Factor and SHOW ALL STEPS: 2x3+10x2+12x
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Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.

Pentagons are two-dimensional polygons having five sides and fifth angles. When we mix the Greek terms "penta" and "gon," which mean "five" and "angles," respectively, we have the word "pentagon."

Here,

we know that a pentagonal prism has five rectangular sides in addition to two pentagonal bases at the top and bottom.

Pentagonal prisms are pentagon-shaped if we look at them from the bottom.

When viewed from the side, a pentagonal prism would have a rectangular shape.

If we were to look at the pentagonal prism from the front, it would appear rectangular.

Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.

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Answer:

1. 1/120

2. 7/24

Step-by-step explanation:

n = 10

Number of defective = 3

1. Probability of all defective =

(Number of defective/n) x (number of defective -1/n -1)...(number of defective -n/n-1)

=3/10 x 2/9 X 1/8

= 6/720

= 1/120

2. probability of none defective

Since 3 are defective, those that are not defective = 7

The probability is therefore:

7/10 x 6/9 x 5/8

= 210/720

= 7/24.

Thus, the total cost of the first 64 units is approximately $2730.67.

To find the total cost of the first 64 units, we need to integrate the marginal cost function over the range of production from x=0 to x=64.

The marginal cost function is given by C'(x) = 8√x.

Integrating this function with respect to x, we get:
C(x) = ∫(8√x dx) = 8 * (2/3)x^(3/2) + C

To find the total cost for the first 64 units, we need to evaluate C(x) at x=64 and x=0 and subtract the results:
C(64) - C(0) = (8 * (2/3) * 64^(3/2) + C) - (8 * (2/3) * 0^(3/2) + C)

Simplifying the equation, we get:
C(64) - C(0) = 8 * (2/3) * 64^(3/2)

Now, compute the value:
C(64) - C(0) = 8 * (2/3) * 512 = (16/3) * 512 ≈ 2730.67

So, the total cost of the first 64 units is approximately $2730.67.

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Answer:

The answer is of this question is 324.

It is a trapezium because there is only one set of parallel opposite edges.

A parallelogram is a quadrilateral with two pairs of parallel edges. In a parallelogram, the opposing edges are of equal length, and the opposing angles are of equal size. Additionally, the internal angles that are supplementary to the transversal on the same side.

The diagonals of a parallelogram must cross one another in order for it to exist. do. As a result, we can conclude that only the third assertion is false, making option (C) Diagonals cut in half opposing lines.

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Answer:

Chris drove the truck for 284 miles.

Step-by-step explanation:

Let us assume the total number of miles driven by Chris be \(x\). Now, as per the question, we can say that the sum of the base fee and the additional charge for each mile will be equal to the total rent that Chris will have to pay when he returns the truck. Next, we know that 1 cent = \(1/100\) $. So, we have,

77 cents = 0.77 $

So, we can say that,

⇒\(15.99+0.77x=234.67\)

⇒\(0.77x=234.67-15.99\)

⇒\(0.77x=218.68\)

⇒\(x=218.68/0.77\)

⇒\(x=284\)

Hence, Chris drove for a total of 284 miles when he returned the truck.

We need to add 4 blue marbles to the bag to make the probability of drawing a blue marble 1/2.

Currently, there are two blue marbles out of a total of eight marbles in the bag, so the probability of drawing a blue marble is 2/8 or 1/4.

Let x be the number of blue marbles we need to add to the bag. After adding x blue marbles, there will be a total of 2 + x blue marbles in the bag, out of a total of 8 + x marbles.

We want the probability of drawing a blue marble to be 1/2, so we can set up the equation:

(2 + x) / (8 + x) = 1/2

Multiplying both sides by (8 + x), we get:

2 + x = (8 + x) / 2

Multiplying both sides by 2, we get:

4 + 2x = 8 + x

Subtracting x from both sides, we get:

4 + x = 8

Subtracting 4 from both sides, we get:

x = 4

Therefore, we need to add 4 blue marbles to the bag to make the probability of drawing a blue marble 1/2.

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The characteristic equation of the matrix is: λ² - 23λ + 132 = 0 and the eigenvalues of the matrix are λ = 11, and λ = 12 and A basis for the corresponding eigenspace for λ = 11 is X₁ = { (3y, y) | y ∈ ℝ }.A basis for the corresponding eigenspace for λ = 12 is X₂ = { (-y, y) | y ∈ ℝ }

The given matrix is:

| 12 -3 |

| -4 11 |

(a) The characteristic equation is found by setting the determinant of the matrix subtracted by the identity matrix equal to zero:

| 12 - λ -3 |

| -4 11 - λ | = 0

Expanding the determinant, we have:

(12 - λ)(11 - λ) - (-3)(-4) = 0

(132 - 12λ - 11λ + λ²) + 12 = 0

λ² - 23λ + 120 + 12 = 0

λ² - 23λ + 132 = 0

(b) To find the eigenvalues, we solve the characteristic equation for λ. Factoring the equation, we have:

(λ - 11)(λ - 12) = 0

Setting each factor equal to zero, we find the eigenvalues:

λ - 11 = 0 => λ = 11

λ - 12 = 0 => λ = 12

So the eigenvalues are 11 and 12.

To find the basis for each eigenspace, we need to solve the equation (A - λI)v = 0 for each eigenvalue, where A is the given matrix, λ is the eigenvalue, and v is the eigenvector.

For λ = 11:

(A - 11I)v = 0

Substituting the values, we have:

| 12 - 11 -3 | | x | | 0 |

| -4 11 - 11 | × | y | = | 0 |

Simplifying, we get the equations:

x - 3y = 0 => x = 3y

Therefore, a basis for the eigenspace corresponding to λ = 11 is:

X₁ = { (3y, y) | y ∈ ℝ }

For λ = 12:

(A - 12I)v = 0

Substituting the values, we have:

| 12 - 12 -3 | | x | | 0 |

| -4 11 - 12 | × | y | = | 0 |

Simplifying, we get the equations:

-3x - 3y = 0 => x + y = 0 => x = -y

Therefore, a basis for the eigenspace corresponding to λ = 12 is:

X₂ = { (-y, y) | y ∈ ℝ }

To summarize:

(a) The characteristic equation is λ² - 23λ + 132 = 0.

(b) The eigenvalues are 11 and 12.

A basis for the corresponding eigenspace for λ = 11 is X₁ = { (3y, y) | y ∈ ℝ }.

A basis for the corresponding eigenspace for λ = 12 is X₂ = { (-y, y) | y ∈ ℝ }

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Answer ⇒

= 76

Step - By -  Step Explanation ⇒

It is not easy to write long division on a laptop as it paper, so I have attached an image from a calculator that I found online.

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define the range of a function

The range of a function is the set of its possible output values. The range of a function refers to the entire set of all possible output values of the dependent variable

STEP 2: Get the range of the function

The range of the function will be:

Answer:

615.44 cm^2

Step-by-step explanation:

here r, radius is 14 cm and π as 3.14

area of circle = π\(r^{2}\)

3.14 * 14^2

3.14 * 14 * 14

615.44cm^2

Answer:

The area of the hubcap is about \(\boxed{\tt{615.44}}\) cm².

Step-by-step explanation:

Here's the required formula to find the area of hubcap :

\(\longrightarrow{\pmb{\sf{Area_{(Circle)} = \pi{r}^{2}}}}\)

Substituting all the given values in the formula to find the area of hubcap :

\(\longrightarrow{\sf{Area_{(Hubcap)} = \pi{r}^{2}}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 3.14{(14)}^{2}}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 3.14{(14 \times 14)}}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 3.14{(196)}}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 3.14 \times 196}}\)

\(\longrightarrow{\sf{Area_{(Hubcap)} = 615.44}}\)

\(\star{\underline{\boxed{\sf{\purple{Area_{(Hubcap)} = 615.44 \: {cm}^{2}}}}}} \)

Hence, the area of hubcap is 615.44 cm².

\(\rule{300}{2.5}\)

Answer:

a^2+2ab+b^2 is the formula

Answer:

K is the angle between JK and KL. It is called the included angle of sides JK and KL.

Answer:

I think its 8

Step-by-step explanation:

Answer:

a) -19/2

Step-by-step explanation:

3(x+6)+6x+9=7x+8

3x + 18 + 6x + 9 = 7x + 8

3x + 6x - 7x = 8 - 18 - 9

2x = -19

2x/2 = -19/2

Therefore, x = -19/2

The candy distributor needs to use 30 kilograms of 10% fat-content chocolate and 70 kilograms of 50% fat-content chocolate to create 100 kilograms of a 14% fat-content chocolate.

To solve this problem, we can use the method of mixture problems, which involves setting up a system of equations. Let x be the number of kilograms of the 10% fat-content chocolate and y be the number of kilograms of the 50% fat-content chocolate.

