Select the correct answer. jackson is conducting an experiment for his physics class. he attaches a weight to the bottom of a metal spring. he then pulls the weight down so that it is a distance of 6 inches from its equilibrium position. jackson then releases the weight and finds that it takes 4 seconds for the spring to complete one oscillation. which function best models the position of the weight?

Answers

Answer 1

The function that best models the position of the weight is s(t) = 6cos (pi/2*t).

How to illustrate the function?

From the information, we know that the spring is going to have a sin or a cos equation.

We have that the maximum distance of the spring is 6 inches and it is achieved at t=0. We have that the function is of the form 6sin(at+B).

We have that the period is 4 minutes and therefore that the time component in the equation needs to make a period (2pi) in 4 minutes.

In general, a=2pi/T where a is this coefficient, T is the period. Finally, for B, since sin(pi/2)=1, we have that B=pi/2 because when t=0, we have that 6sin(B)=6.

Substituting, we have s(t) = 6cos (pi/2*t).

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Related Questions

which fraction is greater 3/6 or 6/10

Answers

Answer:

6/10

Step-by-step explanation:

3/6 = 0.5

6/10 = 0.6

0.6>0.5

Then

6/10 is greater than 3/6

Answer: 3/6 = 0.5 , 6/10 = 0.6

Therefore 6/10 is greater then 3/6
(6/3 > 6/10)

I’m gonna ask this question again can someone help me solve this and leave in terms of pi

Answers

The equation of the circumference of a circle in terms of [tex]\pi[/tex] is [tex]2\pi r[/tex] or [tex]\pi d[/tex].

The circumference for a circle with diameter 10 is [tex]10\pi[/tex].

The circumference for a circle with diameter 19 is [tex]19\pi[/tex].

The circumference for a circle with diameter 30 is [tex]30\pi[/tex].

The circumference for a circle with diameter 16 is [tex]16\pi[/tex].

Relatively easy, right?

The equation of the area of a circle in terms of [tex]\pi[/tex] is [tex]\pi r^2[/tex].

The area of a circle with radius 5 is [tex]25\pi[/tex].

The area of a circle with radius 9.5 is [tex]90.25\pi[/tex].

The area of a circle with radius 15 is [tex]225\pi[/tex].

The area of a circle with radius 8 is [tex]64\pi[/tex].

Hope this helped!

(By the way, I don't know why you're using hard formulas for trying to find the radius or diameter. The diameter is simply twice the radius, and the radius is simply half the diameter.)

Answer:

Circumference = 10[tex]\pi[/tex], 19[tex]\pi[/tex], 30[tex]\pi[/tex], 16[tex]\pi[/tex]

Area = 25[tex]\pi[/tex], 90.25[tex]\pi[/tex], 225[tex]\pi[/tex], 64[tex]\pi[/tex]

Step-by-step explanation:

For the first row we have the radius which is 5, the diameter is 10. The formula for circumference is 2[tex]\pi[/tex]r. So for this one its gonna be 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]

radius = 5

diameter = 10

circumference = 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]5^{2}[/tex] or 25[tex]\pi[/tex]

for the second row

radius = 9.5

diameter = 19

circumference = 2[tex]\pi[/tex]9.5 or 19[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]9.5^{2}[/tex] or 90.25[tex]\pi[/tex]

for the third row

radius = 15

diameter = 30

circumference = 2[tex]\pi[/tex]15 or 30[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]15^{2}[/tex] or 225[tex]\pi[/tex]

for the fourth row

radius = 8

diameter = 16

circumference = 2[tex]\pi[/tex]8 or 16[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]8^{2}[/tex] or 64[tex]\pi[/tex]

pls help ill give brainliest

a=
x=

Answers

Answer:

a = 12

x = 5.714

Step-by-step explanation:

sf = 15 / 9

20 / (15 / 9) = 12

a = 12

sf = 21 / 6

20 / (21 / 6)

x = 5.714

If you want to connect your home network to the internet, you will need a ________ in addition to a modem.

