what is the slope of this line

Answer:

49.1 cm² (round to nearest 10)

Step-by-step explanation:

- use trigonometry to find the height(h) of the triangle

- substitute height and base(b) 12cm into the formula

A = ½ × b × h .

Answer:

48ft.

Using the area formula of length times width, (8x6), we can easily get 48ft, which is how much area the carpet takes up.

The answer to compounded continuously is as follows.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

"Interest on interest," or the ability of interest, is believed to possess originated in 17th-century Italian Republic. it'll build a add grow quicker than interest, that is calculated solely on the principal quantity.

Main body:

formula for compounding = A=\(P(1+r/n)^{nt}\)

given :

P = $2000

R= 6.5%

A) 3 years

t = 3 years

A= \(2000(1+0.065/365)^{365*3}\)

A= $2430.58

B) 6 years

t = 6

A= \(2000(1+0.065/365)^{365*6}\)

A = $2953.9

C) 18 years

t = 18

A= \(2000(1+0.065/365)^{365*18}\)

A= $6443.3

Hence the value of principal after 3, 6 ,18 years will be as follows.

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Answer:

60.01778

Step-by-step explanation:

Answer:

y=-¾x-15/2

Step-by-step explanation:

y--9=-¾(x-2)

y+9=-¾(x-2)

4y+36=-3x+6

4y=-3x+6-36

4y=-3x-30

y=-¾x-15/2

Answer:

75 mm^2

Step-by-step explanation:

use pythageron theorem to find the area of the triangle

7^2=5^2+b^2

b=4.489mm

multiply the of b by the height (5mm) to get the area. usually for the area of a triangle you divide by two, but because there is an identical triangle on the other side, it will be doubled, so dividing it by 2 is redundant.

4.489*5 = 24.49mm^2

Make a rectangle in the middle of the shape, creating a triangle on the right, like they did on the left.  That right triangle is included in the calcualtion above. the rectangle is base *height. The base is 15 - b which was 4.489. therefore the rectanlge is

5*10.1 = 50.5mm^2

add the areas together: 50.5 +24.49 = 75 mm^2

Answer:

8/7

Step-by-step explanation:

Answer:

Answer is: (9)

Step-by-step explanation:

105+(8v+3)=180

(8v+3)=75

8v=72

v=9

Answer:

Step-by-step explanation:

In this scenario, the probability of success, p is 28% = 28/100 = 0.28

Number of samples, n = 160

Probability of failure, q = 1 - p = 1 - 0.28 = 0.72

Mean,µ = np = 0.28 × 160 = 44.8

Standard deviation, σ = √npq = √160 × 0.28 × 0.72 = 5.68

Let x be the random variable representing the number of wood samples from long-leaf pine trees with a fungal disease. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

the probability that you’ll have at least 50 diseased samples to return to your boss is expressed as

P(x ≥ 50) = 1 - P(x < 50)

For P(x < 50)

z = (50 - 44.8)/5.68 = 0.91

Looking at the normal distribution table, the probability corresponding to the z score is 0.819

Therefore,

P(x ≥ 50) = 1 - 0.819 = 0.181

The evaluated integral is -16π.

The given integral is:
∫∫∫(2z) dz dx dy, where the limits are:
z: 0 to 2
x: -2 to 2
y: 0 to √(4 - y²)

First, let's change to spherical coordinates using the following transformations:
x = ρ sin(θ) cos(φ)
y = ρ sin(θ) sin(φ)
z = ρ cos(θ)

The Jacobian determinant for this transformation is:
J(ρ, θ, φ) = ρ² sin(θ)

Now, we need to change the limits of integration:
ρ: 0 to 2
θ: 0 to π/2 (since z ≥ 0)
φ: 0 to 2π (complete revolution around the z-axis)

The integral in spherical coordinates becomes:
∫∫∫(2ρcos(θ) × ρ² sin(θ)) dρ dθ dφ
with the limits mentioned above.

Now, let's evaluate the integral:

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Answer:

19

Step-by-step explanation:

79÷4=19R3

       ≈ 19

Answer: See explanation

Step-by-step explanation:

Yiur question isn't complete but I believe that you want to know the price of the soda.

Let the price of the soda be represented by x.

