Debra is seven years younger than her sister, Pam. The table represents the relationship. Which is the equation representing the relationship between their ages?



(x) (y)

9 2
11 4
13 6
15 8

1. y = x - 2

2. y = 7x

3. y = x + 7

4.y = x - 7

y = x + 2

The distance travelled by rick on 2.5 gallons of gasoline is calculated to be 45 mi.

The given function can be written as d = 18 g , where, d is the distance and g is gasoline.

It is also said that, gasoline g = 2.5 gallons

So, to calculate the distance travelled by rick, we should place the value of g in the equation above.

d = 18 g = 18(2.5) = 45 mi

From the graph, the maximum possible gasoline is 10. So, when we place in the above equation, we have,

d = 18 g = 18(10) = 180 gallons

As, the both quantities on the x-axis and y-axis are positive, the graph is possible in first quadrant only.

The given question is incomplete. The complete question is 'How far can rick drive on 2.5 gallons of gasoline?' The picture of graph is attached in the attachment below.

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As per the given equation, the percentage of the whole chart that is yellow is 15%.

One quarter of the pie chart is blue, which is 25%.

15% of the pie chart is orange.

When we add the percentages of blue and orange sections, we get 25% + 15% = 40%. So, 40% of the pie chart is blue or orange.

As the other two sections, Yellow and Grey, are equal in size, we can assume that they make up half of the remaining 60% of the pie chart. So each of the Yellow and Grey sections make up 30%/2 = 15% of the pie chart.

Therefore, the percentage of the whole chart that is yellow is 15%.

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Answer:

5x + 4

Step-by-step explanation:

Base on the given:

[tex]\mathrm{\frac{9}{3}x+4+2x}[/tex]    → Divide 9 by 3. 9 ÷ 3 = 3

[tex]\mathrm{3x+4+2x}[/tex]    → Combine similar term {2x + 3x = 5x}

No farther can be simplify. Hence, 5x + 4 is the answer.

RevyBreeze

The slope of the Function represents the change in height per day.

A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is

[tex]m=\frac{dy}{dx}[/tex] = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be shown as

tan θ = Δy/Δx

So, the slope of a line is tanΘ.

So as slope represents a change in y per change in x, in the given question as y is height and x is days, slope changes in height per day.

The slope of the Function represents the change in height per day.

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The time it took for Devin to catch Antonio is given as follows:

50 seconds.

The position functions for each of Antonio and Devin can be modeled by linear functions in slope-intercept format, as follows:

y = mx + b.

In which:

Antonio starts 50 meters in front of Devin, hence the functions, considering their velocities, are given as follows:

(these two equations compose the system of equations).

Devin will catch up to Antonio when:

D(x) = A(x).

Hence:

9x = 50 + 8x

x = 50 seconds.

(which is shown by the point of intersection of the graph).

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The solution for the expression when x= 3 is 75

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

x² + 22x

Also from the question, we have

x = 3

This means that the value of x is 3, and we calculate the value of the expression

Substitute the known values in the above equation, so, we have the following representation

x² + 22x = 3² + 22 * 3

Evaluate

x² + 22x = 75

Hence, the solution is 75

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Possible question

Given x² + 22x, calculate the value when x = 3

answer:

1.the total area is quadrupled.

2.(I'm not sure, so sorry!!!!!)

Step-by-step explanation:

somsome else can do number 2 because questions on brainly have a max of 2 answers.... again, so sorry.

Step-by-step explanation:

If one dimension of a figure is quadrupled, its area would increase by a factor of 16 (2 to the power of 4). If one dimension is multiplied by 5, the area would increase by a factor of 25 (5 to the power of 2).

Answer:

[tex]\frac{2A}{h}[/tex] = b

Step-by-step explanation:

A = [tex]\frac{1}{2}[/tex] bh   Multiply both sides by [tex]\frac{2}{h}[/tex]

[tex]\frac{2}{h}[/tex]  x [tex]\frac{A}{1}[/tex] = [tex]\frac{2}{h}[/tex] x  [tex]\frac{h}{2}[/tex] x b

[tex]\frac{2A}{h}[/tex] = b

The name of the number property matched below with each step from the previous step.

The commutative property of addition:

Let a and b are numbers.

a + b = b + a

The change in the position of two numbers in an addition operation does not change the sum.

Given:

We have an expression,

[-5 + (1/2 + 5)] × 2

Applying commutative property of addition,

= [-5 + (5 + 1/2)] × 2

= [ (-5 + 5) + 1/2] × 2

Applying inverse property of addition,

= [0 + 1/2] × 2

Applying identity property of addition,

= 1/2 x 2

Applying inverse property of multiplication,

= 1

Therefore, the solution is 1.

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Answer:

1 = 18

Step-by-step explanation:

Answer:

Step-by-step explanation:

The dimensions of the the garden are 8 x 12

What is Quadratic Equation?

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f. (x).

A = l x w

l = 2w-4

A = w (2w-4)

A = 2w² -4w

96m² = 2w² - 4w

0 = 2w² - 4w - 96 divide both sides by 2

0 = w² - 2w -48

(w-8) ( w +6) = 0

w = 8 since it can't equal -6

length therefore = 2w-4 = 16-4 = 12

Hence, the dimensions of the garden are 8 x 12

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Full question:

A rectangular garden has a length that is 4 meters less than twice its width. Can you set up a quadratic equation to find the dimensions of the garden if its area is 96m^2?

There are 32 home sites on the 8-acre plot.

An acre, a standard unit of measurement used by land sellers, is roughly the same size as a typical football field. An acre is a product of any rectangular land plot with a total area of 4,046 square Metre, or 43,560 square feet. Six plots of 6 x 120 feet each make up an acre.

To find out how many 1/4 acre home sites are on the 8-acre plot, you can divide the total number of acres by the number of acres per home site.

8 acres / 0.25 acres/home site = 32 home sites.

So, there are 32 home sites on the 8-acre plot.

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The equation x + (60 + 70)° = 180° is used to solve for the measure of the vertical angle x = 50°

Vertical angles also called vertically opposite angles are formed when two lines intersect each other, the opposite angles formed by these lines are vertically opposite angles and are equal to each other.

The angle y and x form vertical angles, so x = y

Angle y form a straight line with 60° and 70° so we have the equation to solve for x as:

x + 60° + 70° = 180° {sum of angles on a straight line}

x + 130° = 180°

x = 180° - 130° {subtract 139° from both sides}

x = 50°

Therefore, the measure of the vertical angle x is equal to 50° derived with the equation x + (60° + 70°) = 180°.

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The logarithmic model that calculates the number of years, g(x), for the number of infected tree to reach the value of x is-

  [tex]g(x)[/tex] = ㏑[tex](x) / 0.4[/tex]

The equation can be written as-

[tex]y = f(x) = e x^{0.4x}[/tex]

The natural logarithm is now applied to both sides of the equality after we have isolated y.

[tex]0.4y = ln x[/tex][tex]y = ln x / 0.4[/tex]

This is how the  exponential model as a logarithmic model that calculates the number of years, g(x) can be explained as.

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According to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.

At the margins of the coordinate plane, the curve approaches lines known as asymptotes. When the denominator of such a rational function gets close to zero, vertical asymptotes happen. Since it would divide by zero, a rational function never traverse a vertical asymptote. A graph's vertical asymptote is a vertical line with the equation x=a, where the graph tends to positive or negative infinity as the inputs go closer to a.

For the given graph we can see that the vertical asymptotes are -1 and 3, and there is no horizontal asymptote.

In option A:

[tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex]

The horizontal asymptote is none.

The vertical asymptote is -1 and 3.

Hence, this is the correct option.

Option B:

[tex]F(x) = \frac{1}{(x-2)(x+1 )(x-3)}[/tex]

The horizontal asymptote is 0.

The vertical asymptote is 2, -1 , and 3.

Hence, option B is incorrect.

