The graph of f ( x ) = − 1 /2 ( 1 /2 ) ^x − 3 + 5 is shifted downwards 5 units, and then shifted left 3 units, stretched vertically by a factor of 4 , and then reflected about the x -axis. a . What is the equation of the new function, g ( x ) ? g ( x ) = b . What is the y -intercept? ( , ) c . What is the domain? d . What is the range?

Answer:

To find the 9th term of a geometric sequence, we can use the formula:

an = a1 * r^(n-1)

where:

an = the nth term of the sequence

a1 = the first term of the sequence

r = the common ratio of the sequence

n = the term number we want to find

In this case, we are given that the common ratio is 2/3, the first term is 6, and we want to find the 9th term. So we can plug in those values and get:

a9 = 6 * (2/3)^(9-1)

Simplifying the exponent, we get:

a9 = 6 * (2/3)^8

Using a calculator, we can evaluate the exponent:

a9 = 6 * 0.015625

Multiplying, we get:

a9 = 0.09375

Therefore, the 9th term of the geometric sequence is 0.09375.

Step-by-step explanation:

here's a step-by-step explanation:

We are given the first term of the geometric sequence, a1 = 6, and the common ratio, r = 2/3. We need to find the 9th term, which we can do using the formula:

an = a1 * r^(n-1)

where n is the term number we want to find.

Step 1: Substitute the given values into the formula

a9 = 6 * (2/3)^(9-1)

Step 2: Simplify the exponent

a9 = 6 * (2/3)^8

The exponent 9-1 simplifies to 8.

Step 3: Evaluate the exponent

a9 = 6 * 0.015625

We can use a calculator to evaluate (2/3)^8, which is 0.015625.

Step 4: Multiply to find the 9th term

a9 = 0.09375

Multiplying 6 by 0.015625 gives us the 9th term of the geometric sequence, which is 0.09375.

Therefore, the 9th term of the geometric sequence whose common ratio is 2/3 and whose first term is 6 is 0.09375.

The data modelling function is Price required to recoup printing expenses is equal to 0.1 * (numbers of yearbooks sold) + 45.

A yearbook is a collection of images and text that is issued by an organisation once a year to remember and highlight the happenings at a particular school during the previous academic year. Yearbooks were used in elementary, middle, high, and college and university settings throughout the 20th century.

Using the information in the table,

[tex]n = 5[/tex]

Σ[tex]x = 1175[/tex]

Σ[tex]y = 145[/tex]

Σ[tex](xy) = 41000[/tex]

Σ[tex](x^2) = 287500[/tex]

When these values are inserted into the formula,

[tex]m = (541000 - 1175145) / (5*287500 - 1175^2)[/tex]

[tex]= -0.1[/tex]

Therefore, the slope of the linear function is [tex]-0.1[/tex].

[tex]b = y - mx[/tex]

where we can use any of the data points. Let's use[tex](250, 20)[/tex]

[tex]b = 20 - (-0.1*250)[/tex]

[tex]= 45[/tex]

Therefore, the y-intercept of the linear function is [tex]45[/tex].

[tex]y = -0.1x + 45[/tex]

Therefore,

Price needed to cover the costs of printing [tex]= -0.1*[/tex](number of yearbooks sold) [tex]+ 45[/tex].

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A) the annual rate of change between 1991 and 2000 is -$3,000.

B)  the correct answer to part A in percentage form is -6.67%.
C) where n is the number of years from 2000 to 2003, which is 3, $8,450. approximately.

A) The total change in value between 1991 and 2000 is $45,000 - $12,000 = $33,000. The number of years between 1991 and 2000 is 9. Therefore, the annual rate of change is:

r = (final value - initial value) / (number of years)

r = ($12,000 - $45,000) / 9

r = -$3,000 per year

Thus, the annual rate of change between 1991 and 2000 is -$3,000.

