Two joggers run 8 miles and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile they must travel to return to their starting position?

The measure of ∠1 is 114.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

∠7 = 114

From the figure,

Line a is parallel to line b.

So,

∠7 and ∠1 are alternate exterior angles.

And,

Alternate exterior angles are equal.

So,

∠7 = ∠1 = 114

Thus,

∠1 is 114.

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The greatest number of 0.25 pound servings Becky can make is 18.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Becky has 1.84 pounds of strawberries and 2.62 pounds of cherries.

Now, number of pounds of salads

= 1.84+2.62

= 4.46 pounds

Becky mixes the two fruits together and then scoops out 0.25 pounds of fruit salad for each serving.

So, the number of servings = 4.46/0.25

= 17.84

≈ 18

Therefore, the greatest number of servings is 18.

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Answer:

The probability of rolling a 1 or a 4 on a single roll of the number cube is 2/6, or 1/3. So the expected number of times the number cube will land with a 1 or a 4 on the top face after 400 rolls is 400 * 1/3 = 133.33.

The range that contains this expected value is roughly between 130 and 140, so a good prediction for the number of times the number cube will land with a 1 or a 4 on the top face is between 130 and 140.

Step-by-step explanation:

Answer: 63%

Step-by-step explanation:

22 divided by 35 times 100

To determine if a line is parallel or perpendicular, we can place each line on a sloped intersection shape (y = mx + b) and observe the slope m of each line. Equal slopes result in parallel lines. If the slope is multiplied by -1, then the line is vertical.

Parallel Lines:

Two or more lines that lie in the same plane and do not intersect are called parallel lines. They are equidistant from each other and have the same slope. A straight line equation is usually written in the form of a slope intercept represented by the equation y = mx + b. where "m" is the slope and "b" is the y-intercept. The "m" value defines the slope and tells how steep the line is.

Perpendicular Lines:

A vertical line or perpendicular line is two separate lines that intersect at an angle of 90° to each other. These are straight lines known as perpendiculars that meet each other at certain angles (right angles).

We have already seen what a vertical line looks like. If a shape has an "L" shape, its vertex angles are right angles. Vertical lines always intersect each other, but not all intersecting lines are always perpendicular to each other.

Two main properties of vertical lines:

1. Perpendicular lines always intersect or intersect each other.

2. The angle between two vertical lines is always 90°.

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Equation: 4x = 56  

Answer: 14 tickets

Step-by-step explanation:  

4x = 56  

Lavonne's tickets sold 4 times as many as Kenneth's. This means we would need to multiply Kennneth's ticket by 4 to equal Lavonne's.

4x/4 = 56/4

Now you need to solve the equation by isolating x. Here you have to divide both sides by 4.

x = 14

Kenneth sold 14 tickets.

4(14) = 56

Answer: Her total exercise time was 25 minutes

Yes, Sage and Tom have the same number of talk minutes left in their cell phones. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

The term "arithmetic operations" refers to the four basic mathematical operations that can be used to express any real number. Multiplication, division, addition, and subtraction are the four operations.

We are given that Sage and Tom both started the month with the same number of talk minutes on their cell phones.

So, let 'x' be the number of talk minutes on their cell phones.

Sage talked for 7 minutes with her dad.

So, talk minutes left in Sage's phone = x-7

Tom talked for 4 minutes with a friend and 3 more minutes with his mom.

So, talk minutes left in Tom's phone = x - (4 +3) = x -7

Hence, Sage and Tom have the same number of talk minutes left in their cell phones.

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The only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.

We can use substitution to find which value of x makes the inequality 2x < 18 true by trying each value in the set {7, 9, 36} one by one.

Let's start with x = 7:

2x = 2(7) = 14

14 < 18 is true, so x = 7 satisfies the inequality.

Next, let's try x = 9:

2x = 2(9) = 18

18 < 18 is not true, so x = 9 does not satisfy the inequality.

Finally, let's try x = 36:

2x = 2(36) = 72

72 < 18 is not true, so x = 36 does not satisfy the inequality.

