How many different arrangements of letters can be formed if the letter must be repeats of letters are allowed?

Step-by-step explanation:

what is the problem ?

first you need to put "1" in place of the x and calculate, and then you need to put "2" in place of the x and calculate.

just simple calculation !

(a)

R(1) = 1000×1² / (1² + 4) = 1000 / 5 = 200

$200 million

(b)

R(2) = 1000×2² / (2² + 4) = 4000 / 8 = 500

$500 million

there ! that's all that was needed.

Given:

The Radius of the circle: 2.5 inch

To find:

The area of the circle

Step-by-step solution:

We know that:

The Area of the circle = π(r)²

The Area of the circle = π(2.5)²

The Area of the circle = 3.14 × (2.5)²

The Area of the circle =

Given point:

(2, 24)

To find the constant proportionality:

In general, the constant proportionality is

Hence, the constant proportionality is 12.

We have the following:

let x cost of a box of candy

let y cost of a box of peanuts

resolving the system of equations:

now, for y

Therefore the cost of the box of candy is $ 2 and the cost of the box of peanuts is $ 25

Jimmy is paid $14.50 per hour for a regular forty-hour work week and 5 point time and a half for any hour worked over 40. This pas week, Jimmy earned $754.00 in total pay. How many hours of overtime did Jimmy work? ​

Let

x -----> the total hours worked

we have that

$14.50 --------> 40 hours

5.5($14.50) -------> > 40 hours

so

754=14.50*40+5.5(14.50)x

solve for x

754=580+79.75x

79.75x=754-580

79.75x=174

x=2.2 hours

-3(x + 1) - 5

(-3)(x) + (-3)(1) -5

-3x - 3 -5

-3x - 8

-2(u + 3) + 4u

-2u - 6 + 4u

2u - 6

Answer:

(f o g) = 464

Step-by-step explanation:

f(x) = x² - 3x + 4; g(x) = -5x

(f o g)(4) = f(g(4))

f(g(4)) = -5(4) = -20

f(g(4)) = (-20)² - 3(-20) + 4

f(g(4)) = 464

I hope this helps!

Given the equation

To solve this first pass all x-related terms to the left side of the equation and all other terms to the right side:

And solve

SOLUTION

Let the total number of cards in Ketin's card collection be k

Let the number of baseball cards be b, and

the number of football cards be f

Now, the ratio of baseball cards to football cards is 6 to 7, that is

Also, he has 120 baseball cards.

This means

So, the total number of cards in Ketin's card collection is

Hence the answer is 260

Inga should use the first option that is [tex]2(x^2+6x+9)=3+18[/tex] to solve the quadratic equation.

Given equation:-

[tex]2x^2+12x-3=0[/tex]

We have to find which one of the given options are needed to solve the quadratic equation.

The given quadratic equation can be rewritten as:-

[tex]2x^2+12x[/tex]-3+3=0+3

[tex]\\2x^2+12x[/tex]-3 + 3 + 18=0 +3 +18

[tex]2x^2[/tex] + 12x + 18 = 0 + 3 + 18

Hence, the answer is the first option.

Quadratic equation

Quadratic equations are the polynomial equations of degree 2 in one variable of type [tex]f(x) = ax^2 + bx + c = 0[/tex]where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α, β).

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The longest at an airport has the shape of a rectangle and an area of 2,181,600 this runaway is 180 feet wide how long is the runaway

Remember that

The area ofa rectangle is equal to

A=L*W

in this problem we have

A=2,181,600 ft2

W=180 ft

substitute given values

2,181,600=L*180

Solve for L

L=2,181,600/180

Answer:

The answer is C.

Step-by-step explanation:

In order to solve this, you must use an inequality from one side of the equation.

Inequality is the growing inequality between rich and poor.

First thing you do is divide by 4 from both sides.

[tex]\sf{\dfrac{4x}{4} > \dfrac{-8}{4}}[/tex]

Solve.

Divide these numbers goes from left to right.

-8/4=-2

[tex]\boxed{\sf{x > -2}}[/tex]

Therefore, the graph represents the solution set of the inequality of 4x>-8 is C, which is our answer.

I hope this helps, let me know if you have any questions.

To determine the lateral area of the prism;

To determine total area of the prism;

To determine the volume of the prism;

Hence

The ratio of a quarterback's completed passes to attempted passes is 5 to 8. If he attempted 16 passes, find how many passes he completed. Round to the nearest whole number if necessary.

Let

x -----> number of quarterback's completed passes

y -----> number of quarterback's attempted passes

so

x/y=5/8 -----> x=(5/8)*y -----> equation A

y=16 -----> equation B

substitute equation B in equation A

x=(5/8)*16

x=10

therefore

Answer: y = x/5 + 12/5

Explanation:

The first step is to find the equation of line AC

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept.

