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3 years ago

Find the greatest common factor of 7 and 21.

Mathematics

1 answer:

sertanlavr [38]3 years ago

6 0

Answer: 7

Step-by-step explanation:

Factors of 7 are, 1, and 7. The factors of 21 are, 1, 3, 7, and 21, making 7 the gcf.

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September 6 is a Read Book Day.Polina read 5 times as many pages as Marcus read.Together,the read 108 pages.How many pages did e

Gemiola [76]

Answer:

The number of pages that Polina read was 90 and the number of pages that Marcus read was 18

Step-by-step explanation:

Let

x -----> number of pages that Polina read

y ----> number of pages that Marcus read

we know that

x+y=108 ----> equation A

x=5y -----> equation B

substitute equation B in equation A and solve for y

$5y+y=108\\6y=108\\y=18$

Find the value of x

$x=5y -----> x=5(18)=90$

therefore

The number of pages that Polina read was 90 and the number of pages that Marcus read was 18

3 0

3 years ago

Matthew is making a sequence in which -3 is added to each successive term. The 6th term in his sequence is -1. What is the 1st t

Hatshy [7]

Answer:

The first term is 14.

Step-by-step explanation:

The general formula for this kind of sequence (arithmetic) is a(n) = a(1) + (n-1)c, where c is the common difference. Here, we have a(6) = -1 = a(1) + (6-1)(-3), or -1 +15 = a(1). The first term is 14.

3 0

3 years ago

HELP ASAP

Vera_Pavlovna [14]

Answer:

arc AC = 111°

Step-by-step explanation:

∠APC is a central angle, so arc AC is equal to the measure of ∠APC.

∠APC and ∠BPC are supplementary. So, m∠APC + m∠BPC = 180

m∠APC + 69 = 180

m∠APC = 111

arc AC = 111°

8 0

2 years ago

We learned in that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty

maw [93]

Answer:

(1) The expected number of people who would have consumed alcoholic beverages is 34.9.

(2) The standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3) It is surprising that there were 45 or more people who have consumed alcoholic beverages.

Step-by-step explanation:

Let X = number of adults between 18 to 20 years consumed alcoholic beverages in 2008.

The probability of the random variable X is, p = 0.697.

A random sample of n = 50 adults in the age group 18 - 20 years is selected.

An adult, in the age group 18 - 20 years, consuming alcohol is independent of the others.

The random variable X follows a Binomial distribution with parameters n = 50 and p = 0.697.

The probability mass function of a Binomial random variable X is:

$P(X=x)={50\choose x}0.697^{x}(1-0.697)^{50-x};\ x=0,1,2,3...$

(1)

Compute the expected value of X as follows:

$E(X)=np\\=50\times 0.697\\=34.85\\\approx34.9$

Thus, the expected number of people who would have consumed alcoholic beverages is 34.9.

(2)

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{np(1-p)}=\sqrt{50\times 0.697\times (1-0.697)}=10.55955\approx10.56$

Thus, the standard deviation of people who would have consumed alcoholic beverages is 10.56.

(3)

Compute the probability of X ≥ 45 as follows:

P (X ≥ 45) = P (X = 45) + P (X = 46) + ... + P (X = 50)

$=\sum\limits^{50}_{x=45} {50\choose x}0.697^{x}(1-0.697)^{50-x}\\=0.0005+0.0001+0.00002+0.000003+0+0\\=0.000623\\\approx0.0006$

The probability that 45 or more have consumed alcoholic beverages is 0.0006.

An unusual or surprising event is an event that has a very low probability of success, i.e. p < 0.05.

The probability of 45 or more have consumed alcoholic beverages is 0.0006. This probability value is very small.

Thus, it is surprising that there were 45 or more people who have consumed alcoholic beverages.

6 0

3 years ago

PLEASE HELP ME!!!! WILL MARK BRAINLIEST

FromTheMoon [43]

Answer:

Step-by-step explanation:

Pythagoras's theorem dictates that a squared + b squared = c squared when talking about sides on right angled triangles with a and b being flat sides and c being the hypotenuse which gives us the forumula below

3 squared + 4 squared = 25 route 25 = 5

8 0

3 years ago

Read 2 more answers