Therefore, the only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.

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She paid $0.1282051282 per yard - $0.13 ( rounded ).

Answer:

339.3 cubic m

Step-by-step explanation:

r = Base radius

  = [tex]\frac{Diameter}{2}[/tex]

  = [tex]\frac{6}{2}[/tex] m

Base radius = 3 m

h = Perpendicular height

  = 12 m

Volume of a cylinder: [tex]\pi r^{2} h[/tex]

                                 = [tex]\pi (3 m)^{2} (12 m)[/tex]

                                 = [tex]\pi (108)m^{3}[/tex]

                                 = 339.3 cubic m (Rounded to the nearest tenths place)

For the given rational number √15 × a =  15 × a the value of 'a' is equal to 0 or ( 1 / 15 ).

The expression is written as :

√15 × a =  15 × a

The above expression is a rational number :

Squaring both the side of the expression we get,

⇒ 15 × a =  ( 15 × a )²

⇒  15 × a =  225 × a²

Divide by 15 on the both the side of the equation we get,

⇒ a = 15 a²

⇒ 15a² - a = 0

⇒ a( 15a - 1 ) = 0

⇒ a = 0 or 15a - 1 =0

⇒ a = 0 or a = 1 / 15

Therefore, the value of a for the given rational number is equal to

0 or ( 1 / 15 ).

The above question is incomplete , the complete question is:

If √15 × a =  15 × a is a rational number, what could be the value of  a ? Explain your reasoning.

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Kareem's probability of attending either State or Northern is 0.88, meaning there is an 88% chance that Kareem will attend one of the universities.

Probability is a measure of the likelihood of an event occurring.

Kareem's case, the probability of attending State College is 55%, which means there is a 55% chance that Kareem will attend State College. The probability of attending Northern University is 33%, which means there is a 33% chance that Kareem will attend Northern University.

To determine the probability of attending either State or Northern, we add the individual probabilities of each event. Thus, the probability of attending either State or Northern is:

P(State) + P(Northern) = 0.55 + 0.33 = 0.88

The probability of attending either State or Northern is 0.88, which means there is an 88% chance that Kareem will attend one of these universities. It is important to note that the sum of all probabilities of all possible outcomes is always equal to 1.

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When Y directly varies with X, the direct variation equation is X = 2.

A direct variation is a relationship between two variables when their ratio is constant. One variable is said to vary in direct proportion to another. Y = kx, where k is the variational constant, is the formula for direct variation. If y varies in direct proportion to x and y = 6 when x = 2, the variational constant is k = = 3. Consequently, y = 3x is the equation that describes this direct variation.

If y directly correlates with x, we can apply the direct variation formula as follows:

y = kx

where k is the proportionality constant.

We may utilise the y and x values provided to find k:

y = kx

16 = k(4)

Solving for k, we get:

k = 16/4 = 4

Now we can use the value of k to find x when y = 8:

y = kx

8 = 4x

Dividing both sides by 4, we get:

x = 2

Therefore, when y = 8, x = 2.

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Question:

If y varies directly with x and y = 16 when x = 4, find x when y = 8.

Write and solve a direct variation equation to find the answer.

X =?

So the temperature in City A was 8A C and the temperature in City B was y = x + 1 = 8 + 1 = 9A C.

The problem can be solved by setting up an equation using the information given. Let's call the temperature of City A "x" and the temperature of City B "y". We can then write two equations based on the information given:

4x = 3y + 8

x - 2y = -3

We can use substitution to solve for one of the variables and then use that information to solve for the other. For example, we can substitute 3y + 8 for 4x in the second equation:

x - 2y = -3

x - 2y = 3y + 8 - 3

x - 2y = 3y + 5

x - 5y = 5

We can then solve for y by multiplying both sides of the equation by -1/5:

-5x + 5y = -5

5y = 5x + 5

y = x + 1

We can then substitute this expression for y into one of the original equations and solve for x:

4x = 3(x + 1) + 8

4x = 3x + 3 + 8

x = 8

So the temperature in City A was 8A C and the temperature in City B was y = x + 1 = 8 + 1 = 9A C.

