A triangular prism is 36 millimeters long and has a triangular face with a base of 36 millimeters and a height of 24 millimeters. The other two sides of the triangle are each 30 millimeters. What is the surface area of the triangular prism?

Answers

Answer 1

The surface area of the triangular prism is

5752 square millimeters

How to find the surface area of the triangular prism

The surface area of the triangular prism is

= area of the two side rectangles + area of the base rectangles + area of the 2 triangles

= 2 * 36 * 30 + 36 * 36 + 2 * 1/2 * 36 * 24

= 2160 + 1296 + 1296

= 5752 square millimeters

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Related Questions

A bag has 6 red marbles, 3 blue marbles, and 1 orange marble. In a game to raise money for a class trip, parents pay $5 and pull a marble randomly from the bag. The payout is $10 for pulling an orange marble, $4 for a blue marble, and $1 for a red marble. How much can the class expect to earn per game?

Answers

There are 6 red marbles.
There are 3 blue marbles.
There is 1 orange marble.

To pull a marble from the bag you have to pay $5.

Payout for an orange marble is $10.
Payout for a blue marble is $4.
Payout for a red marble is $1.


Total amount of marbles= 6+3+1
=10.

Multiply the amount of marbles by the amount required to pull a marble
$5^10=$50


Multiply the amount of marbles for each color by the payout.

Red Marbles: 6^1=6
Blue Marbles: 3^4=12
Orange Marbles: 1^10=10

Add the total
$6+$12+$10=$28

Subtract from the $28 from the $50
28-50=22

Therefore, the class can expect to earn approximately $22 per game

12 less than the product of 3 and a number, x, is at most -18

Answers

The given inequality is 3x - 12 ≤ -18. To solve for x, we can add 12 to both sides of the inequality to obtain 3x ≤ -6. Then, dividing both sides of the inequality by 3 gives x ≤ -2. Therefore, any value of x less than or equal to -2 will satisfy the inequality.

In solving the inequality, we first used the addition property of inequalities to add 12 to both sides of the inequality. This property states that if a < b, then a + c < b + c, where c is any real number. By adding 12 to both sides, we were able to isolate the variable term on one side of the inequality.

Next, we used the division property of inequalities to divide both sides of the inequality by 3. This property states that if a < b and c > 0, then a/c < b/c. By dividing both sides of the inequality by 3, we were able to solve for x.

Finally, we found that any value of x less than or equal to -2 will satisfy the inequality. This means that the solution set for the inequality is {x | x ≤ -2}. We also verified that x = -2 is a valid solution to the inequality, which confirms our solution.

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Hydrologists sometimes use Manning's equation to calculate the velocity v, in feet per second, of water flowing through a pipe. The velocity depends on the hydraulic radius R in feet, which is one-quarter of the diameter of the pipe when the pipe a flowing full; the slope S of the pipe, which gives the vertical drop in foot for each horizontal foot; and the roughness coefficient n, which depends on the material of which the pipe is made. The relationship is given by the following. v = 1.486/n R^2/3 S^1/2 For a certain brass pipe, the roughness coefficient has been measured to be n = 0.014. The pipe has a diameter of 3 feet and a slope of 0.4 foot per foot. (That is, the pipe drops 0.4 foot for each horizontal foot.) If the pipe is flowing full, find the hydraulic radius of the pipe. () Find the velocity of the water flowing through the pipe. ()

Answers

The velocity of the water flowing through the pipe is approximately 7.83 feet per second. The hydraulic radius of the pipe can be calculated as follows:

R = d/4

where d is the diameter of the pipe. In this case, the diameter is 3 feet, so the hydraulic radius is:

R = 3/4 = 0.75 feet

Now, we can use the given formula to calculate the velocity of the water:

[tex]v =[/tex][tex]1.486/n[/tex] [tex]R^(2/3) S^(1/2)[/tex]

Substituting the given values, we get:

v = 1.486/0.014 (0.75[tex])^(2/3)[/tex] (0.4[tex])^(1/2)[/tex] ≈ 7.83 feet per second

Therefore, the velocity of the water flowing through the pipe is approximately 7.83 feet per second.

