Answer the following questions regarding the integers from 1 through 1000.

a) How many integers from 1 through 1,000 are multiples of 5 or 9.

b) How many integers from 1 through 1,000 are neither multiples of 5 nor multiples of 9?

The slope of the line is given by m = 5/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 3 , -1 )

Let the second point be Q ( 5 , 4 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 4 - ( - 1 ) ) / ( 5 - 3 )

Slope m = ( 4 + 1 ) / 2

Slope m = 5/2

Hence , the slope of the line is m = 5/2

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The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

334.6 miles

Step-by-step explanation:

Do either

47.8 x 7 = 334.6

or

47.8 + 47.8 + 47.8 + 47.8 + 47.8 + 47.8 + 47.8 + 47.8 = 334.6

The null hypothesis for this scenario is that the valve performs to the specifications, i.e., the mean pressure produced by the valve is 5.9 lbs/square inch. The alternative hypothesis is that the valve does not perform to the specifications, i.e., the mean pressure produced by the valve is not 5.9 lbs/square inch.

To determine if there is sufficient evidence to reject the null hypothesis, we need to perform a hypothesis test.

Since the sample size is greater than 30 and we know the population standard deviation, we can use a z-test. We can calculate the test statistic as:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Plugging in the given values, we get:

z = (6.1 - 5.9) / (0.9 / sqrt(130)) = 2.33

Using a standard normal distribution table, we find that the probability of getting a z-value of 2.33 or greater is approximately 0.01.

Since this probability is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence that the valve does not perform to the specifications.

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We have shown that AD/BE * \((F/C)^2\) = D/E, which means that the equivalent ratio of A/B is to D/E. So the option D/E is correct.

What is the ratio?

Ratio is a mathematical term used to compare two or more numbers. It is expressed as the quotient of one number divided by another number. Ratios can be written in different ways, such as using the colon (:) symbol, as a fraction, or as a decimal.

Let's begin by using the Pythagorean theorem to find the lengths of the sides of triangles ABC and DEF:

AC = \(\sqrt{(A^2 + C^2)}\)

BC = \(\sqrt{(B^2 + C^2)}\)

DF = \(\sqrt{(D^2 + F^2)}\)

EF = \(\sqrt{(E^2 + F^2)}\)

Now we can express A/B in terms of the ratios involving A and D, and B and E:

A/B = (A/C) / (B/C) = (A/C) / (E/F) * (D/F) / (B/C) = AD/BE * \((F/C)^2\)

To show that A/B is equivalent to D/E, we need to show that AD/BE * \((F/C)^2\) = D/E.

Using the ratios we derived above, we can write:

AD/BE * \((F/C)^2\) = (A/C) * (D/F) * \((E/F)^{-1\) * \((C/B)^{-1\)

= (A/C) * (D/F) * (F/E) * (B/C)

= AD/EF * BC/BE

Now we need to show that AD/EF = D/E and BC/BE = 1.

Since triangle ABC and triangle DEF are similar, we have:

A/C = D/F and B/C = E/F

Therefore, we can write:

AD/EF = (A/C) / (E/F) = (D/F) / (F/E) = D/E

BC/BE = (B/C) / (E/F) = (E/F) / (E/F) = 1

Therefore, we have shown that AD/BE * \((F/C)^2\) = D/E, which means that A/B is equivalent to D/E. So the option D/E is correct.

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There are no values within the interval that satisfies the condition stated by Rolle's theorem.

In accordance to Rolle's theorem, a function existing within an closed interval [a, b] has at a least a value c within that interval such that the first derivative f'(c) is equal to the slope of the secant line that passes through the two interval limits. That is to say, Rolle's theorem is defined by the following formula:

f'(c) = [f(b) - f(a)] / (b - a), where a < c < b

Where:

First, evaluate the function f(x) at x = - 4:

x = - 4

f(- 4) = (- 4)³ - 4 · (- 4)² - 16 · (- 4) + 8

f(- 4) = - 64 - 64 + 64 + 8

f(- 4) = - 56

Second, evaluate the function f(x) at x = 4:

x = 4

f(4) = 4³ - 4 · 4² - 16 · 4 + 8

f(4) = 64 - 64 - 64 + 8

f(4) = - 56

Third, determine the first derivative of the function f(x) and evaluate it at x = c:

f(x) = x³ - 4 · x² - 16 · x + 8

f'(x) = 3 · x² - 8 · x - 16

x = c:

f'(c) = 3 · c² - 8 · c + 16

Fourth, find the roots of the quadratic function found in the previous step.

