The square has an area of
196. It contains two
overlapping squares; the larger
of these squares has an area 4
times that of the smaller and the area of their
overlap is 1. What is the total area of the
shaded regions?

Graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

The graph is shown in the pictures

As we know,

The proportional relationship can be defined as:

y ∝ x

y = kx

k is the constant of proportionality:

y = kx is the equation of the line which passes through the origin.

Graph four passes through origin.

Thus, graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.

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Answer:

4.a)  Broken line.

4.b)  True.

5.a)  Solid line.

5.b)  True.

Step-by-step explanation:

When graphing inequalities:

Given inequality:

[tex]y < -\dfrac{1}{2}x+2[/tex]

a)  As the "<" sign has been used, the line will be a broken line.

b)  Substitute (0, 0) into the inequality:

[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 0 & < -\dfrac{1}{2}(0)+2\\0 & < 0+2\\0 & < 2\end{aligned}[/tex]

As zero is less than 2, the solution at (0, 0) is true.

Graphing the inequality

Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:

[tex]\begin{aligned}x=-2: \quad y &=-\dfrac{1}{2}(-2)+2\\y &=1+2\\y&=3\end{aligned}[/tex]

[tex]\begin{aligned}x=4: \quad y &=-\dfrac{1}{2}(4)+2\\y &=-2+2\\y&=0\end{aligned}[/tex]

Plot the points (-2, 3) and (4, 0).

Draw a broken straight line through the points.

Shade below the line.

Given inequality:

[tex]2x+5y \leq 10[/tex]

a)  As the "≤" sign has been used, the line will be a solid line.

b)  Substitute (0, 0) into the inequality:

[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 2(0)+5(0) &\leq 10\\0+0 &\leq 10\\0 &\leq 10\end{aligned}[/tex]

As zero is less than 10, the solution at (0, 0) is true.

Graphing the inequality

Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:

[tex]\begin{aligned}x=-5: \quad 2(-5)+5y &=10\\-10+5y &=10\\5y &=20\\y&=4\end{aligned}[/tex]

[tex]\begin{aligned}x=5: \quad 2(5)+5y &=10\\10+5y &=10\\5y &=0\\y&=0\end{aligned}[/tex]

Plot the points (-5, 4) and (5, 0).

Draw a solid straight line through the points.

Shade below the line.

Emily's prediction was off by 9.09%

Enrique's prediction was off by 11.11%

The percentage is calculated by dividing the required value with the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Emily:

Each month payment = $250

Each month actual payment = $275

The percentage prediction is off by.

=  (275 - 250) / 275 x 100
= 25/275 x 100

= 9.09%

Enrique:

Each month payment = $200

Each month actual payment = $225

The percentage prediction is off by.

= (225 - 200)/225 x 100

= 25/225 x 100

= 11.11%

Thus,

Emily's prediction was off by 9.09%

Enrique's prediction was off by 11.11%

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The equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is 4(x - 2 + y). The equivalent expression will be solved as,

E = 4(x - 2 + y)

E = 4x - 8 + 4y

Therefore, the equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.

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it's a Stratified sampling

Answer:

11 quarters and 4 nickels

Hope this helps! :3

Please mark brainliest! <3

Jess makes $40000 per year as an administrator .

What is an administrator?

Administrators support the efficient operation of offices by carrying out clerical jobs and initiatives. You can be planning project meetings in the construction business as an administrator.

Main Body:

Expenses incurred by Jess = $12000

According to the question , 30% of his annual salary is his expenses

Let his annual salary be x.

so,

⇒30% of x = 12000

⇒ (30/100)*x = 12000

⇒x = 12000*100/30

⇒x= 40000

Hence the salary made by Jess in a year is $40000.

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The amount of money that is reduced from Tiffany's allowance is $8.75

The amount of allowance reduced every time she forget to clean her room = $1.25

Number of times that she forgets to clean her room = 7 times this month

The amount of money is reduced from Tiffany's allowance =  Number of times that she forgets to clean her room × The amount of allowance reduced every time she forget to clean her room

Here we have to use the multiplication to find the amount

Substitute the values in the equation

The amount of money is reduced from Tiffany's allowance = 7 × 1.25

Multiply the terms

= $8.75

Hence, the amount of money that is reduced from Tiffany's allowance is $8.75

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The first and second cars are 7724 feet apart from each other.

