in a random sample of 400 headache suffers, 85 prefer a particular brand of pain killer. how large a sample is required if we want to be 99% confidence that our estimate of percentage of people with headaches who prefer this particular brand of pain killer is within 2 percentage points? round your answer to the next whole number. n:

Answers

Answer 1

A sample size of 669 is required to be 99% confident that the estimate of the percentage of people with headaches who prefer this particular brand of painkiller is within 2 percentage points.

To determine the sample size required to estimate the percentage of people with headaches who prefer a particular brand of painkiller with a 99% confidence level and a margin of error of 2 percentage points, we can use the formula for sample size calculation for proportions.

The formula is given by:

[tex]n = (Z^2 * p * (1 - p)) / E^2[/tex]

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, for a 99% confidence level, Z = 2.576)

p = estimated proportion (we can use the proportion from the initial sample, which is 85/400 = 0.2125)

E = margin of error (0.02 or 2 percentage points)

Substituting the values into the formula:

[tex]n = (2.576^2 * 0.2125 * (1 - 0.2125)) / 0.02^2[/tex]

Calculating the expression:

n = 668.34

Rounding up to the nearest whole number, the required sample size is 669.

Therefore, a sample size of 669 is required to be 99% confident that the estimate of the percentage of people with headaches who prefer this particular brand of painkiller is within 2 percentage points.

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Related Questions

5 x 100 = ? for easy points

Answers

Answer:

500! Just multiply 5 x 1 then add the remaining 2 zeros :)

Step-by-step explanation:

Thank you!

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

[tex]5 \times 100 \\ = 500[/tex]

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Will mark brainliest for the **CORRECT** answer!

Answers

Answer:

4x + 12x = 320

16x = 320

x = 20

Step-by-step explanation:

This is because the diagram shows 4x + 12x and the total being, 320.

4x + 12x = 16x

and 320/16 = 20

so x = 20

hope this helped :)

If y varies inversely with x, and y= 12 when x = 16, what is the constant of variation k?

Answers

Answer:

k = 192

Step-by-step explanation:

Given that,

y varies inversely with x. It can be written as :

[tex]y=\dfrac{k}{x}[/tex]

Where

k is the constant of variation

Put x = 16 and y = 12 in the above formula.

[tex]k=yx\\\\k=16\times 12\\\\k=192[/tex]

So, the value of the constant of variation is equal to 192.

You know this??????????????

Answers

Answer:

y=x+15

Step-by-step explanation:

Please just give me the answer

Answers

9514 1404 393

Answer:

  8

Step-by-step explanation:

The Pythagorean theorem tells you of the relation ...

  x² + 6² = 10² . . . . . . . . . squares of sides total to the square of hypotenuse

  x² = 100 -36 = 64 . . . . . subtract 6²

  x = √64 = 8 . . . . . . . . . . square root

The length of side x is 8 units.

You are charged $16. 05 after tax for a meal. Assume sales tax is 7%, what was the menu price for the meal

Answers

Answer:

$15

Step-by-step explanation:

107% is the price of $16.05

so, 107% = $16.05

Divide both sides by 107:

1% = $0.15

Multiply both sides by 100:

100% = $15.00

HW: using trigonometric identities, show that the solution of the damped forced oscilla from can be written as: (24) Xlt)=12 Fo/m Sin (wo-w)t sin (wotw)t 7 Wo² - w² 2 2 Hint: ure the identifies for addition and Substraction of angles.

Answers

Hence, the required equation is `(24) Xlt)=12 Fo/m Sin (wo-w)t sin (wotw)t 7 Wo² - w² 2 2`.