Jesean buys a pizza for 20$ and 10 drinks. This will be: 20 + 10x

He spends 32$ on the pizza and the sodas together. This can be formed into an equation as:

20 + 10x = 32

10x = 32 - 20

10x = 12

x = 12/10

x = 1.2

Therefore, the soda cost $1.20 each

Using Z-table ,

the required probability that their mean total body protein is between 12.2 and 12.4 kg is 0.691..

We have given that,

The sample is Normal distribution,

the mean of sample(X-bar,) = 12.3 kg

standard deviations of sample(sigma) = 0.4 kg

sample size(n) = 4

confidence interval= (12.2, 12.4)

we have to find the probability that mean body protein is between 12.2 and 12.4 kg

Using the confidence interval formula, for finding the value of Z-value ,

C.I = X-bar +- Z(s/√n)

put all avaliabile values we get,

12.2 = 12.3 + Z(0.4/√4) = 12.3 + Z(0.2)

=> Z = - 0.5

or 12.4 = 12.3 + Z(0.2)

=> Z = 0.1/0.2 = 1/2 = 0.5

so, -0.5 < Z< 0.5

now , using the z-value we can easily calculate the value of p i.e. probability

Use the Z-table , we get p -value is 0.691

Hence , probability that their mean total body protein is between 12.2 and 12.4 kg is 0.691

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Answer:

See below

Step-by-step explanation:

Prolific will bike 2 miles to get to the mechanic at the 6th gas station if the pattern continues.

Assuming the rate remains constant, we can use the equation d = rt, where d is the distance, r is the rate, and t is the time. In this case, we want to find the equation to determine the distance of the Nth gas station.

Let's analyze the given information:

The first gas station is 1.5 miles away.

From the second gas station onwards, each gas station is located at a distance 0.1 miles greater than the previous one.

Based on this pattern, we can write the equation for the distance of the Nth gas station as follows:

d = 1.5 + 0.1(N - 1)

B. To find the distance Prolific will bike to get to the 6th gas station, we can substitute N = 6 into the equation from part A:

d = 1.5 + 0.1(6 - 1)

= 1.5 + 0.1(5)

= 1.5 + 0.5

= 2 miles

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Calculating the mean amount of time that these students spent on the internet yesterday it is not appropriate because sample is a convenience sample to determine condition for population mean.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode.

The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

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The system equation that models the amount of calories from fats (f) and proteins (p) that the individual can consume to reach 1,800 calories is: f + p = 1,200. The equation that relates calories from protein (p) to calories from fat (f) based on the prescribed diet is: p = 3f. Solving the system of equations, we find that the individual should consume 300 calories from fats and 900 calories from proteins.

To find the equation that models the amount of calories from fats and proteins that the individual can consume in order to reach 1,800 calories, we consider that 600 calories will come from carbohydrates. Since the total goal is 1,800 calories, the remaining calories from fats and proteins should add up to 1,800 - 600 = 1,200 calories. Therefore, the equation is f + p = 1,200.

Based on the prescribed diet, the individual is required to consume calories from protein that are three times the calories from fat. This relationship can be expressed as p = 3f, where p represents the calories from protein and f represents the calories from fat.

To solve the system of equations, we substitute the value of p from the second equation into the first equation: f + 3f = 1,200. Combining like terms, we get 4f = 1,200, and dividing both sides by 4 yields f = 300. Substituting this value back into the second equation, we find p = 3(300) = 900.

Therefore, the individual should consume 300 calories from fats and 900 calories from proteins to meet the diet requirements and achieve a total of 1,800 calories.

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The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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cos ∠G = (0.3420) sin ∠G + (15.21 - 19.44 cos (180° - ∠F - ∠G)) / 28.475. Since the sum of the angles in a triangle is 180°, we can find the measure of ∠E by subtracting ∠F and ∠G from 180°:

∠E = 180° - ∠F - ∠G

We can then use the Law of Cosines to solve for the length of side e:

e² = f² + g² - 2fg cos ∠E

e² = (3.9)² + (5.6)² - 2(3.9)(5.6)cos ∠E

Next, we can use the Law of Cosines again to solve for the cosine of ∠G:

g² = f² + e² - 2fe cos ∠G

cos ∠G = (f² + e² - g²) / 2fe

cos ∠G = (3.9² + e² - 5.6²) / (2 × 3.9 × e)

cos ∠G = (15.21 + e² - 31.36) / (7.8e)

cos ∠G = (e² - 16.15) / (3.9e)

