The equation y = –1.25x + 13.5
represents the gallons of water
y left in an inflatable pool after
x minutes. Select all the true
statements.

A. When the time starts, there
are 13.5 gallons of water in
the pool.

B. The tub is being filled at a rate
of 1.25 gallons per minute.

C. The water is draining at a rate
of 1.25 gallons per minute.

D. When the time starts, there
are 1.25 gallons of water in
the pool.

E. The water is draining at a rate
of 13.5 gallons per minute.

F. When the time starts, there
are 12.25 gallons of water in
the pool.

The minimum value of the function is -13 and the minimum value of the function occurs at the point (4, -13).

The function F(x) is a quadratic function with a negative coefficient of the squared term.

Therefore, the function has a maximum value.

To find the maximum value, we need to find the vertex of the parabola.

The x-coordinate of the vertex is given by x = -b/2a, where a and b are the coefficients of the x² and x terms respectively.

In this case, a = -1 and b = -8, so x = -(-8)/(2(-1)) = 4.

To find the minimum value, we substitute this x-value into the function to get F(4) = -(4²) - 8(4) + 19 = -13.

Therefore, the minimum value of the function is -13.

We found in part (1) that the x-coordinate of the vertex is x = 4.

To find the y-coordinate, we substitute this x-value into the function to get F(4) = -13.

Therefore, the minimum value of the function occurs at the point (4, -13).

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Using the given information, Riley bought 3.36 pounds of chicken thighs

From the question, we are to calculate the number of pounds of chicken thighs that Riley bought

We can use proportionality to find how many pounds of chicken thighs Riley bought.

If 5 pounds of chicken thighs cost $23.75, then we can write the following proportion:

Cost/Weight = $23.75/5 lb

We can use this proportion to find the cost per pound of chicken thighs:

That is,

Cost/Weight = $23.75/5 lb = $4.75/lb

Now we can use this rate to find how many pounds of chicken thighs Riley bought:

Cost of chicken thighs bought = $15.96

Weight of chicken thighs = Cost of chicken thighs / Cost per pound of chicken thighs

Weight of chicken thighs bought = $15.96 / $4.75/lb ≈ 3.36 lb

Hence, Riley bought 3.36 pounds of chicken thighs.

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The researcher can be 95% confident that the mean number of hours all the residents of the city are watching news on television is between 1.7538 and 1.8462 hours, with a margin of error of 0.0462 hours.

Based on the information provided, the researcher surveyed 220 residents of the city and found that the mean number of hours they spend watching news on television each day is 1.8, with a standard deviation of 0.35.

The researcher wants to know the margin of error at a 95% confidence level for the mean number of hours all residents of the city are watching news on television.

To calculate the margin of error, we need to use the formula:
Margin of error = Critical value x Standard error

The critical value for a 95% confidence level is 1.96, and the standard error can be calculated as:
Standard error = Standard deviation /square root of sample space

Substituting the values given:
Standard error = 0.35 / sqrt(220) = 0.0236

Therefore, the margin of error can be calculated as:
Margin of error = 1.96 x 0.0236 = 0.0462

So, the researcher can be 95% confident that the mean number of hours all the residents of the city are watching news on television is between 1.7538 and 1.8462 hours, with a margin of error of 0.0462 hours.

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Answer:

13×X + 35= 100 (equation)

X=(100-35)/13 = 5 hours

Answer:

13x+35=100

5 hours

Step-by-step explanation:

New shoes= $100

Hours he makes= $13

Hours he worked= unknown so its "x"

Now it's 5

He already has= $35

13 x 5 = 65) + 35 = 100

Answer:

if vacuole are absent in plant cell then there is no storage of food and ions in the process of and permeability of cell may be distorted

The total students that were there in the third period is equal to 35

Let the total students be x

we have x (1 - 80%) = 7

Such that we would have

x * 0.20 = 7

then 0.20x = 7

Divide through the equation above by 0.20

x = 7 / 0.20

x = 35

Therefore the total students that were there in thev third period is equal to 35

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The monthly payment on the car is approximately $640.62. The correct option is A

The formula for the monthly payment on a continuously compounded loan can be expressed as:

P = (r * A) / (1 - (1 + r)^(-n))

Where

Plugging in the given values, we get:

P = (0.046 * 35000) / (1 - (1 + 0.046/12)^(-6*12))

P ≈ $640.62

Therefore, the monthly payment on the car is approximately $640.62.

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Philip should receive $68.50 in quarterly dividends and the annual yield on this stock is about 2.81%.