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Hey there! Johnny Sins always here to help,

To find out what score Natasha needs to earn on her next test, we can use the following formula:

Average = (sum of all scores) / number of scores

Let's call the score Natasha needs to earn on her next test "x".

Her average so far is:

Average = (94 + 89 + 88 + 92 + 85) / 5 = 90

Her average after her next test will be:

Average = (94 + 89 + 88 + 92 + 85 + x) / 6

Now, we need to set this equal to 90% and solve for x:

90 = (94 + 89 + 88 + 92 + 85 + x) / 6

90 * 6 = (94 + 89 + 88 + 92 + 85 + x)

540 = (94 + 89 + 88 + 92 + 85 + x)

x = 540 - (94 + 89 + 88 + 92 + 85)

x = 540 - 448

x = 92

So, Natasha needs to earn a 92% on her next test to average at least 90%.

_________________________________________________________

No problem for the answer, be sure o give a 5 stars and thanks,

Johnny Sins

Suri has 10.00, and Savi has 3 times as much, or 30.00.

What is algebraic expression?

When we use numbers and words to solve a mathematical problem, we are using algebraic expressions.

Let's use algebra to solve the problem.

Let's say Suri has x amount of money. Then we know that Savi has 3 times as much money, or 3x. We also know that together they have 40.00. So we can write an equation:

x + 3x = 40

Simplifying this equation, we get:

4x = 40

Dividing both sides by 4, we get:

x = 10

So Suri has 10.00, and Savi has 3 times as much, or 30.00.

To check, we can verify that their total is 40.00:

10 + 30 = 40

So, the solution checks out.

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The probability of the selected coin showing heads is 0.77, or 77%.

Probability is the measure of the likelihood of an event occurring. In this scenario, we have three coins in a box, each with different properties.

To calculate the probability of an event occurring, we need to divide the number of favorable outcomes by the total number of possible outcomes. In this case, there are three possible coins we could select, each with a different probability of showing heads.

Now, we need to determine the total number of possible outcomes, which is simply the number of coins we have, which is three.

Next, we need to determine the number of favorable outcomes. For Coin 1, the probability of showing heads is 1 (since it has two heads). For Coin 2, the probability of showing heads is 0.5 (since it is a fair coin with equal probability of heads and tails). For Coin 3, the probability of showing heads is 0.8.

To calculate the probability of showing heads when we randomly select one of these coins, we need to weigh the probabilities of each coin being selected with their corresponding probabilities of showing heads.

Let's say that the probability of selecting each coin is equal (since we have no information to suggest otherwise). Then, the probability of selecting Coin 1 is 1/3, the probability of selecting Coin 2 is 1/3, and the probability of selecting Coin 3 is 1/3.

To calculate the overall probability of showing heads, we can use the following formula:

P(heads) = (P(Coin 1) * P(heads on Coin 1)) + (P(Coin 2) * P(heads on Coin 2)) + (P(Coin 3) * P(heads on Coin 3))

= (1/3 * 1) + (1/3 * 0.5) + (1/3 * 0.8)

= 0.77

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The total amount of money Mario, Giana, and Allan split was $2160. Giana received $640 less than Allan did.

Let x represent the sum of money Mario got.

Giana got three times

Allan got seven times

Total: 2x, 3x, 7x, or 12x.

Allan received $640 more than Giana, therefore

7x = 640 + 3x

4x = 640

x = 160

Total amount split is 12x, or 12 * 160, or $2160.

The total amount of money Mario, Giana, and Allan split was $2160. To determine the overall amount, we must first determine how much money each person received. We know that Giana received three times as much as Mario did, while Allan received seven times as much. So, using 2x, 3x, and 7x, respectively, where x is the amount of money Mario received, we can express how much each person earned.

