The following table shows the world record times for the 200m race for flying start machines (a kind of bicycle). Find the line of best fit model, R(t) , that represents the world record times , t, since 1970. Before determining the equation , we need to convert all years to years since 1970. The first two rows are completed for you . Complete the rest of the table with the correct years since 1970 . After completing the table , use Excel to create a linear regression equation using only the second two columns . Do not use any spaces in your submission .

Using translation concepts, the transformed triangles are given in the graph at the end of the answer.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.

For this problem, the coordinates of triangle PQR are given as follows:

P(-1,-1), Q(-3,-2), R(-3,-4).

The rule for a 90º clockwise rotation around the origin is given by:

(x,y) -> (y,-x).

Hence the coordinates of triangle P'Q'R' are given by:

The rule for a reflection over the y-axis is:

(x,y) -> (-x,y).

Hence the coordinates of triangle P''Q''R'' are given by:

Both triangles are given in the graph at the end of the answer.

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The answers are below.

a) (fog)(x) = f(g(x)) = 2 - ( 3x² +x+5) = -3x² - x - 3

b) (gof)(x) = g(f(x)) = 3*(2 - x)² + (2 - x) +5 = 3x² - 13x + 19

a) (fog)(2) =  -3x² - x - 3 = -3*4 - 2 - 3 = -12 - 2 - 3 = -17

b) (gof)(2) = 3x² - 13x + 19 = 3*4 - 13*2 + 19 = 12 - 26 + 19 = 5

Just replace evaluate the function g(x)= 3x² +x+5 insode of the function f(x) = 2 - xfor the first one.

a) (fog)(x) = f(g(x)) = 2 - ( 3x² +x+5) = -3x² - x - 3

b) (gof)(x) = g(f(x)) = 3*(2 - x)² + (2 - x) +5 = 3x² - 13x + 19

ok, now that you have these two values, just evaluate the equations in x = 2 to get the rest.

a) (fog)(2) =  -3x² - x - 3 = -3*4 - 2 - 3 = -12 - 2 - 3 = -17

b) (gof)(2) = 3x² - 13x + 19 = 3*4 - 13*2 + 19 = 12 - 26 + 19 = 5

These are the outcomes when we evaluate the compositions in x = 2.

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Answer:

true for the first one and also true for the other one.

Simplifying the given value using the law of indices is 6[tex]a^{3}[/tex]

2a * 3[tex]a^{2}[/tex]

=6[tex]a^{3}[/tex]

Index laws are the rules for simplifying expressions involving powers of the same base number.

Here are  the essential  steps to follow to simplify an algebraic expression:

Remove parentheses by multiplying factors.

Use exponent rules  to get rid of  parentheses in terms with exponents.

Combine like terms by adding coefficients.

Combine the constants.

Here's  differently  to explain it: The is used to refer to a specific or particular member of a group.  for instance , "I just saw  the foremost  popular movie of the year." There are many movies, but  just one  particular movie is the most popular.

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[tex]\frac{10.25}{100}[/tex]Answer:

Step-by-step explanation:

The formula for simple interest is: A= P(1+in)

The formula for compound interest is: A=P[tex](1+i)^{n}[/tex]

A= amount after added interest

P= initial amount invested

i= interest rate

n= number of periods (in this case its 7 years)

*REMEMBER THIS FORMULA

a) A=0

P=?

i=10,25

n=7

(simple interest)

a) A= 0 (1 +[tex]\frac{10.25}{100}[/tex] ×7)

=0

b) A=2 000 (1 + [tex]\frac{10.25}{100}[/tex] ×7)

A=3435

c) A= 3 000( 1 + [tex]\frac{10.25}{100}[/tex] ×7)

A= 5152.5

d) 5000(1 + [tex]\frac{10.25}{100}[/tex] ×7)

= 8587.5

It's just a matter of substitution. I hope this helped.

Answer:

(a) $668.39

(b) $634.93

(c) $618.20

(d) $584.74

Step-by-step explanation:

Monthly Payment Formula

[tex]\sf PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}[/tex]

where:

Given:

Down payment = $0

⇒ P = $39,950

[tex]\implies \sf PMT=\dfrac{39950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]

[tex]\implies \sf PMT = 668.3892086[/tex]

Therefore, the monthly payment is $668.39.

Down payment = $2,000

⇒ P = $39,950 - $2,000 = $37,950

[tex]\implies \sf PMT=\dfrac{37950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]

[tex]\implies \sf PMT = 634.9279215[/tex]

Therefore, the monthly payment is $634.93.

Down payment = $3,000

⇒ P = $39,950 - $3,000 = $36,950

[tex]\implies \sf PMT=\dfrac{36950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]

[tex]\implies \sf PMT = 618.197278[/tex]

Therefore, the monthly payment is $618.20.

Down payment = $5,000

⇒ P = $39,950 - $5,000 = $34,950

[tex]\implies \sf PMT=\dfrac{34950\left(\dfrac{0.1025}{12}\right)\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}}{\left(1+\left(\dfrac{0.1025}{12}\right)\right)^{84}-1}[/tex]

[tex]\implies \sf PMT = 584.735991[/tex]

Therefore, the monthly payment is $584.74.

The area covered by circular rug of diameter 7 is 38.5 m².

Circle is locus of points equidistant from a center point. This distance from center to the boundary of circle is radius.

If r is the radius of a circle , then its Area = π(r²)

Given that a circular rug has diameter = 7 m

Then, Let radius of circular rug be  r ,r = diameter /2

r =  7/2 m

Area =  π(7/2)² = (22/7)*(7/2)² m² =  38.5 m²

Therefore , Area of the circular rug is 38.5 m²

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The point that represents an INEFFICIENT point of production is point A.

The correct answer is an option (a)

In this question we have been given a graph of Skateboards vs. Bikes.

We need to find the point that represents an INEFFICIENT point of production.

Inefficient production means the economy can be producing more goods without using any additional resources.

In given production possibility curve, an INEFFICIENT point of production is point A.

Therefore, the point that represents an INEFFICIENT point of production is point A.

The correct answer is an option (a)

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The weight of coffee worth $10 to be added to mixture to worth $6 a pound is 15 pounds the mixture will be  15 pounds

Let the weight of coffee worth $10 to be added to mixture be x pounds

The weight of coffee worth $4 to be added to mixture is 30 pounds

We want a mixture that worth $6 a pound

The weight of mixture of coffee worth $ 6 is the sum of $10 coffee and $4 coffee

    = x + 30

From the above equation we can form a linear equation

              X 10 + 30 ×4 = (x+ 30) 6

    10x + 120= 6x +180

    10x-6x= 180 -120

         4x = 60

               X= 15

Hence, the weight of coffee worth $10 to be added to mixture to worth $6 a pound is 15 pounds

what's a linear equation ?

A linear equation only has one or  variables. No variable in a linear equation is raised to a strength greater than 1 or used because the denominator of a fraction. while you discover pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all the factors lie at the same line

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Answer:

28333.33

Step-by-step explanation:

68000/240% = 28333.33333333333

= 28333.33

Answer:

Step-by-step explanation:

360° - the know angles

360 - 20 - 70 - 20 = 250°

Step-by-step explanation:

Well this is a full circle, and in a full circle, theres 360 degrees.

So if we add up 20, 70 and 20 degrees, it comes to a total of 110 degrees.

If we subtract 110 d from 360 d, we get 250 degrees. Therefore,

Hope this helped

Answer:The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

Step-by-step explanation:

The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

The equation of a circle usually takes the form;

(x-a)² + (y-b)² = r²

where a and b are x- and y- coordinates of the center of the circle.

In this scenario, the center is at the origin (0,0).

In essence, the points on the circle which have an x-coordinate of 1 can be evaluated as follows;

(1-0)² + (y - 0)² = 4²

1 + y² = 16.

y² = 15

y = ±√15.

The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)

Answer:

Step-by-step explanation:

5(9) = 45

Considering the definition of probability and its properties:

Probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

P(A)= number of favorable cases÷ number of total cases

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A ∩ B is verified when A and B occur simultaneously.

A complementary event, also called an opposite event, is made up of the inverse of the results of another event.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

The conditional probability P(A|B) is the probability that an event A occurs, knowing that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. It is defined as:

P(A|B) = P(A∩B)÷ P(B)

In first place, let's define the following events:

You know:

The probability that a student is a freshman or a mathematics mayor is:

P [(F∪M)']= 1- P(F∪M)

7/51= 1 - P(F∪M)

7/51 - 1= -P(F∪M)

-44/51= -P(F∪M)

44/51= P(F∪M)

So, the probability that the student is both a freshman and a mathematics major is calculated as:

P(F∪M)= P(F) + P(M) -P(F∩M)

44/51= 23/51 + 30/51 - P(F∩M)

44/51- 23/51 - 30/51= - P(F∩M)

-3/17= - P(F∩M)

3/17= P(F∩M)

Finally, the probability that the student is both a freshman and a mathematics major is 3/17.

The probability that a student is a mathematics major, knowing that he is also a freshman, is calculated as:

P(M|F) = P(M∩F)÷ P(M)

So:

P(M|F) = 3/17÷ 30/51

P(M|F) = 3/10

Finally, given that the student selected is a freshman, what is the probability that he is also a mathematics major is 3/10.

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136000 many bacteria will there be in 17 hours at a rate of 4 percentage per hour.

What is an example of a percentage?

given ,

          rate = 4%

bacteria  starts growing = 320

                 rate = 4%

  4% = 320

  1 = [tex]\frac{320 * 100}{4} = 8000[/tex]

bacteria will there be in 17 hours =  17 ×  8000

                                                       =  136000

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[tex]3y \geqslant 9 \\ y \geqslant \frac{9}{3} \\ y \geqslant 3[/tex]

Answer: y > 3

Step-by-step explanation: 3y > 9
3y/3 > 9/3

y > 3

Correct answer is D. For the numerical equation, If m = 8 and n = 4, all of the following represent the same value except mn.

Numbers and their operations are used to represent a numerical equation. Statements can also be used to create mathematical expressions.

On calculating, the following values,

If m = 8 and n = 4;

For 1/2m, the value will be -

1/2 × 8 = 4                                                    .......(1)

For n/1 the value will be -

4/1 = 4                                                          .......(2)

For m-n the value will be -

8 - 4 = 4                                                       .......(3)

For mn, the value will be -

8 × 4 = 32                                                     ......(4)

From (1), (2), (3), (4) it can be seen that the value is same instead for mn.

Complete question -

If m = 8 and n = 4, all of the following represent the same value except _____.

1/2 m

n/1

m-n

mn

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Answer: what is question here?

Step-by-step explanation:

Where are answers?

Answer:

m=33

Step-by-step explanation:

Step 1: Subtract 1 from both sides.

3m+1−1=100−1

3m=99

Step 2: Divide both sides by 3

m=33

Step-by-step explanation:

solve:

3m+1=100

3m=99

99/3=33

m=33

check:

m= 33

33*3=99

99+1=100

Answer:

Where is the question?

The amount of Alfalfa hay is 385.71 lbs

The amount of Clover is 572.45 lbs.

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

We have,

Alfalfa hay = 18 % CP

Clover = 4% CP.

The total amount of ration is 600 lbs of a 13% CP.

Let x pounds of alfalfa hay have been used.

The amount of clover will be 600 - x lbs.

The CP amount in 600 lbs mixture will be equal to the sum of CP amounts in x lbs alfalfa and (600 - x) lbs clover.

13% of 600 = 18% of x + 4% of (600 - x)

We need to find x.

13/100 x 600 = 18/100 x (x) + 4/100 x (600 -x)

78 = 18x / 100 + 24 - 4x/100

78 - 24 = 18x/100 - 4x/100

54 = 14x / 100

14x = 54 x 100

x = 5400/14

x = 385.71 lbs

Thus,

The amount of Alfalfa hay= 385.71 lbs

The amount of Clover = 600 - 385.71 = 572.45 lbs.

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The measure of angle A is 62 degrees

Supplementary angles are angles that sunset up to 180 degrees. For instance, if A+B = 180, then A and B are supplementary

The sum of supplementary angles is 180 degrees such that;

<A + <B = 180

Given the following parameters

<A = 2x-4

<B = 4x-14

Substitute

2x-4 +4x-14 = 180

6x - 18 = 180

6x = 198

x = 198/6

x = 33

<A = 2x - 4

<A = 2(330 - 4

<A = 62 degrees

Hence the measure of angle A is 62 degrees

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Cost of a bottle of juice is $ 1.62

Equation for determining the cost of juice is 1.56 + 20x = 33.96

Given,

The cost of a bag of chips = $ 1.56

Number of juice bottles bought by Sarah = 20 pack

Total cost before tax = $ 33.96

Cost of one bottle of juice = x

We have to find x:

Then the equation will be:

1.56 + 20x = 33.96

Add -1.56 to both sides:

1.56 + 20x - 1.56 = 33.96 - 1.56

We get,

20x = 32.4

Now find x,

x = 32.4 / 20

Then,

x = 1.62

That is, the equation for finding the cost of a bottle of juice is 1.56 + 20x = 33.96.

The cost of one bottle of juice is $1,62

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The volume of the shed ordered by Lorie to hold her gardening supplies is (option a) 1423.5 cubic ft.

Given,

Lorie ordered a shed to hold her gardening supplies.

The length of the shed, l = 18.25 feet

The width of the shed, w = 15 feet

The height of the shed, h = 5 1/5 feet = 26/5 = 5.2 feet

We have to determine the volume of the shed:

From the given data we can assume that the shed is like a cuboid. So to determine the volume, we can use the cuboidal formula.

That is,

Volume = length × width × height

V = l × w × h

V = 18.25 × 15 × 5.2

V = 1423.5 feet

Therefore, the volume of the shed ordered by Lorie to hold her gardening supplies is 1423.5 feet.

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Answer:

[tex]{ \tt{( \frac{ - 4}{9} \times \frac{63}{28}) - ( \frac{33}{66} \times \frac{ - 51}{17} ) + ( \frac{5}{8} \times \frac{4}{10)} }} \\ \\ = { \tt{( \frac{ - 4}{28} \times \frac{63}{9}) - ( \frac{1}{2} \times \frac{ - 3}{1} ) + ( \frac{5}{10} \times \frac{4}{8} )}} \\ \\ { \tt{ = ( - 1) - ( - \frac{3}{2} ) + ( \frac{1}{4}) }} \\ \\ = { \tt{ \frac{3}{4} }}[/tex]

Answer:

[tex]\sf \dfrac{3}{4}[/tex]

Step-by-step explanation:

Given expression:

[tex]\implies \sf \left(\dfrac{-4}{9} \times \dfrac{63}{28}\right)-\left(\dfrac{33}{66} \times \dfrac{-51}{17}\right)+\left(\dfrac{5}{8} \times \dfrac{4}{10}\right)[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \times \dfrac{c}{d}=\dfrac{a \times b}{c \times d}:[/tex]

[tex]\implies \sf \left(\dfrac{-4\times63}{9\times28} \right)-\left(\dfrac{33 \times -51}{66 \times 17}\right)+\left(\dfrac{5\times4}{8\times10} \right)[/tex]

Multiply the numbers:

[tex]\implies \sf \left(\dfrac{-252}{252} \right)-\left(\dfrac{-1683}{1122}\right)+\left(\dfrac{20}{80} \right)[/tex]

Reduce the fractions:

[tex]\implies \sf -1-\left(\dfrac{-3}{2}\right)+\left(\dfrac{1}{4} \right)[/tex]

[tex]\textsf{Apply rule}\quad \:a-\left(-b\right)=a+b:[/tex]

[tex]\implies \sf -1+\dfrac{3}{2}+\dfrac{1}{4}[/tex]

Adjust the fractions based on the LCM of 4:

[tex]\implies \sf \dfrac{-4}{4}+\dfrac{6}{4}+\dfrac{1}{4}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]

[tex]\implies \sf\dfrac{-4+6+1}{4}[/tex]

Add the numbers in the numerator:

[tex]\implies \sf \dfrac{3}{4}[/tex]

For the given equation 6e^4x = 14, the value of x is [tex]x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]

Getting x alone on one side of the equation and everything else on the other side will be the first step towards solving for x. The golden rule of algebra states that everything done to one side of an equation must also be done to the other.

Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.

For the given equation,

6e^4x = 14

[tex]x = ln \frac{3^{3/4} * \sqrt[4]{7} }{3}\\ \\x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]

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Answer:

Step-by-step explanation:

0.195/12 = 0.0163 = 1.63%

Hence, the monthly periodic rate is [tex]1.63[/tex]%.

What is the periodic rate?

A periodic interest rate is a rate that can be charged on a loan, or realized on an investment over a specific period of time.

Lenders typically quote interest rates on an annual basis, but the interest compounds more frequently than annually in most cases.

Here given that,

Loan with an APR of [tex]19.5[/tex]%

So, [tex]19.5[/tex]% is

[tex]\frac{19.5}{100}=0.195[/tex]

Annual periodic rate means [tex]12[/tex] months.

then,

[tex]{0.195}{12}=0.0163\\[/tex]

[tex]=1.63[/tex]%

Hence, the monthly periodic rate is [tex]1.63[/tex]%.

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Answer:

3

Step-by-step explanation:

3  seeing as most dogs (5 dogs) are at the age of 3

Answer: 1680

Step-by-step explanation:The answer is 1680 because 56 percent of 3000 is 1680 people and 44 percent of 3000 is 1320 people