A rectangle is 6 inches longer than it is wide. Write and simplify an expression for
the perimeter of the rectangle in terms of the width w.

Answer:

hhhhs jjeguuw iiwhrbmeo

Answer:

y = 5/2 x

Step-by-step explanation:

y varies directly with x meaning this equation : y=kx

you plug in the information given

10 = k(4) and then solve ... k = 10/4 which simplifies to 5/2

The problem entails calculating the probability for a scenario in which the IRS audits 30% of tax returns at random and a married pair has filed separate returns. Calculate the chances of both husband and wife being audited, just one of them being audited, neither of them being audited, and at least one of them being audited.

a) Probability that both the husband and the wife will be audited: (0.3)² = 0.09 or 9%

b) Probability that only one of them will be audited:

c) Probability that neither one of them will be audited: (0.7)² = 0.49 or 49%

d) Probability that at least one of them will be audited: This is the complement of the probability that neither one of them will be audited. So, the probability that at least one of them will be audited is 1 - 0.49 = 0.51 or 51%.

The relevant terms in this question are probability and statistics. To solve for the probability of each scenario, we used the formulas for independent probabilities and complements.

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Answer:

6

Step-by-step explanation:

6 x 6= 36

Answer:

a side legnth cannot be negative

Asumming x is side legnth

Step-by-step explanation:

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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Answer:

x=−y/6− 1/2

x= 1−3y/8

hope it helps

Step-by-step explanation:

\(2x + y = 5 \\ - x + y = 2\)

\(y = 2 + x\)

\(2x + x + 2 = 5 \\ 3x + 2 = 5 \\ 3x = 3 \\ x = 1 \\ y = 2 + x \\ y = 3\)

The box's CA measures 4.7 cm in length.

Given data;

△ABC has a right angle at C, BC = 9.2 centimeters, and ∠A=63°

To know CA;

Let CA = x

As per the given case,

In a triangle sum of angles = 180°

90° + 63° + C = 180°

C = 27°

Now,

From the △ABC;

tan 63° = 9.2/x

x = 9.2/tan 63°

x = 4.687

x = 4.7

Therefore, the length of CA in the box is 4.7 cm

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The dot product of vectors u and v is -30. The angle between the vectors is approximately 108.43 degrees.

In the given problem, we are given two vectors: u = ⟨-12, 0, 6⟩ and v = ⟨1, 3, 4⟩. To find the dot product of these vectors, we multiply the corresponding components of the vectors and sum the results. So, u · v = (-12 * 1) + (0 * 3) + (6 * 4) = -12 + 0 + 24 = -30.

To find the angle between the vectors, we can use the formula cosθ = (u · v) / (||u|| * ||v||), where ||u|| and ||v|| represent the magnitudes of vectors u and v, respectively. The magnitude of u is √((-12)^2 + 0^2 + 6^2) = √180, and the magnitude of v is √(1^2 + 3^2 + 4^2) = √26. Plugging these values into the formula, we have cosθ = -30 / (√180 * √26). Using inverse cosine function, we find θ ≈ 108.43 degrees.

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Answer:

there would be 20 bottles.

Step-by-step explanation:

13 divided by .65 = 20

There are (n + 2ⁿ- 1) * 2ⁿ different ways to select talks for inclusion in the book, given that at least one talk is selected.

We know that at least one talk must be selected, so we have two cases to consider: either one or more than one talk is selected.

Case 1: If only one talk is selected, then there are n possible talks to choose from since any participant could have given the selected talk.

Case 2: If more than one talk is selected, then we need to consider the number of talks that could have been selected. There are a total of 2ⁿ - 1 possible non-empty subsets of talks that could have been selected. However, we need to subtract 1 from this number to exclude the case where no talks are selected.

So the total number of ways to select talks for the book is n + 2ⁿ - 2.

Now we need to consider the number of ways to assign talks on Saturday and Sunday. There are 2ⁿ possible ways to assign talks since each participant can give their talk on Saturday or Sunday.

