A gym employee earn the ame amount each mouth. After working for three month, he earned $4,500. Complete the table to determine how much money he will make over a five-month period. I the relationhip proportional?

Answer:

312 m^2

Step-by-step explanation:

Start by separating the shapes.

you will get:

2 triangles with the dimensions 6m x 8m

1 rectangle with the dimensions: 9m x 8m

1 rectangle with the dimensions: 6m x 9m

1 rectangle with the dimensions: 10m x 9m

1) find the area of every shape

2 triangles with the dimensions 6m x 8m -----> 48m^2 and 48 m^2

1 rectangle with the dimensions: 9m x 8m ----> 72m^2

1 rectangle with the dimensions: 6m x 9m ----> 54 m^2

1 rectangle with the dimensions: 10m x 9m ---> 90m^2

2) add everything up

48m^2 + 48 m^2 + 72m^2 + 54 m^2 + 90m^2 =

312m^2

Carrie will be paid $390 if she puts in 40 hours of work in a week.

The total amount of time of work = 40 hours.

As we are stated that the earnings for 1 hour is $9.75, so, we will perform multiplication to find the earnings for the time she worked. We are performing multiplication because the amount will increase as the number of hours increases.

Performing calculation now.

Amount earned in a week = 9.75 × 40

Performing multiplication on Right Hand Side of the equation to find the amount earned in a week

Amount earned in a week = $390

Thus, the amount paid to Carrie in a week is $390.

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Answer:

y = -7x + 10

Step-by-step explanation:

As the y's are decreasing by 7, the x are increasing by 1.  This gives us a slope of -7.  When x is 0, y is 10 that is our y intercept.

Answer:

Answer: 9 hours. If austin prepared 20 kg of dough in 5 hours, this means he can prepare 4kg of dough an hour. This is because 20/5=4.

The balloon is  above 17.7180 the ground

What is the trigonometry ?

A branch of mathematics called trigonometry looks at how triangle side lengths and angles relate to one another. Applications of geometry to astronomical studies led to the development of the field in the Hellenistic world during the third century BC.

Given

The angle Ф  is 32°

The hypotenuse becomes 24 feet

Let AB be the opposite side

Using trigonometric function of sinФ

ie sinФ = Opposite / hypotenuse

  sin Ф = AB / 24

   AB = sin Ф * 24

  AB =  sin 32° * 24

   AB = 12.7180

As that person is 5 feet tall we have to add 5 to the value

ie

12.7180 + 5

= 17.7180

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Answer:

(3x + 36) is equal to (6x + 9) because they are vertically opposite angles.

3x + 36 = 6x + 9

3x = 27

x = 9

Substitute x = 9 into one of the angles to find the measure.

3(9) + 36 = 63

Angle measure is 63°.

The measure of the angles is 63 degrees.

Both (3x + 36) and (6x + 9) are equal to 63 degrees.

Given that are two vertically opposite angles (3x+36) and (6x+9) we need to find the measure of the angles,

Vertically opposite angles are formed when two lines intersect, and they are equal in measure.

In this case, we have two vertically opposite angles: (3x + 36) and (6x + 9).

Since the angles are equal, we can set them equal to each other and solve for x:

3x + 36 = 6x + 9

To isolate the x term, let's subtract 3x from both sides:

36 = 6x - 3x + 9

Combining like terms:

36 = 3x + 9

Next, let's subtract 9 from both sides:

36 - 9 = 3x

27 = 3x

To solve for x, we divide both sides by 3:

27/3 = 3x/3

9 = x

Now that we know the value of x, we can substitute it back into either of the original equations to find the measure of the angles.

Let's use the first angle (3x + 36):

Angle = 3x + 36

= 3(9) + 36

= 27 + 36

= 63

Hence, the measure of the angles is 63 degrees.

Both (3x + 36) and (6x + 9) are equal to 63 degrees.

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As per the substitution method, the value of (x , y) is (-15/2, 11/2)

Substitution method:

Substitution method is the process of solve one equation for one of the variables. And substitute (plug-in) this expression into the other equation and solve. Then resubstitute the value into the original equation to find the corresponding variable.

Given,

Here we have the following expression.

3x + 5y = 5

Y = -x -2

Now, we need to find the value of x and y.

According to the substitution method, let us consider

3x + 5y = 5 -------------------(1)

Y = -x -2 ---------------------(2)

Now, we have to apply the value of y as -x - 2 in equation (1), then we get,

=> 3x + 5(-x - 2) = 5

When we expand it then we get,

=> 3x - 5x - 10 = 5

Simplify the expression,

=> -2x - 10 = 5

=> -2x = 5 + 10

=> -2x = 15

Then the value of x is,

=> x = -15/2

If the value of x is -15/2. then the value of y is calculated by using the equation (2),

=> y = -(-15/2) - 2

=> y = 15/2 - 2

=> y = (15 - 4)/2

=> y = 11/2

Therefore, the value of (x, y) is (-15/2, 11/2).

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The simplified expression for the complex expression is -56-52i

What is a complex expression?

A complex expression is an expression of the form a+ ib where a , b are constant and i is the imaginary number known as iota. In a + ib a is the real part and b is the imaginary part.

We are given two complex number as (8-8i) and (8+4i)

We have to simplify the given expression

As Complex number are added multiplied subtracted same as real number we can simplify the expression easily

2(8-8i)-9(8+4i)

We multiply the constants inside the bracket

16-16i-72-36i

Separating the terms and simplifying them we get

-56-52i

Hence the simplified expression is -56-52i

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There will be no change in volume reducing the radius by 10%.

What is Direct Proportion?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. Since the other variable is reversed in this case, the inversely proportional relationship is really represented by the same symbol.

For instance, if x and y are two quantities or variables that are intimately linked to one another, we can say x y. The ratio of x and y becomes equal to a constant when the proportionality sign is removed, for example, x/y = C, where C is a constant. In contrast, x and y are represented as x 1/y or xy = C in the case of inverse proportion.
Let the radius be r then
The volume of every sphere is,
[tex]\mathrm{V}=4 \pi \frac{\mathrm{r}^3}{3}[/tex]
In the given question, It is given:
The volume V of a sphere varies in direct proportion to the cube of its radius.

That means:[tex]\mathrm{V}[/tex] ∝ [tex]r^{3}[/tex]
That means:[tex]4 \pi \frac{\mathrm{r}^3}{3} = kr^{3}[/tex]⇒[tex]4 \pi \frac{\mathrm{1}}{3} = k[/tex]
So, The equation is independent of radius.
Hence, There will be no change in volume reducing the radius by 10%.

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Answer: 72 in

Step-by-step explanation:

The shortest side length of the original triangle was 3in, and the newer one is now 12in. From 3in to 12in, you use a scale factor of 4. Hence, we multiply each side length of the original triangle by 4. And to find the perimeter of the new triangle, you add all the sides up.

3(4) + 6(4) + 9(4) = 72 in

Option2 and 4 are the exponential decay from the equation.

Given that,

We have to find which one is exponential decay function.

Exponential decay function is in the form of y=abˣ where a is the initial value and b≠0,  0<b<1. power is x.

Now, Take the 1st option

y=0.25(2)ˣ

Here a is 0.25 and 2 is b

b>1

So, Option 1 is not an exponential decay.

Now, Take the 2nd option

y=2(0.20)ˣ

Here a is 2 and 0.20 is b

b<1

So, Option 2 is an exponential decay.

Now, Take the 3rd option

y=4.2(1.25)ˣ

Here a is 4.2 and 1.25 is b

b>1

So, Option 3 is not an exponential decay.

Now, Take the 4th option

y=0.55(0.91)ˣ

Here a is 0.55 and 0.91 is b

b<1

So, Option 4 is an exponential decay.

Therefore, Option2 and 4 are the exponential decay from the equation.

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Answer:

yes

Step-by-step explanation:

Given that [tex]\cos x\sin x\tan x+\cos^2x=1[/tex]

Substitute [tex]\tan x=\frac{\sin x}{\cos x}[/tex], we obtain:

[tex]\cos x\sin x\frac{\sin x}{\cos x}+\cos^2 x=1[/tex]

Simplifying this, we get:

[tex]\sin x\sin x+\cos^2x=1[/tex]

This is equivalent to:

[tex]\sin^2x+\cos^2x=1[/tex]

Answer:

y + 9 = -2 (x - 9)

Step-by-step explanation:

M (slope) = -2

X=9 and Y=-9

Point-slope form

y - y1 = m(x - x1)

y - - 9 = -2( x - 9)

y + 9 = -2(x -9)

If Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.

Number of cups of blue paint for each art station = 2 cups

Given that,

One cup = 8 ounce

1 gallon = 128 ounce

2 cups of blue paint = 2 × 8

= 16 ounce of blue paint

1 gallon of blue paint = 128 ounce of blue paint

Number of jars that he can fill with 1 gallon of blue paint =  1 gallon of blue paint / 2 cups of blue paint

Here we have to use division

= 128/16

= 8 jars

Hence, if Mr. Dyer pours 2 cups of blue paint into a jar for each art station, then the he can fill 8 jars with 1 gallon of blue paint.

The complete question is:

Mr. dyer pours 2 cups of blue paint into a jar for each art station. how many jars can he fill with 1 gallon of blue paint? One cup = 8 ounce and 1 gallon = 128 ounce

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The values of the domain is the which satisfies the function is x > - 4.

According to the statement

We have to find the domain of the given function

For this purpose, we know that the

In Mathematics,The domain of a function is the set of values that we are  plug into our function.

The given function is a

[tex]y = \sqrt{x+4}[/tex]

And in this function

The domain is the values of the x which we able to put in the function according to the definition.

x+4=0

x=-4.

It means the value of the domain is the [tex]x > - 4[/tex].

The values according to the upper expression satisfies the domain of the function.

So, The values of the domain is the which satisfies the function is x > - 4.

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Based on expression for each side of the equation, the number is -2.

Let us assume the number to be x. So, there will be two sides of equation, that is Left Hand Side and Right Hand Side. Writing the equation for each side.

Left Hand Side = 11x - 21

Right Hand Side = 7x - 29

Equating both sides of the equation.

11x - 21 = 7x - 29

Rewriting the equation with identical values on each side

11x - 7x = 21 - 29

Performing subtraction on both sides of the equation

4x = -8

Shifting 4 to Right Hand Side of the equation

x = -8 ÷ 4

Performing division on Right Hand Side of the equation

x = -2

Thus, the number is -2.

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The probability that a standard normal random variable will be between. 3 and 3. 2 is 0.99932.

What is standard normal random?

We shall read probabilities out rather than directly working with Z's density function to compute probabilities for Z. The elements in the tables are probabilities of the kind P(Zz), and they are tables of cumulative probabilities. Following are a number of examples that will help to clarify how to use the tables.The standard normal random.

Z∼N(0,1)

P(Z<3)=.99865

P(Z>3.2)=.99931

P(3<Z<3.2)=2(0.99931-0.99865)−1=0.99932

Hence the standard normal random variable will be 0.99932.

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The amount of money left with Alizay after shopping is Rs 17700 .

Alizay sold shirts for Rs. 2800.

She sold 14 shirts.

Cost earned from selling 14 shirts = 14 × 2800 = Rs. 39200

Spent on shopping =Rs. 14000

Spent on Grocery = Rs. 7500

Total amount spent = Rs.(14000+7500) = Rs. 21500

Amount of money left = Rs 39200 - Rs 21500 = Rs 17700

Therefore she is left with Rs 17700 .

In the case of a single variable, there is only one viable response. This particular case, in which the variable is accurately referred to as the "unknown," is one to which the term linear equation sometimes relates implicitly.

The Cartesian coordinates of a point on the Euclidean plane can be used to understand each solution in the scenario with two variables. A linear equation's solutions define a line in the Euclidean plane, and each line is the collection of all solutions to a linear equation with two variables.

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Answer:

i think its C. The median points per game is not affected

Step-by-step explanation:

In the given expression 7^(9/4) the values are found to be

Information given in the problem

the expression 7^(9/4)

This equation represents exponents in fraction form and the basics for the calculation is from

a^(b/c) = [tex]\sqrt[c]{a^{b} }[/tex]

Rewriting the expression is done as below

7^(9/4)

= [tex]\sqrt[4]{7^{9} }[/tex]

[tex]\sqrt[4]{7^{9} }[/tex] comparing with [tex]\sqrt[c]{a^{b} }[/tex] gives the following values

a will be equal to 7

b will be equal to 9

c will be equal to 4

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Answer:

1 : 4

Step-by-step explanation:

the ratio of

alternative : total

= 15 : 60 ( divide each part by 15 )

= 1 : 4

In a farm composed of cows and chickens, there are total of 13 heads and 42 feet.

Let 'h’ represent the number of hens the farmer has.

Let 'c’ represent the number of cows the farmer has.

Assume that all hens have two legs and all cows have four.

There are a total of 42 legs. So

2h + 4c = 42 (1)

There are 13 animals in total.

h + c = 13 (2)

Now that we have our system of equations, we can solve by either substitution or elimination.

Elimination

(2) x 2

2h + 2c = 26 (3)

(2)—(3)

2c = 6

c=3

From (2):

c + h = 13

3+h = 13

h= 10

Therefore, the farmer has 3 cows and 10 hens.

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Answer:

B.  6 units

Step-by-step explanation:

Given equations:

[tex]y = -2x^2 + 8x[/tex]

[tex]x-2.23y + 10.34 = 0[/tex]

The points at which the rod is attached to the archway are the points of intersection of the two equations.

Rearrange the second equation to make x the subject:

[tex]\implies x=2.23y-10.34[/tex]

Substitute this into the first equation to create a quadratic:

[tex]y = -2(2.23y-10.34)^2 + 8(2.23y-10.34)[/tex]

[tex]y = -2(4.9729y^2-46.1164y+106.9156) + 17.84y-82.72[/tex]

[tex]y=-9.9458y^2+92.2328y-213.8312+17.84y-82.72[/tex]

[tex]y=-9.9458y^2+110.0728y-296.5512[/tex]

[tex]-9.9458y^2+109.0728y-296.5512=0[/tex]

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Solve the quadratic using the quadratic formula:

[tex]\implies y=\dfrac{-(109.0728) \pm \sqrt{(109.0728)^2-4(-9.9458)(-296.5512)}}{2(-9.9458)}[/tex]

[tex]\implies y=\dfrac{-109.0728 \pm \sqrt{99.12}}{-19.8916}[/tex]

[tex]\implies y=\dfrac{109.0728 \pm \sqrt{99.12}}{19.8916}[/tex]

[tex]\implies y=5.983867702, \quad y=4.982851918[/tex]

As point B is at a higher level than point A, the y-value of point B is approximately 6 units.  

Therefore, point B is 6 units from ground level.

Which shows the following expression after the negative exponents have been eliminated

[tex]a^{2} b^{2}[/tex]

Given the algebraic expression:

[tex]\frac{a^{3}b^{-2} }{ab^{-4} }, a\neq 0, b\neq 0[/tex]

We are required to eliminate the negative exponents and find the resulting expression.

Using the Negative Exponent Law of Indices: [tex]x^{-y} = \frac{1}{x^{y} }[/tex]

Using the Division Law of Indices: [tex]\frac{t^{x} }{t^{y} } = t^{x-y}[/tex]

Therefore:

[tex]\frac{a^{3}b^{-2} }{ab^{-4} } = a^{3-1}.b^{-2-(-4)}\\ \\ Simplifying\\ \\a^{3-1}.b^{-2-(-4)} = a^{2}b^{-2+4}\\ \\ =a^{2} b^{2}\\\\Therefore:\\\\\frac{a^{3}b^{-2} }{ab^{-4} } =a^{2} b^{2}\\[/tex]

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If the measurement of ∠3 & ∠6 is given,i.e.∠3 = 4x + 7 and ∠6 = 2x + 53 then ∠1 = 120 - 6x.

Given, ∠3 = (4x + 7) and ∠6 = (2x + 53)

Let ∠1 = a,

Now, as we know the angle sum property in triangles,

the sum of all the angles in a triangle is 180°.

So, ∠1 + ∠3 + ∠6  = 180°

a + (4x + 7) + (2x + 53) = 180°

a + 6x + 60 = 180

a = 180 - 60 - 6x

a = 120 - 6x

Hence, ∠1 = 120 - 6x, if the ∠3 = 4x + 7 and ∠6 = 2x + 53

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