Question 8 of 25
This question: 1 point(s) possible
An auto repair shop charged a customer $340 to repair a car. The bill listed $100 for parts and the remainder for labor. If the cost of labor is $40 per hour, how many hours of labor did it take to repair
he car?
OA. 5 hours
OB. 6 hours
OC. 7 hours
OD. 6.5 hours

(a) The solution of the equation is √6 + 2.

(b) a = 10 and b = 2, and the solution of the equation is √10 + 7.

((a) To solve this equation, we need to isolate the term with the variable x on one side and move all other terms to the other side.

Let's start by simplifying each term using the fact that;

√24 = √(4 × 6) = 2√6,

√96 = √(16 × 6) = 4√6,

√108 = √(36 × 3) = 6√3, and

√12 = √(4 × 3) = 2√3.

Then, we have:

x√24 + √96 = √108 + x√12

2x√6 + 4√6 = 6√3 + 2x√3

2(√6 + 2√3) = (x√3 + 2x√6)

2√6 + 4√3 = x(√3 + 2√6)

Now, we can equate the coefficients of √6 and √3 on both sides to get a system of equations:

2 = x

4 = 2x

Solving this system, we find that x = 2 and therefore a = 6 and b₁ = 2.

So, the solution of the equation is √6 + 2.

(b) To solve this equation, we also need to isolate the term with the variable x on one side and move all other terms to the other side.

Let's start by squaring both sides of the equation to eliminate the square roots:

(x√40)² = (x√5 + √10)²

40x² = 5x² + 10 + 2x√50 + 10

35x² - 20 = 2x√50

Now, we can square both sides again to eliminate the remaining square root:

(35x² - 20)² = (2x√50)²

1225x⁴ - 1400x² + 400 = 0

This is a quadratic equation in x². We can solve it using the quadratic formula:

x² = (1400 ± √(1400² - 4 × 1225 × 400)) / (2 × 1225)

x² = (1400 ± 200) / 245

x² = 2 or x² = 8/7

Since x² cannot be negative, we have x² = 2 and therefore x = √2.

Substituting this value of x back into the original equation, we have:

x√40 = x√5 + √10

√80 = √10 + √10

√80 = 2√10

So, a = 10 and b = 2, and the solution of the equation is √10 + 7.

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Answer:

Tip is $34

Round up bill amount $170

Step-by-step explanation:

20/ 100 x 170 = $34

Tip is $34

BILL plus tip is $204

Due to Alex's salary falling inside the 22% tax bracket, his short-term capital gains would be subject to the same rate of taxation as his income.

A profit realized from the sale of a capital asset, such as a piece of personal or investment property, that has been possessed for one year or less is referred to as a short-term gain.

These profits are classified as ordinary income subject to tax at your personal income tax rate. Gain earned by selling assets that are held for a year or less are called short-term capital gains.

Alex is a single taxpayer who has taxable income of $80,000.

His investment income is made up of $2,000 in short-term capital gains and $500 in qualifying dividends.

As a result of his tax rate income falling between 38,601 and 425,800, which is below 15%, his qualifying dividends would be subject to a 15% tax.

Hence, we must deduct 15% of 500 and 22% of 2000 before combining them.

15% x 500

= 15 x 5

=  75

22% x 2000

= 22 x 20

= 440.

The total is = 75 + 440 = 515.

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If a square base has a volume of 4 cubic feet, the dimensions that minimize the surface area are: x = 2√2 and h = 4/x^2 = 1/2.

Let x be the side length of the square base and h be the height of the box. Since the volume is 4 cubic feet, we have:

V = x^2h = 4

Solving for h, we get:

h = 4/x^2

The surface area of the box, A, is given by:

A = x^2 + 4xh

Substituting h in terms of x, we get:

A = x^2 + 4x(4/x^2) = x^2 + 16/x

To minimize A, we take the derivative with respect to x and set it equal to zero:

dA/dx = 2x - 16/x^2 = 0

Solving for x, we get:

x = 2√2

To ensure that this is a minimum, we take the second derivative:

d^2A/dx^2 = 2 + 32/x^3

At x = 2√2, this is positive, indicating a minimum.

The box has a square base with side length 2√2 feet and height 1/2 feet.

