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3 years ago

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The Spanish club held a car wash to raise money. The equation y equals 5 x represents the amount of money y club members made fo

r washing X cars. Identify the constant of proportionality. Then explain what it represents in thus situation.

1 answer:

algol [13]3 years ago

7 0

Answer:

the constant of proportionality is 5

it represents the amount of money they made for washing each car

Step-by-step explanation:

y = 5x

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REY [17]

Answer:

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Step-by-step explanation:

Next time use a calculator chuckle nuts

7 0

3 years ago

Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. The article "Methodo

Shkiper50 [21]

Answer:

a) $P(X\leq 4)=0.0183+0.0733+ 0.1465+0.1954+0.1954=0.6288$

$P(X< 4)=P(X\leq 3)=0.0183+0.0733+ 0.1465+0.1954=0.4335$

b) $P(4\leq X\leq 8)=0.1954+0.1563+0.1042+0.0595+0.0298=0.5452$

c) $P(X \geq 8) = 1-P(X$

d) $P(4\leq X \leq 6)=0.1954+0.1563+0.1042=0.4559$

Step-by-step explanation:

Let X the random variable that represent the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. We know that $X \sim Poisson(\lambda=4)$

The probability mass function for the random variable is given by:

$f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...$

And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

$E(X)=\mu =\lambda=4$ , $Var(X)=\lambda=2$ , $Sd(X)=2$

a. Compute both P(X≤4) and P(X<4).

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

Using the pmf we can find the individual probabilities like this:

$P(X=0)=\frac{e^{-4} 4^0}{0!}=e^{-4}=0.0183$

$P(X=1)=\frac{e^{-4} 4^1}{1!}=0.0733$

$P(X=2)=\frac{e^{-4} 4^2}{2!}=0.1465$

$P(X=3)=\frac{e^{-4} 4^3}{3!}=0.1954$

$P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954$

$P(X\leq 4)=0.0183+0.0733+ 0.1465+0.1954+0.1954=0.9646$

$P(X< 4)=P(X\leq 3)=P(X=0)+P(X=1)+ P(X=2)+P(X=3)$

$P(X< 4)=P(X\leq 3)=0.0183+0.0733+ 0.1465+0.5311=0.7692$

b. Compute P(4≤X≤ 8).

$P(4\leq X\leq 8)=P(X=4)+P(X=5)+ P(X=6)+P(X=7)+P(X=8)$

$P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954$

$P(X=5)=\frac{e^{-4} 4^5}{5!}=0.1563$

$P(X=6)=\frac{e^{-4} 4^6}{6!}=0.1042$

$P(X=7)=\frac{e^{-4} 4^7}{7!}=0.0595$

$P(X=8)=\frac{e^{-4} 4^8}{8!}=0.0298$

$P(4\leq X\leq 8)=0.1954+0.1563+ 0.1042+0.0595+0.0298=0.5452$

c. Compute P(8≤ X).

$P(X \geq 8) = 1-P(X$

$P(X \geq 8) = 1-P(X$

d. What is the probability that the number of anomalies exceeds its mean value by no more than one standard deviation?

The mean is 4 and the deviation is 2, so we want this probability

$P(4\leq X \leq 6)=P(X=4)+P(X=5)+P(X=6)$

$P(X=4)=\frac{e^{-4} 4^4}{4!}=0.1954$

$P(X=5)=\frac{e^{-4} 4^5}{5!}=0.1563$

$P(X=6)=\frac{e^{-4} 4^6}{6!}=0.1042$

$P(4\leq X \leq 6)=0.1954+0.1563+0.1042=0.4559$

4 0

3 years ago

A recipe for waffles calls for 2 cups of flour and 3 teaspoons of baking powder. If Jason uses 4 cups of flour, how much baking

Allisa [31]

it is D. 6 tsp.

because cause we know that 2 × 2=4

So we multiply 3 ×2=6

Because we know he is doubling the recipe

the answer is D. 6 tsp. of baking powder

hope it help

8 0

3 years ago

Read 2 more answers

A rancher has 4 comma 700 feet of fencing available to enclose a rectangular area bordering a river. he wants to separate his co

guapka [62]

Area=length*width
let the sides perpendicular to the river be x
then the side parallel to the river is 4,700-2x
A(x)=x(4700-2x)
A(x)=4700x-2x^2

This a quadratic function with a=-2 and b=4700
thus
Maximum area occurs where x=-b/2a=-4700(-2*2)=1,175 ft
length=4700-2(1175)=2,350 ft

4 0

3 years ago

nexus9112 [7]

Answer:

- Equal midpoints of AC and BC.

- The product of the slopes of the diagonals AC and DB is -1.

Step-by-step explanation:

1. Plot the given points, as you can see in the graph attached.

2. Calculate the midpoint of AC and DB:

$M_{AC}=(\frac{-5+(-1)}{2},\frac{-1+5}{2})=(-3,2)\\M_{DB}=(\frac{-9+3}{2},\frac{6+(-2)}{2})=(-3,2)$

Therefore, the midpoint of AC and DB are equal.

3. Calculte the slope of the diagonals AC and DB:

$m_{AC}=\frac{5-(-1)}{-1-(-5)}=\frac{3}{2}\\m_{DB}=\frac{-2-6)}{3-(-9)}=-\frac{2}{3}$

4. Multiply the slopes of the diagonals:

$(\frac{3}{2})(-\frac{2}{3})=-1$ (AC and DB are perpendicular)

5 0

3 years ago