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kirill115 [55]
2 years ago
7

Write the equation of the line in slope-intercept form with the given information. (-7, 13); slope = -2

Mathematics
1 answer:
Musya8 [376]2 years ago
8 0

Answer:

The answer is

y =  - 2x + c \\ 13 =  - 2 \times  - 7 + c \\ c = 25 \\ y =  - 2x + 25

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A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of
notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.98}{2} = 0.01

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.01 = 0.99, so Z = 2.327.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

M = z\frac{\sigma}{\sqrt{n}}

0.0001 = 2.327\frac{0.0003}{\sqrt{n}}

0.0001\sqrt{n} = 2.327*0.0003

\sqrt{n} = \frac{2.327*0.0003}{0.0001}

(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2

n = 48.73

Rounding up

49 measurements are needed.

7 0
3 years ago
Algebraic 3 more than 5 times a number
artcher [175]

Answer:

5x+3

Step-by-step explanation:

substitute x for the unknown number

8 0
3 years ago
WORTH 20 POINTS HELP
vfiekz [6]

Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

So, we have:

QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}

RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}

ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}

TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

m = \frac{y_2 -y_1}{x_2 -x_1}

So, we have:

QR = \frac{9 + 1}{2 + 3} = \frac{10}3

RS = \frac{5-9}{-4 - 2} = \frac{2}3

ST = \frac{5+5}{-4 + 7} = \frac{10}3

TQ = \frac{-5+1}{-7 + 1} = \frac{2}3

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

Read more about parallelograms at:

brainly.com/question/3050890

#SPJ1

6 0
2 years ago
Which best describes the transformation that occurs from
Law Incorporation [45]

Answer:

right 2 , up 3.

Step-by-step explanation:

The -2 moves 2 to the right and the + 3 means 3 up.

6 0
3 years ago
Distribute and evaluating <br> (X + 6) (x - 3)
sesenic [268]

Answer:

x^2+3x-18

Step-by-step explanation: hoped I helped

7 0
2 years ago
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