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1 year ago

Which of the following shows the prime factorization of 36 using exponential notation?

Mathematics

1 answer:

Daniel [21]1 year ago

4 0

Answer:

The prime factorization of 36 using exponential notation is $2^2 \times 3^2$

Step-by-step explanation:

Given: number 36

We have to show the prime factorization of 36 using exponential notation.

Prime factorization is representing a number in form of products of its primes.

Consider the given number 36

36 can be written as 2 × 2 × 3 × 3

In exponential notation it can be written as $2^2 \times 3^2$

Thus, the prime factorization of 36 using exponential notation is $2^2 \times 3^2$

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Tyrone and Terri both bought sofas with installment loans. Tyrone bought a sofa with a

Minchanka [31]

Answer:

Tyrone paid the higher markup rate.

Step-by-step explanation:

Tyrone and Terri both bought sofas with installment loans.

Tyrone bought his own with a sticker price of $1350 by paying $74 a month for 24 months. Therefore,

74 × 24 = $1776

The mark up = $1776 - $1350 = $426

Tyrone markup rate = 426/24 = $17.75 per month

Terri bought his own with sticker price of $950 by paying $52 a month for 24 months. Therefore,

52 × 24 = $1248

mark up = $1248 - $950 = $298

Terri markup rate = 298/24 = $12.4166666667 = $12.42 per month

6 0

2 years ago

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of

Gelneren [198K]

Answer:

$P(X < 24 )= 21.186\%$

$x = 19.78 \ months$

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 26 \ months$

The standard deviation is $\sigma = 4 \ months$

Generally 2 year is equal to 24 months

Generally the percentage of total production will the company expect to replace is mathematically represented as

$P(X < 24 )= P(\frac{X - \mu }{ \sigma} < \frac{24 - 26}{4} )$

Generally $\frac{X - \mu}{\sigma } =Z (The \ standardized \ value \ of \ X )$

$P(X < 24 )= P(Z < -0.8 )$

Generally from the z-table

$P(Z < -0.8) = 0.21186$

$P(X < 24 )= 0.21186$

Converting to percentage

$P(X < 24 )= 0.21186 * 100$

=> $P(X < 24 )= 21.186\%$

Generally the duration that should be the guarantee period if Accrotime does not want to make refunds on more than 6% is mathematically evaluated as

$P(X < x) = P(\frac{X - \mu }{\sigma} < \frac{x - 26}{4} )= 0.06$

=> $P(X < x) = P(Z < \frac{x - 26}{4} )= 0.06$

From the normal distribution table the z-score for 0.06 at the lower tail is

$z = -1.555$

$\frac{x - 26}{4} = -1.555$

=> $x = 19.78 \ months$

6 0

2 years ago

Perform the following computations. retail price of steel-belted radial tire = $89.50 discount offered = 10% federal tax = 12% l

RUDIKE [14]

For the answer to the question above
Retail price of steel-belted radial tire = $89.50
Discount offered = 10% = $8.95
Value before federal tax = $89.50 - $8.95 = $80.55
Federal tax = 12%=$80.55(0.12) =$9.67
Local sales tax = 5% =$80.55(0.05)=$4.03

Selling price = $80.55 +$9.67+$4.03 =$94.25
I hope my answer helped you. Feel free to ask more questions. Have a nice day!

4 0

2 years ago

Hannah and Leah are running around a circular track. Hannah takes 5 minutes to complete one lap, and Leah takes 6 minutes to com

Dima020 [189]

The answer is 30 minutes. Because 6 x 5 = 30 while 5 6 = 30 as well. Hope this helped.

4 0

1 year ago

Read 2 more answers

For ΔABC, ∠A = 4x - 10, ∠B = 5x + 10, and ∠C = 7x + 20. If ΔABC undergoes a dilation by a scale factor of 1 3 to create ΔA'B'C'

VLD [36.1K]

We know that the angles of a triangle sum to 180°. For ΔABC, this means we have:
(4x-10)+(5x+10)+(7x+20)=180

Combining like terms,
16x+20=180

Subtracting 20 from both sides:
16x=160

Dividing both sides by 16:
x=10
This means ∠A=4*10-10=40-10=30°; ∠B=5*10+10=50+10=60°; and ∠C=7*10+20=70+20=90.

For ΔA'B'C', we have
(2x+10)+(8x-20)+(10x-10)=180

Combining like terms,
20x-20=180

Adding 20 to both sides:
20x=200

Dividing both sides by 20:
x=10

This gives us ∠A'=2*10+10=20+10=30°; ∠B'=8*10-20=80-20=60°; and ∠C'=10*10-10=100-10=90°.

Since the angle are all congruent, ΔABC~ΔA'B'C' by AAA.

5 0

2 years ago

Read 2 more answers