If f (2) is an exponential function where f(-2.5) = 9 and f(7) = 91, then find
the value of f(12), to the nearest hundredth.

Answers

Answer 1

Answer:

[tex]f(12) = 323.02[/tex]

[tex]f(12) = 16.7 * 1.28^{12[/tex]

Step-by-step explanation:

Given

[tex]f(-2.5) = 9[/tex]

[tex]f(7) = 91[/tex]

[tex]f(12) = 16.7 * 1.28^{12[/tex]

Required

[tex]f(12)[/tex]

An exponential function is:

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

[tex]f(-2.5) = 9[/tex] implies that:

[tex]9 = ab^{-2.5}[/tex]

[tex]f(7) = 91[/tex] implies that:

[tex]91 = ab^7[/tex]

Divide both equations

[tex]91/9 = ab^7/ab^{-2.5}[/tex]

[tex]91/9 = b^7/b^{-2.5}[/tex]

Apply law of indices

[tex]91/9 = b^{7+2.5}[/tex]

[tex]10.11 = b^{9.5}[/tex]

Take 9,5th root of both sides

[tex]b = 1.28[/tex]

So, we have:

[tex]9 = ab^{-2.5}[/tex]

[tex]9 = a * 1.28^{-2.5}[/tex]

[tex]9 = a * 0.54[/tex]

[tex]a = 9/0.54[/tex]

[tex]a = 16.7[/tex]

f(12) is calculated as:

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

[tex]f(12) = 16.7 * 1.28^{12[/tex]

[tex]f(12) = 323.02[/tex]


Related Questions

What is the answer to this answer fast

Answers

Answer:

Hello! answer: 13

Step-by-step explanation:

12 × 12 = 144

5 × 5 = 25

144 + 25 = 169

√169 = 13

13 × 13 = 169 therefore the length of the missing side is 13 hope that helps!

Hi . So 12 +12 =144
5x5= 25
25 + 144 = 169
169 = 13
So the answer is 13 ❤️

A culture started with 3,000 bacteria. After 6
hours, it grew to 3,600 bacteria. Predict how
many bacteria will be present after 13 hours.
Round your answer to the nearest whole
to four
number,
P - Aekt

Answers

After 13 hours it will grow to 4,900 rounded to the nearest whole would be 5,000

You should mark me brainliest

Hope this helps :D

Find the center and radius of the circle whose equation is given below: (x-1/2)2+(y-6)2=5

Answers

9514 1404 393

Answer:

  center: (1/2, 6)

  radius: √5

Step-by-step explanation:

The standard form equation for a circle of radius r and center (h, k) is ...

  (x -h)^2 +(y -k)^2 = r^2

When we compare this to the given equation:

  (x -1/2)^2 +(y -6)^2 = 5

we see that h=1/2, k=6, and r^2=5.

The center is (h, k) = (1/2, 6); the radius is √5.

Which expression is equivalent to
(5^-2)(5^-1)
A. -1/125
B. -1/5
C. 1/125
D. 1/5

Answers

Answer:

1/125

Step-by-step explanation:

(5^-2)(5^-1) = 5^-3=1/5^3=1/125

D+16/3=17 the steps??!!

Answers

Answer:

11

Step-by-step explanation:

D+16/3=17 the steps?

1. D+16/3=17

Divide 16/3.

D+6 = 17

2. subtract 6 from both side.

D = 11.

Answer is D=35

STEP1:

d + 16
Simplify ——————
3
Equation at the end of step
1
:

(d + 16)
———————— - 17 = 0
3
STEP
2
:
Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 3 as the denominator :

17 17 • 3
17 = —— = ——————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(d+16) - (17 • 3) d - 35
————————————————— = ——————
3 3
Equation at the end of step
2
:

d - 35
—————— = 0
3
STEP
3
:

When a fraction equals zero :

3.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

d-35
———— • 3 = 0 • 3
3
Now, on the left hand side, the 3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
d-35 = 0

Solving a Single Variable Equation:

3.2 Solve : d-35 = 0

Add 35 to both sides of the equation :
d = 35

(easy 7th grade math questions please help) find the measure of the indicated angle in each triangle

Answers

Step-by-step explanation:

Thei answers in picture

Part A: Elijah has 1/2 bag of candy. A bag of candy weighs 5 pounds. How many pounds of candy does Elijah have?

Part B: Elijah has 2 1/2 bags of candy. A bag of candy weighs 5 pounds. How many pounds of candy does Elijah have?

