Write an equation that represents the line.
Use exact numbers.

The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.

Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.

1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is:   8+4+4+4+4=24 units.

2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.

The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.

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Answer:

ANSWER: The number is 3/4 or 4/3 which are reciprocals of each other

Step-by-step explanation:

Answer:

Step-by-step explanation:

You already know the formula for area of a triangle, so we will write it down and then fill it in with the info given.

\(A=\frac{1}{2}bh\) and filling in:

\(54=\frac{1}{2}b(12)\) and we can simplify that a bit by dividing 12 by 2 on the right side to get:

54 = 6b and dividing:

b = 9 inches

Given:

The total cost of 6 tickets for concerts A and 6 tickets for concert B is $1262

The cost of three tickets for concert B is $687.

Required:

To find an average ticket cost for each tour.

Explanation:

Let the cost of tickets for concert A is x and for concert B be y.

Now by using the given information we will make the linear equation.

Then the equations become:

We will solve equation (2) for y.

Now substitute the value of y in equation (1) and get the value of x.

.s

The proportion of population having score between 65 to 110 is 81.85%.

We have-

Mean of population = 80

Standard deviation of population = 15

We are supposed to find the proportion of the population corresponding to scores between 65 and 110.

According to the formula of the Z-score.

z = (x-μ)/σ

X=interval, μ= population mean ,

σ= standard deviation

Here,x = 65,μ= 80,σ= 15 andz = (65-80)/15z = -1

For Z=-1, From the z-table, the area to the left is 0.1587

Now, we need to find the area in the right  It can be calculated as follows.

z = (110-80)/15 = 2.

Area to the left of Z=2.00 is 0.028

So, the area between Z= -1 and Z= 2 is

= Total Area - (area of population below 65 + area of population above 110)=1-(0.1587+0.0228)=0.8185

The proportion of the population corresponding to scores between 65 and 110 is 0.8185 or 81.85%.

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The composition of the relations S ◦ R; S ◦ R is the relation {(1, 1), (1, 2), (2, 1), (2, 2), (3, 2), (3, 3)}.

To find the composition of the relations S ◦ R, you need:

1. Identify the pairs in R and S.
2. For each pair in R, find the pairs in S that have the first element equal to the second element of the pair in R.
3. Form new pairs by combining the first element of the pair in R and the second element of the pair in S.

Given relations:
R = {(1, 2), (1, 3), (2, 3), (2, 4), (3, 1)}
S = {(2, 1), (3, 1), (3, 2), (4, 2)}

Now, let's find S ◦ R:

1. For pair (1, 2) in R, we have (2, 1) in S. The new pair is (1, 1).
2. For pair (1, 3) in R, we have (3, 1) and (3, 2) in S. The new pairs are (1, 1) and (1, 2).
3. For pair (2, 3) in R, we have (3, 1) and (3, 2) in S. The new pairs are (2, 1) and (2, 2).
4. For pair (2, 4) in R, we have (4, 2) in S. The new pair is (2, 2).
5. For pair (3, 1) in R, we have (1, 2) and (1, 3) in R. The new pairs are (3, 2) and (3, 3).

Combining all the new pairs, we have:
S ◦ R = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 2), (3, 3)}

So, S ◦ R is the relation {(1, 1), (1, 2), (2, 1), (2, 2), (3, 2), (3, 3)}.

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Answer:

it is corect

Step-by-step explanation:

function [coefficients] = fourser(n). FOURSER generates the coefficients of the Fourier series up to the user-defined nth value.

coefficients = fourser(n) returns the coefficients of the Fourier series up to the nth value.

The Fourier series represents a periodic function as a sum of sinusoidal functions.

The coefficients obtained from this function can be used to reconstruct the original periodic function.

The function "fourser" calculates the coefficients of the Fourier series up to the nth value.

Fourier series is a representation of a periodic function as a sum of sine and cosine functions.

The coefficients obtained from this function can be used to reconstruct the original periodic function.

The Fourier series is a mathematical tool used to represent a periodic function as a sum of sinusoidal functions.

It provides a way to decompose a complex waveform into simpler components.

The Fourier series coefficients are calculated by integrating the periodic function multiplied by the corresponding trigonometric functions over one period.

The coefficients determine the amplitude and phase of each sinusoidal component in the series.

By summing up these components, the original periodic function can be reconstructed.

The "fourser" function takes an input parameter, 'n', which represents the desired number of coefficients to be calculated.

It returns the coefficients as an output, which can then be used for further analysis or synthesis of the periodic function.

The obtained coefficients can be utilized in applications such as signal processing, image compression, and harmonic analysis.

By increasing the value of 'n', a higher level of detail can be achieved in representing the periodic function, but at the cost of increased computational complexity.

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Answer:

67667.7

Step-by-step explanation:

let the number= Y

the question simply means that 0.15 percent of Y which give 10.5

so, let find Y:

0.15% of Y 10.15

0.15/100×y = 10.15

0.0015y= 10.15

divide bothsides by 0.0015

0.0015y/0.0015= 10.15/0.0015

y=6766.66

y= 6766.7 approximately

The amount in the account two years from now will be $17,548.09. The correct option is D.

Calculate the amount in the account two years from now, we need to consider the compounding of interest over the two-year period.

Calculate the amount after one year. The initial deposit of $5,000 will accumulate interest compounded every 6 months at a nominal rate of 12%.

Since the compounding period is every 6 months, there will be a total of 4 compounding periods over the course of one year.

Using the formula for compound interest, the amount after one year will be:

A1 = P(1 + r/n)^(nt)\(P(1 + r/n)^{(nt)\)

P = Principal amount (initial deposit) = $5,000

r = Nominal interest rate = 12% = 0.12

n = Number of compounding periods per year = 2 (compounded every 6 months)

t = Time in years = 1

A1 = 5000\((1 + 0.12/2)^{(2*1)\) = $5,000\((1 + 0.06)^2\) = $5,000\((1.06)^2\) ≈ $5,638.00

After one year, the amount in the account will be approximately $5,638.00.

Next, we add $10,000 to the account, resulting in a total balance of $5,638.00 + $10,000 = $15,638.00.

Finally, we calculate the amount after the second year by compounding the interest on the new balance. Again, there will be 4 compounding periods over the two-year period.

A2 = \(P(1 + r/n)^{(nt)\)

P = Principal amount (new balance after one year) = $15,638.00

r = Nominal interest rate = 12% = 0.12

n = Number of compounding periods per year = 2 (compounded every 6 months)

t = Time in years = 1

A2 = 15638\((1 + 0.12/2)^{(2*1)} = 15638(1 + 0.06)^2 = 15638(1.06)^2\) ≈ $17,548.09

Therefore, the amount in the account two years from now will be $17,548.09.

The closest answer choice to this amount is D. 17,548.

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Answer:

given - a rectangle ABCD

AB = 40

AC. = 90

BC = ?

in triangle ABC

using Pythagoras theorem

(AB) ² + (BC) ² = (AC) ²

(40)² + (BC) ² = (90)²

(BC) ² = (90)²- (40)²

(BC) ² = 8100 - 1600

(BC) ² = 6500

BC =

\(20 \sqrt{10} \)

Answer:

1/2

Step-by-step explanation:

slope of perpendicular lines are always negative reciprocal of each other.

so slope of the given line = rise over run

that means -2/1 = -2

so slope of a line that is perpendicular to it will be negative of its reciprocal

that will be

\( \frac{1}{2} \)

Answer:

30:15 simplifies to 2:1

Step-by-step explanation:

30 hours spent using electronic devices and 15 spent playing sports. 30 divided by 15 = 2 and 15 divided by 15 = 1.

Answer:

2 is the number of hours using electronic devices :

1 hours playing sports

Also known as 2:1

Step-by-step explanation:

The first step is to simplify the ratio of hours using electronic devices to hours playing sports, which is 30 : 15

30 : 15

If I divide each number by 5 to simplify you get:

6 : 3

Then we divide each number by 2 to simplify:

2 : 1

That is how you get the answer for the ratio of 2:1.

I hope I helped and have a great day! ^-^

Answer: 320

Step-by-step explanation:

64 x 5

Answer:

Answer:d)  320

Step-by-step explanation:

64x5

Answer:

-7

Step-by-step explanation:

might be wrong

Answer:

$-7

Step-by-step explanation:

1-3-6+1

= -2-6+1

= -8+1

= $-7

Answer: x = 1.186

Step-by-step explanation:

To solve, we need to isolate the x variable.

  Given:

\(5^{2x-1}=2^{x+2}\)

   Log both sides of the equation:

\(Log(5^{2x-1})=Log(2^{x+2})\)

   Log power property:

\((2x-1)Log(5)=(x+2)Log(2)\)

   Distribute:

* Think of the Log(5) and Log(2) as a "regular number" that you can divide with, distribute with, etc

\(2xLog(5)-Log(5)=xLog(2)+2Log(2)\)

   Add Log(5) to both sides of the equation and subtract xLog(2) from both sides of the equation:

\(2xLog(5)-xLog(2)=2Log(2)+Log(5)\)

   Factor x from the terms on the left side of the equation:

\(x(2Log(5)-Log(2))=2Log(2)+Log(5)\)

   Divide both sides of the equation by (2Log(5)-Log(2)):

\(x= \frac{2Log(2)+Log(5) }{2Log(5)-Log(2)}\)

   Compute:

x = 1.186

GIVEN:

We are given a circle with center A and diameter CB.

The length of arc CDB is 14;

Required;

We are required to calculate the lenght of the radius.

Step-by-step solution;

The length of an arc with the central angle measured in radians is;

The length of the arc is given, so also is the angle theta (180 degrees, that is half the circle).