We have two equations based on the fat content and the total weight of the mixture:

0.1x + 0.5y = 0.14(100) (equation for fat content)

x + y = 100 (equation for total weight)

We can solve this system of equations using substitution or elimination. Using substitution, we can solve for x in terms of y from the second equation and substitute it into the first equation:

x = 100 - y

0.1(100 - y) + 0.5y = 0.14(100)

10 - 0.1y + 0.5y = 14

0.4y = 4

y = 10

Then we can substitute y = 10 back into the equation for x and get:

x = 100 - y = 100 - 10 = 90

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Answer:

To find the odds in favor of Cody being first, we need to divide the probability of him winning (25%) by the probability of him not winning (75%).

Odds in favor of Cody winning = 25% / (100% - 25%) = 25% / 75%

Simplifying, we get:

Odds in favor of Cody winning = 1/3

Therefore, the odds in favor of Cody being first in the 50m backstroke are 1 to 2 (or 1:2).

Answer:

3/8g + 2 = 5  

Subtract the number 2 from both sides of the equation.

3/8g = 3

Now divide 3/8 from both sides of the equation.

3/8 divided by 3/8 equals 0.  3 divided by 3/8 equals 8.

The final answer is:

g = 8

------------------------------------------------------------------------------------------

Check your answer:

3/8g + 2 = 5

Substitute 8 into the spot where the variable g was.

3/8 X 8 + 2 = 5

So our answer x = 8 is true.

Step-by-step explanation:

I hope that this has helped you to understand this equation. If you have any questions please put them below in the comments. If there are no questions, please have a great rest of your day/night!

The 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.

To calculate the confidence interval, we can use the formula:

Confidence interval = Sample mean ± (Critical value * Standard error)

Given that the sample mean is 42 miles per hour and the standard deviation is 4.2 miles per hour, we need to determine the critical value and the standard error.

Since we have a sample size of 85, we can use the t-distribution with (n-1) degrees of freedom to find the critical value. With a 90% confidence level, the corresponding critical value for a two-tailed test is approximately 1.66.

The standard error is calculated as the standard deviation divided by the square root of the sample size:

Standard error = (Standard deviation) / √(Sample size)

Standard error = 4.2 / √85 ≈ 0.456

Now we can plug in the values into the confidence interval formula:

Confidence interval = 42 ± (1.66 * 0.456)

Confidence interval ≈ (41.29, 42.71)

Therefore, the 90% confidence interval for the average speed of all the cars passing through the intersection is (41.29, 42.71) miles per hour.

Based on the given data and calculations, we can conclude that with 90% confidence, the average speed of all the cars passing through the intersection falls within the range of 41.29 to 42.71 miles per hour.

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Answer: B. $870

Step-by-step explanation:

Correct on Edge2021

Korey’s operating expenses for last month would be $870

The gross profit margin is a profitability raio. Profitability ratios measures the efficiency with which a company generates profit from its asset. Gross profit margin measures the return on sales.

Gross profit margin can be calculated by dividing the gross profit (difference between revenue and cost of goods sold) by revenue (Net sales). It could be expressed as a percentage by multiplying by 100.

Therefore, Gross profit margin = (gross profit ÷ net sales) x 100

Gross profit = $3,320

Net sales = $4,350

Gross profit margin = ($3,320÷$4,350) * 100

0.763 * 100 = 76.3%

4,350 - 3,320 = 1030

That would be 870 dollar.

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The correct answer is: 0, -3, and 3. At  0, -3, and 3 of x does fx) x4-18x2 have a critical point where the graph changes from decreasing to increasing.

To find the critical points where the graph of the function f(x) = x^4 - 18x^2 changes from decreasing to increasing, we need to find the values of x where the derivative of the function is equal to zero or does not exist.

Let's find the derivative of f(x) with respect to x:

f'(x) = 4x^3 - 36x

To find the critical points, we set the derivative equal to zero and solve for x:

4x^3 - 36x = 0

Factor out 4x:

4x(x^2 - 9) = 0

Now we have two factors:

1) 4x = 0, which gives x = 0

2) x^2 - 9 = 0, which gives x = ±3

So, the critical points where the graph changes from decreasing to increasing are x = 0, x = -3, and x = 3.

Therefore, the correct answer is: 0, -3, and 3.

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Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

The height of the cuboid is 2.33 cm. To determine the height of a cuboid whose volume is 594cm³, with a length of 9 cm and a width of 60 mm, it is important to first convert the width into cm.

This can be done by dividing it by 10, since 1 cm = 10 mm. Therefore, the width is 6 cm. Thus, the formula for the volume of a cuboid is V = lwh, where l = length, w = width, and h = height.