The angle of depression is the angle we have to move your eyes downwards to look at the car from the plane. Let's start with the first car, with the 31° angle of depression. Draw an upside-down right triangle with vertices at the plane, the car, and the point 3500 feet in the air above the car (level with the plane). The vertex at the plane is 31° and the right angle is the vertex in the air above the car. The length of the leg from the car to the point in the air above the car is 3500 feet. We like to find the length of the leg from the plane to the point in the air above the car. Since the two sides involved are the legs of the triangle, use tangent:

     tan = opposite/ adjacent

⇒  tan(31°) = 3500/x

⇒ 0.60086 = 3500/x

⇒ 0.67 x = 3500            [ rounding up 0.60086 = 0.67]

⇒ x = 5223.88

That means the first car is 5223.88 feet from the point on the highway below the plane.

We can do something similar with the second car, which has an angle of depression of 53° from the plane. Again, the leg from the car to the point in the air above the car (level with the plane) is 3500 feet, the right angle is at the vertex at the point in the air above the car, and the 53° angle is at the vertex at the plane. We are looking for the length of the other leg, which runs from the plane to the point in the air above the car. Use tangent:

    tan(53°) = 3500/x

⇒ 1.327 = 3500/x

⇒ 1.4x = 3500            [ rounding 1.327 = 1.4]

⇒ x = 3500/1.4
⇒ x = 2500

That means the second car is 2500 feet from the point on the highway below the plane.

Add the two distances together to get the total distance from car to car:

5223.88 + 2500.00 = 7723.88

So, rounded to the nearest foot, the cars are 7724 feet apart.

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sin x = cos (90 - x) or cos x = sin (90 - x)

This identity holds when the two angles are complementary

i.e. they sum up to 90 degrees.

The value of x is 35°

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

cos x° = sin (20° + x°), where 0 < x < 90

We know that,

sin x = cos (90 - x) or cos x = sin (90 - x)

This identity holds when the two angles are complementary

i.e. they sum up to 90 degrees.

x + 90 - x = 90

Now,

cos x = sin (20 + x)

x + 20 + x = 90

2x + 20 = 90

2x = 70

x = 35

Thus,

The value of x is 35°

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Answer:

Step-by-step explanation:

no

The required value of the given equation when x = 5 is y = 585.5

The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.

Given : y = 114.50x + 13

To find ; The value of this equation when x = 5

Thus to find this value we have to simply substitute the value of x in the given equation

Hence, we will get ,

y = 114.50 × 5 + 13

this implies y = 572.5 + 13

which is equal to y  = 585.5

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The sample size required for the true proportion of students who have parents who have remarried is 607.

What is termed the Confidence Interval?

The confidence interval is indeed the range of values within which you expect your forecast to fall a certain proportion of the time if you repeat your experiment or re-sample a population in the same manner.

The alpha value determines the confidence level, which is the percentage of times you anticipate reproducing an approximate between both the upper and lower limits of the confidence interval.

The above problem is based on the use of determining sample size to estimate the true percentage of students given the constraints.

We may also need to consult the table to determine the Z value.

For the given question,

α = 0.5

Consider the Z-table,

Zα/2 = Z (0.1/2)

Z (0.025) = 1.96

Let 'n' be the sample size required for the true proportion of students who have parents who have remarried.

For calculating the margin error 'E' is given 3%.

n = Z² (α/2) / E² × (P°(1 - P°))

Put the given values.

n = (1.96)² / (0.03)²  × (0.28(1 - 0.28))

On solving,

n = 4268.444(0.2016)

n = 860.51

n ≈ 860.51

Thus, the sample size required for the true proportion of students who have parents who have remarried is 860.

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Answer: the answer is  30/11

Step-by-step explanation:

hope it helps:)

The area of the circle in terms of π if the circle has a radius of 16 ft is 256 π ft^2. Option A is correct.

First, let us understand the circle:

A circle is nothing more than a round form with no corners or line segments. In geometry, it is a closed curve shape.

Some formulas related to circle:

Area of the circle = πr^2

Circumference of the circle = 2πr

where, r = radius of the circle.

We are given;

A circle has a radius of 16 ft.

We need to find the area of the circle in terms of π.

Area of the circle = πr^2

Put the value of r in the above formula:

Area of the circle = π 16^2 * ft^2

Area of the circle = 256 ft^2

Thus, the area of the circle in terms of π if the circle has a radius of 16 ft is 256 π ft^2. Option A is correct.

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Answer:

option A

Step-by-step explanation:

The value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.

According to the question,

We have the following expressions:

[tex]49^{-1/2}[/tex]

Now, we will convert the base of these expressions in exponential form in such a way the denominator of powers will get divided:

[tex]7^{2*(-1/2)}[/tex]

[tex]7^{-1}[/tex]

Or it can be 1/7 because we have positive exponents.