Option C:

[tex]F(x) = \frac{x-2}{(x-1 )(x+3)}[/tex]

The horizontal asymptote is none.

The vertical asymptote is 1 and -3.

Hence, option C is incorrect.

Hence, according to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.

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There will be 9 columns which each has 9 blocks and the 10th column will be 5 blocks. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 68 ÷ 7

Simplify the expression, then we have

⇒ 68 ÷ 7

⇒ (63 + 5) / 7

⇒ 63 / 7 + 5 / 7

⇒ 9 + 5/7

There will be 9 columns which each has 9 blocks and the 10th column will be 5 blocks. Then the correct option is D.

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The last D option is missing. The option D is given as,

D. 9 columns which each has 9 blocks and the 10th column will be 5 blocks.

Answer: x=2

Step-by-step explanation:

The recommendations in parts (a) and (b) are not consistent. This is the best example of Simpson’s Paradox.

(a) Allison Feeley's junior year batting average: 15/40 = 0.375 Emily Janson's junior year batting average: 71/201 = 0.353 Allison Feeley's senior year batting average: 76/251 = 0.302 Emily Janson's senior year batting average: 35/120 = 0.292

Using this analysis, Allison Feeley should be awarded the scholarship, as she has the higher batting average in both her junior and senior years.

(b) Outcome: Player | Hit | No Hit | Total At-Bats Fealey | 91 | 200 | 291 Janson | 106 | 215 | 321

Allison Fealey's combined two years batting average: 91/291 = 0.313 Emily Janson's combined two years batting average: 106/321 = 0.331

Using this analysis, Emily Janson should be awarded the scholarship, as she has the higher batting average over the combined junior and senior years.

(c) The recommendations in parts (a) and (b) are not consistent. This is an example of Simpson's Paradox, it shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be different when the crosstabulations are grouped or aggregated.

Therefore, [a] and [b] are not consistent according to Simpson’s Paradox.

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The recommendations in parts (a) and (b) are not consistent. This is the best example of Simpson’s Paradox.

a) Allison Feeley's junior year batting average: 15/40 = 0.375 Emily Janson's junior year batting average: 71/201 = 0.353 Allison Feeley's senior year batting average: 76/251 = 0.302 Emily Janson's senior year batting average: 35/120 = 0.292

Using this analysis, Allison Feeley should be awarded the scholarship, as she has the higher batting average in both her junior and senior years.

(b) Outcome: Player | Hit | No Hit | Total At-Bats Fealey | 91 | 200 | 291 Janson | 106 | 215 | 321

Allison Fealey's combined two years batting average: 91/291 = 0.313 Emily Janson's combined two years batting average: 106/321 = 0.331

Using this analysis, Emily Janson should be awarded the scholarship, as she has the higher batting average over the combined junior and senior years.

(c) The recommendations in parts (a) and (b) are not consistent. This is an example of Simpson's Paradox, it shows that in interpreting the results based upon separate or un-aggregated crosstabulations, the conclusion can be different when the crosstabulations are grouped or aggregated.

Therefore, [a] and [b] are not consistent according to Simpson’s Paradox.

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Answer:

Step-by-step explanation:

from the first ... 3y = 3x + 12 or

y = x + 4

This is the same as the second, so D

The required average speed of the train is calculated to be 60 mph, when the train travels certain distance and stops.  

Distance between station A and station B is given as 120 miles.

A train traveling from station A to station B travels exactly 1/3rd of the distance when it is held up and stops for 16 minutes.

Let, its average speed was x mph.

Then, total time taken if it didn't stop = 120/x h

Now, before stop it took time = ( 1/3 × 120)/x h = (40/x) h

After stop the time it took = 80/(x + 15) h

i.e, 40/x + 16/60 + 80/(x+15) = 120/x  

⇒ 80/(x + 15) + 8/30 = 80/x

⇒ 80(1/x - 1/(x + 15)) = 8/30

⇒ 10 × (15/x² + 15x) = 1/30

⇒ x² + 15x = 10 × 15 × 30

⇒ x² +15x - 450 = 0

⇒ x² +75x -60x - 450 = 0

⇒ (x+75)(x-60) = 0

⇒ x = 60 or, x = -75

As speed cannot be negative, the average speed is 60 mph.

