The volume of a large tank is 525 . It is 16 2/3
wide and 2 4/5
high. What is the length of the tank
​?

Answer:

x = 11

Step-by-step explanation:

[tex] \frac{8}{48} = \frac{x}{x + 55} [/tex]

[tex]8(x + 55) = 48x[/tex]

[tex]8x + 440 = 48x[/tex]

[tex]40x = 440[/tex]

[tex]x = 11[/tex]

The properties used were the distributive property of multiplication over addition, the subtraction property of equality, and the multiplication property of equality.

Properties are statements that are true for a wide range of numbers or equations. They are rules that describe the behavior of mathematical objects and relationships between them.

1) Given 4x-1=27, we can use the addition property of equality to add 1 to both sides:

4x-1+1 = 27+1

Simplifying, we get:

4x = 28

Then, we can use the multiplication property of equality to divide both sides by 4:

4x/4 = 28/4

Simplifying, we get:

x = 7

Therefore, we have proved that if 4x-1=27, then x=7.

The properties used were the addition property of equality and the multiplication property of equality.

2) Given (a/(-6))+2=5, we can use the subtraction property of equality to subtract 2 from both sides:

(a/(-6))+2-2 = 5-2

Simplifying, we get:

a/(-6) = 3

Then, we can use the multiplication property of equality to multiply both sides by -6:

(a/(-6))(-6) = 3(-6)

Simplifying, we get:

a = -18

Therefore, we have proved that if (a/(-6))+2=5, then a=-18.

3) The properties used were the subtraction property of equality and the multiplication property of equality.

Given -9(2x-3)=63, we can use the distributive property of multiplication over addition to simplify the left-hand side:

-9(2x-3) = -18x + 27

Then, we can use the subtraction property of equality to subtract 27 from both sides:

-18x + 27 - 27 = 63 - 27

Simplifying, we get:

-18x = 36

Finally, we can use the multiplication property of equality to divide both sides by -18:

(-18x)/(-18) = 36/(-18)

Simplifying, we get:

x = -2

Therefore, we have proved that if -9(2x-3)=63, then x=-2.

The properties used were the distributive property of multiplication over addition, the subtraction property of equality, and the multiplication property of equality.

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Step-by-step explanation:

as the description says, the area is a rectangle (8×4) minus the half-circle at the right.

the radius of the (half-)circle is 4/2 = 2, as 4 is the diameter.

the area of the circle is

pi×r² = pi×2² = 4pi

the area of the half-circle is then

4pi/2 = 2pi

the area of the rectangle is

8×4 = 32

the total area is

32 - 2pi = 25.71681469... ≈ 25.7 square units

Answer:

  25.7 square units

Step-by-step explanation:

You want the area of a 4 × 8 rectangle with a semicircle of diameter 4 removed from the end.

The area of the enclosing rectangle is ...

  A = LW

  A = (8)(4) = 32 . . . . . square units

The are of the missing semicircle is ...

  A = 1/2πr² . . . . . . where r is half the diameter

  A = 1/2π(4/2)² = 2π ≈ 6.3 . . . . . square units

Then the area of the figure is ...

  A = rectangle - semicircle = 32 -6.3 = 25.7 . . . . . square units

The area of the figure is about 25.7 square units.

The complete table is:

x       f(x)

-8       -8

-1        -8

1          -8

And the graph can be seen in the image at the end.

Here we have the function:

f(x)  = -8

This is a constant function, for every input that we use, the output will be the same one, then:

f(-8) = -8

f(-1) = -8

f(1) = -8

Then the complete table is:

x       f(x)

-8       -8

-1        -8

1          -8

And the graph of these 3 points can be seen in the image at the end.

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Answer:

21

Step-by-step explanation:

20+1=21

The answer of the given question based on the triangle is, option (A) one of the three different points that are equidistant from the three sides of the triangle.

A point of intersection is a point where two or more lines, curves, or surfaces meet or cross each other. In geometry, the point of intersection can be used to find important properties of the objects involved, such as angles, distances, and coordinates.

George is trying to find point that is equidistant from  three sides of the triangle.

The point of intersection of the lines passing through the arcs drawn from the vertices of the triangle using a compass is called the circumcenter of the triangle. The circumcenter is equidistant from three vertices of  triangle, which means that it lies on  perpendicular bisectors of  three sides of  triangle.

