What are the first three terms of the Arithmetic Sequence a_n = 15 – 2(n

A circle is described by the equation x2 y2 14x 2y 14 = 0. what are the coordinates for the center of the circle and the length

bearhunter [10]

Answer:

length is (-7,-1) and radius is 6

Step-by-step explanation:

We are given the expression of the equation of a circle that is

x2 + y2 + 14x + 2y + 14 = 0.

Using completing the squares:

x2 + y2 + 14x + 2y + 14 = 0(x+7)^2 + (y+1) ^2 = -14 + 49 + 1(x+7)^2 + (y+1) ^2 = 36 center thus is at (-7,-1) and the radius is equal to square root of 36 equal to 6.

6 0

1 year ago

GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a m

Harrizon [31]

Answer:

(a) Null Hypothesis, $H_0$ : $\mu \leq$ 3.50 mg

Alternate Hypothesis, $H_A$ : $\mu$ > 3.50 mg

(b) The value of z test statistics is 2.50.

(c) We conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.

(d) The p-value is 0.0062.

Step-by-step explanation:

We are given that Green Beam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a mean of 3.59 mg of mercury. Assuming a known standard deviation of 0.18 mg.

Let $\mu$ = average mg of mercury in compact fluorescent bulbs.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 3.50 mg {means that the average mg of mercury in compact fluorescent bulbs is no more than 3.50 mg}

Alternate Hypothesis, $H_A$ : $\mu$ > 3.50 mg {means that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean mg of mercury = 3.59

$\sigma$ = population standard deviation = 0.18 mg

n = sample of bulbs = 25

So, test statistics = $\frac{3.59-3.50}{\frac{0.18}{\sqrt{25} } }$

= 2.50

The value of z test statistics is 2.50.

Now, P-value of the test statistics is given by;

P-value = P(Z > 2.50) = 1 - P(Z $\leq$ 2.50)

= 1 - 0.9938 = 0.0062

Now, at 0.01 significance level the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is more than the critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.

6 0

3 years ago

78×13-8×78+26×78-78=

Amanda [17]

Applying BODMAS (Order of operations rule)

Where: B is for brackets

O is for 'of' which means multiplication

D is for division

M is for multiplication

A is for addition

S is for subtraction

In this case:

We start with addition then we go to addition and finally we subtract.

(78 × 13) - (8 × 78) + (26 × 78) - 78

= 1014 - 624 + 2028 - 78

= 1014 + 2028 - 624 - 78

= 3042 - 624 - 78

=2340

7 0

3 years ago

Read 2 more answers

QUESTION 17 PLEASE HELP ME ASAPP

Butoxors [25]

Answer: change over time
Explanation: it is decreasing in height therefore is decreasing in altitude

4 0

2 years ago

Read 2 more answers

The length of each side of an equilateral triangle is increased by 6 inches, so the perimeter is now 60 inches. What was the ori

Nimfa-mama [501]

Answer:

14 inches

Step-by-step explanation:

Using this information, we can form an equation.

Since there are 3 sides in a triangle, and each side increased by 6, that means that the perimeter increased by 18 inches. Down below, I did 3x because there are 3 sides in a triangle.

(This is the equation you'd want to do to get the answer)

3x + 3 * 6 = 60

Simplify:

3x + 18 = 60

Same to both sides

3x = 42

Isolate x:

x = 14

Let me know if you have any questions

8 0

3 years ago

What are the first three terms of the Arithmetic Sequence a_n = 15 – 2(n – 1)?