Out of 2,000 students in a high school, 800 of them were randomly selected and asked if they want the school’s mascot to change. Out of those surveyed, 250 want it to change.

With a desired confidence level of 99% and a corresponding z*-score of 2.58, what is the margin of error for this sample survey?

Answer:

75 gophers (about)

Step-by-step explanation:

We will use continuous compounding interest formula:

[tex]P(t)=P_0e^{rt}[/tex]

Where

P(t) is final value (at time t)

P_0 is initial value

r is the compounding rate

t is the time period

Given:

P(t) = 78

r is 1.5% or 1.5/100 = 0.015

t is 3

We solve for P_0, what we want, using algebra as shown below:

[tex]P(t)=P_0e^{rt}\\78=P_0e^{(0.015)(3)}\\78=P_0e^{0.045}\\\frac{78}{P_0}=e^{0.045}\\\frac{78}{P_0}=1.0460\\P_0=74.57[/tex]

So, the initial population was 75 gophers.

The 75 gophers were on the ranch at the beginning of the 3 years according to the exponential growth function.

To solve this problem, we can use the following exponential growth function:

P(t) = P_0 * e^(rt)

where:

P(t) is the population at time t

P_0 is the initial population

r is the annual growth rate

t is the time in years

We know that the population after 3 years is 78 gophers, and the annual growth rate is 1.5%. We want to find the initial population, P_0.

So, we can plug in the following values into the exponential growth function:

P(3) = 78 = P_0 * e^(0.015 * 3)

Dividing both sides by e^(0.015 * 3), we get:

P_0 = 78 / e^(0.015 * 3)

Using a calculator, we can evaluate P_0 to be approximately 75.0.

Rounding up to the nearest whole number, we get an initial population of 75 gophers.

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(6x-3)+(7x-7)

Hope I helped :d

Answer:

[tex]4x^{2} +x+2[/tex]

Answer:

Step-by-step explanation:

When (i) is multiplied to itself it = -1

The number (i)is used for imaginary numbers.

Answer:

399

Step-by-step explanation:

The only expression that does not equal 400 is c. 500 - 200.

From the question, we have the following parameters that can be used in our computation:

a. 2 * 200

b. 800/2

c. 500 - 200

d. 300 + 100

Evaluating each of the options, we have the following

a. 2 * 200 = 400

b. 800/2 = 400

c. 500 - 200 = 300

d. 300 + 100 = 400

Hence, the only option that does not equal 400 is c. 500 - 200.

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Question

Which is not equal to 400

a. 2 * 200

b. 800/2

c. 500 - 200

d. 300 + 100

Answer:

(w - 4)(w - 1)(3w - 5)

Step-by-step explanation:

Using Synthetic division to find the quotient on dividing p(w) by (w - 4)

4 | 3   - 20   37   - 20

            12   - 32    20

   -----------------------------

    3     - 8     5        0 ← remainder = 0

quotient = 3w² - 8w + 5 = (3w - 5)(w - 1)

p(w) = (w - 4)(w - 1)(3w - 5)

Answer: 12inches

Step-by-step explanation:

Area of a circle= 113.04square inches

Area of a circle =pir^2

Pi=3.14

R=?

So we are looking for the radius and from there we will get the diameter

Area=pir^2

113.04=3.14×r^2

R^2= 113.04/3.14

R^2=36

R=square root of 36

R= 6

Diameter =2r

Diameter = 2×6

Diameter = 12inches

Answer:

12 inches

Step-by-step explanation:

3.14 × r² = 113.04

r² = 36

r = 6

Diameter = 2r = 12

sqrt(36/100) = +-6/10

You find the square root of the numerator and the denominator.

Answer:

Next frame (6) is C

Frame 7 is D then A

Frame 8 is D

Frame 9 is scalar, neither, matrix, matrix

Step-by-step explanation:

Doing the assignment rn :)

Answer:

C =AB

2 x 2

second part

c11=-1 c12=3 c21=3 c22=-3

third part

d11=0 d12=6 d21=1 d22=-4

Step-by-step explanation:

Correct on edge 2023

Answer:

A. 1256

Step-by-step explanation:

You have to find the radius of the shaded circle

So you can add 12 + 8 = 20

Or you can find the diameter of the two circles. The diameter of the first circle is 12 + 12 = 24 and the second circle is 8 + 8 = 16 + 20 + 40 is the diameter of the shaded circle. Since radius is half of diameter 40 ÷  2  = 20

So now since you know the radius of the shaded circle you can find the area

A = πr²

A = 3.14 x 20²

A = 3.14 x 400

A = 1256

Madi is 4 and Bracken is 20.

