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A lemonade recipe calls for 1/4 cup of lemon juice for every cup of water. Use the table to answer these questions.

a. What does x represent?

b. What does y represent?

c. Is there a proportional relationship between x and y?

:)

The approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.

We can approximate the area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 using a Riemann sum with 4 rectangles of equal width. The left-hand endpoint of each subinterval will be used.

The width of each rectangle is the length of the interval (5-(-1)) divided by the number of rectangles (4). Therefore, the width of each rectangle is

(5-(-1))/4 = 6/4 = 1.5.

Since we are using the left-hand endpoint of each subinterval, the x-values of the left-hand endpoints of the rectangles are

-1, -1+1.5

-1+1.5+1.5

-1+1.5+1.5+1.5 = -1+4.5=3.5

The height of each rectangle is determined by the value of y at the corresponding x-value.

Therefore, the heights of the rectangles are

3(-1)^2+1=2

3(-1+1.5)^2+1=7.125

3(3.5)^2+1=35.125

3(3.5+1.5)^2+1=46.875

The area of each rectangle is the product of its width and height, so the areas of the rectangles are

2*1.5=3

7.125*1.5=10.6875

35.125*1.5=52.6875

46.875*1.5=70.3125.

Therefore, the approximate area between y=3x^(2)+1 and the x-axis on the interval -1 to 5 is 136.6875.

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Answer: Relation

Step-by-step explanation:

The graph fails the vertical line test.

The point that lies on the circle is represented by the equation (x−3)² + (y+4)² = 6² is (-3,-4).

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h, k) coordinate. Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x-h)² + (y-k)² = r²

The sole point that lies on the circle when a circle is graphed with the equation on the graph and all the specified points are graphed is (-3,-4).

Consequently, the equation (x-3)² + (y+4)² = 6² represents the point on the circle (-3,-4).

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Toby cycles 12 miles each day.

To find out how far Toby cycles each day, we need to add up the distance he covers during his morning and afternoon trips. Here are the steps we need to follow:

Step 1: Determine Toby's cycling distance from his house to his schoolDistance from Toby's house to his school = 4 miles west. Toby bicycles this distance every day. Therefore, his one-way cycling distance from home to school is 4 miles.

Step 2: Determine Toby's cycling distance from his school to Erica's house.Distance from Toby's school to Erica's house = 3 miles south. Toby cycles this distance every day after school. Therefore, his one-way cycling distance from school to Erica's house is 3 miles.

Step 3: Determine Toby's cycling distance from Erica's house to his house.Distance from Erica's house to Toby's house = we don't know. But we know that Toby takes a bike path that goes straight from Erica's house to his own house. Therefore, we can assume that the distance from Erica's house to Toby's house is the hypotenuse of a right-angled triangle with legs of 3 miles (south) and 4 miles (west).

We can use the Pythagorean Theorem to find the hypotenuse: c2 = a2 + b2c2 = 32 + 42c2 = 9 + 16c2 = 25c = √25c = 5 milesTherefore, Toby cycles 5 miles every day on his bike path from Erica's house to his own house.Step 4: Add up Toby's one-way cycling distances to find out how far he cycles each day.Toby's one-way cycling distance from home to school = 4 milesToby's one-way cycling distance from school to Erica's house = 3 milesToby's one-way cycling distance from Erica's house to his house = 5 milesTotal cycling distance = 4 + 3 + 5Total cycling distance = 12 miles.

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List of perfect squares smaller than 10 are: {1, 4, 9}

Subtract 1 from each value to get a new list of {0, 3, 8}

None of these new values are a factor of 12.

The possible answers are: 0, 3, and 8

Jonathan attempted a total of 960 free throws in the season.

To find the total number of free throws Jonathan attempted, we need to determine the percentage of free throws he made.

Since he misses 5% of the free throws, it means he makes 95% of them.

Let's set up the proportion:

Missed free throws / Total free throws = Percentage missed / 100%

48 / Total free throws = 5 / 100

48 x 100 = Total free throws x 5

4800 = 5 x Total free throws

Total free throws = 4800 / 5

Total free throws = 960

Therefore, Jonathan attempted a total of 960 free throws in the season.

