Of interest is to determine the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. A simple random sample of 31 students enrolled in graduate programs was selected, and the age of each student when they took the comprehensive exam was recorded. The mean age at the time of taking the comprehensive exam for this sample of 31 students was 27.5 years with a standard deviation of 2.9 years; there were no outliers in the sample that would lead one to suspect heavy skewness in the distribution. If appropriate, use this information to calculate and interpret a 98% confidence interval for the mean age of students at the time they take the comprehensive exam for all students enrolled in graduate programs that require students to take comprehensive exams. Use this information to answer questions 3-5

Answer:

I worked it outf to be 3π in terms of π, apologies if this is wrong :/

Answer:

[tex](x,y) = (3,1)[/tex]

Step-by-step explanation:

Given

[tex]y < -x + 4[/tex]

[tex]y > 3x - 8[/tex]

Required

Solve graphically

See attachment for graph;

The blue shade represents [tex]y < -x + 4[/tex]

While the green, represents [tex]y > 3x - 8[/tex]

Next, determine the intersection points between the two lines

From the attached graph, we have:

[tex](x,y) = (3,1)[/tex]

Hence, the solution is: [tex](3,1)[/tex]

Step-by-step explanation:

When we observe the figure there are two semicircles , one of radius 14cm . And other will be of 14cm/2 = 7cm ( Since the 2nd semi circle is drawn taking radius of 1st semicircle as diameter.)

Now join T to the center of 2nd semi circle . Therefore , we have

[tex]\tt\to PR = 28cm \\\\\tt\to PQ + 14cm = 28cm \\\\\tt\to PM + MQ = 14cm \\\\\tt\to MQ = 14cm - 7cm \\\\\to\boxed{\orange{\tt MQ = 7cm }}[/tex]

Now , looking at the figure we know that radius is perpendicular to the tangent at point of contact . Here TR is tangent . Therefore ∆TRM is right angled triangle. Using Pythagoras Theorem we have,

[tex]\tt\to 21^2 = RT^2+7^2 \\\\\tt\to RT^2= 441 - 49 \\\\\tt\to RT =\sqrt{392}\\\\\tt\to\boxed{\orange{\tt RT = 19 .79 cm }}[/tex]

Answer:

Only 60 is an identified outlier

Step-by-step explanation:

Given

Age group: 40 to 50

[tex]Min = 60[/tex]           [tex]Q_1 = 70[/tex]           [tex]Median= 73[/tex]

[tex]Q_3 = 76[/tex]              [tex]Max = 85[/tex]

Conditions for outlier

[tex]Value > Q_3 + 1.5 * IQR[/tex]

[tex]Value < Q_1 - 1.5 * IQR[/tex]

See attachment for complete question

Required

Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years

First, calculate the IQR of group 40 to 50.

This is calculated as:

[tex]IQR = Q_3 - Q_1[/tex]

Where:

[tex]Q_3 = 76[/tex] and [tex]Q_1 = 70[/tex]

So:

[tex]IQR = 76 - 70[/tex]

[tex]IQR = 6[/tex]

Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)

Testing 60

Condition 1

[tex]Value > Q_3 + 1.5 * IQR[/tex]

[tex]60 > 76 + 1.5 * 6[/tex]

[tex]60 > 76 + 9[/tex]

[tex]60 > 85[/tex] --- False

Condition 2

[tex]Value < Q_1 - 1.5 * IQR[/tex]

[tex]60 < 70 - 1.5 * 6[/tex]

[tex]60 < 70 - 9[/tex]

[tex]60 < 61[/tex] --- True

Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years

Testing 62

Condition 1

[tex]Value > Q_3 + 1.5 * IQR[/tex]

[tex]62> 76 + 1.5 * 6[/tex]

[tex]62 > 76 + 9[/tex]

[tex]62 > 85[/tex] --- False

Condition 2

[tex]Value < Q_1 - 1.5 * IQR[/tex]

[tex]62 < 70 - 1.5 * 6[/tex]

[tex]62 < 70 - 9[/tex]

[tex]62 < 61[/tex] --- False

Because both conditions are false, then 62 is  not an outlier of group 40 - 50 years

Testing 84

Condition 1

[tex]Value > Q_3 + 1.5 * IQR[/tex]

[tex]84> 76 + 1.5 * 6[/tex]

[tex]84 > 76 + 9[/tex]

[tex]84 > 85[/tex] --- False

Condition 2

[tex]Value < Q_1 - 1.5 * IQR[/tex]

[tex]84 < 70 - 1.5 * 6[/tex]

[tex]84 < 70 - 9[/tex]

[tex]84 < 61[/tex] --- False

Because both conditions are false, then 84 is  not an outlier of group 40 - 50 years

Step-by-step explanation:

Answer:

Angle A = 68 degree

Angle B = 44 degree

Step-by-step explanation:

Sum of all interior angles = Angle A+Angle B+ Angle C

180 = 68+x+x-24

180 = 68+2x-24

180-68 = 2x-24

112+24 = 2x

136/2 = x

68 = x

Therfore, Angle A = 68 degree

Angle B = (x-24)

= (68-24)

= 44 degree

Mark as brainliest.

(1)  Equivalent fractions (2) common denominator

Solution:

1. Equivalent fractions name the same amount.

Equivalent fractions are the same value with different numerator and denominator.

Example:

These values are same.

2. A common denominator is a common multiple of two or more denominators.

Example:

Here 6 is a common multiple of 2 and 3.

Hence the answer is (1)  Equivalent fractions (2) common denominator.

⻏尺闩讠㇄讠丂七 讠丂 闩尸尸尺⼕讠闩セᗪ

Answer:

pentagon

regular polygon

Step-by-step explanation:

A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center

Answer:

176

Step-by-step explanation:

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

SO JML is 88*2

Answer:

[tex]y = \frac{1}{2}x - 4[/tex]

Step-by-step explanation:

Given

[tex]y = \frac{1}{2}x[/tex]

Required

Shift [tex]3\ units[/tex] down and [tex]2\ units[/tex] right

[tex]y = \frac{1}{2}x[/tex]

Shift 3 units down

The rule is: (x,y)=> (x,y-a)

Where a is the number of units shifted down

In this case: [tex]a = 3[/tex]

So, we have:

[tex]y = \frac{1}{2}x[/tex] == > [tex]y = \frac{1}{2}x - 3[/tex]

Shift 2 units right

The rule is: (x,y)=>(x-b,y)

Where b is the number of units shifted right

In this case: [tex]b = 2[/tex]

So, we have:

[tex]y = \frac{1}{2}x - 3[/tex] ==> [tex]y = \frac{1}{2}(x - 2) - 3[/tex]

Open bracket:

[tex]y = \frac{1}{2}x - 1 - 3[/tex]

[tex]y = \frac{1}{2}x - 4[/tex]

Hence, the new equation after the transformation is:

[tex]y = \frac{1}{2}x - 4[/tex]

Answer:

V = 262’144 ft^3, surface area = 24’576 ft^2

Step-by-step explanation:

The volume con be find with this formula =

V = side^3

V = 64^3 = 262’144 ft^3

For find the surface area we can proceed in this way: first of all we can find the area of a face.

A = side^2 = 4096 ft^2

a cube has 6 faces, so we have to the mutiply the value six times.

Surface area = 4096  x 6 = 24’576 ft^2

Answer:

Don't click the site its a scam and will give your phone a virus

Answer:

rate of the current = 2 km/hr

Step-by-step explanation:

d = rt

Let c = rate of the current

Rate of boat downstream = 10 + c

Time going downstream = 24/(10 + c)

Rate of boat upstream = 10 - c

Time going upstream = 24/(10 - c)

Since the total time is 5 hr, then

24/(10 + c) + 24/(10 - c) = 5

24(10 - c) + 24(10 + c) = 5(10 + c)(10 - c)

240 - 24c + 240 + 24c = 500 - 5c^2

480 = 500 - 5c^2

5c^2 = 20

c^2 = 4

c = 2  or  -2

Since a rate cannot be negative, the rate of the current = 2 km/hr

Answer:

x = -3

Step-by-step explanation:

1. Write the equation

3x + 7 = -2

2. -7 from both sides

3x = -9

3. Divide 3 from both sides to get x alone

x = -3

Answer:

Hello There!!

Step-by-step explanation:

3x+7=-2 (-7 from both sides)

-7 -7

3x=-9 (divide by 3 from both sides)

÷3 ÷3

x=-3

hope this helps,have a great day!!

~Pinky~

Answer:

91%

Step-by-step explanation:

The discount is $73 so we would get 73/80.

73/80 is also known as 73÷80

which would equal 0.9125

if we were to covert and round it to a percent, it would be 91%

Answer:

45

Step-by-step explanation:

Answer:

whts the question??

Step-by-step explanation:

Answer:

The volume of cone = Maximum holding of glass = 60 cube cm(cm^3)

Step-by-step explanation:

Cone formula:

[tex] v = \frac{1}{3} \pi \: r {}^{2} h[/tex]

The radius is 3cm and Volume is 60cm^3.

if pi =~ 3 So the "h" is 6.66 cm.

"h" is distance from cone's head to its base.

The "H"( height of glass) = 6.66 + 7 = 13.6 =~ 14

9514 1404 393

Answer:

  13.4 cm

Step-by-step explanation:

The volume of the cone is given by ...

  V = 1/3πr²h

For the given dimensions, we have ...

  60 cm³ = 1/3π(3 cm)²h

  20/π cm = h ≈ 6.37 cm . . . . . . . . . . . divide by the coefficient of h

The overall height of the glass, H, is 7 cm more than the value of h.

  H = 7 cm +6.4 cm = 13.4 cm

The height of the glass is 13.4 cm.

Answer:

Ok, what exactly is the question?

Step-by-step explanation:

Answer:b c

Step-by-step explanation:

did it

Answer:

y= -4x -2

Step-by-step explanation:

-10=-4(2) -2

y= -4x -2

Answer:5/6=25/blank

Step-by-step explanation:so 5/6 the top is times five forget the bottom for now just think of 5 and 25

[5x5] equals 25 so you already got the top

now for the bottom since you multiply the top by five you have to do that to the bottom so that will be    [6x5] that equals 30 so you got your answer

[25/30]

Answer:

it c

Step-by-step explanation:

Answer:

X = 22

Step-by-step explanation:

This is a right triangle which means the angles add up to 90° total. So if 1 side is 15 and another side is 53 then 15 + 53 = 68 and 90 - 68 = 22 so X = 22 which is the missing side.

Answer:

the principle amount

Step-by-step explanation:

I don't know how to explain it without an analogy so...

If a loan is charging a  10% interest amount of a $120 loan than the interest would be $12.

You multiply the interest rate by the total amount and that's how you find the amount of money you make off of interest.

(The total amount and principle amount are the same thing)

Answer:

$488778

Step-by-step explanation:

For a for interest is;

i = PRT/100

Where;

R is rate

P is Principal

T is time

i is interest

We are given;

R = 12.5% = 0.125.

T = 146 days = (146/364) = 0.4011

i = $245

Thus;

245 = (P × 0.125 × 0.4011)/100

Thus;

P = (245 × 100)/(O.125 × 0.401)

P = $488778

Complete question :

Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is 0.13. Each independently constructed a confidence interval based on the point estimate, but Jaime’s interval has a lower bound of 0.097 and an upper bound of 0.163, while Mariya’s interval has a lower bound of 0.117 and an upper bound of 0.173. Which interval is wrong? Why?

Answer:

Mariya's interval

Step-by-step explanation:

Point estimate = 0.13

Mariya's confidence interval :

Lower boundary = 0.117

Upper boundary = 0.173

Jamie's confidence interval :

Lower boundary = 0.097

Upper boundary = 0.163

The correct confidence interval should have an average value equal to the value of the point estimate ;

Jamie's confidence interval average :

(0.097 + 0.163) / 2 = 0.26 / 2 = 0.13

Mariya's confidence interval average :

(0.117 + 0.173) / 2 = 0.29 / 2 = 0.145

Based on the confidence interval average obtained we can conclude that Mariya's interval is wrong as it the average obtained is greater than the point estimate.

0.145 > 0.13

Answer:

4775.22

Step-by-step explanation:

V= πr2h

Input your numbers into the equation, and it will give you this answer.