Sean had 3 building sets and 18 toy cars in his toy box. At his birthday party, he received 20 gifts. He got 3 train sets, 4 building sets and 9 toy cars. The rest of the gifts are comic books. 3/4 of the gifts are wrapped. 1/3 of the wrapped gifts are wrapped in blue wrapping paper and 1/ 5 of them are wrapped with ribbons. What fraction of the gifts are train sets? What fraction of the gifts are comic books? What fraction of his toy cars are new?

The time period of the loan was 1 year.

9514 1404 393

Answer:

  x = 8

Step-by-step explanation:

Corresponding segments are proportional.

  2x/12 = (x+4)/9

  18x = 12(x +4) . . . . . multiply by 9·12

  6x = 48 . . . . . . . . . . subtract 12x

  x = 8  . . . . . . . . . . . . divide by 6

Let's call the amount of money Rosa spent on art supplies "x". Since Rosa spent 1/4 of her money on art supplies, we can write the equation:

x = (1/4) * 300

x = 75

So Rosa spent $75 on art supplies.

Now we can find out how much money she had left after spending the $75 on art supplies.

remaining = 300 - 75

remaining = 225

And we can find out how much she spent on the boots.

boots = (2/5) * remaining

boots = (2/5) * 225

boots = 90

So Rosa spent $90 on the boots.

Let's call the amount of money Rosa spent on art supplies "A". Since Rosa spent 1/4 of her original $300 on art supplies, we can write the equation:

A = 1/4 * $300

A = $75

So, Rosa spent $75 on art supplies.

Next, let's find out how much money she had left after buying the art supplies. We can subtract the amount she spent on art supplies from her original $300:

$300 - $75 = $225

Now, let's find out how much she spent on the boots. We know that she spent 2/5 of the remainder on the boots, so we can write the equation:

B = 2/5 * $225

B = $90

So, Rosa spent $90 on the boots.

Answer: A

Step-by-step explanation:

The parabola has an open hole at x=3 and the line has a closed hole at x=3, so there should be \(x < 3\) for the parabola and \(x \geq 3\) for the line.

This eliminates all the options except for A.

Answer:

240

Step-by-step explanation:

Hello There!

Note: the little arrows indicate that the line can be extended and it's opposite side will never touch indicating that it's a parallelogram

The formula for area of a parallelogram is

\(A=bh\)

where b = base and h = height

the given dimension are

height = 15

base = 16

so all we have to do is plug in the values into the formula

\(A=(15)16\\15*16=240\\A=240\)

so we can conclude that the area of the polygon is

240 square units

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

------------------

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

The graph of the function is attached

The amplitude and the period are 5 and 2π

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

f(x) = 5cos(θ)

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

So, we have

A = 5

Period = 2π/1

Evaluate

A = 5

Period = 2π

Hence, the amplitude is 5 and the period is 2π

The graph of the function is attached

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Answer:

The inverse of f(x) is

 \(f^{-1} (x) = \frac{2 x+3}{4}\)

Step-by-step explanation:

Explanation:-

Given  \(f(x) = \frac{4 x-3}{2}\)

Inverse of f(x)

f(x) is a one-one  function

let f(x₁) and  f(x₂) be two functions are

     \(f(x_{1} ) = \frac{4 x_{1} -3}{2}\)

    \(f(x_{2} ) = \frac{4 x_{2} -3}{2}\)

 ⇒    \(\frac{4 x_{1} -3}{2} = \frac{4 x_{2} -3}{2}\)

  ⇒  4 x₁ - 3 = 4 x₂ - 3

  ⇒  4 x₁ = 4 x₂

  ⇒  x₁ = x₂

Given function is one-one function

                   y = f(x) = \(\frac{4 x-3}{2}\)

              ⇒ 2 y = 4 x - 3

             ⇒  4 x =  2 y + 3

            ⇒   \(x = \frac{2 y + 3}{4}\)

           ⇒ f⁻¹(x)  \(= \frac{2 y + 3}{4}\)

Given function f(x) is onto function

Therefore f(x) is one-one and onto function

           \(f^{-1} (x) = \frac{2 x+3}{4}\)

These statements are about square powers.

Remember that square powers are those powers that have a number 2 as an exponent, which means we must multiply the number by itself.

Having said that, the true statement is

The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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Answer:

A

Step-by-step explanation:

With function transformation, added/subtracted numbers outside of the x always mean the function is being translated up/down. In this case, since the 2 is being replaced with a 4, the new function is 2 units higher than the previous function.

Answer:

the radius is 7

the area is 154

Answer:

864 grams

Step-by-step explanation:

540 divided by 5=108 grams per cupcake

108 times 8=864 grams

Answer:

The Sale Price is $16.80 Dollars

Step-by-step explanation:

First I find out what 30% of 24 is.

24 * 30% = 7.2

Next we subtract.

24 - 7.2 = 16.80

So, the answer is 16.80

Hope this helps! :)

The graph of the function f(x) = 5(2)^x is an upward-sloping exponential curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing the x-axis.

The function f(x) = 5(2)^x represents exponential growth. Let's analyze its graph.

As x increases, the value of 2^x grows exponentially. Multiplying it by 5 further amplifies the growth. Here are a few key points to consider:

When x = 0, 2^0 = 1, so f(0) = 5(1) = 5. This is the y-intercept of the graph, meaning the function passes through the point (0, 5).

As x increases, 2^x grows rapidly. For positive values of x, the function will increase quickly. As x approaches positive infinity, 2^x grows without bound, resulting in the function also growing without bound.

For negative values of x, 2^x approaches zero. However, the function is multiplied by 5, so it will not reach zero. Instead, it will approach y = 0, but the graph will never touch or cross the x-axis.

The function is always positive since 2^x is positive for any value of x, and multiplying by 5 does not change the sign.

Based on these observations, we can conclude that the graph of f(x) = 5(2)^x will be an exponential growth curve that starts at (0, 5) and increases rapidly as x moves to the right, never crossing or touching the x-axis.

The graph will have a smooth curve that rises steeply as x increases. The rate of growth will be determined by the base, in this case, 2. The larger the base, the steeper the curve. The function will approach but never reach the x-axis as x approaches negative infinity.

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Answer:

(C.) d= sqrt (x2-x1)^2+(y2-y1)^2, where d is the distance between points (x1,y1) and (x2,y2).

Step-by-step explanation:

Answer:

\(\Huge \boxed{\mathrm{C }}\)

Step-by-step explanation:

\(\sf The \ distance \ formula \ is \ given \ as:\)

\(d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2 }\)

\(d \Rightarrow \sf distance\)

\((x_1,y_1) \Rightarrow \sf Coordinates \ of \ the \ first \ point\)

\((x_2,y_2) \Rightarrow \sf Coordinates \ of \ the \ second \ point\)

Answer:

The walkway should be 2ft wide.

Step-by-step explanation:

Let x be the width of the walkway surrounding the pool.

The area including the pool is 560ft².

Let's solve for the value of x.

The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.

A = lw

560 = (24 + 2x)(16 + 2x)

560 = 384 + 48x + 32x + 4x²

4x² + 80x + 384 - 560 = 0

4x² + 80x - 176 = 0

Divide the whole equation by 4

x² + 20x - 44 = 0

(x + 22)(x -2) = 0

x = -22; x = 2

Since we are dealing with dimensions, take the one with the positive value.

x = 2ft

Let's check

560ft² = (24ft + 2x)(16ft + 2x)

560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))

560ft² = (24ft + 4ft)(16ft + 4ft)

560ft² = (28ft)(20ft)

560ft² = 560ft² ✔

Answer:

He would drive 536 miles in 5 hours

Step-by-step explanation:

First set up your equation:

804 = 12x

Divide 804 by 12 and get 67 = x

Since per one hour you drive 67 miles, multiply 67 by 8 and get 536.

