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3 years ago

Solve for x: 10^x = 9A. x = log⁡ 9B. x = log^9 ⁡10C. x = log ⁡10

Mathematics

2 answers:

romanna [79]3 years ago

4 0

Answer:

A. x = log 9

Step-by-step explanation:

10^x = 9

Log both sides:

log 10^x = log 9
x log 10 = log 9
x*1 = log 9
x = log 9

Correct choice is A

Tpy6a [65]3 years ago

4 0

Answer:

A x=9

it's right answer ok

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Help me with precal pleaseee

yuradex [85]

Answer: Choice C

$\left[0 , \frac{\pi}{2}\right) \ \ \text{ and } \ \ \left(\frac{\pi}{2}, \pi\right]$

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Explanation:

Let's look at the function y = sec(x) first, which is the secant function.

Recall that secant is 1 over cosine, so sec(x) = 1/cos(x)

We can't divide by zero, so cos(x) = 0 can't be allowed. If x = pi/2, then cos(pi/2) = 0 will happen. So we must exclude pi/2 from the domain of sec(x).

If we look at the interval from 0 to pi, then the domain of sec(x) is $0 \le x < \frac{\pi}{2} \ \ \text{ and } \ \ \frac{\pi}{2} < x \le \pi$

we can condense that into the interval notation $\left[0 , \frac{\pi}{2}\right) \ \ \text{ and } \ \ \left(\frac{\pi}{2}, \pi\right]$

Note the use of curved parenthesis to exclude the endpoint; while the square bracket includes the endpoint.

So effectively we just poked at hole at x = pi/2 to kick that out of the domain. I'm only focusing on the interval from 0 to pi so that secant is one to one on this interval. That way we can apply the inverse. When we apply the inverse, the domain and range swap places. So the range of arcsecant, or $\sec^{-1}(x)$ is going to also be $\left[0 , \frac{\pi}{2}\right) \ \ \text{ and } \ \ \left(\frac{\pi}{2}, \pi\right]$

8 0

3 years ago

A certain kind of sheet metal has, on average, 3 defects per 18 square feet. Assuming a Poisson distribution, find the probabili

Fofino [41]

Answer:

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

In this problem, we have that:

3 defects per 18 square feet.

So for 31 square feet, we have to solve a rule of three

3 defects - 18 square feet

x defects - 31 square feet

$18x = 3*31$

$x = \frac{31*3}{18}$

$x = 5.17$

So $\mu = 5.17$

Assuming a Poisson distribution, find the probability that a 31 square foot metal sheet has at least 4 defects.

Either it has three or less defects, or it has at least 4 defects. The sum of the probabilities of these events is decimal 1.

$P(X \leq 3) + P(X \geq 4) = 1$

We want $P(X \geq 4)$

$P(X \geq 4) = 1 - P(X \leq 3)$

In which

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-5.17}*(5.17)^{0}}{(0)!} = 0.0057$

$P(X = 1) = \frac{e^{-5.17}*(5.17)^{1}}{(1)!} = 0.0294$

$P(X = 2) = \frac{e^{-5.17}*(5.17)^{2}}{(2)!} = 0.0760$

$P(X = 3) = \frac{e^{-5.17}*(5.17)^{3}}{(3)!} = 0.1309$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0057 + 0.0294 + 0.0760 + 0.1309 = 0.242$

Finally

$P(X \geq 4) = 1 - P(X \leq 3) = 1 - 0.242 = 0.758$

75.8% probability that a 31 square foot metal sheet has at least 4 defects.

8 0

4 years ago

PLEASE HELP? Tom Harris, a young father, is twenty-four years old. He wishes to purchase $7,000 of a ten-year term insurance. Wh

velikii [3]

4.15 * 7 = 29.05

I'm pretty sure this is the correct answer.

8 0

3 years ago

Find the ordered pair (x,y) that satisfies the system of equations x + y = 15 x - y = 3.

xxMikexx [17]

Answer:

(9, 6)

Step-by-step explanation:

add equations together: (x + y = 15) + (x - y = 3) --> x + x + y - y = 15 + 3 --> 2x = 18

isolate the variable: 2x/2 = 18/2 --> x = 9, so the x-coordinate is 9

substitute 9 in x's place in one of the equations: 9 + y = 15

solve for y: y = 15 - 9 --> y = 6, so the y-coordinate is 6

combine x and y coordinates together: (9, 6)

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3 years ago

What is the value of x in the equation? 3 2 5 x + 2 3 4 = 7

schepotkina [342]

Answer:

1/65 is the answer. the main part behind it is using subtraction and divison to find the answer

3 0

4 years ago

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