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2 years ago

The table shows a linear function.

Mathematics

1 answer:

FinnZ [79.3K]2 years ago

6 0

Answer:

B) f(x) = -3/5x +5

Step-by-step explanation:

There are several ways you can write the equation of a line from a list of points. When you look through the list and see that one of them is the y-intercept, then the problem can be easier. When you look through the list of answers and see that the required answer is in slope-intercept form, then you know all you need to do is find the slope to go with the intercept you've located.

The point (x, f(x)) = (0, 5) tells you the y-intercept is 5.

The slope, the change in y divided by the change in x for two points, is ...

... (-1 -2)/(10 -5) = -3/5

This is the slope and the coefficient of x in the linear equation.

Now, we know the y-intercept (b=5) and the slope (m=-3/5), so we can fill in the slope-intercept form of the equation of a line:

... y = mx + b

... y = (-3/5)x + 5

You might be interested in

The annual rainfall (in inches) in a certain region is normally distributed with mean 43.2 and variance 20.8. Assume rainfall in

Wittaler [7]

Answer:

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation(which is the square root of the variance) $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Binomial probability 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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem, we have that:

$\mu = 43.2, \sigma = \sqrt{20.8} = 4.56$

Probability that a year has rainfall of more than 50 inches.

pvalue of Z when X = 50. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{50 - 43.2}{4.56}$

$Z = 1.49$

$Z = 1.49$ has a pvalue of 0.9319

1 - 0.9319 = 0.0681

Find the probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

This is $P(X \leq 2)$ when $n = 15, p = 0.0681$ . So

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

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

$P(X = 0) = C_{15,0}.(0.0681)^{0}.(0.9319)^{15} = 0.3472$

$P(X = 1) = C_{15,1}.(0.0681)^{1}.(0.9319)^{14} = 0.3805$

$P(X = 2) = C_{15,2}.(0.0681)^{2}.(0.9319)^{13} = 0.1947$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.3472 + 0.3805 + 0.1947 = 0.9224$

92.24% probability that out of 15 years, at most 2 have rainfall of more than 50 inches.

8 0

2 years ago

Read 2 more answers

PLS HELP ME IM BEING TIMED AND I HAVE 20 MINS TO TURN IN.

Natasha_Volkova [10]

Answer:

2.a) 3 ( x - 1 ) = 5x - 6 (Because the sides of a square are always equal)

b) 3 ( x - 1 ) = 5x - 6

=> 3x - 3 = 5x - 6

=> 3x - 5x = -6 + 3 (Law of transposition)

=> -2x = -3

=> -x = -3/2

=> -x = -1.5

=> x = 1.5 (By cancelling out the negative sign from both the sides)

c) 3(x-1) = 3 (1.5 - 1)

=> 3 (0.5)

=> 3 * 0.5 = 1.5

Both the angles are 1.5 because they are equal

If my answer helped, please mark me as the brainliest!!

Thank You!

8 0

2 years ago

The newly elected president needs to decide the remaining 5 spots available in the cabinet he/she is appointing. If there are 15

skad [1K]

Answer: There are 360360 ways to appoint the members of the cabinet.

Step-by-step explanation:

Since we have given that

Number of eligible candidates = 15

Number of spots available = 5

We need to find the number of different ways the members can be appointed where rank matters

For this we will use "Permutations":

So, the required number of different ways in choosing the members for appointment is given by

$^{15}P_5=360360$

Hence, there are 360360 ways to appoint the members of the cabinet.

7 0

2 years ago

Find the 15th term of the geometric sequence 1, -4, 16, ...

True [87]

Answer:

268,435,456

Step-by-step explanation:

Multiply by -4

5 0

2 years ago

What is the solution to the equation 9-3x = 7?

emmasim [6.3K]

Answer:

x = $\frac{2}{3}$

Step-by-step explanation:

Given

9 - 3x = 7 ( subtract 9 from both sides )

- 3x = - 2 (divide both sides by - 3 )

x = $\frac{-2}{-3}$ = $\frac{2}{3}$

4 0

2 years ago

Read 2 more answers