what is an equation of the line that passes through the points (4,-6) and has a slope of -3
1) y = -3x + 6
2)y = -3x - 6
3)y = -3x + 10
4) y = -3x + 14

Answer:

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Step-by-step explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40.  This means, [tex]\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}[/tex].

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

[tex]f(x)=2x+100[/tex]

This can be checked by using the values given in the problem:

[tex]f(30)=2(30)+120=180\\f(50)=2(50)+120=220[/tex]

The base rate of $120 and $2 per person satisfies the given equation and established values.

Step-by-step explanation:

correct interpretation of the mean?answer choicesA value randomly selected from the distribution of S is expected to be 4.66.In repeated sampling from the distribution of S, the average of the values will approach 4.66.For

The average rate of change of g (x)=-2x³ +5x² from x=2 to x = 3 is

a(x)= -13

It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends. Following is the formula for the average rate of change:

a(x) = [f(b) - f(a)]/(b - a)

where,

a(x) = Average Rate of Change

f(a) = Function Value at a

f(b) = Function Value at b

Given,

g (x)=-2x³ +5x² from x=2 to x = 3

Average rate of change is a(x)

g (x)=-2x³ +5x²

Put x=2 in the above equation

g(2)= -2(2)³+5(2)²

= -16+20

=4

g(2)=4

Now, put x=3 in the above equation

g(3)= -2(3)³+5(3)²

= -57+45

= -9

We know that,

Average rate of change a(x)= (g(b)-g(a))/(b-a)

a(x)= g(3)-g(2)/(3-2)

a(x)= (-9-4)/1

a(x)= -13

Therefore, the average rate of change a(x)= -13

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Answer:

[tex]P = \boxed{\sf 4000}[/tex]

[tex]r=\boxed{\sf 0.03}[/tex]

[tex]n=\boxed{\sf 4}[/tex]

[tex]t=\boxed{\sf 5}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

If you invest $4,000 then the principal amount is $4,000.  As P represents the principal amount:

[tex]\implies P = \boxed{\sf 4000}[/tex]

The interest is 3%.  3% = 3/100 = 0.03.  Therefore:

[tex]\implies r=\boxed{\sf 0.03}[/tex]

"n" represents the number of times interest is applied per year.  

Therefore, if the interest is applied quarterly then:

[tex]\implies n=\boxed{\sf 4}[/tex]

"t" represents the time in years.  Therefore, if you plan to leave the money in the account for 5 years then:

[tex]\implies t=\boxed{\sf 5}[/tex]

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

To calculate the amount in the account after 5 years, substitute the values into the formula and solve for A:

[tex]\implies A=4000\left(1+\dfrac{0.03}{4}\right)^{4 \times 5}[/tex]

[tex]\implies A=4000\left(1+0.0075\right)^{20}[/tex]

[tex]\implies A=4000\left(1.0075\right)^{20}[/tex]

[tex]\implies A=4000(1.16118414...)[/tex]

[tex]\implies A=\$4644.74[/tex]

The gradient of the blue line as shown in the graph is 0.25

The gradient of any line or curve tells us the rate of change of one variable with respect to another.

To calculate the gradient of the blue line, we use the formula below.

Formula:

Where:

From the graph,

Given:

Substitute these values into equation 1

Hence, the gradient of the blue line is 0.25.

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The mean is 1.2 ,variance is 0.96 and standard deviation of the given data is 96 square root.we can find all these data by using formula of probability.

Probability means possibility.It is a branch that deals with occurrence of random event.The value is given in the probability from 0 to 1.Probability is how likely something is to happen.It is  used in real life for analysis data.we can find probability to favorable outcomes divided by total outcomes.

Standard deviation measures how far apart numbers are in a data set.Variance gives us the actual value to how much the numbers in a data set vary from the mean.The variance is equal to the square standard deviation and standard deviation is the square root of the variance.

NOW we have data

Person(ill)=20% =0.20        n=6

For Exactly two  p(x) =2

now we get  24.58% by using binomial theorem and putting value in the formula.

NOW for at least one p(x)>1  By putting value we get 0.7379.

Now for less than three p(x<30) we get 0.9011

Now to find mean

Mean=person (ill) multiply n

Mean = 0.20 * 6

Mean= 1.2

Variance= 1.2*0.80

             =0.96

IN the last we find standard deviation.it will be 96 square root.

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The interest earned over the 1103 day period is $840

Aaliyah will have $7840 in the account at the end of the 1103 day period.

Simple interest is defined as the amount of money that is paid to an individual following an investment that is made to an account.

The amount of money invested = $7,000.00

The rate of interest= 4%

The time of investment = 1103 = 3 years

Simple interest = P×T×R/100

= 7000×4×3/100

= 84000/100

= $840

The amount of money that is in the account at the end of the 1103 day period = 7000 + 840 = $7,840

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In case of APR 5% total payment made is $12,947.42 and in case of APR 8% total payment made is $14,598.94. Therefore the better deal to choose to pay the less payment is 1st case.

APR is the annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR). This does not account for compounding and includes any fees or additional expenditures related to the transaction. Consumers can evaluate lenders, credit cards, or investment goods using the APR as a benchmark figure.

Initial payment is $12,000 with 5% APR and 3 year loan

Monthly payment = P[ i(1+i)ⁿ] / [(1+i)ⁿ-1]

= 12,000[0.05(1+0.05)³]/[1+0.05)³-1]

=$359.65

Over 36 payments total payment is $12,947.42

And in case of 8% APR with a  5 year loan

Monthly payment = 12,000[0.08(1+0/08)⁵] / [(1+0.08)⁵-1]

=$243.31

Over 60 payments total payment is $14,598.94

So, the best deal is 5% APR with a 3 year loan.

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Answer: w ≤ 2200 would represent the situation

The statement as an expression is 2x - 9 = 5 + x

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

Nine less than two times a number is five more than this number.

Express the numbers properly

So, we have the following representation

9 less than 2 times a number is 5 more than this number.

Introduce the equality symbols

So, we have the following representation

9 less than 2 times a number = 5 greater than this number.

Next, we apply the mathematical operators

So, we have the following representation

2 times a number - 9 = 5 + number.

Express the number as x

So, we have

2x - 9 = 5 + x

Hence, the expression is 2x - 9 = 5 + x

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Answer:

Below

Step-by-step explanation:

358.584 is about 360      8.92 is about 9

360 / 9 = 40 approx   by' doing it in your head '

ACTUAL answer = 358.584/8.92 = 40.2   Pretty darn close !

The computation of the profitability ratios for Western Bookkeeping and Tax Service is as follows:

Profitability ratios are the financial ratios that evaluate an entity's ability to convert its earnings (revenue) into profit versus different criteria.

Some of the common profitability ratios include:

Stockholders' equity = $442,600

Total assets = $640,000

Net sales = $480,000

Net income = $36,000

Profit margin ratio = Net income/Net Sales x 100

= $36,000/$480,000 x 100

= 7.5%

= 8%

Return on equity ratio = Net income/Shareholders' Equity x 100

= $36,000/$442,600 x 100

= 8.13%

= 8%

Asset turnover ratio = Net Sales/Total Assets

= $480,000/$640,000

= 0.75

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The triangle ΔBHK and ΔBDE are congruent with each other. Then the side length ED is equal to the side length HK.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

Replace F with H.

The triangles ΔBHK and ΔBDE are shown.

In triangles ΔBHK and ΔBDE, then we have

BD ≅ BH (Given)

∠HBK = ∠DBE (Common angle)

∠BHK = ∠BDE = 90° (Right angle)

The triangle ΔBHK and ΔBDE are harmonious with one another. Then, at that point, the side length ED is equivalent to the side length HK.

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The largest possible value of 2 that satisfies the equation is approximately 1.1.

What is Exponential Form Equation?

Since y=bx, y = b x is a one-to-one inverse of the exponential function, x=by x = b y, it too is a function. We simply swap x and y and solve for y to discover the inverse function, as is the case with all inverse functions.

To solve for m in the equation -2 * log(m) - 24 = -20, we can start by converting the equation into exponential form. To do this, we can raise both sides of the equation to the power of e:

[tex]e^(-2 * log(m) - 24) = e^(-20)[/tex]

Then we can simplify:

[tex]m^(-2) = e^(-20)[/tex]

Then we can solve for m:

          [tex]m = sqrt[e^20]\\\\= sqrt[20*e^9]\\\\= sqrt[20] * sqrt[e^9]\\\\= 2 * 3^(1/2)= 2 * 1.732\\\\= 3.464[/tex]

So m is approximately equal to 3.464

To find the largest value of 2 that satisfies the equation [tex]log(2^2) - log(2 + 1) = 9[/tex],  we can start by expanding the left-hand side of the equation:

       [tex]log(2^2) - log(2 + 1) \\\\=log(2^2 / (2 + 1))\\\\ = log(4/3) = 9[/tex]

Then we can rewrite the equation as:

log(4/3) = 9

Then we can solve for 2:

         [tex]2 = (4/3)^(1/9)\\\\= (4^(1/9)) / 3^(1/9)\\\\= 1.5874010519681994 / 1.4422495703074083\\\\= 1.1[/tex]

So, The largest possible value of 2 that satisfies the equation is approximately 1.1.

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Answer:

B

Step-by-step explanation:

g(x) = 12x - 2

g(1/4) = 12(1/4) - 2  ==> plug in 1/4 for x

g(1/4) = 12 * 1/4 - 2

g(1/4) = 12/4 - 2

g(1/4) = 3 - 2

g(1/4) = 1 ==> B

Answer:

Step-by-step explanation:

To evaluate g(1) for the function g(x) = 12x - 2, you can substitute the value 1 for x in the function:

g(1) = 12(1) - 2

g(1) = 12 - 2

g(1) = 10

Therefore, g(1) = 10. B

Therefore ,the answer of this integration problem comes out to be  4/9.

To describe notions like displacement, area, volume, and other results of the combination of incredibly small inputs, an integral in mathematics imparts numerical values to functions. Integration is a method used in the process of integral discovery.

Here,

Given :

=>  [tex]\int\limits^9_7 {\frac{14}{(x-8)^{2} } } \, dx[/tex]

=> substitute x- 8 =u

=>du/dt =d(x-8)/dx = 1

=>du/dt =1

=> [tex]\int\limits^9_7 14{\frac{1}{(x-8)^{2} } } \, dx[/tex]

Substituting x- 8 =u

=> [tex]\int\limits^9_7 14{\frac{1}{(u)^{2} } } \, dx[/tex]

=> 14 [ [tex]\left \{ {{9} \atop {7}} \right. (\frac{-1}{u} )[/tex]  ]

=> 14( -1/9) + 1/7)

=> 14   ( ( 9 -7 ) / 63 )

=> 14 (2/63)

=> 28/63

=>4/9

Therefore ,the answer of this integration problem comes out to be  4/9.

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One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). the x-intercepts and the y-intercept of the graph of f(x) are

Generally, To find the x-intercepts, we set y equal to 0 and solve for x. In this case, the equation we need to solve is:

f(x) = x^3 - 6x^2 + 11x - 6 = 0

To solve this equation, we can use the fact that (x - 3) is a factor of the function. This means that we can write the function as:

f(x) = (x - 3)(x^2 - 3x + 2)

If (x - 3) is a factor, then x - 3 must equal 0. This gives us one x-intercept at x = 3.

To find the other x-intercepts, we can set the quadratic factor (x^2 - 3x + 2) equal to 0 and solve for x. This gives us the following equation:

x^2 - 3x + 2 = 0

We can use the quadratic formula to solve this equation:

x = (3 +/- √(9 - 8)) / 2 = (3 +/- √(1)) / 2 = (3 +/- 1) / 2

This gives us two more x-intercepts at x = 2 and x = 4.

So the x-intercepts of the graph of f(x) are x = 2, x = 3, and x = 4.

To find the y-intercept, we set x equal to 0 and solve for y. In this case, the equation we need to solve is:

f(0) = 0^3 - 6(0)^2 + 11(0) - 6 = -6

This gives us a y-intercept at (0, -6).

So the y-intercept of the graph of f(x) is (0, -6).

All of the intercepts of the graph of f(x) are, therefore (0, -6), (2, 0), (3, 0), and (4, 0).

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The population of the island after 10 years will be approximately 2385.

The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0e^{(-kt)}[/tex].

Increases in a population's or a dispersed group's membership are referred to as population growth. The actual annual increase in the human population is about 83 million, or 1.1%.

Given,  an island's population grows exponentially and the continuous growth rate is 3% per year and the current population is 1,767.

∴ The population be 10 years from now will be,

[tex]y_{10} = y_0e^{(0.03)\times10}[/tex].

We have written 3% as a decimal and it is the correct way of putting it into the formula for exponential growth or decaying equations.

[tex]y_{10} = 1767e^{0.3}[/tex].

[tex]y_{10} = 1767\times1.35[/tex].

[tex]y_{10} = 2385[/tex].

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Answer:

2.5

Step-by-step explanation:

m is the gradient

to find this we do the change in y/change in x

using the first 2 values we have been given:

change in y= 15-10

change in x= 4-2

5/2= 2.5

the gradient in 2.5

a) The percentage of lemon is 25%

b) The percentage of lemon is 20%

c) The percentage of lemon is 20%

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

a)

Water : Lemon = 3 : 1

Percent of lemon concentrate:

= 1/4 x 100

= 25%

b)

1 part of lemon = 4 part of water

Percent of lemon.

= 1/5 x 100

= 20%

c)

Cups of lemon = 1

Cups of water = 4

Percent of lemon.

= 1/5 x 100

=  20%

Thus,

The percent of each answer is given above.

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The answer of the given expression using BODMAD rule is 25.

What is BODMAS rule?

The BODMAS rule states that the brackets must be solved first, then powers or roots (i.e., of), Division, Multiplication, Addition, and finally Subtraction. Only when the BODMAS rule or the PEDMAS rule is used to solve an expression is the solution deemed to be correct.

(a) 1 x (-6 x -18 - 8) ÷ 4

By using first to simplify the bracket.

1 x ((-6 x -18) - 8) ÷ 4

1 x (108 - 8) ÷ 4

(1 x 100) ÷ 4

100 ÷ 4

25

Hence, the answer of the given expression using BODMAD rule is 25.

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Answer: 16

Step-by-step explanation:

there are 4 1/4 in 1 cup. so it'll be 4 cakes for each cup of oil you have. multiply the number of cakes that can be made per cup (4) by the number of cups you have (4)

(4) x (4) = 16

The distance between the line segments PQ, RS and TV are √53 respectively

The distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.

The formula is given as;

d = √(x₂ - x₁)² + (y₂ - y₁)²

In the first line segment;

P = (0,4), Q = (7, 2)

d = √((7-0)² + (2 - 4)²)

d = √53

b)

R = (-7, 6), S = (-5, -1)

d = √((-1 - 6)² + (-5 --7)²)

d = √53

c)

T = (0, -8), V = (2, -1)

d = √((-1 --8)² + (2 - 0)²)

d = √53

The distance between the lines are all √53 units

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Answer: see below

Step-by-step explanation:

x=0 -3(0)-6y=0 -6y=0 y=0

x=1 -3(1)-6y=0       -4-6y=0    -6y=4      y=4/6 or 2/3

x=2 -3(2)-6y=0      -6-6y=0      -6y=6    y=-1    

x=3 -3(3)-6y=0         -9-6y=0        -6y=9       y= -9/6   or -3/2

x=-1 -3(-1)-6y=0          3-6y=0           -6y=-3       y=1/2  

x              y

-1               1/2

0              0

1               -2/3

2              -1

3             -1 1/2

Alison has traveled six miles on her bike.

Distance is defined as the product of speed and time.

To find how far Alison has ridden her bike, we need to first convert 8 1/2 miles to miles as a mixed number.

We can do this by multiplying the fractional part of the mixed number by the denominator of the fraction:

8 1/2 miles = 8 miles + (1/2 x 2) miles = 8 miles + 1 mile = 9 miles

We can now multiply this distance by 2/3 to find how far Alison has ridden her bike:

9 miles x 2/3 = 6 miles

Therefore, she has ridden her bike 6 miles.

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Answer:

Step-by-step explanation:

If the interest rate is 5%, the monthly payment and total interest would be $2.439.

Interest is the sum of money that must be repaid on a loan or received in exchange for a loan. Principal refers to the borrowed or lent funds. The Amount is the total of the principal plus interest. The term "rate of interest" refers to the rate at which interest is applied to the principal.

Given,

A student receives a subsidized student loan for $10,000 with a 10-year repayment term and interest compounded monthly. Six months after she graduates from college, she will have to begin making payments.

A $10,000 subsidized student loan

Ten-year term of repayment

5.5% interest rate

First, we must determine the loan's future value (FV) over the next six months using the formula below:

FV in 6 months

= Loan Amount× (1 + Interest Rate)⁶ ($10,000×(1 + 0.055) ×6

= $2.7680.

Second, the formula for determining future value is used to determine the monthly payment:

M = FV in 6 months / (((((r)n) - 1) / r).......... (1)

When you enter all the pertinent values into equation (1), you get:

M = $2.7680 / ((((1 + 0.00466666666666667)^144) – 1) / 0.00466666666666667)

M = $2.439

Therefore, if the interest rate is 5.5%, the total amount paid in interest plus monthly payments would be $2.439.

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a. The hare's distance from the starting line is represented by the expression 7.5t.

b. The tortoise's distance from the starting line is represented by the expression 4.5t+820.

c. The number of meters the tortoise is ahead of the hare is represented by the expression 4.5t+820-7.5t.

In the race, the hare is running at a constant speed of 7.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to run that distance. This is represented by the expression 7.5t, where t is the time in seconds it takes the hare to run.

Similarly, the tortoise is crawling at a constant speed of 4.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to crawl that distance, plus the 820-meter head start they were given. This is represented by the expression 4.5t+820, where t is the time in seconds it takes the tortoise to crawl.

To find the number of meters the tortoise is ahead of the hare, we subtract the hare's distance from the starting line from the tortoise's distance from the starting line, which gives us the expression 4.5t+820-7.5t.

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