I need help fast! Answer and explanation please! (see attachment) Solve for x, show your work.

I Need Help Fast! Answer And Explanation Please! (see Attachment) Solve For X, Show Your Work.

Answers

Answer 1

Answer:

x = -5/2

Step-by-step explanation:

3 ^ ( 4x-5) = (1/27) ^( 2x+10)

Rewriting 1/27 as 3^-3

3 ^ ( 4x-5) = (3^-3) ^( 2x+10)

We know that a^b^x = a^(b*c)

3 ^ ( 4x-5) = (3) ^(-3*( 2x+10))

3 ^ ( 4x-5) = (3) ^( -6x-30)

The bases are the same so the exponents are the same

4x-5 = -6x-30

Add 6x to each side

10x -5 = -30

Add 5 to each side

10x -5+5 = -30+5

10x = -25

Divide each side by 10

10x/10 = -25/10

x = -5/2

Answer 2

Answer:

5/2 or 2.5

Step-by-step explanation:

3^(4x - 5) = (3^- 3)^(2x + 10)

3^(4x - 5) = (3)^(- 3 * (2x + 10))

3^(4x - 5) = (3) ^( - 6x - 30)

4x - 5 = - 6x - 30

10x = - 25

= - 25/10

= - 5/2 or 2.5

Hope this helps!


Related Questions

Please answer this correctly

Answers

Answer:

First box is 4

This is because 2 is the stem and the leaves are 1, 2, 4, and 5

so the numbers are 21, 22, 24, and, 25

Second box is 3

This is because 2 is the stem for the leaves 6 and 7

3 is the stem for the leaf 0

So the numbers are 26, 27, and 30

Hope this helped

Answer:

As you know about the stem and leaf plot

1 |7 7 7 8                   => 17, 17, 17, 18

2|1 2 4 5 6 7             => 21, 22, 24, 25, 26, 27

3|0 2 5 5 6 7 7 8 9  => 30, 32, 35, 35, 36, 37, 37, 38, 39

4|1 2                         => 41, 42

Now we count to complete the table:

16-20       |       4    {17, 17, 17, 18}

21-25       |       4    {21, 22, 24, 25}

26-30      |       3    {26, 27, 30}

31-35       |       3    {32, 35, 35}

36-40      |       5    {36, 37, 37, 38, 39}

41-45       |       2    {41, 42}

Hope this helps!

A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have:__________. a) 18 degrees of freedom b) 200 degrees of freedom c) 199 degrees of freedom d) 181 degrees of freedom

Answers

Answer:

The correct answer to the following question will be Option d (181 degrees of freedom).

Step-by-step explanation:

The given values are:

Regression model,

n = 200

Observations,

p = 18

Now,

⇒  [tex]n-p-1[/tex]

On putting the estimated values, we get

⇒  [tex]200-18-1[/tex]

⇒  [tex]181[/tex]

So that the correct choice will be "181 degrees of freedom".

At a cell phone assembly plant, 75% of the cell phone keypads pass inspection. A random sample of 110 keypads is analyzed. Find the probability that more than 78% of the sample keypads pass inspection. Use at least five decimal places for the denominator.

Answers

Answer:

23.27%

Step-by-step explanation:

From the statement we know that random sample n is 110 and that p is 75% and x the percentage to evaluate is 78%

We have that the probability would be equal:

P (x > 0.78) =  [tex]P(z <\frac{x-p}{\sqrt{\frac{p*(1-p)}{n} }})[/tex]

Replacing we have:

[tex]P(z <\frac{0.78-0.75}{\sqrt{\frac{0.75*(1-0.75)}{110} }})[/tex]

P ( z < 0.73) =  1 - P ( z => 0.73)

= 1 - 0.7673

= 0.2327

Therefore the probability is 23.27%

12. If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95% confident that the difference between the sample estimate and the actual market share for its new product was no more than 3%, what sample size would be needed?\

Answers

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Step-by-step explanation:

We have the following info given:

[tex] Confidence= 0.95[/tex] the confidence level desired

[tex] ME =0.03[/tex] represent the margin of error desired

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

The confidence level is 95% or 0.95, the significance is [tex]\alpha=0.05[/tex] and the critical value for this case using the normal standard distribution would be [tex] z_{\alpha/2}=1.96[/tex]

Since we don't have prior information we can use [tex]\hat p= 0.5[/tex] as an unbiased estimator

Also we know that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]  

And rounded up we have that n=1068

Factor 5x4 - 30x2 - 135.

