There are books on a shelf. of these books are new. The rest of them are used. what is the ratio of used books to all books on the shelf?

Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

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Answer:

1:7

Step-by-step explanation:

1 teacher for every 7 kids

The steps to sketch the graph of a rational function in the appropriate order is in the order: 1,4,2,3

The steps to sketch the graph of a rational function will be first to find the function's zeros and vertical asymptotes, and plot them on a number line, the second step is to choose test numbers to t the left and right of each of these places, and find the value of the function at each test number., the third step is to use test numbers to find where the function is a positive and where it is negative and the last step is to sketch the function's graph, plotting additional points as guides as negative.

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Place the steps to sketch the graph of a rational function in the appropriate order.

1)find the function's zeros and vertical asymptotes, and plot them on a number line.

2) use test numbers to find where the function is positive and where it is negative.

3) sketch the function's graph, plotting additional points as guides as negative.

4)choose test numbers to t the left and right of each of these places, and find the value of the function at each test number.​

In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

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Answer:

d

Step-by-step explanation:

P(boy above average grades) P(above average grades) is the right answer. The correct option is C.

The likelihood that event A will occur provided that event B has already happened is known as conditional probability. It is written as "the probability of A given B" and is indicated by the symbol P(A|B).

We must employ conditional probability in order to respond to this inquiry. We are aware that there are 75 pupils in the class overall, with 37 boys and 38 girls. We also know that 22 girls and 23 boys both have GPAs above the national average.

A. Boy with above-average grades equals a boy.

This claim is untrue. The likelihood of picking a guy at random from the class is 37/75, or P(boy). The likelihood of picking a kid from the class who has above-average grades at random is 23/75, or P(boy with average grades). The odds of these two events are not equal.

B. Boy with above-average grades equals P with above-average grades

This claim is untrue. The chance of picking a student with above-average grades at random from the class is P(above average grades), which is (23+22)/75 = 45/75. The likelihood of picking a kid from the class who has above-average grades at random is 23/75, or P(above-average grades boy). The odds of these two events are not equal.

P (boy with above-average grades) C (boy with above-average grades)

This assertion is accurate. P(boy over average grades) = 23/75 and P(above average grades) = 45/75, respectively, are already known values. The odds of these two events are not equal.

D. P(boy | grades over average) = P(boy)

This claim is untrue. The conditional probability that a student will have above average grades given that they are a boy is P(above average grades | boy), which is 23/37. The likelihood of picking a guy at random from the class is 37/75, or P(boy). The odds of these two events are not equal.

Therefore, the correct statement is C. P(boy above average grades) ≠ P(above average grades).

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Answer: x = 4, y = 5

Step-by-step explanation:

To solve by elimination, we must first eliminate one of the variables of the equations. We'll get rid of y, and to do this, you have to multiply 2x - y = 3 by -6.

-6(2x - 7 = 3)

-12x + 6 = -18

Now add -12x + 6 = -18 to with 9x - 6y = 6 to get rid of y.

-3x = -12 Solve for x

x = 4

Now plug x back into the original equation to solve for y.

2(4) - y = 3

8 - y = 3

-y = -5

y = 5

Your final solution is (4, 5)

Answer:height = 5 inches  and the base = 10 inches.

Step-by-step explanation:

Answer: y = 0.794*x + 4.588

Step-by-step explanation:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case the points are:

(-2, 3) and the intersection of the lines:

x + 2y = 0

2x - y - 12  = 0

To find the intersection of those lines, we can first isolate one variable in one side of each equality, i will isolate the variable y.

y = -x/2

y = 2x - 12

Now we can write:

-x/2 = 2x - 12

Solving this we can find the value of x at which both lines intersect.

2x + x/2 = 12

(5/2)*x = 12

x = 12*(2/5) = 4.8

Now we evaluate one of the lines in that point and get:

y = -4.8/2 = -2.4

Then these lines intersect at the point (4.8, -2.4)

Now we can find the slope of our equation.

a = (-2.4 - 3)/(4.8 - (-2)) = 0.794

then we have:

y = 0.794*x + b

And we know that when x = -2, y = 3

then:

3 = 0.794*-2 + b

3 + 1.588 = b = 4.588

Then the equation is:

y = 0.794*x + 4.588

Answer:

y=(-27/34)x+1.412

Step-by-step explanation:

Building of  facundo3141592's answer, the beginning part is correct. The point of intersection between the two lines is (4.8, -2.4)

He got the slope part right, but the answer isn't 0.794, its -27/34. (he forgot the negative) The y intercept is totally wrong. The y-intercept is 1.412 So the answer is y=(-27/34)x+1.412

I hope this helps!

