. Write expressions for the distance in feet that
each animal could run at top speed in a given
amount of time. Tell what the variable in your
expressions represents.

The solution of the system of equation x - y = 4, x + y = 2 is (-1, 3).

System of equation can be formed using different method such as graphical method, elimination method and substitution method.

Therefore, let's solve the system of equation by using elimination method.

x - y = 4

x + y = 2

subtract the equations

2y = -2

divide both sides of 2

y = -2 / 2

y = -1

Hence, let's substitute y in equation(ii)

x + y = 2

x - 1 = 2

x = 2 + 1

x = 3

Therefore, the solution is (-1, 3)

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The value of n when the sum is 143 is n = 12.

What is consecutive numbers?

The term "consecutive" refers to a sequence of numbers. Every pair of numbers has a difference of 1. The mean and median are equal in a set of consecutive numbers. If n is a number, n, n+1, and n+2 would be following it. Examples. 1, 2, 3, 4, 5.

Numbers that follow one another in order, from the smallest to the largest, are referred to as consecutive numbers. There is a consistent pattern to the difference between two consecutive numbers.

Given:

The sum of the first n consecutive odd integers can be found using

s = n^2 - 1, where n is greater than or equal to 1.

Let the sum is 143.

We have to find the value of n.

Plug s = 143 in s = n^2 - 1

⇒      143 = n^2 - 1

⇒ 143 + 1 = n^2

⇒      144 = n^2

⇒        12 = n

⇒         n = 12

Hence, the value of n when the sum is 143 is n = 12.

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A vertical line's equation is provided by the expressions x = an or x = -a, where x denotes any point on the line's x coordinate and a denotes the point at which the line intersects the x-intercept.

The vertical line is either another line that is regarded as the base or a line that is perpendicular to the surface. The vertical lines in coordinate geometry are typically perpendicular to the horizontal lines and parallel to the y-axis. Whether it is going from top to bottom or bottom to top, a vertical line is always a straight line. The standing lines refer to the vertical lines.

A vertical line is a line on the coordinate plane with the same x-coordinate at each point. We discover that when the coordinates are joined when plotting the points for the function x = a on a coordinate plane, a vertical line results.

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This is equivalent to finding the solutions of the equation x1 + x2 + x3 + x4 + x5 = 21 and with an application of Theorem 2: r = 21, n = 5, so we have C(21+5-1, 21) = C(25, 21) = 12,650 solutions

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

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If runners in the half marathon entered in 3 waves and 7 out of eight runners finished the race, runners that did  not finish is 119 runners.

First step is to find the total runners in the 3 waves

Total runners = 341 runners + 295 runners + 316 runners

Total runners = 952 runners

Second step is to find runners that finished the race

Runners (Finished) = 7/8 ×  952 runners

Runners (Finished) = 833 runners

Now let find runners that did not finished

Runners (Unfinished) = 952 runners - 833 runners

Runners (Unfinished) =119 runners

Therefore 119 runners did not finish.

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The answer are, 1) $ 162.18  , 2) $ 17500 ,  3) $28.4.

A percentage is a number or ratio that can be expressed as a fraction of 100.

here, we have,

from the given, we get,

1.) the total price you pay =$153+ $153*6%

                                         =$162.18

2.) you earned = $350000 *5%

                        =$17500

3.) you made = $ 710*4%

                      =$28.4.

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The function for the perimeter of the square is P = 4x.

The term function is defined as a relationship between inputs where each input is related to exactly one output.

Here we have given that Function p represents the perimeter, in inches, of a square with side length x inches.

As we all know that the term square is referred as a regular polygon having four equal sides and equal angles that measure 90° each.

And the term perimeter is defined as  the distance around the edge of a shape.

as we all know the the square has 4 sides which is represented by the term x.

Then the perimeter is calculated as

p = x + x + x + x

Therefore, the resulting function is written as

p = 4x.

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The solution of the given equation is 3+i or 3-i.

What is Quadratic Equation ?

Quadratic Equation can be defined as the equation in which it is in the form of ax^2+bx+c = 0

where a, b , c are constants.

Given,

equation x^2-6x+10 = 0

So for solving the roots , here she used quadratic formula

so,

x = (-b + [tex]\sqrt{b^2 - 4ac}[/tex] )/ 2a  or (-b - [tex]\sqrt{b^2 - 4ac}[/tex] )/ 2a

here a = 1 b = -6 and  c = 10

x =( 6 + [tex]\sqrt{6*6 - 4 * 1*10}[/tex] )/ 2 or ( 6 - [tex]\sqrt{6*6 - 4 * 1*10}[/tex] )/ 2

x = (6 + [tex]\sqrt{36-40}[/tex] ) / 2 or (6 - [tex]\sqrt{36-40}[/tex] ) / 2

[tex]\sqrt{36-40}[/tex] = 2i

so,

x = 6+2i / 2  or 6-2i / 2

x = 3+i or 3-i

Hence, The solution of the given equation is 3+i or 3-i.

