What is the area of the
parallelogram?

The original number is 63.

Now, the tens digit of the original number "x", and the ones digit "y".

We know that the product of the digits is 18,

So, we can write an equation:

xy = 18

We also know that if we reverse the digits, we get a number that is 27 more than the original number.

We can write another equation:

10y + x + 27 = 10x + y

Simplifying this equation, we get:

9x - 9y = 27

Dividing both sides by 9, we get:

x - y = 3

Now we have two equations:

xy = 18

x - y = 3

We can use substitution to solve for x and y. Solving for y in the second equation, we get:

y = x - 3

Substituting this into the first equation, we get:

x(x-3) = 18

Expanding the left side:

x - 3x = 18

x - 3x - 18 = 0

Factoring the left side:

(x-6)(x+3) = 0

So x can be either 6 or -3, but since we are dealing with digits, x must be 6.

Substituting x=6 into the equation y=x-3, we get

y=3.

Therefore, the original number is 63.

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A rectangular prism with a volume of 448 cubic centimeters has a height of 7 centimeters and a length and width of 8 centimeters.

To solve this problem, we need to use the formula for the volume of a rectangular prism, which is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

We are given that the volume of the rectangular prism is 448 cubic centimeters, and the height is 7 centimeters. We also know that the length is equal to the width. Let's call the length and width x.

Substituting the given values into the formula, we get:

448 = x * x * 7

Simplifying this equation, we get:

448 = 7x^2

Dividing both sides by 7, we get:

64 = x^2

Taking the square root of both sides, we get:

x = 8

Therefore, the length and width of the rectangular prism are both 8 centimeters.

To check our work, we can substitute these values back into the formula for the volume:

V = lwh = 8 * 8 * 7 = 448 cubic centimeters

Therefore, our solution is correct.

In summary, we found that a rectangular prism with a volume of 448 cubic centimeters has a height of 7 centimeters and a length and width of 8 centimeters.

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Let's start by finding out how much money Tim will save over the three months:

$45.06 x 3 = $135.18

To find out how much Tom needs to earn each month, we can subtract Tim's savings from the total amount they need:

$210.51 - $135.18 = $75.33

So, Tom needs to earn $75.33 each month for three months to reach their goal of buying the game system.

Answer:

$25.11

Step-by-step explanation:

Tim's savings = 3 x 45.06 = 135.18

The total needed is 210.51.

So subtract what Tim is saving ($135.18) to see what the remainder is.

210.51 - 135.18 = 75.33.

Tom needs to save $75.33 over 3 months. So divide 75.33 by 3.

75.33 / 3 = $25.11.

Check: $25.11 x 3 = 75.33 >>> That's Tom's savings

45.06 x 3 = 135.18 >>> That's Tim's savings

Add them up

75.33 + 138.18 = 210.51

The volume of the triangular prism is 140 cubic units.

To do this, we'll use the formula:

Volume = (Base Area) × Height.

The terms in your question (8, 7, and 5) represent the base, height of the triangular base, and height of the prism, respectively.

Find the base area of the triangle.
Base Area = (1/2) × base × height of triangular base = (1/2) × 8 × 7
Calculate the base area.
Base Area = (1/2) × 8 × 7 = 28
Find the volume of the triangular prism.
Volume = Base Area × Height of the prism = 28 × 5
Calculate the volume.
Volume = 28 × 5 = 140

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Answer:

0.165

Step-by-step explanation:

P(A∩B) =  P(A) × P(B)

=  .33 × 0.5

=  0.165

Answer:

  0.17

Step-by-step explanation:

You want the probability of a 1 or 6 on the first die, and an odd number on the second die when two dice are tossed.

The joint probability is the product of the probabilities of these independent events. The probability of a 1 or 6 is 2/6 = 1/3. There are 3 odd numbers, so the probability of an odd number is 3/6 = 1/2.

The probability both events will occur is ...

  P(A and B) = (1/3)(1/2) = 1/6

  P(A and B) ≈ 0.17

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Answer:

Step-by-step explanation:

To determine the surface area of a rectangular prism, we need the dimensions of the prism. Without the dimensions, I cannot provide a specific surface area.

However, I can explain the formula to calculate the surface area of a rectangular prism. The surface area of a rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh,

where l, w, and h represent the length, width, and height of the rectangular prism, respectively.

Once you have the dimensions of the prism, you can substitute them into the formula and calculate the surface area.