Answers

Answer:

landline

hshdjdh

dbbdhdhdh

bdbdhdhdhe

Answer:

Router

Step-by-step explanation:

Hope this helps

Rearrange the formula to highlight the height

Answers

Answer:

[tex]h = \frac{2A}{b+c}[/tex]

Step-by-step explanation:

Original Equation:

[tex]A = \frac{1}{2} (b+c)h[/tex]

Divide both sides by height

[tex]\frac{A}{h} = \frac{1}{2}(b+c)[/tex]

Raise both sides to the exponent -1 :

[tex](\frac{A}{h})^{-1} = (\frac{1}{2}(b+c))^{-1}[/tex]

Rewrite using the definition of a negative exponent: [tex](\frac{a}{b})^{-x} = (\frac{b}{a})^{x}[/tex]

[tex]\frac{h}{A} = \frac{1}{\frac{1}{2}(b+c)}\\[/tex]

Multiply 1/2 by (b+c)

[tex]\frac{h}{A} = \frac{1}{\frac{b+c}{2}}\\[/tex]

Keep, change, flip

[tex]\frac{h}{A} = \frac{1}{1} * \frac{2}{b+c} = \frac{2}{b+c}[/tex]

Multiply both sides by A

[tex]h = \frac{2A}{b+c}[/tex]

Also I forgot to mention but the exponent (-1) can be ignored after you flip it, since: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex], but since in our case the exponent is 1, and [tex]a^1 = a[/tex], so there's really no need to write out the distribution part, since we just get the same fraction, after flipping it.

Simplify each exponential expression using the properties of exponents and match it to the correct answer.

Answers

The match of solutions with the exponential expressions is

1) [tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}=2[/tex]

2) [tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)=1/2[/tex]

3) [tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} =2[/tex]

4) [tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}=1[/tex]

What are properties of exponents?

The base will be multiplied by itself a certain number of times, as indicated by the exponent (also known as a power or degree).

What are the formulae/ properties for exponents?

Formulae for solving exponents are referred to as exponents formulas. The exponent of a number is written as [tex]x^{n}[/tex], which means that x has been multiplied by itself n times.

[tex]x^{n}(x^{m})=x^{n+m} \\\frac{x^{n} }{x^{m} }=x^{n-m} \\(x^{n} )^{m} =x^{nm} \\((x)(y))^{n}=x^{n}(y^{n} \\x^{0}=1[/tex]

1) the solution of the first expression will be

[tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}[/tex]

[tex](2^3) (3^{-6} ) (5^2) (3^4) / (3^{-2}) (10^2)= (2.2^2.5^2) (3^{-6}.3^4) / (3{^-2}) (10^2)= (2)(10^2) (3^{-2}) / (3^{-2}) (10^2)\\=2[/tex]

2)The solution of the second expression will be

[tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)[/tex]

Any  number with power zero is 1.

So,

[tex](3^3) (1^2) (3^{-3}) (2^{-3}) (2^2)= (2^{(-3+2)})=2^-1\\= 1/2[/tex]

3) The solution of third expression will be

[tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} \\= \frac{(12^7) (2^{-3}) (5^{-3}) (5^2)}{(12^7) (5^{-1}) (2^{-4})} =\frac{(2^-3) (5^{(-3+2)})}{(5^{-1}) (2^{-4})} = \frac{(2^{-3}) (5^{-1})}{(5^{-1}) (2^{-}4)} = \frac{1}{(2^{-1})} = 2[/tex]

4) The solution to the forth expression will be

[tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}\\=2^{0}\\ =1[/tex]

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Answer:

The person above litteraly gave you the answer just reread the first equations and then you will figure it out

Step-by-step explanation:

Write the event as set of outcomes. when we roll two dice, the total showing is eight.

Answers

The numbers below show the number on each dice.
3 5
5 3
4 4
2 6
6 2
Hope this helps, would appreciate brainliest

By selling 20 oranges for#1.35 a trader makes a profit of 8% what is the percentage gain or loss if he sells the same 20 oranges for#1.10?

Answers

Answer:

  12% loss

Step-by-step explanation:

The selling price is the sum of the cost price and the markup. Here, the markup (profit) is expressed as a percentage of the cost price.

Cost price

The relation between selling price and cost price is ...

  selling price = cost price + cost price × markup fraction

  selling price = cost price × (1 + markup fraction)

Then the original cost price is ...

  cost price = (selling price) / (1 + markup fraction)

  cost price = #1.35 / (1 +8%) = #1.25

Profit

After the change in selling price, we can find the markup fraction (profit rate) to be ...

