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3 years ago

When a whole number is multiplied by a decimal smaller than one, what can you conclude about the result?

Mathematics

2 answers:

galben [10]3 years ago

5 0

Answer:

the answer is d

Step-by-step explanation:

When you multiply a whole number by a decimal less than one, you are taking a fraction of the whole number. The resulting number is smaller than the original.

Sophie [7]3 years ago

3 0

Answer:

The answer is D

Step-by-step explanation:

The resulting number is smaller than the original. This is true because if you take 20 times 0.5 it will equal ten. A decimal is pretty much a fraction in another form.

The reason why A is false is because if the number isn't being multiplied by 1 then it can't stay the same.

The reason why B is false is because that is not true as in the example above, 20 times 0.5, it equaled 10 and not less than one.

The reason why C is false is because the the resulting number simply cannot be higher than the original when being multiplied by a decimal smaller than 1.

Hope this helps

- Que

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21 and 22 are complementary angles. The measure of Z1 is 60°. The

Lemur [1.5K]

Answer:

The value of x is 7

Step-by-step explanation:

Complementary angles have a sum of 90°, therefore the equation to solve for x is:

∠1+∠2=90°

60°+5(x-1)°=90°

5(x-1)=30°

x-1=6

x=7

So the value of x is 7

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2 years ago

If avogadro's number of pennies is divided equally among the 231 million men, women, and children in the united states, how many

Anon25 [30]

<span>2.607 x 10^13 dollars per person. Avogadro's number is approximately 6.0221409x10^23. So divide by the 231 million people. Giving (6.0221409 x 10^23) / (231 x 10^6) = 0.02607 x 10^17 = 2.607 x 10^15 pennies But we want dollars, so divide by 100 2.607 x 10^15 / 100 = 2.607 x 10^13 dollars</span>

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3 years ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

3 years ago

The area of a triangle is the product of the base of the triangle times the height of the triangle, divided by two.

Natali [406]

Answer:

A = (1/2)(base)(height)

Step-by-step explanation:

Yes, that's correct:

A = (1/2)(base)(height)

Was there more to this question?

3 0

3 years ago

What is minutes spent on homework

Eduardwww [97]

It appears that you have here a list of the # of minutes spent each day on HW, and that y ou need to sum up this list to answer the question. Unfortunately I cannot read the last numeral.

The answer (assuming that my guess is correct) would be found as follows:

Total hours spent on HW in one week = (18+20+22+11+19+18+ ?? )

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3 years ago