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Harman [31]
3 years ago
15

Find the center and radius of circle and graph it

%2B2%29%5E%7B2%7D%20%3D%209" id="TexFormula1" title="(x-4)^{2} +( y +2)^{2} = 9" alt="(x-4)^{2} +( y +2)^{2} = 9" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
sergeinik [125]3 years ago
3 0

Answer:

centre = (4,-2)

radius = 3

Step-by-step explanation:

The centre-radius form of the circle equation is in the format

(x – h)² + (y – k)² = r²,

with the centre being at the point (h, k) and the radius being "r"

Given in the question an expression which can be write as

<h3> (x – 4)² + (y – (-2))² = 3²</h3>

So, by translating we can say that

centre = (4,-2)

and

radius = 3

 

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The Jackson family went out to dinner. The price of the meal was $43.45. The sales tax was 7% of the price of the meal. The tip
brilliants [131]

Answer: 53.40

Step-by-step explanation:

Tax = 7% of 43.45 = 3.04

Tip = 15% of (3.04 + 43.45) = 6.91

Total = 43.45 + 3.04 + 6.91

3 0
3 years ago
Can somebody help me with this please!!
saul85 [17]

1. -21

2. −39

3.−42

4. -5

5. −3

for the other question u can use calculator :)

8 0
2 years ago
According to the article "Characterizing the Severity and Risk of Drought in the Poudre River, Colorado" (J. of Water Res. Plann
mihalych1998 [28]

Answer:

(a) P (Y = 3) = 0.0844, P (Y ≤ 3) = 0.8780

(b) The probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.

Step-by-step explanation:

The random variable <em>Y</em> is defined as the number of consecutive time intervals in which the water supply remains below a critical value <em>y₀</em>.

The random variable <em>Y</em> follows a Geometric distribution with parameter <em>p</em> = 0.409<em>.</em>

The probability mass function of a Geometric distribution is:

P(Y=y)=(1-p)^{y}p;\ y=0,12...

(a)

Compute the probability that a drought lasts exactly 3 intervals as follows:

P(Y=3)=(1-0.409)^{3}\times 0.409=0.0844279\approx0.0844

Thus, the probability that a drought lasts exactly 3 intervals is 0.0844.

Compute the probability that a drought lasts at most 3 intervals as follows:

P (Y ≤ 3) =  P (Y = 0) + P (Y = 1) + P (Y = 2) + P (Y = 3)

              =(1-0.409)^{0}\times 0.409+(1-0.409)^{1}\times 0.409+(1-0.409)^{2}\times 0.409\\+(1-0.409)^{3}\times 0.409\\=0.409+0.2417+0.1429+0.0844\\=0.8780

Thus, the probability that a drought lasts at most 3 intervals is 0.8780.

(b)

Compute the mean of the random variable <em>Y</em> as follows:

\mu=\frac{1-p}{p}=\frac{1-0.409}{0.409}=1.445

Compute the standard deviation of the random variable <em>Y</em> as follows:

\sigma=\sqrt{\frac{1-p}{p^{2}}}=\sqrt{\frac{1-0.409}{(0.409)^{2}}}=1.88

The probability that the length of a drought exceeds its mean value by at least one standard deviation is:

P (Y ≥ μ + σ) = P (Y ≥ 1.445 + 1.88)

                    = P (Y ≥ 3.325)

                    = P (Y ≥ 3)

                    = 1 - P (Y < 3)

                    = 1 - P (X = 0) - P (X = 1) - P (X = 2)

                    =1-[(1-0.409)^{0}\times 0.409+(1-0.409)^{1}\times 0.409\\+(1-0.409)^{2}\times 0.409]\\=1-[0.409+0.2417+0.1429]\\=0.2064

Thus, the probability that the length of a drought exceeds its mean value by at least one standard deviation is 0.2064.

6 0
3 years ago
How many elements are in the set​ {x | x is an even prime​ number, xless than100​}?
maxonik [38]
The answer is obviously {2}since there are NO EVEN PRIME NUMBERS, except for 2. So,there is only 1 element.
8 0
3 years ago
All the students in a school were weighed. Their average weight was 30.8 kilograms, and their total weight was 16,293.2 kilogram
Zinaida [17]

Answer: 529 students

Step-by-step explanation:

To solve this, we will be using the formula for finding averages:

> (total sum of student weights) ÷ (total sum of students) = (average of student weights)

Plugging in the values that are given in the problem, you get:

> 16,293.2 ÷ x = 30.8

Where x is equal to the total sum of students. From here, it's a simple equation to isolate x, and find out what numerical value x is equal to. In case you are unsure how to do this, I've created a clear step by step process for how to do this (NOTE: The slash represents division, while the asterisk represents multiplication.):

> 16,293.2 / x = 30.8

> (16,293.2 / x) * x = (30.8) * x

> 16,293.2 = 30.8 * x

> (16,293.2) / 30.8 = (30.8 * x) / 30.8

> 529 = x

In total, there are 529 students in the school.

7 0
2 years ago
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