The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.

Answer:

x ≥ 2

Step-by-step explanation:

8x + 3 ≥ 19

8x ≥ 19 - 3

8x / 8 ≥ 16 / 8

x ≥ 2

Answer:

Sure, I can solve for x:8x + 3 ≥ 19Subtracting 3 from both sides:8x ≥ 16Dividing both sides by 8:x ≥ 2Therefore, the solution is x ≥ 2.

Answer:

Let's use "x" to represent the total number of students in the class.

According to the problem, the number of boys is 7/10 of the total number of students, and the number of girls is 3/10 of the total number of students. We can set up the following equation based on this information:

Number of Boys = 7/10 x

Number of Girls = 3/10 x

The problem also tells us that there are 16 more boys than girls in the class. We can set up another equation based on this information:

Number of Boys = Number of Girls + 16

Now we can use these two equations to solve for the total number of students:

7/10 x = 3/10 x + 16

Subtracting 3/10 x from both sides, we get:

4/10 x = 16

Multiplying both sides by 10/4, we get:

x = 40

Therefore, there are 40 students in the class. To find the number of boys and girls, we can use the equations we set up earlier:

Number of Boys = 7/10 x = 7/10 * 40 = 28

Number of Girls = 3/10 x = 3/10 * 40 = 12

So there are 28 boys and 12 girls in the class.

Carter has 13 dimes in his piggy bank

To solve this equation, we need to use the distributive property to simplify the equation:
(x dimes x 10 cents) + (37-x nickels x 5 cents) = $3.10
We can then solve for the number of dimes by isolating the dimes on one side of the equation:
x dimes x 10 cents = $3.10 - (37-x nickels x 5 cents),By dividing both sides of the equation by 10 cents, we can solve for the number of dimes, x:
x dimes = ($3.10 - (37-x nickels x 5 cents)) / 10 cents

Plugging in the value of 37 coins and solving the equation, we get:
x dimes = (3.10 - (37 -x nickels x 5 cents)) / 10 cents
x dimes = (3.10 - 185 + 5x) / 10 centsx dimes = (3.10 - 180) / 10 centsx dimes = 1.30 / 10 centsx dimes = 13 dimes
Therefore, Carter has 13 dimes in his piggy bank.

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Answer:  B. 133 gallons

Step-by-step explanation: 90% of 1330 is 1197. you can take 10% which is 133 and multiply it by 9 to get that answer. then you have to subtract 1197 from 1330 to get you 133

Answer:

42 m2

Step-by-step explanation:

3=18

7=?

=7 × 13 ÷ 3

=42

The amount of concrete needed to make the stairs that leads to the garage is 64 cubic feet

The missing information is added as an attachment

The concrete needed to make the stairs is the volume of the stairs and this is calculated using

Volume = Base area * Height

Where

Base area = 3 * 2 + 2 * 1

Base area = 8

And

Height = 8

So, we have

Volume = 8 * 8

Evaluate

Volume = 64

Hence, the amount needed is 64 cubic feet

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The probability of three or more goals being scored in an EPL match is approximately 0.522, or 52.2%.

To find the probability that three or more goals will be scored in a game, we need to calculate the cumulative probability of the Poisson distribution for x = 3, 4, 5, and so on, up to infinity. This can be written as:

P(X ≥ 3) = 1 - P(X < 3)

where X is the random variable representing the number of goals scored in a match.

To calculate P(X < 3), we can use the Poisson distribution formula:

[tex]P(X = x) = (e^{(-\lambda)} \times \lambda^x) / x![/tex]

where e is the mathematical constant approximately equal to 2.71828, and x! represents the factorial of x.

Using this formula, we can calculate the probabilities of scoring 0, 1, and 2 goals:

[tex]P(X = 0) = (e^{(-2.768)} \times 2.768^0) / 0! = 0.063\\\\P(X = 1) = (e^{(-2.768)} \times 2.768^1) / 1! = 0.174\\\\P(X = 2) = (e^{(-2.768)} \times 2.768^2) / 2! = 0.241[/tex]

To find P(X < 3), we add these probabilities:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.063 + 0.174 + 0.241 = 0.478

Finally, we can calculate the probability of scoring three or more goals using the formula we derived earlier:

P(X ≥ 3) = 1 - P(X < 3) = 1 - 0.478 = 0.522 or 52.2%

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If one flag pole is y feet tall and casts a shadow x feet long, and another nearby flag pole casts a shadow p feet long at the same time of day, we can use similar triangles to determine the shadow of the second flag pole.

