Audrey worked for Beachview House Rentals for four months in the summer. Her gross income was $8,040. Beachview House Rentals withheld $705.67 in federal income tax and $49.10 in other taxes.

The volume of the great Khafre Pyramid, given the height, and length of bases would be 74, 433, 109.33 cubic feet.

To find the volume of the pyramid, we can use the formula:

V = (1/3) x B x h

where B is the area of the base and h is the height of the pyramid.

Since the base is a square, the area of the base can be found by:

B = s^2

where s is the length of a side.

In this case, s = 706 feet, so:

B = 706 ^ 2 = 498, 436 square feet

Now we can plug in the values for B and h:

V = (1/3) x 498,436 x 448

V = 74, 433, 109.33 cubic feet

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The full question is:

The great Khafre Pyramid, the second tallest and second largest of the three ancient pyramids of Egypt, is 448 feet tall, and the length of a side at the base is 706 feet. The base of the pyramid is a square. What is its volume, rounded to the nearest cubic foot?

Answer: 74,433,109

Step-by-step explanation:

Answer:

there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

Step-by-step explanation:

The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

In this case, we want to determine how many ways we can select 3 batteries out of 6. Using the counting principle, we can break down the selection process into three steps:

Select the first battery. There are 6 choices for the first battery.

Select the second battery. There are 5 choices left for the second battery, since we've already selected one.

Select the third battery. There are 4 choices left for the third battery.

Using the counting principle, we can multiply the number of choices for each step to get the total number of ways to select 3 batteries:

6 x 5 x 4 = 120

Therefore, there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

(a) Own price elasticity shows a negative relationship for Current A/C, Fixed deposit A/C, and ATM transactions, while Savings A/C has a positive relationship.

(b) Price elasticity of Current A/C for Savings A/C, Fixed deposit A/C, and ATM transactions is 4.11, 90.90, and 0.000, respectively.

(c) Price elasticity between Savings A/C and Current A/C, Fixed deposit A/C, and ATM transactions is -0.289, -2.450, and 2.44, respectively.

(d) Income elasticity is positive for Current A/C and ATM transactions and negative for Savings A/C and Fixed deposit A/C.

(e) In economic expansion, Current A/C and ATM transactions may improve while Savings A/C and Fixed deposit A/C demand might decline.

(f) Management should consider reducing charges for Fixed deposit A/C and ATM transactions to stimulate demand; Savings A/C requires further investigation.

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Answer:

keep-flip-change

Step-by-step explanation:

This means that you keep the first fraction as it is, flip the second fraction, and change the problem to a multiplication problem.

Answer:

keep-flip-change

Step-by-step explanation:

This means that you keep the first fraction as it is, flip the second fraction, and change the problem to a multiplication problem.

Answer:

Step-by-step explanation:

You want the missing side and angle measures in triangle ABC with AB = 14, AC = 17, and B = 56°.

The law of sines tells you side lengths are proportional to the sine of their opposite angle:

  a/sin(A) = b/sin(B) = c/sin(C)

Side c is given, so we can find missing angle C from ...

  C = arcsin(c/b·sin(B)) = arcsin(17/14·sin(56°)) ≈ 43.1°

Angle A brings the sum of angles to 180°:

  A = 180° -56° -43.1° = 80.9°

Now we have the information required to find side 'a':

  a = b·sin(A)/sin(B) = 17·sin(80.9°)/sin(56°) ≈ 20.2

The missing measures are (A, C, a) = (80.9°, 43.1°, 20.2).

__

Additional comment

We have only rounded the final values in the computations. Intermediate values are used to full calculator precision.

Any value of r between 10/√π and 17/π will satisfy both limits and be a possible radius for the clocks that Paige needs to make.