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Answer:

(x + 7)/(x + 1)

Step-by-step explanation:

Simplify the following:

(x^2 + 11 x + 28)/(x^2 + 5 x + 4)

The factors of 4 that sum to 5 are 4 and 1. So, x^2 + 5 x + 4 = (x + 4) (x + 1):

(x^2 + 11 x + 28)/((x + 1) (x + 4))

The factors of 28 that sum to 11 are 7 and 4. So, x^2 + 11 x + 28 = (x + 7) (x + 4):

((x + 4) (x + 7))/((x + 4) (x + 1))

((x + 7) (x + 4))/((x + 4) (x + 1)) = (x + 4)/(x + 4)×(x + 7)/(x + 1) = (x + 7)/(x + 1):

Answer: (x + 7)/(x + 1)

Next time write the expression how it needs to be, the way you wrote it woould have given a toally different result.

x^2 + 11 x + 28/x^2 + 5 x + 4

Answer:

solving this as you would in algebra 2:

x2+11x+28 / x2+5x+4 = x+7 / x+1

Step-by-step explanation:

solving this as you would in algebra 2:

x2+11x+28 / x2+5x+4

1. on both the top and the bottom you have to find a factor of the last number (in this case 28 and 4) that multiplys to be the number but adds to be the 2nd term (11x and 5x)

2. for the top the two terms would be (x+7) and (x+4). on thebottom half it would be (x+4) and (x+1)

** 7 times 4 equals 28, 7 plus 4 equals 11; 4 times 1 equals 4, 4 plus 1 equals

3. x+4 is common term on both the top side and the bottom half so you cross it out. this leaves us with our answer of: x+7 over x+1

hope this helps:)

The value of the integral is\((1/2) e^4 - 5/2\)

To interchange the order of integration, we need to rewrite the integral as a double integral with the integrand as a function of y first and then x.

The limits of integration for x are from 0 to 2, while the limits for y are from 0 to 1.

So, we can write the integral as:

∫[0,1] ∫[0,2] (x 4ey − 5) dx dy

To integrate with respect to x, we treat y as a constant and integrate x from 0 to 2. This gives:

∫[0,1] [(\(x^{2/2\)) 4ey − 5x] dx dy

Now we integrate with respect to y, treating the remaining function as a constant. This gives:

∫[0,1] [(2\(e^{4y\) − 10) - (0 − 5)] dy

Simplifying the expression, we have:

∫[0,1] (2\(e^{4y\) − 5) dy

Integrating this gives:

[ (1/2) \(e^{4y\)- 5y ] from 0 to 1

Substituting the limits of integration, we get:

[ (1/2)\(e^4\) - 5 ] - [ (1/2) - 0 ]

which simplifies to:

(1/2) \(e^4\)- 5/2

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To calculate the integral by interchanging the order of integration, we need to first write the integral in the order of dy dx.

∫ from 0 to 2 ∫ from 1 to 0 (x 4ey − 5) dy dx

Now, we can integrate with respect to y first.

∫ from 0 to 2 ∫ from 1 to 0 (x 4ey − 5) dy dx
= ∫ from 0 to 2 [(xe4y/4 - 5y) evaluated from 1 to 0] dx
= ∫ from 0 to 2 (x - 5) dx
= [(x^2/2 - 5x) evaluated from 0 to 2]
= -6

Therefore, the value of the integral by interchanging the order of integration is -6.
So the integral of the given function after interchanging the order of integration is:

16e - 10 - 16/3.

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The function represented by the table is: \(Y = (1/2)^X\).This is an example of an exponential function.

An algebraic function is a function created by applying the operation of addition, subtraction, multiplication, division, and extracting the nth root

To determine the type of function represented by the table, we can look at the pattern of the values of X and Y.

As we can see from the table, as X increases by 1, Y is divided by 2. This means that the relationship between X and Y is not linear but rather exponential. Specifically, the function is of the form Y = \(a(1/2)^X,\) where a is a constant.

To find the value of a, we can use one of the points in the table. Let's use the first point, (-4, 16):

16 = \(a(1/2)^(-4)\)

Multiplying both sides by\((1/2)^(-4)\):

\(16 * (1/2)^4\) = a

a = 16 * (1/16) = 1

Therefore, the function represented by the table is:

\(Y = (1/2)^X\)

This is an example of an exponential function.

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Answer:$154

Step-by-step explanation:i did 6 times 9 and added that to 100

Direct variation is represented by this situation and she earn $900

if she works 12 hours.

Direct variation describes a relationship whereby one measure directly affects the other when the first one changes. This is completely opposed by inverse variation. Learn the definitions of direct and inverse variations in this article, along with some instances that have been solved.

