Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. • The equation that relates Runner #2’s distance (in miles) with time (in minutes) is `t=8. 5d`. Find the slope/rate of ch

Answer: Lyda wants to score 80% on a test that is worth 50 points. To figure out how many points she needs to accomplish her goal, we can set up a proportion using her desired percentage as the proportion of points she wants to score over the total number of points on the test.

score / total points = percentage / 100

To figure out the number of points Lyda needs to score, we can use the proportion above and cross-multiply:

score * 100 = percentage * total points

We know that percentage=80 and total points =50, so we can substitute these values:

score * 100 = 80 * 50

score = (80*50) / 100 = 40

So Lyda needs to score 40 points to accomplish her goal of 80%.

The proportion would be score / total points = x/100 = percentage/100 = 40/50 = 8/10

It's worth to mention that scoring 80% on a test means she scored 40 points on a test worth 50, the minimum score to pass is 30 so she got a good grade already.

Step-by-step explanation:

The lengths of each diagonal are given as follows:

As the lengths are different, the polygon TUVW is not a rectangle.

The diagonal length is obtained using the formula for the distance between two points, presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.

The first diagonal is TV, and the length is given as follows:

[tex]TV = \sqrt{(9 - (-5))^2 + (6 - 0)^2} = \sqrt{232}[/tex]

The second diagonal is WU, and the distance is given as follows:

[tex]WU = \sqrt{(-3 - 7)^2 + (-9 - 3)^2} = \sqrt{244}[/tex]

A rectangle has diagonals of equal length, hence the polygon for this problem is not a rectangle.

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Answer:

A. 6x - 4

Step-by-step explanation:

[tex]\sf 8-3(4-2x)[/tex]

Distribute:-

[tex]\sf 8+(-3)(4)+(-3)(-2x)[/tex]

[tex]\sf 8+-12+6x[/tex]

Combine Like Terms:-

[tex]\sf (6x)+(8+-12)[/tex]

[tex]\sf 6x+-4[/tex]

** + * - = -**

[tex]\sf 6x-4[/tex]

Therefore, option A. 6x - 4 is your answer!

_____________________

Hope this helps!

Have a great day!

Answer:

  24

Step-by-step explanation:

You want to know the number such that the triple of the number added to its half part is equal to the difference between four times the number and 12.

The given relation can be expressed in math symbols as ...

  3n +n/2 = 4n -12

Adding 12 -n/2, we get ...

  12 = n/2

  24 = n . . . . . multiply by 2

The number is 24.

Total distance travelled by the family in the truck is 497.98 miles

An equation is an expression that shows the relationship between two or more numbers.

The rental of the truck has a base cost of $49.95, and $1.19 per mile. The average gas mileage is 18 miles per gallon.

Let us assume the total distance travelled was x miles, hence:

Total gas consumed = x miles / 18 miles per gallon = x/18 gallons

The cost is $3.89 per gallon, hence:

Total cost of gas = $3.89 per gallon * x/18 gallons = 3.89x/18

Total cost of journey = 1.19x + 3.89x/18 + 49.95 = 2531x/1800 + 49.95

If $724.85 was charged, hence:

724.85 = 2531x/1800 + 49.95

x = 497.98

Total distance is 497.98 miles

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P= kd/u^2 is the equation which expresses the following relationship p varies derectly with d and inversly with the square of u.

Equation is a mathematical statement that expresses the equality of two expressions. An equation is written as an expression containing an equal sign, with each side of the equal sign representing a mathematical expression. The purpose of an equation is to show the relationship between two or more variables, such as a change in one variable resulting in a change in another. Equations are used to solve problems in mathematics, physics, economics, and many other fields.

The equation states that p is directly proportional to d, and inversely proportional to u squared. This means that as d increases, p increases, and as u increases, p decreases. The constant of proportionality, k, is a measure of the strength of the relationship between p, d, and u.

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The answers for the two questions is described below:

a. The balance sheet is a financial statement that shows a company's assets, liabilities, and equity at a specific point in time. Each transaction will affect one or more of these categories in different ways:

An increase in assets will increase total assets.

An increase in liabilities will increase total liabilities.

An increase in equity will increase total equity.

The income statement is a financial statement that shows a company's revenues, expenses, and net income over a specific period of time. Each transaction will affect net income in different ways:

An increase in revenues will increase net income.

An increase in expenses will decrease net income.

b. The statement of cash flows is a financial statement that shows the cash flows from operating activities, investing activities, and financing activities over a specific period of time. Each transaction will affect one or more of these categories in different ways:

An increase in cash from operating activities will increase cash flows from operating activities.

An increase in cash from investing activities will increase cash flows from investing activities.

