A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 16 ​ft, its width is 7 ​ft, and its surface area is 500 ft2. ​(In the​ figure, h=height. Assume that the given surface area includes that of the top lid of the​ box.)

Based on the rating information of 10.2, a total of 1,800,000 households watched the show that week is 18360000 household.

An evaluation of something's quality or appeal is given a rating. a 10 out of 10 value-for-money rating, as an illustration. The president's standing among the public is at its lowest point since assuming office.

Position is synonymous with ranking, evaluation, appraisal, and categorisation. Additional Ratings

Since 1 rating point is given = 1,800,000

Rating point = 1,800,000 household

Rating point = 10.2 × 1,800,000 household.

Rating point =18360000 household.

Therefore, correct to state that the number of households that watched the show that week are 18360000 household.

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Answer: x=0.545455

Step-by-step explanation:

add 216 to both sides

divided both sides by 1331

take cube root

Answer: 8

Step-by-step explanation:  9 x 8 = 72

The piecewise function for the given problem is;

C(x) = $61.29                           x ≥ 400

C(x) = $61.29 + 0.6(x - 400) if x ≥ 400

A piecewise function is defined as a function that has different definitions depending on which values of x are being used. Piecewise functions are called "piecewise" due to the fact that they are made of "pieces" with different function definitions. To evaluate a piecewise function for a given value of x, find which interval your value fits in, and then use that definition of the function to evaluate.

First, we will find the monthly cost if the 400-minute monthly limit is not exceeded. Then, the total cost would be;

47.35 + 13.94 = 61.29 with just the plan and taxes. So if x ≤ 400, then;

C(x) = 61.29

Now if the 400 minutes is exceeded, the bill will also include $0.60 per additional minute. To find the number of additional minutes, we can take the total number of minutes x and subtract 400. In general, the cost would be;

C(x) = $61.29 + 0.6(x - 400) if x ≥ 400

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Answer:

Step-by-step explanation:

You just need to remember to first convert percentages to decimal form by dividing the percent by 100. Then you can work out the calculations.

Also, remember that if the problem is asking you to find a percentage, you need to turn your decimal answer to a percentage by multiplying by 100.

I used x to represent what we are looking for:

6.5% of $400 = x

0.065 * 400 = $26

12.5% of 100 = x

0.125 * 100 = $12.5

x of 650 = 130

130/650 = 0.2 which equals 20%

x of $4.50 = $5.40

5.40/4.50 = 1.2 which equals 120%

x of $28 = $8.40

8.40/28 = 0.3 which equals 30%

56% of x = $21.84

21.84/0.56 = 39

55% of x = $495

495/0.55 = 900

x of 400 = 120

120/400 = 0.3 which equals 30%

4% of 975 = x

0.04 * 975 = 39

Answer:

See below

Step-by-step explanation:

a. 6.5% of $400:

[tex]= \frac{65}{100}[/tex]× ($400)

= $260

b. 12.5% of $100:

[tex]= \frac{12.5}{100}[/tex] × ($100)

= $12.5

c. 130 is what percent of 650:

[tex]=\frac{130}{650}[/tex]×100%
= 20%

d. $5.40 is what percent of $4.50:

[tex]= \frac{5.40}{4.50}[/tex]×100%
= 120%

e. $8.40 is what percent of $28:

[tex]= \frac{8.40}{28}[/tex]× 100%
= 30%

f. 56% of what number is $21.84:

=[tex]\frac{56}{100}[/tex]× number = $21.84

∴ Number = [tex]\frac{100}{56}[/tex]×$21.84

                 = $39

g. $495 is 55% of what number:

= $495 = [tex]\frac{55}{100}[/tex]× Number

∴Number = [tex]\frac{100}{55}[/tex]×($495)

                 = $900

h. 120 is what percent of 400:

= [tex]\frac{120}{400}[/tex]×100%
= 30%

i. 4% of 975 is what number:

= [tex]\frac{4}{100}[/tex]×975

= 39

The required measure of the angle x in the given right triangle is 12.38°.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
Since the question seems to be incomplete the complete question has been attached after the solution.

