The price of an item is $21.75. You give the cashier a $20 and a $10 bill. What is the change?

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ A=10\\ r=12 \end{cases}\implies 10=\cfrac{\theta \pi 12^2}{360}\implies 10=\cfrac{2\pi \theta }{5} \\\\\\ 20=2\pi \theta \implies \cfrac{20}{2\pi }=\theta \implies \cfrac{10}{\pi }=\theta \implies 3.18\approx \theta[/tex]

Answer:

2 2/3

Step-by-step explanation:

Make them into improper fractions first.

11/2 - 17-6

Then multiply 11/2 so that they have common denominators.

33/6 - 17/6

Then solve.

33/6 - 17/6 = 16/6

Then convert back into a mixed number.

2 4/6 or 2 2/3

Answer: The total is $12,250.

Step-by-step explanation: First, we will calculate the amount that Hillary has deposited over the past 35 years. She has deposited $200 for each of the past 35 years. The total that she has deposited is 200 x 35 = $7,000.

Her employer also deposits into her account 75% of what she has deposited. In order to calculate their contribution you need to multiply $7,000 x .75 = $5,250.

The total that has been deposited into the account is $7,000 + $5,250 = $12,250.

Hillary's total contribution over the 35 years was $84,000. The employer matched 75% of Hillary's contribution, totaling $63,000. The combined contribution of Hillary and her employer for 35 years is $147,000.

Hillary has been depositing $200 into her 401(k) per month for the past 35 years. For 35 years, there are a total of 35 times 12 months which equals 420 months. Given this, Hillary has contributed $200 times 420 months which is $84,000.

Her employer has a 75% match on all her contributions. This means they are adding another 0.75 times the $84,000, which equals $63,000.

Therefore, the total contribution by both Hillary and her employer over the 35 years is both amounts added together: "$84,000 (Hillary’s contribution) + $63,000 (Employer match) = $147,000".

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The correct answer is A.

Hope this helps.

Answer:

The answer is A.

Step-by-step explanation:

This is because it wants you to represent the answer in Slope-Intercept Form. Which is y = mx + b. B is the y intercept, which is where it starts. On a graph, the y-intercept starts at ZERO. The 3 is at the zero, so you know what the first number is. Then, you need to see the fluctuation (change) in the value of each number in the y as you increase in x. As the x increases by one, you can see that the y decreases by two. So now you know, the ROC or Rate of Change is two, which is your slope. Slope is m. So if m is two, that makes 2x.

Hopefully this helps!

Answer:

0.125

Step-by-step explanation:

solving the problem gives 0.125

For this case we must resolve the following expression:

[tex]\sqrt {(0.5) ^ 6}[/tex]

By definition of properties of roots and powers we have to:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So we have to:

[tex]\sqrt {(0.5) ^ 6} = 0.5 ^ {\frac {6} {2}} = (0.5) ^ 3 = 0.125[/tex]

So, we have to:

[tex]\sqrt {(0.5) ^ 6} = 0.125[/tex]

Answer:

0.125

Option B

Answer:

25 feet

Step-by-step explanation:

You can superimpose a triangle in this situation.  The height from the ground to the top of the ladder along the wall is one leg of the triangle, the distance the ladder is from the wall is the other leg, and the length of the ladder is the hypotenuse.  

Use Pythagorean theorem to solve, which is a² + b² = c² where a, and b are the legs, and c is the hypotenuse...

We have

7² + 24² = c²

   49 + 576 = c²

       625 = c²

        25 = c          

*Tecnhically the answer is ±25, but it's a length, so we disregard the negative answer.

The best model for the given data is likely a quadratic model because the y values increase then decrease and then increase again, a typical pattern of a quadratic model.

To determine which model best fits the given set of data: (-4,-2), (-2,1), (2,-2), (4,3), we need to examine the relationship between the x and y values. Based on the given data, there is not a consistent increase or decrease, which suggests that the best model is not linear.

Quadratic model and cubic model can also be tested as they can capture complex patterns, which makes them a good fit for data that has peaks and valleys, such as our data set.

Upon examining the data, we realize there is a pattern where the value of y increases, then decreases, then increases again which is typically of a quadratic model. Therefore, the best fit for this data set is most likely a quadratic model.

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This is F(n) = 3n

The X is an interger which is holding a value

The relationship between Y and X is 3n as we multiply X by 3 to get the value of Y and is proven yet so.