In this scenario, the two flag poles and the ground form two similar right triangles. The height of the first flag pole (y) corresponds to one leg of the first triangle, and the length of its shadow (x) corresponds to the other leg.

Similarly, the height of the second flag pole (h) corresponds to one leg of the second triangle, and the length of its shadow (p) corresponds to the other leg.

Therefore, the height of the second flag pole is equal to the product of the height of the first flag pole and the length of the shadow of the second flag pole, divided by the length of the shadow of the first flag pole.

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Answer:

yes

Step-by-step explanation:

replace r and q with y and x:

y = 4x - 5

It is a line.

By using system of equations, there are 43 free DVD rentals and 46 boxes of microwave popcorn were given away during the promotional campaign.

Let's use the following variables

x: the number of free DVD rentals given away

y: the number of boxes of microwave popcorn given away

We can set up a system of equations to represent the given information:

x + y = 89 (total number of new members signed up)

1x + 2y = 135 (total cost of the incentives)

We can solve for x or y in the first equation and substitute into the second equation

x = 89 - y

1(89 - y) + 2y = 135

89 - y + 2y = 135

y = 46

Substituting y = 46 into the first equation:

x + 46 = 89

x = 43

Therefore, 43 free DVD rentals and 46 boxes of microwave popcorn.

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Answer:

[tex]y = \frac{2}{7} x - \frac{20}{7} [/tex]

Step-by-step explanation:

[tex] - 2 = \frac{2}{7} (3) + b[/tex]

[tex] - \frac{14}{7} = \frac{6}{7} + b [/tex]

[tex]b = - \frac{20}{7} [/tex]

[tex] y = \frac{2}{7} x - \frac{20}{7} [/tex]

Joe is incorrect in claiming that he scored better than 80% of the people who took the test.

The 20th percentile means that Joe's score was equal to or greater than 20% of the other test takers, but lower than 80%. The percentile is not a percentage, so the statement Joe made is false.

It is important to understand that percentile rankings are not the same as percentages. Percentile rankings measure how one’s score compares to others who have taken the same test. For example, if Joe scored in the 20th percentile, it means that 20% of the other test takers had the same or lower scores. On the other hand, percentages measure a proportion of the whole. In Joe's case, 80% would mean that 80 out of 100 test takers had a higher score than Joe.

To be more accurate, Joe could have said that he scored better than 20% of the people who took the test. Percentile rankings are often used to measure an individual's performance in comparison to a larger group of peers. Although Joe might have performed well, it is important to understand the difference between percentile and percentage.

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The percentage of students who played video games in the survey is 52%.

To find this percentage, we first need to calculate the fraction of students who played video games. This can be done by dividing the number of students who played video games by the total number of students surveyed:

Fraction of students who played video games = 130/250

Simplifying this fraction by dividing both the numerator and denominator by 10, we get:

Fraction of students who played video games = 13/25

To convert this fraction to a percentage, we can multiply it by 100:

Percentage of students who played video games = (13/25) * 100

Simplifying this expression, we get:

Percentage of students who played video games = 52%

Therefore, 52% of the students in the survey played video games.

Hence, to find the percentage of students who played video games in a survey, we divide the number of students who played video games by the total number of students surveyed and then multiply the resulting fraction by 100 to get the percentage.

In this case, 130 out of 250 students played video games, so the percentage is 52%.

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The correct option is - Graph B, represent quadratic function "p", when values of "a" and "c" are both less than 0.

f(x) = ax² + bx + c, in which a, b, and c are numbers and an is not equal to zero, is a quadratic function.

The given function :

y = ax² + c.

a < 0 and c <0.

Thus, Graph B, represent function "p", when values of "a" and "c" are both less than 0, and the graph will open downward with c less than 0.