Now we can substitute the expression for ∠E into the equation, and then use that result to solve for cos ∠G:

e² = (3.9)² + (5.6)² - 2(3.9)(5.6)cos (180° - ∠F - ∠G)

e² = (3.9)² + (5.6)² + 2(3.9)(5.6)cos (∠F + ∠G)

cos (∠F + ∠G) = (e² - 3.9² - 5.6²) / (2 × 3.9 × 5.6)

cos (∠F + ∠G) = (e² - 50.65) / 30.24

Now we can use the identity for the cosine of a sum to solve for cos ∠G:

cos (∠F + ∠G) = cos ∠F cos ∠G - sin ∠F sin ∠G

cos 156° cos ∠G - sin 156° sin ∠G = (e² - 50.65) / 30.24

(0.9397) cos ∠G - (0.3420) sin ∠G = (e² - 50.65) / 30.24

Solving for cos ∠G, we get:

cos ∠G = (0.3420) sin ∠G + (e² - 50.65) / (30.24 × 0.9397)

Substituting the expression for e² from the earlier step, we get:

cos ∠G = (0.3420) sin ∠G + (3.9² + (5.6² - 2(3.9)(5.6) cos (180° - ∠F - ∠G)) - 50.65) / (30.24 × 0.9397)

cos ∠G = (0.3420) sin ∠G + (15.21 - 19.44 cos (180° - ∠F - ∠G)) / 28.475

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In the initial list, there were 4 integers.

We have the following system if the mean is m, x is the list's initial sum, and n is the number of integers in the list:

m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).

The initial equation is x = mn.

Therefore, changing x in the other two equations:

m + 2 = (mn + 15) / (n + 1) ..............(1)

m + 1 = (mn + 16) / (n + 2)...............(2)

Based on equation (1):

(m + 2)(n + 1) =  mn + 15

mn + m + 2n + 2 = mn + 15

m + 2n + 2  = 15

m + 2n = 13

m = 13 - 2n.

Now change m in equation (2) to:

13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)

14 - 2n = (13n - 2n^2 + 16) / (n + 2)   Through-multiplication by n + 2:

(14 - 2n)(n + 2) =  13n - 2n^2 + 16

14n + 28 - 2n^2 - 4n =  13n - 2n^2 + 16

10n + 28 = 13n + 16

12 = 3n

n = 4.

Hence, there were 4 integers in the original list.

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Answer: $29850

Step-by-step explanation:

From the question, we are informed that Kevin earned $28,500 in gross wages last year and had $1,350 in capital gains.

The amount of Kevin's income from last year that is subject to income tax will be the addition of the amount he earned and his capital gains. This will be:

= $28500 + $1350

= $29850

Answer:

Write the dependent clause on the line circle the relative pronoun or adverb

Today i went to a movie with my sister, who loves action films

Step-by-step explanation:

Answer:

36/5

Step-by-step explanation:

7.2

7 2/10

7 1/5

7+1/5

7×5/5+1/5

7×5/5+1/5

7×5+1/5

35+1/5

36/5

Answer:

All of these equations have two complex solutions.

Step-by-step explanation:

The two complex solutions of a given equation refer to the two distinct solutions that can be obtained when the equation is solved. In this case, the equation is a polynomial equation with degree two (also known as a quadratic equation). The two complex solutions are found by using the quadratic formula, which states that if a, b, and c are given real or complex coefficients, then the two solutions to the equation ax2 + bx + c = 0 are: x = (-b ± √(b2 - 4ac))/2a. These two values will always be complex if the discriminant, b2 - 4ac, is negative. This means that these two complex solutions represent the two different roots of the equation.

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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Answer:

90 degrees.

Step-by-step explanation:

Assuming x is the bottom right of the blue triangle, x would be 90 degrees, since the triangle has a right angle.

Right angles are always 90 degrees.

I think is may be what you're looking for, hope this helps! If not, please do let me know.

oopss wrong one my bad

Answer: Deshi will have 302 marbles  and Elaheh will have 519.

Step-by-step explanation:

Deshi's Marbles will subtract 125.

427 - 125 = 302.

Elaheh's Marbles will add 125.

394 + 125= 519.

Answer:

x = 40°

Step-by-step explanation:

The base angles of the triangle are 71° and 69° ( vertical angles ) , then

x = 180° - (71 + 69)° = 180° - 140° = 40°