To calculate the quarterly dividend that Philip need to acquire, we need to first calculate the quarterly dividend per share:

Quarterly dividend in step with share = Annual dividend per percentage / 4

In this situation, the once a year dividend in line with proportion is $2.74, so the quarterly dividend per proportion is:

Quarterly dividend per proportion = $2.74 / 4 = $0.685

For the reason that Philip owns 100 shares, his quarterly dividend should be:

Quarterly dividend = Quarterly dividend per share * number of stocks

Quarterly dividend = $0.685 * 100 = $68.50

Therefore, Philip should receive $68.50 in quarterly dividends.

To calculate the once a year yield on this inventory, we want to divide the yearly dividend in line with proportion by the present day stock price, after which multiply by way of 100 to specific the result as a percentage:

Annual yield = (Annual dividend per share / inventory price) * 100

In this case, the annual dividend per percentage is $2.74, and the inventory charge is $97.55. Plugging those values into the components, we get:

Annual yield = ($2.74 / $97.55) * 100

Annual yield ≈ 2.81%

Therefore, the annual yield on this stock is about 2.81%.

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The length that will give a plot with the maximum area allowed is 6 meters.

To find the length that will give a plot with the maximum area, we need to use the formula for the area of a rectangle, which is A = lw, where A is the area, l is the length, and w is the width. In this case, we are given that the area is 45 square meters, and the width is 7.5 meters.

Substituting these values into the formula, we get:

45 = l(7.5)

To solve for l, we divide both sides by 7.5:

l = 45/7.5

Simplifying, we get:

l = 6

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Answer:

y = 1 + 2√7 or y = 1 - 2√7

Step-by-step explanation:

To complete the square, you need to add and subtract the square of half of the coefficient of the y term.

First, you can factor out a 1 from the y^2 - 2y term:

y^2 - 2y - 27 = 0

y^2 - 2y = 27

Next, take half of the coefficient of the y term (-2/2 = -1) and square it (1):

y^2 - 2y + 1 - 1 = 27

The "+1 -1" doesn't change the value of the equation, it's just a way to add 0 to the equation so we can complete the square.

Now you can rewrite the left side as a perfect square:

(y - 1)^2 - 28 = 0

Add 28 to both sides:

(y - 1)^2 = 28

Take the square root of both sides (remembering to include both positive and negative square roots):

y - 1 = ±√28

y = 1 ± 2√7

So the solutions are:

y = 1 + 2√7

y = 1 - 2√7

Answer: y=± 2√7+1

6.29

Step-by-step explanation: Use the formula

(b/2)^2  in order to create a new term. Solve for y by using this term to complete the square.

Answer: I agree the answer is 3

Step-by-step explanation:

Brainliest pls:)

The sum of vectors u  = <4,8>,and v = <-2, 6>  i.e. (u+v) is <2, 14>

To find the sum of vectors u and v (u+v), you need to perform the following steps:

1. Identify the components of vectors u and v: u = <4, 8> and v = <-2, 6>.

2. Add the corresponding components of both vectors: To find the sum (u+v), add the x-components (4 and -2) and the y-components (8 and 6) separately.

3. Calculate the sum of the x-components: 4 + (-2) = 2.

4. Calculate the sum of the y-components: 8 + 6 = 14.

5. Combine the results to form the new vector (u+v): <2, 14>.

So, the sum of vectors u and v (u+v) is <2, 14>.

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Answer is original amount paid to the transportation company was $800.

Let's work backwards from the final amount of $400 to find the original amount paid to the transportation company.

First, we know that percentage given is 80% of what was left after wages went towards supplies. So, if $400 was left after wages were paid, then:

0.8(400) = $320 went towards supplies.

Next, we know that 60% of the original amount went towards wages. So, if $320 went towards supplies, then the remaining amount that went towards wages was:

0.4(original amount) = $320

Solving for the original amount:

Original amount = $320 / 0.4 = $800

Therefore, the original amount paid to the transportation company was $800.

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To find the number of unique types of sneakers, we need to multiply the number of options for each characteristic:

Number of colors: 6

Number of styles: 4

Number of fabrics: 3

Total number of unique types of sneakers = 6 x 4 x 3 = 72

Therefore, the manufacturer makes 72 unique types of sneakers.

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If a scale dilates a two-dimensional object by a factor of 2/3, it means that the image of the object will be reduced by a factor of 2/3. In other words, the length and width of the image will be 2/3 of the length and width of the original object.

