on their next training run, pepe averaged a speed of 2/3 of a mile in 5 minutes, while paula averaged 1/4 of a mile in 2 minutes. if pepe and paula each ran at their individual pace for 60 minutes, how many total miles did they cumulatively run?

Both the methods can be used to solve a mixed fraction including a whole number and a fraction or solving the difference of a whole number and a fraction.

Mixed fractions are type of fractions which involve a whole number and a fraction. This is of the form a [tex]\frac{b}{c}[/tex]. This is actually a + [tex]\frac{b}{c}[/tex].

You can use either methods when solving a whole number and a fraction.

Let us take a whole number 3 and a fraction [tex]\frac{2}{10}[/tex] for instance.

First Method :

Solve it by cross multiplication.

Let the denominator of the whole number 3 be 1.

[tex]\frac{3}{1}[/tex] ± [tex]\frac{2}{10}[/tex] = [(3 × 10) ± (2 × 1)] / (1 × 10) = [30 ± 2] / 10

If the question is for adding, we get, [tex]\frac{3}{1}[/tex] + [tex]\frac{2}{10}[/tex] = (30 + 2) / 10 = 32/10

If the question is finding difference, we get, [tex]\frac{3}{1}[/tex] - [tex]\frac{2}{10}[/tex] = (30 - 2) / 10 = 28/10

Second Method :

Again let the denominator of the whole number be 1.

Find the LCD (Least Common Denominator) of 1 and 10.

This is 10.

So we have to make the denominator of [tex]\frac{3}{1}[/tex] to 10.

Multiply both numerator and denominator with 10, we get 30/10.

A normal multiplication of fractions, if the denominator is same add or subtract the numerators let the denominator be as such.

Now add or subtract [tex]\frac{30}{10}[/tex] ± [tex]\frac{2}{10}[/tex] = (30 ± 2) / 10.

Hence both the methods can be used.

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a. [tex]6x+11=55[/tex]

Subtract 11 from both sides:

[tex]6x+11-11=55-11[/tex]

[tex]6x=44[/tex]

Divide both sides by 6:

[tex]\dfrac{6x}{6} =\dfrac{44}{6}[/tex]

[tex]x=7.333333[/tex]

___________________________

b. [tex]-3x-18=39[/tex]

Add 18 to both sides:

[tex]-3x-18+18=39+18[/tex]

[tex]-3x=57[/tex]

Divide both sides by -3:

[tex]\dfrac{-3x}{-3} =\dfrac{57}{-3}[/tex]

[tex]x=-19[/tex]

___________________________

c. [tex]2x-14=-28[/tex]

Add 14 to both sides:

[tex]2x-14+14=-28+14[/tex]

[tex]2x=-14[/tex]

Divide both sides by 2:

[tex]\dfrac{2x}{2} =\dfrac{-14}{2}[/tex]

[tex]x=-7[/tex]

___________________________

d. [tex]7x+9=58[/tex]

Subtract 9 from both sides:

[tex]7x+9-9=58-9[/tex]

[tex]7x=49[/tex]

Divide both sides by 7:

[tex]\dfrac{7x}{7} =\dfrac{49}{7}[/tex]

[tex]x=7[/tex]

___________________________

Only option d had a solution of x = 7.

Answer:

-6°

Step-by-step explanation:

26.4 - 32.4 = -6

Subtract the absolute values of the both number and give the sign of the larger absolute value.

32.4 - 26.4 = 6

The sign will be negative because -32.4 has a larger absolute value (farther from zero) than 26.4

Answer:

- 6°F.

Step-by-step explanation:

  26.4

-  32.4

= -6.0

The temperature at midnight:

-6°F.

On solving the provided question we can say that - probability distribution, E(X)= 47.5, V(X)= 128.75, [tex]E(X^{2})[/tex] = 2605

A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that different possible experiment results will occur. The sample space and event probabilities are used to build a mathematical description of random occurrences.

