3. Find volume. Show work, round to 2 decimal places.

*square based pyramid*

lines a and b are perlendicularr and the equation of line a is y=x+3.Therefore, after calculation, the equation of line b is y = -x + 3.

Perpendicular refers to a line, ray, or segment that intersects another line or segment at a right angle, or 90-degree angle. The point of intersection is called the point of perpendicularity and is equidistant from the endpoints of the segment.

An equation of a line is a mathematical representation of a straight line. It can be written in various forms, including slope-intercept form, point-slope form, and standard form, and relates the variables x and y.

According to the given information:

If line a has the equation y = x + 3 and line a is perpendicular to line b, then the slope of line b is the negative reciprocal of the slope of line a.

The slope of line a is 1, so the slope of line b is -1/1, which simplifies to -1.

To find the equation of line b, we need to find the y-intercept (b) using the point-slope form of a linear equation. We can choose any point on line b, but since we don't have any specific point given, we can use the y-intercept of line a, which is 3.

So, the equation of line b is y = -x + 3.

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The perimeter of the figure is 38.52.

We have,

The perimeter of the figure:

Side + 18 + 18

From the figure,

82 + 90 + x = 180

172 + x = 180

x = 180 - 172

x = 8

Now,

Using trigonometric identities Sin.

Sin 8 = Side/18

0.14 = side/18

side = 0.14 x 18

side = 2.52

Now,

The perimeter of the figure.

= Side + 18 + 18

= 2.52 + 18 + 18

= 38.52

Thus,

The perimeter of the figure is 38.52.

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The experimental probability that you will roll a three on your next roll is 70%.

To calculate the experimental probability of rolling a number three on the next roll, we need to use the data given in the problem. Out of the 20 rolls that were performed, the number three was rolled 14 times.

The experimental probability is calculated by dividing the number of times the event occurred (in this case, rolling a number three) by the total number of trials.

So, the experimental probability of rolling a number three on the next roll is:

14/20 or 7/10

This means that based on the data from the previous 20 rolls, there is a 70% chance of rolling a number three on the next roll.

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The total amount paid to the finance company if the loan is repaid in 40 years is $317,376.00 (option c).

First, we need to find out how much money the couple borrowed. Since they got financing for 80% of the $150,000 purchase price, they borrowed $120,000 ($150,000 x 0.8 = $120,000).

Next, we need to find the monthly interest rate. Since the interest rate is 6% per year, the monthly interest rate is 0.06/12 = 0.005.

Now we can use the table to find the monthly payment per $1000 of mortgage for a 40-year loan with a 6% interest rate. Looking at the fifth column of the table, we find the entry that corresponds to a 6% interest rate and a 40-year loan, which is 5.86. This means that for each $1000 borrowed, the monthly payment is $5.86.

To find the monthly payment for the couple's $120,000 loan, we multiply the monthly payment per $1000 by 120 (since they borrowed $120,000). So the monthly payment is 5.86 x 120 = $703.20.

Finally, we need to calculate the total amount paid to the finance company over the 40-year period. Since the couple will make 12 payments per year for 40 years, the total number of payments will be 12 x 40 = 480. So the total amount paid will be the monthly payment ($703.20) multiplied by the total number of payments (480). This gives us a total of $317,376.

Therefore, the correct option is (c).

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Cash was paid for salaries during 2014 was $55,100. These are the formulas for calculating the cash salary received in 2014:

Salary paid in cash = Salary expense in 2014 - Reduction in salary payable

The difference between the balance due for salaries at the end of each year—that is, at December 31, 2013 and December 31, 2014—can be used to determine the decline in salaries payable:

Salaries payable at December 31, 2013, compared to salaries payable at December 31, 2014, are $3,700, $1,800, and $1,900, respectively.

The drop in the balance of salaries payable from 2013 to 2014 indicates that the business paid more compensation than it incurred for the year. As a result, the 2014 salary payments in cash are:

Cash paid for salaries equals salaries paid in 2014 less salaries payable, or $57,000 minus $1,900, or $55,100.

Hence, (A) $55,100 is the correct response.

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The thickness of the concrete pad is 58 and 2/81 yd³. So correct option B.

