A number cube with six sides is rolled seven

Which expression is equivalent to 4 x 4 x 4 x 5 x 5 ?

ivann1987 [24]

Answer:

4³×5² or 4³5²

Step-by-step explanation:

This is because there are three consecutive 4s, so you have to put the 4 into exponential form 3 times. So the exponential form for the 4s will be 4³. There are also 2 consecutive 5s so you have to include 2 in the exponential form. So, the exponential form of the 5s is 5². Now you have to somehow multiply them together. You could do this by putting a multiplication sign, (4³×5²) or you could bunch them together and it will mean the same thing (4³5²).

Hope this helps :)

3 0

3 years ago

11.MARTIAN FINDS A SHIRT ON SLAE FOR 10% OFF AT A DEPARTMENT STORE. THE ORIGINAL PRICE WAS $20.Martain must also pay 8.5% sales

Snowcat [4.5K]

A. Find 10% of $20, which is $2. Then subtract the sale 20-2, which is $18
B. Since you know the price without taxes is $18, you have to multiply 8.5% of 18, which is $1.53. $18.00 + $1.53= $19.53

So the answer is $19.53

Hope this helped

5 0

3 years ago

Find the amount in the bank after 7 years if interest is compounded quarterly?

qwelly [4]

Answer:

a) amount in the bank after 7 years if interest is compounded quarterly is $6,605

b) amount in the bank after 7 years if interest is compounded quarterly is $6,612.57

Step-by-step explanation:

We are given:

Principal Amount P= 5000

Rate r= 4% = 0.04

time t = 7 years

The formula used is: $A=P(1+\frac{r}{n})^{nt}$

where A is future value, P is principal amount, r is rate, n is compounded value and t is time

a) Find the amount in the bank after 7 years if interest is compounded quarterly?

If interest is compounded quarterly then n = 4

Using values given in question and finding A

$A=P(1+\frac{r}{n})^{nt}\\A=5000(1+\frac{0.04}{4})^{4*7} \\A=5000(1+0.01)^{28}\\A=5000(1.01)^{28}\\A=5000(1.321)\\A=6,605$

So, amount in the bank after 7 years if interest is compounded quarterly is $6,605

b) Find the amount in the bank after 7 years if interest is compounded monthly?

If interest is compounded quarterly then n = 12

Using values given in question and finding A

$A=P(1+\frac{r}{n})^{nt}\\A=5000(1+\frac{0.04}{12})^{12*7} \\A=5000(1+0.003)^{84}\\A=5000(1.003)^{84}\\A=5000(1.322)\\A=6,612.57$

So, amount in the bank after 7 years if interest is compounded quarterly is $6,612.57

6 0

3 years ago

Fran naders insurance coverage bodily Injury 25/100 and $100,000 property damage. It has a $50-deductible comprehensive and a $5

vladimir2022 [97]

Answer:

$250,000

Step-by-step explanation:

This is the correct question below;

Fran naders insurance coverage bodily Injury 25/100 and $100,000 property damage. It has a $50-deductible comprehensive and a $50-deductible collision. Her car is in age group C and Insurance-rating group 10(or C,10) and her driver-rating Factor is 1.50.

Find her annual premium.

To calculate this, we proceed as follows;

Mathematically,

Annual premium = Face amount * $1000

25/100 * 100,000 * 100

This is 25,000 * 100 = $250,000

7 0

3 years ago

Read 2 more answers

Juan and Lizzy are in the final week of their training for a marathon. Juan's goal is to run one mile on the first day of the we

miss Akunina [59]

Answer:

1. Juan's marathon training schedule is an example of a geometric sequence

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

3. Lizzy will be better prepared for the marathon

Step-by-step explanation:

In the arithmetic sequence there is a common difference between each two consecutive terms

In the geometric sequence there is a common ratio between each two consecutive terms

Juan's Schedule

∵ Juan's will run one mile on the first day of the week

∴ $a_{1}$ = 1

∵ He will double the amount he runs each day for the next

6 days

- That means he multiplies each day by 2 to find how many miles

he will run next day

∴ $a_{2}$ = 1 × 2 = 2 miles

∴ $a_{3}$ = 2 × 2 = 4 miles

∴ $a_{4}$ = 4 × 2 = 8 miles

∴ $a_{5}$ = 8 × 2 = 16 miles

∴ $a_{6}$ = 16 × 2 = 32 miles

∴ $a_{7}$ = 32 × 2 = 64 miles

That means there is a common ratio 2 between each two consecutive days

1. Juan's marathon training schedule is an example of a geometric sequence

Lizzy's Schedule

∵ Lizzy's will run 10 miles on the first day of the week

∴ $a_{1}$ = 10

∵ She will increase the amount she runs by 3 miles each day for

the next six days

- That means she adds each day by 3 to find how many miles

she will run next day

∴ $a_{2}$ = 10 + 3 = 13 miles

∴ $a_{3}$ = 13 + 3 = 16 miles

∴ $a_{4}$ = 16 + 3 = 19 miles

∴ $a_{5}$ = 19 + 3 = 22 miles

∴ $a_{6}$ = 22 + 3 = 25 miles

∴ $a_{7}$ = 25 × 3 = 28 miles

That means there is a common difference 3 between each two consecutive days

2. Lizzy's marathon training schedule is an example of an arithmetic sequence

The rule of the sum of nth term in the geometric sequence is $S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

∵ $a_{1}$ = 1 , r = 2 and n = 7

∴ $S_{7}=\frac{1(1-2^{7})}{1-2}$

∴ $S_{7}$ = 127

∴ Juan will run 127 miles in the final week

The rule of the sum of nth term in the arithmetic sequence is $S_{n}=\frac{n}{2}[a_{1}+a_{n}]$

∵ n = 7, $a_{1}$ = 10 and $a_{7}$ = 28

∴ $S_{7}=\frac{7}{2}(10+28)$

∴ $S_{7}$ = 133

∴ Lizzy will run 133 miles in the final week

∵ 133 miles > 127 miles

∴ Lizzy will run more miles than Juan

3. Lizzy will be better prepared for the marathon

7 0

3 years ago