If f(x) is an exponential function where f(-1.5) 26 and
f(5.5) = 7, then find the value of f(10), to the nearest hundredth.

Answers

Answer 1

Answer:

[tex]f(10) = 1147.25[/tex]

Step-by-step explanation:

Given

[tex]f(-1.5) = 26[/tex]

[tex]f(5.5) = 7[/tex]

Required

f(10)

An exponential function is represented as:

[tex]f(x) = ab^x[/tex]

[tex]f(-1.5) = 26[/tex] impleies that:

[tex]26 = ab^{-1.5}[/tex] --- (1)

[tex]f(5.5) = 7[/tex] implies that

[tex]7 = ab^{5.5}[/tex] --- (2)

Divide (2) by (1)

[tex]26/7 = ab^{-1.5}/ab^{5.5}[/tex]

[tex]3.71429 = b^{-1.5+5.5}[/tex]

[tex]3.71429 = b^{4}[/tex]

Take 4th root

[tex]b = 1.39[/tex]

Substitute [tex]b = 1.39[/tex] in [tex]26 = ab^{-1.5}[/tex]

[tex]26 = a * 1.39^{-1.5}[/tex]

[tex]26 = a * 0.6102[/tex]

Solve for (a)

[tex]a = 26/0.6102[/tex]

[tex]a = 42.61[/tex]

f(10) is calculated as:

[tex]f(10) = ab^{10}[/tex]

[tex]f(10) = 42.61 * 1.39^{10}[/tex]

[tex]f(10) = 1147.25[/tex]


Related Questions

Question 13 plz show ALL STEPS so I can learn thnx

Answers

9514 1404 393

Answer:

  a) (x³ -x² +x +2) +2/(x+1)

  b) (x² +2x -5) +6/(x+3)

Step-by-step explanation:

Polynomial long division is virtually identical to numerical long division, except that the quotient term does not require any guessing. It is simply the ratio of the leading terms of the dividend and divisor. As with numerical long division, the product of the quotient term and the divisor is subtracted from the dividend to form the new dividend for the next step.

The process stops when the dividend is of lower degree than the divisor.

In part (a), you need to make sure the dividend expression has all of the powers of x present. This means terms 0x³ and 0x² must be added as placeholders in the given dividend. They will become important as the work progresses.

Hello can anyone answer this question please I need help

Answers

9514 1404 393

Answer:

maximum: 40(8/3, 8/3)

Step-by-step explanation:

The graph shows the relevant vertex of the feasible region is ...

  (x, y) = (8/3, 8/3).

The value of z there is ...

  z = 11(8/3) +4(8/3) = (88 +32)/3

  z = 40

The length of the base of a triangle is twice it’s height. If the area of the triangle is 441 square kilometers, find the height

Answers

Answer:

21 kilometers

Step-by-step explanation:

Let the height be [tex]x[/tex]. Then, the length of the base is [tex]2x[/tex]. The formula for the area is of the triangle is given by base*height/2. Therefore, the area of the triangle is equal to [tex]\frac{x \cdot 2x}{2} = x^2[/tex], which is in turn equal to 441. Since [tex]x[/tex] must be positive, then [tex]21^2=441[/tex], meaning that the height is [tex]21[/tex] kilometers.

Please proved explanation for answer.

Answers

Answer:

inverse it and do fx and gx inverse its value

During the construction of a road a mountain of 250 metres in height, through it will be the construction of a tunnel. The top of the mountain is seen at an angle of 48°30' from a point P at one end of the mountain, and at an angle of 38° from the other end. How long will this tunnel be?

Answers

Answer:

542.74 m

Step-by-step explanation:

Tan(48.3) = 250/a Multiply by a

a*tan(48.3) = 250 Divide by tan(48.3)

a = 250/Tan(48.3)

a =222.74

By a similar method b = 250/tan(38)

b = 319.99'

The total length =542.73 meters

What is the difference of these fractions? use the number line and equivalent fractions to help find the answer -1 1/4+1/2

Answers

Answer:

1 3/4 or 7/4

Step-by-step explanation:

- 1 1/4 = -5/4

1/2 = 2/4

difference = 5/4+2/4 =7/4

Answer:

first step find LCM method

Every year, a town surveys the size of its wetland ecosystems. This equation estimates the total wetland area, in acres, over time, t, in years.