Given damped forced oscillation equation is,`m d²x/dt² + c dx/dt + kx = Fo sin(wt)`Using trigonometric identities, we can write solution for the given damped forced oscillation equation as,X(t) = Acos(wt + Φ) + Xpwhere Xp = (Fo/k) sin(wt - δ)Let's substitute X(t) in the given equation to get the required equation.```
X(t) = Acos(wt + Φ) + Xp
=> dX(t)/dt = -Awsin(wt + Φ) + (Fo/k)wcos(wt - δ)
=> d²X(t)/dt² = -Aw²cos(wt + Φ) - (Fo/k)w²sin(wt - δ)


```Now, substitute these values in the given damped forced oscillation equation.`md²X(t)/dt² + cdX(t)/dt + kX(t) = Fo sin(wt)`⇒ `m(-Aw²cos(wt + Φ) - (Fo/k)w²sin(wt - δ)) + c(-Awsin(wt + Φ) + (Fo/k)wcos(wt - δ)) + k(Acos(wt + Φ) + (Fo/k)sin(wt - δ)) = Fo sin(wt)`Grouping the terms of sines and cosines, we get⇒ `{-Aw²mcos(wt + Φ) + Awcsin(wt + Φ) + (Fo/k)w²sin(δ) + kAcos(wt + Φ) + (Fo/k)wcos(δ)} = Fo sin(wt) - c(Fo/k)wcos(wt - δ)`Let's solve these equations for `δ` and `A`.```
-Aw²mcos(wt + Φ) + Awcsin(wt + Φ) + kAcos(wt + Φ) = 0      .....................(1)
(Fo/k)w²sin(δ) + (Fo/k)wcos(δ) = Fo sin(wt) - c(Fo/k)wcos(wt - δ)  .....(2)
```Squaring and adding both equations, we get,`(Aw)²m + kA² = (Fo/k)²`or `A = Fo/(k² - mω²)^(1/2)`From equation (1), we have,`(Aw)²m + kA² = 0`or `δ = tan⁻¹(Aw/k)`Substitute values of A and δ in equation (2), we get,`Xp = (Fo/k) sin(wt - δ) = Fo/(k² - mω²)^(1/2) sin(wt - tan⁻¹(Aw/k))`Therefore, solution for the given damped forced oscillation equation is,`X(t) = Acos(wt + Φ) + Xp`= `12 Fo/m Sin (wo-w)t sin (wotw)t / (wo² - w²)²`

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Tell whether the ordered pair is of liner equations (5,-6) 6x+3y=12 4x+y=14

Answers

Answer:

The ordered pair is one of the solution to the system of equations. See below.

Step-by-step explanation:

To tell if the ordered pair is the solution to the system of equations or not, we can do by substituting the ordered pair in both equations.

(x, y) = (5,-6)

Substitute x = 5 and y = -6 in both equations.

First Equation

6x+3y=12

6(5)+3(-6)=12

30-18=12

12=12

Second Equation

4x+y=14

4(5)-6=14

20-6=14

14=14

Because both equations have same sides which mean that both equations are true for (5,-6). Therefore (5,-6) is part of the equations.

A cylinder containing water is fitted with a piston restrained by an external force that is proportional to cylinder volume squared (P = cvc is constant). Initial conditions are 120°C, 90% quality and a volume of 200 L. A valve on the cylinder is opened and additional water flows into the cylinder until the mass inside has doubled. If at this point the pressure is 300 kPa. What is the final temperature, show your solution

Answers

The final temperature of the cylinder is -148.68 °C .

To find the final temperature

Let the final temperature be T₂.

Let the final volume be V₂.

The mass of water inside the cylinder at initial conditions, m₁ = ρV₁

On opening the valve, the water enters the cylinder until the mass doubles. So the mass of water inside the cylinder after the valve is opened, m₂ = 2ρV₁

The pressure and mass are related by the equation, PV = mRT

On simplifying the equation we get,

P = (m/ρ) * RTSo Pρ = mRT ………… (1)

From equation (1),

P₁ρ₁ = m₁R T₁

Substituting the values in equation (1) for final conditions,

P₂ρ = m₂R T₂

We need to find T₂

So, T₂ = (P₂ρ/m₂) * R = (300000 N/m² * 1000 kg/m³)/[2 * 1000 kg] * 8.314 J/(mol K)

= 124.47 K or -148.68 °C

So, -148.68 °C is the final temperature approximately.

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Diane has $334 in her checking account. She writes a check for $112, makes a deposit of $100, and then writes another check for $98. Find the amount left in her account.
Select one:
a. $444
b. $214
c. $224
d. $86

Answers

Answer:

334 - 112 + 100 - 98

Step-by-step explanation:

in HIJ the measure of J=90 feet, JH=81 feet, HI=9 feet. Find the measure of I to the nearest degree. (Please answer how you got this answer)​

Answers

Answer:

63°

Step-by-step explanation:

1) Examing that right triangle, we can find the value of the angle x starting by using a trig ratio and then its reciprocal. Like this:

sin( x ) = 81/91

x = arcsin (81/91)

x = 62.88 = 63

Notice we have the opposite leg and the hypotenuse, so we started with the sine. And to find the value of the angle the arcsin.

2) So, that angle x is 63° (rounding off to the nearest degree)

Will mark brainliest !!!