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Answer: A - (-5, 43)

Step-by-step explanation:

By using the definition of inverse functions we can see that:

a) g(7) = -10

b)(-10,7) is a point on h(x).

c)(7, -10) is a point on j(x)

Remember that if two functions f(x) and g(x) are inverses, then:

f(y) = x

g(x) = y

And also g(f(x)) = x = g(f(x)).

Here we know that functions h(x) and j(x) are inverses, and we also know that:

h(-10) = 7

So for the input -10, we have the output 7.

Then, by using the relation written above, we know that for the inverse function we must have:

j(7) = -10

That is the answer for a.

And for b and c the notation is (input, output), then:

These are the answers of points B and C of the question.

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Answer: The answer is 60.

Step-by-step explanation:

Using the fact that OP || RS, we know that∠RWV = 180° − 130° 1.  ∠RWV = 50° We know that,∠PWQ = ∠RWV = 50° (Since, opposite angles of intersecting lines are equal) Also, for line OP∠OQP + θ = 180° θ = 180° − ∠OPQ = 180° − 110° 2.  θ = 70° 

Answer:

The measure of ∠OPQ is 110°.

Step-by-step explanation:

Draw a line parallel to OP from point Q. Label a point on the line T. (See attached diagram).

Angles SRQ and TQR are alternate interior angles, and so according to the Alternate Interior Angles Theorem, they are congruent.

⇒ m∠TQR = m∠SRQ = 130°

Given m∠PQR = 60° and m∠TQR = 130° then:

⇒ m∠TQP + m∠PQR = m∠TQR

⇒ m∠TQP + 60° = 130°

⇒ m∠TQP = 70°

Angles OPQ and TQP are same-side interior angles, and so according to the Same-side Interior Angles Theorem, they are supplementary (sum to 180°).

⇒ m∠OPQ + m∠TQP = 180°

⇒ m∠OPQ + 70° = 180°

⇒ m∠OPQ = 110°

Therefore, the measure of ∠OPQ is 110°.

Answer:

y=-3x+5

Step-by-step explanation:

A line that is parallel to y=-3x-5 will have the same slope, which is -3.

Using the point-slope form, we can write the equation of the line as:

y - 8 = -3(x + 1)

Simplifying:

y - 8 = -3x - 3

Adding 8 to both sides:

y = -3x + 5

Therefore, the equation of the line in slope-intercept form that is parallel to y=-3x-5 and goes through the point (-1,8) is y = -3x + 5.

Since it is difficult to evaluate this integral exactly, use technology to approximate it. After calculation, the length is approximately 3.9205 (rounded to four decimal places).

To find the length of the function y =[tex]2x^(3/2)/3 - x^(1/2)/2[/tex] over the interval [1, 4], you need to evaluate the integral of the square root of [1 + (y')^2] with respect to x, where y' is the derivative of y with respect to x.

First, find the derivative y':
y'(x) = d(2x^(3/2)/3 - x^(1/2)/2)/dx = x^(1/2) - 1/(4x^(1/2))

Now, find (y')^2:
[tex](y')^2 = (x^(1/2) - 1/(4x^(1/2)))^2[/tex]
Next, find the square root of [1 + (y')^2]:
[tex]√[1 + (y')^2] = √[1 + (x^(1/2) - 1/(4x^(1/2)))^2][/tex]

Finally, evaluate the integral:
Length = [tex]∫(√[1 + (y')^2]) dx[/tex] from x = 1 to x = 4

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The amount of simple interest owed for the loan is $30,010.00.

A method for determining the proportion of interest paid on a sum over a predetermined period of time at a predetermined rate is called simple interest. In simple interest, the principal amount remains unchanged. A straightforward and simple method for calculating money interest is simple interest.

To calculate the simple interest, we use the formula:

Simple Interest = P * r * t

where P is the principal amount, r is the interest rate as a decimal, and t is the time period in years.

Substituting the given values, we get:

Simple Interest = $15,400 * 0.15 * 13

= $30,010.00

Therefore, the amount of simple interest owed for the use of the loan is $30,010.00.

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Right

so 7 is the hypotenuse because it is the biggest. so you have to use 6 and 4 in the formula to see if they equal 7.

(a)²+(b)²=c²

(6)²+(4)²=c²

36+16=c²

(square root) 52=c²

the square root of 52 is 7

so therefore it is a right triangle.

Step-by-step explanation:

Let's use d to represent the number of days it will take Tom to finish the challenge miles.

Since Tom is currently 10 miles into the challenge and plans to run 4 miles each day until he finishes, the total number of miles he will run is 75 - 10 = 65 miles.

If he runs 4 miles each day, we can use the equation:

total distance = distance per day * number of days

to find the number of days it will take Tom to run 65 miles. Plugging in the known values, we get:

65 = 4d

Simplifying this equation, we can solve for d:

d = 65/4

So, it will take Tom d = 16.25 days to finish the running challenge if he runs 4 miles each day. However, since he cannot run a fraction of a day, we can round up the answer to the nearest whole number of days. Therefore, it will take Tom 17 days to finish the challenge.

The equation that can be used to find the number of days, d, it will take Tom to finish running the challenge miles is:

d = ceil(65/4)

where ceil is the ceiling function, which rounds up the result to the nearest whole number.

Answer:

16 days + 1 mile

Step-by-step explanation:

As per the combination method, there are 495 groups of 4 people that can answer the 4 different phone lines when there are 12 people in the office.

To start, we need to determine how many ways we can choose 4 people from a group of 12. We use the formula for combinations, which is:

ⁿCₓ = n! / x!(n-x)!

Where n is the total number of people (in this case, 12) and x is the number of people we want to choose (in this case, 4). The exclamation point symbol (!) denotes the factorial operation, which means we multiply the number by every positive integer less than it down to 1.

So, for this problem, we have:

¹²C₄ = 12! / 4!(12-4)!

= (12 x 11 x 10 x 9) / (4 x 3 x 2 x 1)

= 495

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The pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay is represented in dollars per hour, and it ranges from $12 per hour for a new employee in a low-level position to $60 per hour for a senior developer with extensive experience.

For example, if we look at the table created in part a, we can see that a junior developer with less than a year of experience will earn $18 per hour, while a senior developer with more than 10 years of experience will earn $60 per hour. This means that the pay at the Digital Source is directly related to the employee's experience and job position.

Additionally, the table also shows that the pay rate increases as the employee gains more experience and moves up the career ladder. For instance, a junior developer with less than a year of experience will earn $18 per hour, but a mid-level developer with 3-5 years of experience will earn $35 per hour. This shows that employees are rewarded for their skills and experience, and they have the opportunity to advance their careers and earn higher pay rates.

In summary, the pay at the Digital Source is a variable amount that depends on the employee's job position and experience level. The pay rate ranges from $12 per hour to $60 per hour, and it increases as the employee gains more experience and moves up the career ladder. The company values the skills and expertise of their employees and rewards them accordingly.

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The combined resistance, R, of two resistors with resistances r and s connected in parallel can be calculated using the equation:
[tex]1/R = 1/r + 1/s[/tex]
When an electric current passes through these resistors, the combined resistance depends on the values of r and s. To analyze the behavior of R with respect to r, we can rewrite the equation as:
[tex]R = (rs)/(r + s)[/tex]
R is a function of r and s, and its behavior depends on the values of r and s. If r and s are positive, the function is neither increasing nor decreasing globally, as it depends on both r and s values. However, for specific values of r and s, the function can be either increasing or decreasing locally.
There is no global maximum or minimum for this function because it depends on the specific values of r and s, and it can take any positive value depending on these resistances. So, the answer is none for global maximum or minimum.
In summary, the behavior of the combined resistance R when an electric current passes through two resistors connected in parallel depends on the values of r and s. It is neither globally increasing nor decreasing and has no global maximum or minimum.

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The function f(x) = 5/(x+3), vertical asymptote at x = -3,  domain of the function is all real numbers except x = -3,  range is all real numbers except 0.

A function is a mathematical object that takes one or more inputs (usually represented as variables) and produces a single output. In other words, a function is a relation between sets of inputs and outputs that associates each input value with exactly one output value.

A function can be represented by an equation or a graph. The most common way to write a function is in the form f(x) = y, where x is the input variable and y is the output variable. The function f maps each value of x to a corresponding value of y.

