100 POINTS

Dave wants to rent a two-bedroom apartment in City Fields. The apartment has a monthly rent of D dollars. The fees he has been quoted are shown below. Write an algebraic expression that represents the amount he is expected to pay before renting the apartment.

Answer:

7.6

Step-by-step explanation:

when trying to find the mean of a data set
you begin by finding the sum of all the numbers.
3+5+15=23. Then because there are only three
numbers in the data set you'll need to divide
23 by 3. 23 / 3 = 7.6.

The coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).

To rotate the points of a triangle 90 degrees clockwise, we can use the following formula for a 2D rotation:

x' = x cos(θ) + y  sin(θ)

y' = -x  sin(θ) + y  cos(θ)

Let's apply this formula to each point of the triangle ABC:

For point A(-6, 3):

x' = -6  cos(90°) + 3  sin(90°) = -6 (0) + 3(1) = 3

y' = -(-6)  sin(90°) + 3  cos(90°) = 6 (1) + 3 (0) = 6

So, point A' is (3, 6).

For point B(-2, 3):

x' = -2 cos(90°) + 3 sin(90°) = -2 .0 + 3. 1 = 3

y' = -(-2) sin(90°) + 3 cos(90°) = 2 .1 + 3 .0 = 2

So, point B' is (3, 2).

For point C(-4, 7):

x' = -4 cos(90°) + 7 sin(90°) = -4 .0 + 7 . 1 = 7

y' = -(-4) sin(90°) + 7 cos(90°) = 4.1 + 7 .0 = 4

So, point C' is (7, 4).

Therefore, the coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).

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Answer:

The roots of this function are at -4 and -1.

f(x) = (2x + 8)(-2x - 2)

= (2x + 8)(-2x + (-2))

The height of the pyramid is 12 units

To find the height of the pyramid, we need to use the formula for the volume of a pyramid,

V = (1/3) * B * h,

where V is the volume, B is the area of the base, and h is the height of the pyramid.

In this case, we know that the volume of the pyramid is 120 units cubed, and the base of the pyramid is a triangle with a base of 10 units and a height of 6 units.

Therefore, the area of the base is,

(1/2) * 10 * 6 = 30 square units.

Plugging these values into the formula for the volume of a pyramid, we get:

120 = (1/3) * 30 * h

Multiplying both sides by 3, we get:

360 = 30 * h

Dividing both sides by 30, we get:

h = 12

Therefore, the height of the pyramid is 12 units.

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The ordered pair of the two sequences are (6, 4), (8, 10), (9, 28)

Given data ,

The first sequence is add 10, then divide by 2 starting from 2

The second sequence is multiply by 3, then subtract 2 starting from 2

On simplifying , we get

Let the first number be 2

So , ( 2 + 10 )/2 = 6

Now , ( 2 x 3 ) - 2 = 4

And , the first ordered pair is ( 6 , 4 )

Now , ( 6 + 10 ) / 2 = 8

And , ( 4 x 3 ) - 2 = 10

So , the second ordered pair is ( 8 , 10 )

Now , ( 8 + 10 ) / 2 = 9

And , ( 10 x 3 ) - 2 = 28

So , the third ordered pair is ( 9 , 28 )

Hence , the sequence is solved and (6, 4), (8, 10), (9, 28)

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The probability of drawing 2 red marbles is 0.081 or 8.1%.

There are 15 red marbles and 32 blue marbles, so there are 15+32=47 marbles total.

The probability of pulling a red marble on the first draw is 15/47.

If the first marble drawn is red, then there are 14 red marbles and 32 blue marbles remaining.

So, the probability of pulling a second red marble is 14/46.

To find the probability of both events happening, we multiply the probabilities:

P(both red) = P(first red) × P(second red | first red)

P(both red) = (15/47) × (14/46)

P(both red) = 0.081 (rounded to 3 decimal places)

Therefore, the probability of drawing 2 red marbles is approximately 0.081 or 8.1%.

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Step-by-step explanation:

the answer is 3

the answer is 3

Answer:

3

Step-by-step explanation:

explanation

f(x) =2x + 1 and g(x) = [tex]x^{2}[/tex]- 7

Thus, we have:

(g/f ) (x) = g(x) / f(x) =  [tex]x^{2}[/tex]-7 ÷ 2x ÷ [tex]x^{2}[/tex] + 1

The measure of length c using the law of cosines is 11.79 units

from the question, we have the following parameters that can be used in our computation:

The triangle (see attachment)

The measure of length c is calculated using the following law of cosines

c² = a² + b² - 2ab * cos(C)

So, we have

c² = 10² + 3² - 2 * 10 * 3 * cos(120)

Evaluate

c² = 139

Take the square root of both sides

This gives

c = 11.79

Hence, the value of c is 11.79

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The inequality x ≤ -5 or x ≥ 3 in interval notations is (-∞, -5] ∪ [3, ∞)

Inequality is the  relationship between two expressions or values that are not equal to each other

The inequality x ≤ -5 or x ≥ 3 represents the solution set of all real numbers less than or equal to -5 or greater than or equal to 3.

The  interval notation of the given inequality is (-∞, -5] ∪ [3, ∞)

The closed brace means the number is included and open bracket doesnot includes a number

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The  recursive formula of g(n)  g(1) = -50 and g(n) = g(n-1) - 15

g(n) = g(n-1) - 15

Start with the given formula: G(n) = -50 - 15n

To find the recursive formula, we need to find the value of g(n) in terms of g(n-1).

To do this, we can subtract 15 from both sides of the equation:

G(n) - 15 = -50 - 15n - 15

Simplifying the equation, we get:

G(n) - 15 = -65 - 15n

Rearranging the equation, we get:

G(n) = -65 - 15n + 15

Now, we can substitute g(n-1) for -65 - 15n:

G(n) = g(n-1) - 15

Finally, we can find the value of g(1) by substituting n = 1 into the original equation:

G(1) = -50 - 15(1)

G(1) = -50 - 15

G(1) = -65

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Complete question is also attached below:/

G(n)=−50−15n  complete the recursive formula of g(n)

g(1)=

g(n)=g(n−1) +=

Answer:

Step-by-step explanation:

f(x) = x + 3

g(x) = 2x + 1

g(g(-3)) = g(-5) = -9

f(g(x) = f(2x + 1) = 2x + 1 + 3 = 2x + 4

g(f(x) = g(x + 3) = 2(x + 3) + 1 = 2x + 7

The length of the arcs are calculated to the nearest hundredth as:

12. 14.03 meters      13. 6.91 meters

The formula used to find the length of a an arc is: length of arc = ∅/360 * 2πr, where ∅ is the central angle measure and r is the radius of the circle.

Length of arc XW:

∅ = m<XZW = 180 - 113

∅ = 67 degrees

r = 24/2 = 12 meters

Plug in the values:

length of arc XW = 67/360 * 2 * π * 12 ≈ 14.03 meters

Length of arc XW:

∅ = m<YVU = 180 - 67 - 80

∅ = 33 degrees

r = 24/2 = 12 meters

Plug in the values:

length of arc YVU = 33/360 * 2 * π * 12 ≈ 6.91 meters

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The trigonometric ratio in terms p are

cos 200 = -p

- sin 70 = -p.

To express each of the given trigonometric values in terms of p:

Since the cosine of 0° is equal to 1, we can say that cos 0° = p.

cos 200°: Using the identity

cos(180° + θ) = -cos(θ), we can rewrite

cos 200° = -cos(180° + 20°).

Since cos 20° = p, we can express cos 200° as -p.

sin(-70°): Using the identity

sin(-θ) = -sin(θ), we can rewrite

sin(-70°) as -sin(70°)

=- sin (90- 20)

=  - cos 20

= -p

sin 10°: Since sin 10° is not related to p, we cannot express sin 10° in terms of p.

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The variable a can take infinite many values (including 0)

From the question, we have the following parameters that can be used in our computation:

-12a < -2a

This expression can be expressed as

-2a > -12a

Divide both sides by -2a

So, we have

1 < 6

The above expression is true

This means that the variable a can take infinite many values (including 0) i.e. 0 is a subset of a

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The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.

To find the 95% confidence interval for the difference in proportions between Michigan and New York commuters who drove alone to work, we can use the formula:

CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

Where:

p1 and p2 are the proportions of Michigan and New York commuters who drove alone to work, respectively.

n1 and n2 are the sample sizes of Michigan and New York commuters, respectively.

Z is the critical value corresponding to the desired confidence level (95% confidence level has Z ≈ 1.96).

Given:

Michigan: p1 = 78/100 = 0.78, n1 = 100

New York: p2 = 58/120 = 0.4833, n2 = 120

Plugging in the values:

CI = (0.78 - 0.4833) ± 1.96 * sqrt((0.78 * (1 - 0.78) / 100) + (0.4833 * (1 - 0.4833) / 120))

CI = 0.2967 ± 1.96 * sqrt(0.006456 + 0.004074)

CI = 0.2967 ± 1.96 * sqrt(0.01053)

CI ≈ 0.2967 ± 1.96 * 0.1026

CI ≈ 0.2967 ± 0.201

The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.

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Answer:

904.78 [tex]in^{3}[/tex]

Step-by-step explanation:

The volume formula for a sphere is the following:
[tex]v=\frac{4}{3} \pi r^{3}[/tex]
[tex]d = 2r[/tex]
Replace with values and the answer is 904.78

The  approximate area and circumference of the circle is given as 201 inch² and 20 inch respectively

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant

The area and perimeter of a circle can be calculated using the formula

πr = πd, where r is the radius and d is the diameter of the circle

Area = πr² and

the perimeter is 2πr

r= 8 inch, π = 3.14

Area = 3.14 * 8 * 8

Area = 200.96 square inches

Area = 201 inch²

the perimeter is = 2*3.14*8

The perimeter is = 50.24 square inches

Perimeter = 50 inch

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The area and circumference of the circle with a radius of 8 inches are 200.96 square inches and 50.24 inches respectively.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

The circumference of a circle is expressed as:

C = 2πr

Where r is radius and π is constant pi ( π = 3.14 )

Given that the radius of the circle is 8 inches.

Substituting this value into the formula, we get:

A = πr²

A =  3.14 × ( 8 in )²

A =  3.14 × 64 in²

A = 200.96 in²

Next, we calculate the circumference:

C = 2πr

C = 2 × 3.14 × 8 in

C = 50.24 in

Therefore, the value of the circumference is 50.24 in.

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sec(theta) = 1/cos(theta)

I believe that is your option D

A kilogram of strawberry taffy costs $4, and a kilogram of banana taffy costs $7.

Let us assume

the price of 1 kg strawberry taffy  = $x

And the price of 1kg banana taffy = $y

Then according to given information

the expression for Jon be,

4x + y = 23  ....(i)

the expression for Charlotte be,

5x + 2y = 34 ...(ii)

Now use elimination method

2x(i) - (ii) we get,

3x = 12

 x = 4

Plug it into (i) we get

y = 7

Hence, costs are:

1 kg strawberry taffy  = $4

1kg banana taffy = $7

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The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units

From the graph, the vertices of the land are

A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)

Calculate the distance between adjacent vertices

So, we have

AB = √[(0 - 25)² + (20 - 19)²] = 25.02

BC = √[(20 - 25)² + (2 - 19)²] = 17.72

DC = √[(20 - 5)² + (2 - 0)²] = 15.13

AD = √[(0 - 5)² + (20 - 0)²] = 20.62

The perimeter of the plot land is

P = 25.02 + 17.72 + 15.13 + 20.62

P = 78.49 units

This is calculated as

Area = Plot land - Building - Parking lot

Using the vertices, we have

Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]

This gives

Area = 295 -  45 - 40

So, we have

Area = 210

Hence, the area is 210 square units

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Answer:

The length of the hypotenuse is 100.

Step-by-step explanation:

To find the length of the hypotenuse, we use the following formula:

c=[tex]\sqrt{a^2+b^2}[/tex]

c=[tex]\sqrt{28^2+96^2}[/tex]

c=[tex]\sqrt{10,000}[/tex]

c=100

Therefore, the length of the hypotenuse is 100.

Answer:

10%

Step-by-step explanation:

P(reading paper 'given' that they are <40)

= P(reading paper AND < 40) / P(< 40)

= (4/80) / (40/80)

= 4/40

=1/10

=0.1

=10%

1) Equation for the parabola y = - x² + 36.

2) A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function.

The points of intersection will be: (0,36) and (4, 20)

Table of values for a linear function and the parabola

x        linear function      parabola y = - x² + 36

0        36                                  (0)² + 36 = 36

1        32                                  - (1)² + 36 = 35

2        28                                  - (2)² + 36 = 32

3        24                                   -3² + 36 = 27

4        20                                   -4² + 36 = 20

It is a linear function because the rate of change is constant: for each increase of 1 unit in x, there is a decrease of 4 units in y: ⇒ slope = - 4

Remember to include the two points of intersection in your table. Analyze the two functions; they are there (0,36) and (4, 20)

Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow?

Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.

The domain is all the real values of x between - 6 and 6: - 6 ≤ x ≤ 6

The range is all the values between 0 and 36: 0 ≤ y ≤ 36

The domain represents the horizontal distance between the extremes of the rainbow at the ground.

The range represents: the altitude of the rainbow from the ground (y = 0). The height is at x = 0, y = 36.

The x-intercepts are - 6 and 6, that is the opening of the rainbow at the ground level.

The y-intercept is when x = 0, it is y = 36, and is the height of the rainbow.

Is the linear function you created positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.

The linear function is positive and decreasing. It is positive because it goes above the x-axis, this is y ≥ 0.

The solutions were already signaled: (0,6) and (4, 20). They are the points at which the drone intercepts the rainbow.

The conclusion can be determined from the dot plot is

The median of the data set is 10.

1. The number of observations is 10:

There are total 15 observations.

2. The median of the data set is 10.

From the dot plot the data is

9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12

Thus, the median is 10.

3. Mean = Sum of observation / Total Number of observation

Mean = (9+9+9+9+9+10+10+10+10+10+10+11+11+11+12) /15

Mean= 150/15=10

Thus, the Mean is 10.

4. Range = 12 - 9

Range = 3.

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To find out how many hours they zip lined for, we need to subtract the cost of the gear and trainer from the total bill and then divide the remaining amount by the hourly rate.

Cost of gear per person:

Shoes: $10

Helmet: $3

Gloves: $2.50

Harness: $5.00

Total gear cost per person: $10 + $3 + $2.50 + $5.00 = $20.50

Total cost of gear for 3 people: $20.50 x 3 = $61.50

Cost of trainer: $15.00

Total bill (including gear and trainer): $70.25

Remaining amount for zip lining:

=  $70.25 - $61.50 - $15.00

= $-6.25

Since the remaining amount is negative, it seems there might be an error in the calculation or information provided. The total bill should not be lower than the cost of gear and trainer.

However, if we assume the total bill is correct and there was an error in the calculation, we can proceed with finding out how many hours they zip lined for and how much each person paid.

Approximate number of hours:

Number of hours = Remaining amount / Hourly rate = $6.25 / $4.75 ≈ 1.32 hours

Approximate amount each person paid:

Amount each person paid

= Total bill / 3

= $70.25 / 3

≈ $23.42

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Answer:m-5n

Step-by-step explanation:

Answer:

y = 5(x - 3)^2 - 4 + c

Step-by-step explanation:

The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. To shift the graph three units to the right and four units down, we can modify the constant term c and the linear term bx:

y = a(x - 3)^2 - 4 + c

To make it five times narrower, we can modify the coefficient of the squared term a:

y = (1/5)a(x - 3)^2 - 4 + c

Since we want the shape to be the same as y = x^2, we can set a = 5:

y = 5(x - 3)^2 - 4 + c

The value of c will depend on the specific context of the problem or graph.

Answer:

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

Let the number be n.

Set up an equation per the problem:

Distribute and solve for n:

The number is 10.

The word problem that exemplifies a linear function is

- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.

Option A is the correct answer.

We have,

A linear function is a mathematical model that represents a relationship between two variables that is a straight line.

In this problem,

The cost of Angie's swimming classes is a linear function of the number of months.

The enrollment fee of $50 is a fixed cost that does not depend on the number of months, and the safeguard insurance cost of $10 per month is a variable cost that increases linearly with the number of months.

Thus,

The word problem that exemplifies a linear function is

- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.

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