The graphs below have the same shapes. What is the equation for the red graph?

Answer:

[tex] \frac{3}{2} n {}^{2} + \frac{9}{2} n - 12[/tex]

Step-by-step explanation:

This sequence is a quadratic sequence meaning that we should find the difference and the constant second difference.

The difference between the 4 terms is in the sequence:

9;12;15

The constant second difference is 3.

Use your method of finding the general term:

2a=3 3a+b=9 a+b+c=-6

a=3/2 3(3/2)+b=9 3/2+9/2+c=-6

b=9/2 c=-12

Standard form for quadratic sequence:

[tex] {an}^{2} + bn + c[/tex]

Therefore your general term is the one stated above in the answer.

Hope that helps!

Step-by-step explanation:

hope you can understand

Answer:

Samantha is 8 years and Maurice is 17 years

Step-by-step explanation:

First represent Samantha's brother's age with a variable, x.

Secondly, find Samantha's age. since shes 9 years younger, then it will be her brother's age which is x minus 9

Thirdly, in ten years, they will all age hence 10 will be added to all their ages.

Fourthly, once 10 has been added to their after 10 years, rhen we realise Maurice age will be 1.5 timess Samantha's age... Then you solve the resulting equation.

Answer:

0.339

Step-by-step explanation:

Hope it helped!

Hii!

___________________________________________________________

Answer: 0.339

Explanation:

There are two rounding rules that will help us whenever we need to round a number! These are the rules.

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Now that we know the rules, let's get down to solving our problem! ^^

The nearest thousandth is 3 decimal places.

_._ _ _ <==== Nearest thousandth

The third number after the decimal point is 9. After it is a digit that is less than 5. According to the rounding rules, we should round down.

[tex]\boldsymbol{0.3391=== > 0.339}[/tex]

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Hope that this helped! Best wishes.

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The probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total marbles = 20

Number of blue marbles = 5

P(blue) = 5/20

P(blue∩blue) = P(blue)×P(blue)

= (5/20)(5/20)

= 25/400

= 1/16

= 0.0625 ≈ 0.063

Thus, the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.

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Answer: all real numbers

Step-by-step explanation:

I assume you meant to write:

[tex]f(x)+g(x)=(x+5)+(x+4)=2x+9[/tex]

Since this is a linear function, the domain is all real numbers.

The smallest interior angle of the given regular polygon with 36 sides is; 170°

The formula for calculating the sum of interior angles of a regular polygon is; S = (n − 2) × 180°

where n is number of sides of the polygon

We are told that number of sides of ploygon is 36. Thus;

S = (36 - 2) × 180°

S = 6120°

Thus;

Smallest possible angle of polygon = 6120/36 = 170°

Sum of external angles of a regular polygon is;

S = 360/n

S = 360/36

S = 10°

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Answer:

f(-3) = 7

f(0.1) = 7

Step-by-step explanation:

The function f(x)=7 gives an output of 7 for all inputs. In other words, no matter what we plug in for x, f(x) will equal 7.

When graphed, f(x)=7 produces a horizontal line at y=7. From there, you can also see that any value of x gives an output of 7.

Step-by-step explanation:

as the velocity is not constant over time, we actually have to integrate v(t) over the interval 0<=t<=5 to get the distance.

v(t) = 60×ln(t + 1)

V(t) = 60 × integral(ln(t + 1)) between 0 and 5.

integral(ln(t + 1)) = (t + 1)ln(t + 1) - t + C

V(t) = 60 × ((t + 1)ln(t + 1) - t + C)

the distance traveled between t = 0 and t = 5 is then

60 × ((5 + 1)ln(5 + 1) - 5 + C) - 60 × ((0 + 1)ln(0 + 1) - 0 + C) =

= 60×(6ln(6) - 5 + C) - 60×(1ln(1) + C) =

= 60×(5.750556815... + C) - 60×C =

= 60×5.750556815... = 345.0334089... ≈ 345 km

Answer:

There is a total of 180 employees.

Step-by-step explanation:

men : women

  7    :       5

5 units = 75

   1 unit = 15

12 units = 180

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

Explanation:

The white rectangle is 3 by 6 with area of 3*6 = 18 square inches.

The larger rectangle is 8 by 5 with area of 8*5 = 40 square inches.

The difference of these will get us the shaded area:

40 - 18 = 22 square inches

Answer:

huh

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

x^2+4x+5=0

a=1,b=4^1 C=5

4^2-4×1×5

-4

A number line is just that – a straight, horizontal line with numbers placed at even increments. The distance from the origin to a is |a| for any real number a. Thus, the correct option is C.

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

As we know that in the given function |a|, when any value is given to a, then the value that the function is written is equal to a.

Let a=-5, then the value that the function will return is 5. Which is the distance borigin and a, on the number line.

Hence, The distance from the origin to a is |a| for any real number a. Thus, the correct option is C.

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No. of pounds of seed it takes to plant an 8-acre field = 70 pounds.

No. of acres can be planted per pound of seed = 70/8

= 8.75.

thus, 8.75 acres can be planted per pound of seed.