In this case, the perpendicular bisectors of JL and YZ are shown as lines JK and WX respectively. The circumcenter of triangle JKL is the point where these two lines intersect. This point is equidistant from the sides KL, LJ, and JK of the triangle.

Therefore, the answer is (A) one of the three different points that are equidistant from the three sides of the triangle.

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The answer is B. George is trying to find one of the three different points that are equidistant from the three vertices of the triangle.

The intersection of two or more lines, curves, or surfaces is known as a point of intersection.

George is trying to find one of the three different points that are equidistant from the three vertices of the triangle JKL.

The intersection of the arcs drawn from the vertices of the triangle will be equidistant from those vertices. This point is called the circumcenter of the triangle, and it is the center of the circumcircle that passes through all three vertices of the triangle.

Since George is drawing lines through the arcs and finding their point of intersection, he is finding the circumcenter of the triangle. The circumcenter is one of the three different points that are equidistant from the three vertices of the triangle.

Therefore, the answer is B. George is trying to find one of the three different points that are equidistant from the three vertices of the triangle.

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Amelia was at camp for 6 days. The equation used to determine how many days(D) she was at camp is C x D = 6D and S - (C x D) = E

Given data:

S = initial amount = $54

D = the number of days

C = the cost per day = $6

E: the ending amount = $18

Amelia started with S=$54 and spent C=$6 each day at camp.

Therefore, the total amount she spent at camp is given in an algebraic expression that states the product of two variables:

C x D = 6D

Next, she ended with E=$18. So, the equation can be written in algebraic expression that states the difference between the variable:

S - (C x D) = E

Substituting the values in the equation we get:

54 - 6D = 18

54 - 18 = 6D

36 = 6D

D = 6

Therefore, Amelia was at camp for 6 days.

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To determine the type of vertex created by this quadratic function, we need to find the vertex of the parabola. The vertex of a parabola is the point where the parabola reaches its minimum or maximum value.

The given equation [tex]h(t) = -0.25t^2 + 2t + 4[/tex] represents the height of the basketball as a function of time.

The vertex of a quadratic function in the form of   [tex]f(x) = ax^2 + bx + c[/tex] can be found by using the formula:

[tex]x = -b/2a[/tex]

[tex]y = f(x) = a(x^2) + bx + c[/tex]

where (x,y) is the vertex of the parabola.

Comparing this with the given equation  [tex]h(t) = -0.25t^2 + 2t + 4[/tex] , we see that a = -0.25, b = 2, and c = 4.

Substituting these values in the formula, we get:

[tex]t = -2/(2\times(-0.25)) = 4[/tex]

[tex]h(4) = -0.25(4)^2 + 2(4) + 4 = 6[/tex]

Therefore, the vertex of the parabola is [tex](4, 6)[/tex] . Since the coefficient of the t^2 term is negative, the parabola opens downwards, and the vertex represents the maximum point of the parabola. The quadratic function   [tex]h(t) = -0.25t^2 + 2t + 4[/tex] would create a maximum vertex.

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Answer:

Step-by-step explanation:

Hey Love:

here's the answer,

2/9(9a-44)

After answering the presented question, we can conclude that The equation number of trials is predetermined: We're going to roll the dice 20 times.

An equation is a statement in mathematics that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). For example, 2 + 3 = 5 is an equation because the expression on the left-hand side (2 + 3) is equal to the expression on the right-hand side (5).

Equations are used in many areas of mathematics, science, and engineering to describe relationships between quantities and to solve problems. For example, equations are used to model physical phenomena, such as the motion of objects, the behavior of fluids, and the propagation of waves. They are also used in finance, statistics, and many other fields to analyze data and make predictions.

In this case, the random variable X reflects the number of times a specific number appears after rolling a 20-sided die 20 times.

To see if this situation fits the binomial distribution model, we must look at the four conditions listed below:

The trials are impartial: Each throw of the dice is distinct from the others.

There are just two possibilities: Each roll can produce one of the 20 numbers or none at all.

The likelihood of success is constant: The probability of rolling a given number on a 20-sided dice is the same for each roll.

The number of trials is predetermined: We're going to roll the dice 20 times.

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Answer:

Step-by-step explanation:

15 divided by 15 is 1

3.45 divided by 15 is 0.23

The cost per ounce is 23 cents, or $0.23

Thus, the number of months when the revenue earned will be equal to the business's expenses is 8 months approx)

f(x) = ax² + bx + c, from which a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Even though "width" or "steepness" of a parabola can vary as well as its path of opening, they all share so same fundamental "U" form.