Volume is the measure of the amount of space occupied by a three-dimensional object or substance. It is typically measured in units such as cubic meters, cubic feet, liters, or gallons. The formula for calculating the volume of a simple shape like a cube, rectangular prism, or cylinder involves multiplying its length, width, and height or its base area and height. More complex shapes may require more advanced formulas or techniques for determining their volume. Volume is an important concept in many fields, including physics, engineering, architecture, and chemistry, and is often used to measure quantities such as liquids, gases, and solids.

To find the volume of the concrete pad, we need to multiply the length, width, and thickness of the pad.

First, we need to convert the dimensions to yards by dividing by 3 since there are 3 feet in a yard:

Length: 31 and 1/3 yards = 94/3 yards

Width: 16 and 2/3 yards = 50/3 yards

Thickness: 1/9 yard

Now we can calculate the volume:

V = (94/3) * (50/3) * (1/9)

V = 4700/81 cubic yards

V ≈ 58.02 cubic yards

Therefore, the answer is B. 58 and 2/81 yd³.

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The complete question is:

Mark Twain's quote about breaking down overwhelming tasks into manageable pieces is a valuable lesson for high school students, particularly when it comes to writing. (option d)

In the context of writing, this quote can be particularly helpful. Writing a story or essay can seem like a daunting task, but if you break it down into smaller pieces, it becomes much more manageable. This is where the process of outlining comes in. An outline is essentially a roadmap of your writing, breaking it down into smaller components that you can tackle one at a time.

In mathematical terms, you can think of this process as a series of equations. Each equation represents a small, manageable piece of the overall problem.

By breaking down the problem into smaller equations, you can solve each one individually, which ultimately leads to solving the larger problem. This is similar to how breaking down a writing project into smaller pieces can help you write a well-structured and coherent piece.

Hence the correct option is (d).

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Answer:

A

Step-by-step explanation:

it cant be 9 per hour cuz it is a smaller amount and A is the only one that makes sens

The Hardy-Weinberg equation is a mathematical formula used to calculate the frequency of alleles (alternative forms of genes) in a population.

It states that the frequency of alleles and genotypes in a population will remain constant from generation to generation in the absence of other evolutionary influences.

The equation is expressed as: p² + 2pq + q² = 1

In this equation, p represents the frequency of the dominant allele in the population, and q represents the frequency of the recessive allele.

The superscripts 2 represent the proportion of individuals in the population that are homozygous for that allele (meaning they have two copies of the same allele), while the 2pq term represents the proportion of individuals that are heterozygous (meaning they have one copy of each allele).

The sum of these terms is always equal to 1, as it represents the entire population.

This equation assumes several conditions: that the population is large, randomly mating, with no mutations, migration, natural selection, or genetic drift.

In reality, these conditions are rarely met, and the Hardy-Weinberg equation serves as a useful model for understanding how allele frequencies can change over time due to various evolutionary influences.

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Answer:

230°

Step-by-step explanation:

Because Arc RSP had three letters that means its a major arc or greater than 180°

Arc RP is the portion of the circle not intercepted by the angle so 360 minus the measure of RP is RSP

360 - 130 = 230

The total area of the four offices in the building is 1296 square feet.

When we talk about the area of a shape, we are referring to the amount of space that it occupies. In this case, since the offices are squares, we can find the area of each office by multiplying the length of one side by itself. This is represented by the formula A = s², where A is the area and s is the length of one side.

So, if each office has a side length of 18 feet, we can find the area of one office by plugging that value into the formula: A = 18² = 324 square feet.

Since there are four offices, we can find the total area of all four offices by multiplying the area of one office by 4: 324 square feet x 4 = 1296 square feet.

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The kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

The kite's vertical distance from the ground is the sum of its vertical height from Jennifer's hand and the distance from the ground to the hand

we shall represent the vertical height of the kite from Jennifer's hand with the letter x so that;

x = 36 inches × sin 39°

x = 3 feet × sin 39° {36 inches = 3 feet}

x = 1.8880 feet

kite's vertical distance from the ground = 1.9 ft + 5.5 ft = 7.4 feet

Therefore, the kite's vertical distance from the ground, with an angel of elevation 39° from the line of sight of Jennifer is equal to 7.4 feet.