F(t)= 740(0.95)^t

Which statements are supported by the function?

When t=10, the town is predicted to have around 443 acres of wetlands.

At one time, the town had 740 acres of wetlands.

The wetland area in the town decreases by 5% per year.

When t=10, the town is predicted to have around 492 acres of wetlands.

The wetland area in the town increases by 95% per year.

Answers

Answer:

When t=10, the town is predicted to have around 443 acres of wetlands.

At one time, the town had 740 acres of wetlands.

The wetland area in the town decreases by 5% per year.

Step-by-step explanation:

Given

[tex]f(t) = 740 * (0.95)^t[/tex]

Required

The true statements

[tex](a)\ f(10) = 443[/tex]

We have:

[tex]f(t) = 740 * (0.95)^t[/tex]

Substitute 10 for t

[tex]f(10) = 740 * (0.95)^{10[/tex]

[tex]f(10) = 443[/tex]

Hence, (a) is true

[tex](b)\ f(t) = 740[/tex]

We have:

[tex]f(t) = 740 * (0.95)^t[/tex]

Substitute 740 for f(t)

[tex]740 = 740 * (0.95)^t[/tex]

Divide through by 740

[tex]1 = 0.95^t[/tex]

Express 1 as 0.95^0

[tex]0.95^0 = 0.95^t[/tex]

Cancel out the bases

[tex]0 = t[/tex]

[tex]t = 0[/tex]

Hence, the area had 740 acres initially;

(b) is true

[tex](c)\ r = 5\%[/tex]

We have:

[tex]f(t) = 740 * (0.95)^t[/tex]

Using the general formula

[tex]f(t) = a * b^t[/tex]

By comparison:

[tex]b = 0.95[/tex]

0.95 < 1 means that:

[tex]b = 1 - r[/tex] --- where r = rates

[tex]0.95 = 1 - r[/tex]

Collect like terms

[tex]r = 1 - 0.95[/tex]

[tex]r = 0.05[/tex]

Express as percentage

[tex]r = 5\%[/tex]

Hence, (c) is true

[tex](d)\ f(10) = 492[/tex]

In (a)

[tex]f(10) = 443[/tex]

Hence, (d) is false

[tex](e)\ r = 95\%[/tex]

In (c)

[tex]r = 5\%[/tex] ---- decrement

Hence, (e) is incorrect

Answer: When the town is predicted to have around 443 acres of wetlands.

At one time, the town had 740 acres of wetlands.

The wetland area in the town decreases by 5% per year.

Step-by-step explanation:

Solve by elimination.
8x + 4y = 20
-10x – 5y = –25
A. (14, -1)
B.(-4,4)
c. (0,3)
D. infinite number of solutions

Answers

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

D. infinite number of solutions

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the Answer...}}\\\\\left \{ {{8x + 4y = 20} \atop {-10x - 5y = -25}} \right.\\-----------\\5(8x + 4y = 20)\\4(-10x - 5y = -25)\\\\40x+ 20y = 100\\\-40x-20y=-100\\\\\boxed{0 = 0}[/tex]

⸻⸻⸻⸻

There are an infinite number of solutions.

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

The sum of two integers is -360. One of them is 60, then the other integer is

Answers

2
CNN can. Nxkxmcidnxixnxksnxixnxixmficocc

X^2 + bx + 49 is a perfect squad trinomial what is one possible value of b? & I need help with the others also due soon!

Answers

20. (2) 14

A perfect square trinomial will factor into two expressions that are the same, for example: x^2 + 6x + 9 = (x + 3)(x + 3). Since this problem has a C value of 49, it will factor into (x + 7)(x + 7). 7 doubled is 14, therefore one possible value of B is 7.

