Which of the following equations describes this graph?
A. y=(x-1)^2-
B. y=(x-3)^2+2
C. y=(x+1)^2-2
D. y=(x-2)^2+3

Answer:

Growth: y = 1700(1.25)^t, y = 4000(1.0825)^t, y = 1.5(10)^t

Decay: y =240(1/2)^t, y = 12,000(0.72)^t,  y = 8000(0.97)^t

Step-by-step explanation:

In an exponential equation, growth and decay are determined by the factor you are multiplying by exponentially. If it's under 1 you're basically exponentially dividing the initial value. Over 1 and you are increasing the value.

the graph would steeper, meaning more savings over time

admins, pls delete this, I messed up and don't know how

Answer:

8.50 cm²

Step-by-step explanation:

The dimension of each square is given as 0.5cm by 0.5cm

The area of the a square is, a²

Where, a = side length

Area of each square = 0.5² = 0.25cm

The number of blue colored squares = 34

The total area of the blue colored squares is :

34 * 0.25 = 8.50cm²

Answer:

= ∑ 6*n*x^n-1

Radius of convergence = 1

Step-by-step explanation:

f(x) = 6(1-x)^-2

Maclaurin series can be expressed using the formula

f(x) =  f(0) + f '(0)x + f ''(0)/ 2!  (x)^2 + f '''(0)/3! (x)^3 + f (4)(0) 4! x4 + .

attached below is the detailed solution

Radius of convergence = 1

The Maclaurin series for f(x) = 6 / (1 - x )^2  = ∑ 6*n*x^n-1  ( boundary ; ∞ and n = 1 )

Answer:

-5 it is

Step-by-step explanation:

answer choice a

x^2 - 5x - 1 = 0

a=1, b=-5, and c=-1

next you plug in the numbers into the quadratic formula

-(-5) plus or minus the square root of (-5)^2 - 4(1)(-1)/ 2(1)

after you simply, you should get 5 plus or minus the square root of 29, which is answer choice a

Answer:

option d is correct answer

Answer:

Step-by-step explanation:

D looks good

Given:

The graph of a function.

To find:

The range of the given function using interval notation.

Solution:

Range: The set of y-values or output values are known as range.

From the given graph, it is clear that the function is defined for [tex]0<x<4[/tex] and the values of the functions lie between -2 and 2, where -2 is excluded and 2 is included.

Range [tex]=\{y|-2<y\leq 2\}[/tex]

The interval notation is:

Range [tex]=(-2,2][/tex]

Therefore, the range of the given function is (-2,2].

Answer: The ans is imaginary . option c

Answer:

∠L = 25°

Step-by-step explanation:

Two sides are equal. so , it is an isosceles triangle.

Angles opposite to equal sides are equal.

∠L =  25

Answer:

It has a difference of x=2 of -4

Step-by-step explanation:

It has a difference of x=2 of -4

Given ,

           x ≠ 2 ,

           x - 2 =0

So, we put x = -2 because in question x ≠ 2 .

Then,      x - 2 = 0

              -2 -2 = 0

               - 4 =0

Therefore, it has a difference of x= -2 of -4.

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Answer:

a) 0.0147 = 1.47% probability that none of them graduates from the local community college.

b) 0.9398 = 93.98% probability that at most four will graduate from the local community college.

c) The expected number that will graduate is 2.85.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they will graduate, or they will not. The probability of a student graduating is independent of any other student graduating, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

57% of students who enter the college as freshmen go on to graduate.

This means that [tex]p = 0.57[/tex]

Five freshmen are randomly selected.

This means that [tex]n = 5[/tex]

a. What is the probability that none of them graduates from the local community college?

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.57)^{0}.(0.43)^{5} = 0.0147[/tex]

0.0147 = 1.47% probability that none of them graduates from the local community college.

b. What is the probability that at most four will graduate from the local community college?

This is:

[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{5,5}.(0.57)^{5}.(0.43)^{0} = 0.0602[/tex]

So

[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.0602 = 0.9398[/tex]

0.9398 = 93.98% probability that at most four will graduate from the local community college.

c. What is the expected number that will graduate?

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

In this question:

[tex]E(X) = 5*0.57 = 2.85[/tex]

The expected number that will graduate is 2.85.

Answer:

6

Step-by-step explanation:

We have the expression "3x is 18" and we want to find out x, so the easiest way is to isolate x. The way to do this is by dividing both 3x and 18 by 3, leaving us with 6. This means that our answer for x is 6. I hope this helped and please don't hesitate to reach out for clarification!

Answer:

6

Step-by-step explanation:

3x = 18

Divide both sides by 3

3x / 3 ( the 3s cancel out and we're left with x )

18/3 = 6

We get that x = 6

We can then plug in 6 to x in 3x = 18 to check if our answer is correct

3x = 18

Replace x with 6

3(6) = 18

3(6) = 18

18 = 18

This is true hence we can confirm that x = 6

Answer:

[tex]90[/tex] [tex]ft^3[/tex]

Step-by-step explanation:

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

The formula to find the volume of a rectangular prism is   [tex]V=lwh[/tex]

Let's substitute the number for the length, width, and height now.

[tex]V=(6)(5)(3)[/tex]

[tex]V=(30)(3)[/tex]

[tex]V=90[/tex]

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

Hope this is helpful.

Answer:

The first one is 2

The second one is 0

I hope this helps!

Answer:

First:

[tex]{ \tt{ = 4 + ( - 2)}} \\ = 4 - 2 \\ = 2[/tex]

Second:

[tex] - 3 + 3 \\ = 0[/tex]

Answer:

90 cause 90 times 10 is 900 and 10% times 10 is 100%

Step-by-step explanation:

Answer: 90

Step-by-step explanation: 900 × .10 = 90

Answer:

(0, -9)

Step-by-step explanation:

The y intercept is the y value when x =0

(0, -9)

Answer: hi your question is poorly written below is the correct question

answer :

a) y1 = Asint,   y'1 = Acost  , y"1 = -Asint

b) y2 = Bcost,   y'2 = Bsint , y"2 = - Bcost

c) y = Asint + B cost satisfies the differential equation for any constant A and B

Step-by-step explanation:

y" + y = 0

Proves

a) y1 = Asint,   y'1 = Acost  , y"1 = -Asint

b) y2 = Bcost,   y'2 = Bsint , y"2 = - Bcost

c) y3 = y1 + y2 ,   y'3 = y'1 + y'2,  y"3 = y"1 + y"2

∴ y"1 + y1 = -Asint + Asint

  y"2 + y2 = -Bcost + Bcost

  y"3 - y3 = y"1 + y"2 - ( y1 + y2 )

               = y"1 - y1 + y"2 - y2  

               = -Asint - Asint  + ( - Bcost - Bcost )  = 0

Hence we can conclude that y = Asint + B cost satisfies the equation for any constant A and B

Answer:

The solution to the equation  log3(x+2)=1 is given by x=1

Step-by-step explanation:

We are given that

[tex]log_3(x+2)=1[/tex]

We have to find the graph which shows the  solution to the equation log3(x+2)=1.

[tex]log_3(x+2)=1[/tex]

[tex]x+2=3^1[/tex]

Using the formula

[tex]lnx=y\implies x=e^y[/tex]

[tex]x+2=3[/tex]

[tex]x=3-2[/tex]

[tex]x=1[/tex]

Answer: B. Vertex is a maximum point at (3, 2)

Answer:

34m = c

Step-by-step explanation:

For every month (m) you pay 34 dollars. However many months youu use that service time 34 equals your total cost (c).

Answer:

[tex]let \: cost \: be \: { \bf{c}} \: and \: months \: be \: { \bf{n}} \\ { \bf{c \: \alpha \: n}} \\ { \bf{c = kn}} \\ 34 = (k \times 1) \\ k = 34 \: dollars \\ \\ { \boxed{ \bf{c = 34n}}}[/tex]

Answer:

Step-by-step explanation:

a = 5

b = 15

c = ?

c^2 = a^2 + b^2

c^2 = 5^2 + 15^2

c^2 = 25 + 125

c^2 = 250

sqrt(c^2) = sqrt(250)

c = sqrt(250)

Answer:

The area of the square is increasing at a rate of 40 square centimeters per second.

Step-by-step explanation:

The area of the square ([tex]A[/tex]), in square centimeters, is represented by the following function:

[tex]A = l^{2}[/tex] (1)

Where [tex]l[/tex] is the side length, in centimeters.

Then, we derive (1) in time to calculate the rate of change of the area of the square ([tex]\frac{dA}{dt}[/tex]), in square centimeters per second:

[tex]\frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}[/tex]

[tex]\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}[/tex] (2)

Where [tex]\frac{dl}{dt}[/tex] is the rate of change of the side length, in centimeters per second.

If we know that [tex]A = 25\,cm^{2}[/tex] and [tex]\frac{dl}{dt} = 4\,\frac{cm}{s}[/tex], then the rate of change of the area of the square is:

[tex]\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)[/tex]

[tex]\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}[/tex]

The area of the square is increasing at a rate of 40 square centimeters per second.

Answer:

the answer should be e^3

Step-by-step explanation:

i hope it helps you

Answer:

5.70 < X < 5.89

Step-by-step explanation:

Z = ±1.40507156

z = (x - μ)/σ

1.40507156 = (x - 5.8)/.07

5.70 < X < 5.89

Answer:

15 / 4

Step-by-step explanation:

1 kg = 1000 g

3 kg

= 3 x 1000

= 3000 g

3kg to 800g

= 3kg : 800g

= 3000 : 800

= 30 : 8

= 30 / 8

= 15 / 4

15/4 is the fraction representing the ratio of 3 kilograms to 800 grams.

To express the ratio of 3 kilograms to 800 grams as a fraction in its lowest terms.

we need to convert both the quantities to the same units. Since 1 kg is equal to 1000 g, we can convert 3 kg to grams as follows:

3 kg = 3 * 1000 g = 3000 g

Now, we have the quantities in the same unit, and the ratio becomes:

3000 g to 800 g

To express this ratio as a fraction, we place the quantities over each other:

3000 g

-------

800 g

Now, to simplify the fraction to its lowest terms, we find the greatest common divisor (GCD) of the two numbers (3000 and 800) and divide both the numerator and denominator by this GCD.

The GCD of 3000 and 800 is 200, so dividing both by 200 gives us:

3000 ÷ 200 = 15

800 ÷ 200 = 4

Therefore, the ratio 3 kg to 800 g expressed as a fraction in its lowest terms is 15/4.

In summary, we first converted the units to the same (grams) to make the ratio easier to handle. Then, we represented the ratio as a fraction and simplified it to its lowest terms using the GCD method. The final answer, 15/4, is the fraction representing the ratio of 3 kilograms to 800 grams.

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Answer:

C

Step-by-step explanation:

The triangles are similar and the scale factor can be find out by computing 18/6=15/5=9/3=3

Answer:

i think you answer is correct as it has to be less that 64 yards since it is not on a big slant. using reference from the first section forty yards is not as big as the sectuon you are looking for therefore using estimation, the answer is most likely b 53 and 1 thirds