Mathematics College

find the area of the parallelogram height 8 length 15

Answers

Answer 1

Answer:

Step-by-step explanation:

The area of a parallelogram is given by the formula:

Area = Base * Height

In this case, the base of the parallelogram is 15 and the height is 8, so the area of the parallelogram is given by:

Area = 15 * 8

= 120

Therefore, the area of the parallelogram with a height of 8 and a length of 15 is 120 square units.

Answer 2

Answer:

120 units

area of parallelogram = height x length

a = 8 x 15

a = 120

Related Questions

Determine the measures of the unknown angles.

Answers

Answer:

x = 24

m = 112

z = 44

y = 72

x = 35

Step-by-step explanation:

Number 1

Finding x

- Total angle in a triangle is 180.

- QVS = triangle

180 = ∠Q + ∠V + x

180 = 73 + 83 + x

x = 180 -73 - 83

x = 24

Finding m

- Total angle in a straight line is 180

- RW is a straight line

180 = m + ∠U

180 = m + 68

m = 180 - 68

m = 112

Finding z

- Total angle in a triangle is 180.

- RUS = triangle

180 = m + x + z

180 = 112 + 24 + z

z = 180 - 112 - 24

z = 44

Finding y

- Total angle in a triangle is 180.

- RWT = triangle

180 = z + y + ∠W

180 = 44 + y + 64

y = 180 - 44 - 64

y = 72

Number 2

- Total angle in a triangle is 180.

- Total angle in a straight line is 180.

180 = (180 -120) + 85 + x

180 = 60 + 85 + x

x = 180 - 60 - 85

x = 35

suppose that y1 and y2 are independent and that both are uniformly distributed on the interval (0,1), and Let U1 and U2 be independent uniform random variables, both on (0,1). Let Y1 = U1U2 and let Y2=U2. (a) Find the joint density of Y1 and Y2.
(b) What is the marginal density for Y1?

Answers

a) The joint density of Y1 and Y2 is f(y1, y2) = 1, for 0 ≤ y1, y2 ≤ 1.

b) The marginal density for Y1 is f(y1) = 1, for 0 ≤ y1 ≤ 1.

Explanation:

(a) The joint density of Y1 and Y2 is found by multiplying the two individual densities together. Since Y1 and Y2 are independent, this is simply the product of the two densities.

The density for U1 is the same for all values of U1 on the interval (0,1), which is 1. The density for U2 is also the same for all values of U2 on the interval (0,1), which is also 1.

Therefore, the joint density of Y1 and Y2 is:

f(Y1,Y2) = f(U1U2,U2)

= f(U1) x f(U2)

= 1 x 1

= 1

(b) The marginal density for Y1 is the density of Y1 without regard to Y2. Since Y2 is uniform on (0,1), we can integrate the joint density over the interval (0,1) to obtain the marginal density of Y1:

f(Y1) = ∫f(Y1,Y2)dY2

= ∫1dY2

Y2 = 1

Therefore, the marginal density of Y1 is 1

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Read the following prompt and type your response in the space provided.

Write a real-world problem that could be represented by the inequality.

3x + 6 > 27

Answers

Answer is

Jordan wants to buy a Pokemon card that costs $27 plus $.45 postage. He has $6 saved up. He can earn $3 per hour shoveling snow. How many hours does he have to shovel snow to have enough money to get his card?

3x + 6 > 27

3 is rate of pay, x is hours worked, 6 is money he has saved, he needs to earn more than $27.

(Graphing Proportional Relationships LC)

The table shows a proportional relationship.

x 15 9 21
y 5 3 7

Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (15, 5).
A line passes through the point (0, 0) and continues through the point (7, 21).
A line passes through the point (0, 0) and continues through the point (5, 15).
A line passes through the point (0, 0) and continues through the point (3, 9).

Answers

The graph of the given proportional relation shows that the line passes through the point (0, 0) and continues through the point (15, 5). The relation is represented by the equation y = -0.33x. So, option A is correct.

What is the proportional relationship of the given table of proportions?

The given table shows the x and y coordinates of a line.

