Solve the following a)give the solution in calculator ready form (the exact value of x) and b)approximate the solution to the nearest hundredth.8. 3^2x - 12 * 3^x -28 =0

Answer:

[tex]x=5, y=-2[/tex]

Step-by-step explanation:

[tex]-5y+6x=40 \implies -15y+18x=120 \\ \\ 3y-8x=-46 \implies 15y-40x=-230 \\ \\ \therefore -22x=-110 \implies x=5 \\ \\ \therefore -5y+6(5)=40 \implies y=-2[/tex]

The inverse function of the function f(x) = 12(x+3)  is f(x) = -2x - 3

A function's inverse is a function that offers us the actual value for which the desired function produces a specific outcome.

The function given is:

To find the inverse, we must perform the following procedures.

y takes the place of f(x);

y = -(x+3)/2

Change the x and y variables.

x = -(y+3)/2

Calculate y

2x = - (y + 3)

2x = -y - 3

y = -2x - 3

We get the following in inverted notation:

f(x)⁻¹ = -2x - 3

Thus the obtained inverse function is f(X) =  -2x - 3

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Using similarity of triangles, the length of side GH is given as follows:

GH = 18.

Similar triangles have congruent angle measures, thus the measures of the side lengths are proportional.

In this problem, triangles CAD and HGD are similar, and the equivalent sides are given as follows:

Hence the following proportional relationship is established:

x/12 = 45/30

Applying cross multiplication, we can solve for x, which is the length of side GH, as follows:

30x = 45 x 12 (simplifying by 30)

x = 1.5 x 12 (multiply 1.5 and 12).

x = 18. (which is the length of side GH).

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The subtraction of the numbers, involving scientific notation, is given as follows:

18 - 9.2 x 10^(-4) = 17.99908.

A number in scientific notation is given according to the rule presented as follows:

[tex]a \times 10^b[/tex]

The base is [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.

In this problem, we are given the following subtraction:

18 - 9.2 x 10^(-4).

When two numbers are subtracted, they must have the same base, hence we are going to convert 9.2 x 10^(-4) to base 0.

This means that 4 has to be added to the exponent, meaning that the base has to be divided by 10000 to compensate, then:

9.2 x 10^(-4) = 0.00092.

Then the result of the subtraction is given as follows:

18 - 9.2 x 10^(-4) = 18 - 0.00092 = 17.99908.

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Function : $8000 = $1200 + $700x

They will raise $700 per month for x months -> $700x is the amount of money they raise per month.

Since $8000 is the sum in the function, it is the goal.
Therefore, $1200 in this case means they started with $1200.

The explicit function of the relation is Tn = 4.25 + 0.75n and the cost of a 55 miles ride is $45.5

The sequence of the relation is given as

5.00, 5.75, 6.50, …

In the above sequence, we can see that

The sequence have a common difference of 0.75

This means that the sequence is an arithmetic function

An arithmetic function is represented as

T(n) = a + (n - 1)d

Where

Substitute the known values in the above equation

Tn = 5 + 0.75(n - 1)

Expand

Tn = 5 - 0.75 + 0.75n

Evaluate

Tn = 4.25 + 0.75n

This means that

n = 55

Subsitute n = 55 in the equation Tn = 4.25 + 0.75n

So, we have

T55 = 4.25 + 0.75 * 55

Evaluate the product

T55 = 4.25 + 41.25

Evaluate the sum

T55 = 45.5

Hence, a 55-mile ride will cost $45.5

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Answer:

12 Blueberries and 4 Strawberries

Step-by-step explanation:

12+4 = 16 and 12:4 = 3:1

The volume of a cylinder is: V = π r² h then the volume of a cylinder is 5091.43  cm²

The volume of a cylinder is:

V = π r² h

From the information provided it can be concluded that:

The height of the cylinder is, h = 20 cm

The radius of the base exists, r = 9 cm

Compute the volume of a cylinder as follows:

V = π r² h

substitute the values in the above equation, we get

= (22/7) × 9² × 20

simplifying the above equation, we get

= (22 × 81 × 20) / 7

= 5091.42857

≈ 5091.43

Therefore, the volume of a cylinder is 5091.43 cm².

