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Evaluate the expression given the replacement values.

Answer:

In set-builder notation, the set of solutions is:

[tex]\left \{u|-3<u<7\right\}[/tex]

Step-by-step explanation:

Let's start by isolating the absolute value expression on one side of the inequality:

8 | u - 2 | - 7 < 33

add 7 on both sides:

8 | u - 2 | < 40

divide both sides by 8:

| u - 2 | < 5

Now, in order to remove the absolute value symbols, we need to consider two different cases:

1) what is inside the absolute value symbols is larger than or equal to zero, so in such case when we remove the absolute value we get exactly what was inside:

u - 2 < 5

u < 5 + 2

u < 7

Now the other case;

2) what is inside the absolute value is smaller than zero, then when removing the symbols we get:

2 - u < 5

2 - 5 < u

-3 < u

Then the set of solutions of this inequality are the set of u values such that u is larger than -3 (to the right of -3 on the number line, and smaller than 7 (to the left of the number 7 on the number line.

In graph form this should look like a highlighted segment on the number line that starts at -3 on the left, ends at 7 on the right, and doesn't include the endpoints -3 and 7.

in set builder notation, the set of solutions is given by:

[tex]\left \{u|-3<u<7\right\}[/tex]

Answer:

2.1 is greater

Step-by-step explanation: 2.0113 cannot be rounded up since the last number is 3 if it was above 5 or greater it could have been rounded but would have only affected the second number.

We can define the average rate of change of a function f(x) in an interval [a, b] as:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

Particularly, if we want to find an approximation of the rate of change for a particular value x', we can choose:

a < x' < b

Such that a and b are really close to x'.

Then if we want to find the instantaneous rate of change of g at x = 0, we need to find values of a and b really close to zero.

Looking at the table, we can choose:

a = -0.001

b = 0.001

(are the two closer ones to zero)

Then the rate of change can be written as:

[tex]f(x) = \frac{g(0.001) - g(-0.001)}{0.001 - (-0.001)} = \frac{2.001 - 1.999}{0.002} = 1[/tex]

From that, we can conclude that a good approximation of the instantaneous rate of change is 1.

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Answer:

about $64

Step-by-step explanation:

4 x $15.99 = $63.96

round $63.96 to get $64

Answer:

4^6

Step-by-step explanation:

Because they have the same base (4) and are being multiplied together, the powers simply add together so:

4^2 * 4^4 = 4^(2+4) =4^6

Hope this helped!

Answer:

982.27 = 1 month

12 months in one year

1 month x 12 is 12 months

982.27 x 12 = 11787.24

11787.24 x 2 = 23574.48

So, it is $23574.48

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Answer:

The number of people that will occupy 36000 square feet= 14400 people

Step-by-step explanation:

each person occupies 2.5 square feet.

Area of concert in an area that is 150 feet long and 240 feet wide

Area=150*240

Area=36000 square feet

If one person occupies 2.5 square feet

The number of people that will occupy 36000 square feet

= 36000/2.5

= 14400 people

The number of people that will occupy 36000 square feet= 14400 people

Answer:  Nathan has a proportional relationship between cost and item

Step-by-step explanation:

Using Margareta's statement we will say that if you buy 1 cookie you pay 50 cents and if you by 5 cookies you will pay $2

To find out how much you will pay for one cookie by using the 5 cookies $2 statement we will divide  2 by 5

2/5 = 0.4   which means you pay 40 cents for 1 cookie and that is not equivalent to paying 50 cents per cookie so Margereta method is not proportional.

Nathan sells freshly picked strawberries for $2 per pound and $10 for 5 pounds.  Now we want to know how much you have to pay per pound if you were to buy 5 pounds to $10 .

Divide 10 by 5 to find out how much you will pay per pound.

10/5 = 2    

So Nathan is selling his strawberries at a proportional rate which is $2 per pound.

Answer:

43,680

Step-by-step explanation:

4 in below let him go

5 and above bump him up

8>5 so we bump him up

so 7-> 8

Answer:

43,680

Step-by-step explanation

Rounding numbers to the nearest 10 means finding which 10 they are nearest to. For example, 78 rounded to the nearest 10 is 80.

Solution:

5x^-2

5 * x^-2

5 * 1/x^2

5/x^2

Best of Luck!

The given expression without negative exponent  is [tex]\frac{5}{x^2}[/tex]

Given the indices expression

5x^-2

We are to express with the negative exponent:

According to the indices expression

[tex]x^{-n}=\frac{1}{x^n}[/tex]

Hence the given expression is [tex]\frac{5}{x^2}[/tex]

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Answer:

what does y and x represent no one can answer unless they have x and y

Step-by-step explanation:

Answer:

y=12x

Step-by-step explanation:

Since there are 12 bottles in each box, the total number is the number of boxes multiplied by 12.

For example, buying 1 box will give you 12 bottles (1x12) and buying 2 boxes would give you 24 (2x24).

Therefore the equation of the total number of bottles if you buy x boxes is:

y=12x

Hope this helped!

Answer:

Annual interest rate = 4%

Step-by-step explanation:

We are given;

Principal; P = $20000

Interest; I = $1600

Period; T = 2 years

Formula for simple interest is;

I = PRT

Making R, rate the subject of the formula gives;

R = I/PT

Plugging in the relevant values gives;

R = (1600)/(20000 × 2)

R = 0.04

In percentage form, R = 4%

Answer:

One number is 29, and the other one 45

Step-by-step explanation:

Solve this problem by creating two equations that represents the statements, and solve for the unknowns using substitution:

Let's say that one of the numbers is X , and the other one Y, and assume that Y is larger than X, so when we do their difference we get the 16 units they mention in the problem:

Y - X = 16

The info on the  product of the two numbers will give us our second equation:

X * Y = 1305

Now use the first equation to substitute Y with 16 + X, in the second equation:

X (16 + X) = 1305

16 X + X^2 = 1305

X^2 + 16 X - 1305 = 0

Now use the quadratic formula to solve for X, and we get two possible answers: X = -45 or X = 29

So, since we are looking for whole numbers, we discard the negative answer, and keep X = 29

Then, the value of the other number "Y" is = 29 + 16 = 45

First of all, let's take a look on the question.

[tex]\large{15 + 0 = 15}[/tex]

Here, 0 is added to 15 and the resultant is 15 only. So, we can say that 0 when added with any number gives the same number as the resultant.

So, the property is known as Identity property because 0 is added to get the identity of the same number.

The Correct Option:

[tex] \large{ \boxed{ \red{ \bf{Option \: C}}}}[/tex]

So, let's know more...

So this is the general form of these properties which is general observed in the rational numbers.

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Answer:

no

Step-by-step explanation: 10.1 is .1 higher

Answer:

yes

Step-by-step explanation:

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Answer:

3.18 kg

Step-by-step explanation:

It is given that, Zach purchased 7 pounds of fruits and vegetables.

We know that,

1 kg = 2.20462 pounds

It means that, 1 pound = 0.453592 kg

We need to find how kilograms is 7 pounds. So multiply 7 by 0.453592 to convert into kg.

So,

7 pound = 3.17515 kg

or

7 pounds = 3.18 kg

So, the weight of fruits and vegetables is 3.18 kg.

Answer:

If they are in the same plane

Step-by-step explanation:

I think the answer is A.

Answer:

Explained below.

Step-by-step explanation:

Heterogeneous denotes to a form with different components or features, give the impression as uneven or varied.  

A heterogeneous population or sample is the one where each and every individual has a diverse value for the distinctive characteristic one is interested in.

To select a representative sample from the random heterogeneous material one should divide the material into segments and then use random number, either by the random number table or by the random number generator, to select  random segments of the material.

Answer:

the answer is 28

Answer:

-7

Step-by-step explanation:

4-2x+6=24

10-2x=24

-2x=24-10

-2x=14

X=-7

The solution to the equation is x = -7.

To solve the equation 4 - 2(x - 3) = 24 for the variable x, you can follow these steps:

Step 1: Simplify the expression on the left side by applying the distributive property:

4 - 2x + 6 = 24

Simplifying further:

10 - 2x = 24

Step 2: Move the constant term to the right side by subtracting 10 from both sides:

10 - 10 - 2x = 24 - 10

-2x = 14

Step 3: Divide both sides of the equation by -2 to solve for x:

(-2x) / -2 = 14 / -2

x = -7

Therefore, the solution to the equation is x = -7.

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Answer: [tex]x=-61/2[/tex]

Simplify both sides of the equation

[tex]1/4x+2=(-5/8+-5)[/tex] (Combine Like Terms)

[tex]1/4x+2=-45/8[/tex]

Subtract 2 from both sides

[tex]1/4x+2-2=-45/8-2\\1/4x=-61/8[/tex]

Multiply both sides by 4

[tex]4*(1/4x)=4*(-61/8)\\x=-61/2[/tex]

Answer: 12

Step-by-step explanation:

so

y=-8/9x+4

Your y intercept is 4

For every 9 units you go (to the right) along the x axis, you go 8 units down on the y axis.

Answer:

One of the number is 4 while the other is 7

Step-by-step explanation:

The sum of two numbers is eleven

Let the numbers be x and y

X+ y = 11

One number is thirty-eight less than six times the other

X= 6y-38

X+ y = 11

6y-38 +y= 11

6y+y= 11+38

7y=49

Y= 49/7

Y= 7

X+ y = 11

X+7= 11

X= 11-7

X= 4

Answer:

(5/x)-(18y)

Step-by-step explanation:

First write the expression (5/x) and then the second expression (18y) the write the difference, so basically a subtraction. (5/x)-(18y)

Answer:

It's -2

(5/16)(-4/5)=(-20/80)

(-2)(-4)=(8)

(8)(-20/80)= -160/80

-160/80=-2

Answer:

The cost of one month of gameplay is $99.2

Step-by-step explanation:

295/6 + 50

49.2 + 50

99.2

(I rounded to the nearest tenth on multiple occasions)