Answers

Answer:

20 - 60 - 135

95

Step-by-step explanation:

All you have to do is add/subtract the factors together

Answer:

5(x - 3)(x + 3)(x^2 + 3)

Step-by-step explanation:

First take out the GCF of the 3 numbers (5):-

= 5(x^4 - 6x^2 - 27)

= 5(x^2 - 9)(x^2 + 3)

= 5(x - 3)(x + 3)(x^2 + 3).

The radius of a circle increases from 2 inches to 3 inches. By how many square inches does its area increase? A)5 pi B)2 pi C)Pi D)pi^2

Answers

Answer:

A)5 pi

Step-by-step explanation:

To get the increase, we must find the area of the circle when the radius was 2 inches and subtract it from the area of the circle when the radius increases to 3 inches. The difference is the increase in the area of the circle.

A circle of radius r has an area A given as

A = Pi r²

Hence when the radius was 2 inches, the area A

= Pi × 2²

= 4 Pi square inches

when the radius increases to 3 inches, the area

= Pi × 3²

= 9 Pi square Inches

The increase in area

= 9 Pi - 4 Pi

= 5 Pi

The valve was tested on 270 engines and the mean pressure was 6.6 lbs/square inch. Assume the variance is known to be 0.49. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications

Answers

Answer:

[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]      

The p value for this case would be given by"

[tex]p_v =2*P(z>2.347)=0.0189[/tex]  

For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications

Step-by-step explanation:

Information given

[tex]\bar X=6.6[/tex] represent the sample mean

[tex]s=\sqrt{0.49}= 0.7[/tex] represent the population deviation

[tex]n=270[/tex] sample size      

[tex]\mu_o =6.5[/tex] represent the value that we want to test    

[tex]\alpha=0.1[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value for the test

Hypothesis to verify

We want to verify if the true mean for this case is equal to 6.5 lbs/square inch or not , the system of hypothesis would be:      

Null hypothesis:[tex]\mu= 6.5[/tex]      

Alternative hypothesis:[tex]\mu \neq 6.5[/tex]      

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

And replacing we got:

[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]      

The p value for this case would be given by"

[tex]p_v =2*P(z>2.347)=0.0189[/tex]  

For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications

Write the number six hundred and forty-
nine thousand and six in figures​

Answers

Answer:

649,006

Step-by-step explanation:

Six hundred and forty nine thousand= 649,000

and six so we have

649006

THE ANSWER IS 649,006 HOPE IT HELPS

Annapolis Company's bank statement indicated an ending cash balance of $9,340. Alpha's accountant discovered that outstanding checks amounted to $865 and deposits in transit were $840. Additionally, the bank statement showed service charges of $25. What is the correct adjusted ending cash balance

Answers

Answer:

The correct answer is $9,315

Step-by-step explanation:

Solution

Given that:

The ending cash balance = $9340

Checks outstanding amounted to = $865

The deposit in transit = $840

Bank statement service charges = $25

Now,

We will find the correct adjusted ending cash balance which is given below:

Correct adjusted ending cash balance = Unadjusted Balance - Outstanding Check + Deposit in transit

= $9,340 - $865 + $840

=$8,475 + $840

=$9,315

Hence,

The correct adjusted ending cash balance is $9,315

prove that (81/16)^-3/4 ×[(25/9)^-3/2 ÷ (5/2)^-3]=1​

Answers

Answer:

First write them in positive exponent form

(16/81)¾ × [ (9/25)^3/2 ÷ (2/5)³ ]

(2⁴×¾)/ (3⁴×¾) × [ (3² × ^3/2) / (5² ×^3/2) ÷ 2³/5³)

Simplify the terms

2³/3³ × ( 3³ / 5³ ÷ 2³/5³)

Solve the terms in the bracket

2³/3³ × (3³/5³×5³/2³)

You will get

2³/3³ × 3³/2³ = 1

They will cancel each other so the answer will be 1

Hope this helps.