  1 + markup fraction = (selling price)/(cost price)

  markup fraction = (selling price)/(cost price) -1

  markup fraction = #1.10/1.25 -1 = 0.88 -1 = -0.12

The trader has a 12% loss when selling the oranges at #1.10.

 

Draw at least six different sized rectangles that have an area of 64 square units then find the perimeter of each rectangle.

Answers

Six different sized rectangles that have an area of 64 square units:

1) 64 units x 1 unit
2) 32 units x 2 units

3) 16 units x 4 units

4) 40 units x 1.4 units

5) 20 units x 3.2 unit

6) 10 units x 6.4 units

For given question,

Let l be the length of the rectangle and w be the width of the rectangle.

We know that, the area of a rectangle is equal to

A = l × w

Here, A = 64 square units

So, we get an equation

l × w = 64                     ...............................(1)

let's assume different values of l to get the different values of w.

Case 1) For l = 64 units

substitute in the equation 1

⇒ 64 × w = 64

⇒ w = 64/64

⇒ w = 1 units

The dimensions of the rectangle are 64 units x 1 unit

See the draw in the attached figure 1

Case 2) For l = 32 units

substitute in the equation 1

⇒ 32 × w = 64

⇒ w = 64/32

⇒ w = 2 units

The dimensions of the rectangle are 32 units x 2 unit

See the draw in the attached figure 2

Case 3) For l = 16 units

substitute in the equation 1

⇒ 16 × w = 64

⇒ w = 64/16

⇒ w = 4 units

The dimensions of the rectangle are 16 units x 4 unit

See the draw in the attached figure 3

Case 4) For l = 40 units

substitute in the equation 1

⇒ 40 × w = 64

⇒ w = 64/40

⇒ w = 1.4 units

The dimensions of the rectangle are 40 units x 1.4 unit

See the draw in the attached figure 4

Case 5) For l = 20 units

substitute in the equation 1

⇒ 20 × w = 64

⇒ w = 64/20

⇒ w = 3.2 units

The dimensions of the rectangle are 20 units x 3.2 unit

See the draw in the attached figure 5

Case 6) For l = 10 units

substitute in the equation 1

⇒ 10 × w = 64

⇒ w = 64/10

⇒ w = 6.4 units

The dimensions of the rectangle are 10 units x 6.4 unit

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Every year a man is paid $500 more than the previous year. If he receives $17800 over four years, what was he paid in the first year

Answers

The amount paid to the man in the first year given the total he received in four years is $3,700.

Equation

Amount paid in the first year = xAmount paid in the second year = (x + 500)Amount paid in the third year = x + 500 + 500

= (x + 1000)

Amount paid in the fourth year = x + 500 + 500 + 500

= (x + 1500)

Total payment = $17800

Total payment = first year + second year + third year + fourth year

x + (x + 500) + (x + 1000) + (x + 1500) = 17,800

open parenthesis

x + x + 500 + x + 1000 + x + 1500 = 17800

collect like terms

4x + 3000 = 17,800

4x = 17,800 - 3000

4x = 14,800

divide both sides by 4

x = 14,800/4

x = $3,700

Therefore, $3,700 was paid to the man in the first year.

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On a certain day, the temperature in Bismarck, North Dakota, was below 4∘F. Write an inequality to describe the possible temperatures. Let t represent the temperature.

Answers

The inequality to describe the possible temperature in Bismarck, North Dakota given that t represent temperature is t < 4°F

Inequality

The inequality signs are;

Greater than >Less than <Equal to =Greater than or equal to ≥Less than or equal to ≤

Let

Temperature = t

Temperature in Bismarck, North Dakota, was below 4∘F.

Below in inequality sign means less than <

So

t < 4°F in Bismarck, North Dakota

This means, temperature in Bismarck, North Dakota is less than 4°F

Therefore, t < 4°F is the inequality to represent temperature in Bismarck, North Dakota.

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EEF has vertices D(1, 3), E(2, -4), and F(-3, 1). What are the vertices T<4, 1> (DEF).

Answers

The vertices T<4, 1> (DEF) are D' = (5, 4), E' = (6, -3) and F' = (1, 2)

How to determine the vertices?

The vertices of the triangle are given as:

D(1, 3), E(2, -4), and F(-3, 1).