An increase in cash from financing activities will increase cash flows from financing activities.

It is important to note that it can be complex to classify some transactions into one category or another, and it may require more context of the specific transaction and the company's operations.

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a) A simulation of the probability that a family with 4 children will have 2 boys and 2 girls can be done using coins. We can represent boys as heads (H) and girls as tails (T).

To simulate the birth of one child, we will flip a coin. If it comes up heads, it represents the birth of a boy, and if it comes up tails, it represents the birth of a girl. We will repeat this process four times to simulate the birth of four children.

We can use the simulation to estimate the probability of the family having 2 boys and 2 girls. We can do this by performing the simulation multiple times (e.g. 100, 1000 or more) and counting the number of times that the family has 2 boys and 2 girls.

The probability can be calculated by dividing the number of successful outcomes (2 boys and 2 girls) by the total number of simulations.

b) A simulation of the probability that a basketball player will hit at least 75% of his shots within the groups can be done using coins. We can represent hitting a shot as heads (H) and missing a shot as tails (T). To simulate one shot, we will flip a coin. If it comes up heads, it represents hitting the shot, and if it comes up tails, it represents missing the shot. We will repeat this process four times to simulate the shooting of four shots.

To determine the probability of hitting at least 75% of the shots, we will perform the simulation multiple times (e.g. 100, 1000 or more) and count the number of times that the player hits at least 3 out of 4 shots.

The probability can be calculated by dividing the number of successful outcomes (3 or 4 shots hit) by the total number of simulations

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Answer:

3 minutes

Step-by-step explanation:

30÷1.5=20

1h=60mins

60÷20=3minutes

Therefore , the solution of the given problem of slope comes out to be

y = (-1/2)x + 8.

The slope-intercept formulation of an equation is used to represent each time the formula of a line is stated as y = mx + b. The line's slope is represented by the m. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in the formula y = 3x - 7.

Here,

Locate the slope first.

These two positions (0, 8) and are in the line, therefore we know that (6,5)

Slope: (y2-y1)/(x2 - x1)

Slope = 8-5 / 0-6

Slope = 3/-6 => Slope = -1/2

The gradient is -1/2. When x = 0, you can find the y-intercept. We also know that the line passes through the point (0,8), and since x = 0, the y-intercept is equal to 8.

using the slope-intercept form, which is

Using the equation y = mx + b, where m denotes the slope and b the y-intercept, we get:

y = (-1/2)x + 8

Therefore , the solution of the given problem of slope comes out to be

y = (-1/2)x + 8.

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Answer:

29

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Slope - intercept form is    y = mx + b    you just need to manipulate the given equation to this form

-x +3y = 6         add 'x' to both sides of the equation

3y = x + 6         divide by 3

y = 1/3 x + 2      Done !

The cost of one ticket in Virginia is $8

A System of Linear Equations is when we have two or more linear equations working together.

Given that, 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77, Also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91.

To find the cost of a ticket in Virginia we will establish a system of linear equations and then solve them,

Let V represents the cost in Virginia that of in Maryland be M

Therefore,

4v+5m = 77.......(i)

8v+3m = 91........(ii)

Multiplying the equation eq(i) by 2 and subtracting eq(ii) from eq(i) [Elimination]

(8v+10m = 154)  - (8v+3m = 91)

7m = 63

m = 9

Put m = 9 in eq(i)

4v+5(9) = 77

4v = 77-45

4v = 32

v = 8

Hence, Each ticket in Virginia and Maryland costs $8 and $9 respectively.

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Answer:

3.5. 2.2.

x 4. x 1 1

------ -----------

14.0. 22

220

24.2

Step-by-step explanation:

answer for me is 38.2

are you sure ur math is right?

When the root of x²-bx+c = 0 is decreased by 2, the resulting equation is x²-2x+1, then b = 2 and c = 1

The values of variables satisfying the given quadratic equation are called its roots.

if the roots of a quadratic equation ax²+bx+c = 0 are alpha and beta

alpha + beta = -b/a and

alpha × beta = c/a

when the roots are reduced by 2

alpha-2+ beta-2 = -b/a

(alpha+beta)-4 = -b/a

alpha+ Bata = -b/a + 4

the resulting equation is x²-2x+1 = 0

a = 1, b = -2 and c = 1

therefore alpha +beta = -b/a = -(-2)/1 = 2

therefore 2 = -b/a+4

a = 1

2 = -b+4

b = 4-2 = 2

alpha×beta = c/a = 1/1

(alpha -2)× ( beta -2) = (alpha)( beta) -2(alpha+beta) + 4 = 1-2(2)+4 = 1

therefore b = 2 , c = 1

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Therefore , the solution of the given problem of equation comes out to be a=1 and b =-1.

