2. Communicate and Justify Why is the algebraic
expression x, equivalent to x ¹?

The expression, (–5.5 + 2p)(–2), after simplification is 11-4p.

According to the question,

We have the following expression:

(–5.5 + 2p)(–2)

Now, in order to simplify this expression, we will multiply -2 into the bracket:

(Note that when a number or a variable is multiplied into the bracket then it is multiplied into every number or term within the bracket.)

-5.5*-2+2p*(-2)

We know that when two negative integers are multiplied then the result is positive and when one negative and one positive integer is multiplied then the result is negative.

11-4p

Hence, the expression, (–5.5 + 2p)(–2), after simplification is 11-4p.

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In the function f(2)= -5, 2 is the preimage of the function and 5 is an image of the function.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

Suppose that f(a) = b

In that case, element "b" is the image of element "under the function," while element "a" is the preimage of element "under the function."

In the given function f(2)= -5

2 is the preimage of the function and 5 is an image of the function.

Hence, the 2 is the preimage of the function and 5 is an image of the function.

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Using the concepts of statistics, we got that  if the per capita death rate increased, then the exponential growth model would decrease the initial population size.

We know very well, the set up of a differential equation relating instantaneous population growth with respect to the time to the per capita population growth rate and the current population size at an arbitrary time is as follows:

dN / dt = rN

Now, we are told that the constant, r, is  per capita population growth rate. N is  current size of the population at some time. "r" is the "organisms added per reproductive period" divided by  total population at that time. For instance, if the 10 rabbits are born per month and the current population is 100 rabbits, then r value  = 0.1.

Hence, the exponential growth model  would decrease the initial population size  if the per capita death rate increased.

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Answer:

25.5 feet because of some

Step-by-step explanation:

.,........

Answer:

Step-by-step explanation:

The composition f(-3) has a value of 1

The definition of the function is represented by the graph

So, we call the graph function f(x)

To find the function f(-3), we set the value of x in the function of the graph f(x) to -3

This is represented by

Calculate f(x), when x = -3

So, we look for the corresponsing points on the graph where x = -3

In this case;

The value of the function is 1 when the value of x is -3

This means that

f(-3) = 1

Hence, the value of the function is 1

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(i) Relative growth rate, k = 48 million people/ year

(ii) Population in 2020 is given by 5920 million people.

Given that in 1950, the population of world was 2560 million.

In 1960, the population of world was 3040 million people.

Also it is mentioned that,  world population grows in constant relative proportion.

So, the difference between time = 1960 – 1950 = 10 years

The growth in population = 3040 mil – 2560 mil = 480 million

So the relative growth rate of population is = 480/10 = 48 million/year

Now N be the new population, k be the relative population growth rate, all figures in millions. And t be the time in years passes since 1950.

Then the mathematical model is,

N = 2560 + kt

So for 2020, t = 2020-1950 = 70

k = 48

So, N = 2560+48*70 = 5920

So the population in 2020 is 5920 million people.

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The correct value of the simplified expressions found using the laws of indices gives;

The laws of indices state rules that enable the simplification of the combination of expressions of numbers and variables that are given in index form or involve powers of other numbers or variables

1. [tex]3^{\frac{1}{4} } = \sqrt[4]{4}[/tex]

The radical sign is used for expressing fractional indices.

The correct option is d. [tex]\sqrt[4]{4}[/tex]

2. The radical is in its simplest form when it cannot be further simplified, which gives the radical in its simplest form as option a. [tex]\sqrt{\dfrac{5}{6} }[/tex]

3. The index of a number is the number to which the variable or number is raised

The index of x³ in [tex]\sqrt{x^3}[/tex] is d. 3

4. The given expression has y raised to the power of [tex]\frac{1}{2}[/tex], which gives;

[tex]x\cdot y^\frac{1}{2} = x\cdot \sqrt{y}[/tex]

The correct option is a. [tex]x\cdot \sqrt{y}[/tex]