3 · c² - 8 · c + 16 = 0

In accordance with the quadratic formula, the roots of the expression are 4 / 3 + i 4√2 / 3 and 4 / 3 - i 4√2 / 3, which are not real numbers.

Fifth, determine whether Rolle's theorem are applicable on the roots found in the previous step.

Since the roots of the polynomial 3 · c² - 8 · c + 16 are not real numbers, there are no number within the interval that satisfies Rolle's theorem.

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Answer:

x+4

It's too short. Write at least 20 characters to explain it well.

Answer:

A = 280cm^2

Step-by-step explanation:

we have 2 shapes, a parallelogram, and a rectangle

lets find our area of the rectangle

A = lw

A = 20(7.5)

A = 150

now for the parallelogram

A = bh

A = 20(6.5)

A = 130

now we add to find the entire A

A = 150+130

A = 280

Answer:

False, because for being a function, there must be only one y for each value of x.

Answer:

42.40705%

Step-by-step explanation:

(1 - (23/100)^(19/9) = 1 + r/100

0.57593 = 1 + r/100

r = 42.40705%

The amount left over is  $120,499.85.

The present value of the amount invested in the municipal bond and the high yield savings account has to be determined.

Present value = FV ÷ (1 + r)^(nm)

Where:

r = interest rate

m = number of compounding

FV = future value

Present value of the future value in the high yield savings account:

r = 9/4 = 2.25%

m = 4

200,000 ÷ ( 1 + 0.0225)^(4 x 5)

200,000 ÷ (1.0225^20)

= 128,163.29

Present value of the future value of the municipal bond: r = 6.78 / 2 = 3.39%

m = 2

100,000 ÷ (1 + 0.0339)^(2 x 10)

100,000 ÷ (1.0339^20) = $51,336.86

Amount left over = $300,000 - $51,336.86 - 128,163.29 = $120,499.85

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Answer:

The situation that can be represented by the sum 5.25 ÷ (-1.35) is:

C. Before heating a solution, a scientist measured its temperature to be 5.25 *F. The scientist stopped heating the solution after 1.35 hours. The sum represents the final temperature of the solution.

The respondents who chose alternative B in the study were likely influenced by the description of Linda's personality and interests, which made alternative B appear more representative of Linda's character.

The scenario you described is known as the "conjunction fallacy" and was first documented by Kahneman and Twersky in their influential 1982 study. The fallacy occurs when people assign a higher probability to a conjunction of events (in this case, alternative B) than to one of its individual components (alternative A). However, logically speaking, alternative B cannot have a higher probability than alternative A.

Alternative A: Linda is a bank teller.

Alternative B: Linda is a bank teller and is active in the feminist movement.

When we consider alternative A, we are only focused on Linda's profession, which is being a bank teller. This means that any scenario where Linda is a bank teller, regardless of her other characteristics or affiliations, would fall under alternative A. The probability of alternative A encompasses all the possible instances where Linda is a bank teller, whether she is involved in the feminist movement or not.

On the other hand, alternative B is a conjunction of two events: Linda being a bank teller and Linda being active in the feminist movement. In order for alternative B to be true, both events must be true simultaneously. It is crucial to understand that the probability of two events occurring together (alternative B) is always equal to or lower than the probability of either event occurring alone (alternative A).

Therefore, it is not logically possible for alternative B to have a higher probability than alternative A.

The respondents who chose alternative B in the study were likely influenced by the description of Linda's personality and interests, which made alternative B appear more representative of Linda's character. However, probability-wise, alternative A should have a higher likelihood than alternative B.

