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2 years ago

Which quadrilateral is a trapezoid?

Mathematics

2 answers:

Vera_Pavlovna [14]2 years ago

7 0

The answer to this is C

AnnZ [28]2 years ago

7 0

Answer:

THE ANSWER IS C

Step-by-step explanation:

A trapezoid is a shape with at least a pair of parallel lines

In shape D there are No parallel lines

Therefore its shape C

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Write an equation of a line (in standard form) that has the same slope as the line 3x-5y=7 and the same y-intercept as the line

Vanyuwa [196]

Answer:

$3x-5y=-20$

Step-by-step explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have two standard form equations which we will get a slope and a y-intercept from. We will convert each to slope intercept form to get the information. We will then write a new slope-intercept equation and convert to standard form.

3x-5y=7 has the same slope as the line. Let's convert.

$3x-5y=7\\3x-3x-5y=7-3x\\-5y=7-3x\\\frac{-5y}{-5}=\frac{7-3x}{-5} \\$

$y=\frac{3}{5}x -\frac{7}{5}$

The slope is $m=\frac{3}{5}$ .

2y-9x=8 has the same y-intercept as the line. Let's convert.

$2y-9x=8\\2y-9x+9x=8+9x\\2y=8+9x\\\frac{2y}{2}=\frac{8+9x}{2}$

$y=\frac{8}{2}+\frac{9x}{2} \\y=4+\frac{9}{2}x$

The y-intercept is 4.

We take $m=\frac{3}{5}$ and b=4 and substitute into y=mx+b.

$y=\frac{3}{5}x+4$

We now convert to standard form.

$-\frac{3}{5}x+y=\frac{3}{5}x-\frac{3}{5}x+4\\-\frac{3}{5}x+y=4$

For standard form we need the coefficients of x and y to be not zero or fractions. We need integers but the coefficient of x cannot be negative. So we multiply the entire equation by -5 to clear the denominators.

$-5(-\frac{3}{5}x+y=4)\\3x-5y=-20$

3 0

3 years ago

For number 28, are the 2 graphs parallel, perpendicular or neither?

d1i1m1o1n [39]

The lines are parallel

5 0

3 years ago

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

<em>Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection. </em>

This means that,

<em>Probability that at least one of them needs replacement at the first inspection = </em>

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

5 0

3 years ago

What decimal is equal to 31/100

BlackZzzverrR [31]

Answer:

0.31

Step-by-step explanation:

So if you divide 31 by 100 all you have to do is move the decimal from right to left the number of zeros you have. Here we have 2 zeros so we move from right to left twice.

0.31

4 0

3 years ago

6 Bridesmaids want to make 330 decorations for a wedding. Each

Alex_Xolod [135]

Answer:

about 3.21 hours each

Step-by-step explanation:

First divide 330 by 6 since there are six people.

Every person needs to do 55 decorations.

I would take the average of 2-4 minutes and multiply it by 55.

55 x 3.5 = 192.5 minutes

to convert to hours divide by 60.

192.5 / 60 = 3.21

5 0

3 years ago