Cranberry juice is made with a 16:3:1 ratio of water:sugar:cranberries. How much water,

in gallons, how much water is needed in order to make three gallons of cranberry juice? Express your answer as a

common fraction.

The requried pair of functions which are inverse of each other is f(x) = 13x - 7 and g(x) = x + 7 / 13.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
(A)

Given function,
f(x) = x / 3 + 10
Its inverse function is given as,
f(x) - 10 = x/3
x = 3(f(x) - 10)
change x = g(x) and f(x) = x
g(x) = 3[x - 10]

Similarly,
Inversfunciton,
B. g(x) = 9/x - 5
C. g(x) = x + 7 / 13
D. g(x) = x³/4

Thus, the requried pair of functions which are inverse of each other is f(x) = 13x - 7 and g(x) = x + 7 / 13.

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Answer: X = 88, Y = 26, Z = 11.2

Step-by-step explanation:

First thing is use any linear pair equation that only has one variable.

1. 2x-30 + 34 = 180, Y = 88

Plug in the value of X to a two-variable equation to find the value of y.

2. 2y +88 + 40 = 180, Y = 26

Lastly repeat this step for finding the value of z.

3. 88 + 39 + 5z - 3 = 180, Z = 11.2

Answer: x = 88, y = 26, z = 26

Step-by-step explanation:

The shape shown in the picture is a heptagon.

Sum of interior angle = 900 degrees

Add all the interior angles

x+40+x+22+142+x+39+133+2x-30+114

=5x+460

5x+460=900

5x = 440

x = 88

2y is the exterior angle of x+40

to get 2y, you need to subtract x+40 from 180.

x = 88,

x+40 = 128

2y = 180-128 = 52

y = 26

5z-3 is the exterior angle of x+39

same thing for 5z-3

x = 88,

x+39 = 127

5z-3 = 127

5z = 130

z = 26

The complete distance in feet on the table are a=6, b=7, c=8, d=7, and e=6.

In mathematics, a revolution is a full rotation, or a full 360-degree turn. The item starts and ends in the same location during a 360-degree revolution.

The circumference of the wheel is equal to the length of a full revolution, or 2*pi*radius. The whole rotation of the wheel is 360 degrees.

The eight of the point is 6 feet, and the wheel's radius is 1 feet.

The point will be in its initial position, which is 6 feet high.

The height will thus be a = 6 + 0 = 6 ft.

The point will reach half the whole height of the wheel, or 2 feet, when the distance travelled is pi/2.

Height of b = 6 + 1 = 7 feet will result.

The point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel, when the distance travelled equals pi.

The height will thus be c = 6 + 2 = 8 ft.

The point will be half the whole height of the wheel, or 2 feet, when the distance travelled is 3 pi/2.

The height will thus be d = 6 + 1 = 7 ft.

The point will be in its initial position, which is 6 feet high, when the distance travelled is 2 pi.

The height will thus be e = 6 + 0 = 6 ft.

Hence, the complete distance in feet on the table are a=6, b=7, c=8, d=7, and e=6.

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Answer: The y-intercept for part A is 2 and for part B is -5 and the slope for part A is 3 and for part B is 2. ✅

Step-by-step explanation:

PLEASEEEE GIVE BRANLIEST

The y-intercept is a point on the graph where the line of the function crosses the y-axis. It is represented by the number that is next to the y in the equation of a line (y = mx + b).

The slope is the steepness of the line and it is represented by the number that is next to the x (y = mx + b).

In part A, the y-intercept is 2 and the slope is 3. This means that the line starts at the point (0,2) and for every 1 unit on the x-axis, it goes up 3 units on the y-axis.

In part B, the y-intercept is -5 and the slope is 2. This means that the line starts at the point (0,-5) and for every 1 unit on the x-axis, it goes up 2 units on the y-axis.

So the difference between part A and part B is that the y-intercept for part A is 2 and for part B is -5 and the slope for part A is 3 and for part B is 2. This means that the line in part A starts at a different point and is steeper than the line in part B.