Answer: QN=19

Step-by-step explanation:

Diagonals of an isosceles trapezoid are congruent, so NQ=PM.

By the segment addition postulate, NQ=QR+RN=3x+7.

So,

[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]

So, [tex]QN=3(4)+7=\boxed{19}[/tex]

Answer:

3(4j + 7 + 2j)

12j + 21 + 6j

12j + 6j + 21

18j + 21 ----- (1)

3(6j +7)

18j + 21 --------(2)

eq 1 = eq. 2

both are equal

Step-by-step explanation:

hope you can understand

Answer:

x=12

Step-by-step explanation:

16x-30-(14x-6)=2x-24=0. add 24 on both sides to get 2x=24. divide by 2 on both sides to get x=12

Answer:

Domain = x ≥ 0

Range = y ≥ 20

Step-by-step explanation:

The equation in slope-intercept form would look like this:

y = 4x + 20

The slope is $4 because that is the money that can be made depending on the week. Because he received a random $20 at the beginning, this is just an additional income.

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

In this scenario, the domain (x-values) represent the number of weeks. The range (y-values) represent the total money made.

So the domain is asking, what is the lowest/highest amount of weeks he can save for? We know the number of weeks cannot be negative because he can't save for negative weeks. However, he could save for zero weeks. He can be saving for theoretically infinite weeks. Therefore, the domain is x ≥ 0.

The range is asking, how much money can he save? Since he starts out with a baseline of $20, this is the lowest amount of money he can have. If he were to save for an infinite amount of weeks, he could make an infinite amount of money. Therefore the range is y ≥ 20.

The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is [tex](x,y) \longrightarrow (x+2, y+2)[/tex]

The probability that at least two students share the same birthday is 83.22 %.

There are 365 days in year and there 36 students in the class.

Total sample space, n = 365³⁶

36 students will be selected as [tex]365P_{36}[/tex]

[tex]P(A) = \frac{365P_{36}}{365^{36}} = 0.1678[/tex]

P(A') = 1 - P(A)

P(A') = 1 - 0.1678

P(A') = 0.8322

P(A') = 83.22 %

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[tex]1) \text{ } f(-2)=8(-2)^{2}-3(-2)+2=\boxed{40}\\\\2) \text{ } f(-1)=8(-1)^{2}-3(-1)+2=\boxed{13}\\\\3) \text{ } f(0)=8(0)^{2}-3(0)+2=\boxed{2}\\\\4) \text{ } f(1)=8(1)^{2}-3(1)+2=\boxed{7}\\\\5) \text{ } f(2)=8(2)^{2}-3(2)+2=\boxed{28}[/tex]

Answer:

29/60

Step-by-step explanation:

probability of playing is 290/600 which when simplified is29/60

Answer:

y + 16 = 3(x + 5)

Step-by-step explanation:

When you write an equation in point-slope form, you only need two things: a point and a slope.

Given:

The standard point-slope equation is

y - y₁ = m(x - x₁)

Plug in what you know.

y - (-16) = 3(x - (-5))

Simplify.

y + 16 = 3(x + 5)

This is your equation.

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Answer:

mean = 14 and standard deviation = 3.03

Step-by-step explanation:

mean = sum of all numbers ÷ by the numbers available

= (11 + 12 + 12 + 16 + 19) ÷ 5

= 70 ÷ 5

= 14

FOR STANDARD DEVIATION * USE A SCIENTIFIC CALCULATOR THEY WON'T PENALIZE YOU*

follow these steps:

1. press mode then STAT

2. then press 1-VAR

3. put all the numbers on the table in ascending order

4 after press AC

5. press shift then 1

6. you will see many things but we are only interested in standard deviation, press *Var*

7. then select the standard deviation sign and press the equal sign

The remaining area of the page will be 80 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.

The area of the remaining part will be calculated as;-

Area of the square page will be = 11 x 11 = 121 square inches.

Area of three pictures will be = 15 x 3 = 45 square inches.

So the remaining area will be = 121 - 45 = 80 square inches.

Therefore the remaining area of the page will be 80 square inches.

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Yes it is

Step-by-step explanation:

it is a linear function as it is written in the standard form Y=MX+C

An example of independent events is P(Police Officers and choose cars).

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent if we have:

P(A ∩ B) = P(A)P(B)

                    Police Officers         Firefighters

Cars               12                             3

Trucks            9                              4

SUVs              15                             2

Let  P(A) = Firefighters choose cars

P(B) = Firefighters choose Trucks

P(A ∩ B)  =  Police Officers choose cars

Thus,

P(A ∩ B) = P(A)P(B)

12 = (4) ( 3)

Hence,  an example of independent events is P(Police Officers and choose cars).

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The length of the AC is x^2  + 4x  - 12.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given :

In Parallelogram ABCD, diagonals AC and BD intersect at point E.

such that

AE = x^2 - 12,

CE = 4x

We know that the diagonal of a parallelogram bisect each other.

x^2 - 12 = 4x

x^2  - 4x  - 12= 0

(x-6)(x-2) = 0

Hence, the value of x = 6, 2.

AC = AE + CE = x^2  + 4x  - 12.

The length of the AC is x^2  + 4x  - 12.

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