We have given a triangle where x° is the angle of the right triangle where the hypotenuse is 54 and one legs is 12. With the help of trig ratios
sin x = 12 / 54
x = sin⁻¹(12/54)
x = 12.38°

Thus, the required measure of the angle x in the given right triangle is 12.38°.

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Answer:

  20 cubic yards

Step-by-step explanation:

You want to know the volume in cubic yards of a layer of topsoil that is 6 inches deep over an area 31 feet by 34 feet.

You know that ...

Then the dimensions of the volume being applied are ...

  6 inches = 6/36 yards

  31 feet = 31/3 yards

  34 feet = 34/3 yards

The volume is the product of the dimensions of the space:

  V = LWH

  V = (31/3 yd)(34/3 yd)(6/36 yd) ≈ 19.519 yd³

About 20 cubic yards are needed to fill the garden.

The pattern for the hypotenuse in the Pythagorean spiral is √(a² + b²)

The Pythagorean spiral is formed by drawing squares whose side lengths are given by the Pythagorean triples, which are sets of three positive integers (a, b, c) that satisfy the equation a² + b² = c².

In the Pythagorean spiral, the hypotenuse of each square is the diagonal of the square, which is given by the square root of the sum of the squares of the sides. For a square with side lengths a and b, the hypotenuse (diagonal) is given by:

√(a² + b²)

Since the side lengths of each square in the Pythagorean spiral are given by the Pythagorean triples, the hypotenuse of each square can be calculated using the Pythagorean theorem. Therefore, the pattern for each hypotenuse in the Pythagorean spiral is that it is given by the square root of the sum of the squares of the side lengths, where the side lengths are integers that form a Pythagorean triple.

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Answer:

Step-by-step explanation:

The frequency of a cosine function is related to the number of cycles that the function completes in a unit interval (usually in 2π radians).

The frequency of a cosine function with the form f(x) = A * cos(Bx + C) is given by B/(2π), where A, B, and C are constants.

For the function f(x) = 9cos(4πx) + 10, the frequency is given by 4π / (2π) = 2 cycles per unit interval.

So, the frequency of the function f(x) = 9cos(4πx) + 10 is 2 cycles per unit interval.

Answer:

[B]. (1,-5)

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]

Solve:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]        Since 2y - 2y = 0 we take that away now we have;

[tex]4x=-6\\3x=13[/tex]        Add 4x + 3x = 7x

[tex]\frac{7x}{7} =\frac{7}{7}[/tex] Divide both sides by 7.

[tex]x=1[/tex]

Now substitute x to find y.

[tex]4(1)+2y=-6[/tex]

[tex]4 + 2y =-6[/tex]  Add 6 to the other side.

[tex]10 = 2y[/tex] Divide both sides by 2.

[tex]\frac{10}{2} =\frac{2y}{2}[/tex]

[tex]y = 5[/tex]

Hence, the answer is [B]. (1,-5)

RevyBreeze

Answer:

3rd choice  (x + 8)² + (y - 11)² = 4

Step-by-step explanation:

(x - -8)² + (y - 11)² = 2²

(x + 8)² + (y - 11)² = 4

Step-by-step explanation:

(x - h)² + (y - k)² = r²

h = -8

k = 11

r = 2

(x + 8)² + (y - 11)² = 2²

(x + 8)² + (y - 11)² = 4

The answer is C. (x+8)² + (y-11)² = 4

Step-by-step explanation:

you have to find your five number summary

Answer:2304.9

Step-by-step explanation:

Answer:

  2304.9 ft

Step-by-step explanation:

You want the distance from point A, which is 1246 ft horizontally from a lighthouse to point B, given the angles of elevation to the light are 14° and 5° from points A and B, respectively.

The tangent relation for sides in a right triangle is ...

  Tan = Opposite/Adjacent

In a model of this geometry, the height (h) of the lighthouse is the side opposite the angle of elevation. This lets us write two equations:

  tan(14°) = h/1246

  tan(5°) = h/(1246 +d) . . . . . where d is the distance from A to B

Solving these equations for d, we have ...

  h = 1246·tan(14°) = (1246+d)·tan(5°)

  d·tan(5°) = 1246·(tan(14°) -tan(5°))

  d = 1246·(tan(14°)/tan(5°) -1) ≈ 2304.9 . . . . feet

The distance from point A to point B is about 2304.9 feet.

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Answer: 20% of 160 is 32.

Step-by-step explanation:

The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.

To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.

Let us now find the 20% of 160.

20% = 0.2

percentage = 160 × 0.2

= 32

Step-by-step explanation:

answer is in the picture

The difference in cost between a one-line ad and a four-line ad is 0

From the question, we have the following parameters that can be used in our computation:

c(x) = 40 x ≤ 5

c(x) = 40 + 7(x-4), x>5)

For one line add, we make use of the function

c(x) = 40 x ≤ 5

This is so because 1 is in the domain of x ≤ 5

For four line add, we make use of the function

c(x) = 40 x ≤ 5

This is so because 4 is in the domain of x ≤ 5

So, we have

C(1) = 40 and C(4) = 40

The difference, it

Difference = 40 - 40

Evaluate

Difference = 0

Hence, the difference is 0

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Answer:

1,800 lbs of sand

900 lbs of gravel

600 lbs of cement

Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.

The product of a, b, and c is 27/8.

What is an expression?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, and parentheses) that represents a quantity or a mathematical relationship. Expressions can be simple or complex, depending on the number of terms and the complexity of the operations involved.

The given expression is

                                      [tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2} }[/tex]

To simplify the given expression and write it in the form of ax^by^c, we can start by using the properties of exponents and simplifying the numerator and denominator separately:

Numerator: [tex]6x^2y^(-1) = \frac{6x^2}{y}[/tex]

Denominator: [tex]\sqrt[4]{(16x^5y^2)} = (16x^5y^2)^{(1/4)} = 2x^{(5/4)}y^{(1/2)}[/tex]

Putting the simplified numerator and denominator together, we have:

[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2}} = \frac{6x^2}{y} \cdot \frac{1}{2x^{5/4}y^{1/2}} = \frac{3}{\sqrt{2} \cdot x^{3/4}y^{3/2}}[/tex]

Now we can see that the given expression can be written in the form of ax^by^c, where a = 3, b = -3/4, and c = -3/2. Therefore, the product of a, b, and c is:

a * b * c = 3 * (-3/4) * (-3/2) = 27/8.

Hence, the product of a, b, and c is 27/8.

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Here are the steps to complete the budget, as described in the instructions:

Calculate totals for each type of expense and for each month:

Calculate net income for each month:

Add another column to calculate the percentage of total expenses for each category:

Create two different unique charts:

Label each page tab according to the chart:

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The difference between 3.25 and 1.75 is done and marked on the number line as below.

What is meant by a number line?

A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.

We are asked to plot the difference between 3 [tex]\frac{1}{4}[/tex] and 1 [tex]\frac{3}{4}[/tex] on the number line.

3 [tex]\frac{1}{4}[/tex] = 3 + 1/4 = 3 + 0.25 = 3.25

1 [tex]\frac{3}{4}[/tex] = 1 + 3/4 = 1 + 0.75 = 1.75

Difference = 3.25 - 1.75 = 1.5 = 1 [tex]\frac{1}{2}[/tex]

This can be shown on the number line below.

Each division has the value of 1/4 = 0.25.

We have marked 3[tex]\frac{1}{4}[/tex]  = 3.25 on the number line.

Since we are subtracting 1 [tex]\frac{3}{4}[/tex] = 1.75 from 3.25, we move 7 divisions backward from 3.25 as 7 * 0.25 = 1.75.

So after moving 7 divisions backwards, we land on 1.5, which is the difference we found earlier.

Therefore the difference between 3.25 and 1.75 is done and marked on the number line as below.

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Answer:

D

Step-by-step explanation:

Front

5x4 = 20

Back

5x4 = 20

Top

5x8 = 40

Bottom

5x8 = 40

Right side

8x4 = 32

Left side

8x4 = 32

Add all the sides

20 + 20 + 40 + 40 + 32 +32 = 184

The value of x is [0,∞] and y is [0,∞]. The solution has been obtained by using the elimination method.

What is elimination method?