Answer:

In the context of a linear function, the y-intercept is the point where the line crosses the y-axis and the slope is the rate at which the line increases or decreases as the x-value increases. If two functions have different y-intercepts, it means that they have different starting points on the y-axis. Similarly, if two functions have different slopes, it means that they have a different rate of change. So, in part A and part B, if the y-intercept and the slope of the function in part A are different from the y-intercept and the slope of the function in part B, it means that the two functions have a different starting point on the y-axis and a different rate of change respectively.

Step-by-step explanation:

In the context of a linear function, a line can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b. For example, if the equation of the line is y = 2x + 3, the y-intercept is (0,3).

The slope of the line is the rate at which the line increases or decreases as the x-value increases. It is represented by the value of m in the equation y = mx + b. For example, if the equation of the line is y = 2x + 3, the slope is 2.

If the y-intercept and the slope of the function in part A are different from the y-intercept and the slope of the function in part B, it means that the two functions have different starting points on the y-axis and a different rate of change respectively.

For example, if the equation of the function in part A is y = 2x + 3, the y-intercept is (0,3) and the slope is 2. And if the equation of the function in part B is y = 4x + 1, the y-intercept is (0,1) and the slope is 4. Therefore, the y-intercept and slope of part A are different from the y-intercept and slope of part B.

The correct option is B, a vertical dilation by a factor of 3 and a horizontal shift to the right 2 units transformations are applied to the graph of the function f(x)=10^x to produce the graph of the function g(x)=3(10)^x-2.

An illustration of data or a mathematical function is a graph. Usually, it consists of a collection of plotted points or coordinates connected by lines or curves. A graph's main function is to show the relationship between two or more variables, which facilitates better comprehension and interpretation of the data.

The graph of the function f(x) = 10x is a three-fold vertical extension of the graph of y = 10x. In order to create the graph of g(x) = 3(10)x, a vertical dilation of three times is applied to the graph of y = 10x.

To create the function's graph, a horizontal shift of 2 units to the right is also used g(x) = 3(10)^x-2

So, the answer is B.

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Answer:

y - (-2) = -5/3 (x-6)

Step-by-step explanation:

Using Slope Point Formula (y-y1=m(x-x1) we can use the given slope, and the given coordinate to fill in the equation.

So y1 would be -2 because we only have 1 coordinate, and -2 is the y value. So we have y-(-2)=m(x-x1)

Now we have the slope which is m. The slope is -5/3, so we plug that into m. So now we have y-(-2)=-5/2(x-x1).

Last we plug in x1 to the equation which is 6. So to finish the equation we have y-(-2)=-5/3(x-6).

-Hope this helped

Therefore , the solution to the given problem of equation comes out to be y = 2x + 4.

A proclamation of the equivalency of two expressions is an algebraic equation, which is calculated by performing the algebraic of addition, removal, multiplication, division, raising to a power, or extracting a root to a collection of variables. Examples include (y4x2 + 2xy - y)/(x - 1) = 12 and x3 + 1.

Here,

It is important to remember that parallel lines have the same slopes before trying to determine this line's equation.

As a result, we can predict that the new line will have a slope of 2 because the previous line has a slope of 2.

Now that we have that knowledge, we can utilize it to find the equation using point-slope form and the supplied point.

y - y1 = m(x - x1) (x - x1)

y - 8 = 2(x - 2) (x - 2)

y - 8 = 2x - 4

y = 2x + 4

Therefore , the solution to the given problem of equation comes out to be y = 2x + 4.

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1. y = -1.15x + 102.8 is the equation of the line of best fit.

2. Using the line of best fit's equation, the estimated price is: $62.55.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign.

According to our question-

1. Making use of the two points (20, 80) and (72, 20)

Slope (m) is equal to change in y/change in x, or (80 - 20)/(20 - 72) = 60/-52.

Slope is -1.15 meters.

