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gladu [14]
2 years ago
11

22. A parabola equation is given as y = 3(x - 2)^2 + 5. What are the coordinates of the vertex?

Mathematics
2 answers:
ale4655 [162]2 years ago
6 0

Answer:

vertex: (2, 5)

Step-by-step explanation:

y=3(x−2)2+5

this is a parabola because of one variable squared and the other one is not so now write it in the standard form of parabolas which it is = to

______

Vertical :

(x−h)2=4p(y−k)

Horizontal:

(y−k)2=4p(x−h)2

vertex = (h, k)

______

this y=3(x−2)2+5 equation is vertical since x is squared

subtract 5 from both sides:

y−5=3(x−2)2

divide both sides by 3:

(y−5)13=(x−2)2

vertex:

(2,5)

sergiy2304 [10]2 years ago
5 0

Answer:

(2, 5)

Step-by-step explanation:

The x coordinate is the number inside the parentheses, but with the opposite sign, 2

The y coordinate is the number at the end

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What is the value of the expression 10 (n minus 6) when n = 14?
Scrat [10]

Answer:

The value of the expression is 80.

Step-by-step explanation:

14 - 6 = 8.

10 x 8 = 80.

6 0
3 years ago
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The owner of Matt’s Gas Station wants to study gasoline purchases of customers at his station. In 2017, the mean amount of gas
gulaghasi [49]

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 9

For the alternative hypothesis,

µ ≠ 9

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 9

x = 9.9

σ = 2.5

n = 50

z = (9.9 - 9)/(2.5/√50) = 2.55

Looking at the normal distribution table, the probability corresponding to the area above the z score is 1 - 0.99461 = 0.00539

Recall, population mean is 9

The difference between sample sample mean and population mean is 9.9 - 9 = 0.9

Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 9 - 0.9 = 8.1

the x value for the right tail is 9 + 0.9 = 9.9

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area above the z score as z = 0.00539

We would double this area to include the area in the left tail of z = - 2.55. Thus

p = 0.00539 × 2 = 0.01078

Since alpha, 0.01 < 0.01078, we would reject the null hypothesis

But we are told to use the critical value approach, then

Since α = 0.01, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.01/2 = 0.005

The z score for an area to the left of 0.005 is - 2.575

For the right, α/2 = 1 - 0.005 = 0.995

The z score for an area to the right of 0.995 is 2.575

In order to reject the null hypothesis, the test statistic must be smaller than - 2.575 or greater than 2.575

Since - 2.55 > - 2.575 and 2.55 < 2.575, we would reject the null hypothesis. This corresponds to our previous decision.

b) we would assume normal distribution because the sample size is sufficiently large and the population standard deviation is known.

c) Confidence interval is written in the form,

(Sample mean ± margin of error)

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

The z score for confidence level of 99% is 2.58

Margin of error = 2.58 × 2.5/√50 = 0.91

Confidence interval = 9.9 ± 0.91

The lower end of the confidence interval is

9.9 - 0.91 = 8.99

Therefore, p = 9 will be contained in the interval.

4 0
3 years ago
A quantity, y, varies directly as x When y=10, x=6.<br> Find xwhen y= 14.
grigory [225]

The value of x when y = 14 is 8.4

<h3 />

<h3>How to solve variation ?</h3>

y, varies directly as x. Therefore,

y ∝ x

Therefore,

y = kx

where

  • k =constant of proportionality

Therefore,

10 = 6k

k = 10 / 6

k = 5 / 3

Hence, when y = 14

y = kx

14 = 5 / 3 x

cross multiply

42 = 5x

x = 42 / 5

x = 8.4

learn more on variation here: brainly.com/question/20707320

#SPJ1

7 0
2 years ago
Suppose that 70% of college women have been on a diet within the past 12 months. A sample survey interviews an SRS of 267 colleg
Fofino [41]

Answer:

The probability that 75% or more of the women in the sample have been on a diet is 0.037.

Step-by-step explanation:

Let <em>X</em> = number of college women on a diet.

The probability of a woman being on diet is, P (X) = <em>p</em> = 0.70.

The sample of women selected is, <em>n</em> = 267.

The random variable thus follows a Binomial distribution with parameters <em>n</em> = 267 and <em>p</em> = 0.70.

As the sample size is large (n > 30), according to the Central limit theorem the sampling distribution of sample proportions (\hat p) follows a Normal distribution.  

The mean of this distribution is:

\mu_{\hat p} = p = 0.70

The standard deviation of this distribution is: \sigma_{\hat p}=\sqrt{\frac{p(1-p}{n}} =\sqrt{\frac{0.70(1-0.70}{267}}=0.028

Compute the probability that 75% or more of the women in the sample have been on a diet as follows:

P(\hat p \geq 0.75)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}} \geq \frac{0.75-0.70}{0.028}) =P(Z\geq0.179)=1-P(Z

**Use the <em>z</em>-table for the probability.

P(\hat p \geq 0.75)=1-P(Z

Thus, the probability that 75% or more of the women in the sample have been on a diet is 0.037.

7 0
3 years ago
What is the slope of the line passing through the points. ​
worty [1.4K]

Step-by-step explanation:

1

#Hopeitshelp

8 0
3 years ago
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