The formula for calculating slope of a line is expressed as

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

Considering line AC with points, A(2, 1) and C(1, 6),

x1 = 2, y1 = 1

x2 = 1, y2 = 6

m = (6 - 1)/(1 - 2) = 5/- 1 = - 5

Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Negative reciprocal of - 5 is 1/5

Thus, slope of the perpendicular line passing through B(3, 3) is m = 1/5

We would find the y intercept, c of the line by substituting m = 1/5, x = 3 and y = 3 into the slope intercept equation. We have

3 = 1/5 * 3 + c

3 = 3/5 + c

c = 3 - 3/5

c = 12/5

By substituting m = 1/5 and c = 12/5 into the slope intercept equation, the equation of the line is

y = x/5 + 12/5

Let the price of each ticket be represented by

The price of two tickets will be

The tax on the price of the tickets is 6% which be represented as

The price of the two tickets after tax will be

Therefore,

The price of the tickets after adding an additional booking fee of $20 will be given below as

Since,

We were asked to get the algebraic expression person, we would therefore divide the above expression by 2

Hence,

The algebraic expression to represent the price per person using variable t is

=0.53t + 10

The probability of landing in any colour is:

so if we want to get a red, both times, we to multiply 1/5 twice

so, the probability of getting red twice is 1/25

The row echelon form of the matrix is presented as follows;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]

The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.

The given matrix is presented as follows;

[tex]\begin{bmatrix}-3 &6 &15 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]

The conditions of a matrix in the row echelon form are as follows;

Dividing Row 1 by -3 gives:

[tex]\begin{bmatrix}1 &-2 &-5 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}[/tex]

Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 1&0 &-1 \\\end{bmatrix}[/tex]

Subtracting Row 1 from Row 3 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&2 &4 \\\end{bmatrix}[/tex]

Adding Row 2 to Row 3 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&0 &18 \\\end{bmatrix}[/tex]

Dividing Row 2 by -2, and Row 3 by 18 gives;

[tex]\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}[/tex]

The above matrix is in the row echelon form

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Pizza diameter D is given in mixed form:

Now, me must compare D with the lenght of the square box.

Since the lenght of the box is L=6.38 in. Hence, the box is big enough to

fit the pizza.

Explanation:

The test contains 10 questions, each one can be answered either with 'true' or with 'false' which means that for each question there are only 2 options.

We need to find the number of ways in which the test can be completed.

To answer the question we use the fundamental counting principle:

In this case, there are 2 ways to complete each question, therefore, we multiply that by the 10 questions that we have:

This can be simplified to

which is equal to:

Answer:

1024

The given statement is the product of 2 groups of 7.

This statement can be expressed as

Where each seven represent one group.

Given,

The speed of first train is 175km/h.

The speed of second train is 225 km/h.

Consider, the time taken by first train to meet is x h.

The time taken by the second train to meet is (x-2) h.

The distance is calculated as,

At the meeting point the distance covered by both train is same,

So, taking the distance equation of both trains in equal,

The first train meet to second train after distance,

The second train meet to first train after distance,

Hence, both train meet after 1575 km from the station.

Given

Client takes 1 1/2 of medication one time

Find

how many tablets will client have been taken at the end of 4 days.

Explanation

Client takes medication one time = 1 1/2

Client takes medication three times =

medication for 4 days =

Final Answer

The client takes 18 tablets at the end of four days.

We have a sample that is:

a) We can find the median by first sorting the sample:

The median is the value that has 50% of the values below its values.

In this case, this value is in the third place of the sorted sample and has a value of 160.

b) We have to find the mean.

We can calculate it as:

c) We have to calculate the variance. To find its value we will use the mean value we have just calculated:

d) We have to calculate the standard deviation. As we have already calculated the variance, we can calculate it as:

e) We now have to find the coefficient of variation:

Answer:

a) 160

b) 146

c) 4468.4

d) 66.85

e) 46%

The volume of 2.78 g of copper is 0.626 [tex]cm^{3}[/tex].

According to the question,

We have the following information:

Density of cooper = 4.44 [tex]g/cm^{3}[/tex]

Mass of copper = 2.78 g

We know that the following formula is used to find the density of any material:

Density = Mass/volume

Let's denote the volume of copper be V.

Now, putting the values of mass and density here:

4.44 = 2.78/V

V = 2.78/4.44

V = 0.626 [tex]cm^{3}[/tex]

(Note that the units if mass, volume and density are written with the numbers. For example, in this case, the unit of mass is grams, the unit of volume is [tex]cm^{3}[/tex].)

Hence, the volume of the copper is 0.626 [tex]cm^{3}[/tex].

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Answer:

C. Infinite Solutions

Explanation:

Given the equation

First, open the bracket

Since the left-hand side equals the right-hand side, the system has Infinite Solutions.

From the graph, the solution of the graph is given by the area of intersection of the two functions. The are under the area of the two functions are (-4, 1), (-5, 0), (-4, 4)

The given system is

First, we multiply the first equation by 5.

Then, we combine the equations

Given that the result is not true (75 is not equal to 12), we can deduct that the system has no solutions.

Let x be the side opposite to angle 62 degrees

Let y be the adjacent angle.

The sine of the angle is given as follows:

The cosine is given as: