Sara reduced the time it takes her to run a mile from 12 minutes to 8 minutes. Which is closest to Sara's


percent decrease in the time it takes her to run a mile?



A. 14%


B. 25%


C. 33%


D. 75%

Entonces, concluimos que las papas cuestan 4 pesos por kilogramo y el arroz cuesta 9 pesos por kilogramo.

Para resolver este problema, necesitamos plantear un sistema de ecuaciones lineales con dos incógnitas: el precio por kilogramo de papas y el precio por kilogramo de arroz. Podemos escribir:

12p + 6r = 102

9p + 13r = 153

Donde p es el precio por kilogramo de papas y r es el precio por kilogramo de arroz. Podemos resolver este sistema de ecuaciones usando el método de eliminación. Multiplicando la primera ecuación por 13 y la segunda ecuación por -6, obtenemos:

156p + 78r = 1326

-54p - 78r = -918

Sumando estas ecuaciones, obtenemos: 102p = 408

Dividiendo ambos lados por 102, encontramos que p = 4. Por lo tanto, el precio por kilogramo de papas es de 4 pesos.

Para encontrar el precio por kilogramo de arroz, podemos sustituir p = 4 en una de las ecuaciones originales y resolver para r. Por ejemplo, usando la primera ecuación:

12(4) + 6r = 102

48 + 6r = 102

6r = 54

r = 9

Por lo tanto, el precio por kilogramo de arroz es de 9 pesos.

Entonces, concluimos que las papas cuestan 4 pesos por kilogramo y el arroz cuesta 9 pesos por kilogramo.

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The points (0,10) and (-8,4) are solutions of the system of inequalities.

A system of inequalities refers to a set of two or more inequalities that are graphed together on the same coordinate plane. Each inequality in the system represents a region in the plane where the solution to that inequality lies.

To determine if a point is a solution of the system of inequalities, we need to check if it satisfies both inequalities. Let's check each point given:

(4,6):

8(4) + 5(6) = 47 > 40 (true)

-6(4) + 2(6) = -14 ≥ 18 (false)

(9,8):

8(9) + 5(8) = 97 > 40 (true)

-6(9) + 2(8) = -40 ≥ 18 (false)

(0,10):

8(0) + 5(10) = 50 > 40 (true)

-6(0) + 2(10) = 20 ≥ 18 (true)

(5,-6):

8(5) + 5(-6) = 34 > 40 (false)

-6(5) + 2(-6) = -30 ≥ 18 (false)

(-1,-8):

8(-1) + 5(-8) = -44 ≤ 40 (false)

-6(-1) + 2(-8) = 10 ≥ 18 (false)

(-8,4):

8(-8) + 5(4) = -24 ≤ 40 (true)

-6(-8) + 2(4) = 52 ≥ 18 (true)

Therefore, the points (0,10) and (-8,4) are solutions of the system of inequalities.

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I'm sorry, but you have not provided any data or information about the car's motion. Without this information, I cannot answer your questions accurately. Please provide more details or context about the car's motion.

I am unable to answer these specific questions without any given data. Please provide the data related to the car's acceleration, and I will be happy to help you with the analysis.

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The appropriate null and alternative hypotheses for the experiment are:

Null hypothesis (H0): According to null hypothesis, the average time it takes for a person to experience pain relief from the new pain reliever is not beyond 15 minutes.

Alternative hypothesis (Ha): According to Alternative hypothesis, the average time it takes for a person to experience pain relief from the new pain reliever is significantly less than 15 minutes, indicating that the new ingredient does speed up pain relief.

The alternative and null hypotheses can be written as follows in symbols:

H0: = 15 (where μ is the population mean time for pain relief from the new pain reliever)

Ha: μ < 15

The one-tailed hypothesis test assumes that the new component of the painkiller can only reduce the duration of pain alleviation, not lengthen it. As a result, the rejection region will be in the left tail of the distribution, while the alternative hypothesis is one-tailed to the left.

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The value of y is 116°.

Three given Adjacent angles are 28°, 36° and y°.

When two angles are adjacent, they have a common side between them and share a common vertex where the two sides meet. The angles are said to be adjacent because they are next to each other.

We know that if a ray stands on a straight line, then the sum of adjacent angles is 180°.

So, 28° + y° + 36° = 180°

y° + 64° = 180°

Subtracting 64° from both sides.

y°- 64° = 180° - 64°

y° = 116°

Hence, the value of y is 116°.

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The gardener used 36.9 gallons of gasoline in the lawnmowers in that month.

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

We know that the gardener used a total of 61.5 gallons of gasoline in a month and that 3/5 of that total was used in the lawnmowers.

