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allsm [11]
3 years ago
8

Need help on 1 and 7 please giving out 19 points

Mathematics
1 answer:
Serjik [45]3 years ago
4 0

Answer:

for number one the answer is no for 7 the answer is 5 seconds

Step-by-step explanation:

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}

<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
Solve the following equation: 2(4^2 + 10) =
lesantik [10]

Answer:

52

Step-by-step explanation:

2(4^2 + 10) =

We do what's in the parenthesis first.

4^2 = 16 and 16+10 =26.

2(26)

= 52

3 0
3 years ago
Read 2 more answers
By which rule are these triangles congruent?<br> A) AAS <br> B) ASA <br> C) SAS <br> D) SSS
Veronika [31]

Answer:

the answer is c)SAS

Step-by-step explanation:

as the sides are already given and and both angles will be equal as vertically opposite angles (VOA)are always equal.

3 0
3 years ago
A mailbox that is 36 inches tall is beside a tree.The length of the mailboxes shadow is 28 inches.The length of the trees shadow
mixer [17]

Answer:

10.5 feet

Step-by-step explanation:

In this problem, we have two similar triangles:

- One consists of the mailbox, its shadow and the hypothenuse

- The other one consists of the tree, its shadow and the hypothenuse

The two triangles are similar, so they have same proportions between their sides: therefore, we can apply the rule of three:

\frac{m}{s_m}=\frac{t}{s_t}

where

m = 36 in is the height of the mailbox

s_m=28 in is the shadow of the mailbox

t is the height of the tree

s_t=98 in is the length of the shadow of the tree

Solving for t, we find the height of the tree:

t=\frac{m\cdot s_t}{s_m}=\frac{(36)(98)}{28}=126 in

And since

1 feet = 12 inches

The height of the tree in feet is

t=\frac{126}{12}=10.5 ft

3 0
3 years ago
Please Help Me Will Pick the first correct answer brainliest
dimaraw [331]

Answer:

1 and 4 are correct :)

Step-by-step explanation:

8 0
2 years ago
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