A rectangular solid has sides of 7 cm, 9 cm, and 11 cm. What is its surface area?

Within a specific stretch spanning 5 miles, the roadway inclines approximately 0.53 miles or 2771.64 feet, rounded to the nearest hundredth of a mile.

Trigonometric principles aid in determining the elevation gained by the highway over this distance.

Given:

An angle of ascent (θ) of 6 degrees and a horizontal distance (adjacent side) of 5 miles, our objective is to ascertain the vertical distance (opposite side).

Utilizing the tangent function in trigonometry:

[tex]\[ \tan(\theta) = \frac{{\text{{opposite}}}}{{\text{{adjacent}}}} \][/tex]

[tex]\[ \tan(6^\circ) = \frac{{\text{{height}}}}{{5}} \][/tex]

The calculation for the height is:

height = 5 × tan(6°)

Plugging in the values:

height ≈ 5 × 0.1051

height ≈ 0.5255 miles

To convert this to feet (1 mile = 5280 feet):

height ≈ 0.5255 × 5280  

height ≈ 2771.64 feet

Thus, within this 5-mile segment, the roadway ascends approximately 0.53 miles or 2771.64 feet, rounded to the nearest hundredth of a mile.

Answer:

Option a is correct

200 cartons is the sample size

Step-by-step explanation:

As per the statement:

For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.

First examine how many cartons are examined per shipment.

For every 50th cartons, 1 are examined

For every 100th cartons, 2 are examined

then;

For 1000 cartons , we have 20 are examined.

Examined per shipment  = 20 cartons

We have to find how large is the sample.

Since, there are total 10 shipment

then;

For 10 shipment, we have

[tex]20 \times 10 = 200[/tex] cartons

Therefore, 200 cartons  is the sample size

If the repair took 5 hours, the total cost would be $250.

To find the total cost if the repair took 5 hours, we need to evaluate the function[tex]\(C(x)\) at \(x = 5\).[/tex]

Given that [tex]\(C(x) = 35x + 75\),[/tex] we substitute [tex]\(x = 5\)[/tex] into the function:

[tex]\[C(5) = 35 \times 5 + 75\]\[C(5) = 175 + 75\]\[C(5) = 250\][/tex]

So, if the repair took 5 hours, the total cost would be $250.

Complete correct question:

The function C(x) = 35x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace our alternator, where x is the number of hours of labor. What would be the total cost if the repair took 5 hours?

Answer:

Proportion states that two fractions or ratios are equal.

Let x be the  closing cost amount.

As per the statement:

Tina has to pay 4 percent of the purchase price toward closing costs for her mortgage. If the purchase price is $275,000.

Purchased Price = $275,000

then, by definition of proportion :

[tex]\frac{4}{100}=\frac{x}{275000}[/tex]

By cross multiply we have;

1,100,000 = 100x

Divide both sides by 100 we have;

11,000 = x

or

x = $ 11,000

Therefore, the closing cost amount is, 11,000

Missing number to complete the factorization is 3.

Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.

Given expression

[tex]x^{3}+x^{2} -21x-45=(x+3) (x-5) (x+a)[/tex]

Let a be the missing number

(x + 3) (x - 5) (x + a)

= [tex](x^{2} -5x+3x-15)(x+a)[/tex]

= [tex](x^{2} -2x-15)(x+a)[/tex]

[tex]x^{3}+x^{2} -21x-45=x^{3} +x^{2} a-2x^{2} -2xa-15x-15a[/tex]

By comparing the expressions

-2xa - 15x = -21x

⇒ -2xa = -6x

⇒ a = 3

[tex]x^{2} (a-2) = 1x^{2}[/tex]

⇒ a - 2 = 1

⇒ a = 3

-15a = -45

⇒ a = 3

Hence, missing number to complete the factorization is 3.

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Answer:

it 2 units

Step-by-step explanation:

Answer:

12th grade data set

Step-by-step explanation:

Answer:

Linear equation is V(t) = 1500 - 290t

Step-by-step explanation:

To find the linear equation representing the value of the robot we will calculate per year depreciation in the cost of the robot.

Rate of depreciation = [tex]\frac{\text{(Manufacturing cost in 2005-selling price in 2010)}}{5}[/tex]

                                 = [tex]\frac{[(1.5)(10^{6})-50000]}{5}[/tex]

                                 = [tex]\frac{(1500000-50000)}{5}[/tex]

                                 = [tex]\frac{1450000}{5}=290000[/tex]

If depreciation is represented by V(t) (in $000) then equation will be

V(t) = 1500 - 290t

Final answer:

Erica will have 1 1/6 yards of fabric left after using 2/3 of the 3 1/2 yards she purchased to make a curtain.

Explanation:

The student's question is about how much fabric Erica will have left after using 2/3 of the 3 1/2 yards she bought to make a curtain. To solve this problem, we first need to convert the mixed number of yards of fabric to an improper fraction. We start by multiplying the whole number, 3, by the denominator of the fraction, 2, and then adding the numerator, 1. This gives us (3 × 2) + 1 equals 7, so Erica has 7/2 yards of fabric.

Next, we determine how much fabric she uses by multiplying 7/2 yards by 2/3. Doing the multiplication, (7/2) × (2/3), we can cancel out the common factor of 2 to simplify the calculation. The result is 7/3 yards of fabric used for the curtain.

To find out how much fabric is left, we subtract the used fabric from the total amount Erica originally had, which is 7/2 yards. So, we calculate 7/2 - 7/3 yards. To subtract these fractions, they need to have a common denominator. Multiplying 7/2 by 3/3 and 7/3 by 2/2 gives us equivalent fractions with a common denominator of 6. We now have (21/6) - (14/6) yards, and subtracting these gives us 7/6 yards of fabric remaining. This can also be represented as 1 1/6 yards, which is how much Erica will have left after making the curtain.

The dimensions of the triangle with a base that is 2/3 of its height and an area of 12 square centimeters are a base of 4 centimeters and the height of 6 centimeters.

The question asks for the dimensions of a triangle. We are given that the base is 2/3 of the height and the area is 12 square centimeters. The formula for the area of a triangle is 1/2 * base * height. Since we know that the base is 2/3 of the height, we can denote the height as 'h' and the base as (2/3)h. From here, we can set up the equation 12 = 1/2 * (2/3)h * h, which simplifies to 12 = 1/3 * h². Solving for 'h', we find the height is √36 or 6 centimeters. Given the base is 2/3 of the height, the base, therefore, is 4 centimeters.

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Answer:

Answer is

[tex]x^3-7x^2+17x-20 \\ [/tex]

Step-by-step explanation:

We need to find

[tex](x-4)(x^2-3x+5) \\ [/tex]

Using distribution rule.

[tex](x-4)(x^2-3x+5)=x^3-4x^2-3x^2+12x+5x-20\\\\(x-4)(x^2-3x+5)=x^3-7x^2+17x-20 \\ [/tex]

So the answer is

[tex]x^3-7x^2+17x-20 \\ [/tex]

Final answer:

The quadratic functions are: y = 2(x - 3x² + 1), y = 1/2x² - 13x + 4, and y = 1.

Explanation:

A quadratic function is a polynomial function of degree 2, which means its highest power of x is 2. The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Out of the given options, the quadratic functions are:

a. y = 2(x - 3x² + 1)

c. y = 1/2x² - 13x + 4

d. y = x/x - 1 (this can be simplified to y = 1)

The options b. (y = 5 + 2x) is not a quadratic function because it only has a linear term (power of x is 1).

Answer:

yes

Step-by-step explanation:

When performing certain statistical calculations, finding roots, or working with powers, calculators or computers are necessary for the calculations; otherwise, more traditional methods will be sufficient.

For the function, f(x) = 2x + 1 and g(x) = x² – 7, (f – g)(x) will be D. –x² + 2x + 8

To find (f - g)(x), we need to subtract the function g(x) from the function f(x).

f(x) = 2x + 1

g(x) = x² - 7

(f - g)(x) = f(x) - g(x)

Substituting the given functions:

(f - g)(x) = (2x + 1) - (x² - 7)

Now let's simplify:

(f - g)(x) = 2x + 1 - x² + 7

Combining like terms, we have:

(f - g)(x) = -x² + 2x + 8

Therefore, the answer is D. -x² + 2x + 8.

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Answer:

Ryan use 4. 50 yards of cloth to make 6 backpack.

Step-by-step explanation:

Given : ryan makes 6 backpacks he uses 3/4 of cloth to make each backpack.

To find  : what is the total amount cloth ,in yards ryan use to make all 6 backpacks.

Solution : We have given that

Ryan make a backpack to use =  [tex]\frac{3}{4}[/tex] of a cloth.

Ryan make such 6 backpack = [tex]6*\frac{3}{4}[/tex]

                                                =   [tex]\frac{18}{4}[/tex] .

                                               = 4. 50 yards.

Therefore, Ryan use 4. 50 yards of cloth to make 6 backpack.

The decimal 0.063 can be represented as 6.3% in the percent form.

Thus, option (D) is correct.

Given decimal: 0.063.

As, to convert any decimal into the percentage then multiply the the decimal with 100.

So, to convert 0.063 to a percent multiply it by 100:

= 0.063 x 100

= 6.3

Therefore, 0.063 as a percent is 6.3%.

Thus, option (D) is correct.

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