Paige earned $15.50 per hour. She received a 15% raise. How much more does Paige earn now per hour?

Answer:

Data provide convincing evidence of a difference in SAT scores  between students with and without a military scholarship is explained below in details.

Step-by-step explanation:

This is a quiz of 2 autonomous groups. The population model differences are not understood. it is a two-tailed examination. Let w be the index for scores of students with army research and o be the index for scores of students without army research.

Therefore, the population means would be μw and μo.

The irregular variable is x w - xo = variation in the sample mean records of students with military accomplishments and students without.

For students with military accomplishments,

n = 8

Mean = (850 + 925 + 980 + 1080 + 1200 + 1220 + 1240 + 1300)/8

Mean = 1099.375

Standard deviation = √(summation(x - mean)/n

Summation(x - mean) = (850 - 1099.375)^2 + (925 - 1099.375)^2 + (980 - 1099.375)^2 + (1080 - 1099.375)^2 + (1200 - 1099.375)^2 + (1220 - 1099.375)^2 + (1240 - 1099.375)^2 + (1300 -1099.375)^2 = 191921.875

Standard deviation = √(191921.875/8 = 154.89

For students without military scholarship,

n = 12

Mean = (820 + 850 + 980 + 1010 + 1020 + 1080 + 1100 + 1120 + 1120 + 1200 + 1220 + 1330)/12

Mean = 1073.83

Summation(x - mean) = (820 - 1073.83)^2 + (850 - 1073.83)^2 + (980 - 1073.83)^2 + (1010 - 1073.83)^2 + (1020 - 1073.83)^2 + (1080 - 1073.83)^2 + (1100 - 1073.83)^2 + (1120 - 1073.83)^2 + (1120 - 1073.83)^2 + (1200 - 1073.83)^2 + (1220 - 1073.83)^2 + (1330 - 1073.83)^2 = 238199.4268

Standard deviation = √(238199.4268/12 = 140.89

We would set up the hypothesis.

The null hypothesis is

H0 : μw = μo H0 : μw - μo = 0

The alternative hypothesis is

Ha : μw ≠ μo Ha : μw - μo ≠ 0

Since sample standard deviation is recognized, we would analyis the examination statistic by using the t examination. The formula is

(xw - xo)/√(sw²/nw + so²/no)

From the information given,

xw = 1099.375

xo = 1073.83

sw = 154.89

so = 140.89

nw = 8

no = 12

t = (1099.375 - 1073.83)/√(154.89²/8 + 140.89²/12)

t = 0.37

The formula for determining the degree of freedom is

df = [sw²/nw + so²/no]²/(1/nw - 1)(sw²/nw)² + (1/no - 1)(so²/no)²

df = [154.89²/8 + 140.89²/12]²/(1/8 - 1)(154.89²/8)² + (1/12 - 1)(140.89²/12)² = 21650688.37/1533492.15

df = 14

We would get the probability count from the t test calculator. It becomes

p value = 0.72

Since the level of importance of 0.05 < the p value of 0.72, we would not neglect the null hypothesis.

Therefore, these data do not present an acceptable indication of a difference in SAT scores between students with and without a military scholarship.

Part B

The formula for getting the confidence interval for the difference of two population means is expressed as

z = (xw - xo) ± z ×√(sw²/nw + so²/no)

For a 95% confidence interval, the z score is 1.96

xw - xo = 1099.375 - 1073.83 = 25.55

z√(sw²/nw + so²/no) = 1.96 × √(154.89²/8 + 140.89²/12) = 1.96 × √2998.86 + 1654.17)

= 133.7

The confidence interval is

25.55 ± 133.7

Answer:

480 miles

Step-by-step explanation: 4 times 120

Answer:

-1 + 5s

Explanation:

3 - 4 = -1

2s + 3s = 5s

Answer:

5 − 1

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Statement                                      | Reason                                            

1. m∠A + m∠B + m∠C = 180°         | 1.  Angles in a triangle sum to 180°

2. 28° + x - 4° + 2x = 180°              | 2. Substitution

3. x=(180° - 24°)/3= 156°/3°= 52°   | 3. Algebra

[tex]slope = \tan(angle \: made \: by \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: line \: with \: x \: axis) [/tex]

[tex]or \: [/tex]

[tex] = \frac{y1 - y2}{x1 - x1} [/tex]

Answer:

10a + 5

Step-by-step explanation:

3a - 4 + 5a + 7 + 2(a + 1)

3a - 4 + 5a + 7 + 2a + 2

10a +5

Group the variables and non variables.

sale price of the television is c

Answer:

$79.65

Step-by-step explanation:

115-40.25= 73.75

73.75 x 0.08 = 5.90

73.75 + 5.90 = 79.65

Rick will pay 80.73 dollar in total.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Given that Rick is buying a $115 tennis racquet from a sporting goods store.