So, we can find the relationship among them by writing an equation from the given points as

y - y₁ = {(y₂ - y₁)/(x₂ - x₁)} × (x - x₁)

Here we have (x₁, y₁) = (15, 5); (x₂, y₂) = (9, 3)

⇒ y - 5 = (3 - 5)/(9 - 15) × (x - 15)

⇒ y - 5 = (-2)/(-6) × (x - 15)

⇒ y - 5 = 1/3 × (x - 15)

⇒ 3y - 15 = x - 15

⇒ 3y = x + 0

∴ y = 0.33x

Thus, the equation for the given proportions is y = 0.33x.

Since the line is in the form of y = mx, it passes through th point (0, 0) and continues through the point (15, 5).

So, option A is correct.

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Find the value of K
(x+5) is a factor of the Polynomial p(x)
if p(x)=2x³ +7x²+Kx + 20

Answers

Therefore the value of K is -11

Count the average-case number of + operations performed by the following pseudocode segment. Assume that all possible data sets are equally likely. (Round your answer to two decimal places.) Preconditions: X = {X1, X2, X3, X4,X5} = {10, 20, 30, 40, 50, 60}, where x1 < x2 < X3 < X4 < X5. teo ir 1 while t < 101 do rtet + Xi Liri + 1

Answers

Count the average-case number of + operations performed by the following pseudocode segment. The average-case number of + operations performed is 6.67.

The pseudocode segment is a while loop that runs from t=0 to t=101. For each iteration, it adds Xi to the value of the variable liri. Since the preconditions list X as a set of five integers (10, 20, 30, 40, 50, 60) in increasing order, the variable Xi will take on each of these values in turn. Thus, the loop will perform + operations six times (once for each value of Xi). The average-case number of + operations performed is 6.67 (6 operations in total divided by the number of iterations, i.e. 101).

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What is the inverse of the function below?
f(x) = x/3 -2
O A. f1(x) = 2(x+3)
O B. f¹(x) = 3(x+2)
O c. f¹(x) = 3(x - 2)
OD. f¹(x) = 2(x-3)

Answers

Answer:

f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]

Step-by-step explanation:

The first step to finding the inverse of a function is to let [tex]y=f(x)[/tex].

This would mean [tex]y=\frac{x}{3}-2[/tex].

Then we swap [tex]x[/tex] and [tex]y[/tex] in the formula.

[tex]x = \frac{y}{3} -2[/tex]

Then rearrange for [tex]y[/tex]:

[tex]x=\frac{y}{3}-2 \\\\x+2=\frac{y}{3}\\\\3(x+2)=y[/tex]

This new equation of [tex]y[/tex] is the inverse function.

f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]

Please help me with this question

Answers

Answer:

y = -1/2 x - 1

Step-by-step explanation:

A (-2,0)

B (0,-1)

slope = (-1-0)/(0-(-2)

-1/2

y intercept = -1

y = -1/2 x - 1

Answer:

y = e^(-1/2x -1)

Step-by-step explanation:

You want the equation for y(x), which is graphed as a straight line on a semi-log scale.

Graph

Let z = ln(x). The graph shows a straight line with a z-intercept of -1 and a slope of "rise"/"run" = -1/2. That means the slope-intercept equation for this line can be written as ...

z = -1/2x -1

Equation

Using z = ln(y), we can find the equation for y by taking antilogs:

ln(y) = -1/2x -1

y = e^(-1/2x -1)

Additional comment

The attached graph shows y = f(x) and the line ln(y).

A spherical balloon is being filled with helium at the rate of 9 ft^3/min. How fast is the surface area increasing when the volume is 26 pi ft^3?

Answers

A spherical balloon is being filled with helium at the rate of 9 ft^3/min. the surface area of the balloon is increasing at a rate of approximately 37.1 ft^2/min.

What is the surface area?

Generally, To find the rate at which the surface area is increasing, we need to use the formula for the surface area of a sphere, which is 4πr^2, where r is the radius of the sphere. We also know that the volume of a sphere is (4/3)πr^3.

Since we know the volume of the balloon, we can set up the following equation:

(4/3)πr^3 = 26*π ft^3

Solving for r, we find that the radius of the sphere is approximately 2.15 ft. Plugging this value back into the formula for the surface area, we find that the surface area of the sphere is approximately 28.9 ft^2.

