Select the correct answer.
Find the inverse of function f.
f (x) = 9x + 7
A. f^{\small -1}(x)\ =\ 7x\ +\ 9
B. f^{\small -1}(x)\ =\ -9x\ -\ 7
C. f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}
D. f^{\small -1}(x)\ =\ \frac{7}{9}x\ -\ \frac{1}{9}

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{GUIDE TO FOLLOW: }[/tex]

• [tex]\large\textsf{2 negatives equal positive}[/tex]
• [tex]\large\textsf{2 positives equal positive}[/tex]
• [tex]\large\textsf{1 negative \& 1 positive equal negative}[/tex]
• [tex]\large\textsf{1 positive \& 1 positive equal negative}[/tex]

[tex]\large\textsf{SOME OPERATIONS MAY BE DIFFERENT THAN OTHERS!}[/tex]

[tex]\large\textsf{ANYWHO, LET US ANSWER THIS QUESTION, SHALL WE? }[/tex]

[tex]\mathsf{(-12)(-8)}[/tex]

[tex]\mathsf{= 12(8)}[/tex]

[tex]\mathsf{= 96}[/tex]

[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{96}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

By solving |4n+2|=34 solve for N we get 8 .

What is N factor?

The factorial of a non-negative integer n, denoted by n!, is the  product of all positive of  integers less than or equal to n. The factorial of n also  equals to the product of n with the next smaller factorial: For example, These are  value of 0! is 1, according to the  convention for an empty of product.

Sol-|4n+2|=34
Split into two equations
4n+2 = 34 or 4n+2=-34
4n+2 =34
Rearrange variable to the left side of the equation
4n =34-2
Calculate the sum or difference
4n=32
Devide both side of the equation by the coefficient of variable
n=32/4
Cross out the common factor
n=8
When n=8
LHS = |4×8+2|=34
RHS =34
LHS =RHS
Thus 8 is valid.

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The amount of lemonade Tina made in the starting is 630 ounces.

Given that:-

Fraction of lemonade drank by her family = 1/2

Fraction of lemonade given to neighbors = 1/3 of remaining

Amount of lemonade left with her at the end = 210 ounces

We have to find the amount of lemonade Tina made in the starting.

Let the amount of lemonade Tina made in the starting be 6x.

Hence,

Amount of lemonade drank by her family = (1/2)*6x = 3x

Remaining lemonade = 6x - 3x = 3x

Amount of lemonade given to neighbors = (1/3)*3x = x

Remaining lemonade = 3x - x = 2x = 210 ounces

Hence,

x = 210/2 = 105 ounces

Amount of lemonade Tina made in the starting = 6x = 6*105 = 630 ounces.

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Answer:

1. 8 softballs

2. 16 softballs

3. 24 softballs

4. 32 softballs

5. 40 softballs

6. 48 softballs

Step-by-step explanation:

Solution:

Consider the following injective function:

this is equivalent to:

by cross-multiplication, this is equivalent to:

now, applying the distributive law, we get:

this is equivalent to:

Applying the common factor, we get:

this is equivalent to:

solving for x, we get:

so that, we can conclude that the correct answer is:

Answer:

y = 1/2x - 5

Step-by-step explanation:

The y intercept is negative 5. The line slowly goes one point up and two points to the right, staying positive. This makes it 1/2.

A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

With this in mind we conclude that:

There are 8 values in the data set which are greater than or equal to 20 and less than or equal to 29. This comes from the fact that we have to count how many leafs are in the stem 2.

There are 6 values in the data set which are greater than or equal to 10 and less than or equal to 19. This comes from the fact that we have to count how many leafs are in the stem 1.

There are 14 values in the data set which are greater than or equal to 40 and less than or equal to 49. This comes from the fact that we have to count how many leafs are in the stem 4.

Answer: -4

Step-by-step explanation:

Let the integer be x.

[tex]8(x+1)-x=-20\\\\8x+8-x=-20\\\\7x+8=-20\\\\7x=-28\\\\x=-4[/tex]

So, the integers are -4 and -3.

Total surface area = 620

Moreover, The total area covered by an isosceles triangle is called its area. For an isosceles triangle, the area is easily calculated if the height and base are known. Multiplying the height by the base and dividing it by 2 gives us the area of ​​an isosceles triangle.

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Answer:

Step-by-step explanation:

radius, r = 2√2

let the center be A(a, b):

The distance from the center to any of the 2 points is r.

