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2 years ago

The diameter of the Sun is about 1.4 × 10^6 km. The diameter of Mars is about 7000 km.

Mathematics

2 answers:

Vladimir79 [104]2 years ago

6 0

The answer should be C

Liula [17]2 years ago

4 0

Answer:

C.) 2×10²

Step-by-step explanation:

(Sun dia) / (Mars dia) = (1.4 x 10⁶ km) / (0.7 × 10⁴ km) = (1.4/0.7) × 10²

The ratio of diameters is about 2 × 10².

_____

The applicable rule of exponents is ...

(a^b)/(a^c) = a^(b-c)

The diameter of Mars can be expressed several ways.

7000 = 7×1000 = 0.7×10,000 = 0.7×10⁴

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Kristen invests $ 5745 in a bank. The bank 6.5% interest compounded monthly. How long must she leave the money in the bank for i

podryga [215]

Answer:

1. 10.7 years

2. 17.0 years

3. 2nd option

Step-by-step explanation:

Use formula for compounded interest

$A=P\cdot \left(1+\dfrac{r}{n}\right)^{nt},$

where

A is final value, P is initial value, r is interest rate (as decimal), n is number of periods and t is number of years.

In your case,

1. P=$5745, A=2P=$11490, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

$11490=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},\\ \\2=(1.0054)^{12t},\\ \\12t=\log_{1.0054}2,\\ \\t=\dfrac{1}{12}\log_ {1.0054}2\approx 10.7\ years.$

2. P=$5745, A=3P=$17235, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

$17235=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},$

$3=(1.0054)^{12t},$

$12t=\log_{1.0054}3,$

$t=\dfrac{1}{12}\log_{1.0054}3\approx 17.0\ years.$

3. <u>1 choice:</u> P=$5745, n=12 (compounded monthly), r=0.065 (6.5%), t=5 years and A is unknown. Then

$A=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12\cdot 5},\\ \\A=5745\cdot (1.0054)^{60}\approx \$7936.39.$

<u>2 choice:</u> P=$5745, n=4 (compounded monthly), r=0.0675 (6.75%), t=5 years and A is unknown. Then

$A=5745\cdot \left(1+\dfrac{0.0675}{4}\right)^{4\cdot 5},\\ \\A=5745\cdot (1.0169)^{20}\approx \$8032.58.$

The best will be 2nd option, because $8032.58>$7936.39

5 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=9x-3%20%5Cleqslant%2011x%20-%203" id="TexFormula1" title="9x-3 \leqslant 11x - 3" alt="9x-3 \l

AURORKA [14]

Answer:

0 ≤x

Step-by-step explanation:

9x-3 ≤11x-3

Subtract 9x from each side

9x-9x-3 ≤11x-9x-3

-3 ≤2x-3

Add 3 to each side

-3+3 ≤2x

0 ≤2x

Divide by 2

0/2 ≤2x/2

0 ≤x

6 0

3 years ago

Simplify the expression to one number using order of operations:

geniusboy [140]

<h2><u>COMBINED OPERATIONS</u></h2><h3>Exercise</h3>

First, let's solve the subtraction (in parentheses):

$\mathsf{\dfrac{-8\left(2-6\right)}{2}}$

$\mathsf{\dfrac{-8(-4)}{2}}$

Now, let's solve the multiplication. Remember: in multiplication, two negative numbers will give a positive number:

$\mathsf{\dfrac{-8(-4)}{2}}$

$\mathsf{\dfrac{32}{2}}$

Finally, let's solve the division:

$\mathsf{\dfrac{32}{2} = 16}$

<h3><u>Answer</u>: 16</h3>

5 0

3 years ago

Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator

enyata [817]

Answer:

(a) Increase the differences between the sample means this will increase the Numerator.

(b) Increase the sample variances will increase the denominator.

Step-by-step explanation:

F Ratio = Variance between treatments/ Variance within treatments.

Here,

(a) Increase the differences between the sample means:

- Will increase the Numerator and

- Size of the F-ratio would increase

(b) Increase the sample variances:

- Will increase the denominator and

- Size of the F Ratio would decrease.

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2 years ago

6.012<br> as a mixed number in simplest form.

Novosadov [1.4K]

6 3
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3 years ago

Read 2 more answers