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3 years ago

An infant is 32.625 inches long write this as a common fraction

Mathematics

2 answers:

elena-14-01-66 [18.8K]3 years ago

8 0

32.625 is the same as 32 and 5/8 .

FinnZ [79.3K]3 years ago

3 0

The common fraction is 32 5/8.

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Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by

WARRIOR [948]

Answer:

The answer is below

Step-by-step explanation:

Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:

$z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1$

Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:

$z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\$

$z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]$

3 0

3 years ago

Can someone help me with the areas?

9966 [12]

Answer:

for 1. it is 99 and for 3. it is 343.75

Step-by-step explanation:

for 1. you have to just multiply the length with width

for 3. you have to add both bases (35+20) and multiply the height (55 x 12.5) to it and then divide it by 2 (687.5 / 2)

hope this helps! please heart <3

8 0

2 years ago

Read 2 more answers

3. The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population p

damaskus [11]

Answer:

A)sample proportion = 0.17, the sampling distribution of p can be calculated/approximated with normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281

B) 0.869

C)0.9668

Step-by-step explanation:

A) p ( proportion of population that spends more than $100 per week) = 0.17

sample size (n)= 800

the sample proportion of p = 0.17

standard error of p = $\sqrt{\frac{p(1-p)}{n} }$ = 0.013281

the sampling distribution of p can be calculated/approximated with

normal distribution of sample proportion = 0.17 and standard error/deviation = 0.013281

B) probability that the sample proportion will be +-0.02 of the population proportion

= p (0.17 - 0.02 ≤ P ≤ 0.17 + 0.02 ) = p( 0.15 ≤ P ≤ 0.19)

z value corresponding to P

Z = $\frac{P - p}{standard deviation}$

at P = 0.15

Z = (0.15 - 0.17) / 0.013281 = = -1.51

at P = 0.19

z = ( 0.19 - 0.17) / 0.013281 = 1.51

therefore the required probability will be

p( -1.5 ≤ z ≤ 1.5 ) = p(z ≤ 1.51 ) - p(z ≤ -1.51 )

= 0.9345 - 0.0655 = 0.869

C) for a sample (n ) = 1600

standard deviation/ error = 0.009391 (applying the equation for calculating standard error as seen in part A above)

therefore the required probability after applying

z = $\frac{P-p}{standard deviation}$ at p = 0.15 and p = 0.19

p ( -2.13 ≤ z ≤ 2.13 ) = p( z ≤ 2.13 ) - p( z ≤ -2.13 )

= 0.9834 - 0.0166 = 0.9668

7 0

3 years ago

Read 2 more answers

Solve for x & y. 30x−42y=−6 and 5x−7y=−1

vladimir1956 [14]

Um.. Both of those equations are the exact same. Divide both sides of the first equation by 6. You get:

$\frac{30x - 42y}{6} = \frac{-6}{6} \\ 5x - 7y = -1$

That is the exact same as the second equation. This system has an infinite number of solutions. 5x - 7y = -1 is a line, so basically every point on that line is a solution to the system.

For example, $x = 0$ and $y = \frac{1}{7}$ would work, but so would $x = 1$ and $y = \frac{6}{7}$

4 0

3 years ago

Once again Bri needs help so ya btw make it a step-by-step please

Masja [62]

Answer:

the fourth clock listed option D?

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers