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devlian [24]
4 years ago
7

The circle C has centre A(2,1) and passes through the point B(10,7). Find and equation for C

Mathematics
1 answer:
Semmy [17]4 years ago
7 0
The equation of a circle:
(x-h)^2+(y-k)^2=r^2
(h,k) - the coordinates of the centre
r - the radius

A(2,1) - \hbox{the centre} \\
h=2 \\ k=1 \\ \\
(x-2)^2+(y-1)^2=r^2 \\ \\
\hbox{passes through B(10,7)} \\
x=10 \\
y=7 \\ \\
(10-2)^2+(7-1)^2=r^2 \\
8^2+6^2=r^2 \\
64+36=r^2 \\
r^2=100 \\ \\
\hbox{the equation:} \\ \boxed{(x-2)^2+(y-1)^2=100}
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3 years ago
1. IQ scores of statistics students have a standard deviation less than 15. A. H0:σ≤15, H1:σ&gt;15 B. H0:σ≥15, H1:σ&lt;15 C. H0:
grandymaker [24]

Answer:

1) For this case we want to check if the population deviation is less than 15( alternative hypothesis) and the system of hypothesis are:

H0: \sigma \geq 15

H1: \sigma

B. H0:σ≥15, H1:σ<15

2) For this case we want to check if the population mean \mu is at most 70000 (alternative hypothesis) and the system of hypothesis are:

H0: \mu \geq 70000

H1: \mu

C. H0:µ≥70,000, H1:µ<70,000

3) For this case we want to check if the population proportion p of all internet users that make online purchases is higher than 0.5 (alternative hypothesis) and the system of hypothesis are:

H0: p \leq 0.5

H1: p >0.5

D. H0:p≤0.5, H1:p>0.5

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".  

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".  

Solution to the problem

1) For this case we want to check if the population deviation is less than 15( alternative hypothesis) and the system of hypothesis are:

H0: \sigma \geq 15

H1: \sigma

B. H0:σ≥15, H1:σ<15

2) For this case we want to check if the population mean \mu is at most 70000 (alternative hypothesis) and the system of hypothesis are:

H0: \mu \geq 70000

H1: \mu

C. H0:µ≥70,000, H1:µ<70,000

3) For this case we want to check if the population proportion p of all internet users that make online purchases is higher than 0.5 (alternative hypothesis) and the system of hypothesis are:

H0: p \leq 0.5

H1: p >0.5

D. H0:p≤0.5, H1:p>0.5

7 0
4 years ago
Are there less than 1 million, exactly 1 million, or greater than 1 million milligrams in 1 kilograms?
shusha [124]

Answer: There is exactly 1 million in 1 kilogram

Step-by-step explanation:

6 0
3 years ago
Write the equation of the line in standard form that passes through the point (1, 7) and has a slope of 2. Show all work.
Finger [1]

Answer:

2x - y = - 5

Step-by-step explanation:

First obtain the equation in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (1, 7) into the partial equation

7 = 2 + c ⇒ c = 7 - 2 = 5

y = 2x + 5 ← in slope- intercept form

The equation in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Subtract y from both sides

0 = 2x - y + 5 ( subtract 5 from both sides )

- 5 = 2x - y, that is

2x - y = - 5 ← in standard form

7 0
3 years ago
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