Graph this equation on Desmos and you will see that it first all the criteria

Answer:

30, 000 Nm

Step-by-step explanation:

F = mg = 5000 N

h = 6 m

Work done

W = mgh = 5000*6= 30, 000 Nm

Answer:

30000 nm

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

This is because it is the lowest point on the line.

the area of the windshield, cleaned by the windshield wiper is mathematically given as 0.096inche^2

This is further explained below.

The term "acute area of the windshield glazing" refers to the section of the windshield that measures eight and one-half inches by eleven inches and is located immediately in front of the driver's line of sight, as seen in the image.

Then, let's call the part of the windshield labeled "ABC" A.

\(A=\frac{1}{2} r^2 \theta\)

Now, substituting the given values we get,

\(\begin{aligned}&A=\frac{1}{2} r^2 \theta \\&A=\frac{1}{2} \times(7)^2 \times \frac{\pi}{180} \\\end{aligned}$$\)

A=0.4276

Then let the area of the windshield, ADE, be denoted by the letter A',

\(A^{\prime}=\frac{1}{2} r^2 \theta\)

Now, after replacing those values with the ones we were provided,

\(\begin{aligned}&A^{\prime}=\frac{1}{2} r^2 \theta \\&A^{\prime}=\frac{1}{2} \times(1)^2 \times 60 \times \frac{\pi}{180} \\&A^{\prime}=0.5236\end{aligned}\)

In conclusion, In order to calculate the area of the windshield, you need to take the difference between A and A'.

0.5236-0.4276=0.096

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Answer:

6.5sin(.04x+.4pi)-8

The function intersects its midline at (-pi,-8) and has a maximum point at (pi/4, "-1.5). The  final equation is h(x) = 4 sin(2x +  π /2) + 3.

A function is defined as a relation between the set of inputs having exactly one output each.

The function intersects its midline at (3π/4, 3) then the midline is d= 3.

The amplitude is just the positive distance between the maximum/minimum and the midline,

so the amplitude a = 7 - 3 = 4

Also, given that period is 2π/b and the fact that the period is π from our given maximum,

we have the equation 2π/b= π where b = 2

we know that the phase shift, -c/b is - π/4 (or  to the left)

since -π /4. Therefore, c = π /2.

our final equation is

h(x) = 4 sin(2x +  π /2) + 3.

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Answer:

4.

\(x=8\sqrt{3}\)

\(y=16\)

5.

\(x=3\)

\(y=3\sqrt{3}\)

Step-by-step explanation:

The sides of a (30 - 60 - 90) triangle follow the following proportion,

\(a-a\sqrt{3}-2a\)

Where (a) is the side opposite the (30) degree angle, (\(a\sqrt{3}\)) is the side opposite the (60) degree angle, and (2a) is the side opposite the (90) degree angle. Apply this property for the sides to solve the two given problems,

4.

It is given that the side opposite the (30) degree angle has a measure of (8) units. One is asked to find the measure of the other two sides.

The measure of the side opposite the (60) degree side is equal to the measure of the side opposite the (30) degree angle times (\(\sqrt{3}\)). Thus the following statement can be made,

\(x=8\sqrt{3}\)

The measure of the side opposite the (90) degree angle is equal to twice the measure of the side opposite the (30) degree angle. Therefore, one can say the following,

\(y=16\)

5.

In this situation, the side opposite the (90) degree angle has a measure of (6) units. The problem asks one to find the measure of the other two sides,

The measure of the side opposite the (60) degree angle in a (30-60-90) triangle is half the hypotenuse times the square root of (3). Therefore one can state the following,

\(y=3\sqrt{3}\)

The measure of the side opposite the (30) degree angle is half the hypotenuse (the side opposite the (90) degree angle). Hence, the following conclusion can be made,

\(x=3\)

Aircraft A has 312 seats.

Let's assume that Aircraft B has x seats.

According to the given information, Aircraft A has 105 more seats than Aircraft B. So, the number of seats in Aircraft A can be expressed as x + 105.

The total number of seats in both aircraft is 519, which can be represented by the equation:

x + (x + 105) = 519

Simplifying this equation, we have:

2x + 105 = 519

Subtracting 105 from both sides, we get:

2x = 414

Dividing both sides by 2, we find:

x = 207

Therefore, Aircraft B has 207 seats.

To find the number of seats in Aircraft A, we substitute the value of x back into the expression x + 105:

Aircraft A = 207 + 105 = 312

Hence, Aircraft A has 312 seats.

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The constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

A proportional relationship is a mathematical equation that expresses two variables that are in proportion to one another. In this type of relationship, if one variable is multiplied by a certain constant factor, then the other variable will be multiplied by the same constant factor. For example, if the cost of 3 books is $15, then the cost of 6 books will be $30. In this case, the number of books and the cost of the books are in proportion to one another.

The constant of proportionality is the constant factor by which the two variables are multiplied to obtain each other. In other words, it is the ratio between the two variables that remain constant in a proportional relationship. It can be represented by the letter k, and is calculated by dividing one variable by the other.

