A bed measures 40 inches by 75 inches.

What is the distance between opposite corners of the bed?

The multiplication and division equation that matches the statement are 12 * (55/4) = 165 and (12/1) ÷ (4/55) = 165.

Given the statement "how many 4/55 are in 12?"

The multiplication equation can be written thus,

12 ÷ (4/55) = 12 * (55/4)

= 165

Therefore, there are 165 4/55 in 12.

Division equation:

12 ÷ (4/55) = (12/1) ÷ (4/55)

= (12/1) * (55/4)

= 165

Therefore, 12 divided by 4/55 is equal to 165.

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Answer:

$57.44

Step-by-step explanation:

1. subtract 15% from the bill with coupon:

$56.32 - ($56.32 x 0.15) = $47.87

2. add 20% to this new bill:

$47.87+(47.87 x 0.20) = $57.44

Answer:

d

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Answer:-8

Step-by-step explanation:

Answer: 94 live chickens go in each box.

Step-by-step explanation:     3,572 divided by 38 = 94 so 94 live chickens go in each box.

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Answer:

a pi = 3.14

Step-by-step explanation:

The symbol which compares the two angles is "< ".

What is an angle?

Angles around a point define the sum of angles that can be arranged together so that they construct a full arch. Angles around a point add to 360 °.

π/3 =180/3 = 60 degree

π/3 > 45 degree

45 degree <  π/3

Therefore, the correct answer is option A. <.

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Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

Answer:

Check below:

Step-by-step explanation:

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs so that you can factor out a common factor from each pair.

3x² + 6x + 4x + 8

(3x² + 6x) + (4x + 8)

Step 2: Factoring out the common factors

Factor out the common factors from each pair separately.

3x(x + 2) + 4(x + 2)

Step 3: Factoring out the common factor from the resulting expression

Notice that we have a common factor, (x + 2), in both terms.

(x + 2)(3x + 4)

Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).

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Answer:

82.47

Step-by-step explanation:

.93n = 80

n = 80/.93

n = 82.47

Answer:

D. 44.79

Step-by-step explanation:

\(\frac{43}{96}\) who worked 8 or more years said that e-mail was their favorite communication method.

\(\frac{43}{96}\) ≈ \(\frac{44.79}{100}\)

So around 44.79% who have worked 8 years or more said that email were their preferred communication method. Our answer is D. 44.79.

Answer:

44.79%

Step-by-step explanation:

The distance between two points is a line. The equation of the line is y = 3x - 8

Equation of a line

The equation of a line in slope - intercept form is given as;

y = mx + b

where

m is the slope

b is the intercept

Given the following

slope 'm' = 3

Determine the y-intercept

-2= 3(2) + b

-2 = 6 + b

b = -8

Determine the equation

y = 3x + (-8)

y = 3x - 8

Hence the equation of the line is y = 3x - 8

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Answer:

0

Step-by-step explanation:

Graph Rate of Change:

(0,1) (1,3)

\(\frac{3-1}{1-0}\) = \(\frac{2}{1}\) = 2

Table Rate of Change:

(5,13) (7,17)

\(\frac{17 - 13}{7 - 5}\) = \(\frac{4}{2}\) = \(\frac{2}{1}\) = 2

2 - 2 = 0

The probability that a student drives to school, given that they are a senior, is approximately 0.71, rounded to the nearest hundredth.

We can use Bayes' theorem to find the probability that a senior student drives to school, given that they are a senior.

First, we need to calculate the probability of a student being a senior:

\(P(senior) = \frac{25+5+5}{(2+25+3+13+20+2+25+5+5)} = \frac{35}{100} = 0.35\)

Next, we need to calculate the probability of a senior student driving to school:

P(drive ∩ senior) = 25/100 = 0.25

Now we can apply Bayes' theorem:

P(drive | senior) = P(drive ∩ senior) / P(senior)

P(drive | senior) = 0.25 / 0.35 ≈ 0.71

Therefore, the probability that a student drives to school, given that they are a senior, is approximately 0.71, rounded to the nearest hundredth.

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Answer:

\(1. \: \frac{8v {}^{5} }{u} \)

\(2. \: 32 {}^{6} y {}^{8} \)

Step-by-step explanation:

\(2vu {}^{ - 4} .4u {}^{3} v {}^{4} = 8.(v {}^{1} \times v {}^{4} ).(u {}^{ - 4} \times u {}^{3} ) = 8.v {}^{5} .u {}^{ - 1} = 8.v {}^{5} . \frac{1}{u} = \frac{8v {}^{5} }{u} \)

\(4x {}^{3} y {}^{2} .2y {}^{4} .4x {}^{3} = (4 \times 2 \times 4).(x {}^{3} \times x {}^{3} ).(y {}^{2} \times y {}^{4} ) = 32.x {}^{3 + 3}.y {}^{2 + 6} = 32x {}^{6} y {}^{8} \)

The graph for the given system of equations is shown below

From the question, we are to determine the graph that describes the given system equations

First, we will graph the given system of linear equations.

