Of the 40 students in Ms. Carr's class, 87.5% live less than 10 miles from school. How many of the students in Ms. Carr's class live less than 10 miles from school.

Answer:

Step-by-step explanation:

[tex]\frac{6}{\frac{2}{6} } =6*\frac{6}{2} =6*3=18[/tex]

Answer:

18

Step-by-step explanation:

6/(2/3)

Turn 6 into a fraction first.

(6/1) / (2/6)

(6/1) x (6/2)

36/2

18

Answer:

he drinks 56oz of water

Step-by-step explanation:

divide 21 by 3 that would equal seven than multiply it by 8 which is 56

Answer:

57 ounces

Step-by-step explanation:

[tex]\frac{3 miles}{8oz water}[/tex] × 7 = [tex]\frac{21miles}{56ozwater}[/tex]

The system of linear inequalities are:

[tex]a + b \geq 20\\\\2.50a + 7b\leq 80[/tex]

Solution:

Let "a" be the number of small candles bought

Let "b" be the number of large candles bought

Cost of each small candle = $ 2.50

Cost of each large candle = $ 7

He needs to buy at least 20 candles

Therefore, number of small candles and number of large candles bought must be at least 20

Thus, we frame a inequality as:

[tex]a + b\geq 20[/tex]

"at least" means greater than or equal to

Here, we used "greater or equal to" symbol because, he can buy 20 candles or more than 20 candles also

He can spend no more than 80 dollars

Which means, he spend maximum 80 dollars or less than 80 dollars also

So we have to use "less than or equal to" symbol

Thus, we frame a inequality as:

Number of small candles bought x Cost of 1 small candle + number of large candles bought x Cost of 1 large candle [tex]\leq[/tex] 80

[tex]a \times 2.50 + b \times 7 \leq 80\\\\2.50a + 7b\leq 80[/tex]

Thus the system of linear inequalities are:

[tex]a + b \geq 20\\\\2.50a + 7b\leq 80[/tex]

Answer:

10 rows with the set of 100 blocks is what she will make

Step-by-step explanation:

Where

First row is 1

Second row is 3

Third row is 5

This shows that the blocks are set in an oddly fashion

Meaning each row has a odd number of blocks

Therefore from

1 block- row 1

3 blocks- row2

5 blocks- row 3

7 blocks - row 4

9 blocks- row 5

11 blocks - row 6

13 blocks- row 7

15 blocks - row 8

17 blocks- row 9

19 blocks - row 10

Add of the blocks it amounts to 100 blocks

Meaning the triangular will be at the 10th row when she has use 100 blocks

Answer:

Step-by-step explanation:

Using this formula to find the length of the arc

Arc length = [tex]2\pi r (\frac{\theta}{360} )[/tex]

Here [tex]\theta = \frac{360}{60}\times 45[/tex]   [for 45 minutes]

            [tex]=270^\circ[/tex]

Radius(r) = length of the minute hand = 12 cm

The length of the arc is = [tex]2\pi \times 12\times \frac{270}{360}[/tex]

                                     = 56.57 cm

Therefore the tip of the minute hand on the clock moves 56.57 cm in 45 minutes.

Answer:

4x² - 20x + 16

Step-by-step explanation:

Given

(4x - 4)(x - 4)

Each term in the second factor is multiplied by each term in the first factor, that is

4x(x - 4) - 4(x - 4) ← distribute both parenthesis

= 4x² - 16x - 4x + 16 ← collect like terms

= 4x² - 20x + 16

Answer: four-fifteenths or [tex]\frac{4}{15}[/tex]

Step-by-step explanation:

What is written with words is mathematically expressed as:

[tex]\frac{9}{15}-\frac{2}{6}[/tex]

We can simplify both fractions, by dividing the numerator and denominator of the first by 3 and dividing the numerator and denominator of the second by 2:

[tex]\frac{9}{15}=\frac{3}{5}[/tex]

[tex]\frac{2}{6}=\frac{1}{3}[/tex]

Then:

[tex]\frac{3}{5}-\frac{1}{3}[/tex]

Calculating the least common multiple (l.c.m) in the denominator as [tex]15[/tex]:

[tex]\frac{9-5}{15}=\frac{4}{15}[/tex] This is the result: four-fifteenths

Answer:

9120

Step-by-step explanation:

Rachel bought six 20-cent stamps and eight 30-cent stamps.