The transformation represented by T<4, 1> (DEF) is:

(x,y) = (x + 4, y + 1)

So, we have;

D' = (1 + 4, 3 + 1)

D' = (5, 4)

E' = (2 + 4, -4 + 1)

E' = (6, -3)

F' = (-3 + 4, 1 + 1)

F' = (1, 2)

Hence, the vertices T<4, 1> (DEF) are D' = (5, 4), E' = (6, -3) and F' = (1, 2)

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Which graph represents the equation y2 = –4x?
On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 1, 0), and a directrix at x = 1.
On a coordinate plane, a parabola opens down. It has a vertex at (0, 0), a focus at (0, negative 1), and a directrix at y = 1.
On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 4, 0), and a directrix at x = 4.
On a coordinate plane, a parabola opens down. It has a vertex at (0, 0), a focus at (0, negative 4), and a directrix at y = 4.

Answers

Answer:

its A

Step-by-step explanation:

Answer: The first one (A)

Step-by-step explanation:

Graph f(x) = 2x - 3 on a coordinate plane.
Can you explain what you are going to do in order to graph this equation?
What do you expect the graph to look like?

Answers

Answer:

Create a table.

Plug values into the equation to complete the table.

Use the table to plot points on the graph.

Draw lines through the points on your graph.

The graph should look linear because there is an x that doesn't have a power greater than or less than 1.

As people exited a movie theater, they were informally surveyed about whether they enjoyed the movie or not.

What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent.

Answers

A=41% B=3% hope this helps

Given that and are supplementary angles and that , explain how to find the measure of the complement of .

Answers

The measure of the complement  is 25°.

What is supplementary and complementary angles?

If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

Given that, [tex]A_{1}[/tex] = 115°

sum of two angles  [tex]A_{1}+A_{2} = 180[/tex]°

                                  [tex]A_{2} = 180- A_{1}[/tex]

                                  [tex]A_{2} = 180- 115[/tex]

                                  [tex]A_{2} = 65[/tex]°

Since,  [tex]A_{1}[/tex] and  [tex]A_{2}[/tex] are supplementary angles.

Now,

Complementary angles add to 90, so the complement of [tex]A_{2}[/tex]  is 90 - [tex]A_{2}[/tex] .

Then,

90-65

= 25°

Hence,  The measure of the complement  is 25°.

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Please answer correctly

Answers

Answer:

Option (1)

Step-by-step explanation:

We need a recursive formula.

Eliminate option 3.

The common ratio is 2.

Eliminate options 2 and 4.

So, the answer is option 1.

The chart below shows conversion between kilometers and miles.

Conversion Chart
Kilometer
Miles
2
1.2
7
4.2
20
?
30
18

What is the missing value in the table?

Answers

The missing value in the table is 12.4

Conversion between Units

From the question, we are to determine the missing value in the table

From the given information,

The chart shows conversion between kilometers and miles

The given table is

Kilometers           Miles

2                            1.2

7                            4.2

20                          ?

30                          18

NOTE: 1 kilometer ≈ 0.62 miles

Then, 20 kilometer ≈ 20×0.62 miles

20 kilometer ≈ 12.4 miles

Hence, the missing value in the table is 12.4

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Use the ratio test to determine whether the series is convergent or divergent. 2 4/2^2 8/3^2 16/4^2 ......

Answers

I assume the given series is

[tex]\displaystyle 2 + \frac4{2^2} + \frac8{3^2} + \frac{16}{4^2} + \cdots = \frac{2^1}{1^2} + \frac{2^2}{2^2} + \frac{2^3}{3^2} + \frac{2^4}{4^2} + \cdots = \sum_{n=1}^\infty \frac{2^n}{n^2}[/tex]

By the ratio test, the series diverges, since

[tex]\displaystyle \lim_{n\to\infty} \left|\frac{2^{n+1}}{(n+1)^2} \cdot \frac{n^2}{2^n}\right| = 2 \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = 2 > 1[/tex]

The histogram shows the distribution of minting year for a sample of
100
100100 nickels at a bank.
a histogram. the x-axis is labeled minting year and numbered from 1900 to 2020. the y-axis is labeled nickels and numbered from 0 to 25. there are 12 buckets of equal width. the mids and counts for the buckets are mid: 1905, count: 1. mid: 1915, count: 0. mid: 1925, count: 0. mid: 1935, count: 0. mid: 1945, count: 1. mid: 1955, count: 1. mid: 1965, count: 11. mid: 1975, count: 17. mid: 1985, count: 15. mid: 1995, count: 20. mid: 2005, count: 24. mid: 2015, count: 10.
0
0
5
5
10
10
15
15
20
20
25
25
1900
19001900
1910
19101910
1920
19201920
1930
19301930
1940
19401940
1950
19501950
1960
19601960
1970
19701970
1980
19801980
1990
19901990
2000
20002000
2010
20102010
2020
20202020nickelsminting year
describe the distribution of minting year.
shape: the distribution of minting year is

.
center: the median is somewhere between

years.
spread: the range is approximately

years.
outliers: there are

potential outliers.

