What is the angle relationship ?

The total value of the income stream would be $187,500.

WE are given that integral of R(t) with respect to t ∫[0,5] R(t) dt = ∫[0,5] (30,000 + 3,000t) dt

To determine the total value of the income stream, we need to evaluate the definite integral of the function R(t) over the given interval. The integral of R(t) with respect to t is:

∫[0,5] R(t) dt = ∫[0,5] (30,000 + 3,000t) dt

Evaluating this integral gives:

∫[0,5] R(t) dt = (30,000t + 1,500t²) [0,5]

= (30,000(5) + 1,500(5²)) - (30,000(0) + 1,500(0²))

= 187,500

Therefore, the total value of the income stream is 187,500.

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Step-by-step explanation:

x + y = 17

x = 17 - y

xy = 20

(17 - y)y = 20

-y² + 17y = 20

-y² + 17y - 20 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

y = (-17 ± sqrt(17² - 4×-1×-20))/(2×-1) =

= (-17 ± sqrt(289 - 80))/-2 =

= (-17 ± sqrt(209))/-2

y1 = (-17 + sqrt(209))/-2 = 1.271583853...

y2 = (-17 - sqrt(209))/-2 = 15.72841615...

the 2 numbers are

1.271583853...

15.72841615...

Answer: 4 inches

Step-by-step explanation:

Caterpillars are small, so it wouldnt be 4feet

Brainliest plz ◉‿◉

Answer:

Its bottom left

Step-by-step explanation:

Answer:

The top left option

Step-by-step explanation:

This doesn't have a y-value so it will be the point on the x axis.

An easy way to figure questions like this is to use a graphing calculator.

Hope that helps and have a great day!

\(\begin{aligned}\frac{1}{h-5}+\frac{2}{h+5}&=\frac{16}{h^2-25}\\\frac{(h+5)+2(h-5)}{(h-5)(h+5)}&=\frac{16}{h^2-25}\\\frac{h+2h+5-10}{h^2-25}&=\frac{16}{h^2-25}\\\frac{3h-5}{\cancel{h^2-25}}&=\frac{16}{\cancel{h^2-25}}\\3h-5&=16\\3h&=16+5\\3h&=21\\h&=\frac{21}{3}\\h&=7\end{aligned}\)

Answer:

17: 6:48

18: 9:45

19: 85 minutes or 1 hour and 25 minutes

20: 165 minutes or 2 hours and 45 minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

1)

6:05

+ 0:43

6:48  is the answer

2)

8:00

+1:45

9:45  is the answer

3)

7:55

-6:30

1:25  answer

4)

8:20

-5:35

2:45 answer

Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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Answer:

sqrt 58

Step-by-step explanation:

7^2+3^2=c^2

c=\(\sqrt{58}\)

Answer:

sqrt(58)

Step-by-step explanation:

Use the Pythagorean Theorem.

a^2 + b^2 = c^2

3^2 + 7^2 = c^2

9 + 49 = c^2

58 = c^2

c = sqrt(58)

Answer: sqrt(58)

The definite integral is given by:∫₀² f(x) dx = ∫₀² x ln(1+x²) dx.

The process of finding the integral of a function is called integration, and it involves summing up an infinite number of small areas under the curve of the function.

The result of the integration is a new function that represents the area under the curve of the original function between the given limits of integration. It is an important tool in calculus and is used to solve a wide range of mathematical problems.

To express the limit as a definite integral on the given interval, we must substitute δx with (b-a)/n which is equal to 2/n. Therefore, the limit expression becomes:

lim n → ∞ {nΣi=1} xi ln(1+xi²)δx

Where δx = 2/n, [a, b] = [0, 2].

When we substitute the value of δx in the given expression, we get:

lim n → ∞ {nΣi=1} xi ln(1+xi²)δx=lim n → ∞ {2Σi=1} xi ln(1+xi²)/n

Now, we can express this limit as a definite integral using the following formula:

lim n → ∞ {2Σi=1} xi ln(1+xi²)/n = ∫₀² f(x) dx

where f(x) = x ln(1+x²)

Hence, the definite integral is given by:∫₀² f(x) dx = ∫₀² x ln(1+x²) dx.