The probability of P(A or B) will be 0.68.

The given are the probabilities of two events A and B occurring, therefore, P(A) = 0.32 and P(B) = 0.48, respectively.

Also, the probability of both events occurring simultaneously is given as P(A and B) =0.12.

Therefore, the probability of P(A or B) can be written as,

P(A or B) = P(A) + P(B) - P(A and B)

Substitute the values in the above equation,

P(A or B) = 0.32 + 0.48 - 0.12

P(A or B) = 0.68

Therefore, the probability is 0.68.

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Answer:

Step-by-step explanation:

324/3=108

and the other one is

300 divided by 20  divided by 40 divided by 3

A sample from a population, the goal is to use that sample to make inferences about the population as a whole. The sample statistics that from the sample can be used to estimate the population Parameters.

A sample from a population, the goal is to use that sample to make inferences about the population as a whole. The sample statistics that you calculate from the sample can be used to estimate the population parameters. Here are some sample statistics and the population parameters that they may estimate:

Sample mean: The sample mean is calculated by adding up all the values in the sample and dividing by the number of observations. It is a measure of central tendency that can be used to estimate the population mean.

Sample variance: The sample variance is a measure of how spread out the data is in the sample. It is calculated by subtracting each data point from the sample mean, squaring the result, adding up all the squared differences, and dividing by the sample size minus 1. It can be used to estimate the population variance.

Sample proportion: The sample proportion is the number of observations in the sample with a certain characteristic (e.g. the number of people who prefer coffee over tea) divided by the total sample size. It can be used to estimate the population proportion.

Standard error: The standard error is a measure of the variability of the sample statistic (e.g. the sample mean) across multiple samples. It can be used to estimate the variability of the population parameter (e.g. the population mean) across multiple samples.

Confidence interval: A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence (e.g. 95%). It is calculated using the sample statistic (e.g. the sample mean) and the standard error, and it can be used to estimate the population parameter.

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The two solutions that are viable that relate the tickets purchased and the total cost for attending the play are:

C. The total cost for 2 people to attend the play is $20.

D. The total cost for 10 people to attend the play is $52.

Based on the information provided, the total cost of attending a play when the tickets costs $4 per person, and there is a $12 fee for parking  fee, a linear equation to model the situation is given by;

y = 4x + 12

When x = 5 people, the total cost is given by;

y = 4(5) + 12

y = $32.

When x = 6 people, the total cost is given by;

y = 4(6) + 12

y = $36.

When x = 2 people, the total cost is given by;

y = 4(2) + 12

y = $20.

When x = 10 people, the total cost is given by;

y = 4(10) + 12

y = $52.

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Complete Question;

The linear constraint y = 4x + 12 represents the cost of attending a play at which tickets costs $4 per person, and there is a $12 fee for parking.

Which of the following solutions are viable that relate the tickets purchased and the total cost for attending the play. Select the Two answers

The total cost for 5 people to attend the play is $32.

The total cost for 6 people to attend the play is $24.

The total cost for 2 people to attend the play is $20.

The total cost for 10 people to attend the play is $52.

The total cost for 15 people to attend the play is $100.

Answer:

cost of one hamburger = $2.00; cost of one hot dog = $1.75

Step-by-step explanation:

We can use a system of equations to find the cost of hot dog (represented by the variable, h) and the cost of one hamburger (represented by the variable, b)

We know that:

Thus, our two equations are 7h + 2b = 16.25 and 2h + 7b = 17.50.

Method:  

[tex]2(7h+2b=16.25)\\-7(2h+7b=17.50)\\\\14h+4b=32.50\\-14h-49b=-122.50\\\\-45b=-90\\b=2[/tex]

[tex]7h+2(2)=16.25\\7h+4=16.25\\7h=12.25\\h=1.75[/tex]

Optional Step:  We can check that our answers are correct by plugging in 2 for b and 1.75 for h in both equations and see whether we get 16.25 for the first equation and 17.50 for the second equation.

Checking solutions for first equation:

[tex]7(1.75)+2(2)=16.25\\12.25+4=16.25\\16.25=16.25[/tex]

Checking solutions for second equation:

[tex]2(1.75)+7(2)=17.50\\3.50+14=17.50\\17.50=17.50[/tex]

Answer:

d. 119

Step-by-step explanation:

To solve this problem, we first need to find the cutoff score for the mathematics tutoring program.

