Twenty students from Sherman High School were accepted at Wallaby University. Of those students, eight were offered military scholarships and 12 were not. Mr. Dory believes Wallaby University may be accepting students with lower SAT scores if they have a military scholarship. The newly accepted student SAT scores are shown here.


Military scholarship: 850, 925, 980, 1080, 1200, 1220, 1240, 1300

No military scholarship: 820, 850, 980, 1010, 1020, 1080, 1100, 1120, 1120, 1200, 1220, 1330


Part A: Do these data provide convincing evidence of a difference in SAT scores between students with and without a military scholarship? Carry out an appropriate test at the α = 0.05 significance level.


Part B: Create and interpret a 95% confidence interval for the difference in SAT scores between students with and without a military scholarship.

The 1st digit is 1 out of 10 numbers

The 2nd digit is 1 out of 9 numbers

The 3rd digit is 1 out of 8 numbers

The 4th digit is 1 out of 1 numbers.

Total combinations are 10 x 9 x 8 x 7 = 5040

Since the combination 7654 is one out of the total the probability would be 1/5040

Answer:

x=1

Step-by-step explanation:

(x + 5) - 2(4x - 1) = 0

Distribute

x+5 - 8x +2 =0

Combine like terms

-7x +7 = 0

Add 7x to each side

-7x+7 +7x = 7x

7 = 7x

divide by 7

7/7 = 7x/7

1 =x

Answer:

20/40

Step-by-step explanation:

1/5=40/100*x

x=1/5*100/40

x=20/40 or 10/20 or 0.5

Answer:

6 / 51

Step-by-step explanation:

It is false.

Reason:

The probability of picking a black card at first is:

26 / 52 = 1/2

There are now 25 black cards and 51 cards in total.

The probability of picking another black card, if there's no replacement is now:

25 / 51

Now, there are 24 black cards and 50 cards left in total.

The probability of picking a black card without replacement now becomes:

24 / 50 = 12 / 25

Hence, the probability of picking three black cards without replacement is:

1/2 * 25/51 * 12 / 25 = 300 / 2550

In simplest form, it is 6 / 51

Answer:

Step-by-step explanation:

-7-1=-8

Step-by-step explanation:

Let the number is x. Its reciprocal will be 1/x. According to given condition, we get :

[tex]x+\dfrac{1}{x}=\dfrac{41}{20}\\\\\dfrac{x^2+1}{x}=\dfrac{41}{20}\\\\20x^2+20=41x\\\\20x^2-41x+20=0[/tex]

It is a quadratic equation. The values of x are :

[tex]20x^2-25x - 16x+ 20 =0\\\\5x(4x - 5) -4( 4x - 5) = 0\\\\(5x-4)(4x-5)=0\\\\5x-4=0\ \text{and}\ (4x-5)=0\\\\x=\dfrac{4}{5}\ \text{and}\ x=\dfrac{5}{4}[/tex]

The smaller number is 4/5 and the larger number is 5/4.

Answer: 181 degrees.

Step-by-step explanation:

If we have an angle A, between, then the angle B is coterminal to A if:

B = A + n*360°

where n can be any whole number (if n = 0, we have B = A)

Then, if we take our angle as A = 541°

we can take n = -1 and get:

B = 541° - 1*360° = 181°

Now, if we subtract again 360°, we will end with an angle of negative measure, so 181° is the least positive measure angle that is coterminal with 541°

It reheats the gas from the fuel and releases it more rapidly.

The answer is option A.

In full afterburner at low altitudes, the F-16 can burn in excess of 64,000 pounds an hour. At full throttle, a U.S.-variant F-16 with maximum external fuel stores has about 20 minutes until it's on emergency reserves (which would only last an extra minute or so at full afterburner).

Since the exhaust gas already has a reduced oxygen content, owing to the previous combustion, and since the fuel is not burning in a highly compressed air column, the afterburner is generally inefficient in comparison to the main combustion process.

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Answer:

C (5.3, -6, -14, 3.5, 7)

Step-by-step explanation:

Integers are the sets of positive and negative whole numbers including zero.

In set notation, we denote the set of integers using the letter [tex]\mattbb{Z}[/tex].

From the given options:

In Option C (5. 3, -6, -14, 3.5, 7), we have the number 3.5 and 5.3 which are not whole numbers. Therefore 3.5 and 5.3 are not integers.

Option C is the set which does not contain only integers.

Answer:

1

Step-by-step explanation:

coz  1 x 1 x 1=1

Answer:

90 square feet.

Step-by-step explanation:

Let's set up an equation!

