The group of 23 bully-victims scored an average of 40.1 with a sample standard deviation of 10 on the depression scale. The group of 28 bystanders scored an average of 46.8 with a sample standard deviation of 11 on the same scale. You do not have any presupposed assumptions about whether bully-victims or bystanders will be more depressed, so you formulate the null and alternative hypotheses as:

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Step-by-step explanation:

there is nothing missing. this is a complete proof.

yes, the various steps are correct.

Answer:(2,-3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the numbers are:

If we swap the digits on the largest number, the sum increases by 1 more than x + 2

We are looking for the number x + 4 = ab such that:

By trial method we get the solution:

Since x + 4 = 37, the lowest number is:

Lets verify:

The sum is:

The mean is:

Change the largest number tp 73 and find the sum again:

The sum has increased by 1 more than 35

The overtime rate of pay is K10.25.

The overtime rate of pay can be calculated by multiplying the basic rate pay by the time-and-a-quarter factor. In this case, the basic rate pay is K8.20.

To determine the overtime rate of pay, we need to calculate one-quarter (1/4) of the basic rate pay, and then add that amount to the basic rate pay. One-quarter of K8.20 is calculated as (1/4) * K8.20 = K2.05.

By adding the calculated overtime amount to the basic rate pay, we get the overtime rate of pay: K8.20 + K2.05 = K10.25.

Therefore, the overtime rate of pay is K10.25.

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Answer:

-286

Step-by-step explanation:

45(-6)-16

= -270 - 16

= -286

Step-by-step explanation:

45x - 16

x = -6

45(-6) - 16

-270 - 16

-286

Hope this helps! :)

The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say that number is x,

Quotients of 20 and x will be given as 20/x

20/x - 4 = 0

20/x = 4

x = 20/4 = 5

Hence"The equation associated with the quotient of twenty and a number, decreased by 4, is equal to zero is 20/x - 4 = 0 and that number will be 5".

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Answer:  \(M=\frac{gu^2}{2}-N\)

Work Shown:

\(\frac{u}{\sqrt{2}} = \left(\frac{M+N}{g}\right)^{0.5}\\\\\\\left(\frac{M+N}{g}\right)^{0.5}=\frac{u}{\sqrt{2}}\\\\\\\sqrt{\frac{M+N}{g}}=\frac{u}{\sqrt{2}}\\\\\\\frac{M+N}{g}=\left(\frac{u}{\sqrt{2}}\right)^{2}\\\\\\\frac{M+N}{g}=\frac{u^2}{(\sqrt{2})^2}\\\\\\\frac{M+N}{g}=\frac{u^2}{2}\\\\\\M+N=\frac{gu^2}{2}\\\\\\M=\frac{gu^2}{2}-N\\\\\\\)

Answer:

complementary

Step-by-step explanation:

The total angle is a right angle. Complementary angles are angles that add up to 90 degrees. Right angles are 90 degrees so the answer is complementary.

Answer: Complementary and x=33 degrees

Step-by-step explanation:

We know that together they make a right angle(That's why the square is there and complementary angles are two angles who have the sum of 90 degrees. An right angle is 90 degrees which is why it is complementary. Now, these angles have to be the sum of 90 so:

90-24=66 because we know that one angle is x+24 so we have to subtract 42 from 90(the whole angle) to get 66

66/2=33 which equals x because we have to assume that x is the same and the only way to do that is by dividing it by 2 to get 33 so

X=33

I hope this helps

Hopefully it's brainiest

Answer:

Least common multiple = 150

Step-by-step explanation:

The least common multiple is defined as the smallest multiple that two or more numbers have in common.

We can find the least common multiple by listing the multiples of both numbers:

Multiples of 15:

15, 30, 45, 60, 75, 90, 105, 120, 135, 150

Multiples of 50:

50, 100, 150

Thus, 150 is the least common multiple of 15 and 50.

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

\(\displaystyle P(X=x)=\binom{n}{x}p^xq^{n-x}\\\\P(X=5)=\binom{53}{5}(0.042)^5(1-0.042)^{53-5}\\\\P(X=5)=\frac{53!}{(53-5)!*5!}(0.042)^5(0.958)^{48}\\\\P(X=5)\approx0.0478\)

Part B

\(P(X\leq5)=P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)\\\\P(X\leq5)=\binom{53}{1}(0.042)^1(1-0.042)^{53-1}+\binom{53}{2}(0.042)^2(1-0.042)^{53-2}+\binom{53}{3}(0.042)^3(1-0.042)^{53-3}+\binom{53}{4}(0.042)^4(1-0.042)^{53-4}+\binom{53}{1}(0.042)^5(1-0.042)^{53-5}\\\\P(X\leq5)\approx0.9767\)

Part C

\(\displaystyle P(X\geq 1)=1-P(X=0)\\\\P(X\geq1)=1-(1-0.042)^{53}\\\\P(X\geq1)\approx1-0.1029\\\\P(X\geq1)\approx0.8971\)

Given:

Kelly rows a boat downstream for 54 miles.

Answer:

82 .

Step-by-step explanation:

9x 10 = 90 then 90-8 = 82 that how many spaces are filled .

Answer:

The x intercept is 3

(3,0)

Step-by-step explanation:

3x+y -9 =0

To find the x intercept, set y=9 and solve for x.