Therefore, substituting the known values into the formula, we get: 594 = 9 × 6 × h

Dividing both sides by 54, we get: h = 2.33 (rounded off to two decimal places).

Therefore, the height of the cuboid is 2.33 cm.

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Answer:

Step-by-step explanation:

Let x represent the number of pennies that Al had​ initially.

He agreed to give six thirteenths of his pennies to Bev. It means that the number of pennies that he gave to Bev is 6/13 × x = 6x/13

if she would give six thirteenths of what she got from Al to Carl, it means that the number of pennies that Carl received is 6/13 × 6x/13 = 36x/169

if Carl in turn would give six thirteenths of what he got from Bev to Dani and Dani received 2376 pennies, it means that

6/13 × 36x/169 = 2376

216x/2179 = 2376

216x = 2376 × 2179

216x = 5220072

x = 5220072/216

x = 24167

AI had 24167 pennies initially

The volume of the pyramid is B) 192ft

The volume of a pyramid can be calculated utilizing the condition:

V = (1/3) * base region * height...........(1)

In the case of a square pyramid, the base area is given by the condition:

base area = (edge length)²

Thus, in this issue, we have:

base area = (6 ft)² = 36 ft²

height = 16 ft (given)

Substituting these values into the condition for the volume of a pyramid ( equation (1) ), we get:

V = (1/3) * 36 ft² * 16 ft

V = 192 cubic feet

In this way, the volume of the pyramid is 192 cubic feet.

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Using the concept of integer it can be concluded that Awad's claim is false.

Integer, a positive, negative, or 0 with a complete value. The counting numbers 1, 2, 3, and so forth are used to create the integers, together with the subtraction process. A counting number can be divided by itself and the result is always zero; for instance, 4 divided by 4 equals 0. The result of subtracting a larger number from a smaller one is a negative whole number; for instance, 2 - 3 = 1. By deriving each integer in this way from the counting numbers, a set of numbers that can be closed with the subtraction operation is produced.

You can have positive or negative numbers. Negative numbers are frequently surrounded by brackets to make them simpler to read, for example (-2). Positive numbers typically don't have the + before the number. 3 is actually +3. Positive and negative number combinations can be confusing to add and multiply, thus caution is advised.

Subtraction and Addition

Two "pluses" equal a "plus," and two "minuses" equal a "plus." A negative is made up of a plus and a minus.

Whenever you subtract a negative number, you always end up adding because two negatives make a positive. For example,

n = 4

m = -3

then,

4-(-3) is going to turn into 4+3 = 7.

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Answer:

The third one

Step-by-step explanation:

The only one which gives the last number of the sequence is the third one as subbing in 16 you get 3×16 + 3 = 48 + 3 = 51

Check the picture below, so the parabola looks more or less like so, with a "p" distance of positive 7.

\(\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-5\\ k=4\\ p=7 \end{cases}\implies 4(7)(~~x-(-5)~~) = (~~y-4~~)^2 \implies 28(x+5)=(y-4)^2 \\\\\\ x+5=\cfrac{1}{28}(y-4)^2\implies \boxed{x=\cfrac{1}{28}(y-4)^2 - 5}\)

The quadratic regression equation that best fits the data is:

y = 32.86x² - 379.14x + 1229.14.

Regression equations are obtained inserting the points of a table or of a scatter plot into a calculator.

The choice of calculator is relevant to the type of regression equation desired. For this problem, it is stated that a quadratic regression equation is desired, hence the calculator used is for quadratic regression.

From the table given on the right side of the image, the points that will be used to build the quadratic regression equation are given by the ordered pairs presented as follows:

(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).

Inserting these points into a calculator, the quadratic regression equation that best fits the data from the table is given below:

y = 32.86x² - 379.14x + 1229.14.

The concave up parabola is expected, as the measures in the table start decreasing and after the vertex they increase.

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Answer:

.........................

Step-by-step explanation:

.................................................

Answer:

99.7% of customers have to wait between 8 minutes to 30 minutes for their food.

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 18 minutes

Standard Deviation, σ = 3 minutes

We are given that the distribution of amount of time is a bell shaped distribution that is a normal distribution.

Empirical Formula:

Almost all the data lies within three standard deviation from the mean for a normally distributed data.

About 68% of data lies within one standard deviation from the mean.

About 95% of data lies within two standard deviations of the mean.

About 99.7% of data lies within three standard deviation of the mean.

Thus, 99.7% of the customers have to wait:

`

Thus, 99.7% of customers have to wait between 8 minutes to 30 minutes for their food.

hope this helps

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