For the following exercises, solve the equations below and express the answer using set notation.
14. 2| 4 − x | = 7

The 4-digit positive integers have four different digits where the leading digit is not zero, the integer is a multiple of 5, and 5 is the largest digit is 108.

[tex]5*4*3*1+4*4*3*1=60+28=108[/tex]

Positive integers are the numbers we use to depend: 1,2, 3,4, 1 , 2, three, four, and so forth. Numbers with a fractional component not identical to zero and poor numbers are excluded from a fixed of high-quality integers. The operations of addition, subtraction, multiplication, and division can be finished with tremendous integers.

Positive integers are definitely your counting numbers. wonderful integers are in reality a part of a larger institution of numbers referred to as integers. Integers are all of the whole numbers, each advantageous and poor. by complete numbers, we imply numbers without fractions or decimals.

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We make four cases based on where the multiple of the 5 digits (0 or5) is. The number has to end with either 5 or 0 since it's a multiple of5. In all but the last case, 5 and 0 are used at the end and in another spot that separates the cases.

Case 1: The first digit can't be 0 so it must be 5. There are 4.3 to choose the middle two digits. After that, the last digit has to be 0, so there are a total of 1.4.3.1=12 numbers.

Case 2: The second digit can be 5, leaving 2 choices. The first and third numbers can be chosen in 4.3 ways, like last time. The last digit has to be 0 or 5, but not the one we already used. There are a total of 4.2.3.1=24 numbers.

Case 3: There are the same choices, but the digits 0 and 5 are at the last and second-to-last spots. So there are 4.2.3.1 =24 numbers again.

Case 4: There are 4.3.2 ways to choose the first three numbers. There has to be a 5 in the number because the largest digit is 5. Coincidentally, there are 4.2.3.1 numbers again.

There are a total of 12 + 24.3= (D)84 numbers.

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Answer:

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

We know that:

So the sum of the 8 exterior angles is:

Sum of both interior and exterior angles of 8 angles:

Sum of those 8 interior angles is:

Triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.

Two triangles are said to be congruent if they have the same shape and angles. The ratio of their corresponding sides are also to be proportional.

Given triangle JHK and GHL are congruent based on the angle-angle-angle congruency theorem.

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The other equality which must be stated by Jose is that angles BAC and BAE are congruent and their measures are equal.

It follows from the task content that Jose is trying to prove the congruence of both triangles by means of the Side-Angle-Side congruence theorem.

It therefore follows that since, Jose has identified that the ratio of corresponding sides are equal as indicated in the task content, the equality which Jose has to state is the angle congruence equality.

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The solution to the system of equation is ( -4.5 , -2)

A system of equation is a set of equations that have a common solution.

The set of equation given are

-2x +4y  = 1

-4x +3y = 12

To find the solution , Elimination Method will be used

Multiplying equation 1 by 2 and then

Subtracting equation 1 by 2

-4x +8y = 2

-4x +3y = 12

+        -       -

5y = -10

y = -2

Substituting this value to determine the value of x

-2x -8 = 1

-2x = 9

x = -4.5

Therefore the solution to the system of equation is ( -4.5 , -2)

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[tex]x^3-2x^2+x-1[/tex] is one of the prime factors of the polynomial

The question implies that we determine one of the prime factors of the polynomial.

The polynomial is given as:

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1[/tex]

Expand the polynomial by adding 0's in the form of +a - a

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^7 - 4x^6 +x^6 + 2x^5 -2x^5- 3x^4 + 4x^4 + 2x^3 -6x^3+2x^3- x^2 -3x^2 +4x^2-2x+2x-1[/tex]

Rearrange the terms

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^8 -2x^7 + 2x^5 - 3x^4 + 2x^3 - x^2 + 2x^7 - 4x^6 + 4x^4 -6x^3+4x^2-2x+x^6-2x^5+2x^3-3x^2+2x-1[/tex]

Factorize the expression

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = x^2(x^6-2x^5+2x^3-3x^2+2x-1) + 2x(x^6-2x^5+2x^3-3x^2+2x-1) + 1(x^6-2x^5+2x^3-3x^2+2x-1)[/tex]

Factor out x^6-2x^5+2x^3-3x^2+2x-1

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x^2+2x + 1)(x^6-2x^5+2x^3-3x^2+2x-1)[/tex]

Express x^2 + 2x + 1 as a perfect square

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6-2x^5+2x^3-3x^2+2x-1)[/tex]

Expand the polynomial by adding 0's in the form of +a - a

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^4-x^3 +x^3-2x^3-x^2 -2x^2 +x+x - 1)[/tex]

Rearrange the terms

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^6- 2x^5+x^4-x^3-x^4-2x^3-x^2+x+x^3-2x^2 +x - 1)[/tex]

Factorize the expression

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3(x^3-2x^2+x-1) -x(x^3-2x^2+x-1)+1(x^3-2x^2+x-1))[/tex]

Factor out x^3-2x^2+x-1

[tex]x^8 - 3x^6 + x^4 - 2x^3 - 1 = (x+1)^2(x^3 -x+1)(x^3-2x^2+x-1)[/tex]

One of the factors of the above polynomial is [tex]x^3-2x^2+x-1[/tex].