To find out how much gasoline the gardener used in the lawnmowers, we need to multiply the total amount of gasoline by 3/5:

61.5 gallons x 3/5 = 36.9 gallons

Therefore, the gardener used 36.9 gallons of gasoline in the lawnmowers in that month.

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The probability of not spinning 5 is 81/200.

What is the probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: You spin the spinner, flip a coin, then spin the spinner again.

We have to find the probability of not spinning a 5. Flipping tails, then spinning a 5.

P(not spinning a 5) = 9/10

P(heads)= 1/2 because there is an equal chance to get heads or tails

P(not spinning a 5)= same as before, 9/10 (independent events).

= [tex]\frac{9}{10}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{10}[/tex]

= [tex]\frac{81}{200}[/tex]

Hence, the probability of not spinning 5 is 81/200.

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The ratio to make the portrait proportional is width/42 = 5/8

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

Photograph that is 5 inches wide by 8 inches high.

This means that

Ratio = width/height

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

Ratio = 5/8

Given that he wants the portrait to be proportional to the photograph and 42 inches high.

Then, we have

width/42 = 5/8

Hence, the ratio to make the portrait proportional is width/42 = 5/8

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Answer:

Absoblute value Reflection

Step-by-step explanation:

You can tell it's absolbute value because of the parbolas, and it's reflected acroos the two points. Give brainliest please!

Tardarán aproximadamente 3.6 horas.

Para resolver este problema, podemos establecer una relación proporcional entre el número de hojas impresas y el tiempo requerido. Si 4 impresoras tardan 3 horas en imprimir 5000 hojas, podemos establecer la proporción

4 impresoras / 3 horas = 5000 hojas / x horas

Donde x representa el tiempo que tardarán en imprimir 6000 hojas. Podemos resolver esta proporción utilizando regla de tres:

4 / 3 = 5000 / x

Multiplicando en cruz, obtenemos:

4x = 3 * 5000

4x = 15000

x = 15000 / 4

x = 3750

Por lo tanto, tardarán aproximadamente 3750 horas en imprimir 6000 hojas.

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The statement that best describes how pollination begins is that it starts when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower. Pollination is an essential step in the reproduction of plants, and it allows for the exchange of genetic material between different plants.

Pollination can occur through various methods, including wind, water, and animals such as bees, butterflies, and birds. Once the pollen is transferred, it begins to grow and develop, ultimately leading to the formation of a seed and the growth of a new plant.

Pollination is vital to the continuation of plant life, and without it, many plant species would not be able to survive. It is essential for plant breeders to understand the pollination process, as they can use it to cross different plant varieties and produce new and improved plants.

In conclusion, pollination begins when pollen from the male reproductive organ of a flower is transferred to the female reproductive organ of the same or a different flower, allowing for the exchange of genetic material and the growth and development of new plants.

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Area of triangle = 45.5 in square ≈ 45.5 (rounded to the nearest tenth).

The area of a triangle given its base and height.

The formula for the area of a triangle is:

Area = (1/2) x base x height

In this formula, "base" refers to the length of the side of the triangle that is perpendicular to the height, and "height" refers to the length of the line segment that is perpendicular to the base and passes through the opposite vertex.

In the problem you provided, the base of the triangle is given as 13 inches, and the height is given as 7 inches. So we can plug these values into the formula:

Area = (1/2) x 13 in x 7 in

= 45.5 in square

The units for area are square units, so we write the answer as "inches squared" or "in square".

Finally, we are asked to round the answer to the nearest tenth. Since there is only one decimal place in the answer, the "tenth" place is the same as the "one" place. Therefore, we look at the digit in the "one" place (which is 5) and round up to the nearest whole number. This gives us:

Area of triangle ≈ 45.5 (rounded to the nearest tenth).

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The solution to the expression -(-4) (-6)-3/5(10+5)/1/3 is 15.

To solve this expression, we need to follow the order of operations, which is also known as PEMDAS (parentheses, exponents, multiplication and division, addition and subtraction):

Start with the parentheses: (-4) (-6)= 24, so we can rewrite the expression as:

24-3/5(15)/(1/3)

Now we need to simplify the expression inside the parentheses by adding 10 and 5, which equals 15. Then we need to simplify the division by multiplying the numerator by the reciprocal of the denominator, which is the same as dividing by 1/3. We can rewrite this expression as:

24-3/5*15*3

Multiply 3/5 and 15 first, then multiply that result by 3: 24-9.

Finally, subtract 9 from 24 to get the final answer: 15.