Answers

Answer:

A. 2.5 pounds

B. 12.5 pounds

Step-by-step explanation:

Answer:

a 2.5 b 12.5

Step-by-step explanation:

The girls in Lana’s troop set a goal to sell 1,000 boxes of cookies this year. There are 13 girls in the troop. At least how many boxes of cookies should each girl sell to reach their goal?

Answers

Answer:

[tex]77[/tex]

Step-by-step explanation:

The troop wants to sell a minimum of 1,000 boxes, so we're looking for the smallest number of boxes they can sell and still meet the goal. Since there are 13 girls in the troop, take the ceiling (round up to the nearest whole number) of 1,000 divided by 13:

[tex]\left\lceil \frac{1,000}{13}\right\rceil=\boxed{77}[/tex]

9.
Los conjuntos de parejas ordenadas son ejemplos de funciones, excepto:
A) {(1, 1), (2, 1), (3, 1).(4.1).(5, 1))
B) ((0, 1). (1.2). (2,4), (3.9). (4.16))
C) f(-2, 1), (-1,0), (0, 1).(-1,2), (2, 2))
D) ((-2,-3), (-1,-1). (0, 1), (1,3). (2.5))

Answers

El conjunto de parejas ordenadas que no es una función es: Alternativa C: {(-2,1),(-1,0),(0,1),(-1,2),(2,2)}

Una función se define como un conjunto de parejas ordenadas (x, y) donde no se repite el valor de "x" (corresponde al dominio de la función) En el caso específico del ejercicio, la alternativa C no corresponde con una función ya que tienen dos parejas con el mismo valor de "x":  {(-2,1), (-1,0), (0,1), (-1,2), (2,2)} Estos pares están en negrita, y el valor repetido subrayado.

find the standard deviation for this data set 9, 15, 13, 9, 15 round your answer to the nearest tenth

Answers

Answer:

3.0

Step-by-step explanation:

Sample standard deviation is found by steps below.

Find the mean:

μ = (9 + 15 + 13 + 9 + 15)/5 = 12.2

Find deviations from the mean and their squares:

9 - 12.2 = - 3.2 ⇒ (-3.2)² = 10.2415 - 12.2 = 2.8 ⇒ 2.8² = 7.8413 - 12.2 = 0.8 ⇒ 0.8² = 0.649 - 12.2 = - 3.2 ⇒ (-3.2)² = 10.2415 - 12.2 = 2.8 ⇒ 2.8² = 7.84

Sum the squares:

10.24*2 + 7.84*2 + 0.64 = 36.8

Divide by N - 1 (N - number of samples):

36.8/(5 - 1) = 9.2

Square root is the sample standard deviation:

σ = √9.2 = 3.0 (rounded)

Least common multiples of two- digit numbers. I need two examples. SHOW WORK

Answers

9514 1404 393

Answer:

LCM(21, 51) = 357LCM(42, 90) = 630

Step-by-step explanation:

For a pair of numbers, I find it convenient to think in terms of factors unique to the number, and factors shared with the other number.

Consider the numbers 21 and 51, for example.

  21 = 3·7

  51 = 3·17

The factor 3 is shared by both numbers. The factors 7 and 17 are unique to one number or the other.

If we group these factors like this ...

  (factors unique to 1 [ shared factors ) factors unique to 2]

  = (7 [3 ) 17]

The numbers in ( ) parentheses are the factors of 21, and the numbers in [ ] brackets are the factors of 51.

The LCM (least common multiple) is the product of the factors in those brackets:

  LCM(21, 51) = 7 × 3 × 17 = 357

__

The unique factors of the numbers don't have to be prime (as in the above example); they just cannot be shared. Here's another example for the numbers 42 and 90

  (7 [ 3·2 ) 3·5 ] = (7 [ 6 ) 15] . . . . factors of (42) and [90]

Then the LCM is ...

  LCM(42, 90) = 7 × 6 × 15 = 630

_____

Additional comment

What we have called "shared factors" here is the same as the "greatest common divisor"(GCD) or "greatest common factor" (GCF).

If we divide our little diagram so it shows the product of the two numbers:

  (42)[90] = (7×6)·[6×15]

we can see that the LCM is the quotient of the product and the GCD.

  LCM(A, B) = A·B/GCD(A, B)

This is an occasionally handy relationship, as it is not difficult to find the GCD of a pair of numbers using Euclid's algorithm.