This is the same as the option (c)

Hence, [tex]x^3-2x^2+x-1[/tex] is one of the prime factors of the polynomial

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The polynomial is not a perfect square trinomial. This is false..

It should be noted that a perfect squares trinomial is the algebraic expression which has the form of ax² + bx + c.

The equation given is 9x² - 30x + 25. This will be expanded as:

9x² - 30x + 25.

9x² - 15x - 15x + 25

3x(3x - 5) - 5(3x - 5)

= (3x - 5)(3x - 5)

In this case, 9x² - 30x + 25 is a perfect square binomial of 3x - 5 and not a trinomial.

Therefore, the correct option is false.

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Answer:

32

Step-by-step explanation:

To find the mean of the data set, you find the sum of the data set, and divide it by how much data you have in the data set. In this case you have 18 people (amount of data in the data set) and the sum is 35+2+7+33+25+70+75+40+42+12+15+7+44+20+25+3+65+62 = 582. So divide these two values: [tex]\frac{582}{18} = 32.\overline{33} \approx 32[/tex]

Answer:

32.33

Step-by-step explanation:

Answer:

  2.36 liters

Step-by-step explanation:

The volume Janet wants is 1/3 of 1/2 of the volume of a sphere with radius 15 cm. The formula for the volume of a sphere is given.

The water volume is ...

  V = (1/3)(1/2)(4/3π)(15 cm)³ = 750π cm³ ≈ 2356 cm³

There are 1000 cm³ in 1 liter, so Janet needs about ...

  2356 cm³/(1000 cm³/L) = 2.356 L

Janet should put about 2.36 liters of water in the fish tank.

Answer:

it is all I could.

Hope it helps

The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis

Risk analysis is define as the the process of identifying and analyzing potential issues that could negatively impact key business initiatives or projects. This process is done in order to help organizations avoid or mitigate those risks.

So, The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome is known as risk analysis

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Step-by-step explanation:

there are 2 main approaches (in their core they are the same, of course, but they look different) :

1. use one equation to express one variable by the second, and then use this in the second equation to solve for the remaining variable. with that you go back into the first equation and solve for the first variable.

2. multiply both equations by certain factors as needed, then add both results, so that there is one summary equation with only one variable, and then solve for it. then use that in one of the original equations and solve for the second variable.

using 1.

3x + 2y = 1

3x = 1 - 2y

x = (1 - 2y)/3

2x + 7y = 3

2(1 - 2y)/3 + 7y = 3

2(1 - 2y) + 21y = 9

2 - 4y + 21y = 9

17y = 7

y = 7/17

x = (1 - 2y)/3 = (1 - 2×7/17)/3 = (1 - 14/17)/3 =

= (17/17 - 14/17)/3 = 3/17 / 3 = 1/17

using 2.

multiply first equation by 2, the second by -3

6x + 4y = 2

-6x - 21y = -9

----------------------

0 -17y = -7

-17y = -7

17y = 7

y = 7/17

and so on (as under 1.).

Step-by-step explanation:

First, you can multiply the both equation by one of the coefficient of either X or Y as shown above.

Secondly, after doing that you can multiply one of the equations by the negative sign in order for one of the coefficient to cancel out.

From there you can find X

After getting X , you can put the answer you get into any equation of your choice. collect like terms and then you'll find Y.

Hope this helps. If you don't understand use the picture if the solving above for better explanation. Thanks

Assuming the salary is included in the job descriptions, then they all pay the same amount for the same length of time, meaning he will earn the same amount at any of the jobs. This looks like a trick question.

Answer:

B

Step-by-step explanation:

g(x)=(4-4)²

g(x) =0

and f(x)=x²

f(x)=0²

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

The Central Limit Theorem established that, for a normally distributed random variable X, with mean and standard deviation, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard deviation ;

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

The sample of 112 residents has a mean GPA of 1.7.