SA= 2(xy)+2(xz)+2(yz).

Lets say that x=3 y=6 and z=3

We plug it in.

2(18)+2(9)+2(18)= SA

36+18+36=SA

72+18=SA

90=SA

90 square feet = Surface area.

Answer: There are 6 different ways in which they can share the work.

Step-by-step explanation:

Suppose that Terry selects first the place where he goes, in the selection he has 3 options at random to chose.

Then Edin selects, Edin has two options (because one is already taken)

Then Gordon selects, he has only one options.

The number of combinations is equal to the product of the number of options for each selection, this is:

Combinations = 3*2*1 = 6

There are 6 different ways in which they can share the work.

Answer:

Plane 1

[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]

Plane 2

[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]

Step-by-step explanation:

As each plane is travelling at constant speed, each equation can be modelled after this expression:

[tex]y = y_{o} + \dot y \cdot t[/tex]

Where:

[tex]y_{o}[/tex] - Intial elevation of the airplane, measured in feet.

[tex]\dot y[/tex] - Climbing/Descending rate of the airplane, measured in feet per minute. (Positive - Climbing, Negative - Descending)

[tex]t[/tex] - Time, measured in minutes.

Equations are described below:

Plane 1

[tex]y_{1} = 38250\,ft - \left(750\,\frac{ft}{min}\right)\cdot t[/tex]

Plane 2

[tex]y_{2} = 9400\,ft + \left(550\,\frac{ft}{min}\right)\cdot t[/tex]

Answer:

14.13 in³

Step-by-step explanation:

Volume of a ball (sphere) is:

V = ⁴/₃ π r³

Circumference of a ball (circle) is:

C = 2π r

Use the circumference to find the radius.

9.42 in = 2π r

r = 1.50 in

Use the radius to find the volume:

V = ⁴/₃ π (1.50 in)³

V = 14.13 in³

Answer:

- 8b³+5ab²+7a²b

Step-by-step explanation:

(32ab³ - 20a²b² - 28a³b)/(-4a)= - 8b³+5ab²+7a²b

Step-by-step explanation:

The probability of success = 8/(8 + 17) = 8/25 = 0.32.

Let X be the random variable denoting the number of successes (number of times the individual won a prize) in four picks.

Hence, X ~ Bin(4, 0.32).

Thus, P(X = 1) = [tex]4C_1=(0.32)(1-0.68)^{4-1}=4C_1(0.32)(0.68)^3[/tex]

The probability the individual will win a prize exactly one time is

C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

There are a total of eight ducks with “Win” written on the underside of the duck, and there are 17 ducks with “Lose” written on the underside of the duck.

The probability of success

P = 8/(8 + 17)

P = 8/25

P = 0.32

Let's suppose the X is the random variable denoting the number of the individual won a prize in four picks.

So,

X ~ Bin(4, 0.32).

Thus, P(X = 1) = C(4, 1)(0.32)(1 0.32)⁴⁻¹

= C(4, 1)(0.32)¹ (0.68)³

Thus, the probability the individual will win a prize exactly one time is

C(4, 1)(0.32)¹ (0.68)³ if the total of eight ducks with “Win” written on the underside of the duck.

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Step-by-step explanation:

5x3 + 20x2 + 2x + 8

5x2 (x + 4) + 2(x + 4)

(5x2 + 2) (x + 4)

Answer:

8(3x + 2)

Step-by-step explanation:

→To factorize this expression, you must take out the GCF (Greatest Common Factor). The GCF is the biggest number that you can take out of all the terms in the expression, meaning the number has to be able to be divide by 24x and 16.

→The GCF is 8:

8(3x + 2)

Answer:

8(3x+2)

Step-by-step explanation:

24x+16

8*3*x + 8*2

Factor out an 8

8(3x+2)

Answer:

Slow = 30

Fast = 50

Step-by-step explanation:

So make variables for the speed.

Slow wanderer = x

Faster wanderer = x + 20

The time it took was 2.5 hours.

2.5x + 2.5x + 50 = 200

5x + 50 = 200

x = 30

Answer: 150

Step-by-step explanation: K is constant

250= K (8+2)2

250= K (10)2

250= K (20)

250= K20

divide both sides by 20

250/20= K

12.5= K

THEREFORE

Y= K (4+2)2

Y= 12.5 (6)2

Y= 12.5 × 12

Y= 150

At x = 4 the value of the variable y will be 90 as per the proportionality given.