BRAINIEST AND 10 POINTS

Answers

Answer:

Last answer is correct..

for math the answer was
cylinder with a radius
of 5 units and a height
of 3 units
a cylinder with a radius
of 4 units and a height
of 4 units
a cylinder with a radius
of 3 units and a height
of 6 units
a cylinder with a radius
of 3 units and a height
of 5 units

Answers

Hi how ghgfoifordtpxotx

In the standard equation for a conic section Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, if A = C , the conic section in question is a circle
True
False

Answers

I think the answer is true.

100-19+20+200= what is the answer for this question

Answers

109-19=90
90+20=110
110+200=310

Answer:

301

Step-by-step explanation:

Heres ow you do it,

1- 100-19= 81

2- 81+20= 101

3- 101+200= 301

Hope this helps!!! :)

When you multiply a number by 6 and subtract 5m the product ,you get 7. find the number.​

with solution

Answers

Answer:

x = 2

Step-by-step explanation:

Let the number be x

When we multiply a number by 6 and subtract it by 5, we would get 7.

On multiplication of number x with 6 it will be 6x.12

On subtraction of 5 it will be 6x - 5

6x - 5 = 7

6x = 7 + 5  

6x = 12

x = 12/6

x = 2

Answer:

The number is 2

Step-by-step explanation:

Let the number be n

Multiply the number by 6 = 6n

Subtract 5 from the number , 6n - 5

And we get 7

So , the expression : 6n - 5 = 7

                                6n = 7 + 5

                                6n = 12

                                  n = 2

HELP PLSSSSSSSSSSSSSS!!!!!!!!!!!!!! I will Give Brainlyest!!!

Answers

Answer:

[tex]\frac{21}{8}[/tex]

Step-by-step explanation:

[tex]6\frac{1}{4}=6+\frac{1}{4}=\frac{25}{4}\\\\3\frac{5}{8}=3+\frac{5}{8}=\frac{29}{8}\\[/tex]

finally

[tex]6\frac{1}{4}-3\frac{5}{8}=\frac{25}{4}-\frac{29}{8}=\frac{21}{8}[/tex]

The answer to your question is 2 5/8. If your looking for a non simplified answer then your non simplified answer is 84/32. But your official answer is 2 5/8

I need answer ASAP! Will give Brainliest if the answer is correct!

A square pyramid and its net are shown below. What is the surface area of the pyramid?

Answers

Answer:736

Step-by-step explanation:

The principal is Rs.30,000 the interest rate is 12%. Calculate the total value after 2 year
using compound interest.

Answers

Total value=
112/100 x 112/100 x 30,000
= 37632 Rs

Answer:

37632

Step-by-step explanation:

An=A(1+12%)²

Use the given data to find the minimum sample size required to estimate the population proportion.

a. Margin of error: 0.004: confidence level: 95% p and q unknown
b. Margin of error: 0.009, confidence level: 99%; p and q unknown
c. Margin of error: 0.01; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 52%.

Answers

Answer:

a. The minimum sample size required is of 60,025.

b. The minimum sample size required is of 20,465.

c. The minimum sample size required is 9,589.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

Question a:

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

p and q unknown means that we use [tex]\pi = 0.5[/tex], which is when the largest sample size is needed.

Margin of error: 0.004

We have to find n for which M = 0.004. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.004 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.004\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.004}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.004})^2[/tex]

[tex]n = 60025[/tex]

The minimum sample size required is of 60,025.

b. Margin of error: 0.009, confidence level: 99%; p and q unknown

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

Margin of error: 0.009

We have to find n for which M = 0.009. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.009 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.009\sqrt{n} = 2.575*0.5[/tex]

[tex]\sqrt{n} = \frac{2.575*0.5}{0.009}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.575*0.5}{0.009})^2[/tex]

[tex]n = 20464.9[/tex]

Rounding up:

The minimum sample size required is of 20,465.

c. Margin of error: 0.01; confidence level: 95%; from a prior study, p is estimated by the decimal equivalent of 52%.

Here we have [tex]\pi = 0.52[/tex].

The minimum sample size is n for which M = 0.01. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.01 = 1.96\sqrt{\frac{0.52*0.48}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.96\sqrt{0.52*0.48}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.52*0.48}}{0.01}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.52*0.48}}{0.01})^2[/tex]

[tex]n = 9588.6[/tex]

Rounding up:

The minimum sample size required is 9,589.

Order the following numbers from greatest to least:
0.42,4.2%,
2
4.1 x 101
9

Answers

Answer:4,1x101, 9, 4.1, 2, 0.42, 0.042

Step-by-step explanation:

The RADIUS of the barrel is 2.

What is the circumference of the barrel?

Answers

The circumference is about 12. This would been a bit easier if I knew the diameter.

Step-by-step explanation:

the required formula is C = 2(pi)r.

Here that comes to 6.28(2 units), or 12.56 units.

Find the missing length indicated

Answers

Answer:

The missing length is 80 degrees.

Step-by-step explanation:

Every triangle is equal to 180 degrees. If you add 64 and 36, you get 100. 180-100 is equal to 80, therefor x is equal to 80.

There are 15 books on a shelf. 9 of these books are new. The rest of them are used. what is the ratio of all books​

Answers

Answer:

a)15:6 b)2:3

Step-by-step explanation:

No. of used books=15-9=6

a) 15:6

b)

6:9

2:3

can anyone help me with this. please​

Answers

Answer:

Step-by-step explanation:

using pythagoras theorem

a^2+b^2=c^2

7^2+KL^2=25^2

49+KL^2=625

KL^2=625-49

KL=[tex]\sqrt{576[/tex]

KL=24

take M as reference angle

using tan rule

tan M=/opposite/adjacent

tan M=KL/ML

tan M=24/7

Can someone help me out? Due today! Solve for x. Assume that lines which appear tangent are tangent. 11&12 please

Answers

Answer:

11. C

12. A

Step-by-step explanation:

11. (10 + x + 1)(x + 1) = (x + 5)² (secant-tangent rule)

(11 + x)(x + 1) = (x + 5)(x + 5)

11(x + 1) +x(x + 1) = x(x + 5) +5(x + 5)

11x + 11 + x² + x = x² + 5x + 5x + 25

Add like terms

x² + 12x + 11 = x² + 10x + 25

Collect like terms

x² - x² + 12x - 10x = -11 + 25

2x = 14

2x/2 = 14/2

x = 7

12. (x + 8)(8) = (15 + 9)(9) (secant-secant theorem)

8x + 64 = 216

Subtract 64 from each side

8x = 216 - 64

8x = 152

8x/8 = 152/8

x = 19

You are saving to buy a speed boat. Starting today, you will put $1,000 into an investment account. Each month thereafter, your contribution will be .1% (.001) higher than the month before, so that your contribution next month will be .1% higher than today, and so forth and so on. The investment account has a periodic monthly interest rate of .4% (.004). Ignore taxes. You will make contributions until 5 years from today.
At the end of five years, when you put in your last ­contribution, how much will you have saved?

Answers

Answer:

You will have saved $69,612 after five years.

Step-by-step explanation:

This can be calculated using the for formula for calculating the future value of a growing annuity as follows:

FV = C * (((1 + r)^n - (1 + g)^n) / (r - g)) ……………………………………… (1)

Where;

FW = future value or amount you will have saved after five years = ?

C = first deposit = $1,000

r = periodic monthly interest rate of = 0.4%, or 0.004

g = growth rate of contribution = 0.1%, or 0.001

n = number of months = 5 years * 12 = 60

Substituting all the values into equation (1), we have:

FV = $1,000 * (((1 + 0.004)^60 - (1 + 0.001)^60) / (0.004 - 0.001))

FV = $1,000 * 69.612001854052

FV = $69,612.00

Therefore, you will have saved $69,612 after five years.

A random sample of 432 voters revealed that 100 are in favor of a certain bond issue. A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is A 100 + 1.96 0.5(0.5) 432 100 + 1.645 0.5(0.5) 432 100 + 1.96 0.231(0.769) 432 0.231 +1.96 0.231(0.769) 432 0.231(0.709) 0.231 +1.6451 432​

Answers

Answer:

The 95% confidence interval is [tex]0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}[/tex]

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A random sample of 432 voters revealed that 100 are in favor of a certain bond issue.

This means that [tex]n = 432, \pi = \frac{100}{432} = 0.231[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Confidence interval:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}[/tex]

The 95% confidence interval is [tex]0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}[/tex]

Can someone please help, ty!!
Will mark brainliest!

Answers

Answer:

Distribute 4 to a and -5.

Step-by-step explanation:

Multiplication goes first.

Find the volume plzzzzz thx

Answers

Answer:

144 isnt it? 6x6x4 length x width x height it should be 36x4

Step-by-step explanation i dont know sorry

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