To find the rate at which the surface area is increasing, we need to find the d/dx surface area formula with respect to time. Since the radius of the sphere is changing at a constant rate (9 ft^3/min), we can use the chain rule to find the d/dx surface area.

The d/dx 4πr^2 with respect to r is 8pir, and the d/dx r with respect to time (which we'll call t) is 9 ft^3/min. Therefore, the d/dx surface area with respect to time is:

(d/dx 4πr^2 with respect to r) * (d/dx r with respect to t) = (8πr) * (9 ft^3/min)

Plugging in the value of r that we found earlier (2.15 ft), we get:

(8π2.15 ft) * (9 ft^3/min) = 37.1 ft^2/min

Answers

The total perimeter of the given composite figure is; 74.55 meters

How to find the perimeter of a composite figure?

The perimeter of the given figure can be calculated by dividing the figure into two parts : One is semi-circle and second is rectangle.

To find Perimeter of rectangle :

Length of the rectangle = 18 m

Width of the rectangle = 15 m

Perimeter = (2 × Length) + Width

Perimeter = (2 × 18) + 15

Perimeter = 36 + 15

Perimeter = 51 meters

To find perimeter of semi-circle :

Radius of semi-circle = 15/2 = 7.5 m

Perimeter of semi-circle = π × radius

Perimeter = 3.14 × 7.5

Perimeter = 23.55 meter

So, Total Perimeter of the figure = 51 + 23.55

= 74.55 meter

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take the van der pol equation . (a) set and . convert the above second order differential equation to a two dimensional system of differential equations:

Answers

The van der Pol equation which is a second-order differential equation is given by

d²x/dt² - μ(1 - x²)dx/dt + x = 0

Here we are asked to convert it to a two-dimensional system.

Here we need to set y = dx/dt, where y represents the system's velocity.

Hence we will rewrite it as

d²x/dt² = μ(1 - x²)y + x

Now if we set the derivatives of x and y with respect to time to be equal to different variables we get

dx/dt = y

dy/dt = μ(1 - x²)y + x

Hence we get the above systems of equations as the 2-dimensional representation of the Van der Pol equation where x and y represent the system's position and velocity respectively.

If we set μ = 1 and x = 0, then we get

dx/dt = y

dy/dt = y

Hence we get the system of differential equations representing the behavior of the van der Pol equation with μ = 1 and x = 0 in two dimensions.

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Graph the solution to this inequality on the number line. 2/3z > 4/5

Answers

The solution to the inequality, 2/3z > 4/5, is calculated as z > 1.2. See attachment for the graph of the solution.

How to Solve and Graph the Solution to an Inequality?

The solution to an inequality is determined by finding he value of the variable in the inequality that will make it true.

Given the inequality, 2/3z > 4/5, isolate the variable z to one side to determine its value:

2/3z > 4/5 [given]

Multiply both sides by 3/2:

2/3z × 3/2 > 4/5 × 3/2

z > (4 × 3) / (5 × 2)

z > 12 / 10

Simplify further:

z > 6/5

z > 1.2

The solution is z > 1.2. The graph of the solution is shown in the image that is given in the attachment below.

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Triangle CAT is transformed by a sequence of rigid motions that maps onto triangle DOG. Which three congruency statements would show ASA congruency for these triangles? (select all that apply)

A.∠ A ≅ ∠ T

B.CA ≅ DO

C.AT ≅ OG

D.CT ≅ DG

E.∠ A ≅ ∠ O

F.∠ C ≅ ∠ D

Answers

Answer:

B, E and F.

-----------------------------

Since the triangles CAT and DOG overlap, their corresponding parts are congruent.

As we are looking for ASA congruency, we need to select two angles and the included side.

Let's review the given options, considering names of triangles and the order of vertices in those names.

A. ∠ A ≅ ∠ T

Incorrect as angles T and A are not corresponding.

B. CA ≅ DO

Yes, possible side.

C. AT ≅ OG

Yes, possible side.

D. CT ≅ DG

Yes, possible side.

E. ∠ A ≅ ∠ O

Yes, possible angle.

F. ∠ C ≅ ∠ D

Yes, possible angle.

So we have corresponding angles A and C and the included side must be AC.

Looking, at the options, we can get ASA with combination of options B, E and F.

Please help I've done it but I want to check my answer!

There are several marbles of different colours in a bag in front of you. Your job is to select three marbles and record the colour of each marble you chose. In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles and 3 purple marbles. What are the chances of selecting one red marble, one yellow marble and a blue marble?

Assume that once each marble is chosen, it is not returned to the bag.

Answers

Answer:

the probability of selecting one red marble, one yellow marble, and a blue marble is 1/52. This can also be expressed as a percentage by dividing the probability by 1 and multiplying by 100%, which gives a probability of approximately 1.9%.

Step-by-step explanation:

What are some possible solutions for the following inequality? 2f - 8 ≤ 6f + 4
-4.5
-8
-1
4
0

Answers

Answer:

Solutions: -1, 4, and 0

Step-by-step explanation:

f= -4.5

2f - 8 ≤ 6f + 4

2 (-4.5) -8 ≤ 6 (-4.5) + 4

-9 - 8 ≤ -27 + 4

-17 ≤ -23

Not True

f= -8

2f - 8 ≤ 6f + 4

2 (-8) - 8 ≤ 6 (-8) + 4

-16 - 8 ≤ -48 + 4

-24 ≤ -44

Not true

f= -1

2f - 8 ≤ 6f + 4

2 (-1) - 8 ≤ 6 (-1) + 4

-2 - 8 ≤ -6 + 4

-10 ≤ -2

True

f= 4

2f - 8 ≤ 6f + 4

2 (4) - 8 ≤ 6 (4) + 4

8-8 ≤ 24 + 4

0 ≤ 28

True

f= 0

2f - 8 ≤ 6f + 4

2 (0) - 8 ≤ 6 (0) + 4

0 - 8 ≤ 0 + 4

-8 ≤ 4

True

the questions in this activity refer back to prelab 0, which would be a good place to look if you need any help. in test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again calculate mean, standard deviation, and standard error. 1)which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?

Answers

The most likely statement about the comparison of standard deviation of Test A and Test B is (a) The standard deviations found in Test A and Test B will be about the same .

What is Standard Deviation ?

The term standard deviation is defined as a measure which shows the variation (such as dispersion) from the mean .

it is given that in Test A 100 experimental measurements is taken , and

in Test B 400 experimental measurements is taken .

we know that standard deviation is just square root of average of the square distance of measurements from the mean.

So , it is not affected by the number of experimental measurements .

thus , the standard deviation remain same for both the tests .

Therefore , the correct option is (a) .

The given question is incomplete , the complete question is

In test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again .

Which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?

(a) The standard deviations found in Test A and Test B will be about the same

(b) The standard deviation found in Test A will about be twice as big as the standard deviation found in Test B.

(d) The standard deviation found in Test B will about be twice as big as the standard deviation found in Test A .

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for how many integers $n$ between 1 and 1990 is the improper fraction \[\frac{n^2 7}{n 4}\] not in lowest terms? (a) 0 (b) 86 (c) 90 (d) 104 (e) 105

Answers

Step-by-step explanation:

Drag each tile to the correct box. Arrange the steps in the expansion of the binomial (3x + 2y)³ in the correct sequence. 27x³ + (3x)³ + x 9x²2y + 3x2 × 3x × 4y² + 8y³ 2x1 (3x)²2y + 3(3-1) (3x) (2y)² + (2y)³ 21 27x³ +54x²y +36y² + 8y³ ↓

Answers

The solution of the algebraic expression (3x + 2y)³ is

[tex]\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Now, algebraic expressions are of different types. They are-

Monomial, Binomial and trinomial.

Algebraic expression with only one term is called monomial

Algebraic expression with two terms are called binomial

Algebraic expressions with three terms are called trinomial.

Algebraic expressions with more than three terms are called polynomial.

Based on degree, algebraic expression may be called as linear, quadratic, cubic and so on

Algebraic expression of degree one is called linear

Algebraic expression of degree two is called quadratic

Algebraic expression of degree one is called cubic

The given algebraic expression is (3x + 2y)³

Now,

[tex](3x +2y)^3\\(3x)^3 + 3 \times (3x)^2 \times (2y) + 3 \times 3x \times (2y)^2 + (2y)^3\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]

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Jill is going to make weekly deposits of $100 into an account for 3 years. The account earns 5.2%/a compounded weekly. How much money will she have in her account at the end of 3 years? How much money did she make on this investment?

Answers

Answer:

every week jill is going to make 5.20 dollars then you do 5.20 x 1095 days in 3 years = $5694 a year

Step-by-step explanation:

suppose a statistician wishes to test whether a large number of observations follows an exponential distribution with parameter . he wishes to test this hypothesis exactly, and intends that if the observations follow an exponential distribution with a different parameter, the test should reject the null hypothesis given sufficiently many observations. in addition, he wants to have a numeric statistic that he could report and does not want the procedure to involve rounding off observation numbers into bins. which of the following goodness-of-fit tests would be the most appropriate for this purpose? Chi-squared Test O Kolmogorov-Smirnov Test O Kolmogorov-Liliefors Test Quantile-quantile plots

Answers

How many parameters does an exponential distribution have?

This distribution has no shape parameter as it has only one shape, (i.e., the exponential, and the only parameter it has is the failure rate, \lambda \,\!).

How do you find the parameter of an exponential distribution in R?

The exponential distribution can be simulated in R with rexp(n,λ) where λ is the rate parameter. The mean or expected value of an exponential distribution is 1/λ and the standard deviation is also 1/λ. The variance of an exponential distribution is given by 1/λ2.

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Over 18 days, Sophia rode her bike an average of 12 miles each day.
What is the total number of miles she biked?
Enter your answer as a number like this: 42

Answers

The total Number of miles she biked, was 216.

In the given question, over 18 days, Sophia rode her bike an average of 12 miles each day.

We have to find the total number of miles she biked.

As we know that average is the sum of all numbers divide by total numbers.

As from the question, there is a total average of 18 days.

So the total number of days is 18.

The average distance of her bike for one day is 12 miles.

So we have to find the total number of miles that she biked.

We can find the total number of miles by multiplying the total number of days with the average speed of one day. So;

Total Number of Distance = Total Days × Average Speed of One Day

Total Number of Distance = 18 × 12

Total Number of Distance = 216 miles.

So, the total Number of Distance she biked, was 216 miles.

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Can someone please help me answer the second part of this question

Answers

The compositions of the two given functions are:

g(f(x)) = √(2*x + 29) - 2

f(g(x)) = √(2*x + 25)

How to find the composition of functions?

Here we have the two functions:

f(x) = √(2x + 29)

g(x) = x - 2

We want to find the compositions:

f(g(x))

So we just need to evaluate f(x) on g(x), we will get:

f(g(x)) = √(2*g(x) + 29)

Now we can replace g(x) there:

f(g(x)) = √(2*(x - 2) + 29)

f(g(x)) = √(2*x - 2*2 + 29)

f(g(x)) = √(2*x + 25)

The other composition is:

g(f(x)) = f(x) - 2

g(f(x)) = √(2*x + 29) - 2

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Kaitlyn went on a diet and lost 8% of her body weight. She now weighs 222 pounds.

What was her original body weight?

Answers

To find Kaitlyn's original body weight, we need to determine how much weight she lost and add that amount back to her current weight.

Kaitlyn lost 8% of her body weight, which is equal to 8/100 * 222 pounds = <<8/100*222=17.76>>17.76 pounds.

Therefore, Kaitlyn's original body weight was 222 pounds + 17.76 pounds = <<222+17.76=239.76>>239.76 pounds.

Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.
a) {(a, b) | a and b are the same age}
b) {(a, b) | a and b have the same parents}
c) {(a, b) | a and b share a common parent}
d) {(a, b) | a and b have met} e) {(a, b) | a and b speak a common language}

Answers

Relations in the options (a), (b) and (e) are the Equivalence relations as, the relations are reflexive, symmetric and transitive all.

Given, five relations as,

a) {(a, b) | a and b are the same age}

b) {(a, b) | a and b have the same parents}

c) {(a, b) | a and b share a common parent}

d) {(a, b) | a and b have met}

e) {(a, b) | a and b speak a common language}

we have to find which of them are equivalence relations

a) as, (a , a) ∈ R ∀ a hence, Reflexive.