By the Central Limit Theorem, the best point estimate for the mean GPA for all residents of the local apartment complex is 1.7.

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The sides of the right-angle triangle will be 16 units and 20.30 units. And the missing angle will be 52°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The side AC will be

tan 38° = 12.5 / AC

      AC = 15.999

      AC ≈ 16 units

Then the side AB will be

AB² = 12.5² + 16²

 AB = 20.30 units

We know that the angle sum is 180 degrees. Then we have

∠A + ∠B + ∠C = 180°

38° + ∠B + 90° = 180°

                  ∠B = 52°

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Answer:

9x ^ 6 -9x ^ 2-2x + 1

Step-by-step explanation:

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What's the equation with a slope of -4 that goes through (-1,1)? find it

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The equation used, here is [tex]\bf{y-y1=m(x-x1)}[/tex].

[tex]\bf{y-1=-4(x-(-1)}[/tex] | simplify after putting in the information given

[tex]\bf{y-1=-4(x+1)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                          [tex]\bf{=y-1=-4(x+1)}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

Answer:

In the question, it is given that the fixed cost is $25000 and the expense to produce each doughnut is $0.25.

It is required to represent the cost C of the company as a function of x, the number of doughnuts produced.

To do so, multiply the expense of each doughnut by the number of doughnuts then add the fixed expenses of the doughnut selling company to find the total cost of the company.

Step-by-step explanation:

The expense of each doughnut is $0.25.

The expenses for x doughnuts are $0.25x.

The fixed cost is $25000.

The total cost of the company is the sum of fixed cost and the expenses for the doughnut, C = 0.25x + 25000.

The total cost of the company is, C = 0.25x + 25000.

Yes, a point of inflection exists where f''(x) = DNE.

We know that the point of inflection, also known as the inflection point, is where the function's concavity changes. Changing the function from concave down to concave up, or vice versa, means that. In other words, an inflection point is a location at which the rate of slope change from an increasing to a decreasing manner, or vice versa, occurs. There is no doubt that those points are neither local maxima nor minima. They are called stationary points.

Let's take an example [tex]f(x) = x^{\frac{1}{3} }[/tex]

Here, [tex]f'(x)=\frac{1}{3x^{\frac{2}{3} } }[/tex]

and [tex]f''(x)=-\frac{2}{9x^{\frac{5}{3} } }[/tex]

Clearly f''(x) = DNE at x = 0. We are going to check if x = 0 is a point of inflection or not.

At x = -1, (left side of 0), [tex]f''(-1)=-\frac{2}{9(-1)^{\frac{5}{3} } }=\frac{2}{9} > 0[/tex] (concave up)

At x = 1, (right side of 0), [tex]f''(1)=-\frac{2}{9(1)^{\frac{5}{3} } }=-\frac{2}{9} < 0[/tex] (concave down)

Then by the definition, we can conclude that x = 0 is a point of inflection.

Therefore, a point of inflection exists where f''(x) = DNE.

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Answer:

20 sq in

Step-by-step explanation:

formula is (base * height)/2 so plug it in:

5*8=40

40/2=20

20 sq in

The value of the stamp collection in terms of b is; 45b + 43 cents

We are given;

If there are x 3-cent stamps, then there are 4x number 10-cent stamps

So the number of 2-cent stamps is 1 less than 3 cent stamps and that will be x - 1, 2 cent stamps

Number of 2 cents stamps = b

Thus;  x - 1 = b

x = b + 1

The value of the stamp collection is as follows;

x number of 3 cents stamps = 3(b + 1) = 3b + 3 cents

4x number of 10 cents stamps = 10(4(b + 1)) = 10(4b + 4) = 40b + 40

The value of the 2 cents stamp = 2b cents

Total value is;

2b + 40b + 40 + 3b + 3 = (45b + 43) cents

Complete Question is;

I have 4 times as many 10-cent stamps as 3-cent stamps. I have one less 2-cent stamp than 3 cent stamp. If I have b2-cent stamps, what is the value of my stamp collection in terms of b ?

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Answer:

The distrubutive property

-9(n-4)

=-9n+36

Making 20 groups of 10 is the sampling strategy that can be used to select 200 sales representatives.

What is sampling?

Sampling is the phrase used to describe a statistical procedure in which a predetermined number of observations are chosen from a larger population. More precisely, sampling can be described as the process of choosing a portion of a statistical population in order to estimate the characteristics of the entire population. Samples that are representative of the population under study are sought for by statisticians.

Making 20 groups of 10 is the most effective way of sampling that can be employed here for the sales director to incorporate 200 sales representatives in this situation, with an equal amount of representatives from each region.