Change y - b = m to m = -3 and (a, b) = (72, 20). (x - a)

y - 20 = -1.15(x - 72) (x - 72)

y - 20 = -1.15x + 82.8

y = -1.15x + 82.8 + 20

y = -1.15x + 102.8

The best line of fit is the equation y = -1.15x + 102.8.

2. To calculate the monthly heating expense, y, for a month with an average temperature of 35°F (x), enter x = 35 into the formula: y = -1.15x + 102.8.

y = -1.15(35) + 102.8

y = 62.55

The estimated monthly expenditure is $62.55.

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Answer: Slope:5/3

Y-intercept: y=1.67x+-4

Step-by-step explanation:

Slope:

Take two points and put it in for m=y2-y1/x2-x1

we can use (0,-4) and (3,1)

m=1--4/3-0

m=5/3

m=1.67

Then we use m in y intercept and use the first point as b

y = mx + b

y=1.67x+b

-4 = 1.67(0) + b

-4 = 0 + b

-4 = b

b = -4

y = 1.67x + -4

Y intercept: y = 1.67x + -4

Slope: 5/3

Good luck

The number of flowers that can be planted in 1 hour is 6 flowers.

To solve equations or determine the value of a variable, cross multiplication is employed in mathematical operations. In this procedure, the numerator of one side is multiplied by the denominator of the other side.

Given that the time required to plant trees is:

3. 5 hours = 21 flowers

Convert 3.5 hours into minutes.

3 hours 60 = 180 minutes,

Additional half hour can be represented as: 1/2 hours 60 = 30 minutes.

Total hours is 180 + 30 = 210 minutes.

So it takes, 210 minutes to plant 21 flowers.

The time taken to plant flowers in 60 minutes is:

[tex]x = \frac{(21)(60)}{210} \\\\x=6[/tex]

Hence, the number of plants that can be planted in 1 hour is 6 flowers.

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i got nothin

like what?

81 is the standard form of 3⁴

A number system is defined as a system of writing to express numbers.

The given expression is 3⁴

We need to write in the form of the standard form

3⁴ is nothing but three is multiplied four times

3×3×3×3

Thee times of three for two times

81

Hence, 81 is the standard form of 3⁴

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Answer:

25:5:12

wat

Step-by-step explanation:

follow me

pls

Answer: 10, 5, 12, and 3 compear each other.

Step-by-step explanation: only this way, I don't know is there other

The function will use the formula x^i, where x is the element in x and i is the power.

Let x = [2, 3] and k = 3.

The function get list of powers will calculate the powers of each element in x, from 0 to k.

For the given example, the list of powers will be  l = [[1, 2, 4, 8], [1, 3, 9, 27]].

The first element in l is the powers of 2 from 0 to 3, which are 1, 2, 4, and 8. The second element in l is the powers of 3 from 0 to 3, which are 1, 3, 9, and 27.

To calculate these powers, the function will use the formula x^i, where x is the element in x and i is the power.

For example, to calculate 8 (2^3), the function will use the formula 2^3.

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Answer:

17/5

Step-by-step explanation:

plug in 3/5 for p

2/3(3/5)+3

2/5+3=17/5

Answer: The function y = 5/x is a reciprocal function, which means the graph of the function will be a hyperbola.

The error the student made could be in the following ways:

The student might have plotted the graph as a straight line instead of a hyperbola

The student might have neglected to reflect the graph across the y-axis, since the function is not defined for x = 0

The student might have not plotted the asymptotes of the graph. The graph will have vertical asymptotes at x = 0 and x = infinity.

To correct the error, the student should plot the graph as a hyperbola with vertical asymptotes at x = 0 and x = infinity. And also reflect the graph across the y-axis.

In case of any further doubts student should check with their teacher or a math reference book.

Step-by-step explanation:

The value of n of hours you need to study on Saturday is,

⇒ n = 3.75

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The mean number of hours you study per day is 2.25.