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Answer: 50 * 1,967 = 98,350

50 * 1,000 = 50,000

Step-by-step explanation: 50 * 1,967 = 50 * 1,000 + 50 * 967 = 50,000 + 48,350 = 98,350.

The general solution to the differential equation is y = -1/(3x³ + C)

Where C is an arbitrary constant.

The concept used to solve this differential equation is the separation of variables. Separated the variables on either side of the equation and then integrated both sides to get the general solution with a constant of integration.

Note that, the solution is valid only for y ≠ 0 as the differential equation is undefined for y = 0.

Here we have  

dy/dx = 9x²y²

Solve the differential equation using the separation of variables.

=> dy/dx = 9x² y²

Let's separate the variables by dividing both sides by y² and dx:

=> 1/(y²) dy = 9x² dx

Now we can integrate both sides:

=> ∫1/(y²) dy = ∫9x² dx

Using the power rule of integration, we get:

=> -1/y = 3x³ + C

Where C is the constant of integration.

To solve for y, we can multiply both sides by -1:

=> y = -1/(3x³ + C)

Therefore,

The general solution to the differential equation is y = -1/(3x³ + C)

Where C is an arbitrary constant.

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Answer:

true

Step-by-step explanation:

The key features of the given quadratic equation include the following:

Vertex = (-2, 4)

Axis of symmetry: x = -2.

Direction of opening: downward.

There is a maximum (max) at 4.

y-intercept = (0, 0).

roots: x = -4 and x = 0.

In Mathematics and Geometry, the vertex form of a quadratic equation is modeled by this formula:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the graph of this quadratic equation, we can reasonably infer and logically deduce that its vertex can be determined as follows:

y = -2(x + 2)² +4

Vertex, (h, k) = (-2, 4)

Axis of symmetry, Xmax = -2.

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There were about 557 principals in attendance based on the prediction

To make a prediction about the number of principals in attendance at the conference, we can assume that the proportion of principals in the exhibit room is similar to the proportion of principals in the whole conference.

In the exhibit room, out of 70 people, 52 were principals.

So, the proportion of principals in the exhibit room was 52/70

We can predict the number of principals in attendance at the conference as follows:

Number of principals = proportion of principals x total number of attendees

If we plug in the values, we get:

number of principals = 52/70 x 750 = 557

So, based on this prediction, we can say that there were 557 principals in attendance at the conference.

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An equation which shows how to find p, the price Mrs. Merson paid for the car include the following: B) 5500/p = 55/100.

In Mathematics and Science, a price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.

Based on the information provided about the amount of money that Mersin paid for the car, an equation which shows how to find the price (p) is given by;

55% of p = 5500

55/100 × p = 5500

5500/p = 55/100

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Complete Question:

Mrs. Merson is selling her car. Her research shows that the car has a current value of $5,500,

which is 55% of the amount Mrs. Merson paid for the car. A buyer wants to know the price

Mrs. Merson paid for the car.

• Which equation shows how to find p, the price Mrs. Merson paid for the car?

A) 55/p = 5500/100

B) 5500/p = 55/100

C) p/5500 = 55/100

D) p/5 = 5500/100

The z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.

The formula for calculating the z-score is:

z = (x - μ) / σ

where x is the data value, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (80 - 52) / 9 = 3.11 (rounded to two decimal places)

Therefore, the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9 is approximately 3.1.

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The z-score for a data value of 80 in this data set is approximately 3.1.

Calculate the z-score for a data value of 80 in a data set with a mean of 52 and a standard deviation of 9.

To find the z-score, follow these steps:

Identify the data value (x), mean (µ), and standard deviation (σ).

In this case, x = 80, µ = 52, and σ = 9.

Use the z-score formula:

z = (x - µ) / σ

Plug in the values:

z = (80 - 52) / 9

Perform the calculations:

z = 28 / 9

Round the answer to the nearest tenth: z ≈ 3.1

So, the z-score for a data value of 80 in this data set is approximately 3.1.

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The cost of the car with 60,000 miles would be = $13,000 approximately.