5. The common index of the expression within the parenthesis is [tex]\frac{1}{2}[/tex], which gives;

[tex](x^4\cdot y^2)^\frac{1}{2} = (x^{4\times \frac{1}{2} }\cdot y^{2 \times \frac{1}{2} })=x^2\cdot y[/tex]

The correct option is b. x²·y

6. The value of all numbers raised the power of zero is 1, therefore;

[tex](2^{1/3}\cdot 3^{1/4})^0\cdot (2^{1/5}\cdot 3)^0 = 1 \times 1=1[/tex]

The correct option is b. 1

7. The given expression can be simplified as follows;

[tex]\sqrt[5]{\dfrac{1}{243} } = \sqrt[5]{\dfrac{1}{3^5} } = \sqrt[5]{\left(\dfrac{1}{3} \right)^5} = \dfrac{1}{3}[/tex]

The correct option is therefore; a. 1/3

8. The given expression [tex]\sqrt{225\cdot x^4\cdot y^8} = \sqrt{15^2\cdot x^4\cdot y^8} = 15\cdot x^2\cdot y^4[/tex]

The correct option is [tex]15\cdot x^2\cdot y^4[/tex]

9. The given expression is [tex]\sqrt[3]{216\cdot x^9\cdot y^{15}}[/tex]

[tex]\sqrt[3]{216\cdot x^9\cdot y^{15}} = \sqrt[3]{6^3\cdot x^9\cdot y^{15}} = 6\cdot x^3\cdot y^5[/tex]

The correct option is e. [tex]6\cdot x^3\cdot y^5[/tex]

10. [tex]\sqrt{\dfrac{50}{162} } = \sqrt{\dfrac{25\times 2}{81\times 2} } = \sqrt{\dfrac{25}{81} } = \dfrac{5}{9}[/tex]

The correct option is c. [tex]\frac{5}{9}[/tex]

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Answer:  14.7%

Step-by-step explanation:

% error = (estimated - actual) / (actual) x 100

% error = (17 - 19.5) / 17 x 100 = - 14.7%

The negative sign means that he underestimated the time needed

Answer:

2 3/5

Step-by-step explanation:

First, change all terms to improper fraction

We have;

13/2÷5/2

13/2 ×2/5

13/5

Change to mixed fraction, we have;

2 3/5

Hope it helps.. Please mark brainliest

The simplest simplified form of the given expression is 3 9/10.

First, let us understand the mixed number;

A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the appropriate fraction that results in the mixed number.

Change all the given terms to improper fractions, we will get;

6 1/2 = (6 * 2 + 1) / 2 = 13 / 2

1 2/3 = (1 * 3 + 2) / 3 = 5 / 3

We are given;

13/2 ÷ 5/3

= 13/2 × 3/5

= 39/10

Change to mixed fraction, we will get;

39/10 = 3 9/10

Thus, the simplest simplified form of the given expression is 3 9/10.

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Ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount  received by Annie is $330 and Dermot is $270.

As given in the question,

Total amount share by Annie and Dermot is $600.

Ratio of amount share by Annie and Dermot is 11 : 9

Let x be the amount of money.

11x + 9x = $600

⇒ 20x = $600

⇒20x/20 = $600/20

⇒x= $30

Amount received by Annie is equal to

= 11 × 30

= $330

Amount received by Dermot is equal to

= 9 × 30

= $270

Therefore, ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount  received by Annie is $330 and Dermot is $270.

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Answer:

x < 1 and x > -4 (more down below)

Step-by-step explanation:

First we have to solve the algebra
|-2x - 3| + 2 < 7
|-2x - 3| < 5
1. -2x - 3 < -5                    2.  -2x -3 < 5
-2x < -2                           -2x < 8                        

x < 1                                x > -4 (switch the expression)
Now... The two answers are x < 1 and x > -4

The interval notation is a number line with circles on the two points (answers)
Sorry I can't exactly explain what that is you might have to search it up, but you need a number line like this, and you need to draw another line above the -5 and 1 with an open circle on -5 and 1

    O-----------------------O

<---5, -4, -3, -2, -1, 0, 1, 2-->

For graphing, make a graph with 5 points on each side with 4 quadrants or whatever reasonable size, and draw a vertical line that extends all the way above and below your graph above 1 on line x and a vertical line all the way above and below your graph above above -5 on x, then shade everything in between those two lines.

