5x5=25+1=26+6=
solve the eqation

The average miles per hour that John and his family travel is 55 mph.

American drivers now log a total of 14,263 miles in a single year on average. Around 1,200 miles are driven per month on average, according to this information.

We must divide the whole distance travelled by the total time taken by John and his family in order to determine their average miles per hour:

Total distance x Total time equals average speed.

In this instance, their total journey distance was 137.5 miles, and their total travel duration was 2.5 hours. Hence, we can enter the following values into the formula:

Average speed = 137.5 miles / 2.5 hours

137.5 divided by 2.5 results in:

Average speed is 55 miles per hour.

John and his family therefore travel at an average speed of 55 mph.

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The percentage of illicit drug users in the US are African American is a. 14%

According to data from the National Survey on Drug Use and Health, in 2019, 14.5% of African Americans reported using illicit drugs in the past month, compared to 12.4% of the overall population. While African Americans are overrepresented in state prisons for drug offenses, they do not use drugs at a significantly higher rate than other racial and ethnic groups.

It's important to note that drug use is a complex issue with many social and economic factors at play. It's crucial to approach drug use and addiction with a public health perspective that prioritizes prevention, treatment, and harm reduction over punitive criminal justice approaches.

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Your question is incomplete, but probably the complete question is :

57% of people in state prisons for drug offenses in the US are African American. What percentage of illicit drug users in the US are African American?

a. 14%

b. 28%

c. 42%

d. 56%

George needs to sail close to 3.7 miles from Paradise Island to reach Shipwreck Rock.

Applying  the law of cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

where:

c = the unknown distance

a = 3.7 miles (distance from the dock at the mainland to Paradise Island)

b = 5.6 miles (distance from the dock at the mainland to Shipwreck Rock)

C = 72 degrees (angle formed between the dock at the mainland and Shipwreck Rock)

The we convert the angle from degrees to radians:

72 degrees = (72/360) * 2π radians = 1.2566 radians (approx.)

Substituting  the values into the formula and solving  for c:

c^2 = 3.7^2 + 5.6^2 - 2(3.7)(5.6)cos(1.2566)

c^2 = 13.69

c ≈ 3.7 miles

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Yes its i Think If its not sorry

Answer:

x(6x^2 + 5)

Step-by-step explanation:

To factor the expression 6x^3 + 5x, we can first factor out the greatest common factor of the two terms, which is x. This gives:

x(6x^2 + 5)

We can see that 6x^2 + 5 cannot be factored any further using integer coefficients, so the final factored form of the expression is:

x(6x^2 + 5)

Valerie paid a total amount of $124 this year for her movie club membership and the 14 movies she rented.

In math, the total amount typically refers to the final sum or result of a calculation involving multiple numbers or quantities.

Valerie pays a fixed fee of $40 annually, and she rented 14 movies at a cost of $6 each. Thus, the total amount she paid this year can be calculated as follows:

Total cost of movie rentals = 14 x $6 = $84

Adding the fixed annual fee to the rental costs:

Total amount paid by Valerie this year = $40 + $84 = $124

Therefore, Valerie paid a total of $124 this year for her movie club membership and the 14 movies she rented.

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Answer:

Step-by-step explanation:

Hi ,

9x² - 49y² + 3x + 7y

= [ (3x)² - ( 7y )² ] + ( 3x + 7y )

= ( 3x + 7y ) ( 3x - 7y ) + 1( 3x + 7y )

= ( 3x + 7y ) ( 3x - 7y + 1 )

I hope this helps you.

:)

Answer:

X= 567890

Step-by-step explanation:

Answer:

See below, please.

Step-by-step explanation:

Using the zero product property, we can set each factor equal to zero and solve for x:

(x² - 9)(x + 4) = 0

(x² - 9) = 0 or (x + 4) = 0

For the first factor, we can factor it further as the difference of squares:

(x + 3)(x - 3) = 0

So, either (x + 3) = 0 or (x - 3) = 0, giving us:

x = -3, x = 3, or x = -4

Therefore, the values of x for which (x² - 9)(x + 4) = 0 are -3, 3, and -4.

