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Brilliant_brown [7]
2 years ago
7

LMNP is roatated 90 degrees clockwise around the origin

Mathematics
1 answer:
AlexFokin [52]2 years ago
7 0

It would be c, (1, 0)

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Nancy's garden has the dimensions shown 4 1/2 yard<br><br> 3 3/4 yd . She need find the area
Marina86 [1]

Answer:

The area of Nancy's garden is 16\frac{7}{8}\ yd^{2}

Step-by-step explanation:

I assume that the Nancy's garden is a rectangle shape

To find the area first convert mixed number to an improper fraction

4\frac{1}{2}\ yd=\frac{4*2+1}{2}=\frac{9}{2}\ yd

3\frac{3}{4}\ yd=\frac{3*4+3}{4}=\frac{15}{4}\ yd

Therefore

The area is equal to

A=\frac{9}{2}*\frac{15}{4}=\frac{135}{8}\ yd^{2}

convert to mixed number

\frac{135}{8}\ yd^{2=\frac{128}{8}+\frac{7}{8}=16\frac{7}{8}\ yd^{2}

4 0
3 years ago
A circle is centered at the point (5, -4) and passes through the point (-3, 2).
zepelin [54]

Answer:

(x-5)^2+(y+4)^2=100

Step-by-step explanation:

As we know the given points

Center = (5, -4)

and

Point on circle = (-3,2)

The distance between point on circle and center will give us the radius of circle

So,

The formula for distance is:

\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1})^{2}}\\Taking\ center\ as\ point\ 1\ and\ the\ other\ point\ as\ point\ 2\\d=\sqrt{(-3-5)^{2}+(2-(-4))^{2}}\\d=\sqrt{(-8)^{2}+(2+4)^{2}}\\d=\sqrt{(-8)^{2}+(6)^{2}}\\\\d=\sqrt{64+36}\\d=\sqrt{100} \\ d=10\\So\ the\ radius\ is\ 10

The standard form of equation of circle is:

(x-h)^{2}+(y-k)^{2}=r^{2}

where h and k are the coordinates of the center. So putting in the value:

(x-5)^{2}+(y-(-4))^{2}=(10)^{2}\\(x-5)^{2}+(y+4)^{2}=100

8 0
3 years ago
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
2 years ago
4. Entomologists introduce 20 of one
Lina20 [59]

Answer:

This number can be found using the Rule of 70, which describes the formula dt = 70 / r, where dt is the doubling time, and r is the annual rate of growth.

Step-by-step explanation:

24/6 = 4

20 x 2 = 40 x 2 = 80 x 2 = 160 x 2 = 320

20 ---> 320 in the first day.

Keep doing this equation. Multiply each day's end result by 2 four times for 9 more days.

8 0
3 years ago
Why is the accounting cycle important?
ankoles [38]
Because without it the economy would fail :)
4 0
2 years ago
Read 2 more answers
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