If the racquet is on sale for 35% off and sales tax is 8%,then

First,we need to find 35% of 115.

35% as a decimal is 0.35

0.35 x 115 = 40.25

Now, subtract 40.25 from 115;

115 - 40.25 = 74.75

Now, the sales tax, find 8% of 74.75.

8% as a decimal is 0.08

0.08 x 74.75 = 5.98

Now, subtract add 5.98 to 74.75;

5.98 + 74.75 = 80.73

Therefore, he will pay 80.73 dollar in total.

Learn more about multiplications;

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Answer:

a^2+b^2=c^2

c=15 units

Step-by-step explanation:

You can use the pythagorean theorem to solve this equation. a^2+b^2=c^2.

If you substitute the leg lengths in, the new equation will be 9^2+12^2=c^2, c being the hypotenuse.

Next, you can simplify it to get 81+144=c^2. Simplifying it further, you get 225=c^2, which means that the length of the hypotenuse is 15. Hope this helped! :)

Answer:

15

Step-by-step explanation:

9^2+12^2=c^2

81+144=c^2

225=c^2

15=c

or you can see that this is a 3,4,5 triangle (just 3 times bigger)

hope this helps :)

Answer:

3.75

Step-by-step explanation:

3/80 as a fraction maybe

3 3/4 as a mixed fraction

Answer:

5m to 11m simplified to a ratio would be 5:11.

Step-by-step explanation:

To calculate ratios, try to think of them as fractions instead.

When a ration is expressed in the "a to b" form, you can actually treat it as [tex]\frac{a}{b}[/tex]!

As an example, the ratio of 1 to 2 would be [tex]\frac{1}{2}[/tex]. and the ration of 5 to 9 would be [tex]\frac{5}{9}[/tex].

Hence, the ration of 5m to 11m would be [tex]\frac{5m}{11m}[/tex], which when simplified equals to [tex]\frac{5}{11}[/tex].

Now, we can do the opposite to the fraction! For example, [tex]\frac{10}{19}[/tex] would be equal to 10:19!

Hence, 5m to 11m simplified to a ratio would be 5:11!

Hope this helped!

Answer:

(0,5)

Step-by-step explanation:

Hope this helped, Have a Great Day!!

Answer:9342

Step-by-step explanation:

I am smart UwU

Answer:

The Second choice y+5=-3/4(x-2

Step-by-step explanation:

4y=3x+8 solve for y so it's y=-3/4x+2

and use the slope which is -3/4

2 = x then 5 = y

you used to pass through formula and plug it in soooo it's

y+5=-3/4(x-2)

sorry if this doesn't make any sense, I'm terrible at explaining

to find the number of subscribtion sold we divide the money she made by the price of subscription

monday:

42.80/5.35=8 subscriptions sold

tuesday:

64.20/5.35=12 subscriptions sold

wednesday:

74.90/5.35=14 subscriptions sold

8+12+14=34 subscriptions sold in 3 days

Answer:

34 subscriptions she sold

Ignore this post, I have no Idea what it is, report this so it gets taken down so someone else can answer...

Answer:

The plans will be equal at 160 minutes of call

Step-by-step explanation:

1st plan: y = 0.14x + 30

2nd plan: y = 0.19x + 22

0.14x + 30 = 0.19x + 22

Subtract 0.19x from both sides;

-0.05x + 30 = 22

Subtract 30 from both sides;

-0.05x = -8

Divide both sides by -0.05

x = 160

Answer:

72 feet

Step-by-step explanation:

Given that:

The speed of Erica while descending down the mountain = 36 feet per hour

Time at which the descent was started = 10 AM

Time at which the descent was finished = 6 PM

To find:

The change in elevation after two hours ?

Solution:

First of all, let us learn about the relation between speed, distance and time.

