# 5.7 Simplify and use square roots  (Page 7/8)

 Page 7 / 8

In the following exercises, simplify

$4\left(10.3-5.8\right)$

$\frac{3}{4}\left(15.44-7.4\right)$

6.03

$30÷\left(0.45+0.15\right)$

$1.6+\frac{3}{8}$

1.975

$52\left(0.5\right)+{\left(0.4\right)}^{2}$

$-\frac{2}{5}·\frac{9}{10}+0.14$

−0.22

Find the Circumference and Area of Circles

In the following exercises, approximate the circumference and area of each circle.

$\text{radius}=\text{6 in.}$

$\text{radius}=\text{3.5 ft.}$

1. 21.98 ft.
2. 38.465 sq.ft.

$\text{radius}=\frac{7}{33}\phantom{\rule{0.2em}{0ex}}\text{m}$

$\text{diameter}=\text{11 cm}$

1. 34.54 cm
2. 379.94 sq.cm

## Solve Equations with Decimals

Determine Whether a Decimal is a Solution of an Equation

In the following exercises, determine whether the each number is a solution of the given equation.

$x-0.4=2.1\phantom{\rule{1em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}x=1.7\phantom{\rule{0.2em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}x=2.5$

$y+3.2=-1.5\phantom{\rule{1em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}y=1.7\phantom{\rule{0.2em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}y=-4.7$

1. no
2. yes

$\frac{u}{2.5}=-12.5\phantom{\rule{1em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}u=-5\phantom{\rule{0.2em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}u=-31.25$

$0.45v=-40.5\phantom{\rule{1em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}v=-18.225\phantom{\rule{0.2em}{0ex}}$ $\phantom{\rule{0.2em}{0ex}}v=-90$

1. no
2. yes

Solve Equations with Decimals

In the following exercises, solve.

$m+3.8=7.5$

$h+5.91=2.4$

h = −3.51

$a+2.26=-1.1$

$p-4.3=-1.65$

p = 2.65

$x-0.24=-8.6$

$j-7.42=-3.7$

j = 3.72

$0.6p=13.2$

$-8.6x=34.4$

x = −4

$-22.32=-2.4z$

$\frac{a}{0.3}=-24$

a = −7.2

$\frac{p}{-7}=-4.2$

$\frac{s}{-2.5}=-10$

s = 25

Translate to an Equation and Solve

In the following exercises, translate and solve.

The difference of $n$ and $15.2$ is $4.4.$

The product of $-5.9$ and $x$ is $-3.54.$

−5.9 x = −3.54; x = 0.6

The quotient of $y$ and $-1.8$ is $-9.$

The sum of $m$ and $-4.03$ is $6.8.$

m + (−4.03) = 6.8; m = 0.83

## Averages and Probability

Find the Mean of a Set of Numbers

In the following exercises, find the mean of the numbers.

$2,4,1,0,1,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}1$

$\text{270}$ , $\text{310.50}$ , $\text{243.75}$ , and $\text{252.15}$

$269.10 Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited $3,0,8,1,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}8$ minutes. Find the mean In the last three months, Raul’s water bills were $\text{31.45},\phantom{\rule{0.2em}{0ex}}\text{48.76},\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}\text{42.60}.$ Find the mean.$40.94

Find the Median of a Set of Numbers

In the following exercises, find the median.

$41$ , $45$ , $32$ , $60$ , $58$

$25$ , $23$ , $24$ , $26$ , $29$ , $19$ , $18$ , $32$

24.5

The ages of the eight men in Jerry’s model train club are $52,63,45,51,55,75,60,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}59.$ Find the median age.

The number of clients at Miranda’s beauty salon each weekday last week were $18,7,12,16,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}20.$ Find the median number of clients.

16 clients

Find the Mode of a Set of Numbers

In the following exercises, identify the mode of the numbers.

$6$ , $4$ , $4,5$ , $6,6$ , $4$ , $4$ , $4$ , $3$ , $5$

The number of siblings of a group of students: $2$ , $0$ , $3$ , $2$ , $4$ , $1$ , $6$ , $5$ , $4$ , $1$ , $2$ , $3$

2

Use the Basic Definition of Probability

In the following exercises, solve. (Round decimals to three places.)

The Sustainability Club sells $200$ tickets to a raffle, and Albert buys one ticket. One ticket will be selected at random to win the grand prize. Find the probability Albert will win the grand prize. Express your answer as a fraction and as a decimal.

Luc has to read $3$ novels and $12$ short stories for his literature class. The professor will choose one reading at random for the final exam. Find the probability that the professor will choose a novel for the final exam. Express your answer as a fraction and as a decimal.

$\frac{1}{5};\phantom{\rule{0.2em}{0ex}}0.2$

## Ratios and Rate

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

$28$ to $40$

$56$ to $32$

$\frac{7}{4}$

$3.5$ to $0.5$

$1.2$ to $1.8$

$\frac{2}{3}$

$1\frac{3}{4}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}1\frac{5}{8}$

$2\frac{1}{3}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}5\frac{1}{4}$

$\frac{4}{9}$

$64$ ounces to $30$ ounces

$28$ inches to $3$ feet

$\frac{7}{9}$

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction. Simplify the answer if possible.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
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Abhi
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
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Tamia
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Uday
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a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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China
Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
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Porter
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Yasmin
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Cesar
I'm interested in nanotube
Uday
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
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Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
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Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?