Edgardo created a rectangular prism with a square base. The volume of the prism is 45 cubic inches. The dimensions of the prism are all whole numbers. What is the height of the prism​

Answer:

Step-by-step explanation:

11+6+21+18=56 ft

squared

Answer:

9 years

Step-by-step explanation:
To determine the number of years it will take for the new furnace to pay for itself, we need to compare the cost of running the old furnace for that period with the cost of buying and operating the new furnace during the same time.

Let's calculate the cost of running the old furnace for one year:

Old furnace cost per year = $850

Now, let's calculate the savings in energy costs for the new furnace:

Savings in energy costs per year = 34% of $850

= 0.34 * $850

= $289

The total cost of buying and operating the new furnace for one year is:

New furnace cost per year = Cost of buying the new furnace + Savings in energy costs per year

= $2,500 + $289

= $2,789

To find the number of years it will take for the new furnace to pay for itself, we divide the cost of the new furnace by the annual savings:

Number of years to pay for itself = Cost of buying the new furnace / Annual savings

= $2,500 / $289

≈ 8.65

Since we cannot have a fraction of a year, we can round up to the nearest whole number. Therefore, it will take approximately 9 years for the new furnace to pay for itself.

The probability that the product is a multiple of 3 is given as follows:

p = 7/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are four numbers, hence the total number possible products are given as follows:

4² = 16.

The products that are multiples of 3 are given as follows:

7 products are multiples of 16, out of the 16 products, hence the probability is given as follows:

p = 7/16.

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The solution to the system of equations is x ≈ -4.06 and y ≈ -2.7.

It seems you have provided a system of linear equations. The system can be represented as:

3x + 4y = -23

5x + y = -23

This system can be solved using various methods such as substitution, elimination, or matrix methods. Let's solve it using the method of substitution.

From the second equation, we can express y in terms of x:

y = -23 - 5x

Substituting this value of y into the first equation:

3x + 4(-23 - 5x) = -23

Simplifying the equation:

3x - 92 - 20x = -23

-17x - 92 = -23

-17x = 69

x = -69/17

x ≈ -4.06

Substituting this value of x back into the second equation to find y:

5(-4.06) + y = -23

-20.3 + y = -23

y = -23 + 20.3

y ≈ -2.7

Therefore, the solution to the system of equations is x ≈ -4.06 and y ≈ -2.7.

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The number line with the numbers -4 and 3 graphed is given by the image presented at the end of the answer.

The origin point on the number line is given as follows:

0.

Hence positive numbers and negative numbers are plotted as follows:

The numbers for this problem are given as follows:

-4 and 3.

Hence they are plotted as follows:

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Answer: $31.58

Step-by-step explanation:

Let us say that x is equal to the bill's amount before adding the tip. Please note that a percent divided by 100 becomes a decimal, so 22.1% / 100 = 0.221. We will write an equation to represent this situation.

         x + 0.221x = $38.56

Next, we will solve by combining like terms.

        1.221x = $38.56

Lastly, we will divide both sides of the equation by 1.221.

        x = $31.58

      Camille's bill was $31.58 before adding a 22.1% tip.

Answer:

  x = -5 2/3

Step-by-step explanation:

You want the solution to the rational equation ...

  (x+5)/(x+8)=1+(6)/(x+1)

Casting this into the form f(x) = 0, we have ...

  [tex]\dfrac{x+5}{x+8}=1+\dfrac{6}{x+1}\\\\\\1-\dfrac{3}{x+8}=1+\dfrac{6}{x+1}\\\\\\\dfrac{6}{x+1}+\dfrac{3}{x+8}=0\\\\\\\dfrac{3(2(x+8)+(x+1))}{(x+1)(x+8)}=0\\\\\\3x+17=0\qquad\text{the numerator is zero when the fraction is zero}\\\\\\\boxed{x=-\dfrac{17}{3}}[/tex]

__

Additional comment

The attachment shows the left side and right side expressions are equal when x = -17/3 = -5 2/3.