When x is not equal to 0, y = kx is the equation that describes the linear function known as direct variation. An equation of the form xy = k, where x is not equal to zero and k is a nonzero real number constant, describes the nonlinear function known as inverse variation.

5 hours  = earns $ 375

1 hours = 375/5 = earns $ 75

12 hours  = 75  12 = earns $ 900

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The correct option is d. 4071.50\ cm^3

The volume of the solid, if the ellipse is revolved around its major axis is given by the formula:

V = \frac {4}{3}\pi r^2 R,

where

r is the minor axis, and

R is the major axis.

Given that

r=18/2=9cm, and

R=24/2=12 cm.

The volume of the solid is:

V = \frac {4}{3}\pi \cdot (9\ cm)^2 \cdot (12\ cm)

V = 4\pi \cdot (81\ cm^2) \cdot (4\ cm)

V = 1296\pi\ cm^3

Now,

we substitute π\approx 3.1416 and round off the answer to the nearest hundredth.

We get:

V\approx 4071.50\ cm^3

Therefore, the correct option is d. 4071.50\ cm^3

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The maximum number of different four-digit numbers that Mary can enter is 4096 using Permutation and Combination.

A permutation is an arrangement of objects in a specific order. A combination is a selection of objects without regard to their order.

The number of combinations of a set with n elements is given by the formula:

C(n,r) = n! / (r! (n-r)!)

The maximum number of different four-digit numbers that Mary can enter is 4096, which is the number of codes that can be formed by changing exactly one digit in a four-digit number. Since Mary is required to get exactly one digit wrong each time and not to enter the same four-digit number as she did last time, the security guard will not be able to determine the secret code no matter how many different four-digit numbers Mary enters, as long as Mary does not enter the same code twice. Therefore, the maximum number of different four-digit numbers that Mary can enter without the security guard being able to be certain of the secret code is 4096.

Hence, The maximum number of different four-digit numbers that Mary can enter is 4096.

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The following data shows the daily production of cell phones. 7, 10, 12, 15, 18, 19, 20. Mean The formula for finding the mean is: mean = (sum of observations) / (number of observations).

Therefore, the mean for the daily production of cell phones is: Mean = (7+10+12+15+18+19+20) / 7

= 101 / 7

Mean = 14.43

Variance The formula for finding the variance is: Variance = (sum of the squares of the deviations) / (number of observations - 1) Where the deviation of each observation from the mean is: deviation = observation - mean First, calculate the deviation for each observation:7 - 14.43

= -7.4310 - 14.43

= -4.4312 - 14.43

= -2.4315 - 14.43

= 0.5718 - 14.43

= 3.5719 - 14.43

= 4.5720 - 14.43

= 5.57

Now, square each of these deviations: 56.25, 19.62, 5.91, 0.33, 12.75, 20.9, 30.96 The sum of these squares of deviations is: 56.25 + 19.62 + 5.91 + 0.33 + 12.75 + 20.9 + 30.96

= 147.72

Therefore, the variance for the daily production of cell phones is: Variance = 147.72 / (7-1) = 24.62 Standard deviation ) Mean = 14.43b) Variance per Day = 24.62c) Standard Deviation = 4.96

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Answer:

$40

Step-by-step explanation:

As per linear equation, the original price of the coat is $40.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. When this equation is graphed, it always results in a straight line."

Given, Kisha got the discount of $12.00 while buying the coat.

The coat was on sale for 30% off.

Let, the original price of the coat was $x.

Therefore, the price Kisha saved while buying the coat was:

$(x ×0.3)

= $0.3x

Now, 0.3x = 12.00

⇒ x = (12.00 / 0.3)

⇒ x = 40

Therefore, the original price of Kisha's coat was $40.

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Answer:

15 times 3 is equal to45

The container would hold 2040 cubic feet of shipped goods when it's three-quarters full.

The dimensions of the container are given as 40 ft by 8 ft by 8 ft 6 in. We need to convert the height of 8 ft 6 in to feet by dividing it by 12 since there are 12 inches in a foot:

8 ft 6 in = 8 ft + (6 in / 12) ft

         = 8 ft + 0.5 ft

         = 8.5 ft

Now we can calculate the volume of the container:

Volume = Length × Width × Height

      = 40 ft × 8 ft × 8.5 ft

      = 2720 ft³

To find the volume when the container is three-quarters full, we multiply the total volume by 0.75:

Volume when three-quarters full = 2720 ft³ × 0.75

                              = 2040 ft³

Therefore, the container would hold 2040 cubic feet of shipped goods when it's three-quarters full.