What is the product -3 1/3of -8 7/10 and ?

Answers

Answer:

Brainliest!!!

Step-by-step explanation:

See picture!!

Answer:

29

Step-by-step explanation:

The sum of the ages of ahsan and his mother is 61 years.The difference in their ages is 29 years.By forming a pair of simultaneous linear equations,find (i)ahsan's present age (ii)the age of ahsan's mother when ahsan is 21 years old

Answers

Answer:

a. 16 years

b. 50 years

Step-by-step explanation:

Let us assume the age of Ahsan be X

And, the age of his mother be Y

It is mentioned in the question that the sum of the both ages to be 61 years and their difference is 29 years

So now the equation is as follows

X + Y = 61 .............................. (1)

-X + Y = 29 .............................. (2)

Now solve this

We get

2Y = 90

Y = 45 = Ahsan mother age age

Now put the value of Y in any of the above equation

So X would be

X = 61 - 45

= 16 i.e ahsan age

The mother age is

= 45 years + 5 years

= 50 years

The 5 years come from

= 21 years - 16 years

= 5 years

Please answer this correctly

Answers

Answer:

33.3%

Step-by-step explanation:

The numbers greater than 6 from the spinner are 7 and 8.

2 numbers out of total 6 numbers.

2/6 = 1/3

= 0.333

= 33.3%

Jack knows the surface area of a cylinder and its radius. He wants to find the cylinder's helght. He needs to rewrite the formula A = 2#r(+h)
to find the cylinder's height (h) In terms of the cylinder's surface area (A) and its radius (7). Which is the correct formula?

Answers

Answer:

h= pi(r)2/A or h= 3.14 times 7 times 2 divided by A

Step-by-step explanation:

u need to do the opposite of multiplication which is division to find the height

hope this helps

correct me if this is wrong

The area of a rectangle is 352in2. If the width of the rectangle is x inches, write a function for the perimeter, P(x)

Answers

Answer:2x2

Step-by-step explanation:

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 442 gram setting. It is believed that the machine is underfilling the bags. A 44 bag sample had a mean of 438 grams. Assume the population variance is known to be 576. A level of significance of 0.1 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answers

Answer:

p value is 0.1343

Step-by-step explanation:

Null: u>= 442

Alternative: u < 442

Using the formula for z score:

(x - u)/sd/√n

Where x is 438, u = 442 sd can be determined from the variance = √variance =√576 = 24 and n = 44

z score = 438-442 / (24/√44)

z score = -4/(24/6.6332)

z = -4/3.6182

z =-1.1055

Now let's find the p value at 0.1 significance level using a z score of -1.1055, using a p value calculator, p value is 0.1343 which greatest than 0.1 meaning the day is not sufficient enough to conclude that the machine is underfilling the bags.

Discuss what some of those rules are, and how they get applied in your analysis. If an engineering challenge includes "more than one reasonable estimator," (Devore, p. 249, Example 6.1 in Section 6.1) how do engineers know which to pick, and what issues arise statistically and in engineering management when making those choices?

Answers

Answer:

The engineer must verify and verify through a statistical inference that estimates and possible parameters may emerge, as well as determine what hypothesis tests should be performed to draw the most accurate conclusion.

Step-by-step explanation:

The engineer must assume that there may be more than one reasonable estimator for a different event or experiment; Something that could help you would be to perform an estimation of parameters, in that estimation it is required to know the properties of the estimators; that is to say that the closer the value of an estimator is to the real value of the parameter, it could be said that it is the most efficient or exact extimator.

The total gallons of juice each person consumes a yearly has decreased 4.1% each year. In 1981 each person drink 16.5 gallons of juice on average. What was the approximate amount consumed per person in 2010?

Answers

Answer:

The approximate number of gallons consumed by a person in 2010 will be 4.9 gallons

Step-by-step explanation:

Recall that the formula for exponential decrease is given by a function of the form:

[tex]f(x)=A\.(1-r)^x[/tex]

where A is the initial value, r is the rate of decrease, and x is the time elapsed.

In our case, the initial value of gallons of juice per person (at the starting time = 1981) is 16.5 gallons. So A = 16.5 gallons.

the rate of decrease "r" is the decimal form of: 4.1%, that is r = 0.041

So we have:

[tex]f(x)=16.5\.(1-0.041)^x[/tex]

Now we can calculate what the average number of gallons would be in the year 2010, knowing that between 1981 and 2010 there is an elapsed time in years of: 2010-1981 = 29 years. Then:

[tex]f(29)=16.5\,(1-0.041)^{29}=4.9 \,\, gallons[/tex]

The approximate amount consumed per person in 2010 is  4.9 gallons.

The formula that would used to determine the average gallon of juice consumed in 2010 is:  

FV = P (1 - r)^n

FV = Future value  

P = Present value = 16.5 gallons  

R = rate of decrease = 4.1%  

N = number of years = 2010 - 1981 = 29

16.5 x (1 - 0.041)^29  = 4.9 gallons

A similar question was answered here: https://brainly.com/question/6247153

Which would be appropriate compatible numbers to use to estimate ( 19 4 5 ) ( 4 6 ) ? Using this compatible number, what is the estimated product?

Answers

Answer: first box is 20 (1/2)

Second box is 10

Answer:

Answer: first box is 20 (1/2)

Second box is 10

Step-by-step explanation:

If this net where folded into a cube,which number would be opposite the number 1

Answers

Answer:

if the net where to be folded into a cube number 6 will be opposite number 1.

Step-by-step explanation:

If the net where folded into a cube the number that will be opposite to number 1 will be 6 . The best way to know this is by simply cutting a paper similar to the shape of the net above and numbering them as required . Folding the paper to form a cube, you will discover that the number 6 is opposite the number 1 value.

Or from the picture you will notice when you close the number 5, the number 4 will be on top of number 1 and the 6 can then be bend  down which makes it opposite the number 1.

How many edges and vertices does a prism with 100 sided end faced have ? Please answer as quickly as possible ≈[infinity]

Answers

Answer:

We have 300 edges and 200 vertices

Step-by-step explanation:

A prism is basically a 2D shape which extends into three dimensions. Thus, it has two end faces, and one face for each side on the original shape.

In addition to the two 100-sided polygons at top and bottom, the prism will also have 100 rectangular faces.

We will solve this by Euler’s formula which ks:

V - E + F = 2

where;

V is the number of vertices (corners),

E is the number of edges

F is the number of faces (of any polyhedron).

Number of vertices is 100 surrounding the top while it's 100 at the bottom. So total V = 100 + 100 = 200 .

The number of edges is 100 at the top, and 100 at the bottom. Also an additional 100 separating the hundred vertical faces.

Total number of edges is;

E = 100 + 100 + 100 = 300.

Thus, we have 300 edges and 200 vertices


Information about five planets is shown in the table below.
Planet Diameter (km) Mass (kg)
Mercury 4.88 x 10 3.3 x 1023
Jupiter 1.43 x 10 1.898 x 1027
Earth
1.28 104 5.97 x 1024
Mars
6.78 x 103 6.42 x 1023
Saturn
1.21 10% 5.68 x 1026
a) Write down the name of the planet with the greatest mass.
b) Work out the radius of Mercury giving your answer as an ordinary number.
c) Work out the difference between the masses of Jupiter and Saturn.
Give your answer in standard form.

Answers

Answer:

(a)Jupiter

(b)24.4 km

(c)[tex]1.33 \times 10^{27}$ kg[/tex]

Step-by-step explanation:

Part A

The planet with the greatest ma.ss is Jupiter.

