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erica [24]
3 years ago
13

If​ f(x) and​ g(x) are differentiable functions such that f (1 )equals 4​, f prime (1 )equals 5​, f prime (9 )equals 6​, g (1 )e

quals 9​, g prime (1 )equals 8​, g prime (2 )equals 9​, g prime (5 )equals 10​, find StartFraction d Over dx EndFraction f (g (x ))vertical line Subscript x equals 1 Superscript .
Mathematics
1 answer:
Alex777 [14]3 years ago
8 0

By the chain rule,

(f(g(x)))'=f'(g(x))g'(x)

so that when x=1, we have

(f(g(1)))'=f'(g(1))g'(1)=f'(9)g'(1)=6\cdot8=\boxed{48}

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3. Tom, Sam and Matt are counting drum beats.
just olya [345]

Answer:

<em>When 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.</em>

Step-by-step explanation:

The Least Common Multiple ( LCM )

The LCM of two integers a,b is the smallest positive integer that is evenly divisible by both a and b.

For example:

LCM(20,8)=40

LCM(35,18)=630

Since Tom, Sam, and Matt are counting drum beats at their own frequency, we must find the least common multiple of all their beats frequency.

Find the LCM of 4,10,12. Follow this procedure:

List prime factorization of all the numbers:

4 = 2*2

10 = 2*5

12 = 2*2*3

Multiply all the factors the greatest times they occur:

LCM=2*2*3*5=60

Thus, when 60 beats are heard, Tom hits 15 snare drums, Sam hits 6 kettle drums, and Matt hits 5 bass drums.

6 0
3 years ago
The bad debt ratio for a financial institution is defined to be the dollar values of loans defaulted divided by the total dollar
Nimfa-mama [501]

Answer:

(a) NULL HYPOTHESIS, H_0 : \mu \leq  3.5%

    ALTERNATE HYPOTHESIS, H_1 : \mu > 3.5%

(b) We conclude that the the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks.

Step-by-step explanation:

We are given that a random sample of seven Ohio banks is selected.The bad debt ratios for these banks are 7, 4, 6, 7, 5, 4, and 9%.The mean bad debt ratio for all federally insured banks is 3.5%.

We have to test the claim of Federal banking officials that the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks.

(a) Let, NULL HYPOTHESIS, H_0 : \mu \leq  3.5% {means that the the mean bad debt ratio for Ohio banks is less than or equal to the mean for all federally insured banks}

ALTERNATE HYPOTHESIS, H_1 : \mu > 3.5% {means that the the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks}

The test statistics that will be used here is One-sample t-test;

                T.S. = \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where,  \bar X = sample mean debt ratio of Ohio banks = 6%

             s = sample standard deviation = \sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} } = 1.83%

             n = sample of banks = 7

So, test statistics = \frac{6-3.5}{\frac{1.83}{\sqrt{7} } }  ~ t_6

                             = 3.614

(b) Now, at 1% significance level t table gives critical value of 3.143. Since our test statistics is more than the critical value of t so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the the mean bad debt ratio for Ohio banks is higher than the mean for all federally insured banks.

Hence, Federal banking officials claim was correct.

7 0
3 years ago
At a benefit​ concert, fifteen bands have volunteered to perform but there is only enough time for five of the bands to play. Ho
Iteru [2.4K]

Answer:

360,360

Step-by-step explanation:

So we only have 5 spots, but 15 bands to fill those spots.

For the first spot, we can choose from any of the 15 bands, so we have 15 choices.

For the second spot, we can choose from the 14 remaining bands (because we already chose one for the first spot), so we have 14 choices.

For the third spot, by similar reasoning as above, we have 13 choices; for the fourth spot, 12 choices; and for the last spot, we have 11 choices.

We realize that for each of the 15 possible bands in the first spot, we still have 14 possible bands for the second spot, and so on. Thus, we know to multiply instead of add.

Our answer is: 15 * 14 * 13 * 12 * 11 = 360,360

6 0
3 years ago
During an experiment, Juan rolled a six-sided number cube 18 times. The number two occurred four times. Juan claimed the experim
dem82 [27]
Because u would have to find the undercorse of 010-1 witch makes the out of part by 6

3 0
3 years ago
Find the value of w-9 given that –3w+5 = 2
melamori03 [73]

Answer:

-8

Step-by-step explanation:

Solving for w given the equation, -3w +5 = 2:

-3w +5 = 2 \\ -3w +5 -5 = 2 -5 \\ -3w = -3 \\ \frac{-3w}{-3} = \frac{-3}{-3} \\ w = 1

Solving for w -9 when w = 1

1 -9 \\ -8

3 0
2 years ago
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