessed for damage.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

A convenience sample is a non-random method of sampling that involves selecting subjects that are easy to access or readily available.

Of the methods listed, the convenience sample is the one where the trees are selected based on their proximity to a ranger station:

The 100 trees closest to a ranger station are assessed for damage.

This method is a convenience sample because it does not involve random selection of trees.

Instead, the trees are chosen based on their proximity to a specific location.

This can introduce bias into the sample, as trees near the ranger station may not be representative of the overall health of white pine trees in the state park.

Hence, Option B is correct, The 100 trees closest to a ranger station are assessed for damage.

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9514 1404 393

Answer:

  9/8

Step-by-step explanation:

To clear the fraction in the ratio 4.5 to 4, you can multiply both numbers by 2. This gives you the reduced ratio 9 to 8. As a fraction, that is 9/8.

Answer:

(x-5)^2 + (y+6)^2 = 4

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-5)^2 + (y- -6)^2 = 2^2

(x-5)^2 + (y+6)^2 = 4

Answer:

87,930 Minutes

Step-by-step explanation:

Let us use unit rates for this question. Let's first draw a table.

Minutes   Mile

45               1

This table represents the relation of Sally walking 1 mile in 45 minutes. Let's put the other data we know of in the table.

Minutes   Mile

45               1

                  1954

To find the number of minutes, we must know that if 1 mile takes 45 minutes, we must multiply the number of minutes, which is 45, by 1954 to get the result desired. Let us do that.

1954*45 = 87,930

Minutes   Miles

45               1

87,930      1954

Therefore it will take Sally 87,930 minutes to walk 1,954 Miles.

I Hope This Helps!

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Answer:

3.5

Step-by-step explanation:

in order to find the maximum, we are basically solving to find the vertex of the graph. to find the vertex use :

-b/2a

the 'b' is 112

the 'a' is -16

so :

-112/-32 = 3.5

the answer is B, 3.5

Answer:

D. 6.5

Step-by-step explanation:

The diameter of the cylinder is 1.25 x 2 = 2.5

SK = √1.25² + 6² = √42.25 = 6.5

Answer:

B - They are symmetric over the y-axis

Step-by-step explanation:

A - I couldn't find a way to explain this one

B - Even functions have graph symmetry across the y-axis, I'm not sure if you looking for multiple answers, but I got B as one of them.

C - An odd function has rotational symmetry, and even function has reflects

D - An even function is symmetric over the y-axis not the x-axis

Answer: $1,223.40.

Step-by-step explanation:

Since she earns $22.5 per hour, for 34 hours, she would earn:

$22.5 × 34 = $765

She earn 3% of her sales, therefore find 3% of $15,280:

$15280(3%) = $15280(0.03) = $458.4

Add them together:

$765 + $458.4 = $1223.4

9514 1404 393

Answer:

  $1,223.40

Step-by-step explanation:

Zoe's total pay is the sum of the products of hours and hourly rate, and sales and commission rate.

  Pay = (34 h)($22.50/h) +($15,280)(.03) = $765.00 +458.40

  Pay = $1,223.40

Zoe's pay for the week is $1,223.40.

Answer:

[tex]l=56m[/tex]

Step-by-step explanation:

From the question we are told that:

Angle from vertical [tex]\theta =5.6[/tex]

Horizontal Distance [tex]d=107m[/tex]

Angle of elevation [tex]\gamma=28.6[/tex]

Generally the Trigonometric equation for exterior angles is mathematically given by

[tex]Exterior\ angles=\sum of\ two\ interior\ angles[/tex]

Where

[tex]Exterior angles=90 \textdegree +5.6 \textdegree[/tex]

Therefore

[tex]90 \textdegree +\theta \textdegree=\omega+\gamma[/tex]

[tex]90 \textdegree +5.6 \textdegree=\omega+28.6 \textdegree[/tex]

[tex]\omega=67 \textdegree[/tex]

Generally the equation for The Sine rule is mathematically given by

[tex]\frac{sin \omega }{d}=\frac{sin \gamma}{l}[/tex]

[tex]l=\frac{107 sin 28.6}{sin 67 \textdegree }[/tex]

[tex]l=56m[/tex]

Asnwer: C

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

Answer:

pets bcos a vetenarian is a doctor for animals and tha question also says their owners.