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Answer:

8.41

Step-by-step explanation:

8.14+3.45=11,59

20-11,59=8.41

Answer:

a) x = 20

b) x = 9

Step-by-step explanation:

  a)     [tex]\boxed{\bf Mean =\dfrac{sum \ of \ all \ the \ data}{Number \ of \ data}}[/tex]

          [tex]\dfrac{16 +x + 3 + 14 +57}{5}=22\\[/tex]

                                 x + 90 = 22*5

                                 x + 90 = 110

                                         x = 110 - 90

                                        x = 20

b)

         [tex]\bf \dfrac{4 + x + 5 +6 + 1}{5} = 5[/tex]

                          x + 16   = 5 * 5

                            x + 16 = 25

                                   x = 25 - 16

                                   x = 9

Therefore, the fair price of one raffle ticket is $2.60, which is slightly less than the amount Raul paid ($3).

a) The fair price of one raffle ticket is $3. This is because 500 tickets were sold at this price and one prize of $200 is to be awarded. Therefore, the 500 tickets collected add up to $1,500, while the prize to be awarded is $200. The net amount to be divided among all the ticket holders is $1,300.

b) The fair price of one raffle ticket is $2.60. This is calculated by dividing the total prize money of $200 by the total number of tickets sold (500). Therefore, 500 tickets multiplied by $2.60 gives a total prize money of $1,300 which is equal to the total ticket sales of $1,500 less the prize money of $200.

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Robert is currently 10 years old.Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation: y + 5 = 2(y)

We are given the information that Sharon is five years older than Robert, and five years ago Sharon was twice as old as Robert was then. This means we can create a system of equations to solve for Robert's age.

Let x = Robert's current age

Let y = Robert's age five years ago

Given that Sharon is five years older than Robert, we can set up the following equation:

x + 5 = Sharon's current age

Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation:

y + 5 = 2(y)

Solving the first equation for x, we get x = Sharon's current age - 5. Substituting this into the second equation, we get:

y + 5 = 2(Sharon's current age - 5)

Solving this equation for y, we get y = (Sharon's current age - 5)/2.

Since Sharon is five years older than Robert, Sharon's current age is x + 5. Substituting this into our equation for y, we get:

y = (x + 5 - 5)/2

Simplifying this equation, we get y = x/2. This means that Robert's age five years ago was half of his current age.

Since we know that Robert is currently 10 years old, Robert's age five years ago was 5. Therefore, Robert is currently 10 years old.

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Answer:

Step-by-step explanation:

You ask yourself, "600 is 30% of how many students?". In equation form this looks like:

600 = .30x

Divide both sides by .30 and you'll get that the number of students is 2000

3.31 is an estimate for the radius of the circle.

The circle fοrm is a clοsed twο-dimensiοnal shape because every pοint in the plane that makes up a circle is evenly separated frοm the "centre" οf the fοrm.

Each line tracing the circle cοntributes tο the fοrmatiοn οf the line οf reflectiοn symmetry. In additiοn, it rοtates arοund the center in a symmetrical manner frοm every perspective.

he radius of the circle, we need to use the formula for the area of a sector, which is:

Area of sector = (θ/360) x π x r

the radius of the circle "x" for now, and set up an equation using the given information

51.3 = (120/360) x π x

Simplifying this equation, we get:

= (51.3 x 360)/(120 x π)

x² ≈ 10.95

x ≈ √10.95

x ≈ 3.31

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Answer:

Step-by-step explanation:

45342

The volume of ice cream that fills one waffle cone to the top is 13.09 cubic inches.

The waffle cone has the shape of a circular cone. The volume of a cone is given by the formula [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.

The diameter of the cone is given as 5 inches, so the radius is half of the diameter, or 2.5 inches. The height is given as 6 inches. Substituting these values into the formula, we get:

V = [tex](1/3) * 3.14 * (2.5 inches)^2 * 6 inches[/tex]

V = 13.09 cubic inches

Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches (rounded to two decimal places).

To find the volume of ice cream that fills the waffle cone completely to the top, we first note that the waffle cone has the shape of a circular cone. We use the formula for the volume of a cone, which is [tex]V = (1/3) * \pi * r^2 * h[/tex], where r is the radius of the circular base and h is the height of the cone.

We are given the diameter of the cone, which is 5 inches, and we find that the radius is half of the diameter, or 2.5 inches. We are also given the height of the cone, which is 6 inches. Substituting these values into the formula, we can calculate the volume of the cone as 13.09 cubic inches (rounded to two decimal places). Therefore, the volume of ice cream that completely fills one waffle cone to the top is 13.09 cubic inches.

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Answer:

The remainder when 5x3 + 2x2 - 7 is divided by x + 9 is -692.

Explanation:

We can use long division to divide 5x^3 + 2x^2 - 7 by x + 9:

-5x^2 + 43x - 385

x + 9 | 5x^3 + 2x^2 + 0x - 7

5x^3 + 45x^2

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

-43x^2 + 0x

-43x^2 - 387x

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

387x - 7

Therefore, the remainder when 5x^3 + 2x^2 - 7 is divided by x + 9 is 387x - 7.

