How much would you need to deposit in an account now in order to have $2000 in the account in 15
years? Assume the account earns 2% interest compounded monthly.

If

f(x) = ax ³ + bx ² - 5x + 9

then

f '(x) = 3ax ² + 2bx - 5

Given that f (-1) = 12 and f '(-1) = 3, we get the system of equations

-a + b + 5 + 9 = 12

3a - 2b - 5 = 3

or

-a + b = -2

3a - 2b = 8

Multiply through the first equation by 2 and add it to the second one to eliminate b and solve for a :

2(-a + b) + (3a - 2b) = 2(-2) + 8

-2a + 2b + 3a - 2b = -4 + 8

a = 4

Substitute this into the first equation above to solve for b :

-4 + b = -2

b = 2

Answer is a = 4, b = 2.

First derivative of an equation:

The derivative formula is one of the basic concepts used in calculus and the process of finding a derivative is known as differentiation. The derivative formula is defined for a variable 'x' having an exponent 'n'. The exponent 'n' can be an integer or a rational fraction. Hence, the formula to calculate the derivative is:

               [tex]\frac{d}{dx} x^{n} = n x^{n-1}[/tex]

(Given)

[tex]f(x) = ax^{3} + bx^{2} - 5x + 9[/tex]

And f'(x) we get ,  [tex]f'(x) = 3ax^{2} + 2bx-5[/tex]

Now, also given f(-1) = 12

=> [tex]f(-1) =a (-1)^{3} + b(-1)^{2} - 5 (-1) + 9[/tex]

=> 12 = -a + b +5 + 9

=> a = b + 2 ------( 1 )

Also given,  f'(-1) = 3.

i.e.,  [tex]3 = 3a(-1)^{2} + 2b(-1) - 5[/tex]

3 = 3a -2b -5

From eq - (1) we can replace a.

3 = 3(b + 2) - 2b - 5

3 = 3b + 6 - 2b - 5

b = 2.

a = 4.

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Answer:

1440ft^3

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

i already did it

Answer:

C

Step-by-step explanation:

i it has to be less than gems in more than susans, Jim is making 8.25 per hour, and Susan is making 7.50 per hour.

so the only possible answer would be 7.75

hope this helps!!!

Answer:

C.

Step-by-step explanation:

Jim earns $8.25 every hour

Susan earns $7.5 every hour

So Pierre's hourly rate has to be more than $7.5 but less than $8.25, so therefore Pierre's hourly rate is $7.75 because it is less than $8.25 but more than $7.5

Answer:

The 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars is (-$113.44, -$68.56)

Step-by-step explanation:

Subtraction of normal variables:

When we subtract the normal distributions, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

45 owners of newer cars (less than five years old). The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46

This means that:

[tex]\mu_N = 195[/tex]

[tex]s_N = \frac{46}{\sqrt{45}} = 6.8573[/tex]

40 owners of older cars (more than five years old). For older cars, the mean was $286 with a standard deviation of $58.

This means that:

[tex]\mu_O = 286[/tex]

[tex]s_O = \frac{58}{\sqrt{40}} = 9.17[/tex]

Subtaction:

Sample mean:

[tex]\mu = \mu_N - \mu_O = 195 - 286 = -91[/tex]

Standard error:

[tex]s = \sqrt{s_N^2 + s_O^2} = \sqrt{6.8573^2+9.17^2} = 11.45[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = zs[/tex]

In which s is the standard error.

So

[tex]M = zs = 1.96*11.45 = 22.44[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is -91 - 22.44 = -$113.44

The upper end of the interval is the sample mean added to M. So it is -91 + 22.44 = -$68.56

The 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars is (-$113.44, -$68.56)

Answer:

A. 12/13

Step-by-step explanation:

Remember SOH, CAH, TOA.

In this situation, the function is sine so sine= opposite/hypotenuse.

The side opposite of K is 12.

The hypotenuse is the longest side so it will be 13.

Therefore, sineK= 12/13(a)

Answer:

12/13

Step-by-step explanation:

Answer: the answer is c

Step-by-step explanation:

Answer:

the easiest way to get these numbers is to graph the function, i use desmos.

Step-by-step explanation:

the axis of symmetry is -1

the vertex is -1, 0.5

the domain is all real numbers

the range is all real numbers that are <= 0.5