We have,

To solve this problem, we need to use two formulas related to circles:

Circumference of a circle = 2πr, where r is the radius of the circle

Area of a circle = πr², where r is the radius of the circle

We know that the circumference of a clock must be 34 inches or less, so we can set up the inequality:

2πr ≤ 34

Simplifying, we get:

r ≤ 17/π

We also know that the area of a clock must be 100 inches or larger, so we can set up the inequality:

πr² ≥ 100

Simplifying, we get:

r² ≥ 100/π

Taking the square root of both sides, we get:

r ≥ 10/√π

On the number line, we can plot the two limits:

<------[10/√π)----------------(17/π]------->

Thus,

Any value of r between 10/√π and 17/π will satisfy both limits and be a possible radius for the clocks that Paige needs to make.

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The solutions of the system of inequalities:

y > 4x - 3

y ≥ -2x + 3

Are:

B. (1,2)

C. (1,5)

E. (0,5)

Here we have the system of inequalities:

y > 4x - 3

y ≥ -2x + 3

A solution of the system of inequalities is any pair (x, y) such that it solves both inequalities.

To check that you can graph the system and find the points that lie in the intersection of the shaded areas for both inequalities.

The graph can be seen in the image below, the points that are solutions are:

B. (1,2)

C. (1,5)

E. (0,5)

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Answer:C

Step-by-step explanation:

The exact value of the expression tan[tex]((11\pi )/6 + (7\pi )/4) is (\sqrt{} 3 + 3) / (\sqrt{} 3 - 1).[/tex]

First, we can simplify the argument of the tangent function using the sum identity for tangents:

tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a) * tan(b))

Using this identity, we have:

[tex]tan((11\pi )/6 + (7\pi )/4) = (tan(11\pi /6) + tan(7\pi /4)) / (1 - tan(11\pi /6) * tan(7\pi /4))[/tex]

Next, we can use the values of tangent for 11π/6 and 7π/4. Recall that:

tan(π/6) = 1/√3, tan(π/4) = 1, tan(π/3) = √3

Using the periodicity of the tangent function, we can rewrite the arguments of the tangent function as:

[tex]11\pi /6 = (2\pi + \pi /6), 7\pi /4 = (2\pi + \pi /4)[/tex]

Substituting these values into our expression, we get:

[tex]tan((11\pi )/6 + (7\ \pi/4) = (tan(2\pi + \pi /6) + tan(2\pi + \pi /4)) / (1 - tan(2\pi + \pi /6) * tan(2\pi + \pi /4))[/tex]

Now, we can use the difference identity for tangents:

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a) * tan(b))

We can apply this identity to simplify the tangents in the numerator of our expression:

[tex]tan(2\pi + \pi /6) + tan(2\pi + \pi /4)[/tex]

[tex]= [(tan(2\pi ) + tan(\pi /6)) / (1 - tan(2\pi ) * tan(\pi /6))] + [(tan(2\pi ) + tan(\pi /4)) / (1 - tan(2\pi ) * tan(\pi /4))][/tex]

[tex]= (tan(\pi /6) / (1 - tan(\pi /6) * 0)) + (tan(\pi /4) / (1 - tan(\pi /4) * 0))[/tex]

[tex]= 1/\sqrt{} 3 + 1[/tex]

Similarly, we can simplify the tangents in the denominator of our expression:

[tex]tan(2\pi + \pi /6) * tan(2\pi + \pi /4[/tex])

=[tex](tan(2\pi ) + tan(\pi /6)) * (tan(2\pi ) + tan(\pi /4))[/tex]

[tex]= (0 + 1/\sqrt{} 3) * (0 + 1)[/tex]

[tex]= 1/\sqrt{} 3[/tex]

Substituting these simplified values back into our original expression, we get:

tan[tex]((11\pi )/6 + (7\pi )/4) = [(1/\sqrt{} 3) + 1] / (1 - 1/\sqrt{} 3)[/tex]

Rationalizing the denominator by multiplying both the numerator and the denominator by √3, we get:

tan[tex]((11\pi )/6 + (7\pi )/4) = [(\sqrt{} 3/3) + \sqrt{} 3] / (1 - 1/\sqrt{} 3) = (\sqrt{} 3 + 3) / (\sqrt{} 3 - 1)[/tex]

Therefore, the exact value of the expression tan[tex]((11\pi )/6 + (7\pi )/4) is (\sqrt{} 3 + 3) / (\sqrt{} 3 - 1).[/tex]

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Answer:

you will need to pay $11,916 per year

Step-by-step explanation:

If the total cost of attending the college for 4 years is $14,895 x 4 = $59,580, and your parents will pay 5% of this amount, then they will contribute 0.05 x $59,580 = $2,979 per year.

To determine how much you will need to pay each year, you can subtract your parents' contribution from the total cost:

$14,895 - $2,979 = $11,916

Therefore, you will need to pay $11,916 per year to attend the college after your parents' contribution.

From lowest to highest probability:

B. A fair number cube with faces numbered 1 through 6 is rolled once. The result is divisible by 3.

C. A pair of fair number cubes with faces numbered 1 through 6 is rolled once. The result is a sum of 6.

A. Heads occurs at least twice when a fair coin is tossed three times.

For event B, there are two numbers on the cube that are divisible by 3: 3 and 6. Therefore, the probability of rolling a number that is divisible by 3 is 2/6 or 1/3, which is lower than the probabilities of events C and A.

For event C, there are five ways to obtain a sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1), out of a total of 6 x 6 = 36 possible outcomes. Therefore, the probability of rolling a sum of 6 with two number cubes is 5/36, which is higher than the probability of event B, but lower than the probability of event A.

For event A, the only way to not get at least two heads in three coin tosses is to get all tails, which has a probability of [tex](1/2)^{3}[/tex] = 1/8. Therefore, the probability of getting at least two heads is 1 - 1/8 = 7/8, which is the highest probability among the three events.

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186 cm³ will be the surface area of the given figure.

To calculate the surface area of the given figure, we need to add the surface area of two cubes and reduce the area of the hidden part.

Thus,

Total surface area = Surface area of bigger cube + surface area of the smaller cube - 2* surface area of the hidden part.

So,

Total surface area = 6*(5*5)+6*(3*3)-2*(3*3)

Total surface area = 150+54-18

Total surface area = 186

Therefore, the surface area of the given figure will be 186 cm³.

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Based on the information provided, I think 4) D₂E² is most likely be the formula for the reaction between D+2 and E¹.

This is because D+2 has a charge of 2+ and E¹ has a charge of 1-. In order for the charges to balance out in the resulting compound, two D+2 ions would need to combine with one E¹ ion. This would result in a compound with the formula D₂E².

A formula is a rule that uses letters of the alphabet to portray amounts or quantities which can be changed. We use formula to solve problems in the field of Mathematics, Computer Science, Chemistry, etc.

Different problems have different formulas for solving them. For example, we have a formula for the area of a rectangle, formula to work out simple interest, etc.

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Answer: Not enough information

Step-by-step explanation:

F appears to be the amount of material in the cylinder.  This information alone is not enough to learn the correct answer.  If the figure is drawn to scale and an estimated conjecture is expected, I would try measuring the distances and if there is not an option to say "not enough information" I might choose one of the much larger options.

Ok, seriously, if you're in college and asking this you're seriously not smart.

Everytime Amber goes running she runs 1 mile.

She runs 4 times each week. How many miles does she run in one week.

Number of mile(s) ran in one session =  1 mile.

Number of running sessions in a single week = 4

Total distance covered = 1 x 4 = 4 miles.

Answer:

4

Step-by-step explanation:

Q) 2 less than 1/4 of the product of 8/3 are 9.

Step 1: 8/3 of 9= 24

9÷3= 3

3×8= 24

Step 2: 1/4 of 24= 6

24÷4= 6

6×1= 6

Step 3: 2 less than 6= 4

6-2= 4

Answer= 4

The measure of angle 2 is determined as 78 degrees.

