Moxie earns a salary of $40 a day as a window salesman. In addition, he earns $12.50 for every window he sells and $2.25 for every window that includes a warranty. To get from job-to-job, Moxie must pay $18.25 a day to rent a car.
On Monday, Moxie sells w windows that all include a warranty. Write a
simplified expression to represent the total amount in dollars Moxie makes on Monday.

Three different vectors are [-8, 14],  [-6, 16], and [15, -18].

To find three different vectors that are in the span of the given vectors \(u_1\) = [-3, 8] and \(u_2\) = [-5, 6], we can use linear combinations of these vectors.

Let's call the three different vectors \(v_1\), \(v_2\), and \(v_3\). We can express them as follows:

\(v_1\) = \(u_1\) + \(u_2\) = [-3, 8] + [-5, 6] = [-3 + (-5), 8 + 6] = [-8, 14]

\(v_2\) = 2\(u_1\) = 2[-3, 8] = [-6, 16]

\(v_3\) = -3\(u_2\) = -3[-5, 6] = [15, -18]

Therefore, three different vectors that are in the span of \(u_1\) and \(u_2\) are \(v_1\) = [-8, 14], \(v_2\) = [-6, 16], and \(v_3\) = [15, -18].

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By using the formula for expectation, it can be calculated that-

Expectation of b = 1.79

What is expectation?

At first it is important to know about probability of an event.

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Suppose x is a random variable with the probability function f(x). suppose  \(x_1, x_2, ... ,x_n\) are the values corrosponding to the actual occurance of the event and \(p_1, p_2,...,p_n\) be the corrosponding probabilities.

Expectation is given by the formula

\(p_1x_1+p_2x_2+....+p_nx_n\)

Here, the table is

Number of Books                 Probability

0                                                 0.35

1                                                  0.20

2                                                 0.15

3                                                 0.10

4                                                 0.07

5                                                 0.08

6                                                 0.04

7                                                  0.01

Expectation of b = 0 \(\times\) 0.35 + 1 \(\times\) 0.20 + 2 \(\times\) 0.15 + 3 \(\times\) 0.10 + 4 \(\times\) 0.07 + 5 \(\times\) 0.08 + 6 \(\times\) 0.04 + 7 \(\times\) 0.01

                          = 1.79

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Complete Question

The table is as follows

Number of Books                 Probability

0                                                 0.35

1                                                  0.20

2                                                 0.15

3                                                 0.10

4                                                 0.07

5                                                 0.08

6                                                 0.04

7                                                  0.01

The double asterisk operator (**) is used to raise the radius to the power of 3, which represents r³ in the formula.

To compute the volume of a sphere, the given formula is used. It is: volume of a sphere = (4.0 / 3.0) πr³ where r is the radius of the sphere.

Therefore, to find the volume of the sphere given the sphere_radius and pi, the formula above is used, as shown below: sphere_volume = (4.0 / 3.0) * pi * sphere_radius**3

where sphere_radius is the given radius of the sphere and pi is the constant pi.

The double asterisk operator (**) is used to raise the radius to the power of 3, which represents r³ in the formula.

Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is an irrational number, which means it cannot be expressed as a simple fraction or as a finite decimal. The decimal representation of pi goes on infinitely without repeating.

The value of pi is approximately 3.14159, but it is typically rounded to 3.14 for simplicity in calculations. However, to maintain accuracy, mathematicians and scientists often use more decimal places, such as 3.14159265359, depending on the level of precision required for their calculations.

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Full question:

Given sphere_radius and pi, compute the volume of a sphere and assign to sphere_volume. Volume of sphere = (4.0 / 3.0) π r3

Answer:

x^3 + 9 x^2 + 21 x + 9 = (x^2 + 6 x + 3)×(x + 3) + 0

Step-by-step explanation:

Set up the polynomial long division problem with a division bracket, putting the numerator inside and the denominator on the left:

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

To eliminate the leading term of the numerator, x^3, multiply x + 3 by x^2 to get x^3 + 3 x^2. Write x^2 on top of the division bracket and subtract x^3 + 3 x^2 from x^3 + 9 x^2 + 21 x + 9 to get 6 x^2 + 21 x + 9:

| | | x^2 | | | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

To eliminate the leading term of the remainder of the previous step, 6 x^2, multiply x + 3 by 6 x to get 6 x^2 + 18 x. Write 6 x on top of the division bracket and subtract 6 x^2 + 18 x from 6 x^2 + 21 x + 9 to get 3 x + 9:

| | | x^2 | + | 6 x | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

To eliminate the leading term of the remainder of the previous step, 3 x, multiply x + 3 by 3 to get 3 x + 9. Write 3 on top of the division bracket and subtract 3 x + 9 from 3 x + 9 to get 0:

| | | x^2 | + | 6 x | + | 3

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

| | | | | -(3 x | + | 9)

| | | | | | | 0

The quotient of (x^3 + 9 x^2 + 21 x + 9)/(x + 3) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, x + 3 exactly divides x^3 + 9 x^2 + 21 x + 9 and there is no remainder.