The formula between speed, distance and time is given as:

[tex]Speed = \dfrac{Distance }{Time}[/tex]

Here, we are given that:

Speed = 36 feet per hour

Time = 2 hours

We have to find the Distance now.

Putting the given values:

[tex]36 = \dfrac{Distance}{2}\\\Rightarrow Distance = 36 \times 2\\\Rightarrow Distance = \bold{72\ feet}[/tex]

Change in elevation = 72 feet

Answer:

23

Step-by-step explanation:

Answer:

yes they are the same

Step-by-step explanation:

2x + 28 =40

you subtract 28 from both sides

2x + 28 - 28 = 40 - 28

2x=12

divide 12 by 2 and get 6

2(6)=12

2(x + 14)= 40

So, 2(x) + 2(14)

2x + 28 = 40

So they're both the same, just with 2 different ways to solve the same equation...Hope this helps!!

The solution for 2x + 28 = 40 is 6.

The solution for 2(x + 14) = 40 is 6.

Yes, they have the same solution.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

2x + 28 = 40

Solve for x.

2x = 40 - 28

2x = 12

x = 6

2(x + 14) = 40

Solve for x.

2x + 28 = 40

2x = 40 - 28

2x = 12

x = 6

Thus,

The solution for both equations is the same.

Learn more about solutions to equations here:

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Answer:

A: (-1,5) B: (-2,-1) C: (8,-1)

Answer:

6/7

Step-by-step explanation:

Given the points :

(-5, 2) and (2, 8)

Slope can be obtained by using the relation :

(y2 - y1) / (x2 - x1)

From the points given :

x1 = - 5 ; y1 = 2 ; x2 = 2 ; y2 = 8

(8 - 2) / (2 - (-5))

(8 - 2) / (2 + 5)

6 / 7

Hence, slope between the two points = 6/7

Answer:

[tex]\huge\boxed{\sf t = 4}[/tex]

Step-by-step explanation:

[tex]\sf 3(t+3)+5(3+2t)-76 = 0\\\\Expanding \ Parenthesis\\\\3t + 9 + 15 + 10t -76 = 0\\\\13t + 24 -76 = 0\\\\13t - 52 = 0\\\\Add \ 52 \ to \ both \ sides\\\\13t = 52\\\\Dividing\ both\ sides\ by\ 13\\\\t = 52/13\\\\t = 4\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

3n+7=37 is the equation to solve how many were at each of the large tables

Answer: 6 × 4^x

Step-by-step explanation:

From the question, we are told that scientists released 6 rabbits into a new habitat in year 0 and that each year, there were four times as many rabbits as the year before.

The number of rabbits there after x years will be:

= 6 × 4^x

For example, let us say we want to calculate the number of rabbits after 2 years.

= 6 × 4^x

= 6 × 4²

= 6 × 16

= 96 rabbits

Answer:

1/2

Step-by-step explanation:

Given that,

[tex]\lim_{n \to 1} (\dfrac{1+\cos\pi x}{\tan^2\pi x})[/tex]

Using L Hospital's rule to find it :

[tex]\lim_{n \to a} \dfrac{f(x)}{g(x)}= \lim_{n \to a} \dfrac{f'(x)}{g'(x)}[/tex]

We have,

a = 1, [tex]f(x)=1+\cos\pi x, \ \ g(x)=\tan^2\pi x[/tex]

[tex]f'(x)=\dfrac{d}{dx}(1+\cos\pi x)\\\\=-\pi \sin \pi x\ .....(1)[/tex]

[tex]g'(x)=\dfrac{d}{dx}(\tan^2\pi x)\\\\=2\tan\pi x\times \sec^2\pi x\times \pi\ .....(2)[/tex]

From equation (1) and (2) :

[tex]\lim_{n \to 1} \dfrac{f(x)}{g(x)}= \lim_{n \to 1} \dfrac{-\pi \sin\pi x}{2\tan \pi x\times \sec^2\pi x \times \pi}\\\\\lim_{n \to 1} \dfrac{-\pi \sin\pi x}{2\tan \pi x\times \sec^2\pi x \times \pi}\\\\=\lim_{n \to 1} \dfrac{-1}{2}\times\cos^3\pi x\\\\=\dfrac{-1}{2}\times \cos^3\pi \\\\=\dfrac{1}{2}[/tex]

So, the value of the given function is 1/2.