Answers

Answer:

27

Step-by-step explanation:

Length * width * height to find the volume so it is 3*3*3=27

I need some brainliest :)
3 by 3 by 3 means that the volume is 27 cubic centimeters
3 cm for width, 3 cm for height, 3 cm for length


The
ratio of votes in favor to votes against in an election is 5 to 4.
How many total votes were cast if there are 2,620 votes in
favor?

Answers

Total votes were casted in election are 4716

Given: The ratio of votes in favor to votes against in an election is 5 to 4. 2,620 votes are in favor.

To find: The total number of votes cast.

Let the number of votes against is 4x.

Given the ratio of votes in favor to votes against is 5 : 4

Then, the number of votes in favor is 5x.

According to the question, 2,620 votes are in favor.

So, 5x = 2,620x = 2,620/5x = 524

The number of votes against = 4x = 4 × 524 = 2096

The total number of votes cast = votes in favor + votes against= 2620 + 2096= 4716

Therefore, there were 4716 votes cast in the

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) Which relation is a function?
A) y2- x = 8
B) y2 + 3xy = 9y
C) y2 + x = 8x - 8
D) y =3/y- x2

Answers

Answer:

It is A

Step-by-step explanation:

If the y2 get subtracted by the 8 then itll be 8

Select all that apply. Which numbers are not perfect squares? 36 14 20 16 25 18 24

Answers

Answer:

20, 18, 14, and 24 are all not perfect squares

Step-by-step explanation:

A polygon has the following coordinates: A(-5,2), B(-2,-2), C(2,3), D(6,3), E(6,-5), F(-5,-5). Find the length of EF.
A.
12 units
B.
9 units
C.
11 units
D.
10 units

Answers

Answer:

C

Step-by-step explanation:

got it right on edg

how do you determine if a relation is a function ​

Answers

Answer:

Identify the output values. If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

Step-by-step explanation:

Holly Krech is planning for her retirement, so she is setting up a payout annuity with her bank. She wishes to receive a payout of $1,800 per month for twenty years. She must deposit $218,437.048 and the total amount that Holly will receive from her payout annuity will be $432,000.

A. How large a monthly payment must Holly Krech make if she saves for her payout annuity with an ordinary annuity, which she sets up thirty years before her retirement?

B. how large a monthly payment must she make if she sets the ordinary annuity up twenty years before her retirement?

Answers

A. To save for her payout annuity with an ordinary annuity set up thirty years before her retirement, Holly Krech must make a monthly payment of $175.97.

B. If she sets up the ordinary annuity twenty years before her retirement, Holly Krech must make a monthly payment of $432.00.

What is the monthly payment required for an ordinary annuity set up 30 years before retirement?

To calculate the monthly payment for an ordinary annuity set up thirty years before retirement, we can use the formula for the present value of an ordinary annuity. Given the deposit amount of $218,437.048 and the total amount received from the annuity of $432,000, and solving for the monthly payment, we find that Holly must make a monthly payment of $175.97.

How much must be paid monthly for an ordinary annuity set up 20 years before retirement?

For an ordinary annuity set up twenty years before retirement, we use the same formula for present value. With the deposit amount and total amount received unchanged, we solve for the monthly payment, which comes out to be $432.00.

It's important to note that the monthly payment increases when the annuity is set up closer to the retirement date. This is due to the shorter time period available for saving, resulting in a higher required contribution to reach the desired payout amount.

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Which table represents a quadratic function? No downloadable links or files, I will mark brainliest.

It is not the 3rd option.

Answers

Answer:

where is the table lol

6. Brandon and Charlotte Snifflesworth are visiting three of Americas top tourist attractions. The Snifflesworths

live close to Disney World in Orlando, Florida. They decided to start their trip at Disney World before traveling to

San Francisco, California to see the Golden Gate Bridge and then to Minneapolis, Minnesota to go shopping at the

Mall of America. The bearing from Disney to the Golden Gate Bridge is North 65° West. The bearing from the

Golden Gate Bridge to the Mall of America is North 80° East. The bearing from Disney to the Mall of America is

North 30° West and the distance traveled is 1,320 miles. Find all missing interior angles and distances created from

their triangular trip to America's top tourist attractions. Also find the bearing from the Mall of America to

Disneyland.

Answers

Answer:

The distance from Disney to the Golden Gate Bridge is 2,162.56 miles

The distance from Mall of America to The Golden Gate Bridge  is 1,320 miles

The interior angle at The Golden Gate Bridge is 35°

The interior angle at Mall of America is 110°

The interior angle at Disney is 35°

The direction from Mall of America to Disney is South 30° East

Step-by-step explanation:

The bearing from Disney to the Golden Gate Bridge = North 65° West

The bearing from the Golden Gate Bridge to the Mall of America = North 80° East

The bearing from Disney to the Mall of America = North 30° West

The distance from Disney to the Mall of America = 1,320 miles

Let 'A', 'B', and 'C' represent the interior angles at Disney, The Golden Gate bridge and Mall of America respectively

From the drawing of the triangular trip, we find that the interior angle at C = The sum angles complementary to the bearings at B and at C

Therefore, the interior angle at C = (90° - 65°) + (90° - 80°) = 35°

The interior angle at B = The bearing of C from B - The bearing of A from B

∴ The interior angle at B = 65° - 30° = 35°

B = 35°

∠C = 35° and ∠B = 35°, therefore, the triangle is an isosceles triangle

The interior angle at A = 180° - (∠B + ∠A) = 180° - (35° + 35°) =110°

CA = AB = 1.320

By sine rule, a = sin(110) × 1320/sin(35) ≈ 2,162.56  miles

a = CB = 2,162.56 miles

Therefore, we have;

The distance from Disney to the Golden Gate Bridge = 2,162.56 miles

The distance from Mall of America to The Golden Gate Bridge  = 1,320 miles

The interior angle at The Golden Gate Bridge = 35°

The interior angle at Mall of America = 110°

The interior angle at Disney = 35°

The magnitude of the bearing of Mall of America to Disney = The magnitude of the alternate angle to the bearing of Disney to Mall of America = 30°

∴ The direction from Mall of America to Disney = South 30° East

I’m not sure how to do this someone explain please

Answers

Pictures listed in order... from A-C

Please answer if your know

Answers

Answer:

52 pounds

Step-by-step explanation:

52 pounds

Given the following function, find the integral s voix by substitution : integral 3 (x-2 ] 3 +4 dx by substitution sinhy=3(x-2)

Answers

The simplified expression of integral 3 (x-2 ] 3 +4 dx is (A/3) + 12tanh[tex](sinh^{(-1)}[/tex](3(x-2))) + B

How to find the integral ∫3(x-2)³+4 dx using the substitution sinh(y) = 3(x-2)?

To find the integral ∫3(x-2)³+4 dx using the substitution sinh(y) = 3(x-2), we can start by differentiating both sides of the equation with respect to x to find the differential of y:

d(sinh(y))/dx = d(3(x-2))/dx

cosh(y) * dy/dx = 3

dy/dx = 3/cosh(y)

Now, let's solve for dx in terms of dy:

dx = (cosh(y)/3) dy

Substituting this value of dx in the integral:

∫3(x-2)³+4 dx = ∫(3/cosh(y)) * (3(x-2)³+4) dy

Now, we need to substitute the expression for x in terms of y using the given substitution:

3(x-2) = sinh(y)

x - 2 = sinh(y)/3

x = sinh(y)/3 + 2

Substituting this in the integral:

∫(3/cosh(y)) * (3((sinh(y)/3 + 2) - 2)³+4) dy

Simplifying:

∫(3/cosh(y)) * (sinh(y)³+4) dy

To integrate the expression ∫(3/cosh(y)) * (sinh(y)³+4) dy, we can simplify it first:

∫(3/cosh(y)) * (sinh(y)³+4) dy = 3∫(sinh(y)³/cosh(y)) dy + 12∫(1/cosh(y)) dy

To integrate the first term, we can use the substitution u = cosh(y), which implies du = sinh(y) dy:

3∫(sinh(y)³/cosh(y)) dy = 3∫(u³/u) du = 3∫(u²) du = u³/3 + C

For the second term, we can directly integrate 1/cosh(y) using the identity sech²(y) = 1/cosh²(y):

12∫(1/cosh(y)) dy = 12∫sech²(y) dy = 12tanh(y) + D

Now, substituting back y = [tex]sinh^{(-1)}(3(x-2))[/tex]:

u = cosh(y) = cosh[tex](sinh^{(-1)}(3(x-2))[/tex]) = √(3(x-2)² + 1)

Thus, the integral becomes:

∫(3/cosh(y)) * (sinh(y)³+4) dy = (u³/3 + C) + 12tanh(y) + D

Substituting back u = √(3(x-2)² + 1):

= (√(3(x-2)² + 1)³/3 + C) + 12tanh(y) + D

= (√(3(x-2)² + 1)³ + 3C)/3 + 12tanh(y) + D

= (√(3(x-2)² + 1)³ + 3C)/3 + 12tanh[tex](sinh^{(-1)}(3(x-2)))[/tex] + D

To simplify the expression and combine constants, let's assume (√(3(x-2)² + 1)³ + 3C)/3 = A, and 12D = B.