The property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, Y is directly proportional to (x+2)2 when x=8 y = 250

Since Y ∝ (x + 2)²

Y = k (x + 2)²

Where k is constant

For x = 8 y = 250

Substituting the values

250 = k(8 + 2)²

k = 2.5

Thus for x= 4

y = 2.5 (4 + 2)²

y = 90

therefore, According to the proportionality, the variable y will have a value of 90 at x = 4.

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Answer:

37.8541 litres.

Step-by-step explanation:

To find the amount of gas that she needs to fill her gas tank is 19 -9. She needs 10 gallons to fill her tank.

It says to state in litres, so convert.

1 gallon is about 3.78541 liters, so 10 gallons is 37.8541 litres

Hope that helped : )

Answer:

[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]

And we can find this probability with the complement rule:

[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]

And we can use excel or the normal standard table and we got:

[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]

So then we expect about 81.8% of students that will be promoted

Step-by-step explanation:

Let X the random variable that represent the scores of promotion of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(60,5.5)[/tex]  

Where [tex]\mu=60[/tex] and [tex]\sigma=5.5[/tex]

We want to find the following probability:

[tex]P(X>55)[/tex]

And we can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the z score formula we got:

[tex]P(X>55)=P(\frac{X-\mu}{\sigma}>\frac{55-\mu}{\sigma})=P(Z>\frac{55-60}{5.5})=P(z>-0.909)[/tex]

And we can find this probability with the complement rule:

[tex]P(z>-0.909)=1-P(z<-0.909)[/tex]

And we can use excel or the normal standard table and we got:

[tex]P(z>-0.909)=1-P(z<-0.909)=1-0.182= 0.818[/tex]

So then we expect about 81.8% of students that will be promoted

The domain of a function is the set of all the x terms of the function and the range of a function is the set of all the y terms of a function.

For example, take a look below.

The domain is the set of all x terms in each ordered pair and the

range will be the set of all the y terms in each ordered pair.

Answer:

The best prediction for  the number of years it will take for the population to reach 200,000 is 9.41

Step-by-step explanation:

Year     Population

1              11,920

2              16,800

3              23,300

4              33,000

5             45,750

6             64,000

[tex]y_1 =A _0 e ^{kt _1}\\y_2 = A_0 e^{k t_2}\\(t_1,y_1)=(1,11920)\\(t_2,y_2)=(2,16800)[/tex]

Substitute the values

[tex]11920=A _0 e ^{k} ---1\\16800 = A_0 e^{2k} ---2[/tex]

Divide 1 and 2

[tex]\frac{11920}{16800}=\frac{e^k}{e^{2k}}\\\frac{11920}{16800}=e^{k-2k}\\ln(\frac{11920}{16800})=-k\\k=-1 ln(\frac{11920}{16800})\\k=0.3432\\A_0=y_1 e^{-k t_1}\\A_0=11920 e^{-0.3432}\\A_0=8457.5238[/tex]

The exponential function that passes through the points (1, 11920) and (2, 16800) is[tex]y=8457.5238 e^{0.3432t}[/tex]

Now we are supposed to find  the best prediction for  the number of years it will take for the population to reach 200,000

[tex]200000=8457.5238 e^{0.3432t}[/tex]

[tex]\frac{200000}{8457.5238}=e^{0.3432t}[/tex]

[tex]ln(\frac{200000}{8457.5238})=0.3432t[/tex]

t = 9.41

Hence the best prediction for  the number of years it will take for the population to reach 200,000 is 9.41

Answer:

D.

Step-by-step explanation:

For independent events

P(A and B) = P(A) × P(B)

FINDING P(B)

P(B) = P(A and B) /P(A)

P(B) = 0.6/0.8

P(B) = 0.75

Answer:

the answer to the problem is 35.

Answer:

he horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate. Also called "Abscissa"

Step-by-step explanation:

Answer:

D) is directly related to the risk of the company's assets.

Step-by-step explanation:

Equity which may be defined as what the difference between what your business worth minus what you owe in it.

It can also be put in a way as the remaining value of an owners interest in a particular company after all debt might have been cleared.

Equity= assets - liability

So equity has a lot to do in the risk management of a business or a particular company.

Answer:

the 3rd option is the right one

Answer:

The answer is A.

Step-by-step explanation:

Recall SohCahToa, which tells us that cosine is the ratio of the adjacent side to the hypotenuse. In other words:

[tex]\displaystyle \cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

The adjacent side to ∠C is 10 and the hypotenuse is 26.

Therefore:

[tex]\displaystyle \cos(C)=\frac{10}{26}=\frac{5}{13}[/tex]

Our answer is A.