So for (7, 2):

it satisfies the equation:

(x-a)²+(y-b)² = r²

Substituting x and y:

(7-a)²+(2-b)² = (2√2)²

squaring both sides:

(7-a)² + (2-b)² = 8

a² +b² - 14a -4b + 49+ 4= 8

a² +b² - 14a -4b + 45= 0        (Eqn 1)

For (3, 2):

it also satisfies the equation:

(x-a)²+(y-b)² = r²

Substituting x and y:

(3-a)²+(2-b)² = (2√2)²

squaring both sides:

(3-a)² + (2-b)² = 8

a² +b² - 6a -4b + 9+ 4= 8

a² +b² - 6a -4b + 5= 0        (Eqn 2)

We can now proceed by elimination:

(Eqn 2) - (Eqn 1):

(a² +b² - 6a -4b + 5) - (a² +b² - 14a -4b + 45) = 0

- 6a - -14a+ 5  - 45 = 0

8a - 40 = 0

8a = 40

a = 40/8

Putting a back into (Eqn 2):

a² +b² - 6a -4b + 5= 0

5² +b² - 6(5) -4b + 5= 0

25 +b² - 30 -4b + 5= 0

b² -4b = 0

b(b -4) = 0

Values of b:

POSSIBLE EQUATIONS OF CIRCLE:

Since we have 2 values of b, we have 2 possible centers:

(5, 0) and (5, 4)

Putting the centers into the standard equation of the circle above, we obtain:

PLEASE VOTE AS BRAINLIEST.

BLAISE M.

Answer:

y-intercept= 12.99      slope= 15.00x+12.99

Step-by-step explanation:

Answer:

y = 3

Step-by-step explanation:

12.75y = 38.25

To find the value of y, divide each side by 12.75

12.75y/12.75 = 38.25/12.75

y = 3

Event 4, Event 1, Event 3, Event 2

Number of black marbles in bag A = 11

Number of green marbles in bag A = 9

Total number of marbles in bag A = 11 + 9 = 20

Number of black marbles in bag B = 8

Number of green marbles in bag B = 2

Total number of marbles in bag B = 8 + 2 = 10

Event 1:

Likelihood of choosing a black marble from bag A = 11/20 = 0.55

Event 2:

Likelihood of choosing a black or green marble from bag A = 11/20 + 9/20

Likelihood of choosing a black or green marble from bag A = 0.55 + 0.45

Likelihood of choosing a black or green marble from bag A = 1

Event 3:

Likelihood of choosing a balck marble from bag B = 8/10 = 0.8

Event 4:

Likelihood of choosing a purple marble from bag B = 0

Since there is no purple marble in bag B

Arrangement of the events from the least likely to the most likely will be:

Event 4, Event 1, Event 3, Event 2

Answer:

a = 0 , a = 9

Step-by-step explanation:

a(a - 9) = 0

equate each factor to zero and solve for a

a = 0

a - 9 = 0 ⇒ a = 9

The 'x' and 'y' variables are highlighted in the box

Answer:

x = 7

y = 15

Step-by-step explanation:

Disclosure:  After I had completed my answer, I found that Answerwell had already posted a solution.  It is more straightforward than my approach.  While the answers are the same, I'm still adding mine because 1) I worked hard on it, and 2) it illustrates there can be different ways of reaching a solution.

See attached worksheet.

Answer:

144x - 24

Step-by-step explanation:

A proportion is an equation in which two ratios are set equal to each other. No option is satisfying the proportion

Ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other.

In the given question, rayon drove 320 miles in 5 hours to complete the first part of his trip. 12 hours to drive 768 miles.

we can write this

320miles/5 = 768 miles/12

320miles/768 miles=5/12

In option d the values are not given in a correct way. It doesnot hold for the proportion.

Hence no option is correct.

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A Communication system consists of n components.

a) Binomial distribution,

P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾

b) For 5-component system,

P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5

c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.

Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .

(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.

(b) Now , 5-component system is function . That is n=5

Probability that 5-components system will function is P(X= 5)

= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)

(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is

⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵

Whereas the corresponding probability for a 3-components system

³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3

³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³

5-Component system is better than 3-Components system if

10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³

=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²

Which reduce to

3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0

either p> ½ or p <1

=> p belongs to ( 0.5, 1)

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The simplified form of the given expression is option c 1 1/2x - 1 3/4

Given,

The expression; 1/4 (3x - 7) + 3/4x

We have to simplify this expression;

Simplification of expressions;

To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.

Then,

1/4 (3x - 7) + 3/4x

= 1/4 × 3x - 1/4 × 7 + 3/4x

= 3/4x - 7/4x + 3/4x

= 6x/4 - 7/4

= 3x/2 - 7/4

= 1 1/2x - 1 3/4

Therefore,

The simplified form of the given expression is option c 1 1/2x - 1 3/4

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The slope of the line = rise of the line / run of the line = 2/2 = 1.

The slope (m) of a line can be determined by finding the ratio of the rise of the line to the run of the line, which is, the change in y over the change in x.

Referring to the image attached below, the blue line in the given graph shows the rise of the line while the red line shows the run of the line.

Therefore:

Rise of the line = 2 units

Run of the line = 2 units

Slope of the line (m) = rise/run = 2 units/2 units

Slope of the line (m) = 1

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Answer:

27

Step-by-step explanation:

Divide 270 by 10

The amount of money Kadeesha have in her account after 11 years is $1059.3.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

Given that, principal=$900, rate of interest=1.5% and time period =11 years.

Now, amount =900(1+1.5/100)¹¹

= 900(1+0.015)¹¹

= 900(1.015)¹¹

= 900×1.177

= $1059.3

Therefore, the amount of money Kadeesha have in her account after 11 years is $1059.3.

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The range is the difference between the largest and the smallest and the range is 5.2

This is a graph that is divided into two vertical axes such that one axes represent the stem and the other axis represents the leaf

From the question, we have the following parameters:

Stems = 12, 13, 14, 15, 16, and 17

Each of these stem elements have their own leaves

So, the complete stem and leaf plot is as follows

12     |  3, 3, 6, 7, 9, 9.

13     |  1, 1, 4, 5, 5.

14     |  0, 0, 2, 3, 3, 8, 8, 9.

15     |  2, 2, 2, 2, 2, 3, 5, 5, 7.

16     | 4, 5, 5, 9, 9.

17      | 3 5.

Key

12 | 3 means 12.3.

To determine the range, we simply take the smallest number and the largest number represented by the plot and calculate the difference

In (a), we have

The range is calculated from the smallest number and the largest number represented by the plot

So, we have

Smallest = 12.3

Largest = 17.5

So, the range is

Range = 17.5 - 12.3

Evaluate

Range = 5.2

Hence, the range is 5.2

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The value of k - 0.3753, used  to predict the population in 2017,  the population in 2017 is 508861.

population of given by P = 289.81e^Kt

in 2000 population P(0)=289.81 thousand

in 2006 population P(6) = 363000

363000 = 289810[tex]e^{k6}[/tex]

k = 1/6 ln | 363000 /289810 |

k = 0.3753

Population in 2017  --> t =17

P(15) = 289810[tex]e^{k6}[/tex]

P(15) = 508861.32

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics. It could be a collection of people, things, occasions, organizations, etc. To make inferences, use populations. A population can be all the students at a particular school. It would contain all the students who study in that school at the time of data collection

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The given scatterplot has no correlation. This is because there is no pattern among the dots on the scatterplot.

Correlation is a measure that is used in statistics to measure the linear relationship that exists between two variables. Correlation can either be positive, negative or zero. The closer the correlation coefficient is to one, the higher the correlation.

Positive correlation is when two variables move in the same direction. When drawn on a scatterplot, the line of best fit is upward sloping. The coeffect of correlation for positive correlation is always positive.

Negative correlation is when two variables move in different directions.  When drawn on a scatterplot, the line of best fit is downward sloping. The coeffect of correlation for negative  correlation is always negative.

Zero correlation or no correlation is when there is no relationship between the variables. When drawn on a scatterplot, there is no discernible patterns among the variables.

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Answer: Cumulative frequency distribution

Step-by-step explanation: Not entirely sure but I believe you are looking for this definition based on the question. Hope this helps :)

The given function is

The expression f(-16) means we have to evaluate the function when x = -16.

ok

I erased the answer but it is 22 whole strips

Answer:

665

Step-by-step explanation:

the reasoning is because you divide 525/15 and you get 35 with that you multiply by 19 because you are seeing how far you can get with 19 gallons of gas .

665 miles Santiago can travel on 19 gallons of fuel.

A ratio in mathematics demonstrates how many times one number is present in another.

Given, Santiago's car used 15 gallons to travel 525 miles. Since,

Santiago travels in 15 gallons  = 525 miles

Santiago travels in 1 gallons = 525/ 15 = 35

Santiago travels in 19 gallons = 35* 19 = 665

Therefore,  Santiago can travel 665 miles on 19 gallons of fuel.

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