The complete question is:

Calculate the volume of this cylinder, giving your answer to 1 decimal place.

20 cm

9 cm

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Part a: Range = 4550

Part b: Variance  = 287,034

Part c: Standard deviation =  (287,034)².

For the given question;

The highest net worths (in millions of dollars) for 6 celebrities is shown.

Part a: calculate the range;

Range = highest value - lowest value

Range = George Lucas (5500) - Jerry Seinfeld (950)

Range = 4550

Part b: Calculated the variance;

σ = ∑X²/n - μ² =  ∑(X²- μ²)/n

First find the mean;

μ =  ∑X/n

μ = (5500 + 3700 + 3200 + 1200 + 1000  950)/6

μ = 7775/3

σ =  (5500² + 3700² + 3200² + 1200² + 1000²  950²)/6 - (97775/3)²

σ = 287034

Variance = 287,034

Part c:  Calculated the standard deviation;

standard deviation = σ²

σ² = (287,034)²

Thus, the standard deviation is found as (287,034)².

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The new grade of the student will be 70% and the grade reduced by 10 percent.

This is a rate, number, or amount in each hundred. Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

In the given question, we simply need to add the two percentage together and find the average of the value.

This can be done mathematically as

[tex]\frac{60+80}{2} = 70[/tex]

The average grade will be 70% and this shows that the grade dropped by

[tex]80\% - 70\% = 10\%[/tex]

The grade will go down by 10%.

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Answer:

See below

Step-by-step explanation:

72 %  is .72 in decimal

.72 x = 50 oz     Divide both sides by .72

X = 50 / .72 = 69.44 oz     ( or 69  4/9 oz )

Answer:

6.6666 or 7

Step-by-step explanation:

According to the solving the value of the given function g(n) = -n² -1 h(n) = -2n + 2:

(g o h)(n)  = 2n³ +4n -2.

A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output.

A function is defined technically as a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome.

g(n) = -n² -1 h(n) = -2n + 2

find  (g o h)(n)

We can write it as:

g o h = g  x h

         = (-n² -1) x (-2n + 2)

        = 2n³ + 2n +2n -2

       = 2n³ +4n -2

According to the solving the value of the given function g(n) = -n² -1 h(n) = -2n + 2:

(g o h)(n)  = 2n³ +4n -2.

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The ordered pairs that are also functions are listed below.

1. {(2,4),(3,1),(0,5),(-1,-3)}

2. {(2,4),(-4,1),(0,4),(-3,-0)}

4.{(7,-3),(3,-7),(2,4),(4,2)}

The ordered pairs that are not functions are listed below.

3.{(-2,-3),(4,1),(4,4),(-3,2)}

A function is a relation between two sets of ordered pairs that describe that there should be only one output for each input, or that for every element in set A, there should be one and only one relation in set B.

A relation between two sets of ordered pairs can be considered a function when every X value is associated with only one Y value.

Here in the first, second, and fourth sets of ordered pairs

1. {(2,4),(3,1),(0,5),(-1,-3)}

2. {(2,4),(-4,1),(0,4),(-3,-0)}

4.{(7,-3),(3,-7),(2,4),(4,2)}

Hence, every value in X has only one single value in Y. Hence, all these relations can be considered functions.

In the third set, i.e.,

3.{(-2,-3),(4,1),(4,4),(-3,2)}

It can be seen that element 4 has two values as its output, which are 1 and 4 ((4,1),(4,4)). Hence, it cannot be considered a function.  

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Answer:

about 24.38 feet

Step-by-step explanation:

Graphing window: [0, 30] by [-20, 160]

y1 = 20 + 2x + √(400 + 4x^2)

y2 = 1.6(20 + x + √(400 + x^2))

y1 = y2 when x = 24.3798.