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Answer:

y = 9

Step-by-step explanation:

• Parallel lines have equal slopes

calculate the slope m of  TU using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = T(- 7, 4 ) and (x₂, y₂ ) = U(- 2, - 6 )

[tex]m_{TU}[/tex] = [tex]\frac{-6-4}{-2-(-7)}[/tex] = [tex]\frac{-10}{-2+7}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2

now calculate the slope of VW and equate to - 2

with (x₁, y₁ ) = V(8, 7 ) and (x₂, y₂ ) = W(7, y )

[tex]m_{VW}[/tex] = [tex]\frac{y-7}{7-8}[/tex] = [tex]\frac{y-7}{-1}[/tex]

now equating gives

[tex]\frac{y-7}{-1}[/tex] = - 2 ( multiply both sides by - 1 to clear the fraction )

y - 7 = 2 ( add 7 to both sides )

y = 9

t\The depreciation expense for the year ended December 31, 2009 using the straight-line method is $23,333.33.

The total cost of the equipment is $997,500 ($935,000 + $7,500 + $55,000). The depreciable cost is calculated by subtracting the salvage value from the total cost, which is $960,000 ($997,500 - $37,500).

To calculate the annual depreciation expense using the straight-line method, divide the depreciable cost by the useful life of the equipment. The annual depreciation expense is $106,666.67 ($960,000 ÷ 9).

Since the equipment was only used for a portion of the year, we need to prorate the annual depreciation expense based on the number of units produced.

The depreciation expense for the year ended December 31, 2009 is calculated as follows:

Depreciation Expense = (Annual Depreciation Expense ÷ Total Units of Production) x Units Produced in 2009

Depreciation Expense = ($106,666.67 ÷ 1,920,000) x 426,000

Depreciation Expense = $23,333.33

Therefore, the depreciation expense for the year ended December 31, 2009 using the straight-line method is $23,333.33.

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Answer:

2/5 < 0.42 < 43% < 3/7

Step-by-step explanation:

Let's convert them all to decimals:

43% = 0.43

2/5 = 0.4

3/7 = 0.428571...

0.42 = 0.42

Now we can arrange them in ascending order:

0.4

0.42

0.43

0.428571...

The height of the tree is approximately 20.1 feet.

To determine the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the length of the shadow) of a right triangle.

tan(35°) = height of tree / 35 feet shadow

Rearranging this formula, we get:

height of tree = 35 feet shadow x tan(35°)

Plugging in the given values and using a calculator, we get:

height of tree = 35 x tan(35°) ≈ 20.1 feet

Therefore, the height of the tree is approximately 20.1 feet.

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Answer:

Jack now makes $10.45

Step-by-step explanation:

First, we need to find 10% of 9.50. To do that we must divide 9.50 by 10 or simply move the decimal one place to the left to get 0.95. 0.95 is 10% of 9.50. Now we must ADD 0.95 to 9.50 because Jack is getting a 10% raise.  0.95 + 9.50 = 10.45. Therefore Jack makes $10.45 per hour at his job.

We know that the value of CSC 0 is undefined if the point P(-1,0) is a point on the terminal side of angle 0, an angle in standard position.

If the point P(-1,0) is a point on the terminal side of angle 0, an angle in standard position, then we can use the Pythagorean theorem to find the value of the hypotenuse. The hypotenuse (r) is the distance from the origin to point P, and can be found using the formula r = sqrt(x^2 + y^2), where x = -1 and y = 0.

r = sqrt((-1)^2 + 0^2) = 1

Since csc 0 is the reciprocal of sin 0, and sin 0 = 0/1 = 0, we have:

CSC 0 = 1/sin 0 = 1/0 = undefined.

Therefore, the value of CSC 0 is undefined if the point P(-1,0) is a point on the terminal side of angle 0, an angle in standard position.

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Answer:

A≈166.28

Step-by-step explanation:

Answer:

A≈166.28

Step-by-step explanation:

The area of Coby's room is 80 square feet.

The area of a rectangle is given by the product of its length and width. Here, the length of the room is given as 10 feet and the width is given as 8 feet. Therefore, the area of the room is:

Area = Length x Width

Area = 10 feet x 8 feet

Area = 80 square feet

Hence, the area of Coby's room is 80 square feet. It is important to note that when calculating the area of a rectangle, the units of length are multiplied to obtain the unit of area. In this case, the units of length are feet, so the unit of area is square feet.

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The number of cubes of dimensions of [tex]\frac{1}{8}[/tex] foot that can fit into a rectangular prism of a length of 1 foot, a width of 1 [tex]\frac{3}{8}[/tex] foot, and a height of [tex]\frac{5}{8}[/tex] foot is 55.

Volume of cuboid = l * b * h

where l is the length

b is the breadth

h is the height

l = 1 foot

b = 1 [tex]\frac{3}{8}[/tex] foot = [tex]\frac{11}{8}[/tex] foot

h = [tex]\frac{5}{8}[/tex] foot

Volume of cuboid = 1 * [tex]\frac{11}{8}[/tex] * [tex]\frac{5}{8}[/tex]

= [tex]\frac{55}{64}[/tex] cubic foot

Volume of cube = [tex]s^3[/tex]

where s is the side

s = [tex]\frac{1}{8}[/tex] foot

Volume = [tex]\frac{1}{8}^3[/tex]

= [tex]\frac{1}{64}[/tex] cubic foot

Number of cubes = [tex]\frac{\frac{55}{64} }{\frac{1}{64} }[/tex]

= 55

The number of cubes that fit into the prism is 55.

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The probability of the two oldest Smith children being served first is 2/4 or 50%.

Assuming that all the children have an equal chance of being served first, there are a total of 4 possibilities for the order in which the two oldest Smith children can be served:

Out of these 4 possibilities, only the first 2 would satisfy the condition that the two oldest Smith children are served before the others. So the probability that the two oldest Smith children are served first is 2/4 or 50%.

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The balloon is rising at a rate of approximately 3.532 km/h at this moment.

We will use the tangent function in trigonometry and the concept of related rates.

Let x be the horizontal distance from the observer to the lift-off point (5 km) and y be the vertical distance from the ground to the balloon. The angle between the observer's line of sight and the horizontal is given as π/5.

We can use the tangent function:
tan(θ) = y/x

At the given moment, x = 5 km and θ = π/5, so:
tan(π/5) = y/5

Now, let's differentiate both sides with respect to time (t):
d(tan(θ))/dt = d(y)/dt / 5

We know that d(θ)/dt = 0.4 rad/h, so we can find d(tan(θ))/dt using the chain rule:
d(tan(θ))/dt = (sec^2(θ)) * d(θ)/dt
d(tan(θ))/dt = (sec^2(π/5)) * 0.4

Now, substitute this back into the first equation and solve for d(y)/dt:
(sec^2(π/5)) * 0.4 = d(y)/dt / 5
d(y)/dt = 5 * (sec^2(π/5)) * 0.4

After calculating the expression, you'll find that d(y)/dt ≈ 3.532 km/h. Thus, the balloon is rising at a rate of approximately 3.532 km/h at this moment.

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Answer:

1. 17.2

2. 1/4 or 0.25

3. 3/10 or 30%

4. 15/16

I hope this helped

Step-by-step explanation:

This is a statistical question because it involves collecting data. Most employees work around 40 hours each week.

a. This is a statistical question because it involves collecting data on the number of hours worked by employees each week and analyzing the distribution or pattern of the data.

b. Here's a dot plot of the data provided:

   37: •
   38: ••
   39: ••
   40: ••••••••
   41: •••
   42: ••
   43: •
   47: •

The distribution of the data in the dot plot shows that the majority of employees worked around 40 hours each week, as this is where the data is most heavily clustered. Most of the data are clustered around 40 hours, with a peak at 40 hours. There is a gap between 43 and 47 hours.

c. Based on the distribution of the data, most employees work about 40 hours each week.

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The value of the tangent segment b is 20.15.

The secant-tangent power theorem, also known as the tangent-secant theorem, states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

It is expressed as:

( tangent segment )² = External part of the secant segment + Secant segment.

From the diagram:

Tangent segment = WX = b

External part of the secant segment = YX = 14

Secant segment = ZX = 15 + 14 = 29

Plug these values into the above formula and solve for b.

( tangent segment )² = External part of the secant segment + Secant segment.

b² = 14 × 29

b² = 406

b = √406

b = 20.15

Therefore, the value of b is 20.15.

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To find f(x) for the given function f(x) = 1/1-x, we simply replace the "x" in the equation with whatever input value we want to evaluate the function at.

For example, if we want to find f(2), we would replace x with 2 and get:

f(2) = 1/1-2

f(2) = -1

Similarly, if we want to find f(a), we would replace x with a and get:

f(a) = 1/1-a

Therefore, f(x) = 1/1-x, where x is any input value.
To find f(x) for the given function, simply rewrite the function as it is:

f(x) = 1 / (1 - x)

Here, f(x) represents the function value for any input x, and the expression on the right side indicates how to calculate it.

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Answer:

Probability of spinning 1 or a 2

Fraction=6/8

decimal=0.75

Let me know if it helped

To put the numbers in order from least to greatest, we can use the number line: -3.5 -2.1 -1 -0.5 0.5 2 4 4.2 5 5.8  Two numbers that are opposites and each more than 6 units away from 0 are -7 and 7.

First, let's put the numbers in order from least to greatest:

-3.5, -2.1, -1.5, -1, -0.5, 0.5, 3.5, 4, 4.2, 4.8, 5

Now, let's find two numbers that are opposites and each more than 6 units away from 0. One example would be -7 and 7. These numbers are opposites (since they have the same magnitude but different signs), and they are both more than 6 units away from 0.

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