(n + 2ⁿ - 2) * 2ⁿ

However, we need to subtract the case where no talks are selected and included in the book, which is simply 2^n since each talk can be assigned to either Saturday or Sunday. So the final answer is:

(n + 2ⁿ - 2) * 2ⁿ - 2ⁿ = (n + 2ⁿ - 1) * 2ⁿ.

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Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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Answer:

The rate of change per week is $6.

Step-by-step explanation:

56 - 14 = 42

42/7 = $6

6 dollars were added each week.

Answer:

The percentage of robins is 21%

Step-by-step explanation:

I. When sparrow is 41.5%, blackbird is 3/8 and robin is x,

Find robin by

Total percentage = sparrows + blackbirds + robins

II. Convert blackbird to percentage by

3/8 = x/100 => {means 8 is 100%}

300 = 8x

x = 37.5%

III. Find robins by

100% = 41.5% + 37.5% + x

100 = 79 + x

x = 21%

That makes robins is 21%.

Hope that help :)

Answer: B. statistic

Step-by-step explanation: A characteristic, usually a numerical value, which describes a sample, is called a statistic.

The length of side X in the simplest radical form exists 22/√3.

What is meant by trigonometric identities?

Trigonometry is the study of angles and the angular connections between figures in two and three dimensions. The trigonometric functions that make up trigonometry are cosecant, cosine, cotangent, secant, sine, and tangent. These are also known as the circle functions.

Trigonometric Identities are equality statements involving trigonometry functions that hold true for all values of the input variables in the equation. The side length and angle of a triangle are both subject to a variety of distinctive trigonometric identities.

The triangle is right angled, therefore we can apply trigonometry :

To obtain the value of X which is the hypotenuse :

Using trigonometric identities,

Cosθ = adjacent / hypotenuse

Substitute the values in the above equation, we get

Cos 30 = 11 / X

√3/2 = 11 / X

simplifying the above equation, we get

√3 / 2 × X = 11

X = 11 ÷ √3 / 2

X = 11 × 2 / √3

X = 22/√3

Therefore, the length of side X in the simplest radical form is 22/√3.

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Answer:

Length of arc CE = 3.14 unit (Approx.)

Step-by-step explanation:

Given:

Radius of circle = 3 units

Angle between radius = 60°

Find:

Length of arc CE

Computation:

Length of arc = [θ/360][2πr]

Length of arc CE = [60/360][2(2/7)(3)]

Length of arc CE = [60/360][2(3.14)(3)]

Length of arc CE = [1/6][6(3.14)]

Length of arc CE = 3.14 unit (Approx.)

Answer:

15.08

Step-by-step explanation:

360/48 (2π18)

By completing the square, the quadratic equation 2x² - (1/2)x = 1/8 can be solved to find the values of x.

To solve the given quadratic equation, we can use the method of completing the square. First, we rewrite the equation in the form ax² + bx + c = 0, where a = 2, b = -(1/2), and c = -1/8.

Step 1: Divide the entire equation by the coefficient of x² to make the coefficient 1. This gives us x² - (1/4)x = 1/16. Step 2: Move the constant term (c) to the other side of the equation. x² - (1/4)x - 1/16 = 0.

Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation. In this case, we have (1/4) ÷ 2 = 1/8. Squaring 1/8 gives us 1/64. Adding 1/64 to both sides, we get x² - (1/4)x + 1/64 = 1/16 + 1/64. Step 4: Simplify the equation. The left side of the equation can be written as (x - 1/8)² = 5/64.

Step 5: Take the square root of both sides of the equation. This yields x - 1/8 = ±√(5/64). Step 6: Solve for x by adding 1/8 to both sides. We have two solutions: x = 1/8 ± √(5/64).

Therefore, the solutions to the quadratic equation 2x² - (1/2)x = 1/8, obtained by completing the square, are x = 1/8 + √(5/64) and x = 1/8 - √(5/64).

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The total revenue that will be maximized is 20 - 2a

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

Qd = 20 - P

The revenue equation is calculated using

Revenue = Quantity * Price

So, we have

R = Qd * P

This gives

R = (20 - P) * P

Expand

R = 20P - P²

Differentiate

R' = 20 - 2P

Next, we have

Q = a

So, we have

R = 20 - 2a

Hence, the total revenue that will be maximized is 20 - 2a

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The required solution to the given inequality is x < 7/4.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given that,
To determine the simplified solution of the inequality 1/2x−1/4 < 5/8.
1/2x−1/4<5/8 .

