A company is deciding which box to use for their merchandise. The first box measures 8 inches wide, 6.25 inches long, and 10.5 inches high. The second box measures 9 inches wide, 5.5 inches long, and 11.5 inches high. What is the separate surface areas of both boxes?

2[L + W] =22

L*W = 28

W = 28/L sub this in the first equation

Solve for L:

2 (L + 28/L) = 22

Divide both sides by a constant to simplify the equation.

Divide both sides by 2:

L + 28/L = 11

Write the left hand side as a single fraction.

Bring L + 28/L together using the common denominator L:

(L^2 + 28)/L = 11

Multiply both sides by a polynomial to clear fractions.

Multiply both sides by L:

L^2 + 28 = 11 L

Move everything to the left hand side.

Subtract 11 L from both sides:

L^2 - 11 L + 28 = 0

Factor the left hand side.

The left hand side factors into a product with two terms:

(L - 7) (L - 4) = 0

Find the roots of each term in the product separately.

Split into two equations:

L - 7 = 0 or L - 4 = 0

Look at the first equation: Solve for L.

Add 7 to both sides:

L = 7 or L - 4 = 0

Look at the second equation: Solve for L.

Add 4 to both sides:

L = 7       or L = 4         and        W=4      or W = 7

The area of a 2D form is the amount of space within its perimeter. The given statement is true.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given that radius of the circle is 12 units, and the radius of the sphere is 6 units.

The area of the circle  = π(12)² = 144π units²

The surface area of the sphere = 4π(6)² = 144π units²

As it can be observed that the area of a circle of radius 12 units is equal to the surface area of a sphere of radius 6 units.

Hence, the given statement is true.

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Answer:

The linear equation that represent the situation is [tex]x=20-0.75(10+2)[/tex]

The remaining balance on his gift card is [tex]\$11[/tex]

Step-by-step explanation:

Let

x------> represents the remaining balance

we know that

The linear equation that represent the situation is equal to

[tex]x=20-0.75(10+2)[/tex]

Solve

[tex]x=20-0.75(12)[/tex]

[tex]x=20-9[/tex]

[tex]x=\$11[/tex]

Answer:

its B

Step-by-step explanation:

Answer:

I am 96 percent it is c  

   Hope this helped!!!!

for 1 i got $945.

For 2 i got $826.80.

For 3 i got c.

For 4 i got $2.16.

For 5 i got $52.50

Final answer:

The sample size is calculated to be 200 based on the percentage for Candidate A. From the sample, 120 students said they will vote for Candidate C. Predicting based on this sample, 1,500 students in the school will vote for Candidate C.

Explanation:

To find the number of students in the sample who said they will vote for Candidate C, we need to use the percentages given for each candidate. If Candidate A is 25%, Candidate B is 15%, and Candidate C is 60%, and knowing that 50 students in the sample voted for Candidate A, we can determine the total sample size. Since Candidate A represents 25% of the sample, we can calculate the total sample size using the equation 50 = 0.25 × (total sample size). Solving for total sample size gives us 200.

With the sample size known, we can calculate the number of students who said they will vote for Candidate C by taking 60% of 200, which is 120 students in the sample. To predict the number of students in the school who will vote for Candidate C, we use the proportion of the sample who choose Candidate C to estimate the proportion for the entire school population. Since there are 2,500 students in the school, we predict that 60% of 2,500 will vote for Candidate C, which amounts to 1,500 students.

Answer:

The y-coordinate of the solution is, 10

Step-by-step explanation:

Given the system of equation:

[tex]y = -2x+4[/tex]            ....[1]

[tex]y=x^2+4x+13[/tex]         ....[2]

Equate the equation [1] and [2] we have;

[tex]-2x+4 = x^2+4x+13[/tex]

Add 2x to both sides of an equation:

[tex]4 = x^2+6x+13[/tex]

Subtract 4 from both sides we have;

[tex]0= x^2+6x+9[/tex]

or

[tex]x^2+6x+9=0[/tex]

Using perfect square:

[tex](x+a)^2 = x^2+2ax+a^2[/tex]

⇒We can write the equation as:

[tex]x^2+2 \cdot 3x+3^2=0[/tex]

then;

[tex](x+3)^2 = 0[/tex]

⇒[tex]x+3 = 0[/tex]

Subtract 3 from both sides we have;

x = -3

Substitute value of x in [1] we have;

[tex]y = -2(-3)+4[/tex]

⇒[tex]y =6+4=10[/tex]

Solution for the given system of equation = (-3, 10)

Therefore, the  y-coordinate of the solution is, 10

The area of the actual playground is [tex]\( 15000 \)[/tex] square feet. To solve this problem, we need to understand the relationship between the scale drawing and the actual playground dimensions.