So, he drives 536 miles in 5 hours

Answer: I think 402

Step-by-step explanation: I divided 804 to 4 and I got 201 then I added 201+201= 402 and each 4 hours he went 201 miles so if you add 201 and 201 you get 402 miles. Hope it helped!! :)

To answer this question we will use the following slope-point formula for the equation of a line:

Therefore, the equation of the line that has a slope of 1/3 and passes through the point (-3,3) is:

Simplifying the above equation we get:

Adding 3 to the above equation we get:

Answer:

(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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1.7a+0.3a=0.8

2a=0.8

a=0.4

Answer:

$85

Step-by-step explanation:

(if you need to explain how the anwer was gotten)

34 ÷ 4 = 8.5

8.5 × 10 = 85

The value of the triple integral\(\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}\) by using spherical coordinates \(2\pi(e^{-1}-e^{-9})\).

Given that the triple integral is-

\(\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}\)

E is the region bounded by the spheres which are,

\(x^2+y^2+z^2=1\\\\x^2+y^2+z^2=9\)

In spherical coordinates we have,

x = r cosθ sin ∅

y = r sinθ sin∅

z = r cos∅

dV = r²sin∅ dr dθ d∅

E contains two spheres of radius 1 and 3 () respectively, the bounds will be like this,

1 ≤ r ≤ 3

0 ≤ θ ≤ 2π

0 ≤ ∅ ≤ π

Then

\(\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}\)

\(\int\int\int _{E} \frac{e^{-r^2}}{r}r^2Sin\phi drd\phi d\theta\\\\2\pi \int_{0}^{\pi} \int_1^3 re^{-r^2} dr d\phi\\\\2\pi \int_1^3 re^{-r^2} dr\\\\2\pi(e^{-1}-e^{-9})\)

The complete question is-

Use spherical coordinates to evaluate the triple integral ∭ee−(x2 y2 z2)x2 y2 z2−−−−−−−−−−√dv, where e is the region bounded by the spheres x2 y2 z2=1 and x2 y2 z2=9.

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The values of x and y after solving this system of equations will be 32/35 and -88/105 respectively.

System of equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations.

For a set of two equations, in elimination we make the coefficient of any one variable equal to the coefficient of the same variable in the other equation. This can be done by multiplying or dividing the whole equation accordingly. Then we subtract the equations from each other and solve for one variable.

6x - 3y = 8 (multiplying this equation by -2 to make the coefficient of y equal to that of in the equation 23x + 6y = 16)

Now are equations are

-12x + 6y = -16 and 23x + 6y = 16

subtracting eq 1 from eq 2 gives,

35x = 32 (Note that y has now been eliminated)

x = 32/35

Substituting this value of x in any one of the equations will then give the value of y to be -88/105

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The cost of 20 T-Shirt will be 2560 when cost of one t-shirt is 128.

When a selling price and profit are provided, cost price equals selling price plus profit. When the selling price and loss are disclosed, cost price equals selling price plus loss.

Profit is calculated as S.P. - C.P. If the selling price is less than the cost price, the difference between the two is the loss incurred. Loss is also equal to C.P. - S.P.

We must divide the gross profit by the entire revenue for the year, multiply by 100, and then find the gross profit margin. We must divide net income (or net profit) by the entire annual revenue before multiplying the result by 100 to get the net profit margin.

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Answer:

Maria needs 13 flats of flowers to plant in the bed.

Step-by-step explanation:

Total plants = Number of flowers + Number of spaces

Total plants = 38 + 38 = 76

Since each flat contains 6 plants, we can divide the total number of plants by the number of plants per flat to find the number of flats needed:

Number of flats = Total plants / Plants per flat

Number of flats = 76 / 6 = 12.67