For instance, consider a rectangle with length L and width W. If we dilate this rectangle by a factor of 2/3, the new length and width of the rectangle will be (2/3)L and (2/3)W, respectively. The area of the new rectangle will be (2/3)L x (2/3)W = (4/9)LW, which is 4/9 of the original area. This means that the image is smaller than the original rectangle, and this type of dilation is called a reduction.

Dilations can be used in different applications of mathematics, such as geometry, trigonometry, and algebra. They are useful for changing the scale or size of an object in a proportional way, without altering its basic shape or characteristics.

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The side length of the base of the rectangular prism is approximately 1.2 cm.

The top, bottom, and lateral faces of a rectangular prism are all rectangles, and all the pairings of the opposing faces are congruent. A rectangular prism is a three-dimensional structure with six faces.

Let's denote the side length of the base of the rectangular prism as "x" cm.

We know that the volume of a rectangular prism is given by the formula:

Volume = Base Area x Height

In this case, the base is a square, so its area is given by:

Base Area = x²

We are given that the volume is 24.768 cm³ and the height is 17.2 cm.

Therefore, we can write the equation:

24.768 = x² * 17.2

To find the value of x, we can rearrange the equation:

x² = 24.768 / 17.2

x² = 1.4376

Taking the square root of both sides, we get:

x = √1.4376

x ≈ 1.2

Therefore, the side length of the base of the rectangular prism is approximately 1.2 cm.

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The median of the random variable X with pdf f(x) = 3x−4 for x ≥1 (and 0 is approximately 1.482.

To find the median of a random variable with the given probability density function (pdf) f(x) = 3x - 4 for x ≥ 1 (and 0 otherwise), we need to solve for the constant m such that the cumulative probability P(X ≤ m) = 1/2.

First, we find the cumulative distribution function (CDF) by integrating the pdf:

F(x) = ∫(3x - 4) dx, where the limits of integration are from 1 to x.

F(x) = [(3/2)x² - 4x] evaluated from 1 to x.

Now, set the CDF equal to 1/2 to find the median:

1/2 = [(3/2)m² - 4m] - [(3/2)(1)² - 4(1)]

1/2 = (3/2)m² - 4m - (1/2)

1 = 3m² - 8m

0 = 3m² - 8m - 1

To find the value of m, we solve the quadratic equation above. Unfortunately, it cannot be factored easily, so we use the quadratic formula:

m = (-b ± √(b² - 4ac)) / 2a

In this case, a = 3, b = -8, and c = -1. Plugging in these values:

m ≈ (8 ± √(64 + 12)) / 6 ≈ 1.482

Since the median must be greater than or equal to 1, we take the positive root of the equation: m ≈ 1.482. Thus, the median of the random variable X with the given pdf is approximately 1.482.

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The number of gallons of water the pool can contain is approximately 3393 gallons.

To find the amount of water in gallons the pool can contain, we must find the volume of the cylindrical swimming pool, you can use the formula:

Volume = π * r² * h

Where r is the radius (half the diameter), and h is the height.

In this case, r = 12 feet / 2 = 6 feet, and h = 4 feet.

Volume = π * (6 ft)² * 4 ft ≈ 452.39 ft³

To convert cubic feet to gallons, use the given conversion factor (1 ft³ ≈ 7.5 gal).

Volume ≈ 452.39 ft³ * 7.5 gal/ft³ ≈ 3392.93 gal

Rounding to the nearest whole number, the pool can contain approximately 3393 gallons of water.

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Answer:

(1/6)π(4^2) - (1/2)(2√3)(4)

= 8π/3 - 4√3 = about 1.4

The solution to the differential equation is f(a) = 1/√(12a⁴/125 - 769/5000).

To find f(a), we need to solve the differential equation:

dy/dx = 24yx³

Separating variables, we get:

dy/y³ = 24x³ dx

Integrating both sides, we get:

-1/(2y²) = 6x⁴ + C

where C is the constant of integration.

To find the value of C, we use the fact that the y-intercept of the curve y = f(2) is 5. This means that when x = 2, y = 5. Substituting these values into the equation above, we get:

-1/(2(5)²) = 6(2)⁴ + C

Simplifying and solving for C, we get:

C = -1/(2(5)²) - 6(2)⁴

C = -769/125

So the solution to the differential equation is:

-1/(2y²) = 6x⁴ - 769/125

Solving for y, we get:

y = 1/√(12x⁴/125 - 769/5000)

Therefore, f(a) = 1/√(12a⁴/125 - 769/5000).