The given equations are

Y equals four over X +3

and

Y equals negative 2X subtract four

That is,

y = 4/(x+3)

y = -2x -4

The graph for the given system of equations is shown below

The statement that best describes the graph of the two equations is the statement that describes the graph of the system of equations as shown below

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Answer:

Girls = 390

Step-by-step explanation:

Set up a proportion:

In a sample of 3:2, you have 5 kids in all.

So the the ratio of girls to kids in a sample of 5 is 2:5.

So set up a proportion:

(3/5) = (x/650)

5x = 650(3)

5x = 1950

x = 390

Answer:

Step-by-step explanation:

Let number of boys be b and girls be g. Then we have:

From the first equation b is:

Substitute b in the second equation

Answer:

Slope = 1/3

Step-by-step explanation:

Step 1: Define general form of equation of line

An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept

Step 2: Set up the system to solve for slope M of equation of line

That equation passes 2 points, which are represented in form of (x, y), (3, 7) and (6, 8).

Substitute these values of x and y into the original equation in step 1:

7 = 3M + b

8 = 6M + b

Step 3: Solve the system of equations in step 2 for M

Subtract 1st equation from 2nd equation:

8 - 7 = 6M - 3M + b - b

Simplify both sides:

1 = 3M

Divide both sides by 3:

=> M = 1/3

Hope this helps!

:)

Answer:

\(slope = \frac{1}{3} \)

Step-by-step explanation:

\((3 \: \: \: ,\: \: \: 7) = > (x1 \: \: \: ,\: \: \: x2) \\ (6 \: \: \: ,\: \: \: 8) = > (y1 \: \: \: \: , \: \: \: y2)\)

\(slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{7 - 8}{3 - 6} \\ = \frac{ - 1}{ - 3} \\ = \frac{1}{3} \)

hope this helps

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The number a has to be greater than 636.6197723675814 for the integral ∫[infinity]a1x2+1dx to be less than 0.001.

To determine how large the number a has to be so that ∫[infinity]a1x2+1dx<0.001, we can use the formula for the integral of inverse trigonometric functions:

∫1x2+1dx=tan−1x+C

We can substitute the limits of integration into this formula:

∫[infinity]a1x2+1dx=tan−1([infinity])-tan−1(a)

Since tan−1([infinity])=π2, the formula becomes:

π2-tan−1(a)<0.001

We can rearrange this inequality to solve for a:

tan−1(a)>π2-0.001

Taking the inverse tangent of both sides of this inequality gives us:

a>tan(π2-0.001)

Using a calculator, we can find that:

a>636.6197723675814

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The representation is the numerator in the calculation of variance and the standard deviation is 225)2 + (–425)2 + (–275)2 + (325)2 + (75)2 + (–75)2 = 423,750.

Variance = sum of (data value - mean)² / number of data values

To find the numerator, we need to calculate the mean of the data values first:

Mean = (2400 + 1750 + 1900 + 2500 + 2250 + 2100) / 6 = 2150

Then, the numerator for the variance calculation is:

(2400 - 2150)² + (1750 - 2150)² + (1900 - 2150)² + (2500 - 2150)² + (2250 - 2150)² + (2100 - 2150)²

= 250² + (-400)² + (-250)² + 350² + 100² + (-50)²

= 62500 + 160000 + 62500 + 122500 + 10000 + 2500

= 372500

Using the formula for variance:

Variance = 372500 / 6 = 62083.3333

To find the standard deviation, we take the square root of the variance:

Standard deviation = √62083.3333 ≈ 249

Therefore, the correct option is (A) 372500, the variance is 62083.3333, and the standard deviation is approximately 249.