The simplified expression becomes:

(A/3) + 12tanh[tex](sinh^{(-1)}[/tex](3(x-2))) + B

Since [tex]sinh^{(-1)}(3(x-2))[/tex] is the inverse hyperbolic sine function, we can simplify it using the identity sinh[tex](sinh^{(-1)}(x))[/tex] = x:

(A/3) + 12tanh(3(x-2)) + B

This is the simplified form of the integral ∫(3/cosh(y)) * (sinh(y)³+4) dy after combining constants and simplifying the expression.

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At a particular restaurant, each mini hotdog has 100 calories and each slider has 200 calories. A combination meal with mini hotdogs and sliders is shown to have 1200 total calories and 4 times as many mini hotdogs as there are sliders. Graphically solve a system of equations in order to determine the number of mini hotdogs in the combination meal, x,x, and the number of sliders in the combination meal, yy.

Answers

Answer:

The number of sliders is 2 and the number of hot dogs is 8.

Step-by-step explanation:

Since at a particular restaurant, each mini hotdog has 100 calories and each slider has 200 calories, and a combination meal with mini hotdogs and sliders is shown to have 1200 total calories and 4 times as many mini hotdogs as there are sliders, in order to determine the number of mini hotdogs in the combination meal, X, and the number of sliders in the combination meal, Y, the following calculation must be performed:

2X + Y = 1200

800 + 400 = 1200

800/100 = 8

400/200 = 2

Thus, the number of sliders is 2 and the number of hot dogs is 8.

help please! :)) ill do whatever it is that gets you guys points!!! please help!

Answers

Answer:

7.5 in.

Step-by-step explanation:

Answer:

7.5 in

Step-by-step explanation:

using pythagorean theorem

Hyp²= Opp² + Adj ²

where 9= hyp

5= adj

and x = opp

9²=x²+5²

81=x² + 25

collect like terms

81-25=X²

56=X²

since we're looking for X and not X²

we square root both sides

√x²=√56

x=7.483 approximately 7.5

The sixth grade art students are making a mosaic using tiles in the shape of triangles.Each tile Hans leg measures of 7cm and 4cm. If there are 84 tiles in the mosaic,what I sent the area of the mosaic

Answers

Answer:

1,176 square centimeters

Step-by-step explanation:

The computation of the area of the mosaic is  shown below:

As we know that

The Area of the triangle is

= 1 ÷ 2 × base × height

= 1 ÷ 2 × 7 × 4

= 14

Now 1 tile would be 14 square centimeters

And, there are 84 tiles in the mosaic

So, the total area is

= 84 × 14

= 1,176 square centimeters

How many solutions does the system have?
You can use the interactive graph below to find the answer.
\begin{cases} x+2y=2 \\\\ 2x+4y=-8 \end{cases}









x+2y=2
2x+4y=−8


Choose 1 answer:
Choose 1 answer:

(Choice A)
A
Exactly one solution

(Choice B)
B
No solutions

(Choice C)
C
Infinitely many solutions







How many solutions does the system have? ⎧


x+2y=2
2x+4y=−8

Answers

Answer:

No solution

Step-by-step explanation:

The easiest approach here is to divide the second equation by 2:  x + 2y = -4.

Comparing the first equation with this result, we see that the the two lines never intersect, and thus that there is no solution.

A submarine began at sea level and descended toward the ocean floor at a rate of −0.015 km per minute. Its final depth was −0.3675 km. Estimate how long it took the submarine to reach its final depth by rounding the dividend and divisor to the nearest hundredth.



Estimate of the quotient:

Answers

Answer:

Around 24.5 minutes

Step-by-step explanation:

Answer:

Estimate of the dividend: -0.37

Estimate of the divisor: -0.02

Estimate of the quotient: 18.5

Step-by-step explanation:

I did the test and it was right and I dubble checked it to

The distance between bases on a baseball field is 27.43 meters. Joe has jogged from one base to the next 4.5 times. How far has he jogged?
a. 12.48 meters
b. 40.72 meters
c. 123.43 meters
d. 123.45 meters

Answers

Number of meters Joe jogged is 123.43 meters. Therefore, the correct answer is option C.

Given that, the distance between bases on a baseball field is 27.43 meters.