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Mrs. Lane's average gross monthly income would be $3,135.

To find the monthly income of  Mrs. Lane's,

First, we need to find Mrs. Lane's commission for her bi-weekly commercial sales:

Commission = 22% of $5,625 = 0.22 x $5,625 = $1,237.50

Next, we need to find her hourly wage for a week:

Hourly wage = $8.25 x 40 = $330

Her gross bi-weekly income is the sum of her commission and hourly wage:

Gross bi-weekly income = Commission + Hourly wage

= $1,237.50 + $330

= $1,567.50

To find her gross monthly income, we can multiply her gross bi-weekly income by the number of bi-weekly pay periods in a month:

Gross monthly income = Gross bi-weekly income x Number of bi-weekly pay periods in a month

= $1,567.50 x 2

= $3,135

Therefore, Mrs. Lane's average gross monthly income would be $3,135.

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To select all the tables that show quadratic functions, look for tables with a second-degree polynomial equation in the form of "y = ax² + bx + c".

Tables that show quadratic functions:

(a).

x y

-2 8

-1 3

0 0

1 1

2 4

This table shows a quadratic function in the form of y = x² - 2x.

(b)

x y

-3 0

-2 1

-1 4

0 9

1 16

2 25

3 36

This table shows a quadratic function in the form of y = x².

A quadratic function is a second-degree polynomial function that can be expressed in the general form of "y = ax² + bx + c", where a, b, and c are constants.

In this form, the variable "x" is squared, and the coefficient "a" determines whether the parabola opens upward or downward.

To identify tables that show quadratic functions, we need to look for tables that display data points that follow a quadratic pattern.

That is, the dependent variable (y) changes in a way that corresponds to a quadratic equation.

In the first table, the values of y correspond to the quadratic equation y = x² - 2x. The second table shows a set of data points that corresponds to the quadratic function y = x².

Therefore, these two tables show quadratic functions.

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Measurement is closest to the length of the ramp in feet is 33 feet

Let AB = 26 ft and BC = 19.5 ft

Let AC be the length of the ramp

Let's use the Pythagorean theorem to find the length of the ramp:

AC² = AB² + BC²

where AC is the hypotenuse (the unknown side), and AB and BC are the other two sides given.

Substituting the given values, we get:

AC² = 26² + 19.5²

AC² = 676 + 380.25

AC² = 1056.25

AC = [tex]\sqrt{1056.25}[/tex]

AC = 32.5

Rounding to the nearest feet

AC = 33

Therefore, the measurement closest to the length of the ramp in feet is 33 feet.

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Step-by-step explanation:

5 + 6 + 3   = 14 marbles     5 are red

1st marble red =  5 out of 14   = 5/14

 now there are 13 marbles   4 are red

     2nd marble red             4/13

         and finally ,  3rd marble red = 3/12

5/14  * 4/13  * 3/12 =   5/182  chance for three reds

Answer:

Based on the given graph, we can see that the bars representing salaries above $175,000 span a total of 7 employee salaries. Since each bar spans a width of $50,000, we can estimate that the total number of employees making at least $175,000 is approximately 7 multiplied by 50,000 divided by 10,000, which equals 35%. Therefore, the owner can justify the claim that on average an employee makes at least $175,000 by stating that approximately 35% of the current employees already make at least that amount. However, it's important to note that this calculation is based on estimates and assumptions and should not be used as a definitive answer.

Answer:

side length of cube=4inch

Step-by-step explanation:

volume of cube(V)=64sqinch

length of side(l)=?

Now,

volume of cube(V)=l^3

64=l^3

∛64=l

4=l

l=4inch

Answer: ∠b = 105°

Step-by-step explanation:

     We know that a straight line is equal to 180 degrees. We will create an equation and solve for ∠b.

180° = ∠b + 75°

∠b = 180° - 75°

∠b = 105°

The percent of error in the measurement is 8%. This means that the measured value of 5.52 miles is 8% less than the actual distance of 6 miles.

To find the percent of error, we need to calculate the difference between the measured value and the actual value, divide that by the actual value, and then multiply by 100 to convert to a percentage.

Actual distance around the neighborhood = 6 miles

Measured distance around the neighborhood = 5.52 miles

Difference = Actual distance - Measured distance

Difference = 6 miles - 5.52 miles

Difference = 0.48 miles

Percent of error = (|Difference| / Actual distance) x 100%

Percent of error = (|0.48| / 6) x 100%

Percent of error = 0.08 x 100%

Percent of error = 8%

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