MATHEMATICS COLLEGE

Which expression is the greatest common factor of the two addends in 18x + 30x2?

Answers

Answer 1
Answer:

Answer:

The answer is 6x

Step-by-step explanation:
Answer 2
Answer:

Step-by-step explanation:

I think common factors are

18 = 1 2 3 6 9 18

30 = 1 2 3 10 15 30

So highest common factor is 3

18x + 30x2

3x (6 + 10x)

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A trapezoid has an area of 60 square inches. The height of the trapezoid is 5 inches. What is the length of the longer base if the longer base is three times the length of the shorter base?

Answers

Answer:

Step-by-step explanation:

Remark

Let the shorter base = x

Let the longer base = 3x

h = 5

Area = 60

Formula

Area = (b1 + b2)*h /2

Solution

60 = (x + 3x)*5 / 2                Multiply both sides by 2

2*60 = (x + 3x)*5                  Combine like terms

120 = 4x *5

120 = 20x                             Divide by 20

120/20 = x

x = 6

Therefore the two bases are

x = 6

3x = 18

Answer:

C

Step-by-step explanation:

The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) μ and standard deviation σ=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but you believe that the mean nicotine content is actually higher than advertised. To explore this, you test the hypotheses H0:μ=1.5, Ha:μ>1.5 and you obtain a P-value of 0.052. Which of the following is true? A. At the α=0.05 significance level, you have proven that H0 is true. B. This should be viewed as a pilot study and the data suggests that further investigation of the hypotheses will not be fruitful at the α=0.05 significance level. C. There is some evidence against H0, and a study using a larger sample size may be worthwhile. D. You have failed to obtain any evidence for Ha.

Answers

Answer:

Step-by-step explanation:

This is a test of a single population mean since we are dealing with mean.

From the information given,

Null hypothesis is expressed as

H0:μ=1.5

The alternative hypothesis is expressed as

Ha:μ>1.5

This is a right tailed test

The decision rule is to reject the null hypothesis if the significance level is greater than the p value and accept the null hypothesis if the significance level is less than the p value.

p value = 0.052

Significance level, α = 0.05

Since α = 0.05 < p = 0.052, the true statement would be

At the α=0.05 significance level, you have proven that H0 is true. B.

The volume of this pyramid is 351 m3. If the area of thebase is 81 m² how high is the pyramid?

Answers

9514 1404 393

Answer:

  13 m

Step-by-step explanation:

The volume formula is ...

  V = (1/3)Bh

where B is the base area and h is the height.

Filling in the given values, we can solve for h.

  351 m³ = (1/3)(81 m²)h

  351/27 m = h = 13 m . . . . . divide by the coefficient of h

The height of the pyramid is 13 meters.

At a college, 69% of the courses have final exams and 42% of courses require research papers. Suppose that 29% of courses have a research paper and a final exam. Let F be the even that a course has a final exam. Let R be the event that a course requires a research paper. (a) Find the probability that a course has a final exam or a research paper. Your answer is : (b) Find the probability that a course has NEITHER of these two requirements. Your answer is :

Answers

Answer:

a) 0.82

b) 0.18

Step-by-step explanation:

We are given that

P(F)=0.69

P(R)=0.42

P(F and R)=0.29.

a)

P(course has a final exam or a research paper)=P(F or R)=?

P(F or R)=P(F)+P(R)- P(F and R)

P(F or R)=0.69+0.42-0.29

P(F or R)=1.11-0.29

P(F or R)=0.82.

Thus, the the probability that a course has a final exam or a research paper is 0.82.

b)

P( NEITHER of two requirements)=P(F' and R')=?

According to De Morgan's law

P(A' and B')=[P(A or B)]'

P(A' and B')=1-P(A or B)

P(A' and B')=1-0.82

P(A' and B')=0.18

Thus, the probability that a course has NEITHER of these two requirements is 0.18.

Slope = 3/2, (2,7) is on the line

Answers

Answer:

The answer would be 4.5

A cell phone carrier offers two plans for text messaging. Plan A costs $20 per month plus s0.05 per text. Plan B costs $10 per month plus $0.10 per text. For how many text messages per month are the plans the same cost? O20
O30
O 200
O 300​

Answers

Answer:

200

Step-by-step explanation:

Answer:

ITS C 200

Step-by-step explanation:
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