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Answer:

O

Step-by-step explanation:

We can answer this by using the process of elimination

We want to find the position of 0.5

So let's begin

Looking at the number line...

D and E are both in between negative numbers

0.5 is not a negative number so immediately we can eliminate D and E

So it is between O and M

O is between 0 and 1

.5 is between 0 and 1 so O might be the answer

However let's look at M just to be safe.

M is located between 3 and 4.

Both 3 and 4 are greater than .5 meaning that M cannot represent .5

So we can conclude that O is the best answer

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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Answer:            

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

first you’d do the things in parentheses

In the parentheses you would simplify the exponent first because PEMDAS

(-3)^2 = 9

-4 + 9 - 6 = -1

Then you would do 15 / 3 which equals 5

5 x -1 = -5

-5 + 2 = -3

Answer:

Step-by-step explanation:

the slope-International cept frome y= mx + b was where m is the slope and b y-intercept

y=mx +b

m= -2/5

b=2

slope is :2/5

y-intercept is :2

x.   y  

0.  2

1    8/5

Answer:

Step-by-step explanation:

perp. -5/2

y + 2 = -5/2(x - 2)

y + 2 = -5/2x + 5

y = -5/2x + 3

(A ∩ D) ∩ B' can be rewritten as (tax returns with itemized deductions AND selected for audit) AND (tax returns NOT showing business income).

In words, (A ∩ D) ∩ B' refers to the set of tax returns that meet the following criteria: they have itemized deductions and were selected for audit, but they do not show business income.

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Answer:

EF = 2.37

Step-by-step explanation:

It's given that these are similar triangles.

In similar triangles, the side lengths are proportional.

We can write the following equation based on this information:

\( \frac{11}{3.3} = \frac{7.9}{ef} \)

11EF = 27.03

EF = 2.37

Answer: B

Step-by-step explanation:

The Black Plague or Black Death was spread from Asia to Europe through trading barges or ships. Since a lot of people in Asia contracted the plague, it was natural the rats on the ship also carried the disease. Where the ships landed, rats or their fleas hiding on humans would come with the travelers. While European countries were fighting wars during the plague, it mostly halted because of the sharply increasing deaths from the disease. Religion was used more for trying to cure the Black Death, and ironically there was more food and land for the survivors since there were less mouths to feed.

The scale of the drawing is in the ratio of 1 millimeter : 3 meter

In this, we need to find the ratio that is 1millimeter:x meter where x is the original scaling of the plot.

We have been given that

                   24 millimeters = 72 meters

Now we have to find how many meters is equal to 1 millimeter which will find out by the unitary method.

Thus,   24 millimeters = 72 meters

               1 millimeter = 72/24 meter

               1 millimeter = 3 meter

Hence the scale of the drawing is 1 millimeter : 3 meter

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the null hypothesis is rejected for an observed p-value of at 0.07 at a significance level of 0.05.

At a significance level of 0.05, the p-value of 0.07 indicates that the observed value is not statistically significant. As a result, the null hypothesis cannot be disproven.In other words, the observed value is not strong enough to prove that the null hypothesis is false. Therefore, the null hypothesis is not rejected for an observed p-value of 0.07 at the significance level of 0.05.

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it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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Based on the information provided, the two numbers whose HCF is 101 are 1010 and 1313.

The HCF is the highest common factor or in other words, the highest number by which two numbers can be divided. Let's start by listing the four digits numbers that can be the HCF related to 101.

101 x 10 = 1010

101 x 11 = 1111

101 x 12 = 1212

101 x 13 = 1313

Now, from these numbers, there are two numbers whose difference is 303.

1313 - 1010 = 303

Based on this, the two numbers are 1010 and 1313

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The measure of side EF is 15.

The polygon that has three sides and three vertices is called a triangle.

When it comes to Euclidean geometry, two triangles are said to be comparable if they have the same shape or the same shape as each other's mirror image. One can be produced from the other more precisely by evenly scaling it, perhaps with the addition of further translation, rotation, and reflection.

Since the two triangles are equivalent, their corresponding sides are proportional. So we can write,

BC/EF = CD/FG

Given that, DC =8, BC=5, and FG =24. By substituting these values, we get

5/EF = 8/24

EF = (5*24)/8 = 15

Hence, the value of side EF is 15.