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There are 1,86,78,66,560 possinbe passwords.

The easiest way to count the acceptable passwords is to note that there are 36^6 six-character strings made up of upper-case letters and digits, and 26^6 of them are made up entirely of letters, so there are 36^6 − 26^6 that include at least one digit.

⇒ 36^6 - 26^6

⇒ 2,17,67,82,336 - 30,89,15,776

⇒ 1,86,78,66,560

The answer is 1,86,78,66,560.

A password occasionally called a passcode, is a secret fact, generally a string of characters usually used to confirm a person's identity.

Historically, passwords we're expected to be memorized, but the large range of password-included offerings that common characters get entry to can make memorization of unique passwords for each service impractical.

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Answer:

last option : vertex is 2, -1 . axis of symmetry is x = 2

Answer:

D

(2 -1)

*(^_^)*

...............

The second transformation is a rotation about point H.

It should be noted that a congruent triangle simply means when two triangles have the same sides and the same angles.

As two rigid transformations, to map ΔHJK to ΔLMN.

The first is a translation of vertex H to vertex L, and the second transformation is a rotation about point H.

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Answer:

B. a rotation about point H

Step-by-step explanation:

got it correct on my quiz

The total amount paid by a customer who purchased a CD player at $142.00 and sales tax of 5.5% is $149.81

Amount of sales tax = 5.5% of $142.00

= 5.5/100 × 142

= 0.055 × 142

= $7.81

Total amount paid by customers = Cost of CD player + Amount of sales tax

= $142.00 + $7.81

= $149.81

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1. if we add something in x then it will also add up in value of y

2.  x by 5 times then y value increases by 3*5 = 15 times

3.  if x is added with 5 then y value increases by 8.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

As, per the first part

y=x

So, if we add something in x then it will also add up in value of x.

In second part,

y=3x

If x by 5 times then y value increases by 3*5 = 15 times

In third part, if x is added with 5 then y value increases by 8.

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On the first two pairs you need to write 3 and 4, and 6 and 2.

On the second page we have:

1) 4

2) 2 and 7

3) 1

4) 1 and 3

5) 3.

a) Here we just need to use scientific notation.

For the first case, the numbers that go in the exponent boxes are the same ones that go in the example, which are 4 in the first one and 2 on the second one.

Then, if we want the difference to be 29,400, then we can use 3 on the first box and 6 on the second. OR, because this is an absolute value, we can just invert those.

This is:

6 and 2 on the first two squares, and 3 and 4 on the second two squares.

b) Here we want to make perfect squares.

For example, on the first case we have:

x*2*2

We need to find the value of x such that this is a perfect square. Notice that we can rewrite this as:

x*2*2 = x*4

Then it only is a perfect square if x = 4.

For the second case:

14*x*y

This is only a perfect square if x*y = 14

Then we can use x = 2 and y = 7.

With similar reasoning, on the next box we have:

2*8*x

2*8 = 16, is already a perfect square, so x = 1.

The next one is:

x*3*y

Here we can define x = 3 and y = 1, so we get a perfect square.

Finally:

3*x

Here the only possible value of x is 3.

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The slope of line AB, BC, CD and AD are 1, -1/6, 2, -4/6 respectively. Quadrilateral ABCD with the given vertices is not a parallelogram because neither pair of opposite sides is parallel. Option C

Formula for slope is given as;

Slope = [tex]\frac{y2 -y1}{x2 -x1}[/tex]

A(-4 -1)

B(-1 2)

C(5 1)

D(1 -3)

a. Slope of line AB = [tex]\frac{2- (-1)}{-1 (-4)}[/tex] = [tex]\frac{2+ 1}{-1 + 4}[/tex] = [tex]\frac{3}{3}[/tex] = 1

b. Slope of line BC = [tex]\frac{1-2}{5-(-1)}[/tex] = [tex]\frac{-1}{6}[/tex]

c. Slope of line CD = [tex]\frac{-3 - 5}{1-5}[/tex] = [tex]\frac{-8}{-4}[/tex] = 2

d. Slope of line AD = [tex]\frac{-3 (-1)}{1 -(-4)}[/tex] = [tex]\frac{-4}{5}[/tex]

Quadrilateral ABCD with the given vertices is not a parallelogram because neither pair of opposite sides is parallel. Option C

Thus, the slope of line AB, BC, CD and AD are 1, -1/6, 2, -4/6 respectively.

and quadrilateral ABCD with the given vertices is not a parallelogram because neither pair of opposite sides is parallel. Option C

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