calculate the average rate of change between consecutive data points in parts A through C to determine whether the output in each table is a linear function of the input A) input -5 0 5 8 output -50 -5 40 67B) input 2 7 9 14 output 0 15 18 20C) input -4 0 3 5 output 25.8 1 21.1 34.5A) Select the correct choice below and if necessary, fill-in the answer box to complete your choice. a) The average rate of change between consecutive data points in table a is ___ Thus, the output is a linear function of the input(simplify answer) b) The output is not a linear function of the input.

Answer:

25.46

Step-by-step explanation:

6.7X3.8

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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Answer:

C. 7°F

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find all real solutions of the equation. ( 2 b + 4 ) 2 − 12 = 0

( 2 b + 4 ) 2 − 12 = 0

4b + 8 - 12 = 0

4b - 4 = 0

4b = 4

b = 1

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

check

(2*1+4)*2-12=0

12 - 12 = 0

0 = 0

the answer is good

Answer:

yes

Given a 2D line e.g. (3,10) -> (8.3,16.5), how can I find any point on that line that has has whole-number coordinates?

I can easily iteratively walk along one of the axis in integer steps, seeing if the value on the other axis is integer, but this is slow for very very long lines.

The measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

To find the measure of angle ADM, we need to consider that angle ADM is an inscribed angle and its measure is half the measure of the intercepted arc AD.

Given that the measure of arc CD equals the measure of arc DA, it means that these arcs are congruent.

Therefore, the intercepted arcs AD and CD have equal measures.

Since angle ADM is an inscribed angle intercepting arc AD, the measure of angle ADM is half the measure of arc AD.

Therefore, the measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.

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The calculation of this can be done by first determining the future value of the monthly payments of $327.50

The future value of an annuity can be determined using a financial calculator, mathematical formula, or spreadsheet software. The future value of an annuity is calculated by multiplying the periodic payment amount by the future value factor,

which is based on the number of payments and the interest rate.For example, suppose we want to know the future value of a $500 end-of-month deposit into an annuity that pays 6% interest compounded monthly for five years.

The future value factor for 60 periods at 0.5 percent per month is 80.9747, which can be multiplied by the monthly deposit amount to find the future value of the annuity.500 × 80.9747 = 40,487.35

This means that a $500 end-of-month deposit into an annuity paying 6% interest compounded monthly for five years will have a future value of $40,487.35.

Therefore, to accumulate a $20,000 down payment for a home in five years, you would need to deposit $327.50 per month into the annuity.

 for 60 months using the formula and then solving for the monthly payment amount where FV = $20,000 and n = 60, r = 0.5%.FV = PMT [(1 + r)n – 1] / r$20,000 = PMT [(1 + 0.005)60 – 1] / 0.005PMT = $327.50 (rounded to the nearest cent).

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please use

here m = mass = 2.26 grams\

C = specific heat capacity of water that is 4.2 j / g C

delta T is the difference in temperature.

H = 2.26 * 4.2 * (50 - 25)

H = 237.3 J

so the answer is,

the energy needed is 237.3 Joule or 237.3 J

Answer:

\(1\)

Step-by-step explanation:

\(log(6)-log(16)+log(4)-log(3)+log(20)\)

\(0.77815125038-1.20411998266+0.60205999132-0.47712125472+1.30102999566\)

\(=0.99999999998\)

Answer:

3:5

Step-by-step explanation:

If we count the amount of At symbols, there are 6. The amount of all the symbols combined is 10, meaning there is a ratio of 6:10 for At symbols to all symbols. 6:10 can be simplified, however, by dividing by two.

6 ÷ 2 = 3

10 ÷ 2 = 5

The simplified ratio is 3:5.

≧◡≦

Mocha here! If this answer helped you, please consider giving it brainliest because I would appreciate it greatly. Have a wonderful day!

Answer:

  4. 48, 24, 12

  21. A, B, B, C

Step-by-step explanation:

There are two different questions here. One where you get to make up an exponential function and write a table of values. The other is a statistics problem in which you compare 5-number summaries.

__

For the function f(x) = a·b^x, the value of f(0) is 'a'. The given table shows a=96. The only requirement for choosing 'b' is that it not be 1. We can choose b=1/2, and our table will be ...

  y = 96·(1/2)^x

  \(\begin{array}{c|cccc}x&0&1&2&3\\y&96&\boxed{48}&\boxed{24}&\boxed{12}\end{array}\)

For each increase of x by 1 unit, the value of y is cut in half.

__

The attachment shows you how to find the answers to the questions.

The median is the bar in the middle of the box. The values for the different teams are ...

Team A has the lowest median; Team B has the highest median.

The interquartile range (IQR) is the length of the box. For the different teams, the values are ...

Team B has the smallest IQR; Team C has the largest.

Answer:

\(f(3) = \frac{-26}{9}\)

\(f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}\)

Step-by-step explanation:

Given

\(f(x) = \frac{1}{x^2} - 3\)

Required

Find f(3) and f(2 + h)

Solving f(3)

Substitute 3 for x in \(f(x) = \frac{1}{x^2} - 3\)

\(f(3) = \frac{1}{3^2} - 3\)

\(f(3) = \frac{1}{9} - 3\)

Take LCM

\(f(3) = \frac{1 - 27}{9}\)

\(f(3) = \frac{-26}{9}\)

Solving f(2 + h)

Substitute 2 + h for x in \(f(x) = \frac{1}{x^2} - 3\)

\(f(2 + h) = \frac{1}{(2 + h)^2} - 3\)

\(f(2 + h) = \frac{1}{(2 + h)(2 + h)} - 3\)

\(f(2 + h) = \frac{1}{4 + 2h + 2h + h^2} - 3\)

\(f(2 + h) = \frac{1}{4 + 4h + h^2} - 3\)

Take LCM

\(f(2 + h) = \frac{1- 3(4 + 4h + h^2)}{4 + 4h + h^2}\)

\(f(2 + h) = \frac{1- 12 - 12h - 12^2}{4 + 4h + h^2}\)

\(f(2 + h) = \frac{- 11 - 12h - 12^2}{4 + 4h + h^2}\)

Answer:

220

Step-by-step explanation:

If we lost 12% we still have 100 - 12 = 88% of the employees left. 88% can be written as 0.88. 0.88 * 250 = 220 employees left.

Answer:

A.

Step-by-step explanation:

In the attached file

Answer:

9.8 miles per hour

3·60= 180+35=215 2107÷215=9.8

Answer:

9.8 mph

Step-by-step explanation:

you start off by using the formula associated with finding your desired answer which in this case is

rate=distance/time

x=2107/3hrs 35 minutes or 215 minutes

x=9.8

Answer:

62.5

Step-by-step explanation:

speed = distance / time taken

= 125/2

=62.5miles per hour

One of the Possible values of length and width of the prism are 15 cm and 0.5 cm

In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.

Given here: The volume of the prism is 2¹/₂=2.5 cm³

And the height is 1/3 cm

let the length and breadth of the prism is x and y respectively.

We know the volume of the prism as

1/3 × x×y=2.5

x×y=7.5

Thus possible values of length and breadth are the factors of 7.5

out of which one of the pair whose length is 15 cm and width 0.5 cm

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The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answers:

============================================================

Work Shown:

Part (a)

The origin is the point (0,0) which we'll make the first point, so let (x1,y1) = (0,0)

The other point is of the form (x,y) where y = x^2-3. So the point can be stated as (x2,y2) = (x,y). We'll replace y with x^2-3

We apply the distance formula to say...

\(d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(0-x)^2+(0-y)^2}\\\\d = \sqrt{(0-x)^2+(-y)^2}\\\\d = \sqrt{x^2 + y^2}\\\\d = \sqrt{x^2 + (x^2-3)^2}\\\\\)

We could expand things out and combine like terms, but that's just extra unneeded work in my opinion.

Saying \(d = \sqrt{x^2 + (x^2-3)^2}\) is the same as writing d = sqrt(x^2-(x^2-3)^2)

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

Part (b)

Plug in x = 0 and you should find the following

\(d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(0) = \sqrt{0^2 + (0^2-3)^2}\\\\d(0) = \sqrt{(-3)^2}\\\\d(0) = \sqrt{9}\\\\d(0) = 3\\\\\)

This says that the point (x,y) = (0,3) is 3 units away from the origin (0,0).

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

Part (c)

Repeat for x = 1

\(d(x) = \sqrt{x^2 + (x^2-3)^2}\\\\d(1) = \sqrt{1^2 + (1^2-3)^2}\\\\d(1) = \sqrt{1 + (1-3)^2}\\\\d(1) = \sqrt{1 + (-2)^2}\\\\d(1) = \sqrt{1 + 4}\\\\d(1) = \sqrt{5}\\\\d(1) \approx 2.23606797749979\\\\d(1) \approx 2.24\\\\\)

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

Part (d)

Graph the d(x) function found back in part (a)

Use the minimum function on your graphing calculator to find the lowest point such that x > 0.

See the diagram below. I used GeoGebra to make the graph. Desmos probably has a similar feature (but I'm not entirely sure). If you have a TI83 or TI84, then your calculator has the minimum function feature.

The red point of this diagram is what we're after. That point is approximately (1.58, 1.66)

This means the smallest d can get is d = 1.66 and it happens when x = 1.58 approximately.

The probability that Julie will be a captain, given that she makes the team is 1/3.

Given,

Number of students trying out for a soccer team = 40

Case of probability,

P(A) = n(A)/n(S)

n(A) = number of favourable outcomes, n(S) is the total number of events in the sample space.

Given ,

18 of 40 students will make the soccer team.

⇒ n(S) = 18

Let event A: Julie will be a captain, given that she makes the team

⇒ n(A) = 3

So, the probability that Julie will be a captain, given that she makes the team,

= P(A) = n(A)/n(S)

= P(A) = 3/18

= P(A) = 1/6

Therefore, the probability that Julie will be a captain, given that she makes the team is 1/3.

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Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

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Answer:

Speed of Sharon on country roads = 50 mph

Step-by-step explanation:

Let the speed of Sharon on interstate roads was = a mph

And the speed on country roads = b mph

Time taken by Sharon to travel 390 miles on interstate = \(\frac{\text{Distance}}{\text{Speed}}\)

= \(\frac{390}{a}\) hours

Time taken by Sharon to travel 150 miles on country roads = \(\frac{150}{b}\) hours

"Total time for the trip = 9 hours"

\(\frac{390}{a}+\frac{150}{b}=9\)

\(\frac{130}{a}+\frac{50}{b}=3\) --------(1)

"Her speed on interstate was 15 mph more than on country roads".

a = b + 15 ---------(2)

By substituting the value of a from equation (2) to equation (1),

\(\frac{130}{(b+15)}+\frac{50}{b}=3\)

\(\frac{130b+50(b+15)}{b(b+15)}=3\)

180b + 750 = 3b(b + 15)

180b + 750 = 3b² + 45b

3b² + 45b - 180b - 750 = 0

3b² - 135b - 750 = 0

b² - 45b - 250 = 0

b² - 50b + 5b - 250 = 0

b(b - 50) + 5(b - 50) = 0

(b + 5)(b - 50) = 0

b = -5, 50

But the speed can't be negative,

Therefore, b = 50 mph

Speed of Sharon on country roads was 50 mph.

Consider we need to find the number of elements in the sample space.

Given:

Jo flips a coin {H, T}; then rolls a 6-sided die {1, 2, 3, 4, 5, 6}.

To find:

The number of elements in the sample space of this experiment.

Solution:

Jo flips a coin {H, T}; then rolls a 6-sided die {1, 2, 3, 4, 5, 6}.

So, the sample space is

S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

So, the number of elements in the sample space is 12.

Therefore, the correct option is C.

Answer:

12

Step-by-step explanation:

The equation can you use to find the rental cost, d, of each day they used the RV is 895=8d+55

What does $895 comprises of?

The $895 paid  for the duration of the trip consists of the payments for the RV for 8 days and additional amount of $55 which is for the outdoors upgrade.

The equation that can be used to determine rental cost per , d , per day considers that the total rental cost is number of days, 8 days  multiply by the rental  cost per day, which is d, and also that the final $55 is specifically for outdoors upgrade

Total cost=d*8+$55

Remember total cost of the trip is $895

$895=8d+$55

Which we can rewrite the expression by ignoring the dollar sign as below:

895=8d+55

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The measurement that is closest to the volume of the sphere is given as follows:

1,767.1 in³.

The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

\(V = \frac{4\pi r^3}{3}\)

From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:

r = 0.5 x 15

r = 7.5 units.

Then the volume of the sphere is given as follows:

V = 4/3 x π x 7.5³

V = 1,767.1 in³.

The sphere is given by the image presented at the end of the answer.

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Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)

Answer:

I think the answer is this 2x+3