We may draw up an equation to determine how much money Mario received by taking into account the fact that Allan received $640 more than Giana. It goes like this: 7x = 640 + 3x. x = 160 is the result of solving this equation. Mario thus received $160 whereas Giana received $480 after multiplying 3x by 3 * 160. Allan received $1120 since he was paid $640 more than Giana (7x = 7 * 160). Mario, Giana, and Allan divided the total amount of money as follows: 2x + 3x + 7x = 12x = 12 * 160 = $2160.

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The cost per minute is $0.04.

Unit rates are defined as rates that are expressed as multiples of 1, such as 2 feet per second or 5 miles per hour.

Given:

Sahalin cellphone plan costs $30 a month.

In a month of may she used cellphone 12.5 hours.

First convert 12.5 hours in minute.

As we know 1 hour = 60 minutes

So, 12.5 hours = 12.5 x 60

                       = 750 minutes

and, the cost per minute

= 30/750

= 0.04

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The new perimeter of the quadrilateral is  157.2 ft

Consider the following diagram.

We name the quadrilateral ABCD such that side AB = 12.2 ft, side BC = 16 ft, side AD = 12 ft

Let us assume that the perpendicular or height be DE = 12 ft

From figure we can observe that side AB = side CD

So, side CD = 12.2 ft

The quadrilateral is enlarged by a scale factor of 3

so, the dimensions of the new quadrilateral would be,

A'B' = 3 × AB

     = 36.6 ft

So, C'D' = 36.6 ft                  ............(as AB = CD)

B'C' = 3 × BC

B'C' = 48 ft

And A'D' = 3 × AD

A'D' = 36 ft

We know that the perimeter of quadrilateral is the sum of all the four sides.

So, the perimeter of new quadrilateral A'B'C'D' would be,

A'B' + B'C' + C'D' + A'D'

= 36.6 + 48 + 36.6 + 36

= 157.2 ft

Therefore, the perimeter is 157.2 ft

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Find the complete question below.

Answer:First, we need to find which number when substituted into the equation will give the answer zero. Therefore is a factor. Factorise the quadratic until the expression is factorised fully. Therefore the roots occur when = -3, -2 and 1.

Step-by-step explanation:

Answer:

by reducing it into a quadratic equation and then solving

Step-by-step explanation:

Two ways of solving the system of equations are:

Here we want to identify two ways of solving the system of equations:

-2x + 3y = -5

3x - 4y = 6

One way is using the elimination method, then the option E is true, if we multiply the first equation by 4 and the second by 3 and then we add the two equations, the variable y will be eliminated and we could solve the equation for x.

We also could eliminate the variable x, to do so, we need to multiply the first equation by 3 and the second by 2, and add the two equations.

Then option C is also true.

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Answer:

The ordered pair for point B after it has been reflected over both the x and y-axis is (4, 6).

This is due to the rule for reflecting over the x-axis, which is to negate the value of the y-coordinate of each point, but leave the x-value the same. This means that after reflecting point B over the x-axis, it's new coordinates would be (-4, 6).

The rule for reflecting over the y-axis is to negate the value of the x-coordinate of each point, but leave the y-value the same. This means that after reflecting point B' over the y-axis, it's new coordinates would be (4, 6).

The image of the point after the dilation of scale factor k = -1/2 is:

(-1, -1/3)

If we have a point (x, y), and we dilate it by a scale factor k with the center of dilation on the origin, then the new coordinates of the point are (k*x, k*y).

Here the original point is (3, 1)

And the scale factor is k = -1/3

Then the image of the point after the dilation is:

( -1/3*3, -1/3*1)

(-1, -1/3)

That is the image.

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Answer:

We can write an inequality to represent the weight that the truck can carry:

Weight of Refrigerators + Weight of Pianos <= 6500

Let x be the number of refrigerators and y be the number of pianos. Then we can write:

300x + 475y <= 6500

To determine if 10 refrigerators and 9 pianos would overload the truck, we can substitute the values into the inequality:

300 * 10 + 475 * 9 <= 6500

3000 + 4275 <= 6500

7275 <= 6500

Since 7275 is greater than 6500, this means that 10 refrigerators and 9 pianos would overload the truck.