Hope this helps, sorry if this is wrong! :]

Answer:

Step-by-step explanation:

You want the coordinates of triangle ABC after dilation by a factor of 1/2.

When the center of dilation is the origin, each of the coordinates is multiplied by the dilation factor:

  (x, y) ⇒ (x/2, y/2)

  A(-4, 0) ⇒ A'(-2, 0)

  B(0, 2) ⇒ B'(0, 1)

  C(2, -2) ⇒ C'(1, -1)

Answer:

Step-by-step explanation:

[tex]D=\frac{\theta}{360} \times2\times\pi \times r[/tex]

[tex]D=\frac{60}{360} \times2\times\pi \times 42[/tex]

    [tex]=\frac{1}{6} \times84\times\pi[/tex]

    [tex]=12\pi cm^2[/tex]

Answer:

34.28 meters

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's call the horizontal distance between the boy and the pole "d". Then we can draw a right triangle with the boy's height (5m) as one leg, the distance "d" as the other leg, and the hypotenuse being the distance from the boy's eyes to the top of the pole (which we don't know yet).

We can use the angle of elevation to find the length of this hypotenuse. The angle of elevation is the angle between the horizontal and the line of sight from the boy's eyes to the top of the pole. Since the boy is looking up at the bird, this angle is also the same as the angle between the hypotenuse and the vertical (i.e. the angle at the top of the triangle). So we have:

tan(30°) = opposite/adjacent

where "opposite" is the height of the pole (20m) and "adjacent" is the hypotenuse. Solving for "adjacent", we get:

adjacent = opposite/tan(30°) = 20/tan(30°)

We can simplify tan(30°) to 1/√3, so:

adjacent = 20/(1/√3) = 20√3

Now we can use the Pythagorean theorem to find the horizontal distance "d":

d^2 + 5^2 = (20√3)^2

Simplifying and solving for "d", we get:

d = √[(20√3)^2 - 5^2] = √(1200 - 25) = √1175

So the horizontal distance between the boy and the pole is approximately 34.28 meters (rounded to two decimal places

Answer:

Let x be the number of hopts and y be the number of totts.

The first statement relates to the total amount of money expected to be made:

3x + 7y ≥ 84

This inequality states that the total revenue from selling hopts and totts should be at least $84.

The second statement relates to the total number of units expected to be sold:

x + y ≤ 24

This inequality states that the total number of hopts and totts sold should be at most 24 units. Therefore, the system of inequalities in standard form is:

3x + 7y ≥ 84

x + y ≤ 24

where x ≥ 0 and y ≥ 0 (since we cannot sell a negative number of hopts or totts).

Answer: Let "x" be the number of hopts that Farmer Naxvip plans to sell, and let "y" be the number of totts that she plans to sell. Then we can write the following system of inequalities to model the relationships between the amounts of hopts and totts:

3x + 7y >= 84

x + y <= 24

The first inequality represents the condition that Farmer Naxvip expects to make at least $84, while the second inequality represents the condition that she expects to sell at most 24 units.

Brainliest Appreciated! (:

Part A:

The equation Y = 10X + 5 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, in this equation, the slope is 10 and the y-intercept is 5.

The slope represents the rate of change in the monthly rate of the gym membership. For every one unit increase in the number of months, the monthly rate will increase by $10. The y-intercept represents the initial cost of joining the gym, which is $5.

Part B:

To find out how much money Justin saves the first month by joining the gym at the discounted price, we need to calculate the difference between the regular price and the discounted price for the first month.

The regular price for the first month can be found by plugging in X = 1 into the equation Y = 15X + 20, which gives Y = 35.

The discounted price for the first month can be found by plugging in X = 1 into the equation Y = 10X + 5, which gives Y = 15.

Therefore, Justin saves $20 (35 - 15) the first month by joining the gym at the discounted price rather than the regular price.

Part C:

The system of equations is:

Y = 10X + 5 (discounted price)

Y = 15X + 20 (regular price)

The solution to the system of equations is (-3, -25), which means that if X = -3, then Y = -25 is a solution to both equations. However, this solution is not possible in this situation because X represents the number of months, which cannot be negative. Therefore, the point (-3, -25) is not a valid solution.

Answer:

-11.

Step-by-step explanation:

We know that the velocity function v(t) is the derivative of the position function x(t).

So, we can integrate v(t) to find x(t) up to a constant of integration:

∫v(t) dt = ∫(4 - 6t^2) dt = 4t - 2t^3 + C

where C is the constant of integration.