So the length of the smaller garden's longer leg is about 24.38 feet.

The solutions to all the parts of the question are discussed below.

Inequality in mathematics is a relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given is a rental car company charges a $22 fee to rent a car plus $0.32 per mile.

Assume that [m] represent the number of miles the car is driven by Matt.

Part [A]

We can write the inequality as follows -

22 + 0.32m ≤ 100

Part [B]

The inequality is -

22 + 0.32m ≤ 100

0.32m ≤ 78

m ≤ 78/0.32

m ≤ 243.75

Part [C]

The graph is attached at the end.

Part [D]

22 + 0.32m ≤ 100

22 + 0.32 x 243.75 ≤ 100

22 + 78 ≤ 100

100 ≤ 100             [verified]

Part [E]

The number of miles that can be driven by Matt after renting the car will be 243.5 miles.

Therefore, the solutions to all the parts of the question are discussed above.

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The two variable equation representation of the Jae expenditure of money while buying Video games and gaming accessories will be 60x + 45y = 500

It is given that,

The total money that Jae has =  $500

The cost price of each video game = $60

And, the cost price for each game accessories = $45

We need to find an arithmetic equation representation which is known as equation in two variable

To do that, the question has represented both number of games and gaming accessories that Jae bought with x and y variables

It is given,

Total number of video games he an buy = x

Total number of gaming accessories he an buy = y

Now, the total expenditure that Jae will do in buying Video games and gaming accessories should not exceed $500 as this s the total money he had wit him

Therefore,

60x + 45y = 500

This is the two variable equation representation of the Jae expenditure of money while buying Video games and gaming accessories

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Answer:  between $42 and $54 including both endpoints.

In symbolic form we can say [tex]42 \le p \le 54[/tex] where p is the final price after the discount is applied.

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

Explanation:

10% off means you save 10% but pay the remaining 90%

Then convert 90% to decimal form to get 0.90

If the original price is $60, then the final price is 0.90*60 = 54 dollars.

In other words,

10% of 60 = 0.10*60 = 6 dollars saved

60-6 = 54 is the final price

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

If the discount is 30% then you pay the remaining 70%

0.70*60 = 42

Or you can think of it like this

30% of 60 = 0.30*60 = 18 dollars saved

60-18 = 42 dollars is the final price

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

Let's summarize with this chart:

[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{Discount} & \text{Amount Saved} & \text{Final Price}\\\cline{1-3}10\% & \$6 & \$54\\\cline{1-3}30\% & \$18 & \$42\\\cline{1-3}\end{array}[/tex]

Therefore, the final price after the discount is between $42 and $54 including both endpoints.

Side note: The jump from 10% to 30% is "times 3"; so is the jump from $6 to $18 in the "amount saved" column of the table.

The exponent's expression is 5².

Exponent expression:

An exponent refers to the number of times a number is multiplied by itself.

The property of exponents:

[tex]a^{m} / a^{n}[/tex] = [tex]a^{m-n}[/tex]

The expression is:

[tex]5^{8} / 5^{6}[/tex]

Using the property of exponents we have,

[tex]5^{8-6}[/tex]

= 5²

Therefore the exponent expression is 5².

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Considering the average rate of change of the function, the matched pairs are given as follows:

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given according to the following rule:

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

For the interval given by item 1, between -1 and 2, we have that:

Hence the rate is:

r = (-17 - (-2))/(2 - (-1)) = -15/3 = -5.

Meaning that 1 matches with a.

For the interval given by item 2, between -1 and 0, we have that:

Hence the rate is:

r = (3 - (-2))/(0 - (-1)) = 5/1 = 4.

Meaning that 2 matches with b.

For the interval given by item 3, between 1 and 2, we have that:

Hence the rate is:

r = (-17 - (-2))/(2 - 1) = -15/1 = -15.

Meaning that 3 matches with c.

For the interval given by item 4, between -2 and 0, we have that:

Hence the rate is:

r = (3 - (-17))/(0 - (-2)) = 20/2 = 10.