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About 8 out of 10 people entering a community college need to take a refresher mathematics course. if there
are 850 entering students, how many will probably need a refresher mathematics course?

Answers

Approximately 680 out of the 850 entering students will probably need to take a refresher mathematics course which is calculated using simplified fraction.

We are given that about 8 out of 10 people entering a community college need to take a refresher mathematics course. We need to find out how many of the 850 entering students will probably need this course.

Step 1: Determine the proportion of students who need the refresher course.
The proportion is 8 out of 10, which can be written as a fraction: 8/10.

Step 2: Simplify the fraction.
Divide both the numerator (8) and the denominator (10) by their greatest common divisor, which is 2:
8 ÷ 2 = 4
10 ÷ 2 = 5
So, the simplified fraction is 4/5.

Step 3: Calculate the number of students who need the refresher course.
To find the number of students who probably need the course, multiply the total number of entering students (850) by the simplified fraction (4/5):
850 * (4/5) = (850 * 4) / 5 = 3400 / 5 = 680

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 the measures of the angles of a triangle are shown in the figure below solve for X

Answers

Answer:

x = 13

Step-by-step explanation:

We Know

The sum of angles of a triangle must add up to 180°

We know 2 angles, one is 60° and the other is 90°

Solve for x.

Let's solve

3x - 9 + 60 + 90 = 180

3x + 141 = 180

3x = 39

x = 13

given the expression, (n⁵)⁶ what will exponent be in the simplified exponential form?

Answers

The expression given in a simplified form is n³⁰

What are index forms?

Index forms are described as those mathematical forms that are used to write numbers that are too large or small in more convenient forms.

They are also expressed as a number or variable that is raised to an exponents.

Index forms are also referred to as standard forms or scientific notations.

Following the rules of index forms, we have that;

Add the exponent with like bases and are being multipliedIn expanding the bracket, also multiply the exponents

From the information given, we have that;

(n⁵)⁶

Multiply the exponents

n³⁰

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An eighth-grade student estimated that she needs $9,500 for tuition and fees for each year of college. She already has $5,000 in a savings account. The table shows the projected future value of the account in five years based on different monthly deposits. Initial Balance (dollars) $5,000 $5,000 $5,000 $5,000 Monthly Deposit (dollars) $100 $200 $300 $400 Account Value in Five Years (dollars) $11,000 $17,000 $23,000 $29,000 Problem The student wants to have enough money saved in four years to pay the tuition and fees for her first two years of college. Based on the table, what is the minimum amount she should deposit in the savings account every month? A $200 B $100 C $300 D $400

Answers

$23,000 is more than the $19,000 needed for tuition and fees for the first two years, the minimum amount the student should deposit in the savings account every month is $300 (option C).

What is the account value in five years with a monthly deposit of $300?

The minimum monthly deposit the student should make in order to save enough money for her first two years of college tuition and fees in four years, we need to calculate how much she would need to have in her savings account at the end of four years.

Since the student estimated she needs $9,500 per year for tuition and fees, she will need $19,000 for her first two years. Since she already has $5,000 in her savings account, she needs to save an additional $14,000 in four years.

Looking at the table, we can see that the account value in five years with a monthly deposit of $200 is $17,000. To find out how much the account value would be in four years, we need to calculate the future value of $17,000 with a 4-year time frame and an annual interest rate of 0%, which gives:

Future value = $17,000 x (1 + 0%)^(4 x 12/12) = $17,000

Since the account value with a $200 monthly deposit is only $17,000 after 5 years, which is not enough to cover the $19,000 needed for tuition and fees for the first two years, the student needs to make a higher monthly deposit.

Looking at the table again, we can see that the account value in five years with a monthly deposit of $300 is $23,000. To find out how much the account value would be in four years, we need to calculate the future value of $23,000 with a 4-year time frame and an annual interest rate of 0%, which gives:

Future value = $23,000 x (1 + 0%)^(4 x 12/12) = $23,000

$23,000 is more than the $19,000 needed for tuition and fees for the first two years, the minimum amount the student should deposit in the savings account every month is $300 (option C).

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The Louvre is an art museum in Paris. A glass square base pyramid sits in front of the entrance to the museum. If the pyramid is 35 meters wide at the base and 20. 6 meters tall, what was the minimum amount of glass needed to construct the pyramid?

Answers

The minimum amount of glass needed to construct the Louvre pyramid is approximately 3133 square meters.

What is the minimum amount of glass needed to construct the glass pyramid in front of the Louvre museum in Paris, if the pyramid is 35 meters wide at the base and 20.6 meters tall?

The surface area of a square base pyramid can be calculated by adding the area of the base to the sum of the areas of the four triangular faces.

The area of the square base is simply the width of the base squared:

Area_base = (35 m)^2 = 1225 square meters

The area of each triangular face can be calculated using the formula:

Area_triangle = (1/2) * base * height

For the Louvre pyramid, the base of each triangular face is equal to the width of the base of the pyramid, which is 35 meters. The height of each triangular face can be found using the Pythagorean theorem:

[tex]height^2 = (1/2 * width)^2 + height^2[/tex]

[tex]height = sqrt((1/2 * 35 m)^2 + (20.6 m)^2)[/tex]

height = 29.2 m

Therefore, the area of each triangular face is:

Area_triangle = (1/2) * (35 m) * (29.2 m) = 508.5 square meters

The total surface area of the pyramid is:

Surface_area = Area_base + 4 * Area_triangle

Surface_area = 1225 + 4 * 508.5

Surface_area = 3133 square meters

Since the pyramid is made of glass, we need to calculate the minimum amount of glass needed to construct it. Assuming the glass is thin and flat, we can simply use the surface area of the pyramid to estimate the amount of glass needed.

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Please help asap I need this until tmr

Answers

The following table shows the weight of a cat in pounds and the corresponding number of cans of cat food to be given each day.

To complete the table, we need to use the information that the directions on the small cans of cat food say to feed a cat 1 can of food each day for every 4 pounds of body weight.

For example, for a cat weighing 4 pounds, we need to give 1 can of food each day.

For a cat weighing 5 pounds, we need to give more than 1 can but less than 2 cans of food each day.

To find the exact number of cans, we can use the formula:

cans per day = weight in pounds / 4

Substituting the given values, we get:

cans per day = 5 / 4

cans per day = 1.25

Therefore, for a cat weighing 5 pounds, we need to give 1.25 cans of food each day. We can round this to the nearest tenth to get 1.3 cans per day.

Similarly, we can use the formula to complete the rest of the table:

KIT-E-KAT weight in pounds cans per day

4   1

5   1.3

6   1.5

7   1.8

8   2

9   2.3

10  2.5

11   2.8

12  3

13  3.3

14  3.5

15  3.8

Therefore, the completed table shows the weight of a cat in pounds and the corresponding number of cans of cat food to be given each day.

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In ΔEFG, g = 5. 2 cm, e = 5. 1 cm and ∠F=42°. Find the area of ΔEFG, to the nearest 10th of a square centimeter

Answers

The area of ΔEFG is approximately 6.7 square centimeters.

To find the area of ΔEFG with given sides g = 5.2 cm, e = 5.1 cm, and ∠F = 42°, you can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:

Area = (1/2)ab * sin(C)

In this case, a = g, b = e, and C = ∠F. Plug in the values:

Area = (1/2)(5.2 cm)(5.1 cm) * sin(42°)

Area ≈ 6.675 square centimeters

So, the area of ΔEFG is approximately 6.7 square centimeters to the nearest 10th of a square centimeter.

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Assume that a procedure yields a binomial distribution with n trials and a probability of success of p. use a binomial probability table to find the probability that the number of successes x is exactly .

Answers

To find the probability that the number of successes x is exactly a certain value in a binomial distribution with n trials and a probability of success of p, we can use a binomial probability table. The table will provide us with the probability of getting x successes out of n trials, given a specific value of p.

For example, let's say we want to find the probability of getting exactly 3 successes in a binomial distribution with 10 trials and a probability of success of 0.5. We can use a binomial probability table to find the probability of getting exactly 3 successes, which is 0.117.

It is important to note that the probability of getting a specific number of successes in a binomial distribution is dependent on both the number of trials and the probability of success. Therefore, if we change either of these values, the probability of getting a certain number of successes will also change.

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which of the following becomes key indicator of whether or not a hypothesis can be supported? a. chi-square b. degrees of freedom c. significance level d. critical value

Answers

The significance level is the key indicator of whether or not a hypothesis can be supported. (option c)

In statistical analysis, there are several key indicators that are used to determine whether a hypothesis can be supported. One of these indicators is the significance level, which is denoted by the symbol alpha (α).

Another key indicator is the critical value, which is a value that is determined from a statistical distribution and is used to determine whether the observed data is statistically significant.

The test compares the observed frequencies of the categories to the expected frequencies, assuming that there is no association between the variables. The degrees of freedom refer to the number of categories minus one.

Therefore, to answer the original question, option (c)

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a professor gives his students 6 essay questions to prepare for an exam. only 4 of the questions will actually appear on the exam. how many different exams are possible?

Answers

The different possible exams for the 6 essay questions from which only 4 appear is equal to 15.

n is the total number of items in the set = 6 essay questions

r is the number of items we want to choose = 4 questions

Using combinations,

which is a way of counting the number of ways to choose a certain number of items from a larger set without regard to order.

Choose 4 out of the 6 essay questions, without regard to the order in which they appear on the exam.

Use the formula for combinations,

C(n, r) = n! / (r! × (n - r)!)

Plugging in the values, we get,

⇒C(6, 4) = 6! / (4! × (6 - 4)!)

⇒C(6, 4) = 6! / (4! ×2!)

⇒C(6, 4) = (6 × 5 × 4 × 3) / (4 × 3 × 2 × 1)

⇒C(6, 4) = 15

Therefore, there are 15 different exams possible, each consisting of 4 out of the 6 essay questions provided by the professor.

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The table shows the

average rainfall, in inches, in Miami for each

of the first six months of 2020. Write ordered

pairs for the data in the table

Answers

The ordered pairs for the data in the table include the following:

(1, 2.09)(2, 2.42)(3, 3.00)(4, 3.20)(5, 4.98)(6, 8.27)

What is an ordered pair?

In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the table shown in the image attached below, we can reasonably infer and logically deduce that all of the coordinate points or ordered pairs would be located in quadrant 1.

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Missing information:

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

find cif a = 2.74 mi, b = 3.18 mi and ZC = 41.9°. Enter c rounded to 2 decimal places. C= mi Assume LA is opposite side a, ZB is opposite side b, and ZC is opposite side c.

Answers

Cif a = 2.74 mi, b = 3.18 mi and ZC = 41.9° and c^2 = a^2 + b^2 - 2ab*cos(C)where C is the angle opposite to side c, c comes to be ≈ 4.26 mi.

The Law of Cosines is a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them. To get side c, we can use the law of cosines, which states that c² = a² + b² - 2ab cos(C).
Plugging in the given values, we get:
c² = (2.74)² + (3.18)² - 2(2.74)(3.18)cos(41.9°)
c² ≈ 18.126
Taking the square root of both sides, we get:
c ≈ 4.26 mi
Rounding to 2 decimal places, c ≈ 4.26 mi.
Therefore, the answer is: c ≈ 4.26 mi.

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Franklin is helping his aunt sew a lace border onto 2 quilts. Each quilt is 2. 2 meters wide by 2. 7 meters long. At the craft store, they buy a 20-meter roll of lace. To their surprise, they use up almost all of it. How many millimeters of lace do they have left after finishing the quilts?

Answers

The amount in millimeters of lace they have left after finishing the quilts is 400 millimeters.

Determine how much lace is needed for each quilt. Each quilt has a perimeter that we need to cover with lace. The perimeter is the sum of all sides of a rectangle, which is (2 x width) + (2 x length).

Each quilt is 2.2 meters wide and 2.7 meters long. So, the perimeter of one quilt is (2 x 2.2) + (2 x 2.7) = 4.4 + 5.4 = 9.8 meters.

Since there are 2 quilts, the total lace needed for both quilts is 9.8 meters x 2 = 19.6 meters.

They bought a 20-meter roll of lace. To find out how much lace is left, subtract the total lace used from the initial length of the roll: 20 meters - 19.6 meters = 0.4 meters.

To convert this to millimeters, multiply by 1,000: 0.4 meters x 1,000 = 400 millimeters.

So, Franklin and his aunt have 400 millimeters of lace left after finishing the quilts.

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A right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid m. What is the shape of the cross section?



A. Trapezoid


B. Rectangle


C. Triangle


D. Cylinder

Answers

The shape of the cross section of a right rectangular pyramid sliced vertically (down) by a plane not passing through the vertex of the pyramid m is a trapezoid. (A)

This is because when a pyramid is sliced vertically, the resulting cross section is always a two-dimensional representation of the pyramid's base.

Since the base of a right rectangular pyramid is a rectangle, slicing it vertically will result in a trapezoid-shaped cross section. The top and bottom sides of the trapezoid will be parallel, and the other two sides will be slanted.

In a right rectangular pyramid, the vertex m is located directly above the center of the rectangle base. When a plane is passed through this vertex, it will result in a triangular cross section. However, when a plane is passed through a different point, as described in the question, it will result in a trapezoidal cross section.(A)

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The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In ( - x3 + 9x2 +21x + 1) (0 sxs 10). a) Find the number of units that should be sold in order to maximize the total profit. b) What is the maximum profit? a) The number of units that should be sold in order to maximize the total profit is (Simplify your answer.) b) The maximum profit is approximately $. (Do not round until the final answer. Then round to the nearest dollar as needed.)

Answers

Final Answer:  a. The number of units that should be sold in order to maximize the profit is 7 thousand units.

b. The  maximum profit is approximately $5.51

Conceptual part:   a. In order to find maximum profit we need to differentiate the profit function

so, p(x)= [tex]ln(-x^3+9x^2+21x+1)[/tex]

[tex]dp/dx = (-3x^2+18x+21)/-x^3+9x^2+21x+1[/tex] = 0

[tex]-3x^2+18x+21=0[/tex]

[tex](x-7) (x+1) = 0[/tex]

as profit can't be negative.

hence x=7.

b. We can determine the maximum profit by substituting x=7 in profit function.

[tex]p(7) = ln(-7^3+9*7+21*7+1)[/tex]

[tex]p(7) = ln(246)[/tex]

p(7) = 5.51

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A bottel of orange juice contains 750 mg of vitamin C and has 6 servings. A bottek of cranbery juice contains 134 mg of vitamin C and has 1. 5 servings. Mrs khan wants to compare the amount of vitamin c in the juices. How many milligrams of vitamin c are in 1 serving of each type of juice complete the statment. One serving of________ juice has __________Mg More vitamin C per serving Than one serving of _________ Juice

Answers

After evaluating the conclusion is that one serving of orange juice has 35.7 mg more vitamin C per serving than one serving of cranberry  juice.

According to the provided data , a bottle of orange juice has 750 mg of vitamin C and provides 6 servings. A bottle of cranberry juice has 134 mg of vitamin C and provides 1.5 servings.

Now to evaluate how many milligrams of vitamin C are in 1 serving of each type of juice, we have to  perform division to evaluate the total amount of vitamin C by the number of servings.

For orange juice

750 mg / 6 servings

= 125 mg/serving

For cranberry juice

134 mg / 1.5 servings

= 89.3 mg/serving

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In 2003 the social security tax rate was 6. 2% and the maximum taxable income was $87,000. 0. If Linda earned $54,122, how much did she contribute to social security?

Answers

Linda contributed $3,355.56 to social security in 2003.

The Social Security tax is a payroll tax that is deducted from employees' paychecks to help fund the Social Security program, which provides retirement, disability, and survivor benefits to eligible individuals.

The Social Security tax rate is typically 6.2% for employees and employers, and the maximum amount of taxable earnings is determined each year by the Social Security Administration (SSA).

In 2003, the maximum taxable earnings was $87,000. This means that any earnings above $87,000 were not subject to Social Security taxes.

To calculate Linda's contribution to social security in 2003, we will use the given social security tax rate of 6.2% and her income of $54,122.

Convert the tax rate percentage to a decimal by dividing by 100.
6.2% / 100 = 0.062

Multiply Linda's income by the decimal tax rate.
$54,122 * 0.062 = $3,355.56

Linda contributed $3,355.56 to social security in 2003.

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A spinner has 10 equally sized sections, 6 of which are gray and 4
of which are blue. The spinner is spun twice. What is the probability that the first spin lands on blue and the second spin lands on gray.

Answers

Step-by-step explanation:

since both spins are independent events (one does not have any impact on the other), the sequence does not matter. the probability of first blue and then gray is the same as first gray and then blue.

it is the probability of getting 1 gray and 1 blue result.

a probability is always the ratio

desired cases / totally possible cases.

since 6/10 of the area of the spine are gray, and 4/10 of the area are blue, the probability for any single spin to result in gray is 6/10 = 3/5 = 0.6.

and the probability to result in blue is 4/10 = 2/5 = 0.4

the probability to get 1 gray and 1 blue is then the product of both probabilities :

0.6 × 0.4 = 0.24

it is like rolling a die twice and asking for e.g. two 6s or any other combination of 2 specific numbers. that probability is

1/6 × 1/6 = 1/36

FYI :

the probability of getting gray twice is then

0.6 × 0.6 = 0.36

the probability of getting blue twice is

0.4 × 0.4 = 0.16

as mentioned to get gray first and blue second is

0.6 × 0.4 = 0.24

to get blue first and gray second

0.4 × 0.6 = 0.24

and these are all the possible results you can get in 2 spins.

therefore, the probability for any of them is

0.36 + 0.16 + 0.24 + 0.24 = 1

I have tried doing this question for 20 minutes but I just can't get the answer, (add maths circular measure)
the answer is 17.2cm² supposedly​

Answers

Answer:

17.2 cm²

Step-by-step explanation:

Alr let me try

The angle is 1.2 you got it right. The rest is in the pics

Answer: A(shaded)=17.15 cm²

Step-by-step explanation:

What you did so far is correct.

Given:

r=5

s=6

Solve for Ф  angle:

s=[tex]\frac{part circle}{wholecircle} 2\pi r[/tex]         This way help you find the portion/percent you want

6=(Ф/360) (2[tex]\pi[/tex]5)       >solve for Ф  Divide by (2[tex]\pi[/tex]5) and multiply by 360

Ф=68.75

Solve for pie/sector

Now that you have the angle,  you can use the same concept for area

Area of sector = [tex]\frac{part circle}{wholecircle} \pi r^{2}[/tex]

Area of sector = [tex]\frac{68.75}{360} \pi 5^{2}[/tex]

Area of sector = 15.0 cm²

Now let find y so we can plug into area of triangle

use tan Ф = opposite/adjacent

tan 68.75 = y/5

y=5 * tan 68.75

y=12.86 cm

Area of triangle = 1/2 b h          b=y=12.86     h =5

Area of triangle = 1/2* 12.86*5

Area of triangle = 32.15 cm²

Now subtract area of sector from triangle

A(shaded)=A(triangle)-A(sector)

A(shaded)=32.15- 15.0

A(shaded)=17.15 cm²

4. What is the difference in the radii of the circles? (3 points) (this is for the ana circle question

Answers

The difference between the radii of the two circular tracks is 15ft

How do we calculate?

The total length of track 1 is 220ft, which means that the circumference of the circle is 220ft

we find the diameter of each track.

The circumference of a circle can be found  using the formula

P = πd

d = P /π

track 1, we have

d1 = P1 / π

d1 = 220 / π

d1 = 70.03 ft.

track 2, we have

d2 = P2 / π

d2 = 126 / π

d2 = 40.11 ft.

radius of tract 1  = 35.01 ft

radius of track 2 = 20.05 ft

The difference between the two track radius is

∆r = r1 - r2

∆r = 110 / π - 63 / π

∆r = (110 - 63) / π

∆r = 47 / π

∆r = 14.96 ft.

∆r =  15 ft

In conclusion, difference between the radii of the two circular tracks is  15ft

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#complete question:

What is the difference between the radii of the two circular tracks? Answer the questions to find out.

1. Are the distances of 220 feet and 126 feet the radii, diameters, or circumferences of the two circles?

Calcula dos numeros cuya suma sea 191 y su diferencia 67

Answers

The two numbers are 129 and 62, which satisfy the given conditions: their sum is 191 and their difference is 67 .

You are asked to find two numbers whose sum is 191 and whose difference is 67. Let's use the variables x and y to represent these two numbers.

We can establish the following two equations under the given conditions: 1) x + y = 191 2) x - y = 67

Now we can solve this system of linear equations to find the values of x and y.

We can start by adding both equations:

(x + y) + (x - y) = 191 + 67

2x = 258

Then we'll divide by 2 to find the value of x:

x = 129

Now, we can plug x into Equation 1 to find the value of y:

129 + y = 191

y = 191 - 129

y = 62

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9. the square footage and monthly rental of 15 similar one-bedroom apartments yield the linear


regression formula y = 1.3485x + 840.51, where x represents the square footage and y represents


the monthly rental price. round answers to the nearest whole number.

Answers

Based on the linear regression formula y = 1.3485x + 840.51, you can calculate the monthly rental price (y) for a one-bedroom apartment by plugging in the square footage (x) of the apartment.

The linear regression formula for the 15 similar one-bedroom apartments is y = 1.3485x + 840.51, where x represents the square footage and y represents the monthly rental price. This means that for every square foot increase in the apartment size, the monthly rental price is predicted to increase by $1.35.

The y-intercept of the formula is $840.51, which represents the predicted monthly rental price for an apartment with 0 square footage (this is not possible in reality, but is used in the formula for mathematical purposes). To get the rental price, round your answer to the nearest whole number. For example, if an apartment has 500 square feet, you'd calculate: y = 1.3485(500) + 840.51 ≈ 1344.76, which rounds to $1,345 as the monthly rental price.

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A random number generator picks a number from 12 to 41 in a uniform manner. Round answers to 4 decimal places when possible.



a. The mean of this distribution is


b. The standard deviation is


c. The probability that the number will be exactly 36 is P(x = 36) =


d. The probability that the number will be between 21 and 23 is P(21 < x < 23) =


e. The probability that the number will be larger than 26 is P(x > 26) =


f. P(x > 16 | x < 18) =


g. Find the 49th percentile.


h. Find the minimum for the lower quartile

Answers

The mean of this distribution is 26.5. The standard deviation is 8.0623. The probability that the number will be exactly 36 is P (x = 36) = 0.0286. The probability that the number will be between 21 and 23 is P (21 < x < 23) = 0.0400. The probability that the number will be larger than 26 is P (x > 26) = 0.2857. P (x > 16 | x < 18) = undefined. The 49th percentile is 29.3700. The minimum for the lower quartile is 19.75.

a. The mean of a uniform distribution is the average of the maximum and minimum values, so in this case, the mean is:

mean = (12 + 41) / 2 = 26.5

Therefore, the mean of this distribution is 26.5.

b. The standard deviation of a uniform distribution is given by the formula:

sd = (b - a) / sqrt(12)

where a and b are the minimum and maximum values of the distribution, respectively. So in this case, the standard deviation is:

sd = (41 - 12) / sqrt(12) = 8.0623

Therefore, the standard deviation of this distribution is 8.0623.

c. Since the distribution is uniform, the probability of getting any specific value between 12 and 41 is the same. Therefore, the probability of getting exactly 36 is:

P(x = 36) = 1 / (41 - 12 + 1) = 0.0286

Rounded to four decimal places, the probability is 0.0286.

d. The probability of getting a number between 21 and 23 is:

P(21 < x < 23) = (23 - 21) / (41 - 12 + 1) = 0.0400

Rounded to four decimal places, the probability is 0.0400.

e. The probability of getting a number larger than 26 is:

P(x > 26) = (41 - 26) / (41 - 12 + 1) = 0.2857

Rounded to four decimal places, the probability is 0.2857.

f. The probability that x is greater than 16, given that it is less than 18, can be calculated using Bayes' theorem:

P(x > 16 | x < 18) = P(x > 16 and x < 18) / P(x < 18)

Since the distribution is uniform, the probability of getting a number between 16 and 18 is:

P(16 < x < 18) = (18 - 16) / (41 - 12 + 1) = 0.0400

The probability of getting a number greater than 16 and less than 18 is zero, so:

P(x > 16 and x < 18) = 0

Therefore:

P(x > 16 | x < 18) = 0 / 0.0400 = undefined

There is no valid answer for this question.

g. To find the 49th percentile, we need to find the number that 49% of the distribution falls below. Since the distribution is uniform, we can calculate this directly as:

49th percentile = 12 + 0.49 * (41 - 12) = 29.37

Rounded to four decimal places, the 49th percentile is 29.3700.

h. The lower quartile (Q1) is the 25th percentile, so we can calculate it as:

Q1 = 12 + 0.25 * (41 - 12) = 19.75

Therefore, the minimum for the lower quartile is 19.75.

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D is the centroid of PQR PA= equals 17 BD equals nine and DQ equals 14 find each missing measure

Answers

The centroid of the triangle is D and the measures of sides are solved

Given data ,

Let the triangle be represented as ΔPQR

Now , the centroid of the triangle is D

where the measure of PA = 17 units

The measure of BD = 9 units

And , the measure of side DQ = 14 units

Now , centroid of a triangle is formed when three medians of a triangle intersect

And , from the properties of centroid of triangle , we get

PA = AR

DR = DQ

AD = BD

On simplifying , we get

The measure of side AR = 17 units

PR = PA + AR = 34 units

The measure of side DR = 14 units

BR = BD + DR = 23 units

The measure of side AD = 9 units

AQ = AD + DQ = 23 units

Hence , the centroid is solved

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Mario traced this trapezoid. Then he cut it out and arranged the trapezoids to form a rectangle.

Pls give me a good explanation!

Answers

The calculated area of the rectangle is 70 + 7x


Calculating the area of the rectangle

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

Mario cuts out and arranged the trapezoids to form a rectangle.

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

Area of rectangle  = base * height

In this case, we have

base = 10 + x

Where x is the length of the missing side

Next, we have

height = 7

Substitute the known values in the above equation, so, we have the following representation

Area = 7 * (10 + x)

Evaluate

Area = 70 + 7x

Hence, the area of the rectangle is 70 + 7x

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The polynomial â 2x2 + 700x represents the budget surplus of the town of Alphaville.


Betaville's surplus is represented by x2 - 100x + 80,000. If x represents the tax revenue in


thousands from both towns, enter the expression that represents the total surplus of both


towns together.


The expression that represents the total surplus of both towns together is ?

Answers

The total surplus of both towns together is represented by the polynomial [tex]3x^2 + 600x + 80,000.[/tex]

The expression that represents the total surplus of both towns together is (â 2x2 + 700x) + (x2 - 100x + 80,000).?

To find the total surplus of both towns together, we need to add the budget surplus of Alphaville and Betaville.

The budget surplus of Alphaville is represented by the polynomial [tex]2x^2 + 700x.[/tex]

The budget surplus of Betaville is represented by the polynomial x^2 - 100x + 80,000.

Therefore, the expression that represents the total surplus of both towns together is:

[tex](2x^2 + 700x) + (x^2 - 100x + 80,000)[/tex]

Simplifying this expression, we get:

[tex]3x^2 + 600x + 80,000[/tex]

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Evaluate the limit using L'Hospital's rule
lim (e^x + 2x - 1)/2x

Answers

To evaluate the limit using L'Hospital's rule, we need to take the derivative of both the numerator and denominator separately until we get a determinate form. We have:

lim (e^x + 2x - 1) / (2x)

Taking the derivative of the numerator:

lim (e^x + 2) / 2

Taking the derivative of the denominator:

lim 2

Since we now have a determinate form, we can evaluate the limit by plugging in the value of x. We get:

(e^x + 2) / 2

As x approaches infinity, e^x also approaches infinity, so the limit diverges to positive infinity. Therefore, the limit does not exist.

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