Now, we have another expression:

[tex](\frac{27}{125}) ^{2/3}[/tex]

We will follow the same steps to solve this expression:

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

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

Now, expanding the numerator and denominator of the fraction by multiplying them two times, we have the following fraction:

9/25

Hence, the value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.

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The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%

Z- Score gives an idea how far a data point is from mean .

z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .

Given , mean = 80beats/minute

standard deviation = 10 beats/minute

x = 86 beats/minute

Applying z score formula :

z-score = (x-mean)/standard deviation

P(x>86) = P(z > 86-80/10)

=P(z>6/10)

=P(z>0.6) = 1 - P(z<0.6)

= 1 -0.7257

= 0.2742

Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742

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Answer:

Step-by-step explanation:

The circle represents a 360° angle.

Total spending corresponds to full circle and part of it spent on paper.

The ratio of paper over total is:

This is the part of circle which is:

Correct choice is B.

Answer:

b) 90 degrees

Step-by-step explanation:

Forming the expression,

→ 360° × (300/1200)

Let's solve given expression,

→ 360° × (300/1200)

→ 360° × (1/4)

→ (360°/4)

→ 90°

Hence, the answer is 90°.

The initial value of the function is 75.

The growth factor or growth rate of the function as a percent is 0.25%

An exponential growth model is defined as :

F(x) = A( 1 + r)^x

Where;

A = Initial amount,

r = rate of increase

x = time

Comparing the exponential growth function with the exponential growth model given;

f(x)=75(1.0025)ˣ

A = 75 = Initial amount

The growth rate of the model expressed as a percentage :

Taking :

(1 + r) = 1.0025

1 + r = 1.0025

r = 1.0025 - 1

r = 0.0025

Expressing r as a percentage:

r = 0.0025×100

= 0.25%

Hence we get the required answers.

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For given equation y = -2x - 5,

 x          y

-4         3

-2        -1

 0        -5

 2        -9

In this question we have been given an equation y = -2x - 5

We need to complete the table using given function rule.

for x = -4,

y = -2(-4) - 5

y = 8 - 5

y = 3

for x = -2,

y = -2(-2) - 5

y = 4 - 5

y = -1

for x = 0,

y = -2(0) - 5

y = -5

for x = 2,

y = -2(2) - 5

y = -4 - 5

y = -9

Therefore, for given equation y = -2x - 5,

 x          y

-4         3

-2        -1

 0        -5

 2        -9

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The value of the expression when evaluated is: -18.

Evaluation of an expression involves plugging in the values of the given variables and then solving to determine the value of the expression in it's simplest form.

Given the expression, 4a - |3b + 2c|, to evaluate, substitute a = -2, b = -3, c = 2 into the expression and solve:

4(-3) - |3(-3) + 2(2)|

-13 - |-9 + 4|

-13 - |-5|

-13 - 5

= -18

The value of the expression is: -18.

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If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .

In the question ,

it is given that ,

total numbers of car in the parking lot = 200 cars

number of white cars = 50

number of red cars = 30

number of silver cars = 20

let the number of green cars be "x" ,

So , the number of green cars possible = 200 - 100 = 100

that means x ≤ 100 .

So , P(green) = x/200

Option(a)

p = 0.2 ,

So , x/200 = 0.2

x = 40

Option(b)

p = 0.1 ,

So , x/200 = 0.1

x = 20

Option(c)

p = 0.6 ,

So , x/200 = 0.6

x = 120

Option(d)

p = 0.5 ,

So , x/200 = 0.5

x = 100 ,

We can see that only option(c) gives the number of green cars as 120 , which is not possible .

Therefore , If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .

The given question is incomplete , the complete question

In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. one car will be selected at random from the parking lot. if each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green ?

(a) 0.2

(b) 0.1

(c) 0.6

(d) 0.5

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The equilibrium quantity is 97 items and equilibrium price is $582

The equation of the price  when quantity demanded

p = 873 - 3q

The equation of the price when quantity supplied

p = 6q

At equilibrium price and quantity

873 - 3q = 6q

Move the like terms to one side

6q + 3q = 873

Add the like terms

9q = 873

q = 873 / 9

Divide the terms

q = 97 items

Substitute the value of q in the equation 2

p = 6q

p = 6 × 97

Multiply the terms

p = $582

Hence, the equilibrium quantity is 97 items and equilibrium price is $582

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Answer:

.

Step-by-step explanation:

Step-by-step explanation:

4z-16z+8=0

[4×8]=32

factors of 32

1,2,4,8,....