Step-by-step explanation:

Given,

Amount spent on stamps = $3.60 = 3.60*100 = 360 cents

Let,

x = 20 cent stamps

y = 30 cent stamps

According to given statement;

20x+30y=360      Eqn 1

x = y-2                  Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]20(y-2)+30y=360\\20y-40+30y=360\\50y=360+40\\50y=400[/tex]

Dividing both sides by 50

[tex]\frac{50y}{50}=\frac{400}{50}\\y=8[/tex]

Putting y=8 in Eqn 2

[tex]x=8-2\\x=6[/tex]

Rachel bought six 20-cent stamps and eight 30-cent stamps.

Keywords: linear equation, substitution method

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Final answer:

Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps. We solved a system of equations representing the cost of the stamps and their quantity relationship to determine the numbers.

Explanation:

Rachel spent $3.60 for stamps to mail packages, buying 30-cent stamps and 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. To solve this, we can use a system of equations to represent the total cost and the relationship between the number of stamps:

Let x be the number of 30-cent stamps.

Let y be the number of 20-cent stamps.

Based on the information given:

0.30x + 0.20y = 3.60 (Total cost equation)

y = x - 2 (Relationship between the stamps)

We substitute the second equation into the first equation:

0.30x + 0.20(x - 2) = 3.60

0.30x + 0.20x - 0.40 = 3.60

0.50x = 4.00

x = 8

Now we solve for y using the second equation:

y = 8 - 2

y = 6

So Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps.

Answer:

check the photo.

Step-by-step explanation:

The inverse of the function

f(x) = ax + b is g(x) = (x/a) - (b/a)

(learn it by heart)

the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].

To find the average rate of change of the function over the interval (10 < x < 15), we use the formula:

[tex]\[ \text{Average Rate of Change} = \frac{\text{Change in } f(x)}{\text{Change in } x} \][/tex]

We can calculate the change in [tex]\(f(x)\)[/tex] by subtracting the function values at the end and start of the interval, and the change in x by subtracting the end and start values of x.

Given the function values:

- [tex]\(f(10) = 30\)[/tex]

- [tex]\(f(15) = 24\)[/tex]

And the interval [tex]\(10 < x < 15\)[/tex], the change in [tex]\(f(x)\) is \(f(15) - f(10) = 24 - 30 = -6\)[/tex].

The change in x is [tex]\(15 - 10 = 5\)[/tex].

Now, we plug these values into the formula for the average rate of change:

[tex]\[ \text{Average Rate of Change} = \frac{-6}{5} \][/tex]

So, the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].

The complete Question is given below:

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 < x < 15

x       |   f(0)

0       |   42

5       |   36

10      |   30

15      |   24

20     |   18

25     |   12

Answer:

∠ ABC = ∠ DBE = 65°

∠ ABD = ∠ CBE = 115°

Step-by-step explanation:

See the diagram attached to this question.

Now, ∠ ABC and ∠ DBE are two vertically opposite angles.

So, 3x + 38 = 5x + 20

⇒ 2x = 18

⇒ x = 9

So, ∠ ABC = ∠ DBE = 3(9) + 38 = 65° (Answer)

Again, ∠ ABC and ∠ ABD are supplementary angles.

Then, ∠ ABC + ∠ ABD = 180°

⇒ ∠ ABD = 180° - 65° = 115°

And ∠ ABD = ∠ CBE {Vertically opposite angles}

So, ∠ ABD = ∠ CBE = 115° (Answer)

Answer:

10 Girls

Step-by-step explanation:

This shows that there is twice as many boys in the gym class than girls.

Step 1:  Determine what the ratio relates to the amount

1:2 -> 10:20

10 Girls

20 Boys

Answer:

The enswer is corect because is the biggest then girls to boys

Step-by-step explanation:

Answer:

No the ratio 3:4 is not equal to 4:5

Step-by-step explanation:

3:4 = 3/4 and 4:5 = 4/5

3/4 is equal to 0.75 and 4/5 is equal to 0.8

0.75 [tex]\neq[/tex] 0.8

therefore, 3:4 [tex]\neq[/tex] 4:5

Hope this helps!

Answer:64

Step-by-step explanation:

Add 79 with 37 an you will get 116 you need to know the total angle for a triangle is 180 so 180 minus 116 is 64

The measure of the angle y for the triangle is 64°.

The triangle is a shape having three sides and the sum of the angles of the triangle is always equal to 180°.