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Personal experience generates firsthand knowledge that is derived from an individual's direct involvement or observation of a particular event, situation, or phenomenon. This type of sample is unique to each person and provides a subjective understanding of the subject matter.

Personal experience is an essential source of learning and understanding as it allows individuals to gain insight, develop skills, and form opinions based on their own encounters. It can provide a deep understanding of emotions, perspectives, and nuances that cannot be fully grasped through secondhand information. Personal experiences are often considered valuable as they offer authenticity and a sense of relatability, enabling individuals to connect with others on a personal level. Additionally, personal experiences can serve as a foundation for personal growth and development, shaping one's beliefs, values, and decision-making processes.

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Answer:

9x^2 + 17x

Step-by-step explanation:

(5x - 2)(2x + 3)-3(x - 1)^2

12x^2 + 15x - 4x - 6 -3(x - 1)^2

12x^2 + 11x - 6 - 3(x^2-2-2x)

12x^2 + 11x - 6 - 3x^2 + 6 + 6x

9x^2 + 17x

Answer:

Step-by-step explanation:

Step-by-step explanation:

45+45

90

I guess is the answer

The two equations are Cost: C(x) = 4000 + 35x and Revenue: R(x) = 150x

Given that

Purchase: 4000 for startup and 35 for each produce

Sales: 150 for each

So, we have the cost and revenue functions to be

Cost: C(x) = 4000 + 35x

Revenue: R(x) = 150x

Using “Hoodies produced and sold” for the x-axis and “AED” for the y-axis, the graph of the scenario is attached, labelled and shaded as required in the (b), (c) and (d) parts

This is the point where the lines intersect i.e. when C(x) = R(x)

From the graph, lines intersect at approximately 35

This means that the number of hoodies to break even is approximately 35

This is calculated as

P(x) = R(x) - C(x)

So, we have

P(30) = 150(30) - (4000 + 35(30))

P(30) = -550

This means that you lose 550aed on 30 sales

This is calculated as

P(x) = R(x) - C(x)

So, we have

P(50) = 150(50) - (4000 + 35(50))

P(50) = 1750

This means that you earn 1750aed on 50 sales

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\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ R(\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})\qquad S(\stackrel{x_2}{4}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ RS=\sqrt{(~~4 - (-2)~~)^2 + (~~5 - 3~~)^2}\implies RS=\sqrt{(4 +2)^2 + (5 -3)^2} \\\\\\ RS=\sqrt{ (6)^2 + (2)^2} \implies RS=\sqrt{ 36 + 4}\implies RS=\sqrt{ 40 }\implies RS\approx 6.32\)

The total amount the developer will need in retirement savings to meet their retirement income goal is $1,778,000.

We have,

The developer wants to have enough saved to live off 80% of their current annual gross wage, which is.

= 80% x $88,900

= 0.80 x $88,900

= $71,120

To draw 4% of their retirement savings in the first year, they will need to save:

= $71,120 ÷ 0.04

= $1,778,000

Therefore,

The total amount the developer will need in retirement savings to meet their retirement income goal is $1,778,000.

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Answer:

I can barely see the bottom but I can make out what it is. LEt's also get this clear, I'm only helping because of the profile picture XD

Step-by-step explanation:

20 male

20 female

The answer is "D", 50%.

Answer:

D

Step-by-step explanation:

fifty percent jts head and fifty percent its tail

\(\text{To get the total surface area, all we have to do is multiply } 18 \text{ by } 12, \text{which gets us}\)\($18\cdot12 = \boxed{216\text{ ft}^2}\).

\(\text{So, our answer is } \boxed{216\text{ ft}^2}.\)

Larry needs 216 square feet of carpeting for her rectangular living room.

To find the amount of carpeting Larry needs, we need to calculate the area of her rectangular living room. The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the living room is 18 feet and the width is 12 feet.

So, the area of the living room is:

Area = Length * Width

Area = 18 feet * 12 feet

Area = 216 square feet

Therefore, Larry needs 216 square feet of carpeting for her living room.

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Answer:

hi the correct answer I believe would be 500

Step-by-step explanation:

since it's a 50 out of 50 chance (because it is heads and tails) the only logical way of thinking this through would be half and half

what I did was simply divide 1,000 by 2 to get 500 so there are 500 heads to be expected.

I hope I was any help to this