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The value of the functions are;

a. x = 5/6

b. x> 5/6

c. x = 1

d. x ≤ 1

Note that functions are defined as laws or rules showing the relationship between two variables

From the information given, we have that;

f(x) = 6x - 5

g(x) = -5x + 6

To determine the functions, we have;

f(x) = 0

6x - 5 = 0

collect like terms

6x = 5

x = 5/6

f(x) > 0

6x - 5> 0

6x > 5

x> 5/6

f(x) = g(x)

6x - 5 = -5x + 6

collect like terms

11x = 11

x = 1

f(x) ≤ g(x)

6x - 5 ≤ - 5x + 6

collect like terms

11x ≤ 11

x ≤ 1

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The base angles are of 25 degree.

Given that

Two sides are equal

And one angle of triangle = 130 degree

We know that,

Triangles are three-sided polygons that can be categorized as equilateral, isosceles, or scalene depending on how long their sides are.

And triangles with two equal sides are known as isosceles triangles and

it has two equal angle also.

Therefore,

let the angle is x degree

And we know that sum of interior angles of triangle is 180 degree.

Then,

x + x + 130 = 180

              2x = 50

                x = 25

Hence the required angles are of 25 degree.

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The theoretical probability of having three dogs or three cats is p^3 + q^3.

The theoretical probability of the family having two dogs or two cats depends on the specific probability of each event. Let's assume that the probability of having a dog is 0.5 and the probability of having a cat is also 0.5 (which is a simplification). In this case, the probability of having two dogs is 0.5 x 0.5 = 0.25, and the probability of having two cats is also 0.5 x 0.5 = 0.25. Therefore, the theoretical probability of the family having two dogs or two cats is 0.25 + 0.25 = 0.5 or 50%.

To simulate which two pets the family has using two different coins, we can assign one pet to each coin face (e.g., heads for dog and tails for cat). Then, we can flip both coins and record the outcome to determine which pets the family has. For example, if the first coin shows heads and the second coin shows tails, the family has one dog and one cat.

After flipping both coins 50 times and recording the outcomes in a table, we can calculate the experimental probability of the family having two dogs or two cats. Let's assume that we observed 12 occurrences of two dogs, 10 occurrences of two cats, and 28 occurrences of other outcomes (e.g., one dog and one cat). The experimental probability of the family having two dogs or two cats is (12 + 10) / 50 = 0.44 or 44%.

If the family has three pets, the theoretical probability of having three dogs or three cats can be calculated using a similar approach. Let's assume that the probability of having a dog is p and the probability of having a cat is q (where p + q = 1). Then, the probability of having three dogs is p x p x p = p^3, and the probability of having three cats is q x q x q = q^3. Therefore, the theoretical probability of having three dogs or three cats is p^3 + q^3.

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Answer:

45.75 mph

Step-by-step explanation:

Let's call Sonya's speed before the rest stop "x" (in miles per hour). Then, we know that her speed after the rest stop was "x-5" miles per hour.

We can use the formula: distance = speed x time, to set up two equations based on the given information:

Equation 1: 170 = x * t1 (where t1 is the time Sonya drove before the rest stop)

Equation 2: 320 = (x-5) * (t1+3) (where t1+3 is the time Sonya drove after the rest stop)

We can solve for t1 in Equation 1 by dividing both sides by x:

t1 = 170/x

Now we can substitute this expression for t1 into Equation 2 and simplify:

320 = (x-5) * (170/x + 3)

320 = 170(x-5)/x + 3(x-5)

Multiplying both sides by x gives:

320x = 170(x-5) + 3x(x-5)

320x = 170x - 850 + 3x^2 - 15x

Simplifying and rearranging terms gives a quadratic equation:

3x^2 - 165x + 850 = 0

We can solve for x using the quadratic formula:

x = [165 ± sqrt(165^2 - 4(3)(850))] / (2*3)

x = [165 ± sqrt(27225 - 10200)] / 6

x = [165 ± sqrt(17025)] / 6

x = [165 ± 130.5] / 6

x = 45.75 or x = 9.25

We can ignore the solution x = 9.25 since it doesn't make sense in the context of the problem (Sonya's speed cannot be negative). Therefore, Sonya's speed before the rest stop was 45.75 miles per hour

A) The present value of the lease payments can be computed as $255,294.44, using the lease period, borrowing rate, and the monthly lease payments in the online finance calculator as parameters.

