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3 years ago

How do I solve

1 answer:

4 0

$Use:\\\\(ab)^n=a^nb^n\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}\\\\\sqrt[n]{a}=a^\frac{1}{n}\\------------------------\\\\\left(16n^4\right)^{\frac{5}{4}}=16^\frac{5}{4}\left(n^4\right)^\frac{5}{4}=16^{1\frac{1}{4}}n^{4\cdot\frac{5}{4}}=16^{1+\frac{1}{4}}n^5=16^1\cdot16^\frac{1}{4}\cdot n^5\\\\=16\cdot\sqrt[4]{16}\cdot n^5=16\cdot2\cdot n^5=\boxed{32n^5}\\\\\sqrt[4]{16}=2\ because\ 2^4=16\\\\\text{Answer}\ \boxed{\left(16n^4\right)^\frac{5}{4}=32n^5}$

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Rosita is designing a quilt for her bed. She will use 5/8 of the quilt pieces for the background. What percentage of the quilt w

rodikova [14]

5/8 = 0.625
To turn a decimal into a fraction, move the decimal point two spaces to the right.

0.625 = 62.5%

62.5% of the pieces are used for the background

7 0

3 years ago

jada can write 3 1/4 pages in 8 minutes. At this rate, how many pages could jada write in 24 minutes?

makkiz [27]

Answer:

9 3/4 pages = x

Step-by-step explanation:

$\frac{pages}{minutes} = \frac{pages}{minutes}$ change 3 1/4 to a decimal

$\frac{3.25}{8} = \frac{x}{24}$

$3.25(24) = 8x$

$78 = 8x$

$\frac{78}{8} = x$

$9.75 = x$

$9\frac{3}{4} =x$

working with the fraction

3 1/4 /8 = x/ 24

3 1/4 (24) = 8x

13/4 (24) = 8x

316/4 = 8x

78 = 8x

78/8 = x

9 3/4 = x

7 0

2 years ago

Assume that women's heights are normally distributed with a mean given by mu equals 62.5 in,and a standard deviation given by

Misha Larkins [42]

Answer:

(a) 0.5899

(b) 0.9166

Step-by-step explanation:

Let X be the random variable that represents the height of a woman. Then, X is normally distributed with

$\mu$ = 62.5 in

$\sigma$ = 2.2 in

the normal probability density function is given by

$f(x) = \frac{1}{\sqrt{2\pi}2.2}\exp{-\frac{(x-62.5)^{2}}{2(2.2)^{2}}}$ , then

(a) $P(X < 63) = \int\limits_{-\infty}^{63}f(x) dx$ = 0.5899

(in the R statistical programming language) pnorm(63, mean = 62.5, sd = 2.2)

(b) We are seeking $P(\bar{X} < 63)$ where n = 37. $\bar{X}$ is normally distributed with mean 62.5 in and standard deviation $2.2/\sqrt{37}$ . So, the probability density function is given by

$g(x) = \frac{1}{\sqrt{2\pi}\frac{2.2}{\sqrt{37}}}\exp{-\frac{(x-62.5)^{2}}{2(2.2/\sqrt{37})^{2}}}$ , and

$P(\bar{X} < 63) = \int\limits_{-\infty}^{63}g(x)dx$ = 0.9166

(in the R statistical programming language) pnorm(63, mean = 62.5, sd = 2.2/sqrt(37))

You can use a table from a book to find the probabilities or a programming language like the R statistical programming language.

4 0

3 years ago

Find the volume of triangular prism with the following dimensions. Round to the nearest whole number.

defon

Answer:

<em>124.0 ft^2</em>

Step-by-step explanation:

let b = base of triangle = 7ft

h = height of triangle = 4ft

and

l = height of prism. = 8.5ft

We know,

volume of prism = area of triangular face of prizm × height of prizm

= 1/2 × b × h × l

= 1/2 × 7 × 4 × 8.5

= 7 × 2 × 8.5

= 14 × 8.5

6 0

3 years ago

During first semester the ratio of the number of students in art class to the number of students in gym class was 2:7. However t

elena-s [515]

5/4 = 75/g....cross multiply because this is a proportion
5g = 300
g = 300/5
g = 60
so in 2nd semester, there were 75 students in art class and 60 students in gym class....for a total of 135 students.

1st semester....ratio was 2:7...added = 9
art : 2/9(135) = 270/9 = 30 <=== art class had 30
gym: 7/9(135) = 945/9 = 105 <=== gym class had 105

4 0

3 years ago