All categories

3 years ago

The area of a trapezoid is 864 cm. It has a height of 24 cm, and the length

Mathematics

1 answer:

Bogdan [553]3 years ago

6 0

Answer:=42 cm

Step-by-step explanation:

Strap=(a+b)*h/2 ( where a and b are trapezoid' s bases and h is a height)

So 864=(30+b)*24/2

30+b=864*2/24

30+b=864/12

30+b=72

b=72-30

b=42 cm

You might be interested in

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

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

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.

This means that,

Probability that at least one of them needs replacement at the first inspection =

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

5 0

3 years ago

The function g(x) = –3x2 – 36x – 60 written in vertex form is g(x) = –3(x + 6)2 + 48. Which is one of the transformations applie

navik [9.2K]

The vertex form of the function gives the vertex as (-6,48). The vertex of f(x)=x^2 is (0,0) so from this information, the vertex is moved LEFT 6 and UP 48. This cancels out two options. The coefficient -3 tells us that the graph is flipped or reflected over the x-axis (negative sign flips graph) and that all y-values will be 3 times as large. Larger y-values for the same x inputs makes the graph narrower.

3 0

4 years ago

50% of what number is 140?

babunello [35]

Answer:

The answer is 70

3 0

3 years ago

*I WILL MARK U BRANLIEST AND GIVE 40 POINTS IF U ANSWER ALL THREE*

Gnesinka [82]

Step-by-step explanation:

1. 18(5)=90 18(6)=108

90*108= 9720

Her size of the original work was 9720 inches.

2. 1/2+1/2= 1 1/2=4 ft

The pole is 8 feet tall

3. 3 feet

3 0

3 years ago

Brainlest 5 starred and thanked daily if you get this correct Try your hardest

mart [117]

The cycle number two is the answer

8 0

3 years ago