Here in the given triangle, the two angles are 79° and 37°. The measure of the unknown angle y° will be calculated as:-

y + 79 + 37 = 180

Now solve for the value of angle y below,

y = ( 180 - 79 - 37 )

y = 64°

Therefore, the measure of the angle y for the triangle is 64°.

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Answer:

Unit rate of people per book = 2.5

Step by step explanation:

Given:

Number of peoples =  [tex]10[/tex]

Number of books = [tex]4[/tex]

Their ratios = [tex]10 : 4[/tex]

We have to find the unit rate of people per book.

To find out the unit rate of people per book we have to divide the total number of peoples by the total number of books.

Or

For this we will follow the unitary method:

For [tex]4[/tex] book there are [tex]10[/tex] persons.

For [tex]1[/tex] book there will be [tex]\frac{10}{4}[/tex] persons.

So,

The numeric value = [tex]\frac{10}{4}[/tex]

                               = [tex]2.5[/tex]

There are 2.5 people per book and that it also the unit rate of people per book.

Answer:

This is what I came up with

5. (6,32)

6. That means that when six kites are order it would be the same cost from each company

Step-by-step explanation:

The solution y = 3x + 12 represents a linear relationship between two variables in the given scenario, with an initial cost of $12 and an additional cost of $3 for each unit increase in the independent variable "x." The interpretation of this relationship depends on the specific context of the problem.

The given system of equations can be written in slope-intercept form, which is in the form y = mx + b, where "m" represents the slope of the line, and "b" represents the y-intercept. In this context, the system is as follows:

4 = 3m + b

12 = b

We can solve this system to find the values of "m" and "b."

First, we already know that b = 12 from the second equation.

Now, substitute this value into the first equation:

4 = 3m + 12

Next, isolate "3m" by subtracting 12 from both sides of the equation:

3m = 4 - 12

3m = -8

Finally, divide both sides by 3 to solve for "m":

m = -8/3

So, we have found that m = -8/3 and b = 12.

Now, let's interpret the solution in the context of the scenario:

The equation y = 3x + 12 represents the relationship between "x" (which could represent a quantity like time or another variable) and "y" (which could represent a cost, height, or another quantity). In this specific case, it seems like the equation describes a linear relationship between two variables.

In terms of the scenario, it could mean that there is an initial cost of $12 (the y-intercept) and an additional cost of $3 for each unit increase in "x." This interpretation depends on the context of the problem. For example, if "x" represents the number of items purchased, then $12 could be an initial fee, and $3 could be the cost per item.

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The question probable may be:

 find the system to the solution you have to put in into slope intersecpt form so y=mx+b

so 4=m(3)+b

12=b

y=3x+12 Explain what your solution means in terms of the scenario. *

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction.

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. So, the reciprocal of 7/6 is 6/7. Therefore, 49/50 ÷ 7/6 = 49/50 x 6/7. When we multiply the numerators (49 x 6) and the denominators (50 x 7), we get 294/350. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 14. Therefore, 294/350 simplifies to 21/25.

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Measures of the angles are 24°, 48° and 108°

Step-by-step explanation:

Let angles be 2x, 4x and 9x.

⇒ 2x + 4x + 9x = 180

⇒ 15x = 180

⇒ x = 180/15 = 12

2x = 24°, 4x = 48° and 9x = 108°

The system has one solution

Step-by-step explanation:

Let us revise the type of the solutions of a system of equations

The system of equations is:

y = 2x - 12 ⇒ (1)

y = 3x + 12 ⇒ (2)

∵ The equations are in its simplest form

∵ The coefficients of x in the two equations are different

- That is the 1st case above

∴ The system has one solution

Let us prove that by solving the system

To solve the system of equations equate (1) and (2) to find x

∵ 3x + 12 = 2x - 12

- Subtract 2x from both sides

∴ x + 12 = -12

- Subtract -12 from both sides

∴ x = -24

- Substitute the value of x in equation (1) or (2) to find y

∵ y = 3(-24) + 12

∴ y = -72 + 12

∴ y = -60

∴ The solution of the system is (-24 , -60)

The system has one solution

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The first, second, third, and fifth statements are true, but the fourth and sixth statements are false. The responses are based on evaluating the square root calculations.