B) The journal entry for the lease on September 1, 2024 is as follows:

September 1, 2024:

Debit Lease Expense $8,000

Credit Lease Payable $8,000

(To record the lease liability, payable on September 30, 2024.)

The present value of the lease payments can be computed using an online finance calculator as follows:

N (# of periods) = 36 months (3 years x 12)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $8,000

FV (Future Value) = $0

Results:

Present Value (PV) = $255,294.44

Sum of all periodic payments = $288,000.00

Total Interest = $32,705.56

September 1, 2024:

Lease Expense $8,000 Lease Payable $8,000

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Answer:

The two is in the hundredths place

Step-by-step explanation:

369.425

hundreds  tens ones. tenths hundredths thousandths

3                   6      9    .   4             2                   5

The two is in the hundredths place

Answer:

The place value of 2 in 369.425 is hundredths.

The number 369.425 is a decimal number. It has a whole number part (369) and a decimal part (0.425). The decimal part is divided into tenths, hundredths, thousandths, and so on. The 2 is in the hundredths place.

Step-by-step explanation:

There is not enough information to answer the first question.

For the second question, first term = 2, common ratio = 2

A geometric sequence is a set of numbers where each term following the first is obtained by multiplying the term before it by a fixed quantity, called the common ratio. In other terms, a geometric sequence is one in which every term's ratio to the term before it is constant.

We know that;

T5/T3 = 4

T5 =[tex]ar^4[/tex]

T3 = [tex]ar^2[/tex]

Then;

4 = [tex]ar^4/ar^2[/tex]

4 =[tex]r^2[/tex]

r= 2

Again we have that;

T4 = 16

T4 =[tex]ar^3[/tex]

16 = [tex]a(2)^3[/tex]

a = 2

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The sentences in this paragraph best support the idea that the printing press was an important invention A. They provide examples showing the impact of the printing press on varied groups of people.

With the greater availability of books, people were spurred to develop necessary skills in reading, thus resulting in higher literacy rates and a enhanced societal benefit.

Subsequently, due to simpler, more exact shares of data through printing, scientific progress was greatly boosted. Moreover, churches had the chance to further propagate their supernatural ideas with the aid of the printing press.

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The resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise is Triangle A''B''C'' with vertices at (2, 3), (1, 4), and (5, 1).

To find the resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise, we can follow these steps:
1. Draw Triangle ABC and the line y=-x on a coordinate plane.
2. Reflect Triangle ABC across the line y=-x to get its image, Triangle A'B'C'.
3. Draw the image Triangle A'B'C' on the coordinate plane.
4. Rotate Triangle A'B'C' 90 degrees clockwise around the origin to get its final image.
5. Draw the final image of Triangle ABC, which is Triangle A''B''C''.
To find the coordinates of the image points, we can use the transformation rules for reflections and rotations.
First, let's find the image points after reflecting Triangle ABC across the line y=-x:
- The point A(-2, 3) is reflected to the point A'(-3, 2) by swapping the x and y coordinates and changing their signs.
- The point B(4, 1) is reflected to the point B'(-1, -4) by swapping the x and y coordinates and changing their signs.
- The point C(1, 5) is reflected to the point C'(-5, -1) by swapping the x and y coordinates and changing their signs.
Now, let's find the image points after rotating Triangle A'B'C' 90 degrees clockwise around the origin:
- To rotate a point (x, y) 90 degrees clockwise around the origin, we can use the formulas (-y, x).
- Applying this formula to each image point, we get:
 - A''(2, 3)
 - B''(1, 4)
 - C''(5, 1)
Therefore, the resulting image of Triangle ABC after reflecting it across the line y=-x and rotating it 90 degrees clockwise is Triangle A''B''C'' with vertices at (2, 3), (1, 4), and (5, 1).