This helps you to know what value you plug in for X makes the inequality true (shaded region)

There are 180 three-digit numbers that leave a remainder of 2 when divided by 5 and 128 three-digit numbers that leave a remainder of 6 when divided by 7.

The smallest 3-digit number to leave a remainder of 2 when divided by 5 is 102.

The next number will be 107, and then 112,

The last 3 digit number to leave a remainder 2 when divided by 5 is 997

Therefore here we get an Arithmetic Progression

102, 107, 112, ..., 997

We know that for any term of an A.P

aₙ = a + (n - 1)d

where,

a = first term

n = the order number of that particular value

d = common difference

Here,

a = 102

d = 107 - 102

= 5

The number of 3 digit number for the above problem will be the value of n for 997

Hence we get

997 = 102 + (n - 1)5

or, 102 + 5n - 5 = 997

or, 5n + 97 = 997

or, 5n = 997 - 97

or, 5n = 900

or, n = 900/5

or, n = 180

Next, we need to find the no. of three-digit numbers that leave the remainder of 6 when divided by 7

The smallest 3-digit number to leave the remainder of 6 when divided by 7 is 104

The largest is 993

Therefore, just like before, we get the A.P

104, 111, 118, ..., 993

here,

a = 104

d = 7

aₙ = 993

Hence we get,

993 = 104 + (n - 1)7

or, 104 + 7n - 7 = 993

or, 97 + 7n = 993

or, 7n = 993 - 97

or, 7n = 896

or, n = 128

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The meaning of the x-value when y=90 means that Anthony will use 3.1 hours.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The relationship that can be represented by the equation y=57+7.4x,

where

y represents the expected quiz score

x represents hours spent on homework that week.

When y = 90, the value of x will be:

y=57+7.4x

57 + 7.4x = 90

Collect like terms

7.4x = 90 - 57

7.4x = 23

Divide

x = 23/7.4

x = 3.1

He'll use 3.1 hours.

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There should be 12 emails total.

7.200 and 2.683 are the variance and standard deviation, respectively.

Calculation of expected number of emails, variance and standard deviation:

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Answer:

for example 2(3+1)

to solve with the distributive property you multiply the number outside the parentheses(2) with each inside number(3 and 1) individually.

2(3)+2(1)

now solve

6+2=8

now to check it by solving the regular way

2(3+1), 3+1=4 so

2(4)

8

we can see that the answers are the same.

to use the distributive property with x in it

for example, -3(x-6)

multiply the outside number(-3) with each inside number(x and -6)

-3(x)+(-3)(-6)

simplify

-3x-(-18)

-3x+18

hope this helps!

Answer:

[tex]\frac{6}{5}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3} *\frac{9}{5} =\frac{18}{15} =\frac{6}{5}[/tex]

The value of the product of 2/3 × 9/5 is 6/5.

In the given question, we have to attempt fraction multiplication.

For fraction multiplication, we simply multiply the respective numerators and denominators with each other.

Here, in 2/3 × 9/5 ⇒ 18/15 (since 2×9=18) (since 3×5=15)

Now, since we can see that both the numerator and denominator in the solution can get divided by 3, we can simplify the fraction by dividing both the numerator and denominator by 3.

On dividing by 3, we get ⇒ 6/5

So, on multiplying 2/3 and 9/5, we get 18/15 which we later simplify into 6/5.

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One method is to determine the average hourly rate for all employees, regardless of where they work in your company, what they do, or how many hours they work.

To begin, calculate the total number of hours worked by multiplying the number of weeks in a year by the number of hours worked per week. Divide this figure by the annual salary. For example, if an employee earns $50,000 per year and works 40 hours per week, his or her hourly rate is $50,000/2,080 (40 x 52) = $24.04.

