By increasing the pendulum's mass and releasing the pendulum from a greater height the maximum potential energy
will increase and the maximum kinetic energy will decrease.

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Answer is on the attachment...

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The equation p=5xy+q can be expressed in terms of p,q, and x as y = (p-q)/5x.

The equation p=7x+4q can be expressed in terms of p and q as x = (p-4q)/7x.

Given in the first equation, p = 5xy+q

p-q=5xy

y=(p-q)/5x

Here we need to express y in terms of p,q, and x so we need all these three variables on one side of the equation and y on the other side. Initially we more q to the left-hand side of the equation which makes it p-q=5xy. Now we divide the left-hand side and the right-hand side by 5x making the equation y = (p-q)/5x.

Similarly in the second equation, p = 7x+4q

p-4q = 7x

x = (p-4q)/7

Here we need to express x in terms of p and q so we need all these two variables on one side of the equation and the term x on the other side. First, we will move 4q to the left-hand side of the equation which will make it p-4q=7x. Now, we will divide the whole equation by 7 which will make the equation x = (p-4q) / 7.

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Answer:

Step-by-step explanation:

3p. = 2m - 5q

-2m. = -3p - 5q

Divide through by -2

m. = (3p + 5q) \2

The equation can be rearranged and expressed in terms of p and q is m = (3p+5q)/2.

Given equation 3p = 2m - 5q

3p + 5q = 2m

(3p + 5q) / 2 =m

Hence, m = (3p+5q) / 2  

To express the equation in terms of p and q we need to put all the p and q terms to one side of the equation and m terms to another side of the equation. It can be easily seen that 3p is already on one side and we just need to bring a q term to this side which can be done by shifting 5q from the right-hand side to left-hand side. The equation is now 3p+5q. Now to get the equation in terms of m we need to divide the whole equation by 2 which will give m = (3p+5q) / 2.

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The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x 2 - x 1) 2 + (y 2 - y 1) 2. where (x 1, y 1) and (x 2, y 2) are the coordinates of the two points involved. The order of the points does not matter for the formula as long as the points chosen are consistent.

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Answer:

it is 5 units!

The answer is 6 groups of 0.7 tenths is 4.2. in the decimal form.

What is Decimals?

Decimals are a form of a number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

6 groups of ____ tenths is 4.2

4.2 ÷ 6 = 0.7

Hence,  6 groups of 0.7 tenths is 4.2

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A linear function that describes the cost of a trip, c, in terms of the number of miles, n will be "c=0.60n+0.67n" and cost per mile is $0.6 and $0.67 and the flat fee is $50.

Once you are aware of your mileage and total expenses, calculating cost per mile becomes a straightforward equation. Your cost per mile is calculated by dividing your total expenses by the total number of miles you have driven. Your expenses per mile are influenced by your variable and fixed costs, so you should probably pay closer attention to how much you're shelling out for each mile your drivers cover. You can better understand your primary costs and produce more accurate bids for new contracts by knowing your expenses at this specific level.

Here,

cost per mile,

20/30=$0.67/mile

30/50=$0.60/mile

c=0.60n+0.67n

flat fee,

=$30+$20

=$50

The cost per mile is $0.6 and $0.67, and the flat rate is $50. A linear function that expresses the cost of a trip, c, in terms of the number of miles, n, will be "c=0.60n+0.67n".

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Answer:

9/8 m = 21/8

or

9m/8 = 21/8

Step-by-step explanation:

3m = 7

3/8 × 3m = 3/8 × 7

9/8 m = 21/8

The simplified equation is 14x+8 which has infinitely many solutions as given in the question.

1.Remove parenthesis and combine like terms to simplify either side of the equation.

2.Isolate the variable term on one side of the equation using addition or subtraction.

3.To find the variable, use multiplication or division.

Given equation is:

12x-x+8+ 3x

= 11x+3x+8

=14x+8

Therefore, the simplified equation is 14x+8 which has infinitely many solutions.

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The difference between the distance between the two cities if of 14.842 latitudes.

The earth has one latitude running right in the center called the equator. On either side of the equator, there are 90 more latitudes each.

Therefore, the earth has 181 latitudes.

Now if we see the image we can see that all these latitudes fall on the vertical diameter of the Earth.