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Answer:

Step-by-step explanation:

Answer:h

Step-by-step explanation:

The factor form of the quadratic equations are listed below:

Case 13: (b - 4) · (b - 2)

Case 14: (n + 4) · (n + 2)

Case 15: 2 · (n + 9) · (n - 6)

Case 16: 5 · (n + 2)²

Case 17: 2 · (k + 5) · (k + 6)

Case 18: (a - 10) · (a + 9)

Case 19: (p + 10) · (p + 1)

Case 20: 5 · (v - 2) · (v - 4)

Case 21: 2 · (p + 2) · (p - 1)

Case 22: 4 · (v - 2) · (v + 1)

Case 23: (x - 10) · (x - 15)

Case 24: (v - 5) · (v - 2)

Case 25: (p + 6) · (p - 3)

Case 26: 6 · (v + 10) · (v + 1)

In this problem we find quadratic equations of the form a · x² + b · x + c, whose factor form is introduced below:

a · x² + b · x + c = a · x² + a · (- r₁ - r₂) · x + a · r₁ · r₂ = a · (x - r₁) · (x - r₂)

Where r₁, r₂ are real roots.

Now we proceed to present the factor form of each quadratic equation:

Case 13

b² - 6 · b + 8 = (b - 4) · (b - 2)

Case 14

n² + 6 · n + 8 = (n + 4) · (n + 2)

Case 15

2 · n² + 6 · n - 108 = 2 · (n² + 3 · n - 54) = 2 · (n + 9) · (n - 6)

Case 16

5 · n² + 10 · n + 20 = 5 · (n² + 2 · n + 4) = 5 · (n + 2)²

Case 17

2 · k² + 22 · k + 60 = 2 · (k² + 11 · k + 30) = 2 · (k + 5) · (k + 6)

Case 18

a² - a - 90 = (a - 10) · (a + 9)

Case 19

p² + 11 · p + 10 = (p + 10) · (p + 1)

Case 20

5 · v² - 30 · v + 40 = 5 · (v² - 6 · v + 8) = 5 · (v - 2) · (v - 4)

Case 21

2 · p² + 2 · p - 4 = 2 · (p² + p - 2) = 2 · (p + 2) · (p - 1)

Case 22

4 · v² - 4 · v - 8 = 4 · (v² - v - 2) = 4 · (v - 2) · (v + 1)

Case 23

x² - 15 · x + 50 = (x - 10) · (x - 15)

Case 24

v² - 7 · v + 10 = (v - 5) · (v - 2)

Case 25

p² + 3 · p - 18 = (p + 6) · (p - 3)

Case 26

6 · v² + 66 · v + 60 = 6 · (v² + 11 · v + 10) = 6 · (v + 10) · (v + 1)

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Answer:

Factored completely is: 3x^2 (x+3)(x-2)

according to your question - probs (x-2), no other choice

Step-by-step explanation:

have fun friend & have a good day friend :)

The sum of expression \(1.723 \times 10^{2}\) and \(7.38 \times 10^{3}\) is \(7.5523 \times 10^{3}\). The numbers in scientific notation are added by summing the coefficients while keeping the exponent unchanged.

In scientific notation, numbers are expressed as a coefficient multiplied by a power of 10. To add numbers in scientific notation, we need to ensure that the powers of 10 are the same.

In this case, both numbers are already in scientific notation with powers of 10. We can directly add the coefficients while keeping the exponent the same.

Adding \(1.723 \times 10^2\) and \(7.38 \times 10^3\) gives us a sum of \(7.5523 \times 10^3\). The coefficient represents the numerical value, and the power of 10 indicates the magnitude.

Thus, the expression \(1.723 \times 10^2 + 7.38 \times 10^3\) evaluates to \(7.5523 \times 10^3\), indicating a significant increase in magnitude compared to the individual numbers.

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If the rate of change of a function f is the same from x = -2 to x = 1 as it is from x = 1 to x = 4, then the function is linear.

In mathematics, a linear function is a type of function that can be represented by a straight line on a graph. Linear functions have the form:

y = mx + b

where x and y are variables, m is the slope of the line (i.e., the rate of change), and b is the y-intercept (i.e., the value of y when x = 0). The slope of a linear function determines how much the output (y) changes for a given change in the input (x), and the y-intercept determines where the line crosses the y-axis.

Linear functions are commonly used to model relationships between two variables that have a constant rate of change.

If the rate of change of a function f is the same from x = -2 to x = 1 as it is from x = 1 to x = 4, then the function is linear.

This is because a linear function has a constant rate of change, which means that the change in the output (y) for a given change in the input (x) is the same throughout the entire domain of the function.

In contrast, a quadratic or exponential function has a changing rate of change, which means that the change in the output for a given change in the input varies at different points along the domain of the function.

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Answer:

0.2857

Step-by-step explanation:

We want to determine,

The probability that the battery life is at least 11 hours is 0.2857.

Answer:

C

Step-by-step explanation:

17/10 is correct