Joe has jogged from one base to the next 4.5 times.

Number of meters Joe jogged = Distance between bases on a baseball field × Number of times Joe jogged

= 27.43 × 4.5

= 123.43 meters

Therefore, the correct answer is option C.

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solve the system of differential equations. = 2x 3y 1 = -x - 2y 4

Answers

The given system of differential equations is:

dx/dt = 2x + 3y

dy/dt = -x - 2y + 4

To solve this system, we can use various methods such as substitution, elimination, or matrix methods. Let's use the matrix method.

First, we can rewrite the system in matrix form:

d/dt [x y] = [2 3] [x] + [1]

[-1 -2] [y] + [4]

Next, we define A as the coefficient matrix [2 3; -1 -2], X as the column matrix [x; y], and B as the column matrix [1; 4]. The system can now be written as:

dX/dt = AX + B

To find the solution, we can calculate the eigenvalues and eigenvectors of matrix A. From the eigenvalues, we determine the corresponding eigenvectors and use them to construct the general solution. However, without the specific values of matrix A, it is not possible to provide the exact solution.

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cani get help with thisQ4. 8 Points Given the immediate predecessors and a, m, b for each activity in the table below, compute: a. t, and V for each activity b. ES, EF, LS, and LF for each activity. c. Te and Vp for the pro Read the paragraph.Tabitha sat on the beach and stared at the waves crashing against the sand. Without a doubt, this would be a challenging ride. The towering green waves reminded her of an angry sea creature.Pick the best sentence to finish the paragraph.She had been surfing for years, but these were the biggest waves she had ever seen.See had been surfing for years, but these waves were far larger than anything she had ever seen.She had been surfing for years, but these waves were the scariest ones she had ever seen.She had been surfing for years, but these waves were the most monstrous she had ever seen. 40 POINTS !! 40 POINTS !!PLEASE HELP , DONT SKIP !NO LINKS OR FILES. I give up.. please dont just answer for points PLEASEE HELP MEEE if u get it right then i swear i owe you a brainliest :P The details in persuasive writing serve asthat will support your main point.A. subheadingsB. evidenceC. thesis statementsD. description unidad de 1000 a Cuntos centmetros equivale Which is not true about FP Growth Tree algorithm from following statementsA.it mines frequent itemsets without candidate generationB. There are chances that FP Tree may not fit in the memoryC. FP Tree very expensive to buildD . It extends the original database to build FP tree The composition of the sun is best described as..A / liquid nitrogen and solid magnesium.B / molten rock,primarily iron.C / dense and composed of hot gases .D / lightweight particles of dust . Translate the sentence into an inequality.Twice c is at most 19. I1112211 / 22=>Which of the following hydrogen ion concentrations represents a solution with acidicproperties?A?1 x 10-8 M.?1 x 10-2 MC1 x 10-11 MD1x 10-13 MActivity IndexA NO LINKSS Which factor promoted the development of new forms of entertainment such as dance halls, carnival rides, and professional sports?A. unemployed urban workers needed ways to spend their time, so the would not turn to crime.B. busy city people no longer had time for older, more time-consuming forms of entertainment C. the new middle class had leisure time and extra moneyD. new technologies allowed people all over the world to view entertainment everywhereNOOO LINKS What are the coordinates of the vertex of the parabola described by the equation below? y = -5(x + 2)^2 + 7 A. (2, -7) O B. (-7,-2) O C. (7,2) O D. (-2,7) find the radius of the congruent circles. Thanks and hope you have a good rest of your day!! A vertical column along the left or right edge of a page containing text and/or graphic elements is called the:_________ who lives in a pineapple under the sea? Help me on this question pls!!!!! A 6 kilogram concrete block is dropped from the top of a tall building. The block has fallen a distance of 55 meters and has a speed of 30 meters per second when it hits the ground. a. At the instant the block was released, what was its gravitational potential energy?b. Calculate the kinetic energy of the block at the point of impact. c. How much mechanical energy was "lost" by the block as it fell?d. Explain what happened to the mechanical energy that was "lost" by the block Each day Mrs. Yoder assigns 15 addition and 12 multiplication problems as homework. What is the total number of addition and multiplication problems assigned after 5 days? What is the distance between two points located at (6, 2) and (6, 8) on a coordinate plane?A 4 unitsB 6 unitsC 10 unitsD 12 units The sensory system that controls and monitors the positions of various parts of the body is called the ________.A. gustatoryB. olfactoryC. kinestheticD. Vestibular