All categories

2 years ago

Question: Tell whether each function is linear or non-linear.

Mathematics

1 answer:

grandymaker [24]2 years ago

5 0

Just to avoid some confusion: <u>the first picture is a graph of function A, and the second picture is a graph of function B. </u>

Answer:

D. Function A is non-linear and Function B is linear.

Step-by-step explanation:

A good way to find out if a function is linear is by graphing it. If you graph it and it is a straight line, then it is linear.

So, let's graph the given points from the table of Function A and see if it forms a straight line. When you connect the dots, it's not straight, so Function A is non-linear.

Now let's look at function B. We can graph that too with the given information from the equation - the slope is -1 and the y-intercept is 5. (If you are a bit confused on how to graph it, don't hesitate to ask!) It does form a straight line, so Function B is linear.

You might be interested in

Bill went to the movies with some of his friends. tickets cost $8.50 each . they spent $18.00 total for food . their total was $

Marina86 [1]

18.00 + 8.50 + 8.50 + 8.50 + 8.50 = 52.00

So that's 4 Friends

4 0

2 years ago

(5x+2)[3(x+14)]<br><br> what is the value of x

Julli [10]

Here it is. You can also use the quadratic equation to find the answer.

5 0

2 years ago

The mean amount purchased by a typical customer at Churchill's Grocery Store is $26.00 with a standard deviation of $6.00. Assum

Vadim26 [7]

Answer:

a) 0.0951

b) 0.8098

c) Between $24.75 and $27.25.

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

In a set with mean $\mu$ and standard deviation $\sigma$ , 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.

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.

In this problem, we have that:

$\mu = 26, \sigma = 6, n = 62, s = \frac{6}{\sqrt{62}} = 0.762$

(a)

What is the likelihood the sample mean is at least $27.00?

This is 1 subtracted by the pvalue of Z when X = 27. So

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

By the Central Limit Theorem

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

$Z = \frac{27 - 26}{0.762}$

$Z = 1.31$

$Z = 1.31$ has a pvalue of 0.9049

1 - 0.9049 = 0.0951

(b)

What is the likelihood the sample mean is greater than $25.00 but less than $27.00?

This is the pvalue of Z when X = 27 subtracted by the pvalue of Z when X = 25. So

X = 27

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

$Z = \frac{27 - 26}{0.762}$

$Z = 1.31$

$Z = 1.31$ has a pvalue of 0.9049

X = 25

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

$Z = \frac{25 - 26}{0.762}$

$Z = -1.31$

$Z = -1.31$ has a pvalue of 0.0951

0.9049 - 0.0951 = 0.8098

c)Within what limits will 90 percent of the sample means occur?

50 - 90/2 = 5

50 + 90/2 = 95

Between the 5th and the 95th percentile.

5th percentile

X when Z has a pvalue of 0.05. So X when Z = -1.645

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

$-1.645 = \frac{X - 26}{0.762}$

$X - 26 = -1.645*0.762$

$X = 24.75$

95th percentile

X when Z has a pvalue of 0.95. So X when Z = 1.645

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

$1.645 = \frac{X - 26}{0.762}$

$X - 26 = 1.645*0.762$

$X = 27.25$

Between $24.75 and $27.25.

3 0

2 years ago

An ice cream truck that plays loud music is circling Bulans neighborhood. C(t) models the volume of the music in dB that Bulan h

ELEN [110]

Answer:

5.5 minutes

Step-by-step explanation:

Fill in the given information and solve for t.

75 = -15cos(2πt/15) +65

-10/15 = cos(2πt/15)

t = 15/(2π)arccos(-2/3) ≈ 5.492

The volume reaches 75 dB about 5.5 minutes after the truck arrives.

8 0

2 years ago

How can you tell if a function is quadratic?

Paha777 [63]

There are several ways, but the general format follows f(x) = ax2 + bx + c f(x) = ax² + bx + c, where A, B, and C are non-zero numbers. Another way of finding a quadratic equation is examining the graph of it, you'll notice a "U" shape called a parabola, which come in many shapes but they all retain a "U"-like curve.

3 0

2 years ago