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3 years ago

Select the correct answer. If 25% of a number is 100, what is the number?

Mathematics

1 answer:

vivado [14]3 years ago

5 0

Answer:400

Step-by-step explanation:

25% multiplied by 4 would be 100%. So 100 times 4 is 400. Which means which means 100 is 25% of 400.

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What is the solution to this equation?

Usimov [2.4K]

-0.5 n^2=-18
n^2= 36
n= sqrt (36)=6 or -6

Hope this can help.

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3 years ago

Read 2 more answers

3/4 a - q = k, solve for a

erastova [34]

Answer: a = 4k + 4q ÷ 3

Step-by-step explanation:

6 0

3 years ago

A beam of light from a monochromatic laser shines into a piece of glass. The glass has thickness L and index of refraction n=1.5

boyakko [2]

Additional information to complete the question:

How long does it take for a short pulse of light to travel from one end of the glass to the other?

Express your answer in terms of some or all of the variables f and L. Use the numeric value given for n in the introduction.

T = ___________ s

Answer:

$T = \frac{15}{f}$

Step-by-step explanation:

Given:

Thickness og glass = L

Index of refraction n=1.5

Frequency = f

$Wavelength = \frac{L}{10}$

λ(air) $= \frac{L}{10}$

λ(glass) = λ(air) / n

= $\frac{\frac{L}{10}}{1.5}$

= $\frac{L}{10} * \frac{1}{1.5}$

= $\frac{L}{15}$

V(glass) = fλ(glass)

$= f * \frac{L}{15}$

$T = \frac{L}{V_{glass}} = \frac{15}{f}$

7 0

3 years ago

Value of sin^6 + cos^6+3sin^2cos^2

Sav [38]

Step-by-step explanation:

If you put into a calculator "Sin(6)+Cos(6)+3Sin(2)Cos(2)", you get 1.20368506925. Hope that helps

4 0

3 years ago

A rectangular parking lot has an area of 15,000 feet squared, the length is 20 feet more than the width. Find the dimensions

faust18 [17]

Dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet

<h3>Solution:</h3>

Given that

Area of rectangular parking lot = 15000 square feet

Length is 20 feet more than the width.

Need to find the dimensions of rectangular parking lot.

Let assume width of the rectangular parking lot in feet be represented by variable "x"

As Length is 20 feet more than the width,

so length of rectangular parking plot = 20 + width of the rectangular parking plot

=> length of rectangular parking plot = 20 + x = x + 20

The area of rectangle is given as:

$\text {Area of rectangle }=length \times width$

Area of rectangular parking lot = length of rectangular parking plot $\times$ width of the rectangular parking

$\begin{array}{l}{=(x+20) \times (x)} \\\\ {\Rightarrow \text { Area of rectangular parking lot }=x^{2}+20 x}\end{array}$

But it is given that Area of rectangular parking lot = 15000 square feet

$\begin{array}{l}{=>x^{2}+20 x=15000} \\\\ {=>x^{2}+20 x-15000=0}\end{array}$

Solving the above quadratic equation using quadratic formula

General form of quadratic equation is

${ax^{2}+\mathrm{b} x+\mathrm{c}=0$

And quadratic formula for getting roots of quadratic equation is

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

In our case b = 20, a = 1 and c = -15000

Calculating roots of the equation we get

$\begin{array}{l}{x=\frac{-(20) \pm \sqrt{(20)^{2}-4(1)(-15000)}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{400+60000}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{60400}}{2}} \\\\ {x=\frac{-(20) \pm 245.764}{2 \times 1}}\end{array}$

$\begin{array}{l}{=>x=\frac{-(20)+245.764}{2 \times 1} \text { or } x=\frac{-(20)-245.764}{2 \times 1}} \\\\ {=>x=\frac{225.764}{2} \text { or } x=\frac{-265.764}{2}} \\\\ {=>x=112.882 \text { or } x=-132.882}\end{array}$

As variable x represents width of the rectangular parking lot, it cannot be negative.

=> Width of the rectangular parking lot "x" = 112.882 feet

=> Length of the rectangular parking lot = x + 20 = 112.882 + 20 = 132.882

Hence can conclude that dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet.

3 0

3 years ago