One standard deviation above the mean is equal to:

68 + 1(7.2) = 75.2

Therefore, students scoring higher than 75.2 will not be enrolled in the mathematics tutoring program.

Next, we need to find the proportion of students who score lower than 75.2. To do this, we can use the standard normal distribution table or a calculator to find the z-score corresponding to a score of 75.2:

z = (x - μ) / σ = (75.2 - 68) / 7.2 = 1.022

Using the standard normal distribution table or a calculator, we can find that the proportion of students scoring lower than a z-score of 1.022 is approximately 0.8461.

Therefore, the proportion of students scoring higher than 75.2 is:

1 - 0.8461 = 0.1539

To find the number of students out of 750 who can be expected to be enrolled in the mathematics tutoring program, we can multiply the proportion by the total number of students:

0.1539 x 750 ≈ 115

Therefore, the answer is approximately 115 students, which is closest to option (d) 119.

Answer:

Step-by-step explanation:

[tex]A (t)=\int\frac{t}{1+t^2} dt+c\\=\frac{1}{2} \int \frac{2t}{1+t^2} dt+c\\=\frac{1}{2}\ln(1+t^2)+c\\A(4)=\frac{1}{2}\ln(1+4^2)+c\\30=\frac{1}{2}\ln(17)+c\\c=30-0.5 \ln17\\A(t)=0.5\ln(1+t^2)-0.5\ln17+30\\A(2)=0.5\ln(1+2^2)-0.5 \ln17+30\\A(2)=0.5(\ln 5-\ln 17)+30\\A(2)=0.5\ln (\frac{5}{17} )+30[/tex]

The graph of U + V + W vectors is attached accordingly.

A vector is a number or phenomena with two distinct properties: magnitude and direction. The word can also refer to a quantity's mathematical or geometrical representation.

From the question,

U = (1,5), iV = (-3, 1) and W = (4, -3)

Thus, U + V + W = (1-3+4, 5+1-3)

= (2, 3)

Hence, the attached graph.

Note that In nature, vectors include velocity, momentum, force, electromagnetic fields, and weight.

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Te new matrix after performing the row operation is

[tex]\left[\begin{array}{cc}10&35&-2&-9\\5&5&-5&9\end{array}\right][/tex]

From the question, we have the following parameters that can be used in our computation:

[tex]\left[\begin{array}{cc}-2&-7&-2&-9\\5&5&-5&9\end{array}\right][/tex]

The row operation on the matrix is given as

-5R1 ⇒ R1

This means that we multiply the first row by -5 and then replace the first row with the result

Using the above as a guide, we have the following:

New first row =  (-2  -7) * -5

Evaluate

New first row =  (10  35)

Recall that

[tex]\left[\begin{array}{cc}-2&-7&-2&-9\\5&5&-5&9\end{array}\right][/tex]

So, we have

[tex]\left[\begin{array}{cc}10&35&-2&-9\\5&5&-5&9\end{array}\right][/tex]

Hence, the new matrix after performing the row operation is

[tex]\left[\begin{array}{cc}10&35&-2&-9\\5&5&-5&9\end{array}\right][/tex]

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Answer:

B. y= -1/5x + 1

Step-by-step explanation:

First, I found out that the slope is moving downwards (left to right) that means that the slope is negative. So I crossed out answers C & D. Then, I looked at the slope for answer A and compared it to the graph and the shlope in the graph looks like it didn't go -5/1 (rise/run). Therefore, answer B is correct.

Hope that helps.

Answer:

0.17

Step-by-step explanation:

area of square = 6*6 = 36

area of triangle is (bh)/2 = (4*3)/2=(12)/2=6

6/36 =1/6 = 0.1666666666666 which rounded to the nearest hundredth is 0.17

The ladder reaches 6 feet, 8.49 feet, and 10.39 feet up the wall at angles of 30°, 45°, and 60°, respectively.

Let the height of the ladder on the wall as "h."

At a 30° angle:

Using Trigonometry

sin(30°) = h/12

h = 12 * sin(30°)

h ≈ 6 feet

At a 45° angle:

Using Trigonometry

sin(45°) = h/12

h = 12 * sin(45°)

h ≈ 8.49 feet

At a 60° angle:

Using Trigonometry

sin(60°) = h/12

h = 12 * sin(60°)

h ≈ 10.39 feet

Therefore, the ladder reaches 6 feet, 8.49 feet, and 10.39 feet up the wall at angles of 30°, 45°, and 60°, respectively.