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.

Here,

y' = 3x2 = 3(1) (1) 2 = 3

As a result, the slope-point form of the necessary tangent line is: => y-yo = m. (x - xo) y-1=3(x-1)

The two slopes just need to match for y = x2 + ax + b to share a tangent line at the location (1, 1). (In this manner, the slope-point forms of the two tangent lines will be identical.)

Therefore, y = x2 + ax + b must meet the following two requirements:

It must go through (xo, yo) because: (1, 1).

At this point, it must have a slope (y') of 3.

These will provide us with the two unknowns for our two equations. With the first, we have y'= + axo + b.

⇒ 1 = (1)2 + a(1) + b

⇒ 0 = a + b

and the second one gives us

y=2x0+ a

=> 3 = 2(1) + a

=> a = 1

Looks like we know exactly what a is. All we need is to plug this value into the first equation and we'll find b:

a+b=0

b = -a

b = -1

Therefore , the solution of the given problem of equation comes out to be a=1 and b =-1.

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The values of x and y, given the angles, can be found to be :

The parallel line is drawn such that ( 7 y - 12 ) degrees and ( 6 y + 8 ) degrees are equal to each other.

In the same vein, 4x degrees and 6x - 26 degrees are the same as well. This is because they are vertical angles.

The value of x is:

4x = 6x - 26

6x - 4 x = 26

2x = 26

x = 26 / 2

x = 13

The value of y is :
7 y - 12 = 6 y + 8

7y - 6 y = 8 + 12

y = 20

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All Answers:

1a) The equation that models the situation is: 4.65r + 4.95p = 874.80

1b) Using the equation from part 1a, we know that 4.65r + 4.95p = 874.80. If we know that Alice purchased 87 gallons of regular unleaded gas, we can substitute that value into the equation: 4.65(87) + 4.95p = 874.80. Solving for p, we get: 4.65(87) + 4.95p = 874.80

4.0995 + 4.95p = 874.80

4.95p = 869.805

p = 175.6 gallons

2a) The function that models the number of checked bags, b, as it relates to the total cost, c(b), is: c(b) = 35b + 475.

2b) Number of Bags (b) Total Cost c(b)

0 475

1 510

2 545

3 580

4 615

6 675

8 835

3a) The y-intercept in this scenario represents the total distance travelled when the time spent on the trip is zero. As the distance traveled is 700 miles when time is zero, the y-intercept is (0,700)

3b) The x-intercept in this scenario represents the total time spent on the trip when the distance travelled is zero. As time is zero when the distance traveled is zero, the x-intercept is (0,0)

3c) (2.5, 200) (10, 300)

3d) The domain and range are based on the permissible values of time and distance travelled. Based on the information provided, the domain would be {h | 0 < h < 10} and the range would be {f(h) | 0 < f(h) < 700}

About the last part of the question, it is referring to the fact that life is like a journey, and we should strive to be like runners who run to win the prize, not just to participate. This passage encourages us to put in the hard work and dedication necessary to achieve our goals in life, and to not be satisfied with simply going through the motions. It also reminds us that our ultimate goal should be eternal reward, not temporary ones. In your life, it might mean setting a goal, making a plan, and putting in the effort to achieve it, but also keeping a perspective of what is important in the long run, not just in the short run.

The solution is Option B.

Noise is easily filtered out without damage to the original signal because a narrow range of values is expected

A digital signal encodes data as a sequence of discrete values. A digital signal can only have one value from a finite set of possible values at any given time. A signal which is a discrete function of time, i.e. non-continuous signal, is known as digital signal. Digital computers and digital phones are some of the examples of digital signals

The three types of digital signals are

Continuous-Time/Analog Signal

Discrete-Time Signal

Digital Signal

Given data ,

The digital signals are a more reliable way to encode and transmit information than analog signals

Because , while transmitting information through digital signals , they have less interference over long distances and digital signals offer better clarity

The digital devices only record pieces of sound waves, not full waves.

Now , Analog technology stores information as sound waves; digital technology stores it as strings of ones and zeroes.

Hence , noise is easily filtered out without damage to the original signal because a narrow range of values is expected

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As per the given probability, the flipped coin is Coin A.

Probability in math is know as the entire possible set of outcomes of a random experiment is the sample space or the individual space of that experiment.

Here we have given that you have two biased coins. Coin A comes up heads with probability 0. 1 and Coin B comes up heads with probability 0. 6.

Here we know that you are not sure which is which, so you choose a coin randomly and flip it.

As per the given situation here we have to know that if the flip is heads, then you guess that the flipped coin is B.  

Which is defined that if the the flip is tails, then you guess that the flipped coin is A.  

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The effective annual rate of interest if you do not make any payments for a year is 35%.

Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -

[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]

where -

[A] = final amount

[P] = initial principal balance

[r] = interest rate

[n] = number of times interest applied per time period

[t] = number of time periods elapse

Given is that You just bought a new tablet computer for $500, including tax. There are no required payments for six months, but the company does charge 30% annual interest, compounded monthly, on any unpaid balance.

We can write -

A = 500(1 + 0.3/12)¹²⁽¹⁾

A = 500(1 + 0.025)¹²

A = 500 x (1.025)¹²

A = 675

Effective annual interest rate for a year is as follows -

A = 500(1 + r/1)⁽¹⁾⁽¹⁾

675 = 500(1 + r)

1 + r = 675/500

1 + r = 1.35

r = 0.35

r = 35%

Therefore, the effective annual rate of interest if you do not make any payments for a year is 35%.

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3 tenths and 24 hundredths, after regrouping gives 0.54

In math, regrouping can be defined as the process of making groups of tens when carrying out operations like addition and subtraction with two-digit numbers or larger. To regroup means to rearrange groups in place value to carry out an operation. We use regrouping in subtraction, when digits in the minuend are smaller than the digits in the same place in the subtrahend.

Given here, 3 tenths and 24 hundredths after  regrouping we get

(3 tenths + 24 hundreths) = 0.54

Hence, 3 tenths and 24 hundredths after regrouping gives 0.54

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Answer:

D. g(-13) = 20

Step-by-step explanation:

Given information:

Option A, g(-4) = -11 cannot be true for g since the y-value of -11 is not in the given range.

Option B, g(7) = -1 cannot be true for g since the x-value of 7 is not in the given domain.

Option C, g(0) = 2 cannot be true for g since we have been given g(0) = -2.

Option D, g(-13) = 20 is true for g since the x-value of -13 is in the given domain, and the y-value of 20 is in the given range.

Answer: In the expression (3)(0.2)³(0.8)5, the value that represents the number of successes is 0.8.

This value is associated with the probability of success in the given expression, usually represented as "p" in a binomial distribution.

0.8 is probability of success

(0.8)5 represents number of successes.

It is important to note that 0.8 is a probability of success which means the probability of getting a success outcome in a single trial, and (0.8)5 is the probability of getting five successful outcomes in five trials.

Step-by-step explanation:

As 200 is not a perfect square it is not possible to increase the dimensions of the park by the same number of miles.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

We know the area of a rectangle is (length×width).

Given, Park rangers plan to expand the area of the park to 506 square miles.

Currently, the park has an area of (18×17) = 306 square miles.

Therefore, The amount of square miles they need to increase is (506 - 306)

= 200 miles.

Now, They also want to increase the length and the width by the same amount but 200 is not a perfect square so it is not possible to increase the dimensions by the same amount.

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Answer:

Given that ,

738 students wore red while 162 students wore green.

Therefore , total number of students ,

[tex]\dashrightarrow \: 738 + 162 \\ \dashrightarrow \: 900[/tex]

Now , 738 students out of 900 wore red.

So , percentage of students who wore red ,

[tex]\dashrightarrow \: \frac{738}{9\cancel{00}} \times \cancel{100} \\ \\ \dashrightarrow \: \cancel\frac{738}{9} \\ \\ \dashrightarrow \: 82\%[/tex]

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Answer:

help u with  what

Step-by-step explanation:

It will take 25 hours for Jenny to fill up the tank.

To solve this problem, we divide the capacity of the tank by the rate at which it is being filled:

500 gallons / 20 gallons/hour = <<500/20=25>>25 hours

4x2 - 3y2 - xy should be taken away from 3x² 4y² 5xy 20 obtain X² y²+ 6xy 20

A fraction is a percentage of a whole. This entire sentence could be referring to a single location or a collection of locations. The English word "fraction" originates from the Latin word "fraction," which means "to break." As the first society to comprehend fractions, the Egyptians used fractions to solve a number of mathematical problems, including the distribution of food and resources and the absence of a metal currency.

Assume X is the component that is absent.

As a result, the answer to the question is

(3x2 - 4y2 + 5xy + 20) - (X) = - x2 - y2 + 6xy + 20

To determine the value of X, let's change the words.

X is equal to (-x2 - y2 + 6xy + 20) = 3x2 - 4y2 + 5xy + 20.

X = 4x2 - 3y2 - xy X = 3x2 - 4y2 + 5xy + 20 + x2 + y2 - 6xy - 20

Thus, the expression that should be subtracted is 4x2 - 3y2 - xy.

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