We can convert the degree measure of the angle into radians as follows;

Now we substitute the value of d (degree measure);

Now we take the formula for the length of an arc as follows;

Divide both sides by pi;

Therefore, the radius is

ANSWER:

Answer:

the remaining mass is 7.3 g

Step-by-step explanation:

a=30g

t=200 years

h=98 years

f(98)=a(\(\frac{1}{2} ^{\frac{t}{h} }\)

f(98)=30(\(\frac{1}{2} ^{\frac{200}{98} }\)

f(98)=7.3

The probability of approximately 48% that a player will have a height between 5'2" and 5'6".

To calculate the probability of a player being between 5'2" and 5'6" given that historically, the members of the chess club have had an average height of 5'6" with a standard deviation of 2", we can use the standard normal distribution.

First, we need to convert the heights to z-scores using the formula:

z = (x - μ) / σ

where x is the height we want to find the probability for, μ is the mean height, and σ is the standard deviation.

For 5'2":

z = (62 - 66) / 2 = -2

For 5'6":

z = (66 - 66) / 2 = 0

Next, we can use a standard normal distribution table or calculator to find the area under the curve between these two z-scores.

Using a standard normal distribution table, we can find that the area to the left of z = -2 is 0.0228 and the area to the left of z = 0 is 0.5. Therefore, the area between z = -2 and z = 0 is:

0.5 - 0.0228 = 0.4772

Multiplying this by 100 gives us a probability of approximately 48% that a player will have a height between 5'2" and 5'6".

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Answer: yes if is

Step-by-step explanation:

Answer: Y=1/5x is correct ;))

Step-by-step explanation:

Let the number be n.

Now, "seven less than a number" means we subtract 7:-

n-7

This expression is equal to 18:-

\(\sf{n-7=18}\)

\(\mathcal{SOLUTION:-}\)

\(\bigstar{\boxed{\pmb{n=25}}}\)

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

Nearly 70 percent of the population has an IQ between 85 and 115 on most tests. The scores above 115 are generally considered as “high IQ,” and those above 130 to 132 (depending on the test taken) are usually considered highly gifted and are in the top 2 percent of the population.

The process of finding the derivative of a function is called differentiation.

Differentiation is a fundamental concept in calculus that involves determining the rate at which a function changes with respect to its independent variable. It allows us to analyze the behavior of functions, such as finding slopes of curves, identifying critical points, and understanding the shape of graphs.

The derivative of a function represents the instantaneous rate of change of the function at any given point. It provides information about the slope of the tangent line to the graph of the function at a specific point.

The notation used to represent the derivative of a function f(x) with respect to x is f'(x) or dy/dx. The derivative can be interpreted as the limit of the difference quotient as the interval approaches zero, representing the infinitesimal change in the function.

By applying differentiation techniques, such as the power rule, product rule, chain rule, and others, we can find the derivative of a wide range of functions. Differentiation is a powerful tool used in various areas of mathematics, physics, engineering, economics, and other fields to analyze and solve problems involving rates of change.

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Answer:

the first option

Step-by-step explanation:

the table does not have a constant rate of change so it is not linear.

Rates of change are the change of a quantity over another.

The rate of change of the mass position at 2.1 seconds is -89.6 cm/ s

The given parameters are:

\(\mathbf{A = |5|}\) -- the amplitude

\(\mathbf{T = \frac 13}\) --- the period

The position of the mass is modeled by:

\(\mathbf{y= Acos(wt)}\)

Where:

\(\mathbf{w = \frac{2\pi }{T}}\)

So, we have:

\(\mathbf{w = \frac{2\pi}{1/3}}\)

\(\mathbf{w = 6\pi }\)

\(\mathbf{y= Acos(wt)}\) becomes

\(\mathbf{y = |5|cos(6\pi t)}\)

\(\mathbf{y = 5cos(6\pi t)}\)

Differentiate

\(\mathbf{y' = 5 \times -sin(6\pi t) \times (6\pi)}\)

\(\mathbf{y' = -30\pi sin(6\pi t) }\)

When t = 2.1, we have:

\(\mathbf{y' = -30\pi sin(6\pi \times 2.1) }\)

\(\mathbf{y' = -30\pi sin(12.6\pi) }\)

\(\mathbf{y' = -30\pi \times 0.9510}\)

\(\mathbf{y' = -89.6296}\)

Approximate

\(\mathbf{y' = -89.6}\)

Hence, the rate of change of the mass position at 2.1 seconds is -89.6 cm/ s

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Answer:

93+30=123 so e equals 123

Step-by-step explanation:

To check, do 123-30=93

Answer:

Step-by-step explanation:

1. 1/40 + 1/x

2. 1/32 = 1/40 +1/x

3. $8 per hour

4. about 5.5 hours

5. 1/38 + 1/62 = t/x

6.

1. 16.7

2. 22.2

3. 26.2

4. 29.2

nice pfp

Answer: {-1, 0, 1}

Explanation: The range of a relation is the set of all y-coordinates.

So the range is {1, 0, -1} which would be your answer.

Note however that the range is usually written in ascending order.

In other words, from least to greatest.

So our range can be written as {-1, 0, 1}.