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Answer:

67

Step-by-step explanation:

we have a gap between 1st and 2nd terms of 4. a gap between 2nd and 3rd of 8. 16 for next gap. the gap doubles every time.

so we expect gap between 4th and 5th terms to be 2 X 16 = 32.

35 + 32 = 67. that is the next number in the sequence.

Step-by-step explanation:

marked price = 100%

1% = 100%/100 = marked price / 100

discount = marked price - selling price

discount % = discount / 1% =

= (marked price - selling price) / (marked price)/100 =

= 100×(marked price - selling price) / (marked price)

Answer:

\(y=\frac{3}{4}+2x\)

Step-by-step explanation:

Coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.

From the question, we have the following statements:

As a general rule, circles that have the above features are referred to as concentric circles.

This is so because concentric circles have the same center, and they do not intersect

Hence, coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.

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Answer:34/45

Step-by-step explanation:

Step-by-step explanation:

= P [ 1-R/100 ] T

= 15000 [ 1-12/100] ⁵

= 15000 [100-12/100]⁵

= 15000 [0.88]⁵

= 15000 × 0.52773

= 7915.95..

i hope it's correct....

The sales tax paid 1.15=3y/23

What is Sales tax?

Government-imposed consumption taxes on the purchase of goods and services are known as sales taxes. Typically, a sales tax is assessed at the point of sale, paid to the store, and then forwarded to the government. A company is responsible for paying sales taxes in a specific jurisdiction if it has a nexus there. Depending on the local rules, this could be a physical location, a worker, an affiliate, or some other kind of presence.

Step by step Explaination:

Sales tax: 15%

Converting 15%=15/100

                         =0.15

To show sales tax paid is 3y/23

0.15=3y/23

Multiply both side by 23

23*0.15=3y

3.45=3y

Divide both sode by 3

3.45/3=y

y=1.15

The sales tax paid 1.15=3y/23(as the purchase price includes sales tax).

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Answer:

I'd say D, if I'm wrong please let me know. but I'm 100% sure it's D

Answer:

56.52

Step-by-step explanation:

V=πr²h

V=3.14*3²*2=56.52

The number of "same" types of 2x3 matrices in reduced row echelon form, option (c) 4.

To determine the number of "same" types of 2x3 matrices in reduced row echelon form, we need to consider the possible configurations of the leading entries (pivot positions) in the matrix.

Since we have a 2x3 matrix, there can be at most two leading entries, one in each row. The possible configurations of the leading entries are as follows:

No leading entries (both rows contain only zeros): This is a valid configuration and counts as one type.

Considering the valid configurations, there are a total of 4 "same" types of 2x3 matrices in reduced row echelon form.

Therefore, the answer is c. 4.

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Answer:

acute

Step-by-step explanation:

this is an acute triangle because all angles are less than 90 degrees

it is not obtuse because no angle is over 90 degrees

it is not equiangular because the angles are not equal to each other

and it is not right because there is no right angle

Acute

Triangles can be classified by the size of their angles.

Angle Classification

Angles can be classified into 3 sizes: acute, right, and obtuse.

Triangle Classification

Triangles are classified by their largest angle. If the largest angle is obtuse, then it is an obtuse triangle. If there is a right angle, then it is a right triangle. If the largest angle is an acute angle, then it is an acute triangle. Finally, there is one special classification that technical falls under acute angles. If all of the angles are equal (meaning they are all 60°), then it is an equiangular triangle.

The triangle in the picture has 3 angles that are all under 90°. The largest angle is 76°. Since this is an acute angle, it is an acute triangle.

Answer:

3/8 is left

Step-by-step explanation:

Tom ate 3/8 of the pizza

Take 1 - 3/8

8/8 - 3/8 = 5/8

5/8 of the pizza is left

The brother at 2/5 of the remainder

5/8  * 2/5

2/8

1/4

His brother at 1/4 of the  of the pizza

5/8 - 1/4

5/8 - 2/8

3/8 is left