Solve. -6x^2 – 2 – 3x = -8​

Answer:

a. Their average weight is of 200 pounds.

b. 0.0875 = 8.75% probability that the maximum safe weight will be exceeded

c. 0.0002 = 0.02% probability that the maximum safe weight will be exceeded

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. If 60 people are riding the coaster, and their total weight is 12,000 pounds, what is their average weight?

12000/60 = 200 pounds

Their average weight is of 200 pounds.

b. If a random sample of 60 adult men ride the coaster, what is the probability that the maximum safe weight will be exceeded?

Men means that [tex]\mu = 189, \sigma = 63[/tex].

Sample of 60 means that [tex]n = 60, s = \frac{63}{\sqrt{60}} = 8.13[/tex]

Safe weight will be exceeded if the sample mean is above 200 pounds, which has probability of 1 subtracted by the pvalue of Z when X = 200. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{200 - 189}{8.13}[/tex]

[tex]Z = 1.35[/tex]

[tex]Z = 1.35[/tex] has a pvalue of 0.9115

1 - 0.9115 = 0.0875

0.0875 = 8.75% probability that the maximum safe weight will be exceeded.

c. If a random sample of 60 adult women ride the coaster, what is the probability that the maximum safe weight will be exceeded?

Women means that [tex]\mu = 165, \sigma = 76[/tex]

Sample of 60 means that [tex]n = 60, s = \frac{76}{\sqrt{60}} = 9.81[/tex]

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{200 - 165}{9.81}[/tex]

[tex]Z = 3.57[/tex]

[tex]Z = 3.57[/tex] has a pvalue of 0.9998

1 - 0.9998 = 0.0002

0.0002 = 0.02% probability that the maximum safe weight will be exceeded

Answer:

C and B

Step-by-step explanation:

Parallel is when two lines are exactly parallel from eachother which means they both have to go in the same direction. It has to be two lines that dont meet up with eachother when you continue the lines.

Answer:

[tex]P(B) = 0.3[/tex]

Step-by-step explanation:

We use the following formula for Venn probabilities to solve this question.

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

P((AUB)') = 0.4

This means that:

[tex]P(A \cup B) = 1 - P(A \cup B)' = 1 - 0.4 = 0.6[/tex]

We also have that:

[tex]P(A) = 0.5, P(A \cap B) = 0.2[/tex]

What is P(B)?​

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

[tex]0.6 = 0.5 + P(B) - 0.2[/tex]

[tex]0.3 + P(B) = 0.6[/tex]

[tex]P(B) = 0.3[/tex]

Answer:

hang ups the receiver

Step-by-step explanation:

In this case, there is a difficulty for the call center to determine the average time that each caller spends on each type of request, since there is also the possibility that the recipient will not be interested in the call or hang up when receiving such a call. Therefore, in order to calculate this average in a more real way, the company must statistically monitor this data in relation to each hour of work and how many situations occurred in that hour, how many calls received were answered, how many received a busy signal, how many are not answered and how many calls last less than a minute if the recipient is not interested or hangs up.

Through this data, the company is able to monitor the calls and define telephone service strategies that can retain the customer more if the calls in less than a minute exceed conventional calls.

Answer:

$3.15

Step-by-step explanation:

$4.16+$1.50+$1.19=$6.85

$10.00-$6.85=$3.15

(Sorry if it's wrong.)

Answer:

726

Step-by-step explanation:

Volume = length x width x height

Volume = 1.4 x 1.3 x 3.5 = 6.37 cubic cm

Answer:

SINGH???

Step-by-step explanation:

Answer:

[tex]\huge\blue{\mid{\fbox{\tt{ANSWER}}\mid}}[/tex]

C. n/90 rad/sec.

Answer: 30°

Step-by-step explanation:

we have to find the angle adjacent with the right angle. For this we use the (-).

At this point, I am guessing you know how to use SOH-CAH-TOA, for this one we use SOH so sin. If you have a calculator set it on degree mode, then plug it in as sin⁻₁(), we put it like that because the missing angle has the given number opposite and the hypotenuse. It solves it and now we get 30 for the answer. I dont know if that made sense, tell me if it didnt so I can explain it better.

Answer:

dfsdfsdfsdfsdfsdf

Step-by-step explanation:

its 50.3.2  tags: c c c cc  cc c  c c c ar c free car no yes show two plus pwe

Answer:

y=-2x+5

Step-by-step explanation:

Use the equation y=mx+b

We can find the b(y-intercept) by looking at the graph

The graph crosses the y-axis at (0,5)

We can look at the slope at the graph. We can see its down 4 over 2 so the slope is -2.

Plug that into the equation y=mx+b

y=-2x+5

Answer:

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

Hope helps :)

Answer:

Hi! Your answer is 34! :D

Step-by-step explanation:

The lovely human who answered above me is indeed correct.

I hope you have an amazing day! Please give brainliest!

Answer:

as w → -∞, q(w)→-∞

as w → ∞, q(w)→∞

Step-by-step explanation:

The behaviour tells us how changes y as x changes.

In the left side (as w decreases) we can see that y goes down, then we can see that as w goes to negative infinity, q(w) also goes to negative infinity.

Then we can write:

as w → -∞, q(w)→-∞

In the right side (so when w increases) we can see that q(w) increases, then with the same reasoning as above we have:

as w → ∞, q(w)→∞

Notice that in both cases we only care for the end behavior, and these changes in curvature do not really matter for this kind of analysis.

Answer:

It is a decreasing function for 0 < b < 1.

Step-by-step explanation:

Logarithm function:

The logarithm function is given by:

[tex]F(x) = \log_{b}{(x)}[/tex]

The base b determines if the function increases or decreases.

For 0 < b < 1, the function decreases.

For b > 1, the function increases.

In this question:

By the definition above, it is a decreasing function for 0 < b < 1.

Answer:

1 is the out liar

Step-by-step explanation:

This is because there is a huge gap between 1 and 64. The rest of the numbers are in a cluster.

Answer:

120 cm²

Step-by-step explanation:

Volume = length x wight x height

Volume = 6 x 4 x 5

Volume = 120 cm²

Answer:

3 option

Step-by-step explanation:

Answer:

2s

Step-by-step explanation:

Twice means multiplicaiton of 2

So the answer is 2s

Answer:

if you round it to a whole number... it should be 570

Step-by-step explanation:

just round the tenth place

Answer:

38

Step-by-step explanation:

119.32/3.14 since 3.14 is pi and c=pi*d

Answer:

d≈37.98

Step-by-step explanation:

C=2πr

d=2r

Solving for d

d=C

π=119.32

π≈37.98074

Answer:

(9-8) + 8 = 9

Step-by-step explanation:

Answer: Third option

Step-by-step explanation: doing a point giveaway stay tuned!

Answer:

-2, 3

Step-by-step explanation:

We are given the following inequality:

[tex]x + 2 > 7[/tex]

Solving it, we have that its solution is:

[tex]x > 7 - 2[/tex]

[tex]x > 5[/tex]

So values of x of 5 and lower are counterexamples to this, which means that -2 and 3 are correct options to this question.

Answer:

B is the correct answer

Step-by-step explanation:

-4x+ 2 y= 16