Answer:

Step-by-step explanation:

To find the dimensions of the box, we need to solve for the value of x in the expressions given for its length, width, and height.

The volume of a box is given by multiplying its length, width, and height, so we can write:

V = (x+8) * x * (x-2)

Expanding the expression, we get:

V = (x^3 + 6x^2 - 16x)

We know that the volume of the box is measured in cubic feet, so we can assume that V is a positive value. Therefore, we can set V equal to some positive number, such as 1000 or 2000, and solve for x using algebraic techniques such as factoring or the quadratic formula.

For example, if we set V = 1000, we can write:

1000 = x^3 + 6x^2 - 16x

Simplifying and rearranging the terms, we get:

x^3 + 6x^2 - 16x - 1000 = 0

Using a graphing calculator or other mathematical software, we can find that the real solution to this equation is approximately x = 10.5.

Therefore, the dimensions of the box are:

- Length: x+8 = 18.5 feet

- Width: x = 10.5 feet

- Height: x-2 = 8.5 feet

The candy store will use 103 grams of sugar in 10 hours.

To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).

To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.

We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.

So the calculation would be:

10.3 grams/hour x 10 hours = 103 grams

Therefore, the candy store will use 103 grams of sugar in 10 hours.

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Answer:

The shape of each cut surface is a rectangle. The dimensions of the first cut surface are 8 inches by 10 inches, and the dimensions of the second cut surface are 10 inches by 20 inches.

The area of the first cut surface is 8 inches x 10 inches = 80 square inches. The area of the second cut surface is 10 inches x 20 inches = 200 square inches.

To find the total area Jenny needs to paint, we need to add the area of the first cut surface to the area of the second cut surface.

Total area = Area of first cut surface + Area of second cut surface

Total area = 80 square inches + 200 square inches

Total area = 280 square inches

Therefore, Jenny needs to paint a total area of 280 square inches.

The percentage of adults who planned to file their taxes electronically is approximately 63%.

A random telephone survey of 1,051 adults (aged 18 and older) was conducted by an online tax preparation and e-filing service. The survey results showed that 664 of those surveyed planned to file their taxes electronically.

Total number of adults surveyed = 1,051

Number of adults who planned to file their taxes electronically = 664

Percentage of adults who planned to file their taxes electronically is;

= (Number of adults who planned to file their taxes electronically / Total number of adults surveyed) x 100%

=(664/1051) x 100%

= 63.16 %

Therefore, the percentage of adults who planned to file their taxes electronically is approximately 63%.

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Step-by-step explanation:

If they are RIGHT triangles   then the Pythagorean theorem would apply

c^2 = a^2 +  b^2      where   c is the long side ( hypotenuse)

4)  does  10^2   =  6^2 + 8^2 ?

               100 = 36 + 64          Yes....it is a right triangle

5) does 8^2 = ( sqrt26)^2 + sqrt(28^2) ?

              64 =  26 + 28           NO....it is NOT a right triangle

6)  you should try this one yourself .....

Therefore, the area that the carpet needs to cover is: LW - 18 square feet.

Area is a mathematical term that refers to the amount of space occupied by a two-dimensional object or shape. It is typically measured in square units such as square feet, square meters, or square inches.

Here,

If the tiled floor is excluded from the area that needs to be covered by the carpet, then we need to find the area of the living room without the tiled floor and add the tiled floor's area to it.

Let's assume that the living room is a rectangular shape with length L and width W.

The area of the living room without the tiled floor is:

Area = L x W - (6 x 3) (since the tiled floor has an area of 6 ft x 3 ft)

Area = LW - 18 square feet

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To use Laplace transforms to solve the initial value problem where primes indicate derivatives with respect to t, follow these steps.

Write down the given differential equation and initial conditions. Apply the Laplace transform to both sides of the differential equation, using the properties of Laplace transforms for derivatives. Substitute the initial conditions into the transformed equation to get a new equation with no derivatives.Solve this new equation for the Laplace transform of the desired solution function. Apply the inverse Laplace transform to find the solution function in the time domain.Remember to be accurate and concise while solving the problem.