Given data:

monthly expenses's function: y = 2.75x + 7.5 .

revenue function:  y = 0.2x² + 1.5x

x is the number of months

y is the amount of money (dollars)

monthly expenses = revenue function

2.75x + 7.5  = 0.2x² + 1.5x

On simplification:

0.2x² + 1.5x - 2.75x -  7.5 = 0

0.2x² - 1.25x -  7.5 = 0

Divide equation by 0.2

x² - 6.25x -  37.5 = 0

standard form of quadratic eq: ax² + bx + c = 0

On comparing:

a = 1, b = -6.25 and c = -7.5

Using the quadratic formula:

x = [tex](-b + \sqrt{b^{2} - 4 ac } )/ 2a[/tex] and x = [tex](-b - \sqrt{b^{2} - 4 ac } )/ 2a[/tex]

Put the values:

x = [tex](6.25 + \sqrt{-6.25^{2} - 4 *1*(-7.5) } )/ 2*1[/tex]

x = (6.25 + 8.31)/2

x = 7.28 (number of months)

x = 8 months approx

and x = [tex](6.25 - \sqrt{-6.25^{2} - 4 *1*(-7.5) } )/ 2*1[/tex]

x = (6.25 - 8.31)/2

x = -1.03 (negative value not taken)

Thus, the number of months when the revenue earned will be equal to the business's expenses is 8 months approx)

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complete question:

The monthly expenses of a business can be modeled by y = 2.75x + 7.5 The revenue generated by the business can be represented by the function y = 0.2x² + 1.5x.  In each function, x is the number of months since the business opened and y is the amount of money in thousands of dollars. After how many months will the revenue earned be equal to the business's expenses.

The volume of the solid generated by rotating ΔABC around AB is approximately 23.39 cubic units.

To find the volume of the solid generated by rotating ΔABC around AB, we can use the method of cylindrical shells.

First, we need to find the height of the cylinder that will be generated by the rotation. This height is simply the length of AB, which is 2.

Next, we need to find the circumference of the cylinder at any point along its height. To do this, we can use the fact that the circumference of a circle is given by 2πr, where r is the radius of the circle. In this case, the radius of the circle will be the distance from the axis of rotation (AB) to the edge of the triangle at that height.

Let x be the distance from vertex A to the point on AB directly below it. Then, at any height h, the radius of the circle will be given by:

r = BC - x

To find x, we can use the Pythagorean theorem. Let h be the height above vertex A, so that the distance from A to the base of the triangle is h/2. Then, the distance from vertex A to the point on AB directly below it is:

[tex]x = \sqrt{AB^2 - \left(\frac{h}{2}\right)^2} = \sqrt{2^2 - \left(\frac{h}{2}\right)^2}[/tex]

Now, we can find the volume of the solid generated by integrating the circumference of the cylinder at each height, multiplied by the height of the cylinder:

[tex]V = \int_0^2 2\pi\left(BC - \sqrt{2^2 - \left(\frac{h}{2}\right)^2}\right)dh[/tex]

We can simplify this integral using the substitution u = h/2, which gives:

[tex]V = 4\pi\int_0^1\left(BC - \sqrt{4 - u^2}\right)du[/tex]

Now, we need to plug in the values of BC and evaluate the integral:

[tex]V = 4\pi\int_0^1\left(5 - \sqrt{4 - u^2}\right)du[/tex]

= [tex]4\pi\left[\left(5u - \frac{u}{2}\sqrt{4 - u^2} - 2\arcsin\left(\frac{u}{2}\right)\right)\Bigg|_0^1\right][/tex]

≈ 23.39

Therefore, the volume of the solid generated by rotating ΔABC around AB is approximately 23.39 cubic units.

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To calculate the 95% confidence interval for the difference in mean weekly sales for the two movie theaters, follow these steps:

Step 1: Gather the data for the random sample of 25 weeks.

Step 2: Calculate the mean and standard deviation for each movie theater's weekly sales.

Step 3: Calculate the difference in mean weekly sales for the two movie theaters (subtract the mean of theater 2 from the mean of theater 1).

Step 4: Calculate the standard error of the difference by taking the square root of [(standard deviation of theater 1^2 / number of weeks) + (standard deviation of theater 2^2 / number of weeks)].

Step 5: Determine the critical value for a 95% confidence interval using a t-table or calculator (for a two-tailed test with 24 degrees of freedom, the critical value is approximately 2.064).