To find the constant of proportionality from a graph, we need to look at the slope of the line. The slope is the ratio between the change in the y-values and the change in the x-values, which is also known as the rise over run. If the graph shows a proportional relationship, then the slope will remain constant throughout the graph.

For example, if the graph shows the relationship between the number of hours worked and the amount of money earned, and the slope is 10, then the constant of proportionality is 10. This means that for every hour worked, the person earns $10. The equation for this proportional relationship can be written as y = 10x, where y represents the amount of money earned and x represents the number of hours worked.

In conclusion, the constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

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Answer:

3

Step-by-step explanation:

-(4)+7=3

plug in 4 for d and since it is -d it would be -4

7-4=3

4580 or 4600 is the best answer I have gotten for this question

Answer: The domain is in the picture

Step-by-step explanation:

Answer:

- 14x +3

Step-by-step explanation:

hope this helps u. : )

The value of trigonometric ratio tan A = 2/ √5.

One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.

Given:

We have opposite side to A = 2

and, adjacent side to A = √5

Using Trigonometry

tan A = opposite side / adjacent side

tan A = 2/ √5

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Answer: 10/40 or 1/4

Step-by-step explanation:

Add up all the amount of rolls, so 10+6+4+8+6+6=40

then add the probability of rolling a 3 or 6 = 10

divide that quantity out of the whole

answer is 10/40 and simplified is 1/4

hope it helps

ZCBE and ZDEB are same-side interior angles.

is the correct answer

The total price of the graphing calculator is $80.07.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Given that,

Original price of the graphing calculator = $83

There is a 15% off on the site on all orders over $50.

Price of the calculator will be 100 - 15 = 85% of the actual price.

Price of the graphing calculator after the discount = 85% × 83

                                                                                    = 0.85 × 83

                                                                                    = $70.55

Sales tax on the discounted price = 4.5%.

Price after adding sales tax = $70.55 + (4.5% × 70.55)

                                              = $73.72475

There is a shipping fee of $6.35.

Total price = $73.72475 + $6.35

                  = $80.07475

Hence the total price is a. $80.07.

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The correct answer is (a) $234.95.

what is compund interest?

Compound interest is a type of interest where the interest is added to the principal amount of a loan or investment, and then the interest for the next period is calculated based on the new total. This means that the interest earned in each period is added to the original principal, and then interest is calculated on the new total for the next period.

ax + b = 0

where a and b are constants. The variable x appears only with the first power, and the coefficient a is not equal to zero.

Here's the explanation:

The school will pay 10% of the cost of the copy machine in cash, which is:

10% of $5,500 = 0.1 x $5,500 = $550

So the amount that needs to be financed through the credit union is:

$5,500 - $550 = $4,950

The credit union will charge 4% per year compounded monthly for 2 years. To calculate the monthly payment, we first need to calculate the total amount that will need to be paid back after 2 years, including interest. We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the total amount to be paid back

P = the principal amount (the amount borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

In this case:

P = $4,950

r = 0.04 (4% as a decimal)

n = 12 (monthly compounding)

t = 2 (2 years)

Plugging in these values, we get:

A = $4,950(1 + 0.04/12)^(12*2) = $5,365.39

So the total amount that needs to be paid back is $5,365.39. To calculate the monthly payment, we can use the formula for a fixed-payment loan:

P = (rA)/(1 - (1+r)^(-n))

where:

P = the monthly payment

r = the monthly interest rate (as a decimal)

A = the total amount to be paid back

n = the number of payments (in this case, the number of months)

In this case:

r = 0.04/12 = 0.0033333 (monthly interest rate)

A = $5,365.39

n = 2*12 = 24 (2 years, with monthly payments)

Plugging in these values, we get:

P = (0.0033333 x $5,365.39)/(1 - (1 + 0.0033333)^(-24)) = $234.95

So the school's monthly payment will be $234.95. Therefore, the correct answer is (a).

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According to Polynomial System, the correct answer is that the roots of f(x) are (x+1).

A polynomial system (sometimes just a polynomial system) is a set of simultaneous equations f₁ = 0,..., fₙ = 0. where fi is a polynomial in multiple variables such as x₁,..., xₙ over the fields. k.

This is due to the zero product property that when two binomials are multiplied by 0, one of their factors must be 0.

A simple example of a system of polynomial equations is

x²+y²- 5 = 0

      xy-2 = 0.

Its solutions are the four pairs (x, y) = (1, 2), (2, 1), (-1, -2), (-2, -1). These solutions are easily verified by substitution, but proving that there are no other solutions requires more work.

Based on above description, we can say that:

(x+1) must be 0.

(x+1)=0

x=-1

Thus, If (x-1)=0 then x is 1 instead of -1 in question.

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Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.