| | | x^2 | + | 6 x | + | 3 | (quotient)

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9 |

| -(x^3 | + | 3 x^2) | | | | |

| | | 6 x^2 | + | 21 x | + | 9 |

| | | -(6 x^2 | + | 18 x) | | |

| | | | | 3 x | + | 9 |

| | | | | -(3 x | + | 9) |

| | | | | | | 0 | (remainder) invisible comma

(x^3 + 9 x^2 + 21 x + 9)/(x + 3) = (x^2 + 6 x + 3) + 0

Write the result in quotient and remainder form:

Answer: Set up the polynomial long division problem with a division bracket, putting the numerator inside and the denominator on the left:

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

To eliminate the leading term of the numerator, x^3, multiply x + 3 by x^2 to get x^3 + 3 x^2. Write x^2 on top of the division bracket and subtract x^3 + 3 x^2 from x^3 + 9 x^2 + 21 x + 9 to get 6 x^2 + 21 x + 9:

| | | x^2 | | | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

To eliminate the leading term of the remainder of the previous step, 6 x^2, multiply x + 3 by 6 x to get 6 x^2 + 18 x. Write 6 x on top of the division bracket and subtract 6 x^2 + 18 x from 6 x^2 + 21 x + 9 to get 3 x + 9:

| | | x^2 | + | 6 x | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

To eliminate the leading term of the remainder of the previous step, 3 x, multiply x + 3 by 3 to get 3 x + 9. Write 3 on top of the division bracket and subtract 3 x + 9 from 3 x + 9 to get 0:

| | | x^2 | + | 6 x | + | 3

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

| | | | | -(3 x | + | 9)

| | | | | | | 0

The quotient of (x^3 + 9 x^2 + 21 x + 9)/(x + 3) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, x + 3 exactly divides x^3 + 9 x^2 + 21 x + 9 and there is no remainder.

| | | x^2 | + | 6 x | + | 3 | (quotient)

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9 |

| -(x^3 | + | 3 x^2) | | | | |

| | | 6 x^2 | + | 21 x | + | 9 |

| | | -(6 x^2 | + | 18 x) | | |

| | | | | 3 x | + | 9 |

| | | | | -(3 x | + | 9) |

| | | | | | | 0 | (remainder) invisible comma

(x^3 + 9 x^2 + 21 x + 9)/(x + 3) = (x^2 + 6 x + 3) + 0

Write the result in quotient and remainder form:

Answer: x^3 + 9 x^2 + 21 x + 9 = (x^2 + 6 x + 3)×(x + 3) + 0

Answer:

14 units

Step-by-step explanation:

E2020

Answer:

k

Step-by-step explanation:

Answer:

increase = 59-50

increase = $9.00

Percent = (increase/whole value) x 100

Percent = (9/50) x 100

Percent  = 18%

Mark Brainliest

Therefore, the surface represented by the given equation is a sphere centered at the origin with a radius of 6 units.

The given equation rho^2(sin^2(φ)sin^2(θ) + cos^2(φ)) = 36 represents a surface in spherical coordinates. Let's break down the equation to identify the surface:

ρ^2(sin^2(φ)sin^2(θ) + cos^2(φ)) = 36

Here, ρ represents the radial distance, φ is the polar angle, and θ is the azimuthal angle.

By analyzing the equation, we can see that it combines both the azimuthal and polar angles. The terms sin^2(φ)sin^2(θ) and cos^2(φ) involve both angles.

The equation ρ^2(sin^2(φ)sin^2(θ) + cos^2(φ)) = 36 describes a sphere centered at the origin with a radius of 6 units. The constant value of 36 indicates that the squared radial distance from the origin to any point on the surface is 36.

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The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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Answer:

$432

Step-by-step explanation:

$450 divided by 100% time 20% = $90

450 + 90 = 540$

Then 540 divided by 100% time 20% = $108

$540 - $108 = $432

The final price is $432

Answer:

The answer is C

Step-by-step explanation:

Since the line above the letters is an arrow that means the two points have to create a line like that. Therefore, the answer is DB.

Answer:

DB

Step-by-step explanation:

Why others rejected?

E C

E B is rejected as points are not on one line

The polynomial representing the area of the is 49n² - 25

The formula for area of a square is expressed as;

Area = a²

Where a is the side length

From the image shown, we can see that the side length takes the value (7n - 5)

Substitute the value into the formula

Area = a²

Area = (7n - 5)²

Area = (7n - 5) ( 7n + 5); this is so because of the difference of two squares

Expand the bracket

Area = 49n² + 35n - 35n - 25

collect like terms

Area = 49n² - 25

Thus, the polynomial representing the area of the cube is 49n² - 25

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Answer:

1) 5
the smallest integer besides one that both sides are divisible by is 5
2) 2

make both denominators the same 35/40, and 16/40. because 16 can only go into 35 twice the answer is 2

Answer:

30)49

34) 14

38) 3

42) 1

46) 6

Step-by-step explanation:

Answer:

division is right.

Step-by-step explanation:

The last step in evaluating the problem  \(5 . 2 3 \ \div \ (4 + 6)\)  will be Division.

Evaluating means to calculate the value of given problem.

BODMAS means Bracket off, Order, Division, Multiplication, Addition, Subtraction. i.e. if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by 'order' (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right.

Here, to evaluate the problem we will use the BODMAS Rule.

We have,

\(5 . 2 3 \ \div \ (4 + 6)\)  

\(5.23 \ \div \ 10 \\)

\(0.523\)

So, in the last step we use division, which was according to the BODMAS Rule.

Hence, we can say that the last step in evaluating the problem  \(5 . 2 3 \ \div \ (4 + 6)\)  will be Division.

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Answer:

16

Step-by-step explanation:

8(2) = 16

Answer:

16

Step-by-step explanation:

Answer:

1. Mean, because there are no outliers that affect the center

Step-by-step explanation:

Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

The mean = ΣX / n

n = sample size, n = 15

Mean = 34 / 15 = 2.666

The median = 1/2(n+1)th term.

1/2(16)th term = 8th term.

The 8th term = 2

The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.

Both interquartile range and standard deviation are measures of spread and not measures of centre.

The two trains are first equidistant from the child after π/3 minutes.

1. The functions f(x) = 2sin²θ and g(x) = −1 + 4sinθ − 2sin²θ intersect at the values in the interval [0, 2π).

Given functions f(x) = 2sin²θ and g(x) = −1 + 4sinθ − 2sin²θ

To find the values in the interval [0, 2π) where these two functions intersect, we need to set them equal to each other and then solve for θ as follows:

2sin²θ = −1 + 4sinθ − 2sin²θ.4sinθ

= 1 + 2sin²θsinθ

= (1/4) + (1/2)sin²θ

As 0 ≤ sinθ ≤ 1, the range of the right-hand side is between (1/4) and 3/4.

Now let u = sin²θ, so we have sinθ = ±√(u)

Taking the positive square root, sinθ = √(u).

Thus, we need to find the values of u for which (1/4) + (1/2)u occurs.

This is equivalent to solving the quadratic equation:

2u + 1 = 4u²u² - 2u - 1

= 0(u + 1/2)(u - 1)

= 0u

= -1/2, 1

As u = sin²θ, the range of u is [0, 1].

Therefore, sin²θ = 1 or -1/2. Since the value of sinθ cannot be greater than 1, sin²θ cannot be equal to 1.

Therefore, sin²θ = -1/2 is impossible.

Thus sin²θ = 1 and sinθ = 1 or -1.

Hence, the possible values of θ are 0, π/2, 3π/2, and 2π.2.

Given two functions as y = 2cos2x and y = 3 + cos x.

We have to find the number of minutes it will take until the two trains are first equidistant from the child.

Let the two trains are equidistant from the child at t minutes after the start of the motion of the first train.

So, the distance of the first train from the child at time t is 2cos2t.

The distance of the second train from the child at time t is 3+cos(t).

Equating these two distances, we get;

2cos2t

3+cos(t)2cos2t- cos(t) = 3...(1)

To solve the above equation (1), we need to express cos2t in terms of cos(t).

Using the formula,

cos2θ = 2cos²θ -1cos2t = 2cos^2t -1cos²t

= (cos(t)+1)/2(cos²t + 1)

=\((cos(t) + 1)^2/4\)

Now, the equation (1) becomes:2(cos² + 1) - cos(t) - 3 = 0

On solving the above equation, we get:cos(t) = -1, 1/2

We need the value of cos(t) to be 1/2. Therefore, t = 60° = π/3.

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Answer:

The Answer is 4. 6x-4y=6

Answer:

Step-by-step explanation:

Step one:

Plan 1

charges = $27 monthly

the total charges is expressed as

y=27------1

Plan 2

charges= $11 monthly

extral= $0.05 per call

let x be the number of calls

the total is expressed linearly as

y=0.05x+11--------2

Step two:

equating 12 and 2 we have

27=0.05x+11

collect like terms

27-11=0.05x

16=0.05x

divide both sides by 0.05

x=16/0.05

x=320

the inequality for which plan A is more economical is

0.05x+11<27 for x<=320

Answer:

Improper Fraction: 15 /2

Mixed Number: 7 1/2

Step-by-step explanation:

You want to add the improper fractions together: 3/2 + 5/2 + 7/2 = 15/2

To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible.

