Solve: 3a - 2.4 = 5.1 a = ____

The table shows the input and output of a function Table(input:3,4,6,11. Output:5,7,11,21) (a) Explain what makes this set of da

Maslowich

Answer:

(a) The data set is a function, since for each input value {3,4,6,11} there is a single output value {5,7,11,21}

(B) A function is a mathematical relationship that associates one or more inputs with a single output value. So that the data set is not a function, there should be - for one or more values of the input - more than one output.

for example, if for the input value {3} there were two outputs {5, -5} then, the data set would not be a function.

The frelation $y ^ 2 = x$ is not a function because:

When x = 1, y = +1 and y = -1.

(c) The set of data provided can be represented by the equation of a line of the form y = mx + b

The slope is:

$m=\frac{y_2-y_1}{x_2-x_1}$

$m =\frac{7-5}{4-3}$

m = 2

$b = y_1-mx_1$

b = 5 - 2*3

b = -1

Then, the function is:

y = 2x-1

You can substitute any of the points shown in the equation and check that equality is satisfied, for example:

(11 , 21)

y = 2 (11) -1

y = 22-1

y = 21. The equation is satisfied. The same goes for the rest of the values.

4 0

3 years ago

How to do y-intercept and slope

givi [52]

I'm not sure but I had it then I forgot

5 0

3 years ago

What do you think the value of represents in the function? How can you predict what the graph of a quadrati function will look l

allochka39001 [22]

Answer:

Step-by-step explanation:

Parts of the question are missing.

y = a(x-h)² + k is a vertical parabola.

If a is positive, the parabola opens upwards.

If a is negative, the parabola opens downwards.

The vertex is at (h, k)

7 0

2 years ago

Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distribut

defon

Answer:

0.8665 = 86.65% probability that the sample mean would be at least $39000

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean $39725 and standard deviation $7320.

This means that $\mu = 39725, \sigma = 7320$

Sample of 125:

This means that $n = 125, s = \frac{7320}{\sqrt{125}} = 654.72$

The probability that the sample mean would be at least $39000 is about?

This is 1 subtracted by the pvalue of Z when X = 39000. So

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

By the Central Limit Theorem

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

$Z = \frac{39000 - 39725}{654.72}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

1 - 0.1335 = 0.8665

0.8665 = 86.65% probability that the sample mean would be at least $39000

4 0

2 years ago

In a fruit cocktail, for every 15 ml of orange juice you need 5 ml of apple juice and 50 ml of coconut milk. What is the ratio o

Kruka [31]

Answer:

1/14:5/7:3/14

Step-by-step explanation:

Since orange=15

Apple=5

Coconut milk=50

50+15+5

70

So

Orange=15/70

Divide both by 5

=3/14

Apple=5/70

Divide both by 5

=1/14

Coconut milk=50/70

Divide both by 10

=5/7

So the ratio of apple to coconut to orange

1/14:5/7:3/14

8 0

2 years ago

Solve: 3a - 2.4 = 5.1 a = _____