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Set up a proportion and solve each problem. Round each answer to the nearest tenths. 5) What is 35% of 74? 6) 78 is what percent of 95? 7) Find what% of 54 is 6. 8) 28 is 60% of what number?

Answers

Answer 1

Answer:

Answer:

5) 35 / 100 = X / 74 X = 2590 / 100 = 25.9

or .35 * 74 = 25.9

6) 78 / 95 = X * 100

X = 7800 / 95 = 82.1 %

or X = 78/95 * 100 = 82.1 %

7) 60/100 * X = 28

X = 2800 / 60 = 46.7

Or .6 * X = 28

X = .28 / .6 = 46.7

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Хf(x)
Use the table of values to find the function's values.
If x = 0, then f(0) =
If f(x) = 27, then x =
33
-3 -2
17
0
-15
N
-7
3
27

Answers

For our particular data set, the value of the function f(x) is -2 when x = 0 (or f(0) = -2), and the value of x is 3 when f(x) = 27.

From the provided data, we see that we have specific values of x that correspond to certain values of the function f(x). Therefore, our goal is to find the value of f(x) when x = 0, and to find the value of x when f(x) = 27.

We start by finding the function value f(0). Looking at our data, we find an entry where x = 0, we observe that its corresponding f(x) value is -2. Thus, the value of the function f(x) is -2 when x = 0, so we have f(0) = -2.

Next, we're tasked with finding the value of x when f(x) = 27. To do this, we flip our perspective and look for entries in our data where f(x) = 27. After searching, we see an entry where f(x) equals to 27, and in this entry, the corresponding x value is 3. Therefore, when f(x) = 27, the value of x is 3.

In conclusion, for our particular data set, the value of the function f(x) is -2 when x = 0 (or f(0) = -2), and the value of x is 3 when f(x) = 27.

For more such question on function visit:

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Answer:

If x = 0, then f(0) = -15

If f(x) = 27, then x = 3

2) On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is t= d. How long will it take the airplane to travel 800 miles? Show your work 500

Answers

The equation for relation of time with distance travelled is,

$t=(1)/(500)d$

Substitute 800 for d in the equation to determine the time required for travelling 800 miles.

$\begin{gathered} t=(1)/(500)\cdot800 \n =(8)/(5) \n =1.6 \end{gathered}$

So airplane take 1.6 hours to travell 800 miles.

Answer: 1.6 hrs

For which value of k does the system has no solutions?Equation:
3x + y = 4
kx + y = −2
Answers:
A: -3
B: -2
C: 3
D: 4

Answers

Answer:

The answer to this question is 4

Step-by-step explanation:

When we slice a three-dimensional object, we expose new faces that are two dimensional. The two-dimensional face is called ______________.

Answers

Answer:

Cross section

Step-by-step explanation:

Cross section refers to the new two dimensional face exposed when we slice through a three dimensional objects.

It can also be the surface or shape exposed by making a straight cut through something, especially at right angles to an axis.

Cross section is the plane surface(two-dimensional objects) formed by cutting across a solid shape (three-dimensional shape) especially perpendicular to its longest axis.

A reservation service employs six information operators who receive requests for information independently of one another, each according to a Poisson process with rate ???? = 2 per minute. a. What is the probability that during a given 1 min period, the first operator receives no requests? (Round your answer to three decimal places.) b. What is the probability that during a given 1 min period, exactly three of the six operators receive no requests? (Round your answer to five decimal places.)

Answers

Answer:

a) 0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b) 0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the binomial distribution.

Poisson distribution:

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

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

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

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

In which $C_(n,x)$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

Poisson process with rate 2 per minute

This means that $\mu = 2$

a. What is the probability that during a given 1 min period, the first operator receives no requests?

Single operator, so we use the Poisson distribution.

This is P(X = 0).

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

$P(X = 0) = (e^(-2)*2^(0))/((0)!) = 0.135$

0.135 = 13.5% probability that during a given 1 min period, the first operator receives no requests.

b. What is the probability that during a given 1 min period, exactly three of the six operators receive no requests?

6 operators, so we use the binomial distribution with $n = 6$

Each operator has a 13.5% probability of receiving no requests during a minute, so $p = 0.135$

This is P(X = 3).

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$P(X = 3) = C_(6,3).(0.135)^(3).(0.865)^(3) = 0.03185$

0.03185 = 3.185% probability that during a given 1 min period, exactly three of the six operators receive no requests

A fair die is rolled 8 times. What is the probability that the die comes up 6 exactly twice? What is the probability that the die comes up an odd number exactly five times? Find the mean number of times a 6 comes up. Find the mean number of times an odd number comes up. Find the standard deviation of the number of times a 6 comes up. Find the standard deviation of the number of times an odd number comes up.

Answers

Answer:

0.2605, 0.2188, 1.33, 4, 1.0540, 1.4142

Step-by-step explanation:

A fair die is rolled 8 times.

a. What is the probability that the die comes up 6 exactly twice?

b. What is the probability that the die comes up an odd number exactly five times?

c. Find the mean number of times a 6 comes up.

d. Find the mean number of times an odd number comes up.

e. Find the standard deviation of the number of times a 6 comes up.

f. Find the standard deviation of the number of times an odd number comes up.

a. A die is rolled 8 times. If A represent the number of times a 6 comes up. For a fair die the probability that the die comes up 6 is 1/6 - Thus A ~ Bin(8, 1/6)

The probability mass function of the random variable A is

$p(A) = \left \{ {(8!)/(x!(8 - x)!)*((1)/(6) )^(A)*((5)/(6) )^(8-A) } \right. for A=0,1, ...8$