To calculate the cost of the car form the given graph above is to draw a straight line that connects most of the points of interception.

From the graph, the most appropriate point of interception would be on $13,000 since each line in y-axis represents a thousand dollars.

Therefore, the cost of the car with 60,000 miles would be = $13,000 approximately.

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The costs of each treat are

To solve this, we use the followign representations

x = cookies

y = ice cream 1

z = ice cream 2

Treat 1

Using the columns to generate the system of equations, we have

x + y + z = 25.71

z + 2x = 23.21

3y = 26.94

So, we have

y = 8.98

The other equations become:

x + 8.98 + z = 25.71

z + 2x = 23.21

When solved, we have

x = 6.48

z = 10.25

Treat 2

Using the rows to generate the system of equations, we have

x + 2y = 7.17

y + 2x = 5.37

3z = 14.97

So, we have

z = 4.99

The other equations when solved, we have

x = 1.19

y = 2.99

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Answer:

To find the value of Clare's home in 2006 after an 18% increase, we can use the following formula:

Value in 2006 = Value in 2001 x (1 + Percent Increase)

Plugging in the values given in the problem, we get:

Value in 2006 = $135,000 x (1 + 0.18)

Simplifying this expression, we get:

Value in 2006 = $135,000 x 1.18

Value in 2006 = $159,300

Therefore, Clare's home was worth $159,300 in 2006 after an 18% increase in value from its original price of $135,000 in 2001.

Therefore, the solution to the equation 10ˣ = 23 is: x = log(23) that is option B.

An equation is a mathematical statement that shows that two expressions are equal. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be solved to find the value(s) of the variable(s) that make the equation true.

Here,

Taking the logarithm of both sides of the equation 10ˣ = 23:

log(10ˣ) = log(23)

Using the power rule of logarithms, the left-hand side simplifies to:

x log(10) = x

Since log(10) = 1, we have:

x = log(23)

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Answer:

1/2

Step-by-step explanation:

Since the events are independent, P(A and B) = P(A) * P(B)

P(X and Y) = P(X) * P(Y)

                  = 2/3 * 3/4

                  = 2/4

                   = 1/2

Answer:

[tex]r = \sqrt{ {3}^{2} + {( - 7)}^{2} } = \sqrt{9 + 49} = \sqrt{58} [/tex]

[tex] {x}^{2} + {y}^{2} = 58[/tex]

Answer: To find the decimal expansion of 5/7, we can perform long division as follows:

0.7│5.0

    4 2

 ────

  8 │ 30

    28

  ───

20 │ 200

    196

  ────

      4

Hence, 5/7 = 0.714285... where the digits 714285 repeat indefinitely. To find the maximum number of digits in the repeating block of digits, we can observe that the repeating block will be at most 6 digits long because 7 has a factor of 2 and 5, and therefore 7 divides 10^6 - 1 = 999999.

In fact, we can see that the repeating block in this case has 6 digits, since the digits 714285 repeat indefinitely, and there are 6 digits in this repeating block. Therefore, the maximum number of digits in the repeating block of digits in the decimal expansion of 5/7 is 6.

Step-by-step explanation:

The solution for the equation -x² + 2x + x - 3x = -9 + 2 + 6 is derived to be x = 1

We shall solve for x by simplifying the equation and making x the subject as follows:

-x² + 2x + x - 3x = -9 + 2 + 6

-x² + 3x - 3x = 8 - 9

-x² = -1

multiply both sides by -1 we have;

x² = 1

take square root of both sides

x = √1

x = 1

Therefore, the equation -x² + 2x + x - 3x = -9 + 2 + 6 will have a solution for the value of x = 1

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The sales tax owed on a $124.54 purchase at Walmart with an 8.5% sales tax rate is $10.59.

Suppose you spent $124.54 at Walmart and the sales tax rate is 8.5%. To calculate how much sales tax you owe, we first need to convert the sales tax rate from a percentage to a decimal. We do this by dividing the percentage by 100. So, the sales tax rate in decimal form is:

8.5% ÷ 100 = 0.085

Next, we multiply the purchase price by the sales tax rate in decimal form to calculate the amount of sales tax owed:

$124.54 × 0.085 = $10.59

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