To find a positive number such that the sum of and is as small as possible, we need to use optimization. This problem requires optimization over a closed interval. The given problem is as follows, Let x be a positive number. Find a positive number such that the sum of and is as small as possible. So, we need to minimize the sum of and . Now, let's use calculus to find the minimum value of the sum.To find the minimum value, we have to find the derivative of the sum of and , i.e. f(x) with respect to x, which is given by f '(x) as shown below:

f '(x) = 1/x^2 - 1/(1-x)^2

We can see that this function is defined on the closed interval [0, 1]. The reason why we are using the closed interval is that x is a positive number, and both endpoints are included to ensure that we cover all positive numbers. Therefore, the problem requires optimization over a closed interval. This means that the minimum value exists and is achieved either at one of the endpoints of the interval or at a critical point in the interior of the interval.

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Answer:

12

Step-by-step explanation:

y = 6; z = 6

3y - z = 3(6) - 6 = 18 - 6 = 12

Answer:

12

Step-by-step explanation:

3y-z is asking 3 x 6 - 6, which equals 12

(3 x 6 = 18 and 18 - 6 = 12)

Answer:

2/5, 0.85, 1 3/4, 22/7

Step-by-step explanation:

Lets change all of these to decimals so we can compare them.

2/5 = 4/10 = 0.4 = 0.40

0.85 is already ready to go.

1 3/4 = 1.75

22/7 = 3.142857...

So from smallest to biggest

.40, .85, 1.75, 3.14

Which are in their original form:

2/5, 0.85, 1 3/4, 22/7

Answer:

a)

A (1, 0)
B (3,0)

b)

P(0,3)

c)

Q(2, -1)

Step-by-step explanation:

The equation (x-1)(x-2) is a quadratic equation and represents the equation of a parabola

Part a)

The x-intercepts at A and B represent the zeros of the function

Set (x-1)(x-3) = 0 ===> x = 1 and x =3

So the x-intercepts which are the x values at y = 0 are
A(1, 0) and B(3,0)

Part b

P is the y intercept and can be obtained by setting x = 0 and solving for y
==> y = (0-1)(0-3) = -1 x -3 = 3

So P(0, 3)

Part c

Q is the vertex of the parabola and represents a minimum point for the graph

The minimum value for x can be found by differentiation the function with respect to x and setting it equal to 0 and solving for x value

We have y = (x-1)(x-3) = x² -1x - 3x + 3 using the FOIL method

y = x² - 4x + 3

dy/dx = 2x -4

Setting dy/dx = 0

==> 2x - 4 = 0

x2x = 4

x = 2

So the minimum occurs when x = 2

At x = 2,

y = (2-1)(2-3) = 1 x -1 = -1

So the vertex is at (2, -1) which is point Q

Answer:

The rate of change/cost per mile driven can be calculated by finding the slope of the line that connects the points (1,10.70) and (0,10). The slope is the change in the y-value divided by the change in the x-value, so the slope of the line is (10.70-10)/(1-0) = $0.70/mile.

The point (0, 10) represents the cost of the driving service when 0 miles are driven. In other words, the service costs $10 for no miles driven.

The equation that models the function in the table is C(m) = $10 + $0.70m. The first term represents the cost of the service when no miles are driven and the second term represents the cost per mile driven.

Answer:

98 m long

Step-by-step explanation:

588/6 = 98 m long

Answer:

0

Step-by-step explanation:

The first derivative of the function f(x) = 14x^(3/2) - 10x^(1/2) can be found by applying the power rule for derivatives. According to the power rule, the derivative of x^n with respect to x is given by nx^(n-1). Applying this rule, we differentiate each term of the function:

f'(x) = d/dx [14x^(3/2)] - d/dx [10x^(1/2)]

      = 14 * (3/2)x^(3/2 - 1) - 10 * (1/2)x^(1/2 - 1)

      = 21x^(1/2) - 5x^(-1/2)

      = 21√x - 5/√x

      = 21√x - 5/√x.

Therefore, the first derivative of f(x) is f'(x) = 21√x - 5/√x.

To find the second derivative, we differentiate the first derivative with respect to x. Applying the power rule again, we get:

f''(x) = d/dx [21√x - 5/√x]

       = d/dx [21x^(1/2)] - d/dx [5x^(-1/2)]

       = 21 * (1/2)x^(1/2 - 1) - 5 * (-1/2)x^(-1/2 - 1)

       = 21 * (1/2)x^(-1/2) + 5 * (1/2)x^(-3/2)

       = 21/2√x + 5/2x^(3/2).

Therefore, the second derivative of f(x) is f''(x) = 21/2√x + 5/2x^(3/2).

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