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3 years ago

Which statement best describes the function represented by the graph

Mathematics

1 answer:

a_sh-v [17]3 years ago

8 0

Answer:

Where is the graph?

Step-by-step explanation:

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Suppose f and g are continuous functions such that g(6) = 6 and lim x → 6 [3f(x) + f(x)g(x)] = 45. Find f(6).

aleksandr82 [10.1K]

Since g(6)=6, and both functions are continuous, we have:

$\lim_{x \to 6} [3f(x)+f(x)g(x)] = 45\\\\\lim_{x \to 6} [3f(x)+6f(x)] = 45\\\\lim_{x \to 6} [9f(x)] = 45\\\\9\cdot lim_{x \to 6} f(x) = 45\\\\lim_{x \to 6} f(x)=5$

if a function is continuous at a point c, then $lim_{x \to c} f(x)=f(c)$ ,

that is, in a c ∈ a continuous interval, f(c) and the limit of f as x approaches c are the same.

Thus, since $lim_{x \to 6} f(x)=5$ , f(6) = 5

Answer: 5

7 0

4 years ago

Find the distance between the points. (4,6),(9,6)

andrezito [222]

Answer:

Step-by-step explanation:

Find the difference between coordinates:

(x²-x1) = (9 - 4) = 5

(y²-y1) = (6 - 6) = 0

Square the results and sum them up:

(5)² + (0)² = 25 + 0 = 25

Now Find the square root

3 0

3 years ago

A boat travels 32 miles on 4 gallons of fuel. How many miles per half gallon is that?

Firdavs [7]

The answer is 4 miles

7 0

3 years ago

ccording to the U.S. National Weather Service, at any given moment of any day, approximately 1000 thunderstorms are occurring wo

viva [34]

Answer:

The critical value of z for 99% confidence interval is 2.5760.

The 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).

Step-by-step explanation:

Let X = number of lightning strikes on each day.

A random sample of n = 23 days is selected to observe the number of lightning strikes on each day.

The random variable X has a sample mean of, $\bar x=8.1\ mn$ and the population standard deviation, $\sigma=0.51\ mn$ .

The (1 - α)% confidence interval for population mean μ is:

$CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Compute the critical value of z for 99% confidence interval is:

$z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.5760$

*Use a z-table.

The critical value of z for 99% confidence interval is 2.5760.

Compute the 99% confidence interval for population mean number of lightning strike as follows:

$CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\=8.1\pm2.5760\times\frac{0.51}{\sqrt{23}}\\=8.1\pm0.2738\\=(7.8262, 8.3738)\\\approx(7.83, 8.37)$

Thus, the 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).

The 99% confidence interval for population mean number of lightning strike implies that the true mean number of lightning strikes lies in the interval (7.83 mn, 8.37 mn) with 0.99 probability.

3 0

3 years ago

The vertices of triangle ABC are A(5,2), B(-1,-6) and C(1,5). If Triangle DEF is similar to Triangle ABC and AB/DE=5, what could

astraxan [27]

Answer:

D(-5,3) and E(-5,1)

Step-by-step explanation:

|AB|² = (-1-5)² + (-6-2)²

|AB|² = 36 + 64

|AB|² = 100

|AB| = 10

AB/DE = 5

|DE| = 10/5 = 2

D(-5,3) and E(-5,1)

|DE|² = (-5+5)² + (3-1)²

|DE|² = 4

|DE| = 2

Verified

5 0

3 years ago

Read 2 more answers