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Tcecarenko [31]
3 years ago
6

Simplify each expression. Use positive exponents.

Mathematics
2 answers:
mario62 [17]3 years ago
4 0

Answer:

Step-by-step explanation:

(A) The given expression is:

m^3n^{-6}p^0

Simplifying this expression, we get

=m^3n^{-6}(1)

=\frac{m^3}{n^6}

which is the required simplified form.

(B) The given expression is:

\frac{a^4b^{-3}}{ab^{-2} }

Simplifying the above equation using the exponent rule, we have

=\frac{a^3}{b}

which is the required simplified form.

(C) The given expression is:

(x^{-2}y^{-4}x^3)^{-2}

Simplifying this expression, we get

=(\frac{x}{y^4})^{-2}

=(\frac{y^4}{x})^2

=\frac{y^8}{x^2}

which is the required simplified form.

Semmy [17]3 years ago
3 0
To simplify each expression, we need to group all the terms that have the same bases and flock them if necessary to one side. One rule that applies is that negative exponents goes to the other side in order to be positive.

<span>1. m3n-6p0 ; p0 =1 , so, m3/n6
2. </span><span>a^4b^-3/ab^-2  = a^4a-1 / b^-2b^3 = a^3/b
3. </span><span>(x^-2y^-4x^3) -2 = (x^-2x^3 y^-4 )^-2 = (x/y^4)^-2 = y^16/x^2</span>
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I am having trouble with converges and diverges<br>​
inna [77]

Answer:

d. converges, -25

Step-by-step explanation:

An infinite geometric series converges if the absolute value of the common ratio is less than 1.

Here, the common ratio is 4/5:

| 4/5 | = 4/5 < 1

So the series converges.  The sum of an infinite geometric series is:

S = a₁ / (1 − r)

where a₁ is the first term and r is the common ratio.

Here, a₁ = -5 and r = 4/5:

S = -5 / (1 − 4/5)

S = -25

5 0
2 years ago
The Tour de France is a bike race around the country of France. The bike race is a three week race that covers approximately 2,2
valentinak56 [21]

Answer:

Approximately 54.54% of race happened in the first week.

Step-by-step explanation:

We are given the following in the question:

Length of bike race in three weeks = 2,200 miles

Race covered in first week = 1,200 miles

Percentage of race covered in first week =

=\dfrac{\text{Race covered in first week}}{\text{Total length of race}}\times 100\%\\\\=\dfrac{1200}{2200}\times 100\%\\\\=54.54\%

Thus, approximately 54.54% of race happened in the first week.

4 0
3 years ago
A radio manufacturer believes that the length of life of WPPX model radio is normal with µ=12 years and σ=2.5 years. (a) What pe
kicyunya [14]

Answer:

(a) 5.48%

(b) 17.82 years

(c) 21.19%

(d) 15.21 years

Step-by-step explanation:

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

µ=12 years and σ=2.5 years.

(a) What percent of the radios will function for more than 16 years?

For x = 16

z = 16 - 12/2.5

z = 1.6

Probability value from Z-Table:

P(x<16) = 0.9452

P(x>16) = 1 - P(x<16)

1 - 0.9452

= 0.054799

Converting to percentage = 0.054799 × 100

= 5.4799%

Approximately = 5.48%

(b) Suppose the company decides to replace 1% of the radios. Find the length of the guarantee period. i.e. find X.

find the z score of the 99th percentile = 2.326

Hence:z = (x-μ)/σ

2.326 = x - 12/2.5

Cross Multiply

2.326 × 2.5 = x - 12

5.815 = x - 12

x = 12 + 5.815

x = 17.815

Approximately = 17.82 years

(c) What percent of the radios that will fail to satisfy the guarantee period of 10 years? , i.e. less than 10 years?

When x < 10

Hence,

z = 10 - 12/2.5

z = -0.8

Probability value from Z-Table:

P(x<10) = 0.21186

Converting to percentage

0.21186 × 100

= 21.186%

Approximately = 21.19%

(d) If 10% of the radios will function for more than X years, find X.

The z score would be : 100 - 10%

= 90th percentile z score

We find the z score of the 90th percentile = 1.282

Hence:z = (x-μ)/σ

1.282 = x - 12/2.5

Cross Multiply

1.282 × 2.5 = x - 12

3.205 = x - 12

x = 12 + 3.205

x = 15.205

Approximately = 15.21 years

4 0
3 years ago
Choose the correct answer.
Morgarella [4.7K]

Answer: Oh the answer is 30.00

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Order these numbers from least to greatest. 103 , 3.48 , 12 , −13
Arada [10]
-13, 3.48, 12, 103 .................
8 0
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