Adding 1/4 on both sides of the equality,

1/2x < 5 / 8 + 1 / 4
Multiply by 2 on both sides of equality,
1 / 2x < 7 / 8
x < 7 / 4

So, the solution of inequality lies x greater than 7/4, as of the given conditions.

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Answer:

$500

Step-by-step explanation:

100-12=88

88/100=440/x

88x=100(440)

88x=44000

/88.  /88

x=500

hopes this helps

The equation that represents the situation in which case the percent of successful free throws is 75% during the game is; ( 8 + x ) = 0.75 ( 15 + x ).

It follows from the task content that the equation which represents the situation in which case the percent of successful free throws rises to 75% is to be determined.

As evident in the task content; Initially, Shaq made 8 out of 15 free throws he attempted.

Therefore, let the number of consecutive free throws he has to make to raise the success rate to 75% be; x.

Therefore, it follows from percent proportion that;

( 8 + x ) / ( 15 + x ) = 75 / 100

The simplified equation which represents the required situation is therefore;

( 8 + x ) = 0.75 ( 15 + x ).

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To find the curl of F, we need to compute the determinant of the following matrix:

| i    j    k   |

| ∂/∂x ∂/∂y ∂/∂z |

| 2xy  10y  7z  |

Expanding the determinant, we get:

i(7 - 0) - j(0 - 0) + k(0 - 20x)

= (7 - 20x)k

Therefore, the curl of F is (0, 0, 7 - 20x).

To check if there is a function f such that F = ∇f, we need to compute the partial derivatives of each component of F with respect to the corresponding variable. If these partial derivatives are equal, then there exists a scalar function f such that F = ∇f.

∂F_x/∂y = 2x

∂F_y/∂x = 2x

Since these partial derivatives are not equal, there is no function f such that F = ∇f. Therefore, the answer is "no" (n).

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Given a normal distribution with a mean of 70 and a standard deviation of 6, the z-score corresponding to the mean would equal 0.

To find the z-score corresponding to the mean in a normal distribution, we can use the formula:

z = (x - μ) / σ

Where:

z is the z-score

x is the value

μ is the mean

σ is the standard deviation

In this case, the mean (μ) is 70 and the standard deviation (σ) is 6. We want to find the z-score for the mean, so x = μ.

Plugging these values into the formula:

z = (70 - 70) / 6

z = 0 / 6

z = 0

Therefore, the z-score corresponding to the mean is 0.

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5) m<EBF= 474

6)m<ABC= 70

5) 20x-10= x+390

5) 20x-10 3x+15+60=474

20x-10=390  

3x+15= 24

plug in the x into the equation: (x+20)---> (20x20)=400

400-10= 390

6) 3x+1+2x+14= 28

3x= 9

2x=4

plug in the x into the equation: (3x+1)----> 2x+14= 28

7 is a bit confusing...

8 G and F is confusing me sorry...

this was so fu-cking hard sorry it took long...

Answer: 49/55

7/11 x 7/15 x 3

49/165 * 3

147/165

49/55

The percentage of workers who were late for work in the cheese factory is 90%.

To determine the percentage of workers who were late for work in the cheese factory, we need to compare the number of workers who arrived after 7 am to the total number of workers.

Given that there were five workers present at 7 am and a total of 50 workers in the factory, we can calculate the number of workers who arrived late by subtracting the number of workers who were present at 7 am from the total number of workers.

Late workers = Total workers - Workers present at 7 am

Late workers = 50 - 5 = 45 workers

Now, to find the percentage of late workers, we divide the number of late workers by the total number of workers and multiply by 100:

Percentage of late workers = (Late workers / Total workers) * 100

Percentage of late workers = (45 / 50) * 100

Percentage of late workers = 90%

Therefore, the percentage of workers who were late for work in the cheese factory is 90%.

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