The diagram shows a regular dodecagon.Work out the size of one interior angle

A sweatshirt that was originally priced at $42.50 has been marked down to $34.00. What is the percent decrease?

vichka [17]

Answer:

The answer is 20%

I hope this helps :)

6 0

3 years ago

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Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 33% of all homeowners are ins

Lina20 [59]

Answer:

(a) The probability mass function of X is:

$P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...$

(b) The most likely value for X is 1.32.

(c) The probability that at least two of the four selected have earthquake insurance is 0.4015.

Step-by-step explanation:

The random variable X is defined as the number among the four homeowners who have earthquake insurance.

The probability that a homeowner has earthquake insurance is, p = 0.33.

The random sample of homeowners selected is, n = 4.

The event of a homeowner having an earthquake insurance is independent of the other three homeowners.

(a)

All the statements above clearly indicate that the random variable X follows a Binomial distribution with parameters n = 4 and p = 0.33.

The probability mass function of X is:

$P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...$

(b)

The most likely value of a random variable is the expected value.

The expected value of a Binomial random variable is:

$E(X)=np$

Compute the expected value of X as follows:

$E(X)=np$

$=4\times 0.33\\=1.32$

Thus, the most likely value for X is 1.32.

(c)

Compute the probability that at least two of the four selected have earthquake insurance as follows:

P (X ≥ 2) = 1 - P (X < 2)

= 1 - P (X = 0) - P (X = 1)

$=1-{4\choose 0}\ (0.33)^{0}\ (1-0.33)^{4-0}-{4\choose 1}\ (0.33)^{1}\ (1-0.33)^{4-1}\\\\=1-0.20151121-0.39700716\\\\=0.40148163\\\\\approx 0.4015$

Thus, the probability that at least two of the four selected have earthquake insurance is 0.4015.

3 0

3 years ago

Solve the equation for x. 2 3 x −1 9 x + 5 = 20 x =

zubka84 [21]

Answer:

5/2

Step-by-step explanation:

23x-19x+5=2x

23x-19x-2x=5

2x/2=5/2

x=5/2

3 0

3 years ago

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You have a bag of 12 blue marbles and 12 red marbles. each are labeled 1-12. so you have 24 marbles in total (1-12 for each colo

Softa [21]

Answer:

The probability of the first marble being blue and second being red is a 50/50 because you have 12 red and 12 blue so 50/50

Step-by-step explanation:

8 0

3 years ago

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Adjust the equation so the line passes through the points. Y=x+1

lapo4ka [179]

Answer:

Slope=

2.000

=1.000

x−intercept=

−1

1

=−1.00000

y−intercept=

1

=1.00000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-(x+1)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve y-x-1 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-x-1 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 1/1 so this line "cuts" the y axis at y= 1.00000

y-intercept = 1/1 = 1.00000

Calculate the X-Intercept :

When y = 0 the value of x is 1/-1 Our line therefore "cuts" the x axis at x=-1.00000

x-intercept = 1/-1 = -1.00000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.000 and for x=2.000, the value of y is 3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.000 - 1.000 = 2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 2.000/2.000 = 1.000

Geometric figure: Straight Line

1. Slope = 2.000/2.000 = 1.000

2. x-intercept = 1/-1 = -1.00000

3. y-intercept = 1/1 = 1.00000

3 0

3 years ago