In 12 years Madi will be 16 and bracken will be 32 which is twice the age of Madi.

Answer: 900 square meters. 30x30

Step-by-step explanation: a square is the biggest area you can have, so 120 divided by 4 is 30, and then 30 times 30 is 900.

The volume of the pyramid is  167.6 cube inch (approx).

Step-by-step explanation:

Given,

Each length (l) of the base of the pyramid = 8.3 in

Height(h) of the pyramid = 7.3 in

To find the volume of the pyramid.

Formula

Volume of the pyramid = [tex]\frac{1}{3}[/tex]×area of the base×height

Area of the base = l²

Now,

The volume of the pyramid =  [tex]\frac{1}{3}[/tex]×l²×h

=  [tex]\frac{1}{3}[/tex]×8.3²×7.3 cube inch = 167.6 cube inch (approx)

The volume of the pyramid is calculated using the formula for a pyramid's volume, V = (1/3)bh, with a base area of 68.89 in² and height of 7.3 in, which gives a volume of approximately 167.5 in³.

To find the volume of a pyramid with a square base, we can use the formula V = (1/3)bh, where b is the area of the base and h is the height of the pyramid. First, calculate the area of the square base by squaring the side length: b = s² = 8.3 in × 8.3 in = 68.89 in². Next, use this base area in the formula to get the volume: V = (1/3) × 68.89 in² × 7.3 in.

Doing the calculation, we find that V = (1/3) × 68.89 in² × 7.3 in = 167.4757 in³. To round to the nearest tenth, the volume of the pyramid is approximately 167.5 in³.

Answer: The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym

Step-by-step explanation:

Hi, to answer this question we have to write an equation for the cost of Bella's Gym

Jon's Gym: f(x) = 30x + 150

Bella's Gym has a signup fee of $50 and charges $45 dollars per month.

So, we have to multiply the number of months (x) by the cost per month, and add the signup fee cost (50).

Bella's Gym: f(x) = 45x+ 50

Since Jon's signup fee is 150 and Bella's signup fee is 50 , the difference of both costs is 100 (150-50=100), and since Jon's gym has the more expensive fee:

The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym

Final answer:

The statement that the signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym is true.

Jon's Gym charges $30 per month while Bella's Gym charges $45 per month; thus, Jon's Gym charges $15 less, not more.

Explanation:

Comparing the costs of gym memberships at Jon's Gym and Bella's Gym requires analysis of the initial signup fees and the monthly rates. The function for Jon's Gym, f(x) = 30x + 150, indicates a signup fee of $150 and a monthly rate of $30. Bella's Gym has a signup fee of $50 and a monthly rate of $45. To determine the true statement, we compare these numbers directly:

The other statements provided in the question can be dismissed as false:

Therefore, the correct statement is that The signup fee at Jon's Gym is $100 more than the signup fee at Bella's Gym.

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

85%

Step-by-step explanation:

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator. 0.85 × 100100.

= (0.85 × 100) × 1100 = 85100.

Write in percentage notation: 85%

Answer:

85%

Step-by-step explanation:

To convert a number to a percent, you need to multiply it by 100 and add a percent symbol to the end. 0.85*100=85%. Hope this helps!

Answer:

31

Step-by-step explanation:

The range can be found by subtracting the lowest number in the set from the highest, so one can conclude how large the gap in between the two is.

the lowest number her is 68 and the highest is 99

99-68=31

Answer:

31 is the range

Step-by-step explanation:

the range is the number between the highest data and the lowest data. You take your largest number in the data and subtract it from the highest.