It has a ma.ss of [tex]1.898 X 10^{27}$ kg[/tex]

Part B

The diameter of Mercury = 4.88 X 10

Radius = Diameter/2

Therefore:

Radius of Mercury

[tex]=\dfrac{4.88 X 10}{2}\\ =2.44 X 10\\=24.4$ km[/tex]

Part C

[tex]M$a.ss of Saturn = 5.68 X 10^{26}\\$Mass of Jupiter = 1.898 X 10^{27}\\$Difference in their ma.ss =(1.898 X 10^{27})-(5.68 X 10^{26})\\=1.33 \times 10^{27}$ kg[/tex]

A rectangular bin is going to be made with a volume of 492 in3. The base of the bin will be a square and the top will be open. The cost of the material for the base is 0.8 cents per square inch, and the cost of the material for the sides is 0.6 cents per square inch. Determine the dimensions of the bin that will minimize the cost of manufacturing it. What is the minimum cost

Answers

Answer:

base side = 9.037 inches

height = 6.024 inches

Minimum cost = 196 cents

Step-by-step explanation:

The volume of the bin is given by:

[tex]Volume = side^2 * height[/tex]

and the surface area of the bin is given by:

[tex]Surface\ area = side^2 + 4*side*height[/tex]

The cost of the bin will be:

[tex]Cost = 0.8*side^2 + 0.6*4*side*height[/tex]

[tex]Cost = 0.8*side^2 + 2.4*side*height[/tex]

From the volume equation, we have:

[tex]height = 492 / side^2[/tex]

Now the cost will be:

[tex]Cost = 0.8*side^2 + 2.4*side*492/side^2[/tex]

[tex]Cost = 0.8*side^2 + 1180.8/side[/tex]

To find the side that gives the minimum cost, we can find the derivative of Cost in relation to side and then make it equal zero:

Abbreviating Cost as C and side as s, we have:

[tex]dC/ds = 0.8*2*s - 1180.8/s^2[/tex]

[tex]1.6s - 1180.8/s^2 = 0[/tex]

[tex]1.6s = 1180.8/s^2[/tex]

[tex]1.6s^3 = 1180.8[/tex]

[tex]s^3 = 738[/tex]

[tex]s = 9.037\ in[/tex]

Finding the height of the bin, we have:

[tex]height = 492 / 9.037^2[/tex]

[tex]height = 6.024\ in[/tex]

The minimum cost is:

[tex]Cost = 0.8*9.037^2 + 1180.8/9.037 = 196\ cents[/tex]

Write an equation for a polynomial function that has the given roots

-2. 3i , and 5

Answers

Answer:

x^4 - 3x^3 - x^2 - 27x - 90 = 0.

Step-by-step explanation:

If 3i is one root then another is -3i.

In factor form we have:

(x + 2)(x - 5)(x - 3i)(x + 3i) = 0

(x^2 - 3x - 10)(x^2 -9i^2) = 0

(x^2 - 3x - 10)(x^2 + 9) = 0

x^4 + 9x^2 - 3x^3 - 27x - 10x^2 - 90 = 0

x^4 - 3x^3 - x^2 - 27x - 90 = 0.

Jamie is investing $47,000 in an account paying 9.26% interest compounded continuously. What will Jamie's account balance be in 17 years?

Answers

9514 1404 393

Answer:

  $226,863.29

Step-by-step explanation:

The amount is given by ...

  A = Pe^(rt)

where principal P is invested at annual rate r for t years.

  A = $47,000×e^(0.0926×17) ≈ $226,863.29

Answer:

the answer is $226,863.29

Customer account "numbers" for a certain company consist of 2 letters followed by 3 numbers. Step 2 of 2 : How many different account numbers are possible if repetitions of letters and digits are not allowed?

Answers

Answer:

Step-by-step explanation:

letters can be chosen in 26×25=650 ways

digits can be chosen in 10×9×8=720 ways

total number of ways=650×720=468000 ways.

Fraud detection has become an indispensable tool for banks and credit card companies to combat fraudulent credit card transactions. A fraud detection firm has detected some form of fraudulent activities in 2%, and serious fraudulent activities in 0.75% of transactions. Assume that fraudulent transactions remain stable.
a. What is the probability that fewer than 2 out of 110 transactions are fraudulent?
b. What is the probability that fewer than 2 out of 105 transactions are seriously fraudulent?