The given question is incomplete. The complete question is 'Find the average speed of the train before it stopped for 16 minutes.'

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The number of miles that Tyee will travel in 8 hours, given the speed is 216 miles

To find the number of miles that Tyree would drive in 8 hours, given the speed he is going, you first need to find the speed Tyree is going which is:

= Number of miles travelled / Number of hours

= 54 / 2

= 27 miles per hour

The number of miles that Tyree would travel in 8 hours is:

= Number of hours of travelling x Speed travelled

= 8 x 27

= 216 miles

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The total number of ounces needed to serve all guests (6 oz/guest * 80 guests) and then divide that number by the size of the bottle (25.4 oz) to get the total number of bottles needed.

In order to calculate the number of champagne bottles needed to serve all 80 guests, we need to use the formula for calculating the total number of ounces needed. The formula is: Number of bottles * size of bottle + total ounces of glasses * number of guests. In this case, the number of bottles needed is: (6 oz/guest * 80 guests)/25.4 oz bottle = 18.9 bottles. Therefore, 19 champagne bottles will be needed to serve all 80 guests. This is because each bottle holds 25.4 ounces and each guest needs 6 ounces of champagne, so we need to calculate the total number of ounces needed to serve all guests (6 oz/guest * 80 guests) and then divide that number by the size of the bottle (25.4 oz) to get the total number of bottles needed.

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Answer:

14

Step-by-step explanation:

f(3) = 3(3) - 5 + 10

f(3) = 9 - 5 + 10

f(3) = 4 + 10

f(3) = 14

Answer:

14

Step-by-step explanation:

Start by finding f(3), which would include plugging in a 3 everywhere you see an x

f(3) = 3(3)-5

f(3) = 9-5

f(3) = 4

Now we can use f(3)+10 because we know what f(3) is, it's 4. So replacing it

f(3) + 10 is now 4+10, which equals 14

Answer:

see below

Step-by-step explanation:

h = 6

r = 8 ==> area = πr² = 3.14*8² = 3.14 *64 =201.0

top & bottom = 2*200.96 = 401.9

r=8 ==> perimeter = 2πr = 2*3.14 *8 = 16* 3.14 =50.2

lateral area = h*perimeter = 6*50.24 = 301.44

so it's about 100 sq inch less

Answer:

X = C - B

--------

A

Step-by-step explanation:

Solving for X is pretty much getting X alone on one side of the equal sign. That's when we would do the "opposite" of what the original equation is showing. And we do that to both sides.

For example, we see +b. The opposite of addition is subtraction, so we do just that. We do -b on BOTH sides of the equal sign. b -b = 0. It cancels it out. c-b is just as it says. So now we have ax = c-b.

Now we see ax are right next to each other with no symbol, which means they are being multiplied. The opposite of multiplication is division. So we'll do that exactly. We will divide A on both sides. ax/a gets rid of that a and leaves the x alone. Dividing c-b/a gives you just that, making the answer X = C-B/A

Answer:

16.6666666666667%

Step-by-step explanation:

17/102 = x/100

17*100/102 = x

x = 16.66666667

Answer:

The percent is:

16.667%

Step-by-step explanation:

17 / 102 = 0.16667

0.16667 * 100 = 16.667%

Answer:

$152

Step-by-step explanation:

160*.95 = 152

The height of the triangle which is also called the altitude is; 6.63 cm

The triangle is an Isosceles Triangle that has two congruent sides and we have the parameters as;

Length of congruent sides = 12 cm.

Base length = 10 cm

Half of the base will be 5 cm and as such, we can use the Pythagorean Theorem to find the altitude as;

Altitude² = Hypotenuse² - Base length²

Thus;

A² = 12² - 10²

A = √44

A ≈ 6.63 cm

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