The statements we are analyzing are related to the square root of 1.8 (√1.8). Let's work through them:

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Answer:8

Step-by-step explanation:

There are 12 months in a year if you divide by 3 you get 4 and whatever you do to the numerator you have to do the denominator vice versa so you would multiply by four and get eight so it would be eight months

Answer:

2/3 of a year is 8 months

Step-by-step explanation:

Answer: 198 pencils per class

Explanation:

22 boxes * 45 pencils = 990 pencils

990 pencils / 5 classes = 198 pencils per class

Answer: 198 pencils per class

Explanation:

22 boxes * 45 pencils = 990 pencils

990 pencils / 5 classes = 198 pencils per class

.

Answer:

42.06 ft²

Step-by-step explanation:

          2 sides = 2(2.7 ft × 3.2 ft) = 2 × 8.64 ft² =   17.28 ft²

 Front + back =  2(2.1 ft × 3.2 ft) = 2 × 6.72 ft² =   13.44 ft²

Top + bottom =   2(2.1 ft × 2.7 ft) = 2 × 5.67 ft² =   11.34 ft²

                                                         Total area = 42.06 ft²

Answer:

[tex]\displaystyle A = \frac{12}{5}[/tex]

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Calculus

Integration

Integration Property [Addition/Subtraction]:                                                       [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Splitting Integral]:                                                               [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify bounded region. See attached graph.

y = 3x - 6

y = -2x + 8

Bounded by x-axis and between those 2 lines (already pre-determined; taking an integral always takes it to the x-axis).

Step 2: Analyze Graph

See attached graph.

Looking at our systems of equations on the graph, we see that our limits of integration is from x = 2 to x = 4.

We don't have a continuous top function through the interval [2, 4] (it switches from y = 3x - 6 to y = -2x + 8), so we need to split it into 2 integrals to find the total area.

We can either use the graph and identify the intersection point, which is x = 2.8, or we can solve it algebraically (systems of equations - substitution method):

Our 2 intervals would be [2, 14/5] and [14/5, 4] for their respective integrals.

Step 3: Find Area

Our top functions are the linear lines y = 3x - 6 and y = -2x + 8 and our continuous bottom function is the x-axis (x = 0).

We can redefine the linear lines as f₁(x) = 3x - 6, f₂(x) = -2x + 8, and g(x) = 0.

Integration

We have found the area bounded by the x-axis and linear lines y = 3x - 6 and y = -2x + 8.

Topic: Calculus BC

Unit: Area between 2 Curves, Volume, Arc Length, Surface Area

Chapter 7 (College Textbook - Calculus 10e)

Hope this helped!

Answer:

A = 12/5 units

Step-by-step explanation:

USING ALGEBRA:

We can find the intersection point between these two lines;

Set these two equations equal to each other.

Add 2x to both sides of the equation.

Add 6 to both sides of the equation.

Divide both sides of the equation by 5.

Find the y-value where these points intersect by plugging this x-value back into either equation.

Multiply and simplify.

Multiply 6 by (5/5) to get common denominators.

Subtract and simplify.

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

Add 6 both sides of the equation.

Divide both sides of the equation by 3.

Set the second equation equal to 0.

Add 2x to both sides of the equation.

Divide both sides of the equation by 2.

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a Triangle:

Substitute 2 for b and 14/5 for h.

Multiply and simplify.

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

Answer:look

Step-by-step explanation:

The diagonals of a rectangle exist congruent the necessary conditions are

A. Opposite sides are congruent.

C. Opposite sides are perpendicular.

A quadrilateral exists named a rectangle if the opposite sides exist congruent and parallel to each other. All interior angles exist as right angles and are congruent.

To verify that the diagonals of a rectangle exist congruent the necessary conditions are:

1. Opposite sides of a rectangle exist congruent.

2. All right angles exist congruent.

Therefore, the correct answer is options A and C.

A. Opposite sides are congruent.

C. Opposite sides are perpendicular.

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Answer:

37 1/3

Step-by-step explanation:

14 divided by 3/8=

14*8/3=

37 1/3

Answer:3/2

Step-by-step explanation:

Answer:

option B.) 5 + 2r = 20 is correct

Step-by-step explanation:

Carrie mows a lawn, she charges a flat fee of $5 plus an hourly rate, r.

The amount Carrie earns for mowing lawns for t number or hours

= 5 + rt

Carrie worked for 2 hours and charged a total of $20.

Therefore we can write

20 = 5 + r [tex]\times[/tex] 2    [tex]\Rightarrow[/tex] 20  =  5 + 2r

Therefore option B.) 5 + 2r = 20 is correct