f(x) = 5•3x what is the domain of the exponential function

Answer:

Step-by-step explanation:

4x + 6 + 24 - 2x =

2x + 30

Answer:

-12 and 2

Step-by-step explanation:

1. Notice that both numbers have to be negative. This means that one number has to be negative, and the number with the largest value has to be negative.

2. Think of numbers that multiply to -144

3. Check and see if they add to -10

4. The only numbers that satisfy this are -12 and 2

The area of the figure is obtained to be approximately 74.1 units².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The rectangle has the length of 6 units.

The rectangle has the breadth of 10 units.

The semicircle has a diameter of 6 units.

The semicircle has the radius of 3 units.

The formula for area of rectangle is -

Area (r) = l × b

Substitute the values into the equation -

Area (r) = 6 × 10

Area (r) = 60 units²

The formula for area of semicircle is -

Area (r) = πr² / 2

Substitute the values into the equation -

Area (s) = [3.14 × (3)²] / 2

Area (s) = 28.26 / 2

Area (s) = 14.13 units²

The total area of the diagram is -

Total Area = Area (r) + Area (s)

Substitute the values into the equation -

Total Area = 60 + 14.13

Total Area = 74.13 units²

Therefore, the area of the figure is 74.1 units².

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The sum of the infinite geometric series is: ²/₅

The formula for the sum of an infinite geometric series is;

[tex]S_{\infty} = \frac{a}{1 - r}[/tex]

where;

a is first term

r is common ratio

The first term is; a = ⁴/₁₅

Common ratio; r = ⁴/₉ ÷ ⁴/₁₅ = ⁵/₃

r = ²⁰/₂₇  ÷  ⁴/₉ = ⁵/₃

Thus;

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ (⁵/₃ - 1)

[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ ²/₃

= ²/₅

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Answer:

How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;S_∞ = a/(1 - r)where;a is first termr is common ratioThe first term is; a = 4/15Common ratio; r = (4/9)/(4/15) = 5/3r = (20/27)/(4/9)  = 5/3Thus;S_∞ = (4/15)/((5/3) - 1)S_∞ = (4/15)/(2/3) = 2/5

Answer:

To determine the flexible budget for the Cutting Department, we need to use the information provided to adjust the original budget for the actual level of production.

First, we need to calculate the variable cost per hour of production:

Variable cost per hour = Direct labor / Hours of production

Variable cost per hour = $37,260 / 4,140 hours

Variable cost per hour = $9

Next, we can use this variable cost per hour to calculate the flexible budget for the actual level of production:

Flexible budget = (Variable cost per hour x Actual hours of production) + Fixed costs

Flexible budget = ($9 x 4,500 hours) + $43,370

Flexible budget = $40,500 + $43,370

Flexible budget = $83,870

Therefore, the flexible budget for the Cutting Department, based on the actual level of production of 4,500 hours, is $83,870.

Answer: A. Nikko by 2 inches

Step-by-step explanation: Because 82 inches = 6ft 10in, which is 2 inches taller than Ricco.

1) The system of inequalities that models this scenario will be:

6x + 3y ≤ 24

6x + 3y ≥ 4

2)
i) the solution for y is y ≤ 5 - 2x.
ii) the solution for y is y ≥ 3 - x.

3) The graph is attached accordingly.

a)
Let's use the variables x and y to represent the number of Mickey pretzels and Mickey bars, respectively, that Mrs. Tobie can buy. We want to ensure that at least four children get one snack each, so the inequality for the total number of snacks should be greater than or equal to 4.

Also, Mrs. Tobie has a budget of S24, so the cost of the snacks should be less than or equal to S24. Putting these together, we get:

6x + 3y ≤ 24 (budget constraint)

6x + 3y ≥ 4 (at least four snacks)

So the system of inequalities that models this scenario is:

6x + 3y ≤ 24

6x + 3y ≥ 4

b)

To solve for y in each inequality, we need to isolate y on one side of the inequality sign.

For the first inequality, we have:

x + y ≥ 3

Subtracting x from both sides, we get:

y ≥ 3 - x

So the solution for y is y ≥ 3 - x.

For the second inequality, we have:

6x + 3y ≤ 15

Dividing both sides by 3, we get:

2x + y ≤ 5

Subtracting 2x from both sides, we get:

y ≤ 5 - 2x

So the solution for y is y ≤ 5 - 2x.

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That statement that best describes the relationship between x and y in the given equations is: d. In y = 25x, the value of y is 25 times the value of x, and in y = x + 25, the value of y is 25 more than the value of x.

In the equation y = 25x, the value of y is directly proportional to x and is 25 times greater than x. This means that as x increases, y increases by a multiple of 25. For example, if x = 2, then y = 50 (25 x 2), and if x = 4, then y = 100 (25 x 4).

In the equation y = x + 25, the value of y is equal to the value of x plus 25. This means that y is always 25 greater than x, regardless of the value of x. For example, if x = 2, then y = 27 (2 + 25), and if x = 4, then y = 29 (4 + 25).

The answer is option d.

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Answer:

Step-by-step explanation:

(9/4 * 8/7) - (3/8*4/1) =

(72/28) - (12/8)

18/7 - 3/2

36/14 - 21/14

15/14 = 1 1/14

Answer:

in absolute value you consider both the positive and negative side of the expression in the absolute bar.

The data in the triangle is not sufficient to find the asked values in the question.

The relationship in between sides and angles for non-right (oblique) triangles is known as the Law of Sines. It simply asserts that for all sides and angles of a given triangle, the ratio of the length of a side to the sine angle opposite this side is the same.

You must know between two angles but one side of the triangle (AAS or ASA) either two sides and an angle opposing one of them in order to employ the Law of Sines (SSA).

g/sinG = h/sinH = f/sinF

Where G, H and F are the angles and g, h and f are the angles' opposing sides.

Put the values:

g/sin136 = 13/sinH = 7/sinF

The three pairs of expression are-

HF/sin136 = 13/sinH ;   13/sinH = 7/sinF and g/sin136 = 7/sinF.

HF = 13*sin136/sinH

HF = 10.97/SinH

From the found 3 expression, each has two missing value.

Thus, the angles F and H is not possible to find.

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Answer:

The graph of the function y = 100(1.05) is shown below.

b. Calculate the cost of the hotel per night after six years.

The cost of the hotel per night after six years is $130.25. This is calculated by plugging in t = 6 into the equation y = 100(1.05)^t and solving for y.

c. What is the overall cost of 7 nights at the hotel in its sixth year of operation?

The overall cost of 7 nights at the hotel in its sixth year of operation is $910.75. This is calculated by multiplying the cost per night after six years ($130.25) by 7 nights.

2 LEARNING RESOURCES

Discuss the advantages of using online learning resources for students.

One of the main advantages of using online learning resources for students is convenience. Online learning resources can be accessed from virtually any location with an internet connection, allowing students to learn from the comfort of their own homes or from mobile devices when they are on the go. Furthermore, online learning resources reduce the need for students to commute to and from a physical school, meaning that students have more time for their studies, hobbies, and other activities.

Another advantage of online learning resources is adaptability. Online learning resources may be tailored to the needs of each individual student and can easily be adjusted should a student’s needs

Answer:

Step-by-step explanation:

To find the expected difference in height between a child 49 months of age and a child 16 months of age, we need to first find the average height of each child and then find the difference between them.

For a child who is 49 months old, the average height can be found by substituting x = 49 in the given equation:

y1 = 2.9sqrt(49) + 20.1 = 42.7 inches

For a child who is 16 months old, the average height can be found by substituting x = 16 in the given equation:

y2 = 2.9sqrt(16) + 20.1 = 28.9 inches

Therefore, the expected difference in height between the two children would be:

y1 - y2 = 42.7 - 28.9 = 13.8 inches

So we can expect the child who is 49 months old to be, on average, 13.8 inches taller than the child who is 16 months old.

Answer:

Gold ring = 6180

Step-by-step explanation:

Gold ring = ?

I = prt

= 19000 x 6% x 2

= 2180

Amount to be paid= 19000 + 2180

= 21180

gold ring = 21180 - 15000

= 6180

Answer:

p = 6

Step-by-step explanation:

Answer:

y = 4

x = 4√2 or 5.66

Step-by-step explanation:

If the △ is a right △ with 1 angle 45o, then the other angle is also 45o. This △ will be isosceles right triangle with y = 4

Pythagorean theorem: c^2 = a^2 + b^2

x^2 = y^2 + 4^2

x^2 = 4^2 + 4^2

x^2 = 32

x = √32 = 4√2 = 5.66

The value of the investment modeled by the function V(t) = 50(0.9)^t Decreases at a decreasing rate, starting with an initial value of 50.

We are given the investment value function V(t) = 50(0.9)^t. This function describes the value of an investment over time, t. Let's analyze the behavior of V(t) and find a statement that is supported by this function.

1. The initial value of the investment is V(0) = 50(0.9)^0 = 50(1) = 50. So, the investment starts with a value of 50.

2. The function V(t) contains a term (0.9)^t, which indicates that as time passes, the investment value decreases. This is because 0.9 is between 0 and 1, so raising it to a power of t (as t increases) results in a smaller value.

3. The rate of decrease is not constant, as the function is exponential, not linear. This means the value of the investment decreases at a decreasing rate over time.

Based on the behavior of V(t), the following statement is supported:

As time passes, the value of the investment modeled by the function V(t) = 50(0.9)^t decreases at a decreasing rate, starting with an initial value of 50.

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-1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

A null hypothesis is a statistical hypothesis that presupposes that there is no link between two variables in a population or that there is no meaningful difference between two populations. It serves as the beginning point of a statistical hypothesis test and is typically marked as H0. A null hypothesis serves as a reference point against which the alternative hypothesis may be compared. The alternative hypothesis is accepted if there is sufficient evidence from the data to reject the null hypothesis. The null hypothesis is not rejected if there is insufficient evidence in the data to support it.

Using a significance threshold of 0.05, we may use a conventional normal distribution table or calculator to get the essential z value. The value that corresponds to the 0.025 percentile is the crucial z value (or the 0.975 percentile, depending on the direction of the alternative hypothesis).

The z value for the 0.025 percentile, as determined by a typical normal distribution table, is -1.96.

Hence, -1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

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Using inequality, x < 63.33, Student take 62 and adult take 68.

By utilizing the "equal tο" symbοl in mathematics, equatiοns are nοt necessarily balanced οn bοth sides. Sοmetimes it can be abοut a "nοt equal tο" relatiοnship, which denοtes that οne thing is better than οr wοrse than anοther.

A relatiοnship between twο numbers οr οther mathematical expressiοns that yields an unfair cοmparisοn is referred tο as an inequality in mathematics. Certain algebraic mathematical expressiοns are referred tο as inequalities.

The student's ticket sells fοr $5,

adult ticket sells fοr $950,

Tοtal auditοrium = 130,

If x represents the number οf student, then adult = 130 - x,

∴ 5x + 9.5y > 950

insert y = 130 - x5x + 9.5(130 - x) > 950,

5x + 1235 - 9.5 x > 950

x < 63.33

∴ Student take 62 and adult take 68.

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Answer:

the answer is c because every side of a triangle sides are he same so c is your answer

Answer:

A

Step-by-step explanation:

simply divide each ter by -7x ..

After addressing the issue at hand, we can state that Therefore, function  g(-2) = 0 and g(4) = -4.

Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.

When x = -2, g(x) = 0.

When x = 4, g(x) = -4.

Therefore, g(-2) = 0 and g(4) = -4.

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Using percentage, we can find:

1- 84600

2- 385400

3- 20811.6

4- 7576776

A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage. This percent symbol can always be converted to a fraction or decimal equivalent by "dividing by 100".

Now in the question,

Downpayment = 18% of 470000

= 84600

original amount financed =

470000-84600

= 385400

Monthly payment = 5.4% of 385400

= 20811.6

Total payment in 30 years = 7576776

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The answer of the given question based on the compound interest is  the balance after 6 years is $14,162.62 (option a).

Amount refers to total value of something, usually in terms of a money. It can also be used in  context of a quantity of something, such as an amount of the  time or an amount of the material.

formula for the compound interest is :

A = P(1 + r/n)^(nt)

Where,

A = final amount

P = principal amount

r = annual interest rate

n = the number of times interest is to be compounded per year

t = time in years

In this case, we have:

P = $1,000

r = 3.75% = 0.0375 (annual interest rate as a decimal)

n = 12 (monthly compounding)

t = 6 years

Substituting the  values into  formula, we will get:

A = 1000(1 + 0.0375/12)⁽¹²*⁶⁾

A = $1,4162.62

Therefore, the balance after 6 years is $14,162.62 (option a).

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Answer:

A or 420

Step-by-step explanation:

Remember Length x Width x Height. 12 * 5 is 60, then 60 * 7 is 420.

The probability of getting someone who tested positive, given that he or she had the disease, is 0.9.

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of getting someone who tested positive, given that he or she had the disease, is equal to the probability that the individual has the disease and tests positive ( P(positive | disease) ).

This can be calculated using the formula P(A|B) = P(A∩B) / P(B)

P(positive | disease) = P(positive ∩ disease) / P(disease)

                    = 141 / (141+16)

                    = 0.898

Therefore, the probability of getting someone who tested positive, given that he or she had the disease, is 0.898, which is 0.9.

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Answer:

To multiply polynomials, you can follow these steps:

Distribute each term of the first polynomial to each term of the second polynomial.

Combine like terms.

Simplify the resulting expression.

Here is an example:

(2x + 3)(x - 4)

Distribute:

2x(x - 4) + 3(x - 4)

Combine like terms:

2x^2 - 8x + 3x - 12

Simplify:

2x^2 - 5x - 12

So, (2x + 3)(x - 4) = 2x^2 - 5x - 12.

Step-by-step explanation:

Step-by-step explanation:

For RIGHT  triangles the cos of an angle = adjacent LEG / hypotenuse

 so for THIS triangle   cos 55°  = x / 9.3

    re-arrange to    9.3 * cos 55° = x    

       use calculator to find x = ~ 5.3 units   (rounded)

Answer:

x = 5.3

Step-by-step explanation:

As triangle XYZ is a right triangle, and we have been given angle X, the side adjacent the angle, and the hypotenuse, we can use the cosine trigonometric ratio to solve for x.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for x:

[tex]\implies \cos 55^{\circ}=\dfrac{x}{9.3}[/tex]

[tex]\implies x=9.3 \cos 55^{\circ}[/tex]

[tex]\implies x=5.3342608...[/tex]

[tex]\implies x=5.3\; \sf (nearest\;tenth)[/tex]

Therefore, the value of x is 5.3 to the nearest tenth.

Answer: 9.60

Step-by-step explanation:

Labeled price = $ 12

Discount = 20% of labeled price = 12 x 20%

= 12 x 2 / 10 = 24 / 10 = $ 2.4

Sale price = Labeled price - Discount.

Sale price = $ 12 - $ 2.40 = $ 9.60

Thus the sale price of the case of soda is 9.60 $

The volume of the resulting block of wood is 576 in³. The correct option is the second option 576 in³

From the question, we are to determine the volume of the resulting block of wood.

From the given information,

The dimensions of the block of wood is 10 in. by 10 in. by 6 in.

First, we will calculate the original volume of the block of wood.

The original block of wood has a volume of

V = 10 x 10 x 6

V = 600 in³

Now, we will determine the volume og the hole that was cut through

The dimensions of the hole is 2 in. by 2 in. by 6 in.

Volume of the hole = 2 x 2 x 6

Volume of the hole = 24 in³

The resulting block would have a volume of

Volume of resulting block = 600 - 24

Volume of resulting block = 576 in³

Hence, the volume is 576 in³.

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