To find the measure of angle 2, we need to find the value of x.

let angle 1 = 5x + 3

let angle 2 = 6x - 12

To find the value of x in the equation 5x + 3 = 6x - 12, we can follow these steps:

Step 1: Subtract 5x from both sides of the equation to isolate the x term on one side.

5x + 3 - 5x = 6x - 12 - 5x

This simplifies to:

3 = x - 12

Step 2: Add 12 to both sides of the equation to isolate the x term on one side.

3 + 12 = x - 12 + 12

This simplifies to:

15 = x

So, the value of x in the given equation is 15.

The measure of angle 2 = 5x + 3

= 5(15) + 3

= 78

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Answer: Total expenses if 3 widgets are produced is $11,018.00

Step-by-step explanation: The variable cost per unit is given by the coefficient of q in the expense function. In this case, the variable cost is $6.00 per widget. To find the variable costs to produce 2 widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for 2 widgets = 2 x $6.00 = $12.00 Therefore, the variable costs to produce 2 widgets is $12.00. To find the variable costs to produce q widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for q widgets = q x $6.00 = $6q Therefore, the variable costs to produce q widgets is $6q. To find the total expenses if 3 widgets are produced, we can use the expense function and substitute q = 3:E = 6.00 q + 11,000

E = 6.00 (3) + 11,000

E = 18.00 + 11,000

E = 11,018.00 Therefore, the total expenses if 3 widgets are produced is $11,018.00.

The equation of the line of best fit using two points on the line is y = 2х + 2. Option B is the answer.

Using thе slоpe-interсept form оf а lineаr еquаtion: y = mх + b, where m is thе slоpe оf thе line аnd b is thе y-interceрt.

Тo find thе slоpe, we cаn use thе formulа:

m = (y2 - y1)/(х2 - х1)

where (х1, y1) аnd (х2, y2) аre two pоints on thе line.

Using thе pоints (4, 10) аnd (6, 14), we get:

m = (14 - 10)/(6 - 4) = 2

So thе slоpe оf thе line is 2.

Тo find thе y-interceрt, we cаn use one оf thе pоints аnd thе slоpe. Let's use thе рoint (4, 10):

y = mх + b 10 = 2(4) + b 10 = 8 + b b = 2

So thе y-interceрt is 2.

Рutting it аll togethеr, we get thе еquаtion оf thе line оf bеst fit:

y = 2х + 2

Therefore, thе аnswer is В. y = 2х + 2.

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Answer:

Step-by-step explanation:

To calculate the probability that a visitor's first ride at a theme park will be either the roundabout or the pirate ship, we add 20% and 0.42. To convert 20% to a decimal, we divide it by 100, which gives us 0.20. Adding this to 0.42 gives us a total probability of 0.62. Therefore, there is a 62% chance that a visitor's first ride at the theme park will be either the roundabout or the pirate ship. It's important to note that the probability of each ride individually is not provided, so we cannot determine the likelihood of a visitor riding each ride separately.

The probability in terms of decimal will be 0.62 .

Given,

The probability that a visitor's first ride at a theme park will be the roundabout or the pirate ship is 20% +0.42 .

Here,

To calculate the probability that a visitor's first ride at a theme park will be either the roundabout or the pirate ship, we add 20% and 0.42.

To convert 20% to a decimal, we divide it by 100, which gives us 0.20.

Adding this to 0.42 gives us a total probability of 0.62.

Therefore, there is a 62% chance that a visitor's first ride at the theme park will be either the roundabout or the pirate ship.

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Answer: 0.48 or 48%.

Explanation: The experimental probability of an event happening is calculated by dividing the number of times the event occurred by the total number of trials.

In this case, the total number of cones sold is 47 (pistachio) + 51 (other flavors) = 98

The number of cones with pistachio ice cream is 47.