Now, By definition of mean we get;

⇒ Mean = (2 + 1.75 + 2.5 + 2.75 + 3 + 0 + n) / 7

⇒ 2.25 = (12 + n) / 7

⇒ 2.25 × 7 = 12 + n

⇒ 15.75 = 12 + n

⇒ n = 15.75 - 12

⇒ n = 3.75

Thus, The value of n = 3.75

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Part A 0.124

Part B 0.733

Part C 0.408

P(A) is the product of the number of outcomes in event A and the overall sample space. The chance of event A occurring, for instance, is 3/6, or 0.5, if we have a sample space of 6 outcomes (such as when rolling a die), and event A consists of 3 of those outcomes (such as when rolling a 1, 2, or 3).

A mathematical representation of a random process, known as a probability model, is used to express the possibility of certain events occurring. A list of all potential outcomes and the likelihood that each outcome will occur make up its two basic parts.

Using the table Given :

1.) P(AP Statistics) = 90 / 725 = 0.124

2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733

3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408

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Solving the provided question, we cans say that by quadratic equation, the age where a person's systolic pressure is 127.54 mm Hg is 46

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared.

systolic pressure for a person of age 45 years, just plug in y = 45:

systolic pressure is 127.54 mm Hg, plug in P = 127.54

P = 0.004y2 - 0.02y + 120

127.54 = 0.004y2 - 0.02y + 120

0 = 0.004y2 - 0.02y - 7.54

Use the quadratic formula to solve this. The quadratic formula (for ay2 + by + c = 0) is:

y = [-b ± √(b2 - 4ac)]/(2a)

In this case a = 0.004, b = - 0.02 and c = - 7.54 so:

[tex]y = [-b + \sqrt{(b2 - 4ac)]/(2a)}\\y = [-(-0.02) +\sqrt{((0.02)2 - 4(0.004)(-7.54))]/(2(0.004))}\\y = [0.02 + \sqrt{(0.0004 + 0.12064)]/0.008}\\y = [0.02 + \sqrt{0.12104]/0.008}\\y = [0.02+ 0.3479]/0.008\\ y = [0.02 + 0.3479]/0.008 or y = 0.3679/0.008 = 45.989\\ y = [0.02 - 0.3479]/0.008 or y = -0.3279/0.008 = -40.989\\[/tex]

Since -40.988 makes no sense (40.989 years before birth), we throw that answer out.

The age where a person's systolic pressure is 127.54 mm Hg is 46

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Answer:

W = -8

Step-by-step explanation:

Sorry fir taking so long, the description is pretty long, and difficult to type, but if you need one let me know :D

The graph shown in 'Option 1' shows the continuous data.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

There are four graph is shown in image.

We know that;

Continuous data changes over time and can have different values at different time intervals. Continuous data is made up of random variables, which may or may not be whole numbers.

And, Continuous data is measured using data analysis methods such as line graphs, skews, and so on.

Hence, By definition of Continuous data; We get;

⇒ The graph shown in 'Option 1' shows the continuous data.

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Answer: 0.6x=54

$90

Step-by-step explanation: Start by saying the question out loud in a different format:

60% of what is $54?

We know that of means multiplication and is means equals. This helps us create the equation:

60% x what= $54

Then, we need to make 60% a number we can work with by changing it into a decimal: 0.6. We also need to make 'what' something easier to use as well, so we will use x in place of what:

0.6x=54

Then, get x by itself, which is also called isolating the variable. You do this by dividing by 0.6 on both sides, which is known as using inverse operations.

You should get x=90.

This means that $54 is 60% of $90 and $90 is Noah's goal.