Functions can be classified based on their properties, such as their domain (set of allowable input values), range (set of output values), and behavior (e.g., increasing, decreasing, constant, etc.). Some common types of functions include linear, quadratic, exponential, trigonometric, and logarithmic functions.

The function f(x) = 5/(x+3) has a vertical asymptote at x = -3, since the denominator becomes zero at that point.

The domain of the function is all real numbers except x = -3, since division by zero is undefined.

To find the range, we can consider what happens to the function as x approaches -3 from both sides. As x approaches -3 from the left (i.e., as x gets closer and closer to -3 from values less than -3), the function becomes increasingly negative. As x approaches -3 from the right (i.e., as x gets closer and closer to -3 from values greater than -3), the function becomes increasingly positive. This means that the range of the function is all real numbers except 0.

Therefore, the asymptote is x = -3, the domain is all real numbers except x = -3, and the range is all real numbers except 0.

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The measure of the missing angles of the right triangle are 57 degree and 33 degrees.

The sum of the interior angles of a triangle equals 180 degrees.

From the diagram:

Angle A =  (4x - 7) degrees

Angle B = (3x - 15) degrees

Angle C = 90 degrees

In a right triangle, the sum of the two acute angles is 90 degrees.

So, we have:

angle A + angle B + 90 = 180 (sum of angles in a triangle)

(4x - 7) + (3x - 15) + 90 = 180

Solve for x

4x - 7 + 3x - 15 + 90 = 180

4x + 3x - 15 - 7 + 90 = 180

7x - 15 - 7 + 90 = 180

7x + 68 = 180

7x = 180 - 68

7x = 112

x = 112/7

x = 16

Therefore, the missing angles will be:

angle A = (4x - 7) =  4(16) - 7 = 57 degrees

angle B = (3x - 15) = 3(16) - 15 =  33 degrees.

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Answer:

The measure of the missing angles of the right triangle are 57 degree and 33 degrees.

Step-by-step explanation:

The water level is rising at a rate of 32 ft/min when the water is 6 inches deep.

How to solve rise of water level?

Let's first draw a diagram to better understand the problem:

            /|\

           / | \

          /  |  \

         /   |h \

        /    |   \

       /     |    \

      /      |     \

     /       |      \

    /        |       \

   /         |        \

  /_________|

       b

where h is the height of the water, b is the width of the trough at water level, and 10 is the length of the trough.

Since the trough is being filled at a rate of 12 ft³/min, the volume of water in the trough is increasing at a rate of 12 ft³/min. Let's use this to find the rate at which the water level is rising.

The volume of water in the trough is given by the formula:

V = (1/2)bh²

where b is the width of the trough at water level, h is the height of the water, and 1/2 is the area of the triangular cross-section of the trough. We want to find the rate at which h is changing when h = 6 inches = 0.5 ft.

Differentiating both sides of the formula with respect to time t, we get:

dV/dt = (1/2)(db/dt)(h^2) + (1/2)(b)(2h)(dh/dt)

where db/dt is the rate at which the width of the trough at water level is changing, and dh/dt is the rate at which the water level is changing (i.e., the rate we want to find).

We know that dV/dt = 12 ft³/min and h = 0.5 ft. We also know that the width of the trough at the water level is 3 ft. To find db/dt, we need to use similar triangles. The triangle formed by the water and the sides of the trough is similar to the isosceles triangle at the end of the trough. Therefore, the ratio of the width of the trough at the water level to the height of the water is constant:

b/h = 3/1

Solving for b, we get:

b = 3h

on diffrentiating

db/dt = 3(dh/dt)

Substituting the values we know into the formula for dV/dt, we get:

12 = (1/2)(3h)(h²) + (1/2)(3h)(2h)(dh/dt)

12 = (3/2)h³+ 3h²(dh/dt)

4 = h²(dh/dt)

Solving for dh/dt, we get:

Therefore, the water level is rising at a rate of 32 ft/min when the water is 6 inches deep.

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Answer:$10

Step-by-step explanation: We are given the ratio 9:1. Meaning for every 9 dollars he spends on healthy food, he can spend a dollar on snacks. If he intends on paying 100 dollars total, how much will he spend on snacks?

He would have spent 90 dollars on healthy food, and 10 dollars on snack food. Totaling 100 dollars.