A lifeguard at a swimming pool gives one-hour swim lessons to children in the morning before the pool is open to the public. She earns four dollars per class and fifty cents per swimmer. The minimum wage in her state is $7.25. She hopes to earn more than that amount of money during each class. Write an inequality that models the situation and find the minimum number of students she must teach in each class so that her earnings for that hour exceeds the minimum wage in her state.

Answer:

a=5, b=-2

Step-by-step explanation:

If you simplify the equation, you get:

3ax +6 -4x -4b - 11x - 14 = 0 =>

3ax - 15x -4b -8 = 0

group together x's and constants:

(3a-15)x -8 -4b = 0

To make this 0 for all x, we have to find an a such that 3a-15 = 0 and b such that -8-4b = 0. this leads to a=5, b=-2

A triangle's angles always add up to a total 180º, and a right triangle always has an angle equal to 90º.

90º + 34º + xº = 180º

124º + xº = 180º

xº = 56º

Answer: 1

Step-by-step explanation:

8 likes playing soccer

6 likes swimming

2 likes both

So in other words, because the 2 students likes swimming and playing soccer, they must be coming from the combined number of students (8+6=14) leaving only 1 who doesn't like to play either swimming/soccer.

There are 3 students who do not like either playing soccer or swimming and it can be determined by using set operation.

Given that,

In a class, there are 15 students. 8 of them like playing soccer, 6 of them like swimming, and 2 like both and swimming and playing soccer.

We have to determine,

How many students do not like either playing soccer or swimming?

According to the question,

Let x be the number of students who do not like either playing soccer or swimming.

Total number of students = n(U) = 15

Number of students who like playing soccer = n(A) = 8

Number of students who like swimming = n(B) = 6

Then,

The number of students like both = 2

Number of students who like swimming = Total number of students who like swimming - number of students like both

Number of students who like swimming  = 6 -2 = 4

And Number of students who like playing soccer = Total number of students who like playing soccer - number of students like both

Number of students who like swimming  = 8 -2 = 6

Therefore,

The total number of students = Number of students who like swimming + Number of students who like swimming + Number of students who do not like either playing soccer or swimming.

[tex]\rm 15 = (8-2) + (6-2) + x +2\\\\15 = 6+4+x+2\\\\15 = 12+x\\\\x = 15-12\\\\x=3[/tex]

Hence, there are 3 students who do not like either playing soccer or swimming.

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Answer:

(x + 6)² + (y - 2)² = 75

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 6, 2) and r = 5[tex]\sqrt{3}[/tex], hence

(x - (- 6))² + (y - 2)² = (5[tex]\sqrt{3}[/tex] )², that is

(x + 6)² + (y - 2)² = 75

Answer:

150°

Step-by-step explanation:

(30x+30)=2(20x-5)

x=4

AB=30×4+30=150

Answer:

150°

Step-by-step explanation:

The angle at the centre subtended by arc AB is twice the inscribed angle, that is

30x + 30 = 2(20x - 5) ← distribute

30x + 30 = 40x - 10 ( subtract 40x from both sides )

- 10x + 30 = - 10 ( subtract 30 from both sides )

- 10x = - 40 ( divide both sides by - 10 )

x = 4

Hence

arc AB = (30 × 4) + 30 = 120 + 30 = 150°

Answer:  [tex]y-7=-\frac{1}{4}(x+5)[/tex]

Step-by-step explanation:

The equation of the line in Point-Slope form is:

[tex]y-y_1=m(x-x_1)[/tex]

Where "m" is the slope and ([tex]x_1,y_1[/tex]) is a point on the line.

You can identify that in the equation of the line [tex]y-3=4(x+2)[/tex], the slope is:

[tex]m=4[/tex]

By definition, the slopes of perpendicular lines are negative reciprocals. Then, the slope of the other line is:

[tex]m=-\frac{1}{4}[/tex]

 Finally, knowing that this line passes through the point (-5, 7),you can substitute this point and the slope into the equation  [tex]y-y_1=m(x-x_1)[/tex] to get the equation of this line:

 [tex]y-7=-\frac{1}{4}(x-(-5))[/tex]

 [tex]y-7=-\frac{1}{4}(x+5)[/tex]

Answer: The graph is shifted 6 units to the right.

Step-by-step explanation:

It is important to remember that:

When [tex]f(x-k)[/tex], then the function is shifted "k" units to the right.

Knowing this and given the quadratic parent function [tex]y=x^2[/tex] and the function [tex]y-1=\frac{1}{2}(x-6)^2[/tex], you can observe that one of the transformations is the following:

[tex]f(x-k)[/tex]

Where:

[tex]k=6[/tex]

Therefore, you can notice that the effect is:

The graph is shifted 6 units to the right.