The rule which represent the function as shown in the table is:

                 [tex]f(n)=3n[/tex]

We are given a table as follows:

  x       2          -1         0

  y       6          -3         0

Now we are asked to find the function which represent these table of values.

a)

    [tex]f(n)=n+3[/tex]

Here x is represented by n and y by f(n)

when n=2 we must have f(n)=6

Hence, we put n=2 in the given expression and check,

[tex]f(2)=2+3=5\neq 6[/tex]

Hence, this is not a correct function.

b)

[tex]f(n)=\dfrac{1}{3}n[/tex]

Again we check for n=2

We have:

[tex]f(2)=\dfrac{1}{3}\times 2=\dfrac{2}{3}\neq 6[/tex]

Hence, it is not a correct expression.

So we are left with option: c)

c)

[tex]f(n)=3n[/tex]

By putting the value of n=2,-1 and 0

we see that the expression matches the table of values.

( since,

when n=2 we have:

[tex]f(2)=3\times 2=6[/tex]

when n= -1 we have:

[tex]f(-1)=3\times -1=-3[/tex]

and when n=0 we have:

[tex]f(0)=3\times 0=0[/tex] )

Hence, this is a correct expression.

Answer:

No 1 inch cubes will fit

28 one-half inch cubes will fit

Step-by-step explanation:

No cubes with a side length of 1 inch will fit because one dimension of the prism is only 1/2 inches, so we can't fit a 1 inch cube in anywhere.

Since one dimension is 1/2 inch, we can line up 1/2 inch cubes along the other 2 dimensions.  Let's say that the 1/2 inch dimension is the base, the 2 inch dimension is the height, and the 7/2 inch dimension is the length.

We can stack the cubes 4 high, (2 inches of height with 1/2 inch being the cube height, there are 4 halves in 2).

We can place 7 cubes along the length (7/2 inches = 3.5 inches.  There are 7 halves in 3.5).  

So we can have 4(7) = 28  one half inch cubes can fit in to the prism

Answer:

option D

D. x = 5, y = 2

Step-by-step explanation:

Given in the question two equation,

Equation 1

5.3x + y = 28.5

Equation 2

4.2x + 3.1y = 27.2

rearrange equation 1 in terms of y

y = 28.5 - 5.3x

Substitute the value of y in equation 2

4.2x + 88.35 - 16.43x = 27.2

4.2x - 16.43x = 27.2 - 88.35

-12.23x = -61.15

x = 61.15/12.23

x = 5

put value of x in any of the equation

y = 28.5 - 26.5

y = 2

Let B = the weight of box B

Let 2B = the weight of box A

Let 2B + 30 = the weight of box C

B + 2B + 2B + 30 = 640

5B = 610

B = 122 pounds, weight of box B

2B = 2(122) = 244 pounds, weight of box A

2B + 30 = 2(122) + 30 = 274 pounds, weight of box C

hope this helps

Answer: 90b (grams)

Step-by-step explanation:

Given statement : A box weighs 90 grams.

Let b denotes the number of boxes, then the weight of b boxes will be :-

[tex]\text{Total weight of b boxes}=b\times\text{Weight of one box}\\\\\Rightarrow\ \text{Total weight of b boxes}=b\times90\\\\\Rightarrow\ \text{Total weight of b boxes}=90b[/tex]

Hence, the expression for the weight  ( in grams) of b boxes : 90b

Answer:   (x - 2)(7x + 13)  which is equivalent to 7x² - x - 26

Step-by-step explanation:

[tex].\qquad \dfrac{g(x)}{x^2+x-6}=7x+13\\\\\\\implies g(x)=(x^2+x-6)(7x+13)\\\\.\qquad \qquad =(x+3)(x-2)(7x+13)\\\\\\\text{What is g(x) divided by x+3?}\\\\\dfrac{g(x)}{3}=\dfrac{(x+3)(x-2)(7x+13)}{x+3}\\\\\\.\qquad =(x-2)(7x+13)\\\\\\.\qquad =7x^2+13x-14x-26\\\\\\.\qquad =\large \boxed{7x^2-x-26}[/tex]

Answer:

2 is your answer. 36 divided by 6 is 6. 6 divided by 3 eaquls 2

Step-by-step explanation:

Answer:

(36÷6)÷3 = 2

Step-by-step explanation:

First, you would solve what is in the parentheses.

(36÷6)÷3 = (6)÷3           Now, find 6÷3

                = 6÷3 = 2

so,  (36÷6)÷3 = 2

I hope you find this helpful. :)

Answer:

No solution

Step-by-step explanation:

Each side of the equation,once distributed, has 5x.

The 5x's cancel out to x= x-5

Which is incorrect and has no solution.

Answer:

No solution

Step-by-step explanation:

Answer:

Reflection across the line y=x followed by translation 10 units to the right and 4 units up.

Step-by-step explanation:

Triangle ABC has vertices at points A(-6,2), B(-2,6) and C(-4,2).

1. The reflection across the line y=x has the rule

(x,y)→(y,x).

Thus,

2. The translation 10 units to the right and 4 units up has the rule

(x,y)→(x+10,y+4).

Thus,

Points A'B'C' are exactly the vertices of the triangle A'B'C'.

The sequence of transformations that maps triangle ABC to triangle A’B’C’ is a reflection across the y-axis, followed by a translation 8 units to the right and 10 units up.

The sequence of transformations that maps triangle ABC to triangle A’B’C’ is a reflection across the y-axis, followed by a translation 8 units to the right and 10 units up.

First, the reflection across the y-axis changes the x-coordinate to its opposite. So, the new coordinates of point A are (-2, 5), the new coordinates of point B are (-3, 2), and the new coordinates of point C are (-5, -1).

Next, the translation moves the triangle 8 units to the right and 10 units up. So, the new coordinates of point A are (6, 15), the new coordinates of point B are (5, 12), and the new coordinates of point C are (3, 9).

Answer:

both of them togther need to equal 180 so

10x-20+6x+8=180

16x-12=180

16x=192

192/16=12

x=12

Step-by-step explanation:

Answer:

y = 3x + 3

Step-by-step explanation:

The graph passes through the points (-1, 0) and (0, 3).

Slope = m = Δy/Δx = (y₂ - ₁)/(x₂ - x₁) = (3 - 0)/(0 - (-1)) = 3/1 = 3.

The y-intercept (b) is at y = 3.

The equation for a straight line is

y = mx + b

Thus, the equation for your line is

y = 3x + 3

Answer: # is 1.15 miles

2/5 of a mile is the same as 4 tenths of a mile. 3/4 of a mile is the same as .75. So ---- .75 plus .4

Step-by-step explanation:

Answer:

f(x)⁻¹ = 3x/(2 - x)

Step-by-step explanation:

Find the inverse of f(x) = 2x/(x+3)

The first step is to let f(x) = y

y = 2x/(x+3)

Then make x the subject of the formula

y = 2x/(x+3)

y(x + 3) = 2x

yx + 3y = 2x

yx - 2x = -3y

x(y - 2) = -3y

x = -3y/(y - 2)

∴ f(x)⁻¹ = -3x/(x - 2)

Dividing both numerator and denominator by -1;

f(x)⁻¹ = 3x/(2 - x)

No, the frequencies do not decrease from the maximum frequency to a low frequency

Answer:

Yes, all the requirements are met.

Step-by-step explanation:

Frequency Distribution is a graph or table which shows the frequency of different outcome.

Normal Distribution has bell like-shape.

Since here the value of frequency is less for score 50-69 then it increases from 70- 109 then the frequency is again decreasing from score 110-149. So the curve of frequency distribution when plotted appears like bell-shaped. Hence, It appears like a normal distribution.

Answer:

Step-by-step explanation:

Each factor corresponds to a zero of the function.

If (x+4) is set = to 0, the corresponding root is x = -4.

If (-7x - 60) is set = to 0, the corresponding root is x = -60/7.

The factors (-7x-60)(x+4) represent the roots or solutions of the original quadratic equation in its expanded form, which are obtained by setting each factor equal to zero and solving for x.

The factors (-7x-60)(x+4) in the factored form represents the roots of a quadratic equation. In a quadratic equation of the form ax² + bx + c = 0, the roots or solutions of the equation can be obtained by factoring the quadratic expression. In this case, the equation being factored must have been -7x² - 28x - 60x - 240 = 0. The roots are the values that make each factor equal to zero, so the roots of the original equation are obtained by solving -7x-60 = 0 and x+4 = 0, to get x = -60/(-7) = 8.57 and x=-4.

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Answer: 890.12 cm^3

Step-by-step explanation:

The formula for the volume of a cylinder is

[tex]V=\pi *r^2*h[/tex]

V=628.3185307 cm^3

or simply

V=628.32 cm^3

Since, you know the radius of the hemisphere on top, you also know the radius since the height of the hemisphere is the same as it is wide.

Next, the formula for the volume of a sphere is

[tex]V=\frac{4}{3} \pi *r^3[/tex]

so the volume of a hemisphere is half of that or:

[tex]V=\frac{2}{3} *\pi *r^3[/tex]

V= 261.7993878 cm^3

or simply

V=261.80 cm^3

Finally, you add both of the volumes together to get

V= 890.1179185 cm^3

or simply

V=890.12 cm^3

Answer:

x = 5√3; y = 5

Step-by-step explanation:

Finding y:  The sine function links the 30° angle, the 10 unit hypotenuse and the side opposite the angle, y:

sin 30° = 1/2 = y/10

Solve the equation of ratios

1        y

-- = -----  using cross-multiplication first:  2y = 10 → y = 5

2     10

We can now find x either by using a similar approach and the cosine function or by using the Pythagorean Theorem:

x² + y² = 10² = 100  →  x² = 100 - y²  =  100 - 5²  = 75

If x² = 75, then x = ±√75 = ± (√25)·(√3)   →  ±5√3

Since lengths are always positive,   take x = 5√3 as the answer.

a) the first and last one : 6x + 9x and 15x

b) second and third one : 4*1 + 4*9y and 4 + 36y

pls mark brainliest!

Answer:

You'll need [tex]36\ ft^{2}[/tex] of outdoor carpet for this hole

Step-by-step explanation:

we know that

The area of the outdoor carpet is equal to the area of the triangle minus the area of the rectangle

step 1

Find the area of the rectangle

The area of rectangle is equal to

[tex]A=bh[/tex]

we have

[tex]b=3\ ft[/tex]

[tex]h=2\ ft[/tex]

Calculate the area

[tex]A=(3)(2)=6\ ft^{2}[/tex]

step 2

Find the area of the triangle

[tex]A=(1/2)bh[/tex]

we have

[tex]b=12\ ft[/tex]

[tex]h=7\ ft[/tex]

Calculate the area

[tex]A=(1/2)(12)(7)=42\ ft^{2}[/tex]

step 3

Find the difference

[tex]42\ ft^{2}-6\ ft^{2}=36\ ft^{2}[/tex]

Answer:

79.25 square inches

Step-by-step explanation:

To find the area of the figure, split it into two shapes - a rectangle and a semi-circle.

The area of a rectangle is A = b*h. Substitute b = 10 and h = 4.

A = 4*10 = 40.

The area of a semi-circle is A =1/2 πr². Substitute r = 5 since the diameter is 10.

A =1/2 π5² = 12.5π = 39.25.

Add the two areas together.

39.25 + 40 = 79.25

Yeah the correct option is option D

Answer:

Correct choce is (a). 30.

Step-by-step explanation:

Given equation is [tex]f(x)=x^2-x[/tex].

Now we need to find the value of (fof)(3). Then select correct matching choice from the given choices. Where given choices are:

(a). 30

(a). 33

(a). 6

(a). -6

Now let's find  [tex](fof)(3)[/tex]

[tex](fof)(3)=f(f(3))[/tex]

[tex](fof)(3)=f(3^2-3)[/tex]

[tex](fof)(3)=f(9-3)[/tex]

[tex](fof)(3)=f(6)[/tex]

[tex](fof)(3)=6^2-6[/tex]

[tex](fof)(3)=36-6[/tex]

[tex](fof)(3)=30[/tex]

Hence correct choce is (a). 30.

Answer:

The correct answer is option A.  30

Step-by-step explanation:

It is given that

f(x) = x² - x

To find f o f(3)

F(x) = x² - x

f(3) = 3² - 3

     = 9 - 3  6

f o f(3) = f(6)

f(6) = 6² - 6

      = 36 - 6 = 30

Therefore the correct answer is f o f(3) = 30

The correct option is Option a.  30

410 is your answer, 2 subtractions signs next to eachother make a plus sign, so in the end it’s just 356+54 :)

Answer:

410

Step-by-step explanation: