12. What is the sign of the following? Answer "positive," "negative," or "zero." (CONSIDER SLOPE OF TANGENT)

a. f'(2)
c. f'(4)
e. f'(7)
b. f'(x) in the interval (1, 3)
d. f'(x) in the interval (3,6)
f. f'(x) in the interval (6, 9)
g. f'(x) in the interval (9, 12)
Find the interval(s) where the function is increasing and the interval(s) where it is decreasing:
27. h(x):
37. h(x)=
15. f(x) = 3x +5 17. f(x) = 2x²+x+1 21. g(x)= x³ + 3x² +1
1
2x + 3
83. AVERAGE SPEED OF A HIGHWAY VEHICLE The average speed of a vehicle on a stretch of Route 134 between 6 A.M. and 10 A.M. on a
typical weekday is approximated by the function f(t) = 20t-40√t+50 (0 ≤t≤4)
where f(t) is measured in miles per hour and t is measured in hours, with t = 0 corresponding to 6 A.M. Find the interval where fis
increasing and the interval where f is decreasing and interpret your results.

Answer:

c(x) = .19x + 32.50

Step-by-step explanation:

The cost depends on the number of copies.  The x value is the number of copies and the y value is the cost

c(x) = mx + b  We need to find the rate of change.

(50,42) (150.61)  The rate of change is the change in y over the change in x.

The y values are 61 and 42.  The x values are 150 and 50

[tex]\frac{61-42}{150-50}[/tex] = [tex]\frac{19}{100}[/tex] = .19

We also need the y intercept.  We will use the slope of .19 and the x and y values of one of the points. We could use either point, I am going to use the point (50,42)

y = 42

x = 50

m =.19

y=mx + b

42 = .19(50) + b

42 = 9.5 + b  Subtract 9.5 from both sides

32.50 = b

y = mx + b

y = .19x + 32.50 or

c(x) = .19x + 32.50

Answer:

x> 2

Step-by-step explanation:

18< 9x  Divide both sides by 9

2<x  or x > 2  All the numbers greater than 2 is a solution.

Using theoretical probability, the probability of selecting green ball is 3/11, not selecting green ball is 8/11, selecting orange ball is 6/11 and not selecting orange ball is 5/11.

In the given question,

A bag has 2 red, 3 green, and 6 orange balls.

So total number of balls = 2+3+6 = 11

We have to find the theoretical probability.

(a) We have to find the theoretical probability of selecting green ball.

P(G) = Total number of green balls/Total number of balls

P(G) = 3/11

Hence, the probability of selecting green ball is 3/11.

(b) Now we have to find the theoretical probability of not selecting green ball.

Except green ball there is having red and orange i.e.

Total remaining balls except green = 2+6 = 8

P(G) = Total number of balls except green balls/Total number of balls

P(G) = 8/11

Hence, the probability of not selecting green ball is 8/11.

(c) Now we have to find the theoretical probability of selecting orange ball.

P(G) = Total number of orange balls/Total number of balls

P(G) = 6/11

Hence, the probability of selecting green ball is 6/11.

(d) Now we have to find the theoretical probability of not selecting orange ball.

Except orange ball there is having red and green balls i.e.

Total remaining balls except orange = 2+3 = 5

P(G) = Total number of balls except orange balls/Total number of balls

P(G) = 5/11

Hence, the probability of not selecting orange ball is 5/11.

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Since we are give the area, the length, and the width, we could put it in a formula.

2592=(16)(12)h

Multiply 16 x 12= 192

So now the formula is 2592= 192h

lastly, we divide 192 from 2592

h= 13.5 mm

The length of the line is 10ft  

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse in familiar algebraic notation, a2 + b2 = c2

Given that A kite is flying 8 ft off the ground. Its line is pulled taut and casts a 6-ft shadow

We have to find a third side

By using Pythagoras' theorem. a^2+b^2=c^2

8^2+6^2=c^2

64 +36 = c^2

c^2= 100

c^2= 10

Therefore the length of the line is 10ft

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From the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).

As given in the question,

For the given graph of a function,

Number of points represented on the graph are 5

Points are a, b, c, d, e

Point a, c, e are on the x-axis.

Relative extreme value representing the maximum and minimum value of the graphed function.

For the given graph,

Maximum value represented by point d.

Minimum value represented by point b.

Number of points representing relative extreme values are 2 ( b and d).

Therefore, from the given graph of the function, the number of points on the graph representing relative extreme value are two (b and d).

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Answer:

2 + (-10) = 12

Step-by-step explanation:

The great answers. Thank you. I hope for help to you.

The number of ways the digits of the given number can be arranged would be = 5,040

Factorials are mathematical expressions that are used to show the number of ways a variable can be arranged in a data set.

The number of digits found in the number 7,550,000 = 7

The number of ways the digits can be arranged would be the factorials of 7 (7!) ;

= 7×6×5×4×3×2×1

= 5,040

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Refer to the attachment for your graph.

We solved the system of equations graphically by graphing both equations and identifying the intercept.

The solution is:

(2.41, -1.03)

Here we have only one system of equations, which is:

-x²*y = 6

-x + 2y⁶ = 0

There are multiple ways of solving this, for example, we could isolate the variable "y" on the first equation:

y = -6/x^2

And replace that in the second equation, so we have an equation that only depends on x, but there is an easier way.

We can just graph both equations on the same coordinate axis and see in which points do the graphs intercept. Each intercept will be a solution of the system.

The graph can be seen below, there we can see that the only intersection point is at (2.41, -1.03), so that is the solution of the system.

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The linear function f with  f(0) = 7 and f(3) = 1 is  y = -2x + 7

Linear equation can be represented in slope intercept form as follows:

y = mx + c

where

Therefore,

f(0) = 7 and f(3) = 1

Using linear equation

7 = m(0) + b

b = 7

1 = m(3) + 7

1 - 7 = 3m

-6 = 3m

m = - 6 / 3

m = -2

Therefore, the linear function is y = -2x + 7

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The y-intercept for the given function is (0, -68).

The given function is f(x)=21x²-31x-68.

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (31/42,−6673/84)

Focus: (31/42,−556/7)

Axis of Symmetry: x=31/42

Directrix: y=−3337/42

Plot (0, -68) and (31/42, -6673/84)

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

y-intercept is (0, -68).

Hence, the y-intercept for the given function is (0, -68).

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Answer: As x approaches infinity, f(x) approaches infinity.

As x approaches -infinity, f(x) also approaches - infinity.

Step-by-step explanation:

You can either graph this function on an online graphing (such as desmos. com) calculator to see the end behavior, or you can try inputting some numbers in. You could put in the number 1,2,3 and see that the graph will keep on increasing to positive infinity, and input the numbers -1,-2,-3 to see that the numbers will decrease to negative infinity.

Answer:

chocolate- 2 dollars walnuts- 4

Step-by-step explanation:

2 x3=6. 14-6=8

8÷2=4

Answer: (y - 1) = 4(x + 8)

Step-by-step explanation:

The point-slope form is (y - y₁) = m(x - x₁), where:

So, the point-slope of this line would be (y - 1) = 4(x + 8).

The number of each type of stamp used is as follows:

Melinda needed to mail a package. She used .02 stamps and .10 stamps to mail the package. She used 15 stamps worth 0.78. The number of each type of stamp she used can be calculated as follows:

let

x = number of 0.02 stamp

y = number of 0.10 stamp

Using system of equation,

x + y = 15

0.02x + 0.10y = 0.78

multiply equation(ii) by 50

x + y = 15

x + 5y = 39

4y = 24

y = 24 / 4

y = 6

Hence,

x = 15 - 6

x = 9

Therefore, the number of 0.02 stamps is 9 and the number of 0.10 stamp is 6.

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Withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]

What do you mean by simple interest and compound interest?

Simple interest can be defined as the amount that is paid back using borrowed money over a period of time.

simple interest:

Simple interest can be defined as the principal of a loan or deposit that an individual puts into a bank account.

Compound interest:

Compound interest is interest that accrues on the principal and accrues interest.

Given:

Principal, P = $710000

Rate of interest, r = 8.25%

Time period, t = 20 years

withdrawal at the end of 20 years , A = [tex]P(1+r)^{t}[/tex]

A = [tex]710000(1+8.25/100)^{20}[/tex] = [tex]710000(1+0.0825)^{20}=710000(1.0825)^{20}[/tex]

Therefore, withdraw at the end of each of the next 20 years is [tex]710000(1.0825)^{20}[/tex]

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1. An equation representing the number of days Amir has been reading and the number of pages he has read is y = 35x.

2. An equation representing the number of days Jesse has been reading and the number of pages she has read is y = 30 + 30x.

3. The system of equations from 1 and 2 is y = 35x and y = 30 + 30x.

4. At the end of Friday, after solving the equations, both Jesse and Amir read 210 pages each, with Jesse spending 7 days and Amir 6 days.

5. For Jesse and Amir, the equation solutions are y is 210 pages and x is 6 days.

6. After solving the equations, it will take Amir 6 days to catch up with Jesse and each person must have read 210 pages or a total of 420 pages.

A system of equations involves using more than one equation solved simultaneously.

Jesse's reading rate per day = 30 pages

Amir's reading rate per day = 35 pages

The number of pages read by Jesse, y = 30 + 30x

The number of pages read by Amir, y = 35x

Where x = the number of days they have been reading

y = 30 + 30x and y = 35x

35x  = 30 + 30x

35x - 30x = 30

5x = 30

x = 6 (30/5)

y = 30 + 30x

y = 30 + 30(6)

y = 210

y = 35x

y = 35(6)

y = 210

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[tex]a=\frac{6}{5}[/tex].

[tex]a+\frac{4}{5} =\frac{1}{\frac{1}{2} }[/tex]

[tex]a+\frac{4}{5} =1*\frac{2}{1} \\ \\a+\frac{4}{5} =2[/tex]

[tex]a+\frac{4}{5}-\frac{4}{5} =2-\frac{4}{5}\\ \\a=\frac{2}{1}-\frac{4}{5}\\\\a=\frac{2*5}{1*5}-\frac{4}{5}\\ \\a=\frac{10}{5}-\frac{4}{5}\\ \\a=\frac{10-4}{5} \\ \\a=\frac{6}{5}[/tex]

[tex](\frac{6}{5} )+\frac{4}{5} =\frac{1}{\frac{1}{2} }\\ \\\frac{10}{5} =2\\ \\2=2[/tex]

[tex]a=\frac{6}{5}[/tex].

The expression 2(3+4) can be expressed as 2×7

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

For example the factors of 8 are 1,2,4,8. i.e 1×8=8, 2×4= 8

considering the expression 2(3+4), the value is 2(7)= 14

Therefore the expression can be expressed as product of two factors (2 and 7) as 2×7.

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Answer:

as decimal

0.27083333333

Answer:

2 3/5 divided by 9 3/5 is 32

The range of six numbers is 8

According to the question,

Total number of Number = 6

Mean of number = 8

Ratio of numbers = 1 : 1 : 2 : 2 : 3 : 3

Let the common factor in numbers be "x"

Then , sum of number will be x + x + 2x + 2x + 3x +3x

=> 12x

Mean = sum of quantity / Number of quantity

8 = 12x / 6

Calculating the value of x,

12x = 48

=> x = 4

Substituting the value of x,

Number will be : 4 , 4 , 8 , 8, 12 , 12

Range = highest number - smallest number

Here , highest is 12 and smallest is 4

Therefore , Range = 12 - 4

=> 8

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Answer:

La altura en metros de cada piso es:

3.2 metros

Step-by-step explanation:

1 hectómetro = 100 metros.

1.92 metros = 1.92 * 100 = 192 m

192/60 = 3.2 metros/piso

Hay un total de 2730 combinaciones posibles.

en carrera de 15 caballos si se consideran 3 posiciones

entonces número de combinaciones posibles = 15 * 14 * 13 = 2730 combinaciones posibles

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The groups would 1 x 1000+  2 x 10 + 1 x 1 + 6 x 1/10

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation can be used to quickly and easily fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome.

Given:

Divide: 5,108 ÷ 5

Now, dividing

   5 | 5108  | 1021.6

        5

   _______

        0 10

            10

        _____

             0 8

                 5

          _____

                 3 0

                 3 0

               ______

                   0

Hence, the groups would 1 x 1000+  2 x 10 + 1 x 1 + 6 x 1/10

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The value of the functions f(-1), f(2), and f(5) are -2, 4, -2 respectively.

What is the function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). The number of dependent variables for a function is 1 and the number of independent variable for a function is 1.

Given function is:

[tex]f(x)=\left\{\begin{matrix}-2 & \text{if } x \ne2 \\ 4 & \text{if } x=2\end{matrix}\right.[/tex]

The meaning of the above function is when x is not equal 2, then the value of f(x) is -2 and when x is equal 2, then the value of f(x) is 4.

The dependent variable is f(x). The independent variable is x.

So the value of f(-1) is -2 since x = - 1 ≠ 2.

So the value of f(2) is 4 since x = 2.

So the value of f(5) is -2 since x = 5 ≠ 2.

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Answer:

Step-by-step explanation:

The maximum that the company can expect for returned items is C. $5972.65

How to calculate the value?

From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.

In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.

The maximum the company can expect for returned items will be:

= (15% + 4%) × Profit

= 19% × $31,435

= 0.19 × $31,435

= $5972.65

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Answer: x=-y+9

y=-x+9

Step-by-step explanation:

Answer:

The asymptote indicates that as the number of weeks the farmer has had the cats increases, the population of mice approaches 0.

The y-intercept represents the number of mice the farmer had in the barn at the time he adopted the cats.

The line y = 0 is an asymptote of the graph.

The y-intercept is 800.

Step-by-step explanation:

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