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The probability that he draws a pair of tens is  1/2652 or approximately 0.000378 which is approx 0.04%

The probability of drawing a pair of tens from a standard deck of cards is (number of ways to get a pair of tens) / (total number of possible outcomes).

In this case there are 4 tens (2 of hearts, 2 of diamonds, 2 of spades, 2 of clubs) and he is drawing 2 cards from the deck, so there is only 1 way to get a pair of tens. There are 52 cards in a standard deck, so the total number of possible outcomes is 52 * 51 = 2652.

So the probability of drawing a pair of tens is 1/2652 or approximately 0.000378 which is approx 0.04%

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The prediction model equation is constructed using outputs from an R script.

We are creating a regression model to accurately predict fuel economy using horsepower, quarter mile time, and rear axle ratio as predictors. We will include interaction terms for horsepower and quarter mile time, as well as for horsepower and rear axle ratio.

The prediction model equation is written below, based on the outputs obtained from the R script:

Fuel Economy = β0 + β1*Horsepower + β2*Quarter Mile Time + β3*Rear Axle Ratio + β4*Horsepower*Quarter Mile Time + β5*Horsepower*Rear Axle Ratio

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Answer:

A

Step-by-step explanation:

9 x 2 = 18

9 x 5m = 45m

A: Percentage of the survey respondents did not like either hamburgers or burritos 16.09 %

B: Percentage of students who like hamburgers also like burritos 0.65%

C: Those who like Hamburgers but not burritos.

Like Hamburgers ↓  Does Not Like Hamburgers↓    Total↓

Likes burritos →                 39                           38                                   77

Does not like burritos →    95                           33                                 128

Total →                                134                           71                                 205

A: The proportion of survey respondents who dislike both hamburgers and burritos

33 such respondents are present.

hence, percentage

33/205X100= 16.09%

B: Marginal relative frequency of all hamburger-loving customers

It will be the proportion of respondents overall to the total number of consumers who like hamburgers.

Thus, ratio

135/205= 0.65

C: The data point with the strongest correlation between its two components is described in Part C.

To do this, we must determine the proportion of the four data points to the total.

Those who enjoy burritos and hamburgers 0.29

Who doesn't like burritos but prefers hamburgers 0.71

who prefer burritos to hamburgers 0.53

Those who do not enjoy hamburgers or burritos 0.47

So, the answer is those who like Hamburgers but not burritos.

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Answer:

A(-5, -3).

Step-by-step explanation:

3x - 2y >= -14

-2y >= -14 - 3x

y <= (-14-3x)/ -2

y <= 7 + 1.5x

The circles with numbers with no consecutive numbers between the circle joined by a line segment are given as

1 - 3 - 5

|          |

7        8

|          |
2 - 4 - 6

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Numbers:

1 to 8.

Now,

1 - 3 - 5

|          |

7        8

|          |
2 - 4 - 6

Thus,

The circle has numbers where no consecutive circles are having consecutive numbers joined by a line segment.

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Take the root of both sides and solve. The value of c is 13.19.

The Pythagorean theorem aids in determining the lengths of a right triangle's sides. It indicates that a and b are the sides that make up the right angle, and c is the hypotenuse, and that a2+b2=c.

The square of the difference between two integers may be calculated using the a + b whole square formula as well as the binomial term when squared.

Take the root of both sides and solve.

Exact Form:

== √174,-√174

Decimal Form:

c = 13.19090595...,-13.19090595.

Take the root of both sides and solve. The value of c is 13.19.

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According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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A region on one side of a line might be used to visually depict an inequity IS X+4.

Rearrange the equation so that "y" is on the left and the rest is on the right.

Plot the "y=" line (make it a solid line for y or y and a dashed line for y or y>).

Shade above the line for "more than" (y> or y) or below the line for "less than" (y or y).

A region on one side of a line might be used to visually depict an inequity. Inequalities with or > symbols are displayed with a dashed line to indicate that the line is not part of the region. Inequalities with the symbols or are plotted with a solid line to demonstrate that the line is

Inequalities with the symbols or are plotted with a solid line to demonstrate that the line is X+4.

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The value of y in the equation -3y+2y = 10 is y = -10

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. A linear equation can have a variable or two variables. Examples of linear equation with two variables is 2x+2y = 5 and example of linear equation with a variable is 2x+5 = 12. The variables here are x and y

-3y + 2y = 10 is an example of linear equation with a variable

-3y + 2y = 10

-y = 10

divide both sides by -1

y = -10

therefore the value of y is -10

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Answer:

There are 86 acres of old-growth trees.

Step-by-step explanation:

In order to answer the question, we need to calculate the 0.2% of 43,000.

We can calculate this stating that exists a linear relationship between the percentage and the amount of acres. We also need to state that 43,000 acres are the 100% of the acres.

Therefore, we can write the following equation to calculate the percentage :

If we solve the equation in terms of ''x'' :

The height of the triangle as calculated from the data given above is found out to be as √60 meters.

The given question can be solved by the implication of Pythagorean theorem as the figure is in the form of a triangle.

Let the, base of the triangle be , 2 meters

the hypotenuse be , 8 meter.

Therefore the height of the pole will be ,

AB² = AC²  - BC²

      = 64 - 4

      = 60

Then , we can say that AB = √60

Therefore, the height of the pole is found to be as √60 meters.

Pythagoras theorem states that the sum of two side of a triangle is equal to the hypotenuse of that triangle , AB² = AC²  - BC² .

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The probability a player will be more likely to wear a white jersey than a blue jersey because P(White) > P(Blue). Option C is correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Probabilities of wearing specific jersey colors,
Yellow 0.47

Blue 0.18

White 0.35

So,
P(Yellow)> P(White) > P(Blue).

It implies that, from the options, the player will be more likely to wear a white jersey than a blue jersey because P(White) > P(Blue).

Thus, option C is correct.

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Answer: C: The player will be more likely to wear a white jersey than a blue jersey because P(White) > P(Blue).

Step-by-step explanation:

The function required in the right triangle is as follows;

tan A = 5 / 12

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The angles of a right angle triangle can be found using trigonometric ratios as follows:

Hence,

tan A = opposite / adjacent

opposite side = 20 units

adjacent side = 48 units

Therefore,

tan A = 20/ 48

tan A = 20/ 48 ÷ 4 / 4

Hence,

tan A = 5 / 12

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The volume of the prism ( above fig.) is equals to the 900 cubic units. So, first one option is right answer of this problem.

Prisms and pyramids are very important solid shapes. They have many uses in real life. Each type of pyramid or prism has different formulas for volume and area. The general formula of volume, V = Base area × Height

Here, we take the triangular part of the prism as the base. We have, a prism with triangular base.

Triangular base area = 1/2 × B × H

Base length of triangle, H = 15

Height of triangle, B = 8

Triangular base area = 1/2×15×8 = 60 square units

Volume of prism , V = 60 sq. units × 15 units

= 900 cubic units

Hence, the volume of prism is 900 cubic units.

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She used 1/12 kg of salt when preparing the dinner.

An equation shows the relationship between numbers and variables in an expression.

There are 5/6 kg of salt in the kitchen. Mrs. Jackson used 1/10 of the salt when she was preparing dinner. Hence:

Amount of salt used = (1/10) * (5/6)kg = 1/12 kg

She used 1/12 kg of salt

The amount of salt remaining is the difference between the initial salt available and the quantity of used salt. Hence:

Salt remaining = 5/6 kg - 1/12 kg = 3/4 = 0.75 kg

Mrs. Jackson had 0.75 kg of salt remaining.

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The given number is a solution of 2(3x + 1) 2 7x + 4 is 0.

Analyze a number to see if it is an equation's solution.

For the variable in the equation, substitute the integer.

On both sides of the equation, simplify the expressions.

Check the equation to see if it's correct. The number provides a solution if it is accurate. The figure isn't a solution if it's false.

Equations with just one solution. If you solve an equation and the result is a variable equal to a number, the problem only has one solution.

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The two variables in this equation are x and y, and the nonzero value k is also referred to as the constant of variation. A line across the origin represents the graph of the equation y = kx, and its slope is k.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

How do you define "variable"?

A variable is a value that could alter when used in a mathematical problem or experiment. A variable is often represented by a single letter. Generic symbols used frequently for variables include the letters x, y, and z.

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3 units is the distance from y-axis to the given point (3, 4).

Distance between two things or points is measured, and it can sometimes be quantitatively and sometimes qualitatively.

The word "distance" in physics can refer to a real-world length or, more frequently, to an estimate based on a number of other factors.

The length of the line segment that connects two points on a plane represents their distance.

To calculate the distance between two places, one usually uses the formula d=((x2 - x1)2 + (y2 - y1)2).

So, we have the point:

(3,4)

Any given point's x coordinate indicates how far it is from the y-axis, and then we can conclude that the distance of the point (3,4) from the y-axis is 3.

Therefore, 3 units is the distance from y-axis to the given point (3, 4).

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