21. (4) 2, -12

x^2 + 10x + 25 = 24 + 25

(x + 5)^2 = 49

x + 5 = +/- 7

x = 2, -12

22. (3) 3 + sqrt(17)

x^2 - 6x = 8

Complete the Square

x^2 - 6x + 9 = 8 + 9

(x - 3)^2 = 17

x - 3 = +/- sqrt(17)

x = 3 + sqrt(17), 3 - sqrt(17)

23. (1) 1, -5

x^2 + 4x - 5 = 0

x^2 + 4x = 5

x^2 + 4x + 4 = 5 + 4

(x + 2)^2 = 9

x + 2 = +/- 3

x = 1, -5

Hope this helps!

The amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events.

a. The student requires more than 55 minutes to complete the quiz.
b. The student completes the quiz in a time between 30 and 40 minutes.
c. The student completes the quiz in exactly 37.23 minutes.

Answers

Answer:

a) 0.1667 = 16.67% probability that the student requires more than 55 minutes to complete the quiz.

b) 0.3333 = 33.33% probability that the student completes the quiz in a time between 30 and 40 minutes.

c) 0% probability that the student completes the quiz in exactly 37.23 minutes.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniformly distributed between 30 and 60 minutes.

This means that [tex]a = 30, b = 60[/tex]

a. The student requires more than 55 minutes to complete the quiz.

[tex]P(X > 55) = \frac{60 - 55}{60 - 30} = 0.1667[/tex]

0.1667 = 16.67% probability that the student requires more than 55 minutes to complete the quiz.

b. The student completes the quiz in a time between 30 and 40 minutes.

[tex]P(30 \leq X \leq 40) = \frac{40 - 30}{60 - 30} = 0.3333[/tex]

0.3333 = 33.33% probability that the student completes the quiz in a time between 30 and 40 minutes.

c. The student completes the quiz in exactly 37.23 minutes.

Probability of an exact value in a continuous distribution, such as the uniform distribution, is 0%, so:

0% probability that the student completes the quiz in exactly 37.23 minutes.

find the solution to this system of equations x+y=1
2x-y+z=1
x+2y+z=8/3

Answers

9514 1404 393

Answer:

  (x, y, z) = (1/3, 2/3, 1)

Step-by-step explanation:

We can use the first equation to write an expression for x that can be substituted into the other equations.

  x = 1 -y

  2(1 -y) -y +z = 1   ⇒   -3y +z = -1

  (1 -y) +2y +z = 8/3   ⇒   y +z = 5/3

Subtracting the first of these equations from the second gives ...

  (y +z) -(-3y +z) = (5/3) -(-1)

  4y = 8/3

  y = 2/3

  z = 5/3 -y = 1

  x = 1 -y = 1/3

The solution is (x, y, z) = (1/3, 2/3, 1).

What is the area of the shaded part of the figure?

Answers

Answer:

14cm²

Step-by-step explanation:

3x2=6,

3x2=6,

2x1=2,

6+6+2=14 cm^2

An investor puts $800 into an account that pays 7.5% interest compounded annually. The total amount A in the account after t years is given by which function below?
A = 800(1.75) ^t
A = 800(1.075) t
A = 800(1.075)^ t
A = 800 + (1.075)^ t

Answers

Answer:

A = 800( 1.075)^(t)

Step-by-step explanation:

The equation for interest is

A = p (1+r/n) ^ nt   where p is the principle, r is the interest rate, n is the number of times per year  and t is the years

A = 800( 1+ .075/1)^(1*t)

A = 800( 1.075)^(t)

Let's see

[tex]\\ \tt\leadsto A=P(1+r/n)^{nt}[/tex]

n is 1

[tex]\\ \tt\leadsto A=P(1+r)^t[/tex]

[tex]\\ \tt\leadsto A=800(1+0.075)^t[/tex]

[tex]\\ \tt\leadsto A=800(1.075)^t[/tex]

Option C

An account manager for a local software firm believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected: Salesperson Number of Contacts Sales (in millions) 1 14 24 2 12 14 3 20 28 What is the dependent variable

Answers

Answer:

Amount of sales

Step-by-step explanation:

The dependent variable also called the measured or predicted variable is simply the variable obtained due to inputs in of the independent variable. It is the variable which is being measured in an experiment. Here, the test is that the number of sales depends on the number of contact. Here, the number of contacts will has an influence or determines the amount of sales, hence, the number of contacts is the independent variable while the amount of sales is the dependent variable.

Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
y = 12x-8
y = 8x
A. (4, 12)
B. (5, 11)
C. (2,16)
O D. (3, 15)

Answers

Answer:

C. (2,16)

Step-by-step explanation:

[tex]y=12x-8\\y=8x\\\\\\8x=12x-8\\-4x=-8\\x=2\\\\y=8(2)=16[/tex]

Answer:

It might be B

Step-by-step explanation:

12(5)-8

8(11)

52

88

Write an expression 9 multiplied by t

Answers

Answer:

9t

Step-by-step explanation:

That's 9 multiplied by t

Help me please, Domain & Range problem

Answers

Answer:

Domain: all reals

Range: 4 ≤y <∞

Step-by-step explanation:

The domain is the possible input values(x)

From the arrows at the left and right ends on the graph, the inputs can be all reals

The range is the possible output values (y)

Y goes from 4 to infinity

4 ≤y <∞

25[tex]25^x=125^x^+^3[/tex] = 125x + 3

Answers

Answer:

x = -9

Step-by-step explanation:

25^x = 125 ^(x+3)

Rewriting

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

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

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

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

The bases are the same so the exponents are the same

2x = 3x+9

Subtract 3x from each side

2x-3x = 3x+9-3x

-x =9

x = -9

Answer:

x is -9

Step-by-step explanation:

Which expression is equivalent to 7√x^2/5√y^3? Assume y≠0

Answers

Answer:

Step-by-step explanation:

If the √y³ term is in the denominator, then the expression needs to be written with parentheses:  7√x²/(5√y³)

Internet providers: In a survey of 780 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $64.22 with standard deviation S10.75. Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $42.72 and $85.72. pprosimately bell-shaped. The number of plans that cost between $42.72 and $85.72 is:_________

Answers

Answer:

Hence the number of plans that cost between $42.72 and $ 85.72 is

95.44 %.

Step-by-step explanation:

Now the given are

μ = $64.22.

σ = $10.75.

Here,

[tex]P\left ( 42.72 < x< 85.72 \right )=P\left ( \frac{42..72-64.22}{10.75}< \frac{x-\mu }{\sigma } < \frac{85.72-64.22}{10.75}\right )\\P\left ( 42.72 < x< 85.72 \right )= P\left ( -2.00< Z <2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (Z<2.00\right )-P\left ( Z<-2.00 \right )\\P\left ( 42.72 < x< 85.72 \right )= P\left (0.9772\right )-P\left (0.0228\right )\\Probability = 0.9544[/tex]

Probability = 95.44%.

Which of the following choices shows the complete factorization of 50?
52 • 5
2 • 25
52 • 2
None of these choices are correct.

Answers

Answer: None of these choices are correct

Explanation

The factorization of 50 is 2*5^2

None is correct

True or false : There exists a function f such that f(x) <0, f'(x) > 0, and F"(x) < 0 for all x.

Answers

Answer:

false

Step-by-step explanation:

f can never have x next to it

Your friend offers to place a bet with you. He will pay you $1 if your favorite sports team wins the game on Tuesday night. But you will pay him $3 if his team wins. Your team has an 80% chance of winning, whereas his only has a 20% chance. This bet is in your favor. True or False.

Answers

False because $1 =$1 not $3

True. The expected value of the bet is positive ($0.2),

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Let's calculate the expected value of the bet for both outcomes:

If your team wins: You get paid $1, so the expected value is 0.8 × $1 = $0.8

If your friend's team wins: You pay $3, so the expected value is 0.2 × -$3 = -$0.6

The overall expected value of the bet is the sum of these two outcomes: $0.8 + (-$0.6) = $0.2

Since the expected value of the bet is positive ($0.2), this means that on average, you can expect to win money if you take this bet. Therefore, the bet is in your favor.

Learn more about probability here:

brainly.com/question/11234923

#SPJ2

What is the different of (5-3x) and (5x-10)

a. 8x-5

b. 15-8x

c. 8x + 15

d. none of the above

Answers

Answer:

15 - 8x

Step-by-step explanation:

Remark

This all depends on how you read the question. In other words, which comes first 5 - 3x or 5x - 10. It's not clear.