B) To convert the rate of change to percentage form, we need to divide it by the initial value and multiply by 100:

r = (-$3,000 / $45,000) * 100%

r = -6.67%

Therefore, the correct answer to part A in percentage form is -6.67%.

C) If the value continues to drop by the same percentage, we can use the following formula to find the value in 2003:

value = initial value * (1 + r)^n

where n is the number of years from 2000 to 2003, which is 3. Plugging in the values, we get:

value = $12,000 * (1 - 0.0667)^3

value = $8,454.58

Rounding to the nearest $50, we get the value in 2003 to be $8,450.

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Answer:

x = 45

Step-by-step explanation:

since the lines are congruent, then the opposite angles will be the same.

2x+90=180

Hope this helps

The volume of the Cylinder formed  approximately 16.37 cubic units.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two parallel circular bases, connected by a curved lateral surface. It is similar to a prism, but instead of having polygons as its bases, it has circles. The lateral surface of a cylinder is formed by the set of all straight lines connecting the points on the edge of one base to the corresponding points on the edge of the other base.

Now,

To find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x⁸about the y-axis, we can use the method of cylindrical shells.

First, we need to express the equation y=5+x⁸ in terms of x, so we can integrate with respect to x:

y = 5 + x⁸

y - 5 = x⁸

x = (y - 5)¹/⁸

Next, we need to determine the limits of integration. The region is bounded by x=0 and x=1, so we integrate from x=0 to x=1.

Volume of a cylindrical shell is

V = 2πrhΔx

In this case, the radius r is simply x, the height h is y, and Δx is dx. So, we have:

V = 2πxy dx

V = 2πx(5+x^8) dx

V = 10πx dx + 2πx⁸ dx

Integrating with respect to x from x=0 to x=1, we get:

V = [5π + 2π/10] - [0 + 0]

V = 5.2π

Therefore, the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x⁸ about the y-axis is approximately 16.37 cubic units.

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hii

what's the best way to recreate the incident as it happened and to picture

Answer:

1.49 minutes

Step-by-step explanation:

Let the number of minutes be x.

Deandre paid $17.43 for $7 to start  and 7 cents per minute.

Mathematically,

7x+7=17.43

7x= 17.43-7

7x = 10.43

∴ x = 10.43/7

x = 1.49 minutes.

Hope this helps! :)

The measure of the angles is 143°

From the given diagram, the given measures are alternate exterior angles and they are equal.

Given the following parameters

∠A =7x + 24

∠B = 3x + 92

Equate

7x + 24 = 3x + 92

7x - 3x = 92 - 24

4x = 68

x = 17

Determine the measure of the angles

∠A = ∠B = 7x + 24

∠A = ∠B = 7(17) + 24

∠A = ∠B = 143 degrees

Hence the measure of the angles is 143°

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Answer: true

Step-by-step explanation:

6:8 = 12:16

12:16 less than 14:16

Answer: The answer is B!

Step-by-step explanation:

If you multiply 22.2 by 8.3, you get 84.36 (if you move the decimal point one space, otherwise you'd get 843.6.) Then if you estimate it, you would get 84.58.

Answer: 87

Step-by-step explanation:

(74+85+x)/3  = 82

3(82)=74+85+x

246 = 74+85 + x

246-74-85=x

x= 87

Answer: is mature enough to vote

Step-by-step explanation: the second drop box is asking about the opposing claim, which is the one that the professor gives.

Answer:

the last option, " is mature enough to vote".

Step-by-step explanation:

Professor Steinberg believes that 16 old can vote as their brains are mature enough to make informed decisions like voting.

The quotient gives (f/g)(4) = -16/3 and the value that is not in the domain is x = 1.

Here we know that:

f(x) = (x + 4)(x - 6)

g(x) = x - 1

And we want to find the quotient between these functions:

(f/g)(4)

So first let's find the values of the functions when x = 4.

f(4) = (4 + 4)*(4 - 6) = 8*-2 = -16

g(4) = 4 - 1 = 3

Then the quotient is:

(f/g)(4) = -16/3

Now, the values that are not in the domain of f/g are the values that make the denominator equal to zero, because we can't divide by zero.

g(x) = 0 = x - 1

         1  =x

The denominator is zero for x = 1, so that value is not in the domain.

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The translation of f(x) to g(x) is described by - translation of 4 units up.

As you translate a figure, you slide it left, right, up, or down. This implies that the coordinates for such vertices of the figure will alter on the coordinate plane.

Apply the identical modification to every point in order to graph a translation.

As there is the shift of coordinates on y axis upward by 4 units units.

Thus, the translation of f(x) to g(x) is described by - translation of 4 units upward.

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Answer:

Step-by-step explanation:

To determine the mean number of water tanks supplied to the construction site in March 2022 during weekdays, we need to add up the number of tanks supplied during weekdays and divide by the number of weekdays in March 2022:

March 2022 had 23 weekdays.

From the information given, we don't know the number of tanks supplied during weekdays in March 2022. Therefore, we cannot calculate the mean number of tanks supplied during weekdays in March 2022.

The numerical data recorded on the calendar in ANNEXURE A by the contractor was the number of water tankers supplied to the construction site on each day of the month.

To determine the modal number of water tankers that were supplied to the construction site in June 2022, we need to find the number that appears most frequently in the data:

From the information given, we don't have the data on the number of water tankers supplied to the construction site in June 2022. Therefore, we cannot determine the modal number of water tankers supplied in June 2022.

Given that the water tanker has a fuel capacity of 460 litres and the rate of fuel consumption of the Mercedes water tanker averages 5 km/l, we can calculate the distance traveled on a full tank of fuel:

The distance traveled on a full tank of fuel is 460 litres x 5 km/l = 2,300 km.

Finally, we are given the prices of fuel per litre in March and June 2022:

In March 2022, the price of diesel 50 ppm was R19.55 per litre.

In June 2022, the price of diesel 50 ppm was R24.14 per litre.

Answer:

Hmm.. not quite sure why you multiplied A with 10 yds. I am going to assume M=meters.

A.) You can convert to whatever units you like, but I am going to convert into meters.

0.89/yd * 0.9144yd/m = $0.97 > $0.94.. So.. A Lumber yard is selling the same rope for less expensive.

B.) You convert feet until you get to the correct units. like this....

550 ft * 1yd/3ft * .9144m/yd * $.97/m = $162.62

550 ft * 1yd/3ft * .9144m/yd * $.94/m = $157.58

taking the difference would be $5.03.

I believe for answer A, you forgot to convert...or converted differently. Hope this helps.

Step-by-step explanation:

Answer:

Since $0.973/m is greater than $0.94/m, the lumber yard sells the rope for a lower price

So Jim would save $6.19 if he purchased 650 ft of the less expensive rope before taxes.

Step-by-step explanation:

Answer:

Step-by-step explanation:1.) Each person receives 5/6 of a cake.

To see why, we can think of dividing the 5 cakes into 6 equal parts. This would give us 30 equal parts, and each person would receive 5 of these parts. So, the fraction of a cake each person receives is:

5/30 = 1/6

2.) Each person receives 3/8 of a pizza.

To see why, we can think of dividing the 3 pizzas into 8 equal parts. This would give us 24 equal parts, and each person would receive 3 of these parts. So, the fraction of a pizza each person receives is:

3/24 = 1/8

3.) Each person receives 1/2 of a granola bar.

To see why, we can think of dividing the 4 granola bars into 8 equal parts. This would give us 32 equal parts, and each person would receive 4 of these parts. So, the fraction of a granola bar each person receives is:

4/32 = 1/8

1/8 ÷ 2 = 1/16

So, each person receives 1/2 of a granola bar, which is equal to 1/8 ÷ 2 = 1/16.

4.) Each pie has 2.4 pounds of blueberries.

To see why, we can divide the 12 pounds of blueberries by the 5 pies:

12 ÷ 5 = 2.4

So, each pie has 2.4 pounds of blueberries.

5.)

4 ÷ 5 = 4/5

5 ÷ 4 = 1 1/4

12 ÷ 30 = 2/5

30 ÷ 12 = 2 1/2

Answer: 1) 5/6

              2) 3/8

              3) 4/8 OR 1/2

              4) 12/5lb OR 2 2/5lb OR 2.4lb

              5) 4/5

                  5/4 OR 1 1/4

                  12/30 OR 2/5

                  30/12 OR 5/2 OR 2 1/2

Step-by-step explanation:

The average number of siblings for the group is 1.3.

We must compute the total number of siblings and divide it by the total number of children in the group to determine the average number of siblings for the group.

There are a total of: siblings in the bunch.

3 + 8 + 9 = 20 (1 sibling times 3 children) + (2 siblings times 4 children) + (3 siblings times 3 children)

The total number of kids in the group is: 5 + 3 + 4 + 3 = 15

As a result, the group as a whole has an average of:

20/15 = 1.33 (rounded to the nearest tenth) (rounded to the nearest tenth)

So, the group as a whole has 1.3 siblings on average.

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Answer:

$839.95

Step-by-step explanation:

To get the amount of tax Ella would have to pay for, multiply the price of the computer by the tax rate

785 x .07 = 54.95

Then add the computer price and tax to get how much she paid for in total

785 +54.95= $839.95

Answer:

1065.09 square meters

Step-by-step explanation:

The inner circle has a diameter of 21.4 cm

Its radius is half that = 21.4/2 = 10.7 m

Area of the inner circle = π (10.7)² = 114.49π  m²

The outer circle has a radius
= radius of inner circle + 10.6
= 10.7 + 10.6

= 21.3 m

Therefore the area of the outer circle
= π(21.3)² = 453.6π m²

Area of shaded region
= Area of outer circle - Area of inner circle

= 453.6π - 114.49π  
= 339.2 π

Taking π = 3.14

Area of shaded region
= 339.2  x 3.14
= 1,065.088 m²
= 1065.09 m² (rounded to nearest hundredth)

The equation for the relationship between the total fee and vertical distance is: y = 100 + x/3000.

Vertical distance is the measurement of the straight line distance between two points in a vertical plane. It is the difference between the higher and lower altitudes of two points and is measured in a straight line from the highest point to the lowest point.

This equation can be explained as follows. The total fee for a trip to climb Mount Kilimanjaro is split into two parts. The first part is the initial fee of $100, which is a fixed cost independent of the distance climbed. The second part is the cost per vertical meter, which is calculated by dividing the vertical distance climbed (x) by 3000 (the constant fee for each vertical meter climbed) and then multiplying the result by the constant fee. Therefore, the equation for the relationship between the total fee and vertical distance is y = 100 + x/3000.

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Answer: To find the height of the ramp, we need to use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ramp, porch, and ground form a right triangle, with the height of the ramp being the missing side.

We know that the ramp begins 96 centimeters from the porch and is 100 centimeters long. Let's represent the height of the ramp with the variable "h". Then, we can write the Pythagorean theorem equation:

h^2 + 96^2 = 100^2

Simplifying this equation, we get:

h^2 + 9216 = 10000

Subtracting 9216 from both sides, we get:

h^2 = 784

Taking the square root of both sides, we get:

h = 28

Therefore, the height of the ramp is 28 centimeters.