We can find the value of C by using the initial condition that the particle is at position x=7 at t=1:

x(1) = 4(1) - 2(1)^3 + C = 7

C = 5

So, the position function is:

x(t) = 4t - 2t^3 + 5

To find the position of the particle at time t=2, we can substitute t=2 into the position function:

x(2) = 4(2) - 2(2)^3 + 5 = -11

Therefore, the position of the particle at time t=2 is -11.

If the shoppers spent a total of $197 in books, the amount that Eric spend is $144.

Let's assume that Todd spent x dollars in the bookstore.

According to the problem, Eric spent $15 less than three times the amount that Todd spent, which can be written as:

3x - 15

The total amount spent by both shoppers is $197, so we can set up the equation:

x + (3x - 15) = 197

Simplifying and solving for x, we get:

4x - 15 = 197

4x = 212

x = 53

Therefore, Todd spent $53 in the bookstore.

To find how much Eric spent, we can substitute Todd's value into the expression we derived for Eric's spending:

3x - 15 = 3(53) - 15 = 144

So Eric spent $144 in the bookstore.

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90% people entering the emergency department is within the interval of [0.1559, 0.2933].

The confidence interval of the percent of patients entering the emergency department who are admitted to the hospital is [0.1763, 0.3137]. It is not reasonable for the hospital to assume that 25% of people who enter the emergency department are admitted to the hospital. Here's why.How to calculate a 90% two-sided confidence interval for p, the percent of people entering the emergency department who are admitted to the hospital:$$CI_p =\bigg(\hat{p}-Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\bigg)$$ where $\hat{p} = \frac{x}{n}$, $\alpha = 0.10$, $Z_{\alpha/2} = 1.645$ (for a 90% confidence interval), and $n = 187$. The margin of error is given by $$ME = Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$Plugging in the values, we get $$\hat{p} = \frac{42}{187} = 0.2246$$$$ME = 1.645 \cdot \sqrt{\frac{0.2246\cdot 0.7754}{187}} \approx 0.0687$$Therefore, the confidence interval for $p$ is $$CI_p = (0.2246-0.0687, 0.2246+0.0687) = (0.1559, 0.2933)$$The 90% two-sided confidence interval for the percent of people entering the emergency department who are admitted to the hospital is [0.1559, 0.2933].Since the interval doesn't include 0.25, the hospital should not use the assumption that 25% of people who enter the emergency department are admitted to the hospital. This is because the interval does not overlap with the value of 0.25. As a result, we are 90% confident that the true proportion of people who are admitted to the hospital after entering the emergency department is within the interval of [0.1559, 0.2933].

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value of variable x is 65 degree.

A straight line is a geometric object that extends infinitely in both directions and has a constant slope or gradient. It is the shortest distance between two points, and it can be described by an equation in the form of y = mx + c, where m is the slope or gradient of the line and c is the y-intercept.

The term "supplementary angles" refers to two angles whose sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary angles, then:

∠A +∠B = 180 degrees

To find value of x

A straight line's angle total is 180°.

2x+50°=180°

2x=130°

x=65

Hence, value of variable x is 65 degree.

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a) The probability of that happening is P(W1 = 1, W2 = 2) = P(W1 = 2, W2 = 1) = p1p2.

b) P(W1 = 1)P(W2 > 1) + P(W1 = 1)P(W2 > 2) + P(W1 = 2)P(W2 > 3) + ...= p1(1 - p2) + p1(1 - p2)p2 + p1p2(1 - p2) + ...= p1(1 - p2)(1 +p2 + p22 + ...) = p1(1 - p2)/(1 - p2)2= p1/(1 - p2)2

c) The probability that their minimum value is k is P(min(W1, W2) = k) = P(W1 = k, W2 > k) + P(W1 > k, W2 = k) = p1(1 - p2)k-1p2 + p2(1 - p1)k-1p1

d) The probability that their maximum value is k is P(max(W1, W2) = k) = P(W1 = k, W2 = k) + P(W1 = k, W2 > k) + P(W1 > k, W2 = k) = p1p2k-1 + p1(1 - p2)k-1 + p2(1 - p1)k-1

a) P(W1 = W2)The probability that W1 = W2 is 0. If W1 and W2 have different values, then W1 is equal to either 1 or 2. The probability of that happening is P(W1 = 1, W2 = 2) = P(W1 = 2, W2 = 1) = p1p2. The probability of that happening is P(W1 = 1, W2 = 2) = P(W1 = 2, W2 = 1) = p1p2.b) P(W1 < W2)The probability of W1 being less than W2 is P(W1 = 1, W2 = 2) + P(W1 = 1, W2 = 3) + P(W1 = 2, W2 = 3) + ... This may be written as P(W1 = 1)P(W2 > 1) + P(W1 = 1)P(W2 > 2) + P(W1 = 2)P(W2 > 3) +...= p1(1 - p2) + p1(1 - p2)p2 + p1p2(1 - p2) + ...= p1(1 - p2)(1 + p2 + p22 + ...) = p1(1 - p2)/(1 - p2)2= p1/(1 - p2)2