Step 6: Multiply the critical value by the standard error to get the margin of error.

Step 7: Calculate the lower and upper bounds of the confidence interval by subtracting and adding the margin of error from the difference in mean weekly sales.

The result will be the 95% confidence interval for the difference in mean weekly sales for the two movie theaters.

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Answer:

12:4

=3:1 (Simplified )

Answer:

best choice to answr is letter B.

Step-by-step explanation:

Square feet is the standard unit of measure for area in the United States and is commonly used for measuring the area of rooms and other surfaces, including floors and walls. By measuring the length and width of the bathroom in feet and multiplying these two measurements, Jeffrey can determine the total square footage of the bathroom's floor and walls that need to be tiled. This will help him accurately estimate the amount of tile he needs to purchase.

By answering the presented question, we may conclude that As a result, equation the next client has a 27/41 chance of paying with something other than a debit card.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.

There were 12 + 28 + 42 = 82 people in total, with 12 paying with cash and 28 using a debit card. As a result, the number of consumers who did not use a debit card is 82 - 28 = 54.

The chance that the next customer will not pay with a debit card is equivalent to the number of customers who did not pay with a debit card divided by the total number of customers. As a result, the likelihood is:

54/82

This fraction can be simplified by splitting the numerator and denominator by their largest common factor, which is 2:

54/82 = (2 × 27)/(2 × 41) = 27/41

As a result, the next client has a 27/41 chance of paying with something other than a debit card.

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The value of k is approximately 10.33.

What is the exterior angle?

An exterior angle is an angle that forms a linear pair with an interior angle of a polygon. It is formed by extending one of the sides of the polygon. In other words, it is the angle formed between a side of a polygon and the extension of an adjacent side.

In a triangle, the measure of an exterior angle is equal to the sum of the measures of its two remote interior angles. In this problem, the exterior angle to the bottom left interior angle is (5k - 3) degrees, and the corresponding remote interior angle is (9 + k) degrees. Therefore, we can write:

(5k - 3) = (9 + k) + x

where x is the other remote interior angle of the triangle.

Simplifying this equation, we get:

5k - 3 = 9 + k + x

4k = 12 + x

x = 4k - 12

Now, we know that the sum of the interior angles of a triangle is 180 degrees. So, we can write:

(9 + k) + (5k - 3) + x = 180

Substituting x with 4k - 12, we get:

(9 + k) + (5k - 3) + (4k - 12) = 180

Simplifying this equation, we get:

18k - 6 = 180

18k = 186

k = 10.33 (rounded to two decimal places)

Therefore, the value of k is approximately 10.33.

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Answer: 23 meter

Step-by-step explanation:

meters "above"

elevation means the distance above sea level

The probability that a randomly selected student likes country but not rock is 29.4%.

We know that,

P(country but not rock) = P(country) - P(country and rock)

So to calculate P(country), we know from the survey that 162 students like country and to calculate P(country and rock), we need to subtract the number of students who like all three types of music (7) from the number of students who like both country and rock (22), which gives us 22 - 7 = 15.

Therefore, P(country but not rock) = 162/500 - 15/500 = 147/500 = 0.294.

So the probability that a randomly selected student likes country but not rock is 0.294 or 29.4%.

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2(6×7) + 2(3×7) + 2(3×6)

= 162

The volume of container M can be calculated using the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we have:

V = π(3 in)^2(9.5 in)

V ≈ 254.47 cubic inches

Let x be the volume of one box of sugar. According to the problem, the cook emptied one box of sugar into the container, and then added some fraction of another box to completely fill it. This means that the total volume of sugar added is equal to 1 + some fraction of x.

We can set up an equation to solve for x:

1 + (1/n)x = 254.47

where n is the fraction of the second box of sugar added.

Solving for x, we get:

x = (254.47 - 1) n

x = 253.47n

To find the value of n, we can subtract 1 box of sugar from the total volume added, and then divide by the volume of one box:

n = (254.47 - 1) / x

n = 253.47 / x

Substituting the expression for x from above, we get:

n = 253.47 / (253.47n)

n^2 = 253.47 / 1

n ≈ 15.93

Therefore, the volume of one box of sugar is approximately:

x ≈ 253.47 / 15.93

x ≈ 15.91 cubic inches

Burger Quick has a smaller IQR (Interquartile Range) than Super Fast Food, indicating that the middle 50% of the data is more tightly clustered around the median.

Super Fast Food is able to estimate their wait time more consistently because it has a smaller range, which means the wait times reported by the 20 people are more closely clustered around the median wait time of 12 minutes.

Burger Quick may predict wait times more reliably than Super Fast Food due to a reduced IQR (Interquartile Range).

The IQR is a measure of the spread of the middle 50% of data, defined as the difference between the third (Q3) and first (Q1) quartiles. A lower IQR shows that the middle 50% of the data is more closely grouped around the median, implying that the data is more consistent.

Burger Quick has an IQR of 14.5 (Q3=24, Q1=9.5) in this situation, while Super Fast Food has an IQR of 7 (Q3=15.5, Q1=8.5). As a result, Burger Quick has a lower IQR and can predict their wait time more reliably than Super Fast Food.

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The correct option is B, that the reason that justifies that the lines are parallel.

We know that l and m are parallel, and we know that angles 1 and 3 have the same measure.

Notice that angles 1 and 3 are in opposite quadrants (second and fourth). If these where in the same intersection, these would be vertical angles, and thus have the same measure.

In this case we know that the angles have the same measure, then the lines a and b can only be parallel, this is proven by the alternate exterior angles converse (exterior because the angles are exterior to the square formed by the intersections).

So the correct option is B.

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Answer:

156

Step-by-step explanation:

The value of the expression 2x^2 - 5xy when x = -3 and y = 8 is 138.

To find the value of the expression, 2x^2 - 5xy, when x = -3 and y = 8, we just need to substitute the given values into the expression.

So, 2x^2 - 5xy becomes 2*(-3)^2 - 5*(-3)*8 = 2*9 + 15*8 = 18 + 120 = 138

Therefore, the value of the expression 2x^2 - 5xy when x = -3 and y = 8 is 138.

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The first term of the polynomial in standard form must be 4y⁴

If Julian wrote the last term as -3x⁴, the terms with the highest degree must have a coefficient of 3.

To get the standard form, we need to combine like terms and arrange the terms in descending order of degree.

The polynomial can be simplified as follows:

4x²y²-2y⁴-8xy³+9x³y+6y⁴-2xy³-3x⁴+x²y²

= -3x⁴ + (4x²y² + x²y²) + (-2y⁴ + 6y⁴) + (-8xy³ - 2xy³) + 9x³y

= -3x⁴ + 5x²y² + 4y⁴ - 10xy³ + 9x³y

Therefore, the standard form of the polynomial is

-3x⁴ + 5x²y² + 4y⁴ - 10xy³ + 9x³y

= 4y⁴ + 5x²y² + -3x⁴ - 10xy³ + 9x³y

The term with the highest degree is -3x⁴, and the terms are arranged in descending order of degree. The answer is not one of the options given.

Therefore, the first term of the polynomial in standard form must be 4y⁴.

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Answer:

To solve this problem, we can use a system of equations. Let x be the number of ounces of solution A and y be the number of ounces of solution B. Then we have: x + y = 150 (total solution) 0.35x + 0.85y = 0.4(150) (total salt) Simplifying the second equation, we get: 0.35x + 0.85y = 60 Multiplying both sides of the first equation by 0.35 and subtracting from the second equation, we get: 0.5y = 15 y = 30 Substituting y = 30 into the first equation, we get: x + 30 = 150 x = 120 Therefore, the scientist should use 120 ounces of solution A and 30 ounces of solution B to obtain

The scientist should use 135 ounces of solution a and 15 ounces of solution b to obtain 150 ounces of a mixture that is 40% salt. This can be answered by the concept of system of equations.

To solve this problem, we can use a system of equations. Let x be the number of ounces of solution a used, and y be the number of ounces of solution b used. We want to find x and y such that:

x + y = 150 (we need 150 ounces of the mixture)

0.35x + 0.85y = 0.4(150) (the total amount of salt in the mixture should be 40% of 150 ounces)

We can solve this system of equations by first multiplying the second equation by 100 to get rid of the decimals:

35x + 85y = 6000

Then we can use the first equation to solve for one variable in terms of the other:

y = 150 - x

Substituting this into the second equation, we get:

35x + 85(150 - x) = 6000

35x + 12750 - 85x = 6000

-50x = -6750

x = 135

Therefore, the scientist should use 135 ounces of solution a and 15 ounces of solution b.

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Answer:

B(t) = 125*(1.3)^t

Step-by-step explanation: