Identify the domain and range of the exponential function.

I am trying to help my son with his math and am about to cry. Lol. May you please help me? Thank you

The correct statement regarding the relative minimums of each function is given as follows:

The minimum of h(x) is farther left and down from the minimums of f(x) and g(x).

The function f(x) is defined as follows:

f(x)= √x.

It has a relative minimum at (0,0), which is one the first quadrant.

The function g(x) is defined as follows:

√x-3+1

It is a translation of 3 units right and 1 unit up of f(x), hence the minimum has coordinates (3,1), which is on the first quadrant.

The function h(x) is defined as follows:

h(x)= √x+1-2

It is a translation of 1 unit left and 2 units down of f(x), hence the minimum has coordinates (-1, -2), which is on the third quadrant.

The third quadrant is farther left and down from the first quadrant.

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We can cοnclude that the expοnential functiοn represented by the given table is [tex]y = 3(0.5)^x[/tex]

An expοnential functiοn is a mathematical functiοn οf the fοrm [tex]f(x) = ab^x[/tex], where a and b are cοnstants and b is greater than 0 and nοt equal tο 1. It is a type οf mathematical mοdel that describes a prοcess where a quantity grοws οr decays at a rate prοpοrtiοnal tο its current value οver time οr space.

An expοnential functiοn has the fοrm:

[tex]\mathrm y = ab^x[/tex]

where "a" is the initial value οf the functiοn, and "b" is the grοwth factοr οr base οf the functiοn.

Tο find the equatiοn οf the expοnential functiοn represented by the given table, we can use the first twο data pοints tο determine the values οf "a" and "b", and then check if the remaining data pοints fit the functiοn.

Using the first data pοint (0, 3), we get:

[tex]3 = ab^0[/tex]

3 = a

Using the secοnd data pοint (1, 1.5), we get:

[tex]1.5 = ab^1[/tex]

1.5 = 3b

b = 0.5

Therefοre, the equatiοn οf the expοnential functiοn represented by the given table is:

[tex]y = 3(0.5)^x[/tex]

We can check the remaining data pοints tο see if they fit the functiοn:

Fοr [tex]x = 2, y = 3(0.5)^2 = 0.75[/tex]

Fοr[tex]x = 3, y = 3(0.5)^3 = 0.375[/tex]

Since all the data pοints fit the equatiοn, we can cοnclude that the expοnential functiοn represented by the given table is:

[tex]y = 3(0.5)^x[/tex]

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The price οf the jacket was $115.

Let's start by defining sοme variables tο represent the unknοwn quantities:

Let x be the price οf the shirt

Let y be the price οf the jacket

Frοm the prοblem statement, we knοw that:

y = 2x + 17 (the cοst οf the jacket was $17 mοre than twice the price οf the shirt)

x + y = 164 (the tοtal cοst οf the shirt and jacket was $164)

We can use these twο equatiοns tο sοlve fοr the values οf x and y. One way tο dο this is tο substitute the expressiοn fοr y frοm the first equatiοn intο the secοnd equatiοn, and then sοlve fοr x:

x + (2x + 17) = 164

3x + 17 = 164

3x = 147

x = 49

Nοw that we knοw the price οf the shirt is $49, we can use the first equatiοn tο sοlve fοr the price οf the jacket:

y = 2x + 17

y = 2(49) + 17

y = 115

Therefοre, the price οf the jacket was $115.

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Therefore , the solution of the given problem of equation comes out to be spot A's coordinates are (80,-20).

In mathematical formulas, it is common to use the same variable term to guarantee agreement between two claims. Mathematical assertions, also known as equations expression, are employed to convey the equality of numerous academic figures. In this case, the normalise method adds b + 6 using the data of y + 6 rather than splitting 12 into two parts.

Here,

Let (a,b) represent the location of point A. Consequently, the inclination of the line through (0,0) and (a,b) is

=> m = (b - 0) / (a - 0) Equals b / a

This line being parallel to the initial road gives us:

=>  m = -1/4

Therefore:

=>  b / a = -1/4

=>  b = -a/4

=>  √[(a - 0)² + (-a/4 - 0)²] = √(17a²/16)

From (a,-a/4) to (85,0), the distance is:

=>  √[(85 - a)² + (0 - (-a/4))²] = √[(85 - a)² + (a/4)²]

These two separations are equal, so we can put them at the same value and find a:

=>  √[(85 - a)² + (a/4)²] = √(17a²/16)

When we square both edges, we obtain:

=>  (85 - a)² + (a/4)² = 17a²/16

=>  16(85 - a)² + a² = 17a²

=>  16(7225 - 170a + a²) + a² = 17a²

=>  115600 - 2720a + 17a² + a² = 17a²

=>  18a² - 2720a + 115600 = 0

=> 9a² - 1360a + 57800 = 0

=>  a = (1360 ± √(1360² - 4957800)) / (2*9)

=>  a = (1360 ± √(307600)) / 18

=>  a = (1360 ± 560) / 18

=>  a = 80 or a = 40/9

Point A's y-coordinate is:

=> b = -a/4 = -80/4 = -20

Consequently, spot A's coordinates are (80,-20).

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Answer:

82.28

this was really easy,

The probability in a random sample of 55 18 to 29-year-olds that 20 will say they currently have a subscription to Hulu is: 0.087.

This is a binomial distribution problem, where n = 55 and the probability of success (i.e. a person subscribing to Hulu) is p = 0.41.

The probability mass function of a binomial distribution is:

P(X = x) = (nCx) * p^x * (1-p)^(n-x)

where nCx is the binomial coefficient (i.e. the number of ways to choose x items from n items).

So, in this case, we want to find P(X = 20):

P(X = 20) = (55C20) * 0.41^20 * (1-0.41)^(55-20)

P(X = 20) ≈ 0.087

Therefore, the probability that in a random sample of 55 18 to 29-year-olds, 20 will say they currently have a subscription to Hulu is approximately 0.087or 8.7%.

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Answer:

the scale factor = 3

Step-by-step explanation:

the question is basically saying: how did (12,-4) jump to (36,-12)

we can make d represent the scale factor used to get (12,-4) to (36,-12)

so,

12d = 36

-4d = -12

all there's left to do is to simply solve for d, which is 3

Answer:

3

Step-by-step explanation:

Amount used:

8 - 7.25 = 0.75

He used 0.75 cup

Each day he had 0.25 cup.

0.75/0.25 = 3

Answer: 3

The mistake that Rafael made is interchanging the y-values with the x-values.

The real slope of the line is 25.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (100 - 50)/(4 - 2)

Slope, m = 50/2

Slope, m = 25.

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The correct function equivalent to the original function V = 40,000(0.64) is V = 40,000(0.64)ⁿ.

Percent is a way of expressing a fraction or a decimal as a fraction of 100. It is denoted by the symbol "%". For example, the fraction 3/4 can be written as 75% and the decimal 0.5 can be written as 50%. Percentages are commonly used in everyday life to express values such as discounts, interest rates, and success rates.

Here,

The original function V = 40,000(0.64) models the value, V, of a $40,000 car after t years, where the car depreciates at a rate of 36% per year. The expression 0.64 represents the remaining value of the car after one year, which is obtained by subtracting 36% from 100% (i.e., 100% - 36% = 64%).

To find an equivalent function, we need to simplify 0.64. We can write 0.64 as 0.8², since 0.8 multiplied by itself gives 0.64.

So, V = 40,000(0.64) is equivalent to V = 40,000(0.8²), which simplifies to V = 40,000(0.64). This means that both expressions represent the same function that models the value of the car after t years, given that the car depreciates at a rate of 36% per year.

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An equation for a rational function with the given characteristics is found as:  f(X) = a(x+4)(x) / (x+2)(x-4).

As x = -2 and X = 4 have vertical asymptotes, the denominator will contain the equations (x+2) and (x-4)

The terms (x+4) and 1 will be in the numerator since the x intercepts are (-4,0) , respectively (x-0).

Our current formula is f(X) = a(x+4)(x) / (x+2)(x-4)

We examine the horizontal asymptote to determine the value of A.

The limit of a function as x -> infinity would be - 3 since the horizontal asymptote reflects what the function looks like as x approaches infinity.

Thus,  an equation for a rational function with the given characteristics is found as:  f(X) = a(x+4)(x) / (x+2)(x-4)

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Using Pythagoras theorem, we can find the length of the missing side to be 10 units.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, also referred to as the Pythagorean theorem.

The Pythagorean Theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of its other two sides.

In the given triangle, the base is given as:

b = 6 units.

height, h = 8 units.

Let the missing side be = x.

Now as per the Pythagoras theorem,

x² = 8² + 6²

⇒ x² = 64 + 36

⇒ x² = 100

⇒ x = 10.

Therefore, the length of the missing side of the triangle here is 10 units.

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m = (-12 - 5) / (3 - (-5))

m = (-17) / (3 + 5)

m = (-17) / 8

Therefore, the slope between the points (-5, 5) and (3, -12) is -17/8.

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Therefore , the solution of the given problem of data plot comes out to be value (r) is roughly 0.975.

The most typical way to display data in a graph is to demonstrate how two additional factors relate to one another. Digital and hand-drawn sketches are both acceptable. From the beginning position, move two or more pieces to the correct and three pieces up. The reference system must display the numerals for positions 2, 3, and 4. In your points, be very clear. The pinkish haze with the letter P stands in for the number 2.3.

Here,

We must compute several numbers in order to determine the Pearson correlation coefficient r for the information provided in the table.

Before anything else, we figure out the average and standard deviation of the amount of TV airings (x) and car sales (y):

mean(x) = (40 + 30 + 20 + 50 + 10) / 5 = 30

mean(y) = (30 + 20 + 10 + 40 + 20) / 5 = 24

These mean numbers allow us to determine the standard deviation:

=> SX = √ (( (40-30)² + (30-30)² + (20-30)² + (50-30)² + (10-30)²) / 4)

≈> 15.81

=> SY = √(( (30-24)²+ (20-24)² + (10-24)² + (40-24)² + (20-24)²) / 4)

≈> 8.16

Next, we determine x and y's covariance:

=> cov(x,y) =

=> [(40-30)(30-24) + (30-30)(20-24) + (20-30)(10-24) + (50-30)(40-24) + (10-30)(20-24)] / 4

≈>  125

Last but not least, we can figure out the Pearson association coefficient:

0.975 r = cov(x,y) / (s x * s y)

As a result, the table's data's Pearson correlation value (r) is roughly 0.975. This shows a significant positive correlation between the volume of car purchases and the frequency of the TV ad.

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Answer:

Step-by-step explanation:

[tex]S=40R+20[/tex]

To calculate the standard error σM for a sample, we can use the formula [tex]σM = s / \sqrt{n}[/tex], where s: sample standard deviation and n: sample size.

The formula for calculating the standard error, M, which indicates the standard deviation of the sampling distribution of the mean, is as follows:

[tex]σM = σ / \sqrt{n}[/tex]

where σ: population standard deviation and n: sample size.

If we don't know the population standard deviation, we estimate it using the sample standard deviation s. We use formula:

[tex]σM = s / \sqrt{n}[/tex]

We can apply the method above with the sample size n and the sample standard deviation s if we are given a sample and asked to determine the standard error M for this sample.

By adding up each value in the sample and dividing by the sample size, we can determine the sample mean x, from which we may compute the sample standard deviation. The sample variance is then determined by adding up the squared deviations between each value and the sample mean, then dividing the result by the sample size less one. Lastly, we calculate the sample standard deviation by taking the square root of the sample variance.

Once we have calculated the sample standard deviation s and the sample size n, we can plug these values into the formula for σM:

[tex]σM = s / \sqrt{n}[/tex]

and calculate standard error.

In conclusion, the formula M = s / [tex]\sqrt{n}[/tex]n, where s: sample standard deviation and n: sample size, can be used to compute the standard error M for a sample.

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After making the minimum payment of $125, the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.

If the minimum monthly payment of $125 is made, we can calculate the new balance, unpaid balance, and interest charge as follows:

The interest rate per month is (18% per year) / 12 = 1.5% per month.

First, we calculate the interest charge for the month on the unpaid balance:

Interest charge = (1.5% per month) x ($5000 unpaid balance)

Interest charge = $75

Next, we subtract the minimum payment from the unpaid balance to get the new unpaid balance:

Unpaid balance = $5000 - $125

Unpaid balance= $4875

Then, we add the interest charge to the new unpaid balance to get the new balance:

New balance = $4875 + $75

New balance = $4950

Finally, we can calculate the purchasing power as the credit limit minus the new balance:

Purchasing power = $5000 - $4950

Purchasing power = $50

Therefore the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.

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Answer:

8

Step-by-step explanation:

line WL is a straight line intersecting line GZ at J so angles LJW is 180o

therefore

LJG + GJH + HJW = 180

9x + 90 + 18 = 180

9x = 180 - 90 - 18

9x = 72

x = 72/9 = 8

Answer:

[tex]A=\frac{4}{6} *600 = 400\\B=\frac{2}{6} *600 = 200[/tex]

So, Jane's hourly rate is $6.00 per hour.

In mathematics, division is a basic arithmetic operation that involves splitting a number or quantity into equal parts or groups. It is the inverse operation of multiplication, where we find out how many times one number (the divisor) can fit into another number (the dividend) without leaving any remainder.

Here,

However, we can calculate her hourly rate by dividing her total earnings by the number of hours she worked.

From the payroll information provided, Jane earned $120.00 for 20 hours of work. Therefore, her hourly rate would be:

Hourly rate = Total earnings / Number of hours worked

Hourly rate = $120.00 / 20 hours

Hourly rate = $6.00 per hour

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Answer:

Step-by-step explanation:

a. 25% of 5000 tickets = 0.25 x 5000 = 1250 tickets

Total sales of $45 tickets = 1250 x $45 = $56,250

b. 15% of 5000 tickets = 0.15 x 5000 = 750 tickets

Total sales of $35 tickets = 750 x $35 = $26,250

c. General admission tickets = Total tickets - Reserved tickets

= 5000 - 1250 - 750

= 3000 tickets

d. Total sales for general admission tickets = Number of general admission tickets x Price per ticket

= 3000 x $20

= $60,000

e. Total sales = Sales of $45 tickets + Sales of $35 tickets + Sales of general admission tickets

= $56,250 + $26,250 + $60,000

= $142,500

The volume and sum of the composite shape is 13L² and 13V³ respectively

A square is a closed two-dimensional shape (2D shape) with four sides that are equal and parallel to each other. Also, In Euclidean Euclidean geometry, a square is a regular quadrilateral which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles

The composite is made up of 13 squares in total

The area of 1 square is given as A = S²

The volume of the composite is 13L³ units

Hence there are 13 squares. the sum of the areas and volume of the square is 13 S²

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The interquartile range for the amounts of money spent by some male students on their holidays is £ 160.

To find the interquartile range (IQR) on a box plot, the IQR is the difference between the upper and lower quartiles. The upper quartile (Q3) is the median of the upper half of the data, and the lower quartile (Q1) is the median of the lower half of the data.

The interquartile range for the amount spent by male students on their holidays is :

= Q3 - Q 1

= 800 - 640

= £ 160

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The values of x and y such that the table represents a function are given as follows:

x = 8, y = 7.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

The input-output pairs for the function in this problem are given as follows:

Hence the x-value can only by 8 or 12, and we choose y = 8, while the y-value is free, hence we choose y = 7.

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Answer:

61,770

Step-by-step explanation:

6.177 x [tex]10^{4}[/tex]

[tex]10^{4}[/tex] = 10,000

6.177 x 10,000 = 61,770

So, the answer is 61,770

On solving the provided question, we can say that Given that you have already waited for 10 minutes, the inequality that you will have to wait another six minutes or longer is around 0.0183.

A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.  

Applying the exponential distribution's memoryless characteristic, we have:

P(Y ≥ 6 | Y > 10) = P(Y ≥ 16)

= 1 - P(Y < 16)

= 1 - F(16) (16)

where F(t) is the exponential distribution's cumulative distribution function (CDF) with a mean of 4 minutes.

F(t) = 1 - e(-t/) yields the CDF of an exponential distribution with mean, where t 0. As a result, we have:

[tex]P(Y \geq 6 | Y > 10) = 1 - F(16) (16)\\= 1 - (1 - e^(-16/4))\\= e^(-4) (-4)\\≈ 0.0183[/tex]

Given that you have already waited for 10 minutes, the likelihood that you will have to wait another six minutes or longer is around 0.0183.

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