Answers

Answer:

a) 35.17% probability that fewer than 2 out of 110 transactions are fraudulent

b) 81.35% probability that fewer than 2 out of 105 transactions are seriously fraudulent

Step-by-step explanation:

For each transaction, there are only two possible outcomes. Either they are fradulent(or seriously fraudulent), or they are not. Transactions are independent. So we use the binomial probability distribution 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.

a. What is the probability that fewer than 2 out of 110 transactions are fraudulent?

2% are fraudulent, so [tex]p = 0.02[/tex]

110 transactions, so [tex]n = 110[/tex]

This is

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

In which

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

[tex]P(X = 0) = C_{110,0}.(0.02)^{0}.(0.98)^{110} = 0.1084[/tex]

[tex]P(X = 1) = C_{110,1}.(0.02)^{1}.(0.98)^{109} = 0.2433[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.1084 + 0.2433 = 0.3517[/tex]

35.17% probability that fewer than 2 out of 110 transactions are fraudulent.

b. What is the probability that fewer than 2 out of 105 transactions are seriously fraudulent?

0.75% are seriously fraudulent, so [tex]p = 0.0075[/tex]

105 transactions, so [tex]n = 105[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

[tex]P(X = 0) = C_{105,0}.(0.0075)^{0}.(0.9925)^{105} = 0.4536[/tex]

[tex]P(X = 1) = C_{105,1}.(0.0075)^{1}.(0.9925)^{104} = 0.3599[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.4536 + 0.3599 = 0.8135[/tex]

81.35% probability that fewer than 2 out of 105 transactions are seriously fraudulent

Google I would like to purchase 10 bags of chicken wings the store is selling three bags for $51.00 what is the cost of 10 bags of chicken wings

a. 61.00
b. 71.00
c. 170.00
d. 130.00 ​

Answers

Answer:

A 61.00

Step-by-step explanation:

51 Added to 10 Equals 61.00 which is the Cost of 10 Bags of chicken Wings. Your Welcome.

State whether the decay is linear or​ exponential, and answer the associated question. The value of a car is decreasing by 9​% per year. If the car is worth ​$11 comma 000 ​today, what will it be worth in two​ years? g

Answers

Answer:

ExponentialA(2)=$9109.10

Step-by-step explanation:

Since the value of the car decreases by a common factor each year, the decay is exponential.

An exponential decay function is of the form

[tex]A(t)=A_0(1-r)^t$ where:\\Initial Value, A_0=\$11,000\\$Decay Factor, r=9%=0.09[/tex]

Therefore, the function modeling the car's decay is:

[tex]A(t)=11000(1-0.09)^t[/tex]

We want to determine the car's value in two years.

When t=2

[tex]A(2)=11000(1-0.09)^2\\A(2)=\$9109.10[/tex]

The value of the car in 2 years will be A(t)=$9109.10

Final value of the car after 2 years will be $9109.10

 Value of the car decay by 9%.

Since, 9% is a common factor by which the value of car is decreasing,

Therefore, decay will be exponential.

Expression for the exponential decay is given by,

[tex]P=P_0(1-\frac{r}{100} )^t[/tex]

Here, [tex]P=[/tex] Final price

[tex]P_0=[/tex] Initial price

[tex]r=[/tex] Rate of decay

[tex]t=[/tex] time

  If initial price of the car [tex]P_0=11000[/tex], rate of decay [tex]r=0.09[/tex] and [tex]t=[/tex] Number of years

By substituting the values in the expression,

P = [tex]11000(1-0.09)^2[/tex]

  = 11000(0.91)²

  = $9109.10

   Therefore, final value of the car after 2 years will be $9109.10

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If f(x) = x^2 is reflected over the x-axis and the shifted 4 units down, what is the equation of the new function, g(x)?

Answers

Answer:

g(x) = -x² - 4

Step-by-step explanation:

In this case, we are only changing a (reflection and vertical shrink/stretch) and k (vertical movement)

k = -4 because we are moving 4 units down

a = -1 because we are just reflecting over the x-axis

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