Largest 99

smallest 68

99 - 68 = 31

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Answer:

65

Step-by-step explanation:

Use the formula: a²+b²=c²

63²=3969

16²=256

Add them = 4225 = c²

[tex]\sqrt{4225} = \sqrt{c^2}[/tex]

65 = c (or x in this case)

Answer:

17.96

Step-by-step explanation:

To find the hypotenuse we are will have to use Sine, since we are only given the degree and opposite leg. [tex]sin(degree)=\frac{Opposite}{Hypotenuse}[/tex]

[tex]sin(63)=\frac{16}{x}[/tex]

Let's cancel the x on the right side by multiplying both sides by x

sin(63)x = 16

Divide both sides by sin(63)  [Or 0.866, depending on the type of calculator you have]

sin(63)x ÷ sin(63) = 16 ÷ sin(63)

x = 17.9572198

Answer:

27

Step-by-step explanation:

so the right answer is of option D...

Answer:

The answer is D: sin 11pi/6

<3

Step-by-step explanation:

The expression that is equivalent to the given expression is Sin(11π/6).

The given trigonometric expression is: [tex]Sin \frac{7\pi }{6}[/tex]

[tex]Sin\frac{7\pi }{6}[/tex] can be written as [tex]Sin(\pi +\frac{\pi }{6} )[/tex]

The value of [tex]Sin(\pi +\theta)[/tex] is [tex]-Sin\theta[/tex].

So, [tex]Sin(\pi +\frac{\pi }{6} )=-Sin\frac{\pi }{6}[/tex]

We know that

[tex]Sin(2\pi -\theta)=-Sin\theta[/tex]

Or, [tex]-Sin\theta=Sin(2\pi -\theta)[/tex]

So, [tex]-Sin\frac{\pi }{6} =Sin(2\pi -\frac{\pi }{6} )[/tex]

[tex]-Sin\frac{\pi }{6} =Sin\frac{11\pi }{6}[/tex]

So, the required expression is [tex]Sin\frac{11\pi }{6}[/tex].

Therefore, the expression that is equivalent to the given expression is Sin(11π/6).

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The domain of y = cosec(x) includes all real numbers except for the integer multiples of [tex]\pi[/tex], where the sine function equals zero and the cosecant function is undefined.

The domain of a function is the set of all possible input values (usually x values) for which the function is defined. In the case of y = cosec(x), the cosecant function is the reciprocal of the sine function, meaning cosec(x) = 1/sin(x). Since the sine of an angle can be zero and division by zero is undefined, the domain of y = cosec(x) must exclude any x values where sin(x) = 0.

The sine function is zero at integer multiples of [tex]\pi[/tex], so the domain of cosec(x) is all real numbers except for integer multiples of [tex]\pi[/tex]

Answer:

C

Step-by-step explanation:

Given

- 4([tex]\frac{5}{2}[/tex] + [tex]\frac{3}{2}[/tex] x) >  8 ← distribute parenthesis on left side

- 10 - 6x >  8 ( add 10 to both sides )

- 6x >  18

Divide both sides by - 6, reversing the symbol as a result of dividing by a negative quantity

x < - 3 → C

Answer: hamburger $3.00

Coke $1.50

Step-by-step explanation:

2hamburgers & 3cokes= $10.50

4hamburgers & 4cokes= $18.00

Let hamburger represent H

And coke represent C

2H +3C= 10.50.......equation 1

4H+4C= 18.00.......equation 2

2H =10.50 -3C...........equation 3

The 4H can be rewriting as

2(2H) right

So substitute for the 4H

So we have,

2(2H) +4C= 18

Substitute for 2H

2(10.50 -3C) +4C =18

Open the bracket

21 -6C +4C= 18

21-2C= 18

-2C = 18-21

-2C = -3

Minus cancel minus

C= 3/2 = $1.5

Substitute for c in equation 1

2H+3C =10.50

2H+3(1.5)= 10.50

2H+4.5=10.5

2H= 10.5-4.5

2H =6

H= 6/2

H=$3

So

An hamburger cost $3.00

A coke cost $1.50

Answer:

Last one

Step-by-step explanation:

f(x) = Asin(Bx) + C

C = 0

A = 5

B = 2pi/12 = pi/6

f(x) = 5 sin[(pi/6)x]

Answer:

3.5 feet

Step-by-step explanation:

Diameter = 7 feet

Radius = Diameter × [tex]\frac{1}{2}[/tex]

Radius = [tex]\frac{7}{2}[/tex] = 3.5 feet