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4 years ago

Divide 72 rolls into 2 groups so the ratio is 3 to 5.

Mathematics

2 answers:

alina1380 [7]4 years ago

5 0

3+5=8

72/8=9

9x3=27
9x5=45

27:45

madam [21]4 years ago

3 0

$3x\ and \ 5x\\\\
3x+5x=72\\
8x=72\ \ \ |divide\ by\ 8\\x=9\\\\
3x=3*9=27\\
5x=5*9=45\\\\
Ratio\ of\ rolls:\ \ 27:45.$

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Find the length of a line segment with endpoints of -9 and 7.

Luda [366]

<span>If you imagine a straight line, with -9 all the way on the left, then mark along the line in one number increments until you get up to 7, you will find that in total the line is 16 segments in total. Mathematically, this is a question of absolute value, ie absolute value of -9 = +9, and therefore 9 + 7=16.</span>

6 0

3 years ago

Find a counterexample to show that the statement is false. Assume all sets are subsets of a universal set U = {1, 2, 3, 4, 5}. (

natka813 [3]

Answer:

For subsets A={1,2},B={2,3},C={1,2 5} of U = {1, 2, 3, 4, 5}.

A ∪ (B − C) = (A ∪ B) − (A ∪ C) does not hold.

Step-By-Step Explanation:

U = {1, 2, 3, 4, 5}.

A={1,2}

B={2,3}

C={1,2 5}

For the Left Hand Side

B-C={3}

A ∪ (B − C)= {1,2} ∪ {3} ={1,2,3}

Likewise, the Right Hand Side:

(A ∪ B)={1,2,3}

(A ∪ C)={1,2,5}

(A ∪ B)- (A ∪ C)= {1,2,3}-{1,2,5}={3}

Since, {1,2,3} ≠ {3}, A ∪ (B − C) = (A ∪ B) − (A ∪ C) does not hold.

7 0

3 years ago

For f(x) = 4 - x and g(x) = 2x + x + 7, find the following functions.

Alenkinab [10]

Answer: a. -3(x+1), b. 19-3x, c. -9 and d. 13

Step-by-step explanation:

Lets begin with a. (fog)(x)=f(g(x))

=f(2x+x+7), Note that 2x+x+7=3x+7

=f(3x+7) (where there is x if the function f(x) we

substitute x by 3x+7)

=4-(3x+7) =4-3x-7=-3x-3= -3(x+1).

b. (gof)(x)=g(f(x))=g(4-x) (where there is x in the function

g(x) we substitute with 4-x)

= 3(4-x)+7 = 19-3x

c. (fog)(2) = -3(2+1) = -9 (we now substitute x with 2 in -3(x+1). )

d. (gof)(2) = 19-3(2)=19-6=13. (Again we now substitute x with

2 in 19-3x)

3 0

3 years ago

Lennon has a checking account. He withdrew $130 from an ATM Tuesday. Wednesday he deposited $240. Friday he wrote a check for $5

lesantik [10]

Answer:

he has $314 left

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The mean per capita income is 20,90820,908 dollars per annum with a standard deviation of 407407 dollars per annum. What is the

LiRa [457]

Answer:

$z=\frac{20880-20908}{\frac{407}{\sqrt{55}}}= -0.51$

$z=\frac{20936-20908}{\frac{407}{\sqrt{55}}}= 0.51$

Then we can find the probability of interest with this difference:

$P(-0.51$

And using the normal standard distribution or excel we got:

$P(-0.51$

So then the probability that the sample mean would differ from the true mean by less than 28 dollars from the sample of 55 is approximately 0.390

Step-by-step explanation:

We define the variable of interest as the per capita income and we know the following properties for this variable:

$\mu=20908$ and $\sigma=407$

We want to find this probability:

$P(20908-28$

We select a sample size of n=55 and we define the z score formula given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

We can find the z score then for 20880 and 20936 and we got:

$z=\frac{20880-20908}{\frac{407}{\sqrt{55}}}= -0.51$

$z=\frac{20936-20908}{\frac{407}{\sqrt{55}}}= 0.51$

Then we can find the probability of interest with this difference:

$P(-0.51$

And using the normal standard distribution or excel we got:

$P(-0.51$

So then the probability that the sample mean would differ from the true mean by less than 28 dollars from the sample of 55 is approximately 0.390

7 0

3 years ago