If you do the first one first, you get

5 - 3x - (5x - 10)         Remove the brackets.

5 - 3x - 5x + 10          Collect like terms

15 - 8x                       So that makes the middle one correct.

Now do it the other way.

5x - 10 - (5 - 3x)

5x - 10 - 5 + 3x

8x - 15

That answer isn't available here. So ..

The answer is 15 - 8x

Which Function is represented by the Graph

Answers

Answer:b

Step-by-step explanation:

Answer:

y = -2|x| + 1.

Step-by-step explanation:

We start with y = 2x which is a straight line passing through the origin with a slope of 2.

Taking the absolute value of x ( |x| ) gives  a graph shaped like a letter V with the point  at the origin.

Making that negative ( y = -2|x| ) inverts it vertically and then the  + 1 translates it up 1 unit.

give me examples of equivalent expressions of square root 54 with a radican of 3

Answers

Try this answer 3√54

lee has a collection of dvds he had 8 dramas 15 comedies and 2 westerns if he selects at random a dvd to watch what is the probability that he will select a western

Answers

Answer:  2/25

Explanation:

There are A = 2 westerns out of B = 8+15+2 = 25 movies total

The probability of selecting a western is A/B = 2/25

In decimal form, this is 2/25 = 0.08 which converts to 8%

Answer:

2/25

Step-by-step explanation:

so first u have to add them all up to get 25 because 8 +15+2=25. then, since there are 2 westerns, the probability that he will select a western is 2 out of 25

Mr. G wants to cut boards that are 1 1/2 foot long. If he has an 18 foot long board, how man pieces can he cut?

Answers

Answer:

18 ft* (1 piece/ 1 1/3 ft)= 13.5 pieces.

Step-by-step explanation:

What are the coordinates of A’ after a 90° counterclockwise rotation about the origin.

Answers

Answer:

A' (- 1, - 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ), then

A (- 5, 1 ) → A' (- 1, - 5 )

Other Questions
Last year Diana sold 800 necklaces. This year she sold 1080 necklaces. what is the percentage increase of necklaces she sold? How does the type of material an object is made of affect its ability to absorb or release thermal energy? Help! Given that tan=-1, what is the value of sec, for 3/2 According to this excerpt, Odysseusis fearful of the Cyclops.is prideful and overly confident.has been weakened by the Cyclops.has regrets about staying on the island. Find the missing side or angle.Round to the nearest tenth.b=3a=9c=11C= ? What is the new law the American government enacted for promoting small businesses in the country? O The Small Businesses Act of 1954.O The Small Businesses Act of 1953.O The Small Businesses Act of 1955.O The Small Businesses Act of 1958. b. For what game knee exercise helps the players? answers please formula which of the following would be included in the set of electrical plans for individual residence?A. Individual romex cablesB. Power panels to be installedC. routes of cablesD. Wire sizes A company made a profit of $90,000 in the year 2006. In 2010, the same company made a total profit of $135,000. If the rate of change is a constant, what is the average rate of change of the companys profit in dollars per year? HELP Anyone know the answer?? Help pls! What is the value of x if e^3x+6 =8? Answer: Nathan and Diana are married and have three married children and seven minor grandchildren. For tax year 2020, what is the maximum amount they can give to the family (including the sons- and daughters-in-law) without using any of their unified transfer tax credit BRAINLIESTT A spinner is divided into 8 equal-sized sections, and each section is labeled with a number 1 through 8.if Kathryn spins the arrow on the spinner twice, what is the probability that the arrow will land on a section with an odd number the first timeand a number greater than 6 on the second spln? A government agency is getting rid of older workstations. The agency will donate these workstations, along with other excess computer systems, to nearby schools. Management reminds the systems administrators about the data sanitization and disposal policy. What policy items are applicable for these IT systems, prior to donating to the schools someone knows the answer would help me What body of government ruled Salem at the time of the trials?a dictatorship ruled by Reverend Halea monarchy ruled by a king and queena theocracy ruled by the Puritan churchan oligarchy ruled by a Native American confederation How will public broadcasting give meaning to social responsibility theory in an essay write the 7 physical quantities with units Green house effect is caused by a) Green plants b) Infra red rays c) UV rays d)X-ray