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Answer:No

Step-by-step explanation:

Because each X is an input, this means that Y is obviously the output.

In order for a set of data, there must ALWAYS be one output for every input, no more, no less. Because this particular set of data has multiple Y values with respect to different X values, this is not a function. Your correct answer is "No, because for each input there is not exactly one output."

Answer:

x = [tex]\frac{17}{5}[/tex]

Step-by-step explanation:

(8x - 12) = (3x + 5) ← remove parenthesis

8x - 12 = 3x + 5 ( subtract 3x from both sides )

5x - 12 = 5 ( add 12 to both sides )

5x = 17 ( divide both sides by 5 )

x = [tex]\frac{17}{5}[/tex]

or x = 3.4 ( in decimal form )

Answer:

-10

Step-by-step explanation:

I added a photo of my solution

Answer:

Answer is -10

Step-by-step explanation:

Required value of the given expression is (1+√2)

Given expression is [tex]tan \frac{11\pi}{8} [/tex]

We want to solve it.

Now,

[tex] \tan( \frac{11\pi}{8} ) = \tan( \frac{3\pi}{8} + \frac{8\pi}{8} ) \\ = \tan( \frac{3\pi}{8} + \pi ) \\ = \tan( \frac{3\pi}{8} ) [/tex]

Finding [tex] \tan( \frac{3\pi}{4} ) [/tex]

Let,

[tex] \tan(2t) = \tan( \frac{3\pi}{4} ) = - 1[/tex]

Use half angle identity,

[tex] \tan(2t) = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ - 1 = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ {tan}^{2} t - 2tant - 1 = 0[/tex]

Let,[tex]x = tant[/tex]

So,[tex] {x}^{2} - 2x - 1 = 0[/tex]

Now, [tex]x = 1 \pm \sqrt{2} [/tex]

So,

[tex]tant = tan \frac{3\pi}{8} = 1 \pm \sqrt{2} [/tex]

[tex]tan \frac{3\pi}{8} [/tex] is positive,then required value is 1+√2.

So, option D is the correct answer.

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The following question is incomplete.

Please complete the question so it can be answered.

Without the actual Production possibility frontier table or chart we cannot determine the exact quantities.

However, based on the information provided, we can determine that the production combo of 9 pies and 8 tarts is a point on Daisy's PPF.

This means that Daisy can produce 9 pies and 8 tarts per week using her available resources of 5 lbs of flour.

To fully analyze production possibilities of Daisy, we would need to see her complete PPF, which would show all possible combinations of pies and tarts that she could produce with her resources.

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Using FOIL method for the multiplication, we have:

1: 3x (5x - 4) = 15x² - 12x

2: x²(5x² + 3y + 1) = 5x⁴ + 3x²y + x²

3: (4x + 3)(4x -5)  = 16x² - 8x - 15

4: (7x - 3)(4x - 5) = 28x² - 47x + 15

FOIL is an acronym that stands for "First, Outer, Inner, Last". It is a mnemonic device that is commonly used to remember the process of multiplying two binomials.

No. 1

3x (5x - 4) = 3x*5x + 3x*(-4)

                 = 15x² - 12x

No. 2

x²(5x² + 3y + 1) = x²*5x² + x²*3y + x²*1

                        = 5x⁴ + 3x²y + x²

No. 3

(4x + 3)(4x -5) = 4x(4x-5) + 3(4x-5)

                    = 4x*4x + 4x*(-5) + 3*4x + 3*(-5)

                    = 16x² - 20x + 12x - 15

                    = 16x² - 8x - 15

No. 4

(7x - 3)(4x - 5) = 7x(4x - 5) - 3(4x - 5)

                      = 7x*4x  + 7x*(-5) - 3*4x - 3*(-5)

                      = 28x² - 35x -12x + 15

                      = 28x² - 47x + 15

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If Kelly is flying a kite to which the angle of elevation is 70 degrees. The string on the kite is 65 meters long. The kite is about 61 meters above the ground.

We can use trigonometry to solve the problem. Let's call the height of the kite above the ground "h".

Using trigonometry, we can write:

sin (70) = h / 65

Solving for h, we get:

h = 65 * sin(70)

h= 65 * 0.9397

h ≈ 61 meters

Therefore, the kite is about 61 meters above the ground.

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Answer:9.22

Step-by-step explanation:

You dont need the left side of this triangle to figure out the answer. You can use the fact that the remaining side to find is of a right triangle and use pythagorean theorem to solve.

Since 11 is the hypotenuse, and the pythagorean theorem states that a^2 +b^2 = c^2, the hypotenuse being c, you can reverse the equation like this:

11^2-6^2=rt^2

if you plug this in, you get that rt is exactly equal to 9.21954445729

Since you asked for it rounded to the nearest hundredth, you can round it to 9.22

By the 46th day, there are 400 water lilies in the pond. the estimate you made: a). close to 46 (or exactly right) because it was estimated well.

We know that the regression equation is: y = 3.915(1.106)ˣ and that the pond can hold 400 water lilies.

y = 3.915(1.106)ˣ

Here, y is equal to the number of water lilies the pond can hold.

So, y = 400

And,  x is the required time taken.

So,

400 = 3.915(1.106)ˣ

⇒ (1.106)ˣ = 400/3.915    

⇒ (1.106)ˣ = 102.17

Taking logarithm on both sides, we get

log (1.106)ˣ = log (102.17)

⇒ x log (1.106) = log (102.17) .............. [log aˣ = x loga]

⇒ x = [log (102.17)/log (1.106)]    

⇒ x = 45.92

x ≅ 46

So, the pond will take 46 days to become full.

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Complete question:

Regression equation: y = 3.915(1.106)ˣ . The pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation. the pond will be full by the end of day.

Answer:

b

Step-by-step explanation:

just did it

By definition, direct variation takes the following form:

y=kx

Where k is the proportionality constant.

You can find k given the information in the problem:

7=3k

k=3/7

You can now find y when x=7 as follows:

y=(7*3)

Values can be substituted. Then:

y=(7*7)/3

y=49/3

If y varies directly from x, then the value of y = 49/3 when x = 7.

If y varies directly from x, we can write its relationship in the form of the equation below :

y = m*x

Where m is the slope of the line on the graph.

From the given data:

y=7

x=3,

We can substitute these values in the above equation and find m :

7 = m*3

m = 7/3

So, the equation can also be written as follow:

y = 7/3 x

Finding y when x=7, then substituting the x value in the above equation we get:

y = (7/3)*(7)

y = 49/3

Therefore the value of the y = 49/3.

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The expression 75 + 1.45x represents the total cost of a training session with Terrell

Let x be the distance (in miles) that Terrell must drive to and from the training session.

Then the total cost C of the training session, in dollars, can be expressed as:

C = 75 + 1.45x

Therefore, the expression 75 + 1.45x represents the total cost of a training session with Terrell, including both the base fee and the additional cost for driving.

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Answer:

f(x) = (x + 5)² + 3

Step-by-step explanation:

f(x) = x² + 10x + 28

to complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 10x

f(x) = x² + 2(5)x + 25 - 25 + 28

     = (x + 5)² + 3 ← in vertex form

Answer:

Apparently it's 4800 according to desmos.

Step-by-step explanation:

Step-by-step explanation:

x y

-3 150

-2 300

-1 600

0 4800

As you can see, for negative values of x, the area burned becomes smaller and smaller as x becomes more negative. This is because the equation y = 4800(2)^x has a base of 2, which means that as x becomes more negative, 2^x becomes smaller and smaller, causing y to become smaller and smaller as well.

The approximate volume of the remaining solid is option (b) 77 cubic inches

The volume of the rectangular prism is given by

V_rectangular prism = base area x height = 4 x 4 x 6 = 96 cubic inches

The volume of the cylinder is given by

V_cylinder = π x r^2 x h = π x 1^2 x 6 = 6π cubic inches

To find the volume of the remaining solid, we need to subtract the volume of the cylinder from the volume of the rectangular prism

V_remaining solid = V_rectangular prism - V_cylinder = 96 - 6π ≈ 77 cubic inches (rounded to the nearest whole number)

Therefore, the correct option is (b) 77 cubic inches

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