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3 years ago

Find the slope of the line through each pair of points. (17,-6),(-11,7)

1 answer:

8 0

Slope is rise over run or
(y1-y2)/(x1-x2)

(x,y)
x1=17
x2=-11
y1=-6
y2=7

slope=(-6-7)/(17-(-11))=(-13)/(17+11)=(-13)/(28)=

the slope is -13/28

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1. Find the phase shift of the function y = 5cos(2x + pi/2).

kolezko [41]

Answer:

see explanation

Step-by-step explanation:

The cosine function in standard form is

y = acos(bx + c)

where a is the amplitude, period = $\frac{2\pi }{b}$ and

phase shift = - $\frac{c}{b}$

here b = 2 and c = $\frac{\pi }{2}$ , thus

phase shift = - $\frac{\frac{\pi }{2} }{2}$ = - $\frac{\pi }{4}$

the amplitude = | a |

which has a maximum of a and a minimum of - a

y = 4cosx ← has a maximum value of 4

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3 years ago

given the value points (0, 25), (5, 20), (12, 13), (9, 16) and (21, 4), find the value of the correlation coefficient for the da

lara [203]

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4 years ago

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Alja [10]

Answer:

The third one

Step-by-step explanation:

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3 years ago

Read 2 more answers

A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 17 randomly selected pens yield

Leno4ka [110]

Answer:

0.762 = 76.2% probability that this shipment is accepted

Step-by-step explanation:

For each pen, there are only two possible outcomes. Either it is defective, or it is not. The probability of a pen being defective is independent from other pens. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

17 randomly selected pens

This means that $n = 17$

(a) Find the probability that this shipment is accepted if 10% of the total shipment is defective. (Use 3 decimal places.)

This is $P(X \leq 2)$ when $p = 0.1$ . So

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{17,0}.(0.1)^{0}.(0.9)^{17} = 0.167$

$P(X = 1) = C_{17,1}.(0.1)^{1}.(0.9)^{16} = 0.315$

$P(X = 2) = C_{17,2}.(0.1)^{2}.(0.9)^{15} = 0.280$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.167 + 0.315 + 0.280 = 0.762$

0.762 = 76.2% probability that this shipment is accepted

8 0

4 years ago

Find the value of x and y. Show all your work neat and<br> in order.

Mazyrski [523]

Answer:

x = 21°

y = 29°

Step-by-step explanation:

a) Solving for x

Note that:

(3x - 3)° and 60° are Alternate interior angles, and alternate interior angles are equal to each other, hence:

3x - 3 = 60° (Alternate interior angles)

Add 3 to both sides

3x - 3 +3 = 60 + 3

3x = 63°

x = 63°/3

x = 21°

b) Solving for y

Notes that:

(3x - 3)° and (4y + 4)° are Consecutive interior angles and the sum consecutive interior angles is 180°

3x - 3 + 4y + 4 = 180°

3x + 4y - 3 + 4 = 180°

3x + 4y + 1 = 180°

Note that x = 21

Hence

3(21) + 4y + 1 = 180°

63 + 1 + 4y = 180°

64 + 4y = 180°

Subtract 64 from both sides

64 - 64 + 4y = 180° - 64

4y = 116°

y = 116/4

y => 29°

8 0

3 years ago