Hence the distance covered by all 181 latitudes = 2 X radius of the Earth

= 2 X 6378 km

= 12756

Assuming that all the latitudes are equidistant, we get the distance between 2 latitudes to be

12756/181

= 70.475 km

Let the two cities be A and B. It is given that the distance between the two cities is 1046 km and one is due north of the other.

Therefore the difference in latitudes between the two cities is

1046/70.475

= 14.842 latitudes

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Answer:

Step-by-step explanation:[tex]x2{12}5\\ =18[/tex]

Answer:

30 feet^3

Step-by-step explanation:

length x width x height

3 x 2 x 5

=30

In probability theories, events which can never occur together are classified as "mutually exclusive events" that is option A.

Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, serve as an obvious illustration. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot get both outcomes. Since they do not occur at the same time, such events are also known as disjoint events.

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The factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)

A quadratic equation is any equation that can be rearranged in standard form as ax²+bx+c=0 where x represents an unknown value and a, b, and c represent known numbers. In general, a = 0; equations with a = 0 are considered degenerate because the equation becomes linear or even simpler. The numbers a, b, and c are the equation's coefficients, and they can be distinguished by referring to them as the quadratic coefficient, linear coefficient, and constant or free term, respectively.

To find x-intercept y=0

y≥x²+2x-8

x²+2x-8≥0

x²+4x-2x-8≥0

x(x+4)-2(x+4)≥0

(x-2)(x+4)≥0

∴x≥-4, x≥2

∴(-∞, -4]∪[2, ∞)

Therefore, the factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)

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Answer:

Probability = A. 2 / 5

Step-by-step explanation:

Probability = ( Number of Favorable Outcomes ) / (Total Number of Outcomes )

So the Total Number of Students = 20

Number of Students ( Dots ) scored more than 15 = 3+2+1+2 = 8

Probability = 8 / 20 = 2 / 5

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Answer: 12/20= 3/5

Step-by-step explanation:

you have to count all the dots on the dot plot to find your denominator which is 20.

then you count all the dots that are fifteen or more and there are 12 so 12/20 is the probability which is simplified into 3/5.

The number of pairs of the parallel lines after the rotation is 2

The transformation is described by

Rotation by 90° counterclockwise about vertex G

There are four types of transformation, and they are:

As a general rule of rotation:

When a shape, line or an angle is rotated, the size of the properties in the rotated figure remains unchanged

Before rotation, a rhombus has two pairs of parallel sides

This means that the parallel sides would remain parallel after rotation

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Probability that customer buy parsley given buy any of two herb  

                =   0.5714

What is probability in math?

Parsley ( 0.4 , 0.6 )

buy  = B ∩ P = 0.08

Don't buy = DB ∩ P = 0.12

Cilantro = ( 0.15 , 0.85 )

buy  = B ∩ C = 0.06

Don't buy = DB ∩ C = 0.34

Don't buy anything = DB = 0.4

P( Buy anything ) = P(B∩P) + P( B ∩ C )

                          = 0.08 + 0.06 = 0.14

Now, P( P/B) = P( P ∩ B)/P(B)

                    = 0.08/0.14  = 4/7  = 0.5714

Hence, probability that customer buy parsley given buy any of two herb

                                          =   0.5714

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Answer: 2[tex]\sqrt{2}[/tex]

Step-by-step explanation: First plug in the value, which is [tex]\sqrt{8}[/tex]

Then divided to 2[tex]\sqrt{2}[/tex]

Jade and Jordan both have a total of 35 trading cards altogether.

Given, Jade has 28 trading cards. He has 4 times as many trading cards as Jordan.

As, Jade has 28 trading cards

Let Jordan has 'x' trading cards.

Now, as Jade has 4 times as many trading cards as Jordan.

So, 28 = 4x

4x = 28

x = 7

So, Jordan has 7 trading cards.

Now, they both have a total of 35 trading cards altogether.

Hence, Jade and Jordan both have a total of 35 trading cards altogether.

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Step-by-step explanation:

-8(x + 7.5) ≤ 10?

expand left side:

-8x - 60 ≤ 10

subtract 60 to both sides:

-8x - 60 + 60 ≤ 10 + 60

-8x ≤ 70

dive both sides by -8: (Remember when dividing by a negative number, you flip the direction of the inequality sign)

-8x/-8 ≥ 70/-8

x ≥ -35/4

reduce right side:

x ≥ -35/4 or x ≥ -8.75 [depends on if you need fractional or decimal format]

so in set builder format: [-35/4 , ∞) or [-8.75 , ∞) [depends on if you need fractional or decimal format]

The modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.

R-squared (R2) would be a statistical measure that quantifies the proportion of the variation explained from an independent variable other variables within a regression model for a dependent variable.

Thus, the modified r squared tells us more about the relationship among sales, price, as well as advertising by explaining approximately 60% of a variance in sales.

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Using a system of equations, it is found that:

Leah takes 3 minutes to run a lap and 6 minutes to walk a lap.

The variables of the system of equations are presented as follows:

She requires 84 minutes to do 8 laps running and 10 laps walking, hence the first equation is:

8x + 10y = 84.

She requires 66 minutes to do 2 laps running and 10 laps walking, hence the second equation is:

2x + 10y = 66.

Simplifying by 2, we have that:

x + 5y = 33.

x = 33 - 5y.

Replacing in the first equation, we can find the time it takes to walk a lap, as follows:

8(33 - 5y) + 10y = 84.

264 - 40y + 10y = 84

30y = 180

y = 180/30

y = 6 minutes.

Then the time it takes to run a lap is obtained as follows:

x = 33 - 5y = 33 - 5(6) = 33 - 30 = 3 minutes.

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The solution for u in the expression given as 7/u = 3/11 is u = 25.7

From the question, the algebraic expression is given as

7/u = 3/11

There is no constant to add to or subtract from the expression

So, the equation remains the same

7/u = 3/11

Multiply both sides of the equation by u

This gives

u * 7/u = 3/11  * u

Evaluate the products

So, we have the following equation

7 = 3/11u

Multiply both sides of the equation by 11/3

This gives

11/3 * 7 = 3/11u * 11/3

Evaluate the products in the above expression

77/3 = u

So, we have

25.6667 = u

Approximate

25.7 = u

Rewrite as

u = 25.7

Hence, the solution is u = 25.7

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The probability of landing on an even number or a number greater than two is 5/6.

A fair die is rolled. We need to find out the probability of landing on an even number or a number greater than two.

Let the event of landing on an even number be denoted by the variable E1. Let the event of landing on a number greater than two be denoted by the variable E2. We need to calculate P(E1 ∪ E2).

P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)

P(E1 ∪ E2) = (3/6) + (4/6) - (2/6)

P(E1 ∪ E2) = 5/6

Hence, the probability of landing on an even number or a number greater than two is 5/6.

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Answer:

15y

Step-by-step explanation:

3 times 5 is 15 with the variable

Answer:

( y + 3 ) = - ( x + 6 )

Step-by-step explanation:

The Equation of Line in Point-Slope Form is

[tex](y-y_1)=m(x-x_1)\\where\ m \is \ the \ slope\ and \ (x_1 , y_1) \ is \ any \ point \ on \ the \ line[/tex]

So by Substitution by the Givens

( y - (-3) ) = -1( x - (-6) )

( y + 3 ) = - ( x + 6 )

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The standard deviation of the length of this plant be 25.

m = 60(mean)

Let the standard deviation be s,

As, the probability for 50<x<70 be 0.75

Z = (x−m)/s

for x=50,

Z=0

for x=70,

Z=(70−50)/s=20/s

Now, the probability for 50<x<70 be,

P(50<x<70) = 0.75

In the standard form 0<z<(20/s)

using Z-table, the area from 0 to 20/s,

= 0.75

s = 25

Hence, the standard deviation of the length of this plant be 25.

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The probability that the sample mean would be higher than 88.4 or smaller than 84.4 is 0.85582

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ = 86

sample size, n = 140

standard deviation, σ  = 11

The probability

P(z > 88.4) + P(z < 84.4)

z score for z < 88.4

z = (88.4 - 86) / 11

= 0.21818 p value = 0.41364

z score for z < 84.4

z = (84.4 - 86) / 11

=  -0.14545

p value for z < -0.14545 = 0.44218

The probability required = 0.41364 + 0.44218 = 0.85582

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