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Answer:

=====================

The distance between points (x₁, y₁) and (x₂, y₂) is:

So we have both segments with same length of 5 units

The direction angle of the vector q = 4i + 3j is approximately 36 degrees.

To determine the direction angle of a vector, we can use the formula:

θ = tan^(-1)(y/x)

Given the vector q = 4i + 3j, we can identify the components as x = 4 and y = 3.

θ = tan^(-1)(3/4)

θ ≈ 36 degrees

Therefore, the direction angle of the vector q = 4i + 3j is approximately 36 degrees.

The direction angle of the vector q = 4i + 3j, rounded to the nearest degree, is approximately 36 degrees.

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Answer:

no

Step-by-step explanation:

it was slower the way there and if he was going 40 it would have taken the same time to get there as it would have to go back

Answer:

Yes.

Step-by-step explanation:

Reiko's average speed was 80 miles per hour. That is more than 40 miles per hour. Even if it took him longer to drive from A to B, his speed would still be more than 40 miles per hour to have the average speed be 80 miles per hour.

Hope this helps!

The probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a population of marks on a biology final test that is normally distributed with a mean of 78 and a standard deviation of 6. We want to know the probability that a class of 50 has an average score that is less than 77.
Using the central limit theorem, we can calculate the standard error of the mean as follows:
standard error of the mean = standard deviation / square root of sample size
standard error of the mean = 6 / √50
standard error of the mean = 0.8485
Next, we need to calculate the z-score for a sample mean of 77:
z-score = (sample mean - population mean) / standard error of the mean
z-score = (77 - 78) / 0.8485
z-score = -1.18
We can use a standard normal distribution table or calculator to find the probability associated with a z-score of -1.18. The probability of a sample mean less than 77 is approximately 0.1190 or 11.90%.
Therefore, the probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

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The corner points of the feasible region are:

(0, 0), (19/12, 0), (0, -19/11), and (-6, 0).

The given system of linear inequalities is:

-15x + 9y ≤ 0-12x + 11y ≤ -19 3x + 2y ≤ -18

Now, we need to find the corner points of the feasible region and for that, we will solve the given equations one by one:

1. -15x + 9y ≤ 0

Let x = 0, then

9y ≤ 0, y ≤ 0

The corner point is (0, 0)

2. -12x + 11y ≤ -19

Let x = 0, then

11y ≤ -19,

y ≤ -19/11

Let y = 0, then

-12x ≤ -19,

x ≥ 19/12

The corner point is (19/12, 0)

Let 11

y = -19 - 12x, then

y = (-19/11) - (12/11)x

Let x = 0, then

y = -19/11

The corner point is (0, -19/11)

3. 3x + 2y ≤ -18

Let x = 0, then

2y ≤ -18, y ≤ -9

Let y = 0, then

3x ≤ -18, x ≤ -6

The corner point is (-6, 0)

Therefore, the corner points of the feasible region are (0, 0), (19/12, 0), (0, -19/11) and (-6, 0).

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Answer:

9/4

Step-by-step explanation:

2 1/4 = 9/4 From mixed fraction to an improper fraction: "the numerator of the improper fraction" = "denominator" xx "the whole number" + "the numerator of the mixed fraction" The denominator remains as it is. So 2 1/4 = (4 xx 2 + 1)/4 = 9/4

Answer:

9/4

Step-by-step explanation:

Multiply the denominator which is 4 by the whole number which is 2.

4 x 2 = 8

Next add the numerator to the 8.

8 + 1 = 9

The 9 is now the numerator and keep the original denominator.

9/4

Answer:

The explanation Marc can give

Jose is, you should have added 12 and –12 for the xy terms

Step-by-step explanation:

Josh calculation

-8x^2y-17xy^2+12xy-8+5x^2y-xy^2-12xy=-3x^2y-18xy^2+24xy-8

Correct calculation

-8x^2y-17xy^2+12xy-8+5x^2y-xy^2-12xy

Collect like terms

= -8x^2y+5x^2y-17xy^2-xy^2+12xy-12xy-8

= -3x^2y-18xy^2-8

The explanation Marc can give

Jose is, you should have added 12 and –12 for the xy terms.

Answer:

A

Step-by-step explanation:

Edg