Step-by-step explanation:

Step-by-step explanation:

The parent square root function is given by f(x) = √x. The function g(x) is obtained by applying the following transformations to the parent function:

Shift the graph 3 units to the left: f(x+3)

Shift the graph 4 units down: f(x+3)-4

Add a constant 3: f(x+3)-4+3 = f(x+3)-1

Take the square root: g(x) = √(f(x+3)-1) = √(√(x+3)-1)

Therefore, the graph of f is translated 3 units to the left and 1 unit down to obtain the graph of g. None of the given options accurately describe the transformation, so the correct answer is option E: None of the above.

[tex]4x^2+20x-24 = 4x^2-4x+24x-24 = 4x(x-1)+24(x-1) = (4x + 24)(x-1)\\[/tex]

[tex]= 4(x+6)(x-1)[/tex]

When 1. 384 is divided by 0. 4, the quotient would be 3. 46.

One way to divide 1. 384 by 0. 4 is to use the fact that division is the same as multiplying by the reciprocal of the divisor. The reciprocal of 0. 4 is 1 / 0. 4 or 2. 5. Therefore, we can rewrite the division as:

1. 384 / 0. 4 = 1. 384 x 2.5

We can then use multiplication to get the result:

1. 384 × 2. 5 = 3. 46

Therefore, 1. 384 divided by 0. 4 equals 3. 46.

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Through the given statement we can say that the vertical distance travelled by the ball  is 84 m.

One limitation of this model is that it assumes that the ball rebounds to the same percentage of its previous maximum height after every bounce.

The formula for vertical distance from the earth is y = - 1 2 g t 2 y = - frac 1 2 g t 2 y=-21gt2, where g is the acceleration of gravity and h is an elevation.

So :

C) the required total vertical distance that the given dropped ball travels until its bouncing stops:

= (12 m) + 2*(12 m)*(3/4)*[1 + 3/4 + (3/4)^2 + (3/4)^∞] [the factor 2 is for equal distance being covered up and down after each bounce of the ball]

= (12 m) + (24 m)*(3/4)*

(sum of an infinite GP series whose 1st term is 1 and common ratio is 3/4)

= (12 m) + (24 m)*(3/4)*[1/(1 - 3/4)]

= (12 m) + (24 m)*(3/4)*4

= (12 m) + (72m) = 84 m

D) This model's assumption that the ball will always bounce back to a certain proportion of its maximum height is one of its limitations. In fact, the rebound height can differ from one bounce to the next due to factors like air resistance, the ball's elasticity, and the surface it bounces on.

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Answer:

Step-by-step explanation:

The equation would be

f(x) = (x - 1)^2 + 1

The mean of the data-set represented by the frequency table is given as follows:

d) 13.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

We have a frequency distribution, hence each observation is considered to be the midpoint of each interval, and thus the sum of the observations is given as follows:

5 x 4 + 10 x 7 + 15 x 9 + 20 x 5 = 325.

The number of observations is given as follows:

4 + 7 + 9 + 5 = 25.

Hence the mean is given as follows:

325/25 = 13.

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Answer:

[tex]y=-\frac{2}{3}x+2[/tex]

Step-by-step explanation:

The formula for equation of a line is [tex]y=mx+b[/tex] where m is the slope, b is the y-intercept, and (x,y) can represent any point on the line. We calculate the slope using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. We are subtracting the y-coordinates in the numerator and the x-coordinates in the denominator.

[tex]\frac{0-2}{3-0} = -\frac{2}{3}[/tex]

You can subtract the coordinates of your second point from your first point and you will get the same slope. Just be sure not to mix up the order.

Now that we have our slope, we can either pull the y-intercept off the graph; the line crosses the y-axis as y = 2, or we can solve our equation for the value of b.

We can pick any point on the line to solve for b. It is recommended to use one of the intercepts because either the x or y component will be zeroed out. I will use the point (0,2)

[tex]y = mx + b\\y = -\frac{2}{3}x +b\\2 = (-\frac{2}{3})(0) + b\\b = 2[/tex]

Now we have all the parts of our equation in slope-intercept form.

[tex]y = -\frac{2}{3}x +2[/tex]