d) Distribution of min(W1, W2)If W1 and W2 are independent geometric random variables with parameters p1 and p2, respectively, then the probability that their minimum value is k is P(min(W1, W2) = k) = P(W1 = k, W2 > k) + P(W1 > k, W2 = k) = p1(1 - p2)k-1p2 + p2(1 - p1)k-1p1e) Distribution of max(W1, W2)If W1 and W2 are independent geometric random variables with parameters p1 and p2, respectively, then the probability that their maximum value is k is P(max(W1, W2) = k) = P(W1 = k, W2 = k) + P(W1 = k, W2 > k) + P(W1 > k, W2 = k) = p1p2k-1 + p1(1 - p2)k-1 + p2(1 - p1)k-1

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Answer:

d. 27/4, or 6.75

Step-by-step explanation:

[tex]2( \frac{1}{8} + 4) - ( \frac{3}{16} \times 8)[/tex]

[tex]2( \frac{33}{8} ) - \frac{3}{2} [/tex]

[tex] \frac{33}{4} - \frac{3}{2} = \frac{33}{4} - \frac{6}{4} = \frac{27}{4} = 6.75[/tex]

The simplified difference quotient for the function [tex]\(f(x)=6\) is \(\frac{x+h-1}{h/6}\).[/tex]

The difference quotient for the function \(f(x)=6\) is given by the formula \( \[tex]frac{f(x+h)-f(x)}{h}\)[/tex]. To simplify this difference quotient, substitute the given value of \(f(x)\) into the equation:

[tex]\( \frac{f(x+h)-f(x)}{h} = \frac{f(x+h)-6}{h} \).[/tex]  Next, substitute the value of \(f(x)\) into the numerator:

[tex]\frac{6(x+h-1)}{h} \\[/tex]  .

Finally, divide both sides of the equation by 6 to simplify the equation:

[tex]\( \frac{6(x+h-1)}{h} = \frac{x+h-1}{h/6} \)[/tex]

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Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon. The expression is cost = ($8/pound) x pp - $1.

The functional connection between cost and output is referred to as the cost function. It examines the cost behaviour at various output levels under the assumption of constant technology. An essential factor in determining how well a machine learning model performs for a certain dataset is the cost function. It determines and expresses as a single real number the difference between the projected value and expected value.

Given that, the price per pound of walnuts is $8.

2 pounds x $8/pound = $16

Alexander would get $1 off the final amount.

Thus,

$16 - $1 = $15

So Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon.

The expression for the cost can be written as:

cost = ($8/pound) x pp - $1

Hence, Alexander would have to pay $15 to buy 2 pounds of walnuts with the coupon. The expression is cost = ($8/pound) x pp - $1.

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Answer:

8 apples

Step-by-step explanation:

Step-by-step explanation:

n = Nancy's apples.

j = Jay's apples.

a = Ava's apples.

n = 22

n = j × 2

j = n / 2 = 22/2 = 11

j = a + 3

a = j - 3 = 11 - 3 = 8

Ava has 8 apples.

When we simplify the equation, we obtain: 2y + 20 = 56 2y = 36 y = 18 Hence, mL = 140 – 2y = 104°, mP = 104°, and mN = mO = (180° – mL – 84° – (4y–4)°)/2 = 76°.

The base angles are equivalent because the LNOP is an isosceles trapezoid. As a result, mP = mL. Since we now know that a quadrilateral's total angles equal 360°, we can say. 360° = mL + mN + mO + mP Inputting the values provided yields: m∠L + 84° + (4y-4)° + m∠L = 360° When we simplify the equation, we obtain: 2m∠L + 4y + 80 = 360 2m∠L = 280 - 4y m∠L = 140 - 2y The non-parallel sides of LNOP are congruent since it is an isosceles trapezoid. As a result, mN = mO. We are aware of: 180° - mL = mN + mO Inputting the values provided yields: 84° + (4y-4)° = 180° - (140-2y)° When we simplify the equation, we obtain: 2y + 20 = 56 2y = 36 y = 18 Hence, mL = 140 – 2y = 104°, mP = 104°, and mN = mO = (180° – mL – 84° – (4y–4)°)/2 = 76°.

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