Meaning that 4 matches with d.

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The mean number of individuals per sample who do not exercise regularly = 7

According to the survey 58% of the Americans does not exercise.

Hence probability of not exercising, p = 58/100 = 0.58

Define a random variable X denoting the number of people who does not exercise.

Then X follows the binomial distribution.

If p denotes the probability of success and if n is the sample size or number of trials, then

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ gives the probability of the random variable X.

Here, the sample size, n = 12

For a binomial distribution, mean, μ = np

Therefore,  mean number of individuals per sample who do not exercise regularly = np

               = 12 x 0.58

               = 6.96

               ≈ 7

The question is not complete. Find the complete question below:

According to the Behavioral Risk Factor Surveillance System, 58% of all Americans adhere to a sedentary lifestyle (sedentary means does not exercise).

a. If you selected repeated samples of 12 from the U.S. population, what would be the mean number of individuals per sample who do not exercise regularly?

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A)  The probability that at least one of the two students will be in class on a given day is; 0.92

B)  If at least one of the two students is in class on a given day, the probability that a is in class that day is; 0.8696

In probability theory, the occurrence of the events may depend on its relative events which are called dependent events while the events not dependent on their relative events are referred to as independent events. For dependent events, if conditional probabilities are required , we will make use of the Baye's Theorem and the total probability theorem sometimes.

We are given;

Probability that student A attends class = 80% = 0.8

Probability that student B attends class = 60% = 0.6

A) The probability that at least one of the two students will be in class on a given day is;

P = 1 - Probability that that neither show up to class on any given day.

P(A ∪ B) = 1 - P(A∼ ∩ B∼)

Where  P(A∼ ∩ B∼) = (1 - 0.8) × (1 - 0.6)

P(A∼ ∩ B∼) = 0.08

Thus;

P(A ∪ B) = 1 - 0.08

P(A ∪ B) = 0.92

B) We want to find the probability that student A was in the class given that at least one of them was in the class.

This is obviously a case of conditional probability which will give us the formula;

P(A|A ∪ B) = P(A ∩ (A ∪ B))/P(A ∪ B)

= P(A)/P(A ∪ B)

= 0.8/0.92

= 0.8696

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Answer: Yes because an example of a proportional problem is 54x = 103

I am pretty sure that is the answer

By using the synthetic substitution in the function f(x) = [tex]x^3+4x^2-5x+11[/tex], the value of f(-3) = 35

The function is

f(x) = [tex]x^3+4x^2-5x+11[/tex]

The function is defined as the relationship between the one variable and another variable. If one variable is dependent variable and another variable will be independent variable

To find the value of f(-3), first we have to substitute the value x = -3 in the given function

The function is

f(x) = [tex]x^3+4x^2-5x+11[/tex]

Substitute the value of x = -3

f(-3) = [tex](-3)^3+4(-3)^2-5(-3)+11[/tex]

= -27 + 36 + 15 + 11

= 35

Hence, by using the synthetic substitution in the function f(x) = [tex]x^3+4x^2-5x+11[/tex], the value of f(-3) = 35

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Julie received an amount of $134.4 when she cashed her paycheck.

Let x be the amount of the paycheck.

She gave her brother ten dollars.

She then paid $30 for the car's petrol.

So she departed with an amount equal to x-40.

She now spent half of the remaining accounts on a new camping tent.

Spent camping = (x - 40)/2

Remaining = x - 40 - (x - 40)/2

She paid $29.45 for a pair of running shoes.

Therefore, remaining =  x - 40 - (x - 40)/2 - 29.45

As per the question, she had $17.75 remaining.

So x - 40 - (x - 40)/2 - 29.45 = 17.75

Rearrange the terms and solve for x,

(x - 40)/2 = 47.2

x - 40 = 94.4

x = 134.4

Therefore, she received an amount of $134.4 when she cashed her paycheck.

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First, draw a diagram to visualize the situation:

As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.

Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:

Therefore, the distance between the points (-5,4) and (8,-3) is: √218.