Graphically, we can plot the points representing the weight of the refrigerators and pianos on the x-y plane, and shade the region below the line representing the inequality to show the combinations of refrigerators and pianos that would not overload the truck. Any point above the line would represent a combination of refrigerators and pianos that would overload the truck.

Answer:

7275lb

Step-by-step explanation:

Let R be the number of refrigerators and P be the number of pianos. The total weight of the load can be represented as:

Weight = 300R + 475P

The weight must be less than or equal to 6500lb, so we have the inequality:

300R + 475P <= 6500

To graph this inequality, we can first rewrite it in slope-intercept form:

475P <= 6500 - 300R

P <= (6500 - 300R) / 475

Next, we can plot the points (0, 13.68), (22, 0) on the coordinate plane, where (0, 13.68) corresponds to the y-intercept and (22, 0) corresponds to the x-intercept. The graph will be a line that starts at the y-intercept and goes down to the right, passing through (22, 0).

The truck could carry up to 22 refrigerators (when R = 22, P = 0), or up to 13.68 pianos (when R = 0, P = 13.68), or any combination of refrigerators and pianos that results in a weight of less than or equal to 6500lb.

As for the specific case of 10 refrigerators and 9 pianos, the weight can be calculated as:

Weight = 300 * 10 + 475 * 9 = 3000 + 4275 = 7275

This would overload the truck, as the weight of 7275lb is greater than the maximum allowed weight of 6500lb.

The perimeter of a square with length of a side given as 2/3g + 1 cm is 8/3g + 1 cm.

Let's call the length of a side of the square "s". According to the information given, s = 2/3g + 1 (in cm).

The perimeter of a square is equal to the sum of the lengths of all four sides, so we can write an expression to represent the perimeter as follows:

P = 4s

Substituting the expression for s from above, we get:

P = 4(2/3g + 1)

So, the expression for the perimeter of the square in terms of g is:

P = 4(2/3g + 1)

Therefore, P = 8/3g + 1.

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Complete question: the length of a square is( 2/3g+1)cm use this information to write an expression to represent the perimeter of the square.

The functions are solved for the inverses and matched as follows

1. not inverse function

2. not inverse function

3. inverse functions

4. not inverse function

5. not inverse function

6. not inverse function

1. g(n) = -1/n + 1 and f(n) = -1/(n - 1)

say y = g(n) = -1/n + 1

y - 1 = -1/n

-y + 1 = 1/n

n = -1/(y - 1)

interchanging the variables

y = -1/(n - 1)

2. The cube root of 4 not in the inverse hence this is not inverse function.

3. g(x) = (x + 2)³ - 3 and f(x) = ∛(x + 3) - 2

say y = g(x) = (x + 2)³ - 3

y + 3 = (x + 2)³

x + 2 = ∛(y + 3)

x = ∛(y + 3) - 2

interchanging the variables

y = f(x) = ∛(x + 3) - 2 this is inverse functions

4.f(n) = 4/(n - 1) - 3 and g(n) = -2/n + 1

say y = f(n) = 4/(n - 1) - 3

y + 3 = 4/(n - 1)

1 / (y + 3) = (n - 1) / 4

4 / (y + 3) = n - 1

4 / (y + 3) + 1 = n

interchanging the variables

y = 4/(n + 3) + 1 this is not inverse functions

5. g(x) = 4/(x - 3) - 2 and f(x) = -2/(x + 1)

say y = g(x) = 4/(x - 3) - 2

y + 2 = 4/(x - 3)

1 / (y + 2) = (x - 3) / 4

4 / (y + 2) = x - 3

4 / (y + 2) + 3 = x

interchanging the variables

y = 4/(x + 2) + 3 this is not inverse functions

6. f(x) = 2/(x - 3) - 1 and g(x) = -3(-x + 2) - 2

say y =  f(x) = 2(x - 3) - 1

y + 1 = 2/(x - 3)

1 / (y + 1) = (x - 3) / 2

2 / (y + 1) = x - 3

2 / (y + 1) + 3 = x

interchanging the variables

y = 1/(x + 1) + 3 this is not inverse functions

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