Answers

All the parts of the questions about the given histogram have been answered below.

What is a histogram?A histogram is a graph that depicts the frequency of numerical data using rectangles. The vertical axis of a rectangle represents the distribution frequency of a variable (the amount, or how often that variable appears).

(A) The distribution of minting year:

According to the histogram, the distribution of minting years is 1900-1910 and 1940-2020.

(B) The median:

Add the two middle numbers together and divide them by two to get the median.

10 + 15 / 2 = 12.5

So, the median is somewhere between 10-15.

(C) The range:
The range is computed by subtracting the lowest and highest values.

25 - 0 = 25

So, the range is 25.

(D) The potential outliers:

According to the histogram, the potential outliers are 1910-1940.

Therefore, all the parts of the questions have been answered.

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Answer:

Step-by-step explanation:

I got it right on khan

please help im sorry it is late but please i dont understand

Answers

Answer:

416 people

Step-by-step explanation:

The way you get the answer is by adding up the number of people from the sample, which gives you 175 people. After finding that you take the number of people who like pretzels (26) and divide it by 175, giving you 0.16 or 16%.
This means 16% of people will like pretzels, so you apply this to the actual number of people coming, 2600, and find 16% of 2600 (0.16 x 2600) which is 416 people. I hope this makes sense :)

In mr. wilson's geometry class, 12 of the students received a's and 20 received b's. in his statistics class, 11 of the students got a's and 15 got b's. in which class did mr. wilson's students earn a higher ratio of a's to b's? a. statistics b. neither, the ratios are equivalent c. geometry d. not enough information

Answers

In (A) statistics class Wilson's students earn a higher ratio of a's to b's.

What are ratios?A ratio in mathematics describes how many times one number contains another. For example, if a dish of the fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon to orange ratio is 6:8, while the orange to total fruit ratio is 8:14.

To find the higher ratio:

Given -

Geometry class = a:b = 12:20 = 3:5Statistics class = a:b = 11:15

As we can observe that 3:5 < 11:15.

Therefore, in (A) statistics class Wilson's students earn a higher ratio of a's to b's.

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You start at (-4, 0). You move left 1 unit and down 5 units. Where do you end?

Answers

Answer: (-5, -5)

Step-by-step explanation:

(-4, 0)

Here, -4 is our x value and 0 is our y value

The x value moves horizontal (left and right) while the y value moves vertical (up and down)

If we move 1 unit left, we change x by -1 so, -4 -1 = -5

If we move 5 units down, we change y by -5 so, 0 -5 = -5

Therefore,

our new endpoint is: (-5, -5)

a. How many feet is [tex]\frac{1}{5}[/tex] of a mile? ______

b. How many feet is [tex]\frac{1}{100}[/tex] of a mile? ______

Answers

Answer:

a. 1056 ft

b. 52.8 ft

Step-by-step explanation:

1 mile = 5280 feet

a.

[tex]\frac{1}{5} *5280 = 1056[/tex]

Therefore 1/5 of a mile is 1056 feet.

b.

[tex]\frac{1}{100} *5280=52.8[/tex]

Therefore 1/100 of a mile is 52.8 feet

A gallon of Moo Milk costs 5.12$
What is the price, in dollars, of an 8 ounce glass of Moo Milk?

Answers

Answer:

$0.32

Step-by-step explanation:

8 ounces is 1/16 of a gallon so

5.12*(1/16) = 0.32

Answer:

32 cents (0.32 dollars)

Step-by-step explanation:

One gallon contains 128 ounces

Calculate the cost of each ounce:

[tex]\frac{5.12}{128} =0.04[/tex]

costs 4 cents an ounce

Calculate the cost of 8 ounces:

[tex](8)(4)=32[/tex]

Hope this helps

A grocery store sells a bag of 3 oranges for $1.23. If Latanya spent $3.28 on oranges, how many did she buy?