E(X)= (20 * 0.05) + (30 *0.05)+ (40 * 0.35) + (50 * 0.20) + (60 *0.35)

      = 1+ 1.5 + 14 + 10 + 21

      = 47.5

V(X)= ((20-38)2 * 0.05) + ((30-38)2 *0.05)+ ((40-38)2 * 0.35) + (50-38)2 * 0.20) + ((60-38)2 *0.35)

      = 16.2 + 3.2 + 1.4 + 28.8 +169.4

      = 128.75

[tex]E(X^{2})[/tex]=

              =(202 * 0.05) + (302 *0.05)+ (402 * 0.35) + (502 * 0.20) + (602 *0.35)

             = 20 + 45 + 560 + 500 +1260

            =2605

[tex]V(X^2)[/tex]   =  2605 - ( 47.5)2

               = 2385 - 2256.25

          =128.75

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Answer:

0-2 sec

Step-by-step explanation:

From the graph you can see the height is going UP from 0-2 sec...from then on it is going downward....

The equations represent circles that have a diameter of 12 units and a center that lies on the y-axis  is x2 + (y – 3)2 = 36,x2 + (y – 3)2 = 36

How to Find diameter of the circle?

The standard form for finding the equation of a circle is expressed as;

(x-a)^2 + (y-b)^2 = b=r^2

where;

(a, b) is the center of the circle

r is the radius of the circle

Given the following:

diameter = 12 units

radius = 12/2 = 6 units

By substituting the values we these two equations.

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The SUV will be $5,299.13 worth than the car 5 years after their model years.

What is the meaning of rounded to the nearest cent?

Look at the number to the right of the whole cents when rounding money to the closest cent. In this instance, it is 9. Increase the cents by one if the figure is five or above. The cents should remain the same if the number is four or less. Given that 9 is more than 5, $3.299 equals $3.30.

Given that,

The value of a car can be predicted by using the function

f(x)=12,000(0.89)^x

Where x years from its model year.

To find the current value of the car, put x = 0 in the model equation:

f(0)=12,000(0.89)^0

f(0) = 12,000.

To find the value of the car after 5 years, put x = 5 in the model equation:

f(5)=12,000(0.89)^5

f(5) = 6700.871

The difference of the value of car is 12,000 - 6700.871 = $5299.129 = $5299.13 (rounded to the nearest cent)

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The solution of the mixed number as a whole number is 11.4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

A mixed number is the combination of a whole number and a proper fraction. It usually denotes a number between two whole numbers.

The given fraction is 11(⁴/₁₀). The mixed number can be simplified as below,

E = 11(⁴/₁₀)

E = 114 / 10

E = 11.4

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Answer:

1/2

Step-by-step explanation:

Let's say the number is 1.5

1.5 = 1 + 0.5

(1.5 = 1 + 0.5)*10 ==> multiply by 10 to remove decimals

15 = 10 + 5

5 is half of 10

Hence, 0.5 is half of 1 ==> 0.5 = 1/2

Salaried employees get paid more for additional hours worked but they must keep up with their responsibilities and complete necessary tasks even if that means working extra hours. The correct option is A

Salaried employees can be defined as someone who receives a fixed amount of pay salary regardless of how many hours they work each weeks. Salaried employees enjoy the security of steady paychecks and they tend to pull in higher overall income than hourly worker.

Therefore the correct option is A Salaried employees get paid more for additional hours worked.

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Answer:

use the Pythagoras theorem

Step-by-step explanation:

x²+(2x)²=x²+4x²=5x²

square root of 5x²= (square root of 5)x

The equation of the line that represents the straight line in the graph will be y = (3/2)x.

An association between various factors brings about a straight model when a diagram is shown. The variable will have a level of one.

The straight condition is given as,

y = mx + c

Where m is the incline of the line and c is the y-block of the line.

From the figure, the line is passing through the origin. Then we have

y = mx + c

0 = m (0) + c

c = 0

Then the equation of the line is written as,

y = mx

From the figure, the line also passes through points (4, 6). Then we have

6 = 4m

m = 3/2

Then the equation of the line is given as,

y = (3/2)x

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Answer: The value of x-[tex]\sqrt{x}[/tex]= 2

Step-by-step explanation: [tex]x^{2}[/tex] - 16[tex]\sqrt{x}[/tex]

Let [tex]u= \sqrt{x}[/tex], then

[tex]u^{2} = x\\^u{4} =x^{2}[/tex]

substituting these into the original equation

[tex]u^{4} -16u -12 =0[/tex]

This factor is easy as -

[tex](u^{2} -2u -2) (u^{2} +2u +6) =0[/tex]

[tex]u^{2} -2u -2=0\\[/tex]

The value of the integral [tex]\int\limits^2_0 {f(x)} \, dx[/tex] is 5. The value of the integral [tex]\int\limits^5_2 {f(x)} \, dx[/tex] is 0. The value of the integral [tex]\int\limits^8_0 {f(x)} \, dx[/tex] is 25.

The definite integral of a function over a limit represents the area under the curve bounded by the limit as given in integration.

The integral represents the area under the curve.

(a) [tex]\int\limits^2_0 {f(x)} \, dx[/tex] = area of the triangle with base 2 and height 5.

Area = (1/2)2 x 5 = 5 units square

(b) [tex]\int\limits^5_2 {f(x)} \, dx[/tex] = area under the triangle with base 1 and height 5 - area above the triangle with base 1 and height 5 = 0

(c) [tex]\int\limits^8_0 {f(x)} \, dx=\int\limits^2_0 {f(x)} \, dx+\int\limits^4_2 {f(x)} \, dx+\int\limits^8_4 {f(x)} \, dx[/tex]

⇒ 5 + 0 + 4 x 5 = 25 units sqaure.

Hence "integral [tex]\int\limits^2_0 {f(x)} \, dx[/tex] is 5. Integral [tex]\int\limits^5_2 {f(x)} \, dx[/tex] is 0. The value of the integral [tex]\int\limits^8_0 {f(x)} \, dx[/tex] is 25".

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Answer:

To determine at what depth the rescue sub will meet the injured diver, we need to first calculate how long it will take the diver to reach the surface. Because the diver is rising at a rate of 10 feet per minute, and she has a 7 minute supply of air, it will take her 7 minutes to reach the surface.

Next, we need to calculate how long it will take the rescue sub to reach the diver. Because the diver is 250 feet below the surface, and the sub is descending at a rate of 30 feet per minute, it will take the sub 250 feet / 30 feet/minute = <<250/30=8.33>>8.33 minutes to reach the diver.

Finally, to determine at what depth the two will meet, we need to subtract the time it takes the diver to reach the surface (7 minutes) from the time it takes the sub to reach the diver (8.33 minutes). This gives us a total time of 8.33 minutes - 7 minutes = 1.33 minutes.

Since the diver is rising at a rate of 10 feet per minute, and the total time is 1.33 minutes, the depth at which the two will meet is 1.33 minutes * 10 feet/minute = 13.3 feet. Rounding to the nearest foot, we get a depth of 13 feet. Therefore, the rescue sub and the diver will meet at a depth of approximately 13 feet.

Answer:

the eqn given by the function is y=9---(1)

given point is(-3,9)=(X,y)

we know,

y=mx

mx=9 [from 1]

or,m(-3)=9 [from point]

or,m=9/-3

:.m=-3

hence, slope=-3

1) curl = del x

2) grad(div ) = del(div )

3) div(curl(grad )) = div(curl(grad))

What is Scalar field and Vector field?

1) The curl of a vector field is a vector field that describes the local rotational motion of the field. It is defined as the cross product of the del operator (a vector operator that operates on scalar and vector fields) and the vector field:

    curl = del x

2) The gradient of the divergence of a vector field is a scalar field that describes the local rate of change of the divergence of the field. It is defined as the del operator applied to the divergence of the field:

   grad(div ) = del(div ).

3) The divergence of the curl of the gradient of a scalar field is a scalar field that describes the local rate of change of the curl of the gradient of the field. It is defined as the divergence of the curl of the gradient of the field:

   div(curl(grad )) = div(curl(grad)).

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1/6 because $160 as a fraction is 1/6

Answer:

angle A is obtuse

angle B is acute

angle C obtuse

angle D is right

Answer:

Step-by-step explanation:

A is Obtuse Angle

B is Acute Angle

C is Obtuse Angle

D is Right Angle

The linear inequalities that represent the graph are y ≤ (1/2)x - 1 and y > 2x - 4. Then the correct option is C

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

The intercepts are 2 and -1. Then the equation of the line is given as,

x / 2 + y / (-1) ≤ 1

y ≤ (1/2)x - 1

The intercepts are 2 and -4. Then the equation of the line is given as,

x / 2 + y / (-4) > 1

y > 2x - 4

The straight disparities that address the diagram are y ≤ (1/2)x - 1 and y > 2x - 4. Then, at that point, the right choice is C

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In order to determine the school that was given the fewest laptops, sort numerically in ascending order (second option)

A numeric data is a dataset that is made up of numbers. An example of a numeric data is the age of students in a class. The best colours of students in a class is not an example of numeric data.

The data that contains information on the number of laptops that was given to a school would be numeric. For example, a school can recieve 100 laptops while another school would receive 10 laptops.

In order to sort a numeric data in ascending order, it means that the smallest numbers would be arranged first.

For example consider this data set 2, 5 100, 1000, 4, 90. In order to arrange in ascending order, this would be the order of the numbers: 2, 4, 5, 90, 100, 1000.

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The number of cans Tara collected is 35.

Mrs. Kenney's class is holding a canned food drive for Thanksgiving. Tara collected 10 more cans than Phil. Laurie collected twice as many cans as Tara.  They collected 130 cans altogether.

Therefore, let's find the number of cans Tara collected.

Hence, using equation,

let

x = number of cans Phil collected

Number of cans Tara collected = x + 10

Number of cans Laurie collected = 2(x + 10) = 2x + 20

Therefore,

x + x + 10 + 2x + 20 = 130

4x + 30 = 130

4x = 130 - 30

4x = 100

x = 100 / 4

x = 25

Hence, Tara collected 25 + 10 = 35 cans.

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Answer:

3/8

Step-by-step explanation:

Simplify the following:

18/48

The gcd of 18 and 48 is 6, so 18/48 = (6×3)/(6×8) = 6/6×3/8 = 3/8:

Answer: 3/8

Answer:

7 hours

Step-by-step explanation-35/-5=7

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles. In other words, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the angles opposite those sides, then we have:

a/sin(A) = b/sin(B) = c/sin(C)

In the given triangle, we are given the values of B and c, so we can use the Law of Sines to find the other side lengths and angles. We have:

a/sin(A) = c/sin(C)

Since c = 43 and C = 135°, we can plug these values into the equation to find a:

a/sin(A) = 43/sin(135°)

To find the value of a, we just need to solve for a by multiplying both sides of the equation by sin(A). We have:

a = 43 * sin(A) / sin(135°)

We know the value of B, so we can use the Law of Sines again to find the value of A:

sin(A) / a = sin(B) / b

Since B = 8° and b is unknown, we can plug these values into the equation to find a:

sin(A) / a = sin(8°) / b

To find the value of A, we just need to solve for A by dividing both sides of the equation by sin(A)/a. We have:

A = asin(8°) / b

Now that we know the values of A and c, we can use the Law of Sines one more time to find the value of b:

sin(A) / a = sin(B) / b

Since A and a are unknown, we can plug the known values into the equation to find b:

sin(A) / a = sin(B) / b

To find the value of b, we just need to solve for b by multiplying both sides of the equation by sin(B)/b. We have:

b = sin(B) / (sin(A) / a)

At this point, we have all the necessary values to compute the values of a, A, and b. We can plug the known values into the equations we derived above to find the unknown values.

First, let's find the value of a:

a = 43 * sin(A) / sin(135°)

We know the values of A and B, so we can plug these values into the equation to find a:

a = 43 * sin(A) / sin(135°)

  = 43 * sin(180° - C - B) / sin(135°)

  = 43 * sin(180° - 135° - 8°) / sin(135°)

  = 43 * sin(37°) / sin(135°)

To compute the value of sin(37°), we can use a calculator or look up the value in a table of sines.

The 99% confidence interval for the mean wage of all judges is given as follows:

($61.5, $68.5).

We have the standard deviation only for the sample, hence the t-distribution is used to obtain the confidence interval.

The equation that defines the bounds of the confidence interval is given as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 25 - 1 = 24 df, is t = 2.797

The remaining parameters are given as follows:

[tex]\overline{x} = 65, s = 6.25, n = 25[/tex]

Hence the lower bound of the interval is calculated as follows:

65 - 2.797 x 6.25/5 = $61.5.

The upper bound of the interval is of:

65 - 2.797 x 6.25/5 = $68.5.

The problem asks for the 99% confidence interval for the mean wage of all judges.

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The solution to the system of linear equations is where they intersect which is at (- 0.5, 1.5).

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

From the graph of two lines in the coordinate system, every square box has a side length of 1 unit.

Now, The solution of the system is the point at which these two lines intersect.

By, Observing the graph we conclude that at (- 0.5, 1.5) they intersect and it is the solution of these two linear equations.

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The number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.

A region's size on a plane or curved surface is expressed by a measurement known as an area. Unlike the area of a plane region or plane area, which refers to the area of a shape or planar lamina, surface area describes the area of an open surface or the boundary of a three-dimensional object.

Given:

A sheet of the card is 20 centimeters by 30 centimeters,

The diameter of a badge, d = 60 mm or 6 cm,

Calculate the area of the sheet as shown below,

[tex]Area = length \times width[/tex]

Area = 20 × 30 = 600 cm²

Calculate the area of the badge as shown below,

[tex]Area = \pi d^2 / 4[/tex]

Area = 3.14 × 6² / 4

Area = 28.26 cm²

To calculate the number of badges[tex]No\ of\ badges = Area\ of \ sheet / Area \ of badge[/tex], use the formula given below,

Number of badges = 600 cm² / 28.26 cm²

Number of badges = 21.23 or 21

Therefore, the number of badges that can be cut from a piece of card, which is 20 centimeters by 30 centimeters, is 21.

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As Silas says Frotastic is a better deal. Because at Frotastic we get 1 ounce at $0.48

The ounce is derived from the Ancient Roman uncia, which was equal to one-twelfth (1/12) of a Roman pound and weighed around 27.35 grams, or 0.967 of an Avoirdupois ounce (libra). This originally meant "unit" because it originates from the Latin uno ('one'). The word "uncia" was borrowed twice: once into Old English as "ynsan" or "yndsan" from an unrecorded Vulgar Latin version that palatalized the "c" before the I to become the present English word "inch."

Here at Fromazing, 1 ounce of Frozen Yougurt costs $0.50 per ounce

whereas at Frotastic  5oz = $2.40

1oz = 2.40/5

= 0.48$

8oz = $3.84

1oz = 3.84/8

= $0.48

11 oz = $5.28

10z = 5.28/11

=$0.48

similar case for 14 oz = $6.72

1oz = 6.72/11

=$0.48

Therefore Frotastic is a better deal as Silas said

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The radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.

By using the expression to approximate the radius of a circle, we want to compare the radius of the two pools.

The expression for the radius of a circle is:

R = √(A/3)

Where A is the area of said circle.

The circular kiddie swimming pool has an area of 28ft^2, we just replace that in the above expression to get:

R =  √(28 ft^2/3) = 3 ft

The full-sized pool has an area of 113 ft^2, then its radius is:

R' = √(113 ft^2/3) = 6 ft

To see how much greater is the radius of the full-sized pool than the radius of the kiddie pool, we just take the quotient:

R'/R = 6ft/3ft

= 2

Hence, the radius of the full-sized pool is 2 times larger than the radius of the kiddie pool.

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