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notka56 [123]
2 years ago
9

Explain why the graph below does not represent a direct variation. a. the line does not intercept the x-axis c. the line does no

t go through the origin b. the line intercepts the y-axis d. the line is not straight Please select the best answer from the choices provided
Mathematics
1 answer:
Rama09 [41]2 years ago
3 0

The graph is not a direct variation because the line does not go through the origin; option C.

<h3>What is a direct variation?</h3>

A direct variation is a relationship between two or more quantities in which as one quantity increases, the other quantity also increases. Similarly, if the other quantity decreases, the other decreases as well.

For the graph of a direct variation, the line must pass through the origin.

Therefore, the graph does not represent a direct variation because the line does not go through the origin.

In conclusion, direct variation involves a corresponding increase or decrease in two related quantities.

Learn more about direct variation at: brainly.com/question/2633726

#SPJ1

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A pen company averages 1.2 defective pens per carton produced (200 pens). The number of defects per carton is Poisson distribute
nlexa [21]

Answer:

a. P(x = 0 | λ = 1.2) = 0.301

b. P(x ≥ 8 | λ = 1.2) = 0.000

c. P(x > 5 | λ = 1.2) = 0.002

Step-by-step explanation:

If the number of defects per carton is Poisson distributed, with parameter 1.2 pens/carton, we can model the probability of k defects as:

P(k)=\frac{\lambda^{k}e^{-\lambda}}{k!}= \frac{1.2^{k}\cdot e^{-1.2}}{k!}

a. What is the probability of selecting a carton and finding no defective pens?

This happens for k=0, so the probability is:

P(0)=\frac{1.2^{0}\cdot e^{-1.2}}{0!}=e^{-1.2}=0.301

b. What is the probability of finding eight or more defective pens in a carton?

This can be calculated as one minus the probablity of having 7 or less defective pens.

P(k\geq8)=1-P(k

P(0)=1.2^{0} \cdot e^{-1.2}/0!=1*0.3012/1=0.301\\\\P(1)=1.2^{1} \cdot e^{-1.2}/1!=1*0.3012/1=0.361\\\\P(2)=1.2^{2} \cdot e^{-1.2}/2!=1*0.3012/2=0.217\\\\P(3)=1.2^{3} \cdot e^{-1.2}/3!=2*0.3012/6=0.087\\\\P(4)=1.2^{4} \cdot e^{-1.2}/4!=2*0.3012/24=0.026\\\\P(5)=1.2^{5} \cdot e^{-1.2}/5!=2*0.3012/120=0.006\\\\P(6)=1.2^{6} \cdot e^{-1.2}/6!=3*0.3012/720=0.001\\\\P(7)=1.2^{7} \cdot e^{-1.2}/7!=4*0.3012/5040=0\\\\

P(k

c. Suppose a purchaser of these pens will quit buying from the company if a carton contains more than five defective pens. What is the probability that a carton contains more than five defective pens?

We can calculate this as we did the previous question, but for k=5.

P(k>5)=1-P(k\leq5)=1-\sum_{k=0}^5P(k)\\\\P(k>5)=1-(0.301+0.361+0.217+0.087+0.026+0.006)\\\\P(k>5)=1-0.998=0.002

5 0
3 years ago
An abstract sculpture in the form of a triangle has a base 21 meters and a height of 12 meters. Find the are of the triangle.
charle [14.2K]
The area of a triangle could be determined using the following formula
\boxed{a= \frac{1}{2} \times b \times h}

plug in the numbers
a =  \frac{1}{2} \times 21 \times 12
a =  \frac{1}{2} \times 252
a= \frac{252}{2}
a = 126

The area of the triangle is 126 square meters
8 0
3 years ago
What is the reciprocal of 8 8/5 ?
Ksenya-84 [330]

Answer:

\frac{5}{48}

Step-by-step explanation:

The reciprocal of a number n is \frac{1}{n}

Given 8 \frac{8}{5}, change to an improper fraction

= \frac{5(8)+8}{5} = \frac{48}{5}, thus

reciprocal = \frac{1}{\frac{48}{5} } = \frac{5}{48}

3 0
3 years ago
If the area of the following parallelogram is 30 square centimeters, what is the length of the base?
sleet_krkn [62]

Answer:

5 cm

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
321.5 is between ________ and ________ on the number line.
Lena [83]

321.5 is between ___321_____ and ___322_____ on the number line.

Answer

B

321 and 322

8 0
3 years ago
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