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2 years ago

Consider the graph show?

Mathematics

2 answers:

Aleks [24]2 years ago

4 0

Answer:

Answer: B) Y = 2x

Step-by-step explanation:

The pattern of the proportional relationship is every 1 move on the "X" line moves up 2 places in the "Y" line. Notice that the first mark is (1, 2) and the second mark is (2, 4), and the third mark that you see on the graph is (3, 6). Notice that you add 2 on the "Y" axis every time you move once on the X-axis. If you multiply 2 x what ever number is on the horizontal line (X), you will get the next point in the proportional relationship. 1 x 2 = (1, 2), 2 x 2 = (2, 4), and 3 x 2 = (3, 6). Therefore, the answer is B) Y = 2x

Naily [24]2 years ago

3 0

Answer:

$y = 2x$

when X=1

y=2(1)=2

X=2

y=2(2)=4

X=X

y=2X

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A shop sells a particular of video recorder. Assuming that the weekly demand for the video recorder is a Poisson variable with t

julia-pushkina [17]

Answer:

a) 0.5768 = 57.68% probability that the shop sells at least 3 in a week.

b) 0.988 = 98.8% probability that the shop sells at most 7 in a week.

c) 0.0104 = 1.04% probability that the shop sells more than 20 in a month.

Step-by-step explanation:

For questions a and b, the Poisson distribution is used, while for question c, the normal approximation is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}$

In which

x is the number of successes

e = 2.71828 is the Euler number

$\lambda$ is the mean in the given interval.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Poisson distribution can be approximated to the normal with $\mu = \lambda, \sigma = \sqrt{\lambda}$ , if $\lambda>10$ .

Poisson variable with the mean 3

This means that $\lambda= 3$ .

(a) At least 3 in a week.

This is $P(X \geq 3)$ . So

$P(X \geq 3) = 1 - P(X < 3)$

In which:

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

Then

$P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498$

$P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494$

$P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0498 + 0.1494 + 0.2240 = 0.4232$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 1 - 0.4232 = 0.5768$

0.5768 = 57.68% probability that the shop sells at least 3 in a week.

(b) At most 7 in a week.

This is:

$P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)$

In which

$P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498$

$P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494$

$P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240$

$P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240$

$P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680$

$P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008$

$P(X = 6) = \frac{e^{-3}*3^{6}}{(6)!} = 0.0504$

$P(X = 7) = \frac{e^{-3}*3^{7}}{(7)!} = 0.0216$

Then

$P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008 + 0.0504 + 0.0216 = 0.988$

0.988 = 98.8% probability that the shop sells at most 7 in a week.

(c) More than 20 in a month (4 weeks).

4 weeks, so:

$\mu = \lambda = 4(3) = 12$

$\sigma = \sqrt{\lambda} = \sqrt{12}$

The probability, using continuity correction, is P(X > 20 + 0.5) = P(X > 20.5), which is 1 subtracted by the p-value of Z when X = 20.5.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20 - 12}{\sqrt{12}}$

$Z = 2.31$

$Z = 2.31$ has a p-value of 0.9896.

1 - 0.9896 = 0.0104

0.0104 = 1.04% probability that the shop sells more than 20 in a month.

5 0

2 years ago

Find the difference.

Vsevolod [243]

$5.\\12\dfrac{3}{10}-7\dfrac{7}{10}=11\dfrac{10+3}{10}-7\dfrac{7}{10}=11\dfrac{13}{10}-7\dfrac{7}{10}=4\dfrac{6}{10}=4\dfrac{6:2}{10:2}=\boxed{5\dfrac{3}{5}}\\\\11-7=4\\\\\dfrac{13}{10}-\dfrac{7}{10}=\dfrac{13-7}{10}=\dfrac{6}{10}\\\\6.\\8\dfrac{1}{6}-3\dfrac{5}{6}=7\dfrac{6+1}{6}-3\dfrac{5}{6}=7\dfrac{7}{6}-3\dfrac{5}{6}=(7-3)+\dfrac{7-5}{6}=4\dfrac{2}{6}=4\dfrac{2:2}{6:2}=\boxed{4\dfrac{1}{3}}$

$9.\\7\dfrac{1}{6}-2\dfrac{5}{6}=6\dfrac{6+1}{6}-2\dfrac{5}{6}=6\dfrac{7}{6}-2\dfrac{5}{6}=(6-2)+\dfrac{7-5}{6}=4\dfrac{2}{6}=\boxed{4\dfrac{1}{3}}\\\\10.\\9\dfrac{3}{12}-4\dfrac{7}{12}=8\dfrac{12+3}{12}-4\dfrac{7}{12}=8\dfrac{15}{12}-4\dfrac{7}{12}=(8-4)+\dfrac{15-7}{12}=4\dfrac{8}{12}\\\\=4\dfrac{8:4}{12:4}=\boxed{4\dfrac{2}{3}}$

5 0

3 years ago

Write an equation that represents the line use exact numbers

RSB [31]

Answer:

y = (-6/7)x - 1

Step-by-step explanation:

There's a dot where this line crosses the y-axis; it's represented by the point (0, -1). Consequently, the y-intercept, b, of this line is -1.

As x increases from -6 to 0, y decreases from 7 to -1. The change in x is 7 units and the change in y is -6 units. Thus, the slope of this line is

m = rise / run = -6 / 7.

Again, the y-intercept is b = -1.

Thus, inserting the knowns into the slope-intercept form of the equation of a straight line results in:

y = (-6/7)x - 1

3 0

3 years ago

The value of x must be greater than what?

alexandr402 [8]

Answer: I believe it would be the hypotenuse, i not to sure but I hope this helps in some way

Step-by-step explanation:

8 0

3 years ago

Solve 2m-44=76-8m and give the right answer

attashe74 [19]

Answer:

m = 12

Step-by-step explanation:

2m − 44 = 76 − 8m

Move all terms containing m to the left side of the equation

10m − 44 = 76

Add 44 to both sides of the equation

10m = 120

Divide each term by 10 and simplify.

10m/10 = 120/10

m = 12

4 0

3 years ago

Read 2 more answers