Let's denote:

- [tex]\( l \)[/tex] as the length of the scale drawing,

- [tex]\( w \)[/tex] as the width of the scale drawing,

- [tex]\( L \)[/tex]  as the length of the actual playground, and

- [tex]\( W \)[/tex] as the width of the actual playground.

Given that the dimensions of the actual playground are 50 times the dimensions of the scale drawing, we have the following relationships:

[tex]\[ L = 50l \][/tex]

[tex]\[ W = 50w \][/tex]

We are given that the area of the scale drawing is 6 square feet. The area of a rectangle is given by the formula [tex]\( \text{Area} = \text{length} \times \text{width} \).[/tex] So, for the scale drawing:

[tex]\[ \text{Area of scale drawing} = l \times w = 6 \][/tex]

Now, we need to find the length and width of the actual playground and then calculate its area.

From the relationship between the actual playground and the scale drawing, we have:

[tex]\[ L = 50l \][/tex]

[tex]\[ W = 50w \][/tex]

So, we can express [tex]\( l \) and \( w \)[/tex] in terms of [tex]\( L \) and \( W \)[/tex]:

[tex]\[ l = \frac{L}{50} \][/tex]

[tex]\[ w = \frac{W}{50} \][/tex]

Now, let's substitute these expressions into the equation for the area of the scale drawing:

[tex]\[ \text{Area of scale drawing} = \left(\frac{L}{50}\right) \times \left(\frac{W}{50}\right) = 6 \][/tex]

[tex]\[ \frac{L \times W}{2500} = 6 \][/tex]

To find the area of the actual playground, we need to solve for [tex]\( L \times W \):[/tex]

[tex]\[ L \times W = 6 \times 2500 = 15000 \][/tex]

Therefore, the area of the actual playground is [tex]\( 15000 \)[/tex] square feet.

Answer:

Step-by-step explanation:

Answer:

[tex]\frac{\pi }{3}[/tex]

Step-by-step explanation:

[tex]sin^{-1}(\frac{\sqrt{3} }{2})[/tex]

In, 30-60-90 degree triangle ,

the sides are in the ratio [tex]1: \sqrt{3} :2[/tex]

[tex]sin(60)= \frac{opposite}{hypotenuse}[/tex]

for 60 degree, opposite side = square root (3)

hypotenuse = 2

So [tex]sin(60)= \frac{\sqrt{3}}{2}[/tex]

when we move sin to the other side then it becomes sin^-1

[tex]60= sin^{-1}\frac{\sqrt{3}}{2}[/tex]

angle 60 degree is [tex]\frac{\pi }{3}[/tex]

[tex]sin^{-1}(\frac{\sqrt{3} }{2})=\frac{\pi }{3}[/tex]

The expression that is equivalent to sin⁻¹(sqrt. 3/2) is π/3.

The expression that is equivalent to another is one that yields the same output no matter the arrangement of the figures and signs.

For the expression,  sin⁻¹(sqrt. 3/2), the equivalent can be obtained thus;

sin 60 = opposite/hypotenuse

sin 60 = √3/2

60 = sine⁻¹√3/2

=  π/3.

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The volume of a cube is found with the following formula:

[tex] l \times w \times h [/tex]

The length, width, and height must all be the same value in a cube. This means that you can replace variables l, w, and h with one variable, s:

[tex] \boxed{s} \times s \times s = s^3 [/tex]

The expression s can represent the length of a side of the cube.

The expression represents s, the length of a side of the cube is [tex]\rm s^3=64[/tex].

The volume of the cube formula is:

The volume of a Cube = Length × Width × Height

The volume of a cube is 64 cubic inches.

where s is the length of a side of the cube.