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Freddie the frog must have been asleep for 5 nights.

Let's analyze Freddie's progress day by day:

On each day, Freddie climbs up 3 m, and on each night, he slips back 4 m. This means that his net progress each day is -1 m.

Let's denote the number of nights Freddie was asleep as n.

On the 16th day, Freddie's total progress is 29 m. Since his net progress each day is -1 m, we can set up the equation:

16(3 m) + n(-4 m) = 29 m

48 m - 4n m = 29 m

Now, let's solve for n:

48 m - 29 m = 4n m

19 m = 4n m

n = 19 m / 4 m

n ≈ 4.75

Since n represents the number of nights Freddie was asleep, it can only be a whole number. We cannot have a fraction of a night. Therefore, we can round n up to 5.

In other words, Freddie was asleep for 5 nights.

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The formula for calculating distance that Ben covered will be [tex]500 m/minute * Time.[/tex]

The distance between 2 points in physical space is the length of a straight line between them.

In physics and math, to calculate the distance covered by Ben while cycling, we can use the formula for distance which is: Distance = Speed × Time.

Given:

Ben cycles at average speed of 500 m/minute.

We will substitute the values into the formula which is:

Distance = 500 m/minute × Time.

Therefore, the formula for calculating distance that Ben covered will be [tex]500 m/minute * Time.[/tex]

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The completed frequency tree is:

The ratio in its simplest form is 28:25.

b) The ratio of people who played volleyball and had a sandwich to people who neither played volleyball nor had a sandwich is:

28 / (X + Y)

7 people who did not play volleyball also did not have a sandwich. So Y must be 7, and X must be the remaining number of people who did not play volleyball and did have a sandwich:

X = 25 - Y = 25 - 7 = 18

Thus, the ratio simplifies to:

28 / (18 + 7) = 28 / 25

So the ratio is 28:25.

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Answer:

Step-by-step explanation:

1

Answer:

19.63

Step-by-step explanation:

area = [tex]\pi r^{2}[/tex]

where r is the radius.

The diameter is double the radius.

So divide the diameter by 2 to find the radius.

5/2 = 2.5

Now plug into the area formula and solve.

area = [tex]\pi 2.5^{2}[/tex]

area =6.25 [tex]\pi[/tex]

area = 19.6349540849

The problem didn't say anything about what to round to. If you round to the hundredths place, this would be 19.63.

To find the surface area of the new prism after reducing it by a scale factor of 1/4, we need to apply the scale factor to the surface area of the original prism.

Let's denote the surface area of the new prism as A_new and the surface area of the original prism as A_original.

We know that the scale factor is 1/4, which means the new dimensions are 1/4 of the original dimensions. Since the surface area is affected by the square of the scale factor, we can set up the following equation:

A_new = (1/4)^2 * A_original

Given that the surface area of the original prism is 526ft, we can substitute this value into the equation:

A_new = (1/4)^2 * 526

A_new = (1/16) * 526

A_new = 32.875 ft^2

Therefore, the surface area of the new prism after reducing it by a scale factor of 1/4 is 32.875 square feet.

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Answerb:

Step-by-step explanation:

Answer:

About 25 years.

The shortest route from:

To find the shortest routes between the training camps we can use an algorithm, like Dijkstra's algorithm to calculate the distance.

We calculate for each of the routes:

1. From Feline to Bovine:

Feline -> Thirty-Nine -> Bovine

Total distance: 6 + 1 + 9 = 16 miles

2. From Lupine to Thirty-Nine:

Lupine -> Canine -> Thirty-Nine

Total distance: 3 + 7 + 1 = 11 miles

3. From Canine to Feline:

Canine -> Thirty-Nine -> Feline

Total distance: 1 + 6 + 11 = 18 miles

4. From Arachnid to Lupine:

Arachnid -> Thirty-Nine -> Feline -> Lupine

Total distance: 1 + 6 + 11 + 11 = 29 miles

5. From Canine to Thirty-Nine:

Canine -> Thirty-Nine

Total distance: 1 mile

6. Shortest route from Lupine to Bovine:

Lupine -> Canine -> Bovine

Total distance: 3 + 7 + 7 = 17 miles

7. From Arachnid to Feline:

Arachnid -> Thirty-Nine -> Feline

Total distance: 1 + 6 = 7 miles

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