So the experimental probability of the next cone sold having pistachio ice cream is 47/98 ≈ 0.48 or 48%

Therefore, the experimental probability that the next cone sold will have pistachio ice cream is about 0.48 or 48%.

The answer to the statement that the rate of change is 5 is D. No, because y does not change by 5 every time x changes by 1.

To determine if the rate of change of the function is 5, we need to find the difference in y-values divided by the difference in x-values:

Δy / Δx

Let's calculate the rate of change between consecutive points:

From x = -5 to x = -4:

(2 - 1) / (-4 - (-5)) = 1 / 1 = 1

From x = -4 to x = -3:

(3 - 2) / (-3 - (-4)) = 1 / 1 = 1

From x = -3 to x = -2:

(4 - 3) / (-2 - (-3)) = 1 / 1 = 1

From x = -2 to x = -1:

(5 - 4) / (-1 - (-2)) = 1 / 1 = 1

For each consecutive pair of points, the rate of change is 1, not 5.

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Answer:

4

Step-by-step explanation:

slope of the line that passes through the points (3, 6) and (1, -2)

=  [tex]\frac{y2-y2}{x2-x1}[/tex]

= [tex]\frac{-2-6}{1-3}[/tex]

= [tex]\frac{-8}{-2}[/tex]

= 4

the two lines are parallel.

therefore, the slope of the line that passes through the point (-1, 1) is 4.

The cereals have a calorie count of 120 or less per serving.

What is the range of calories per serving for the cereals?

To find the range of the number of calories per serving, we need to subtract the smallest value from the largest value in the data set.

The smallest value in the data set is 90 calories (cereal 8), and the largest value is 210 calories (cereal 6).

Therefore, the range of the number of calories per serving for the cereals is:

210 - 90 = 120

So the answer is (B) 120.

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The set (A∪C)∩B contains the elements 7 and 11, which are the only elements that are in both A∪C and B.

What is the set?

Sets are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.

To find (A∪C)∩B, we first need to find the union of A and C, which is the set of all elements that are in either A or C or both.

A∪C = {3, 4, 7, 11, 12, 13, 14, 15, 16, 17, 18}

Next, we need to find the intersection of this union with set B, which is the set of all elements that are in both A∪C and B.

(A∪C)∩B = {7, 11}

Therefore, the set (A∪C)∩B contains the elements 7 and 11, which are the only elements that are in both A∪C and B.

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you'll want to work with the center-radius form of a circle equation for this. the center formula is [tex](x - h)^2 + (y - k)^2 = r^2[/tex], where [tex](h, k)[/tex] is your center and r is your radius. plug in the information your circle gives you: [tex]A(-3, 12)[/tex], [tex]\text{radius} = 5[/tex]

[tex](x + 3)^2 + (y - 12)^2 = (5)^2[/tex]  ... simplify the right side

[tex](x + 3)^2 + (y - 12)^2 = 25[/tex] ... from here, you need to foil both of your binomials to convert this to the "general form" that your answer choices are in.

[tex](x + 3)^2 = (x + 3)(x + 3) = x^2 + 6x + 9[/tex]

[tex](y - 12)^2 = (y - 12)(y - 12) = y^2 - 24y + 144[/tex]

[tex]x^2 + 6x + 9 + y^2 - 24y + 144 = 25[/tex] ... combine like terms

[tex]x^2 + 6x + y^2 - 24y + 153 = 25[/tex] ... subtract 25

[tex]x^2 + 6x + y^2- 24y + 128 = 0[/tex] is your equation. reorder it so that it's from the highest degree to the lowest:  

[tex]\boxed{\bold{x^2 + y^2 + 6x - 24y + 128 = 0}}[/tex]

Answer:

2

Step-by-step explanation:

[tex] \frac{(15 - 7)}{4} = \frac{8}{4} = 2[/tex]