Answers

Answer: 8 Oranges

Step-by-step explanation:

Given information

3 Oranges = $1.23

Total cost = $3.28

Determine the unit price of an orange

Unit price = Cost ÷ Number of Oranges

Unit price = 1.23 ÷ 3

Unit price = $0.41 / orange

Determine the number of oranges bought

Number of orange × Unit price = Total cost

N × (0.41) = (3.28)

Divide 0.41 on both sides

N = 3.28 ÷ 0.41

[tex]\Large\boxed{Number~of~oranges=8}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

help math pls lots of points!!!!!

Answers

Answer:

(f ○ g)(11) = - 1

Step-by-step explanation:

evaluate g(11) then substitute the result obtained into f(x)

g(11) = 11 - 7 = 4 , then

f(4) = [tex]\sqrt{4}[/tex] - 3 = 2 - 3 = - 1

Okay so this is super tricky, there is a riddle on my math quiz. Yk for extra credit and its 25% of my grade, according to Mr. Wells.
If you have 1 cow that is worth $2,500 and 2 cats worth $100. But one dog is worth $7000, what would the outcome be if there was only 1 of each animal? Hint: It could be division or multiplication.
A. 2 cats and one dog
B. 1 cow and 1 dog
C. $600 for each animal
D. If you think its none of these listed, you may write your own!
Note: this makes no sense whatsoever, so please help. Mr. Wells is a good teacher, but this question is hard

Answers

If there was just one of each animal, the outcome would be that of 1 cow and 1 dog.

Option(B) is correct.

The average cost, or how much it generally costs to produce a unit, can be discovered using the cost function.

If you own two cats worth $100 each and a cow worth $2,500. One dog, though, is worth $7000.

Cost of 1 cow = $2500

Cost of 2 cats = $100

Thus, cost of 1 cat = $100/2 = $50

Cost of 1 dog = $7000

If there was only 1 of each animal, total cost = $(2500+50+7000) = $9550.

This outcome resembles the situation of having 1 cow and 1 dog.

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Assume the four intersecting lines are parallel. In this figure, A = 36, B = 24, and C = 60 . If D = 33,
what are the measurements of E and F?

Answers

Using the proportionality theorem, the measurements are: c. E = 22 and F = 55.

What is the Proportionality Theorem?

If two transversals intersect three or more parallel lines, they divide the lines in such a way that the smaller segments are proportional to each other or have ratios that are equal to each other.

Given the following:

A = 36,

B = 24,

C = 60

D = 33.

Since all lines are parallel, then:

A/D = B/E = C/F

Find the measure of E using the ratio, A/D = B/E:

36/33 = 24/E

Cross multiply

E = (24 × 33)/36

E = 22

Find the measure of F using the ratio, A/D = C/F:

36/33 = 60/F

Cross multiply

F = (60 × 33)/36

F = 55

The answer is: c. E = 22 and F = 55.

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Create a visual plot of the data in the table by constructing a bar graph.

3. What is the average view of the dress code? How did you come to this
conclusion?

4. The dress code will be changed if more than 60% of the school feels like a
change is needed. If 40% of this majority agrees on the same change, that will
be what is done with the dress code. Will the dress code change? Do we know
which option will occur? Be sure to explain your reasoning.

Answers

The average view of the dress code is that this dress is not good

Explain how Rashad could collect data to ensure that it is a random sample of the population.

For Rashad's sample to be a random sample gotten from the population, the following must be considered.

First, he must have a defined population. In this case, his population is all the students in his high school (non students are not to be considered)Next, he must have a defined sample size (say 10% or 20% of the total number of students in the school)Next, he must select students at random (a perfect example of this is one of every five or ten students that enters the school gate.Lastly, he must collect data for his sample

Create a visual plot of the data in the table by constructing a bar graph.

To do this, we simply create a bar graph.

The response would go into the x-axis, while the number of people would go into the y-axis

See attachment for bar graph

What is the average view of the dress code? How did you come to this conclusion?

The average view of the dress code is that this dress is not good

It is considered the average view of the dress code because it is the opinion with the most frequency

Will the dress change?

The number of students that do not like the dress as:

210 + 206 + 770 = 1186

Their percentage is

Percentage = 1186/(210 + 206 + 770 + 358)

Percentage = 77%

This means that

Yes, the dress will change

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