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The equation of L2 is y = 2x/3 + 23/3.

The equation of L3 is y = -3x/2 - 7.

The equation of L2 in standard form is 2x/3 - y = -23/3.

The x and y intercepts of L3 are (-4.667, 0) and (0, -7) respectively.

The point of intersection between L2 and L3 is (-6.769, 3.154).

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about line 1 (L1) and line 2 (L2), we have the following equation;

Equation of line 1 (L1): 3x + 2y = 12

y = -3x/2 + 12

Since line L2 is perpendicular to L1 at (2, 9) and a slope of 2/3, the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y - 9 = 2/3(x - 2)

y = 2x/3 + 23/3

Since L3 is parallel to L1 and passes through point (-4, -1), the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y + 1 = -3/2(x + 4)

y = -3x/2 - 6 - 1

y = -3x/2 - 7

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The solutions to the equations are;   x = = √5+3 and x= -√5 + 3

The given equation is 4x²2²-12x+9=5

we get, 4x²2²-12x+9=5

Dividing both sides by 25, we get

4x²2²-12x= -4

Taking square root on both sides, we get

x= -√5 + 3

x =  √5+3

Therefore,  x = = √5+3 and x= -√5 + 3

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The customer would pay a net price of $760 per item after all discounts have been applied. It's important to note that the Actual discount percentage and net price per item may vary depending on the terms of the sale and the specific furniture center's policies.

Furniture centers often offer trade discounts to their customers to encourage orders. A trade discount is a reduction in the listed price of a product or service that is offered to trade customers, such as retailers, wholesalers, or other businesses. The discount is usually a percentage of the list price, and the actual amount of the discount depends on the quantity of the product ordered and the terms of the sale.

In addition to trade discounts, furniture centers may offer additional discounts to their customers who meet certain criteria. For example, they may offer a percentage discount for orders over a certain amount or for customers who pay in full at the time of purchase. These additional discounts are intended to encourage customers to place larger orders and to reward them for their loyalty to the furniture center.

To calculate the net price per item, you need to know the list price of the item, the trade discount percentage, and any additional discounts that may apply. For example, let's say that the list price of a piece of furniture is $1,000, and the trade discount offered by the furniture center is 20%. If the customer's invoice total is high enough to qualify for an additional discount of 5%, the net price per item would be calculated as follows:

List price: $1,000

Trade discount: 20% x $1,000 = $200

Price after trade discount: $1,000 - $200 = $800

Additional discount: 5% x $800 = $40

Net price per item: $800 - $40 = $760

So, the customer would pay a net price of $760 per item after all discounts have been applied. It's important to note that the actual discount percentage and net price per item may vary depending on the terms of the sale and the specific furniture center's policies.

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The fixed cost per ball went to $4.5 when the company produce 22,500.

fixed cost per ball is three dollars when the company produces 15,000

fixed cost per ball went x to produce 22,500

So,

3 : 15000 = x : 22,500

3/15,000 = x/22,0/500

cross product

3 × 22,500 = 15,000 × x

67,500 = 15,000x

divide both sides by 15,000

x = 67,500 /15,000

x = 4.5

Therefore, the fixed cost per ball to produce 22,500 is $4.5

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If bought a variety of fruits to bring to a party, the probability that Johnny chooses an apple or a pear after making a random selection from the bag is 0.066 or 6.6%.

The probability that Johnny chooses an apple or a pearl is the chance that either an apple or a pearl is chosen from the 50 pieces of fruits, which is determined by the multiplication of the two probabilities.

Probability refers to the likelihood of achieving an expected outcome or result amid the possibility of many outcomes.