3x+0-9=0

3x -9=0

Add 9 to each side

3x-9+9=9

3x =9

Divide by 3

3x/3 = 9/3

x =3

The x intercept is 3

(3,0)

Answer:

.85x-5

Step-by-step explanation:

If you say .15x suppose x is 1

.15*1= .15

Is 15% off 1 = .15 no its .85 thats why in these types of problems we do 100%-15%=85% and then .85*x

After deducting the discounts given to the customer, the current price the customer will pay is $(0.85x - 5).

Given parameters:

discount rate of the shirt, = 15%

original price of the shirt, = $x

additional discount on the sales price = $5

To find:

Note:  the original price of the shirt = 100% of x

The current price of the shirt = original price - given discounts

Convert the percentage to decimal by dividing it by 100

Thus, after the discount the customer will pay $(0.85x - 5)

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It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

To multiply the square roots V7 and V2, we can combine the numbers inside the square roots and simplify the result.

V7 * V2 = V(7 * 2) = V14

Multiplying the numbers under the square roots, we get 7 * 2 = 14. Therefore, the product of V7 and V2 is V14.

This means that the square root of 14 is the result of multiplying V7 and V2. However, it is important to note that V14 cannot be further simplified because 14 does not have any perfect square factors.

In summary, the product of V7 and V2 is V14. It is worth mentioning that when multiplying square roots, we can multiply the numbers inside the square roots and keep the square root symbol intact, unless the numbers inside have perfect square factors that can be simplified further.

It is always a good practice to simplify the result whenever possible, but in this case, V14 is the simplest form of the product of V7 and V2.

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The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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(2x−6)+4(x−3)

Use distributive property:

(2x-6) + 4x -12

Remove the parenthesis:

2x-6 + 4x -12

Combine like terms:

6x -18

Answer:

Step-by-step explanation:

Let w represent the width of the field in yards. Then 4w-9 is the length. The perimeter is given by the formula ...

  P = 2(L+W)

Substituting given values, we have ...

  492 = 2((4w-9) +w)

  246 = 5w -9 . . . . . . . divide by 2

  255 = 5w . . . . . . . . add 9

  51 = w . . . . . . . . . divide by 5

  4w -9 = 4(51) -9 = 195 . . . . the length of the field

The width is 51 yards.

The length is 195 yards.

Answer:

Step-by-step explanation:

Walk through examples of solving systems of equations with elimination. ... 2) Use elimination to solve the following system of equations. − 7 y − 4 x = 1 quad -7y-4x = 1 ... Systems of equations with elimination: 2x-y=14 & -6x+3y=-42 · Systems of ... (2 of 2) · Systems of equations number of solutions: y=3x+1 & 2y+4=6x.

The number of years it would take is approximately equal to 53 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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Answer:

$4.98

Step-by-step explanation:

50*16%=8 (pennies), 50*40%=20 (dimes)

8+5=13 (nickels), 50-(8+20+13)=9 (quarters)

So the money in total is 8*0.01+20*0.1+13*0.05+9*0.25=$4.98

ANSWER: $4.98

Steps for pennies:

1.) 50 * .16 = 8

8 pennies out of 50 coins

2.) 1 cent * 8 = 8 cents

Steps for dimes:

1.) 50 * .40 = 20

20 dimes out of 50 coins

2.) 10 cents * 20 = 200 cents = $2

Steps for nickels:

1.) 8 + 5 = 13

13 nickels out of 50 coins

2.) 5 cents * 13 = 65 cents

Steps for quarters:

1. 8 + 20 + 13 = 41

2. 50 - 41 = 9

3. 9 * .25 = $2.25

FINAL STEP:

8 cents + $2 + 65 cents + $2.25 = $4.98

ANSWER: the bag contained $4.98

*to change a percentage into a decimal move the decimal point 2 places to the left. Ex.) 50% > 50. > .50

50% = .50

The cos x = adjacent side / hypotenuse = -4/5.Hence, the value of cos x is -4/5.

Given that sin x = 3/5 and x is in the second quadrant. We need to find the value of cos x.

To solve this problem, we will use the trigonometric identity.Sin²x + Cos²x = 1.We know sin x, which is in the second quadrant. Let's construct a right-angled triangle to find the value of cos x.

In the second quadrant, the value of sin x is positive, while the value of cos x is negative. This means that the adjacent side of the triangle is negative. In this case, we can label the adjacent side as -4 and the hypotenuse as 5.

Using the Pythagorean theorem, we can solve for the opposite side.

Opposite side = √(hypotenuse² - adjacent side²)

Opposite side = √(5² - (-4)²)

Opposite side = √(25 - 16)

Opposite side = √9

Opposite side = 3

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Answer:

this is a tough one but i know that sometimes it may seem hard but, with the right amount of practice, the hardest equations become the easiest to overcome. (Hint: Use PEMDAS)

Step-by-step explanation:

hope this helps you!

Answer:

I cant answer it i just need to talk to you its mya......

Step-by-step explanation:

Answer:

112.5$

Step-by-step explanation:

\(80 - 60 = 20 \\(20 \div 80)100 = 25\% \\ 75\% \times 150 = 112.5 \)

Answer:

\(=-6w^2-31w-35\)

Step-by-step explanation:

Apply Foil.
\(\left(3w+5\right)\left(-2w-7\right)=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)\)
\(=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)\)
\(=-6w^2-31w-35\)

Solution:

The solution to the given system of equation is the intersection point created with the 2 lines. The solution must satisfy all equations. We can see the intersection. To identify the solution, plot the solution on the graph.

Option C is correct.

~Refer to image for plotted solution~