Answer:

c is 80 and b is 100

Answer: C would be 80 degrees, and B would be 100 degrees

Hope this helps! :D

(a) the value of a material weighing 5 kg is 31.25

(b)the value of a material weighing 50 kg is 3125

(c) the weight of a material worth 720 is 24 kg

Variation is a relation between a set of values of one variable and a set of values of other variables

If the value Q of a material is directly proportional to the square of its weight W. We can write:

Q α W²

Q = kW²   (where k is constant of proportionality)

If a material weighing 20 kg is worth 500, we have:

Q = kW²

500 = k × 20²

500 = 400k

k = 500/400

k = 5/4

k = 1.25

(a)the value of a material weighing 5 kg

Q = kW²

Q = 1.25 × 5² = 31.25

(b)the value of a material weighing 50 kg

Q = kW²

Q = 1.25 × 50² = 3125

(c)the weight of a material worth 720

Q = kW²

720 = 1.25 × W²

W² = 720/1.25

W² = 576

W = √576

W = 24 kg

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Therefore ,in light of this, the solution (n -2) * 180 can be used to solve the following polygon issue, where is the actual number of sides.

It has straight sides. A polygon's vertices (or corners) are the points at which two of its sides meet. A figure with three or more straight sides is known as a closed, two-dimensional polygon. Any form with angular sides, such as a triangle or a rectangle, is a polygon. Open-sided or curved figures are not considered to be polygons.

Here,

example

The sum of each internal angle in a polygon can be calculated by applying the formula (n-2)*180, where n is the total number of sides in the polygon.

The required polygon has nine sides, hence the sum of external angles in this case is (9-2)*180, or 7, which is equivalent to 1,260 degrees.

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The better deal among the options is 9 dollars per pound.

Joe´s mother is deciding whether or not she should buy a 14- ounce package of coffee on sale for $8.50. She also knows she can buy the same coffee for $9.00 per pound.

Therefore, let's find the better deal.

We have to convert the weight to the same units.

1 ounce = 0.0625 pounds

14 ounces = ?

cross multiply

mass = 0.0625 × 14 = 0.875

Therefore, one deal is 0.875 pounds for $8.50 and the other is 9 dollars per pounds.

Hence,

price per pounds = 8.50 / 0.875 = 9.7 dollars per pounds

Therefore, the better deal is 9 dollars per pounds.

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The integral represents a graph of the signed area, and the geometry is calculated. The area is found to be 100 units².

A plane that is created when two perpendicular coordinate axes cross each other is known as a cartesian plane. Everywhere in the Cartesian plane, the functions define the boundaries of regions with regular geometrical patterns. The right triangle and other regular regions are good examples of how the area of a region may be computed using the geometry of the region.

The given function is [tex]\int\limits^{10}_{-10} {|x|} \, dx[/tex].  The function of this integrand is defined as f(x)=|x| with -10 ≤ x ≤ 10. Now, the graph is drawn for this function.

From the graph, we can tell the base and height of the two right-angle triangles are 10 units and 10 units. Then, the area is,

[tex]\begin{aligned}A&=2\left(\frac{1}{2}\times b\times h\right)\\&=2\times \frac{1}{2}\times 10 \times 10\\&=\mathrm{100\;{units}^2}\end{aligned}[/tex]

The area can also be calculated by solving the integrals,

[tex]\begin{aligned}\int\limits^{10}_{-10} {|x|} \, dx &=\int\limits^0_{-10} {-x} \, dx +\int\limits^{10}_0 {x} \, dx\\&=\left[\frac{x^2}{2}\right]^{0}_{-10} +\left[\frac{x^2}{2}\right]^{10}_{0}\\&=\frac{1}{2}(100+100)\\&=\mathrm{100\;units^2}\\\end{aligned}[/tex]

The required answer is 100 units².

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The situation described is discrete data and the domain would be {x E Z | x >=0} where Z represents the set of integers and x is greater or equal to 0

What is the domain of a function?

The domain of a function is the set of all input values (also known as the independent variable) for which the function produces a valid output (also known as the dependent variable). In other words, it is the set of all input values for which the function is defined.

The situation described is discrete data.

The domain or set of all possible x-values for this situation would be the set of non-negative integers (x = 0, 1, 2, 3, ...) since the cost of each song is $3.00 and Clarissa can only buy a whole number of songs, not a fraction or decimal of a song.

Hence, the situation described is discrete data and the domain would be {x E Z | x >=0} where Z represents the set of integers and x is greater or equal to 0.

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