Fruits      Units

Bananas   24

Apples      15

Pear           11

Total        50

The Probability of choosing a banana = 0.48 (24 ÷ 50)

The chance of choosing an apple = 0.3 (15 ÷ 50)

The likelihood of choosing a pear = 0.22(11 ÷ 50)

The probability of choosing an apple or a pear = 0.066 (0.3 x 0.22)

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Answer: 4+9=10+3

Step-by-step explanation:

We can subtract the number, 4 to get 3. The extra one from the 4 would go to the nine.

a) A table and a graph for this situation is shown in the image below.

b) You can use the table or graph to predict how many weeks it will take Martha to earn enough money to pay for the new computer by comparing the week when her savings are both equal.

c) Since the x-value and y-value in both the table and the graph increase simultaneously, it is an example of linear growth.

In this scenario, the variable x would represent the number of weeks while the variable y would represent the total amount of savings. Since Martha received $200 for her birthday and makes $150 each week, a linear equation in slope-intercept form that models the situation is given by;

y = mx + c

y = 150x + 200

Next, we would use an online graphing calculator to make a table and a graph for this situation as shown in the image attached below.

Part b.

The table and the graph both have the total amount of savings (y) equal to $1,850 when x is equal to 11 weeks. This ultimately implies that, it would take Martha between 11 weeks to save enough money to buy this new computer.

Part c.

By critically observing the table and the graph, we can logically deduce that there is a linear relationship between the variables because both the x-value and y-value increase simultaneously.

Therefore, this is an example of a linear growth.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

450 cm in meter is 4.5 meters

Step-by-step explanation:

450cm = 4.5m

The derivative of [tex]f(x) = \sinh{(7e^x + 2)}[/tex] is given as follows:

B. [tex]7e^x\cosh{(7e^x + 2)}[/tex]

The function in this problem is given as follows:

[tex]f(x) = \sinh{(7e^x + 2)}[/tex]

This function is a composite function, hence we use the chain rule for derivatives, which state that:

If f(x) = f(g(x)) then f'(x) = g'(x)f'(g(x)).

The inner and outer functions are given as follows:

The derivative of the hyperbolic sine is given as follows:

cosh(x).

(derivative of the outer function).

The derivative of the exponential is given as follows:

[tex](7e^x + 2)^{\prime} = 7e^x[/tex]

(derivative of the inner function).

Hence the derivative of the function is given as follows:

[tex]7e^x\cosh{(7e^x + 2)}[/tex]

(application of the chain rule).

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The equation of the line that passes through the points (-2, 4) and (3, 9) is y = x + 6.To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) using the given points (-2, 4) and (3, 9).

First, let's find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the values from the points:

m = (9 - 4) / (3 - (-2)) = 5 / 5 = 1

Now that we have the slope, we can proceed to find the y-intercept (b). We can choose either of the given points to substitute into the equation.

Using the point (-2, 4):

4 = 1(-2) + b

4 = -2 + b

b = 6

Therefore, the y-intercept (b) is 6.Now we have the slope (m = 1) and the y-intercept (b = 6), so the equation of the line in slope-intercept form is:

y = x + 6.

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The smallest angle that is in the triangle STU is 9 degrees.

A triangle can be solved by using information provided to determine the triangle's unknown side lengths and angles. Depending on the information at hand, a triangle can be solved in a variety of ways as we see here.

To find the side u

[tex]u^2 = (41b)^2 + (44b)^2 - 2(41b * 44b)Cos 128\\u^2 = 1681b^2 + 1936b^2 - 3608b^2Cos 128\\u^2 = 3617b^2 - 2221b^2\\u^2 = 1396b^2[/tex]

u = 37b

Then Using the sine rule;

a/Sin A = b/Sin B

37b/Sin 128 = 41b/SinB

B = sin-1 (41b * Sin 128/37b)

B = 61 degrees

Then;

C = 180 - (128 + 61)

C = 9 degrees

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