MATHEMATICS COLLEGE

Write this fraction in the simplest form 15/25

Answers

Answer 1
Answer:

15/25  Divididing numerator and denominator by 5 we get:

3 / 5
Answer 2
Answer: If 15/25 is 0.6 you can then convert it to a 3/5

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A coin is flipped until 3 heads in succession occur. list only those elements of the sample space that require 6 or less tosses. is this a discrete sample space? explain

A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let Xrepresent the number of occupants in a randomly chosen car.a. Find the probability mass function of X.

b. Find P(X ≤ 2).

c. Find P(X > 3).

d. Find μX.

e. Find σX

Answers

Answer:

a) X    1       2      3       4       5

P(X) 0.7  0.15  0.10  0.03  0.02

b) P(X \leq 2) = P(X=1) +P(X=2) = 0.7+0.15=0.85

c) P(X >3) = 1-P(X \leq 3) = 1-[P(X=1) +P(X=2)+P(X=3)]=1-[0.7+0.15+0.1]= 0.05

d) E(X) = \sum_(i=1)^n X_i P(X_i) = 1*0.7 +2*0.15+ 3*0.1+4*0.03+ 5*0.02= 1.52

e) E(X^2) = \sum_(i=1)^n X^2_i P(X_i) = 1*0.7 +4*0.15+ 9*0.1+16*0.03+ 25*0.02=3.18

Var(X) = E(X^2) -[E(X)]^2= 3.18- (1.52)^2 = 0.8996

\sigma= √(Var(X))= √(0.8996)= 0.933

Step-by-step explanation:

Part a

From the information given we define the probability distribution like this:

X       1       2      3       4       5

P(X) 0.7  0.15  0.10  0.03  0.02

And we see that the sum of the probabilities is 1 so then we have a probability distribution

Part b

We want to find this probability:

P(X \leq 2) = P(X=1) +P(X=2) = 0.7+0.15=0.85

Part c

We want to find this probability P(X>3)

And for this case we can use the complement rule and we got:

P(X >3) = 1-P(X \leq 3) = 1-[P(X=1) +P(X=2)+P(X=3)]=1-[0.7+0.15+0.1]= 0.05

Part d

We can find the expected value with this formula:

E(X) = \sum_(i=1)^n X_i P(X_i) = 1*0.7 +2*0.15+ 3*0.1+4*0.03+ 5*0.02= 1.52

Part e

For this case we need to find first the second moment given by:

E(X^2) = \sum_(i=1)^n X^2_i P(X_i) = 1*0.7 +4*0.15+ 9*0.1+16*0.03+ 25*0.02=3.18

And we can find the variance with the following formula:

Var(X) = E(X^2) -[E(X)]^2= 3.18- (1.52)^2 = 0.8996

And we can find the deviation taking the square root of the variance:

\sigma= √(Var(X))= √(0.8996)= 0.933

A can of paint covers 400 square feet how many cans will needed to cover 3,000 square feet

Answers

Answer:

7 and a half cans of Paint ( 7.5 cans of paint )

Step-by-step explanation:

If one can of paint covers 400 square feet then this should be easy. Since you need 3,000 square feet covered with paint (and one paint can cover 400 sq) then just divide 3,000 by 400.

This will show you how many times 400 can go into 3,000 which is the same as saying "how many cans of paint can i used to cover 3,000 square feet?"

Hope this helped!

-Greg

Assume that the amount of time that it takes an employee to service a car at an oil change facility follows the uniform probability distribution between 21 and 38 minutes. What is the probability that a randomly selected car will require less than 25 minutes to service?

Answers

Answer:

The probability is  P(X < 25) = 0.308

Step-by-step explanation:

From the question we are told that

   The amount of time is uniform probability distribution between 21 and 38 minutes.

  Given that the amount of time is uniformly distributed then  the probability that a randomly selected car will require less than 25 minutes to service is mathematically evaluated as

           P(X < 25) = ( 25 - 21)/(38 - 21)

=>       P(X < 25) = 0.308

     

Find the sum of the first six terms of a geometric progression .​

Answers

Question:

Find the sum of the first six terms of a geometric progression.

1,3,9,....

Answer:

S_6 = 364

Step-by-step explanation:

For a geometric progression, the sum of n terms is:

S_n = (a(r^n - 1))/(r - 1)

In the given sequence:

a = 1

r = 3/1 =3

n = 6

So:

S_n = (a(r^n - 1))/(r - 1)

S_6 = (1 * (3^6 - 1))/(3 - 1)

S_6 = (3^6 - 1)/(2)

S_6 = (728)/(2)

S_6 = 364

Choose the correct simplification of 9x^2(4x + 2x^2 − 1)

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

18x⁴ + 36x³ - 9x²

▹ Step-by-Step Explanation

9x²(4x + 2x² - 1)

36x³ + 18x⁴ - 9x²

18x⁴ + 36x³ - 9x²

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

The mean SAT score in mathematics, M, is 600. The standard deviation of these scores is 48. A special preparation course claims that its graduates will score higher, on average, than the mean score 600. A random sample of 70 students completed the course, and their mean SAT score in mathematics was 613. a) At the 0.05 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 48.

Answers

Answer:

Step-by-step explanation:

The mean SAT score is \mu=600, we are going to call it \mu since it's the "true" mean

The standard deviation (we are going to call it \sigma) is

\sigma=48

Next they draw a random sample of n=70 students, and they got a mean score (denoted by \bar x) of \bar x=613

The test then boils down to the question if the score of 613 obtained by the students in the sample is statistically bigger that the "true" mean of 600.

- So the Null Hypothesis H_0:\bar x \geq \mu

- The alternative would be then the opposite H_0:\bar x < \mu

The test statistic for this type of test takes the form

t=\frac{| \mu -\bar x |} {\sigma/√(n)}

and this test statistic follows a normal distribution. This last part is quite important because it will tell us where to look for the critical value. The problem ask for a 0.05 significance level. Looking at the normal distribution table, the critical value that leaves .05% in the upper tail is 1.645.

With this we can then replace the values in the test statistic and compare it to the critical value of 1.645.

t=\frac{| \mu -\bar x |} {\sigma/√(n)}\n\n= (| 600-613 |)/(48/\sqrt(70)}\n\n= (| 13 |)/(48/8.367)\n\n= (| 13 |)/(5.737)\n\n=2.266\n

since 2.266>1.645 we  can reject the null hypothesis.

Answer:

The null hypothesis is that the SAT score is not significantly different for the course graduates.

Alternate hypothesis: there is a significant difference between the SAT score achieved by the course graduates as compared to the non-graduates.

Apply the t-test. The Test Statistic value comes out to be t = 1.738 and the p-value = 0.0844

Since the p-value is larger than 0.05, the evidence is weak and we fail to reject eh null hypothesis.

Hope that answers the question, have a great day!
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