When budgeting for future projects, keep in mind that if you pay Bill $18 per hour, Lisa $16, and Hank and Jake $14, your labor costs will vary depending on who you send to the job site.

However, if you can use Bill less frequently each week and Hank or Jake more frequently, you might be able to budget for next month using the $15.82 per hour figure.

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Answer:

a = (c - by) / x

Step-by-step explanation:

ax + by = c

ax = c - by

a = (c - by) / x

The probability is 0.061 to record his or her age for her favorite music genre is pop.

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur. An event's probability is a number between 0 and 1, where 0 indicates impossibility and 1 represents certainty. The more likely an occurrence is, the more likely it will occur. A simple example is tossing a fair (unbiased) coin. Because the coin is fair, all outcomes are equally likely; the probability of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of "heads" or "tails" is 1/2.

Given,

Age       Users     Pop-music

13-24     47%        85%

25-34     25%        59%

35-more  28%       23%

Let the total population be 100 then

Age    Users    Pop-music

13-24    47%        85% of 47=39.95

25-34    25%       59% of 25=14.75

35-more  28%      23% of 28=6.44

Persons having favorite music game as pop=34.95+14.75+6.44

=61.14

Probability=61.14/100c₁

=0.061

Therefore, the probability is 0.061.

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Answer:

y= -20/9

Step-by-step explanation:

4y+5/3=y-5

3y= -(5+5/3)

3y= -20/3

y= -20/9

Answer:

Collect like terms

4y-y=-10/2-5/3

3y=-5-5/3

5-5/3

LCM=3

3/1=3×5=15

3/3=1×5=5

15-5÷3

10/3

3y=10/3÷3

3y=30/3

y=10

The percentage of people that have a blood glucose level between 100 and 125 is 21.945%

From the question, the given parameters about the distribution are

Mean value of the set of data = 85

Standard deviation value of the set of data = 25

The actual data values = 100 and 125

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

For x = 100, we have:

Substitute the given parameters in the above equation

z = (100 - 85)/25 = 0.6

For x = 125, we have:

Substitute the given parameters in the above equation

z = (125 - 85)/25 = 1.6

The percentage between 100 and 125 is then calculated as:

P(100 < x < 125) = P(z < 1.6) - P(z < 0.6)

From the z table of probabilities, we have;

P(100 < x < 125) = 0.9452 - 0.72575

This gives

P(100 < x < 125) = 0.21945

Express as percentage

P(100 < x < 125) = 21.945%

Hence, the percentage is 21.945%

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Answer:

to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.

Step-by-step explanation:

Step-by-step explanation:

-8(x + 7.5) ≤ 10?

expand left side:

-8x - 60 ≤ 10

subtract 60 to both sides:

-8x - 60 + 60 ≤ 10 + 60

-8x ≤ 70

dive both sides by -8: (Remember when dividing by a negative number, you flip the direction of the inequality sign)

-8x/-8 ≥ 70/-8

x ≥ -35/4

reduce right side:

x ≥ -35/4 or x ≥ -8.75 [depends on if you need fractional or decimal format]

so in set builder format: [-35/4 , ∞) or [-8.75 , ∞) [depends on if you need fractional or decimal format]

Answer:

40

Step-by-step explanation:

Looking at the other examples, its shows the the second number is always 4 times bigger/ahead then/of the first number.

answer:

x = 18, 60.

step-by-step explanation:

evaulating (3x+6) = (4x-12) and solving for x gives us x = 18. you didn't include the angle, so i can't give you that. but

(3x+6) = 60

(4x-12) = 60

if those were your angles, you would have an equilalateral triangle (all sides/angles even) and your missing angle would also be 60.

multiply x times y divide by 6 on both sides and you got your answer

Answer:

$1097.46

Step-by-step explanation:

Assume P is the finall price.  The markup of 26% can be written in decimal form as 0.26.  This is in additon to the full price paid for the gold ring, so we can add 1.00 to 0.26 to arrive at the factor 1.26.  Multiply 1.26 times the store cost of $871 to find the amount after 26% markup:

 ($871)*(1.26) = $1097.46