The side of the cube is;

[tex]\rm The \ volume \ of\ a\ Cube = Length \times Width \times Height \\\\ The \ volume \ of\ a\ Cube =s \times s \times s\\\\The \ volume \ of\ a\ Cube =s^3\\\\s^3=64[/tex]

Hence, the expression represents s, the length of a side of the cube is [tex]\rm s^3=64[/tex].

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Answer:  The correct option is (A) 42.7 units.

Step-by-step explanation:  Given that the radius of the circle center at O is 24 units and OC is 11 units.

We are to find the length of chord AB.

We have,

in the right-angled triangle OCB (m∠OCB = 90°),

OB = 24 units and OC = 11 units.

Using Pythagoras theorem in ΔOCB, we have

[tex]OB^2=OC^2+BC^2\\\\\Rightarrow BC=\sqrt{OB^2-OC^2}\\\\\Rightarrow BC=\sqrt{24^2-11^2}\\\\\Rightarrow BC=\sqrt{576-121}\\\\\Rightarrow BC=\sqrt{455}\\\\\Rightarrow BC=21.33.[/tex]

Since OC is perpendicular to chord AB, so AC = BC.

Therefore, we get

[tex]AB=AC+BC=2\times BC=2\times 21.33=42.66=42.7.[/tex]

Thus, the required length of AB is 42.7 units.

Option (A) is CORRECT.

There is no such sum of two numbers that is a prime number and less than 4.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

It is not possible to have a sum of two numbers that is a prime number and less than 4.

The only possible sums of two numbers less than 4 are:

1 + 1 = 2

1 + 2 = 3

2 + 2 = 4

Out of these, only 2 and 3 are prime numbers.

However, the sum of any two numbers less than 4 that is equal to 2 or 3 necessarily involves at least one number equal to 1, and 1 is not a prime number.

Therefore,

There is no such sum of two numbers that is a prime number and less than 4.

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To find the number of units the company needs to sell to make maximum profit, we need to find the vertex of the parabola represented by the profit function. The vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. In this case, the company needs to sell 1500 units to make a maximum profit.

The profit function is given as p(x) = -2[tex]x^2[/tex] + 60x - 2, where p is the profit in thousands of dollars and x is the number of units sold in hundreds. To find the quantity that yields the maximum profit, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. In this case, a = -2 and b = 60. Plugging these values into the formula, we get x = -60 / (2*(-2)) = 15. Since x represents the number of units sold in hundreds, the company needs to sell 1500 units to make a maximum profit.

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A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. Set up the formula for the area of a circle. The formula is A = π r 2 it equals the area of the circle, and r equals the radius.

Solve for the radius.

Plug the area into the formula.

Divide the area by.

Take the square root.

Answer:

B. ma

Step-by-step explanation:

In a circle, equal chords are equidistant from the centre.

In the given circle, OE = JR = 3.8.

Therefore, chords OE and JR are equal.

Hence, they should be equidistant from the center.

Their distances from the center are:

ML and MA

So, ML is congruent to MA.

Answer:

1,302 square feet

Step-by-step explanation:

Be

A = 2,224 total square feet to paint

B = 922 square feet already painted

C =? square feet left to paint

According to the description given,

A = B + C

Isolating C,

C = A - B

C = 2,224 - 922

C = 1,302 square feet left to paint

Hope this helps!

ayeee i know you i think

Hence, the tax rate is [tex]8[/tex]%.

What is the tax rate?

A tax rate is a percentage at which an individual or corporation is taxed.

The United States, both the federal government and many of the states, uses a progressive tax rate system, in which the percentage of tax charged increases as the amount of the person's or entity's taxable income increases.

Here given that,

Lamar buys $[tex]75[/tex] worth of clothes. He pays $[tex]81[/tex],including sales tax.

So,

Sales Tax = $[tex]81[/tex] - $[tex]75[/tex]

= $[tex]6[/tex]

Then the Sales Tax Rate

= [tex]\frac{6}{75}[/tex]  × [tex]100=8[/tex] %

Hence, the tax rate is [tex]8[/tex]%.

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Answer:

the answer would be A B and D

Step-by-step explanation:

had to figure it out myself -.-