Answer:

Yes D is the correct answer :)

Answer:

Yes, D

Step-by-step explanation:

Answer:

Adam runs at a rate of 11 minutes per mile.

Step-by-step explanation:

Take 143 minutes and divide by 13 miles and you will get the answer of 11 minutes.

PLEASE MARK ME BRAINEIST.

Answer:

it would take him 11 minuets to run a mile

Step-by-step

143 divided by 13 is 11 which means each mile takes 11

you can also check the answer by multiplying 13 times 11 which is 143

Answer:

E

Step-by-step explanation:

The percentage of the whole week that Adam spends in sleeping is 33%.

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

According to the give question.

Adams sleeps for nine hours each night, five nights a week.

⇒ Number of hours he sleep for five nights = 5 × 9 = 45 hours

Also, 11 hours for two nights a week.

So, the total number of hours Adam sleeps in a week = 45 + 11 = 56 hours

And, total number of hours in a week = 24 × 7 = 168

Therefore,

The percentage of the whole week that Adam spends in sleeping

= (total number of hours Adam sleep in a week/Total numbers of hour in a week) × 100

[tex]=\frac{56}{168}[/tex] × 100

= 33.33%

= 33%

Hence, the percentage of the whole week that Adam spends in sleeping is 33%.

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Answer:

95% provides more information

Step-by-step explanation:

The confidence interval is obtained by using the relation :

Xbar ± Zcritical * σ/√n

(Xbar - (Zcritical * σ/√n)) = 5.22 - - - (1)

(Xbar + (Zcritical * σ/√n)) = 5.98 - - (2)

Adding (1) and (2)

2xbar = 5.22 + 5.98

2xbar = 11.2

xbar = 11.2 / 2 = 5.6

Margin of Error :

Xbar - lower C.I = Zcritical * σ/√n

Zcritical at 90% = 1.645

5.6 - 5.22 = 1.645 * (σ/√n)

0.38 = 1.645 * (σ/√n)

(σ/√n) = 0.38 / 1.645 = 0.231

Therefore, using the se parameters to construct at 95%

Zcritical at 95% = 1.96

Margin of Error = Zcritical * σ/√n

Margin of Error = 1.96 * 0.231 = 0.45276

C.I = xbar ± margin of error

C. I = 5.6 ± 0.45276

C.I = (5.6 - 0.45276) ; (5.6 + 0.45276)

C. I = (5.147 ; 6.053)

Hence, 95% confidence interval provides more information as it is wider.

[tex]11.4[/tex]

[tex] \to \: 1.14 \times {10}^{1} [/tex]

Answer:

Hes correct ^

Step-by-step explanation:

Answer:

I wish I knew that answer

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

3.8 is the answer

68.4÷18=3.8

Answer:

a) The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.

b) We are 90% sure that the mean amount owed in student loans of graduates of  all four-year business colleges is between $13,600 and $15,162.

Step-by-step explanation:

Question a:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 25 - 1 = 24

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0639

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.0639\frac{1892}{\sqrt{25}} = 781[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 14381 - 781 = $13,600

The upper end of the interval is the sample mean added to M. So it is 14381 + 781 = $15,162

The 90% confidence interval for the mean amount owed in student loans of graduates of four-year business colleges is ($13,600, $15,162), having a margin of error of $781.

b) Interpret the confidence interval you have computed.

We are 90% sure that the mean amount owed in student loans of graduates of  all four-year business colleges is between $13,600 and $15,162.

Answer:

2.8 litres

Step-by-step explanation:

8.22 mg per 3.039 mL

2.704 mg per 1 mL

7.469 gram = 7469 milligrams

7469 milligrams per 2,761.34927mL

= 2.761 litres = 2.8 litres

Explanation:

Each vertical asymptote is due to a division by zero error.

For instance, the vertical asymptote x = 3 is from the factor (x-3) in the denominator. If we plugged x = 3 into (x-3), then it turns into 0 and we cannot have 0 in the denominator.

Similarly, the factor (x+3) leads to x = -3

So overall, we have (x-3)(x+3) in the denominator.

Answer:

a = 50t

Step-by-step explanation:

A function is rise over run, or y/x.

In this graph, the rise (y) is the account balance, while the run (x) is time. To solve for the slope, or the "equation modeled by the graph," we need to divide the rise by the run.

The graph is shown in terms of (a, t). If we look at the first point, (50,1), the rise is 50 and the run is 1. 50/1 is 50. Therefore, a = 50t, since a = 50 and t = 1.

To check, we can try another point, (100, 2). The rise is 100 and the run is 2. Divide these together and you still get 50. You are multiplying the "t" value by 50 to get the "a" value.

Therefore, it's a = 50t

Answer:

The range of the 95% data (X) =  238.3 days <  X < 289.9 days

Step-by-step explanation:

Given;

mean of the normal distribution, m = 264.1 days

standard deviation, d = 12.9 days

between two standard deviation below and above the mean is 96% of all the data.

two standard deviation below the mean = m - 2d

                                                                   = 264.1 - 2(12.9)

                                                                   = 238.3 days

two standard deviation above the mean = m + 2d

                                                                    = 264.1 + 2(12.9)

                                                                     = 289.9 days

The middle of the 95% of most pregnancies would be found in the following range;

238.3 days <  X < 289.9 days

if the formula is [tex]\frac{(B+b)}{2} .h[/tex] we just need to plug in the values

21/2 = 10.5 x 5 = 52.5

hope it helps :)

Answer:

A = 52.5 in^2

Step-by-step explanation:

The area of a trapezoid is

A = 1/2 (b1+b2)h

where b1 and b2 are the bases and h is the height

A = 1/2 ( 14+7)*5

A = 105/2

A = 52.5 in^2

Answer:

a) 0.0749 = 7.49% probability that the student makes more than $15,000.

b) 0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Full-time Ph.D. students receive an average of $12,837 per year.

This means that [tex]\mu = 12837[/tex]

Standard deviation of $1500

This means that [tex]\sigma = 1500[/tex]

a. The student makes more than $15,000.

This is 1 subtracted by the p-value of Z when X = 15000.

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

[tex]Z = \frac{15000 - 12837}{1500}[/tex]

[tex]Z = 1.44[/tex]

[tex]Z = 1.44[/tex] has a p-value of 0.9251.

1 - 0.9251 = 0.0749

0.0749 = 7.49% probability that the student makes more than $15,000.

b. The student makes between $13,000 and $14,000.

This is the p-value of Z when X = 14000 subtracted by the p-value of Z when X = 13000.

X = 14000

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

[tex]Z = \frac{14000 - 12837}{1500}[/tex]

[tex]Z = 0.775[/tex]

[tex]Z = 0.775[/tex] has a p-value of 0.7708.

X = 13000

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

[tex]Z = \frac{13000 - 12837}{1500}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

0.7708 - 0.5438 = 0.227

0.227 = 22.7% probability that the student makes between $13,000 and $14,000.

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given that:

Mean = $12837, standard deviation = $1500

a) For >15000:

z = (15000 - 12837)/1500 = 1.44

P(z > 1.44) = 1 - P(z < 1.44) = 1 - 0.9251 = 0.0749

b) For >13000:

z = (13000 - 12837)/1500 = 0.11

For <14000:

z = (14000 - 12837)/1500 = 0.78

P(0.11 < z < 0.78) = P(z < 0.78) - P(z < 0.11) = 0.7823 - 0.5438 = 0.2385

7.49% of the student makes more than $15,000, while 23.85% of the student makes between $13,000 and $14,000

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Answer:

Step-by-step explanation:

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