The elimination approach involves removing one of the variables from the system of linear equations by employing addition or subtraction together with multiplication or division of the variable coefficients.

We are given two equations as

7x + 14y = 28     ....(1)

5x + 10y = 20     ....(2)

Now, on multiplying equation (1) by 10, we get the equation as

70x + 140y = 280     ....(3)

On multiplying equation (2) by 14, we get the equation as

70x + 140y = 280     ....(4)

Since, we are getting the same equations so, the system has infinitely many solutions.

Hence, the value of x is [0,∞] and y is [0,∞].

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Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

What is meant by budget?

Let's assume that Hannah needs to use x gallons of soda and y gallons of fruit drink to make 168 gallons of punch.

We know that the cost of soda is $1.57 per gallon and the cost of fruit drink is $2.41 per gallon, and Hannah's budget requires that the punch cost $1.66 per gallon.

So we can set up the following system of equations:

x + y = 168 (total amount of punch)

1.57x + 2.41y = 1.66(168) (total cost of punch)

Simplifying the second equation:

1.57x + 2.41y = 278.88

Now we can use substitution or elimination method to solve for x and y.

Using substitution:

x = 168 - y

1.57(168 - y) + 2.41y = 278.88

264.36 - 1.57y + 2.41y = 278.88

0.84y = 14.52

y = 17.29

So Hannah needs 17.29 gallons of fruit drink.

Using x + y = 168, we can find that she needs 150.71 gallons of soda.

Therefore, Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

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B is significantly more affordable and better than A, renting for $1.62 per square foot.

Yard and feet are used to estimate the length. Both of the units are used in the royal and US customary system of measurements. The value of one yard is equal to three feet.

To compute Square yard to Square Feet, where Square yard is equal to 9 Square Feet, multiply the value in Square yard by 9. one can also use the Square yard to Square Feet calculator.

1 yard² = 9 feet²

A rents for $33 per yard squared

hence A rents $33 for 9 feet squared

hence A rents $3.67 per feet squared( $33/9) which is costlier than $1.49 per feet squared

Thus, as B is more economical, it is better.

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The measure of a from the triangle ATD is 27 units. Therefore, the option B is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

From the given triangle ADT, ∠A=46°, ∠D=84°, AT=37, AD=t and TD=a.

By angle sum property,

∠A+∠D+∠T=180°

46°+84°+∠T=180°

130°+∠T=180°

∠T=50°

sin46°/a=sin84°/37=sin50°/t

0.7193/a=0.9945/37=0.7660/t

0.7193/a=0.9945/37

0.9945a=0.7193×37

0.9945a=26.6141

a=26.6141/0.9945

a=26.76

≈27

0.9945/37=0.7660/t

0.9945t=0.7660×37

0.9945t=28.342

t=28.342/0.9945

t=28.5

Therefore, the option B is the correct answer.

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Answer:

he constant of proportionality is $1.80, since for every 3 lemons the total cost increases by $1.80.

The equation that relates the total cost, y, and the number of lemons, x, is:

y = 1.80 * (x/3) + b

where b is the y-intercept, which represents the cost of 0 lemons. We'll need additional information to determine the value of b.

Here is a table with the values of y and x, assuming b = 0:

x (Number of Lemons) y (Total Cost)

0 0

3 1.80

6 3.60

9 5.40

... ...

Step-by-step explanation:

The following statements are true:

A:The car makes a complete revolution in 10 seconds

B:The maximum height of the Ferris wheel is 65 feet

A full rotation or turning around a focal point is referred to as a revolution. Revolution is the act of rotating around a fixed point or axis . Examples of this include the rotation of a planet around its star or a wheel around its axle.

A. The car makes a complete revolution in 10 seconds:

This can be deduced from the fact that the height of the Ferris wheel car returns to 35 feet after 10 seconds, which means that it has completed one full revolution.

B. The maximum height of the Ferris wheel is 65 feet:

This can be seen from the table, where the height of the Ferris wheel car reaches 65 feet at 2.5 seconds and 12.5 seconds.

C. If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel: This can be seen from the table, where the height of the Ferris wheel car is 35 feet at 0 seconds.

It is not possible to determine the radius of the Ferris wheel based on the given information alone.

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