Slope-intercept form: y= mx + b (m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y))

To find the slope, use the slope formula and plug in 2 points:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

(x₁ , y₁) = (5, 2)

(x₂ , y₂) = (10, 6)

[tex]m=\frac{6-2}{10-5} =\frac{4}{5}[/tex]

[tex]y=\frac{4}{5}x+b[/tex]    To find b, plug in a point into the equation (5, 2)

[tex]2=\frac{4}{5}(5)+b[/tex]

2 = 4 + b

-2 = b

[tex]y=\frac{4}{5}x -2[/tex]

Answer:

y = 4/5x -2

Step-by-step explanation:

equation of a line passing through two points is given by

y - y₁ = m (x - x₁), where m = (y₂ - y₁) / (x₂ - x₁)

y₂ = 6, y₁ = 2

x₂ = 10, x₁ =5

m = (6-2)/(10-5)

m = 4/5

y - 2 = 4/5 (x - 5)

multiply both sides by 5

5(y -2) = 4(x - 5)

5y -10 = 4x -20

5y = 4x -20 +10

5y = 4x -10

divide through by 5

y =4/5x -2

The answer is C 84. Your welcome

Answer: The graph of g(x) is the graph of f(x) compresed vertically.

Step-by-step explanation:

Given the parent function [tex]f(x)^2[/tex], there are some transformations rules:

If [tex]f(x)=a(x^2)[/tex] when [tex]a>1[/tex], then it is stretched vertically.

If [tex]f(x)=a(x^2)[/tex] when [tex]0<a<1[/tex], then it is compresed vertically.

If [tex]f(x)=(ax)^2[/tex] when [tex]0<a<1[/tex], then it is stretched horizontally.

If [tex]f(x)=(ax)^2[/tex] when [tex]a>1[/tex], then it is compresed horizontally.

In this case for [tex]g(x)=\frac{2}{5}x^2[/tex], it has the form [tex]f(x)=a(x^2)[/tex] and [tex]0<a<1[/tex], then the graph of g(x) is the graph of f(x) compresed vertically.

The graphs of the functions f(x) = x^2 and g(x) = 2/5x^2 both represent parabolas, with g(x) being vertically compressed by a factor of 2/5 compared to f(x), which makes the g(x) graph appear narrower and less steep than the f(x) graph.

The functions f(x) = x2 and g(x) = 2/5x2 both represent parabolas, which are U-shaped curves on a graph. The significant difference between these two functions is their scaling, or how they stretch or compress vertically. The function f(x) = x2 has no scaling factor, which means it represents a standard square function with a one-to-one ratio. On the other hand, the function g(x) = 2/5x2 has a scaling factor of 2/5, meaning the graph of g(x) compared to f(x), will be vertically compressed by a factor of 2/5. This means the heights on the graph of g(x) are 2/5 times the corresponding heights on the graph of f(x). Therefore, the g(x) graph will appear narrower and less steep than the f(x) graph.

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The answer is 12 because there are 16 cups in 1 gallon. 192/16 is 12! Hope this helps! :)

Answer:

Convert 192 cups to gallons. Enter your answers in the boxes. There are (16) cups in 1 gallon. Therefore, 192 cups is equal to (12) gallons.

For this case we must simplify the following expression:

[tex]x ^ {12}[/tex]

By definition of power properties we have to:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then we can rewrite the expression as:

[tex]x ^ {- 12} = \frac {1} {x ^ {12}}[/tex]

ANswer:

[tex]x ^ {- 12} = \frac {1} {x ^ {12}}[/tex]

Answer:

[tex]\frac{1}{x^{12}}[/tex]

Step-by-step explanation:

The given expression is [tex]x^{-12}[/tex]

We never leave the final expression having a negative exponent.

So, we must change this negative exponent to a positive exponent.

In order to do that, we use the below property of exponent:-

[tex]x^{-m}=\frac{1}{x^m}[/tex]

Here m = 12

Therefore, by using this property, we get

[tex]x^{-12}\\\\=\frac{1}{x^{12}}[/tex]

Thus, the simplified form is

[tex]\frac{1}{x^{12}}[/tex]

Answer:

there is a SMALL DIFFERENCE in the mean number of stray cats placed in homes by a new leash on life animal clinic each week and the mean number of stray cats placed in homes by no ruff stuff animal each week

Step-by-step explanation:

i got it right lol

There is a small difference in the mean number of stray cats placed in homes.

We have given the mean of each distribution

The mean is the mathematical average of a set of two or more numbers that can be computed with the arithmetic mean method or the geometric mean method.

Therefore we can say that,

There is a small difference in the mean number of stray cats placed in homes by a new leash on life animal clinic each week and the mean number of stray cats placed in homes by no ruff stuff animal each week.

Therefore there is a small difference in the mean of each distribution.

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Answer:

The measure of angle B is [tex]132\°[/tex]

Step-by-step explanation:

step 1

Find the value of x

we know that

In an inscribed quadrilateral, opposite angles are supplementary

so

[tex]x\°+(2x+36)\°=180\°[/tex]

[tex]3x=180\°-36\°[/tex]

[tex]3x=144\°[/tex]

[tex]x=48\°[/tex]

step 2

Find the measure of angle B

[tex]B=(2x+36)\°[/tex]

[tex]B=(2(48)+36)\°=132\°[/tex]

Answer:

[tex]6x-4y[/tex] →  4.  [tex]2(3x-2y)[/tex]

[tex]6-4x[/tex] →    3.  [tex]2(3-2x)[/tex]

[tex]6x-4x[/tex] →  1. [tex]2x[/tex]

[tex]6x-4[/tex] →   2. [tex]2(3x-2)[/tex]

Step-by-step explanation:

You need to:

 Factor out 2 from [tex]6x-4y[/tex],  then you get the equivalent expression:

[tex]=2(3x-2y)[/tex] this matches with OPTION 4

Factor out 2 from [tex]6-4y[/tex], then you get the equivalent expression:

[tex]=2(3-2x)[/tex] this matches with OPTION 3

Make the subtraction for [tex]6x-4x[/tex],  then you get the equivalent expression:

[tex]=2x[/tex] this matches with OPTION 1

Factor out 2 from [tex]6x-4[/tex],  then you get the equivalent expression:

[tex]=2(3x-2)[/tex] this matches with OPTION 2

Answer:

6x-4y=2(3x-2y),

6-4x=2(3-2x),

6x-4x=2x,

6x-4=2(3x-2)

Step-by-step explanation:

We have been given 4 expressions

6x−4y, 6−4x, 6x−4x, 6x−4

Now we need to simplify or factor so that we can match each expression with an equivalent expression.

6x-4y=2(3x-2y)

6-4x=2(3-2x)

6x-4x=2x

6x-4=2(3x-2)

Now we can easily see that right side is unique for each of the given expression which can be easily matched with given choices.

Answer:

it is 1500 and .97 on  

Step-by-step explanation:

Answer:

a = 1500 (initial Bone density)

b = 0.97 (remaining percentage every year)

x = x (years)

Step-by-step explanation:

The question already sets x as the "years" variable, and the function must be expressed:

[tex]f(x) = a*b^x[/tex]

Then we can set a as the initial bone density: 1,500 kg/mg3

and b as the remaining percentage after each year: 100% - 3% = 97%

In decimal notation: 97% is equivalent to 0.97

The x exponent of b represents the succesive density reduction each year.

For example, replacing for values for the first 5 years we obtain the following results:

(Note: results are limited and rounded to two decimals)

[tex]f(x) = 1500*0.97^1 = 1455[/tex]

[tex]f(x) = 1500*0.97^2 = 1411.35[/tex]

[tex]f(x) = 1500*0.97^3 = 1369,01[/tex]

[tex]f(x) = 1500*0.97^4 = 1327,94[/tex]

[tex]f(x) = 1500*0.97^5 = 1288,10[/tex]

Answer:

[tex]\large\boxed{(16+5i)+(6-7i)=22-2i}[/tex]

Step-by-step explanation:

[tex](16+5i)+(6-7i)=16+5i+6+7i\qquad\text{combine like terms}\\\\=(16+6)+(5i-7i)=22-2i[/tex]

Answer:

22-2i

Explanation:

16+6=22

5i-7i=-2i

Answer:

B: 18x + 25

Step-by-step explanation:

2(9x+11)+3

Distribute the 2

2*9x + 2*11 +3

18x +22 +3

Combine like terms

18x +25

Answer:

32

Step-by-step explanation:

The face closest to us has 4 by 4 unit cubes which is 16 cubes.

There are 2 faces deep in the cubiod so the total is 32 unit cubes.

Answer:

The size of the cuboid is 32, or approximately 5.66 squared.

Step-by-step explanation:

First, find the dimensions of the cuboid.

(4)(4)(2)

Next, multiply the numerics (the values).

(4x4)x2 = 16x2 = 32

The cuboid's volume is 32, or about 5.66 squared.

Answer:

[tex] \frac{5x + 2}{x} = \frac{ - 12}{x - 1} [/tex]

[tex]equivalent \: to \\ \: (5x + 2)(x - 1) = - 12x[/tex]

For this case we must find an expression equivalent to:

[tex]\frac {5x+2} {x} = \frac {-12} {x-1}[/tex]

We multiply both sides of the equation by "x":

[tex]5x+2 = \frac {-12x} {x-1}[/tex]

We multiply both sides of the equation by "x-1":[tex](5x+2) (x-1) = - 12x[/tex]

ANswer:[tex](5x+2) (x-1) = - 12x[/tex]

3rd one for the answer all the other ones are wrong. It shifted down

ANSWER

[tex]y = \sqrt[3]{x + 4} - 1[/tex]

EXPLANATION

The given function is

[tex]y = \sqrt[3]{x} [/tex]

The transformation

[tex]y = \sqrt[3]{x + k} - c[/tex]

shifts the graph of the base function k units left and c units down.

Since the graph is shifted 4 units left, k= 4

Also, the graph is shifted 1 unit down.

This implies that c=1

The new equation is

[tex]y = \sqrt[3]{x + 4} - 1[/tex]

The last option is correct.

Answer:

-10√5 + 30

Step-by-step explanation:

This is a product of two monomials, so we would kind of like FOIL this.

F - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT.

O - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT.

I - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT.

L - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT.

Doing this will give 5 - 10√5 + 25. Combine like-terms to end up with -10√5 + 30 [or 30 - 10√5].

I am joyous to assist you anytime.

Answer: I think the answer is the second box.

Step-by-step explanation: It says 20 males have watched the show. I hope I helped you. If I am wrong, tell me in a polite way. :D

Hello there! The answer is the second chart, or B.

To find the answer, look at the parts of the question.

Let's start in the beginning. Note how it says "Of the 80 participants, 30 were male and 50 were female". This means that, looking at the options, in the "total" row, there should be a value for "30" by male, "50" by female and 80 at the bottom. This means that it cannot be A since this option says that there were 80 females and 80 males and 160 total, or C since it says there are 80 males and 55 females with a total of 135.

Next, it says that 45 have watched the show and 35 have not. If you look at the options left B and D, the only one the has these numbers for have and have not watched is B, making this the correct answer.

I hope this helps and have a great rest of your day! :)

Answer:

y=0.5x+3

Step-by-step explanation:

The statement that is always true is that supplementary and complementary angles are always adjacent angles.

The statement that is ALWAYS TRUE is (C) Supplementary and Complementary angles are always adjacent angles. Supplementary angles are two angles that add up to 180 degrees, while complementary angles are two angles that add up to 90 degrees. Adjacent angles are two angles that have a common vertex and a common side between them. So, it is always true that supplementary and complementary angles are adjacent angles because they share a common side.

Check the picture below.

recall the diameter is twice as long as the radius, thus d = 2r = 38.42 or rounded up to 38.

Answer:

C

Step-by-step explanation:

Since you are basically interested in what the graph looks like, there is no need to go beyond a good graphing program like Desmos. The graph is provided below.

Red: y = -1/2  x + 4

Blue:2y + x = -8

Since both of them have the same slope, they never meet.

The correct answer is C: No solution

Answer:

B)4,989,600

Step-by-step explanation:

The letters of 'MATHEMATICS'  contains 11 letters.

The following letters repeats twice, TT,MM,AA.

When we talk of distinguishable wasy, we are referring to arrangement without repetition.

Therefore the letters of "MATHEMATICS" can be arranged in [tex]\frac{11!}{2!2!2!}=4,989,600[/tex] distinguishable ways.

The correct answer is B.

The volume is (area of cross-section) x (length) .

-- The cross-section is a triangle.  The area of a triangle is

Area = (1/2) (base) (height) .

In this one, the base is 9/4 m and the height is 3-1/3 m .

Area = (1/2) (9/4 m) (3-1/3 m)

Area = (1/2) (9/4) (10/3)

Area = 90/24 m² .

-- Volume = (area of cross-section) x (length)

Volume = (90/24 m²) x (7-1/3 m)

Volume = (90/24) x (22/3) m³

Volume = (1,980 / 72) m³

Volume = 27.5 m³  

Answer:

3

Step-by-step explanation:

Graphing the best-fit quadratic curve for the data-set can be done using Ms. Excel Application.

The first basic step is to enter the data into any two adjacent columns of the excel workbook. Highlight the two columns where the values have been entered, click on the insert tab and then select the x,y scatter-plot feature. This will create an x,y scatter-plot for the data.

Next, click on the Add Chart Element feature and add a polynomial trend-line of order 2 which is basically a quadratic curve. Finally, check the display equation on chart box. This step will plot the quadratic curve as well as give the equation of the best-fit quadratic curve.

The attachment below shows the best-fit quadratic curve to the data-set and its corresponding equation.

A good approximation for the value of c from the equation is thus 3. This is simply the y-intercept of the curve. 3.21 is closer to 3.