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2 years ago

Write the equation for the function graphed below.

Mathematics

1 answer:

avanturin [10]2 years ago

6 0

Given the vertex of the parabola at point (2, -3):

The quadratic function in vertex form is:

f(x) = (x - 2)^2 - 3

where the vertex (h, k) is the minimum point = (2, -3).

You might be interested in

Use the pattern below for questions 6 - 8.

Yuliya22 [10]

Answer:

See below

Step-by-step explanation:

The sequence given

6, 19, 58, 175

We see the pattern: triple the previous term plus 1

2) 19 = 6*3 + 1
3) 58 = 19*3 + 1
4) 175 = 58*3 + 1

Next two terms

5) 175*3 + 1 = 526
6) 526*3 + 1 = 1579

Following two terms

7) 1579*3 + 1 = 4738
8) 4738*3 + 1 = 14215

4 0

3 years ago

Explain on the next slide how in 3 hours the car wouldn't travel 160 miles.

rosijanka [135]

Answer:

the car would have to be going under 5mph

Step-by-step explanation:

5 0

2 years ago

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.9 minutes and a standard deviation of 2.9

Eva8 [605]

Answer:

a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes

c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

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 establishes 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 of 8.9 minutes and a standard deviation of 2.9 minutes.

This means that $\mu = 8.9, \sigma = 2.9$

Sample of 37:

This means that $n = 37, s = \frac{2.9}{\sqrt{37}}$

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

320/37 = 8.64865

Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So

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

By the Central Limit Theorem

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

$Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}$

$Z = -0.53$

$Z = -0.53$ has a p-value of 0.2981

0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

275/37 = 7.4324

Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So

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

$Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}$

$Z = -3.08$

$Z = -3.08$ has a p-value of 0.001

1 - 0.001 = 0.999

0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So

0.2981 - 0.0010 = 0.2971

0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

7 0

2 years ago

X2 =5. What is the answer for X

grin007 [14]

Answer:

x=2.5

Step-by-step explanation:

First, you do 5 divided by 2, because you are trying to find a missing factor. After that, your answer, which is 2.5, is what x equals.

Hope that helps!

7 0

3 years ago

Read 2 more answers

The table shows the number of calories in four meals and the cost of each meal.

Aleksandr-060686 [28]

Answer:

A weak negative correlation

Step-by-step explanation:

$correlation, r = \frac{∑(y-\alpha)(x-\beta }{\sqrt{∑(y-\alpha)^2∑(x-\beta )^2 } }$

where,

$\alpha = \frac{∑y}{n} \\\beta =\frac{∑x}{n} \\∑ = summation$

$\alpha = \frac{3230}{4} = 807.5\\\\\\\beta =\frac{46}{4} = 11.5$

$therefore,\\\\r= -0.12924$

This represents a weak negative correlation

6 0

3 years ago

Read 2 more answers