A 48-foot rope is cut into three lengths. The second length of rope is twice the first length. The third length of rope is one-fifth the first length. What is the third length?

Answer:

3.9 x [tex]10^{8}[/tex]

Step-by-step explanation:

0.39 is not in scientific notation.  For a number to be in scientific notation the first factor has to be 1 or greater, but less then 10.  0.39 is less than one.

First we must write 0.39 in scientific notation.  We need to move the decimal so that the number is greater than 1, but less than ten.  If we move the decimal one place to the right, we get 3.9.  The standard number is smaller than 3.9.  How much smaller?  [tex]10^{-1}[/tex] smaller.

0.39 in scientific notation would be 3.9 x [tex]10^{-1}[/tex].  We cannot forget the [tex]10^{9}[/tex], so our number looks like this now:

3.9 x [tex]10^{-1}[/tex] x [tex]10^{9}[/tex]  The product of powers principle tells us that if we have powers with the same bases, we can add the exponents.

3.9 x [tex]10^{-1+9}[/tex]

or 3.9 x [tex]10^{8}[/tex]

Answer:

hope this explanation helps you

Answer:

[tex]\textsf{b)} \quad -\dfrac{3\sqrt{13}}{13}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

[tex]\textsf{If}\; \tan(\theta)=-\dfrac{2}{3} \implies \sf O=2 \; \textsf{and} \; A=3.[/tex]

Use Pythagoras Theorem to calculate the length of the hypotenuse:

[tex]\sf \implies O^2+A^2=H^2[/tex]

[tex]\implies \sf H=\sqrt{O^2+A^2}[/tex]

[tex]\implies \textsf{H}=\sqrt{2^2+3^2}[/tex]

[tex]\implies \textsf{H}=\sqrt{13}[/tex]

Therefore, substituting the values of A and H into the cosine ratio:

[tex]\implies \cos \theta=\dfrac{3}{\sqrt{13}}[/tex]

[tex]\implies \cos \theta=\dfrac{3}{\sqrt{13}}\cdot \dfrac{\sqrt{13}}{\sqrt{13}}[/tex]

[tex]\implies \cos \theta=\dfrac{3\sqrt{13}}{13}[/tex]

As the terminal side of the angle is in Quadrant II, and cosine is negative in Quadrants II and III, the exact value of cos(θ) is:

[tex]\implies \cos \theta=-\dfrac{3\sqrt{13}}{13}[/tex]

Answer:

157.41

Step-by-step explanation:

It can be identified that, given the figure, there is a rectangle and 2 semicircles.

Let's find the area of the rectangle first: A=L*w

Plugging in the given values => A=7.5*15.1 which equals 113.25.

Now the area for the semicircles: 1/2(3.14*r^2)

First, we need to find the radius. To find the radius, you just have to divide the diameter by 2. So, 7.5/2=3.75.

We can plug square the radius which is 3.75 and plug it into the formula: 1/2(3.14*3.75^2)=>22.078125.

22.078125 is the area of only one semicircle so we need to multiply it by 2 because we have two semicircles. So, we get 44.15625.

Finally, we can add them all up to find the total area of the figure: 113.25+44.15625=157.40625.

Rounding to the nearest hundredth=>157.41

Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

The solution of the logarithmic equation is approximately 5.66 .

The logarithm is a simpler way to write a exponential equation.

The exponential equation nˣ = b is written as logₙ b = x ( read as logarithm of b to the base of n is equal to x).

The various properties of logarithm are:

The given equation is :

log₂ x = 2.5

This equation is of the form  logₐ b=n

We know that from the properties of logarithm logₐ b=n is equivalent to aⁿ=b.

So the given equation can be written as

[tex]x=2^{2.5}[/tex]

Solving we get

x=5.6568....

or, x≈5.66

Therefore the logarithm equation has a solution for x where the value of x is approximately 5.66.

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Answer:

0.5

Step-by-step explanation:

Answer: the answer is 0.5 or 1/2

Step-by-step explanation:

Answer:

6 people

Step-by-step explanation:

To figure this out, let's set up an equation.

We know 30 people went last year to Universal, and that this is 5 times as many people as who went the year before

So to figure out how many went the year before, we divide 30 by 5

30/5 = 6

So 6 people went to Universal the year before.

I hope this helps :)

Answer:

6 x 10^18

Step-by-step explanation:

u multiply numbers as normal and add exponents when they are being multiplied to each other

Answer:

C. 6 x 10^18

Step-by-step explanation:

Hope it helped :)
(Ik it was already answer but I just wanted to answer)

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$10000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]10000=P\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies 10000=P(1.0125)^{16} \\\\\\ \cfrac{10000}{(1.0125)^{16}}=P\implies 8197.46\approx P[/tex]

Using set builder notation, the domain of the given function is;

{x | x ≠ 5}

The domain is all values of x that makes the given expression undefined.

The given expression is;

y = (1 - 7x)/8 - 1/|3x - 15|

To find the value of x that will make the expression undefined, it means that we will equate the denominator to zero to get;

|3x - 15| = 0

Thus;

3x = 15

x = 15/3

x = 5

Thus, using set builder notation, the domain of the given function is;

{x | x ≠ 5}

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Answer: 120 degrees (originally said 150 degrees, but thats a weird ladder)

Step-by-step explanation: 6 x 4 = 24, 6 x 60 = 360, 4 = 60, 10 x 2 = 20, 4 x 5 = 20, 60 x 5 = 300. 20 / 2 = 10, 300 / 2 = 150, 150 / 1.17 = 120 most likely

X²-X+6

X+6

Han produced hot chocolate by combining 6 tablespoons of cocoa with 4 cups of milk. For every spoonful of cocoa, 0.67 glasses of milk are required.

The relationship between two values is described by a ratio. It displays how frequently one value appears in another. The answer to this question will depend on how many cups of milk there are to every tablespoon of chocolate.

Divide the provided cups of coffee by the cost of the tablespoon of coffee to get the required quantity of milk per tablespoon of chocolate.

Cups per tablespoon of coffee equal cups of milk divided by tablespoons of cocoa.

Given that,

Number of cups of milk = 4

Tablespoons of cocoa = 6

4/6=0.67 cups

Therefore, for every spoonful of cocoa, 0.67 glasses of milk are required.

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Answer:

Kinetic energy

Step-by-step explanation:

because when something is in motion it gains kinetic energy

Answer:

9, 18, 27, 36, 45

Step-by-step explanation:

multiples is like finding the factors. like 1*9=9 and 2*9=18, 9*3=27, 4*9=36, 9*5=45

You need 8 cups of juice for 12 cups of seltzer.

Representing the first statement in ratio form. So, number of cups of juice: number of cups of seltzer = 2:3. Similarly, for second statement, let the number of cups of juice be x.

Forming the equation with ratio on both sides -

2:3 = x:12

Writing the mentioned equation as fraction to solve for the value of x

x = (2 × 12)/3

Performing multiplication in numerator to find the value of x

x = 24/3

Dividing the numerator and denominator by 3 to find the value of x

x = 8

Therefore, 8 cups of juice is needed for 12 cups of seltzer.

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The value when it was purchased is  $160,000 in linear equation.

What in mathematics is a linear equation?

Let the original price be = x

Decreased value  = 0.35

Current value = 104000

x - 0.35x  = 104000

0.65x = 104000

x = 104000/0.65

x = 160,000

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Answer:

A

Step-by-step explanation:

He paid $376.20

In the given picture with 4 lines l, m and r, s. The l and m, r and s line are parallel lines.

Given that,

There is a picture with 4 lines l, m and r, s.

We have to check that those lines are parallel or not

To check that the line are parallel we have a condition.

If two lines are cut by the transversal and corresponding angles are congruent then we can say that those 2 lines are parallel.

In the figure we can see that ∠2 and∠6 are congruent.

So, we can say that lines r and s are parallel lines.

Similarly,

In the figure we can see that ∠1 and∠7 are congruent.

So, we can say that lines l and m are parallel lines.

Therefore, the l and m, r and s line are parallel lines.

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6 inches more than 2 times the height, 54 square inches the base and height is

b=13.8 inches

h=3.9 inches

Let base and height be b and h respectively,

So ,

b=2h+6

Area = b*h= 54 square inches

So,

(2h+6)(h)=54

2h²+6h=54

h²+3h=27

h²+3h-27=0

h= [tex]\frac{-3 +\sqrt{3^{2}-4(-27)(1) } \\}{2}[/tex]

h=[tex]\frac{-3 +\sqrt{9+108} \\}{2}[/tex]

h=[tex]\frac{-3 +\sqrt{117} \\}{2}[/tex]

h=[tex]\frac{-3 +10.8\\}{2}[/tex]

h=3.9 inches

b=2h+6=13.8 inches

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The quantity of unit squares necessary to completely cover a shape is its area. As a result, it is stated and measured in square units.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

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Answer:

NOT possible to draw

Step-by-step explanation:

Answer:

graph the following

x=-1 y =5

it look like a two line

Step-by-step explanation:

Answer:

360 million written in scientific notation is 3.6 × 108.

Step-by-step explanation:

The rate of change of the linear equation that has the given points on its graph is; -2.

The rate of change of a linear function can be determined by using the following formula:

Rate of change = change in y / change in x = y2 - y1 / x2 - x1.

Given the following points on a graph of a linear function:

​(−5​,4​) = (x1, y1)

​(−2​,−2​) = (x2, y2)

Plug in the values

Rate of change = change in y / change in x = (-2 - 4) / (-2 -(-5))

Rate of change = -6 / 3

Rate of change = -2 / 1

Rate of change = -2

Thus, the rate of change of the linear equation that has the given points on its graph is; -2.

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Answer:

100,000

Step-by-step explanation

week 1: 10

week 2: 10x10= 100

week 3: 100x10=1,000

week 4: 1,000x10=10,000

week 5: 10,000x10= 100,000

Have an amazing day/night!!

Answer:

18.64% discount

Step-by-step explanation:

If she had a $22 discount and bought the radio for $96, then the original cost was $118.

discount = (22 * 100) / 118

Answer:

[tex]2\sqrt{5}[/tex]

Step-by-step explanation:

You can use the Pythagorean Theorem, which is [tex]a^{2}+ b^{2}= c^{2}[/tex]. So the the distance from -9 to -5 is 4 and the distance from 8 to 6 is 2.

So [tex]4^{2} +2^{2} =c^{2}[/tex]. Which equals [tex]20=c^{2}[/tex].

Then you square root [tex]c^{2}[/tex] to make it c, then you do that to the other side. So you have [tex]\sqrt{20}=c[/tex].

Which equals [tex]2\sqrt{5}[/tex].

Or you can use the Distance Formula, which is [tex]\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex].

The [tex]x_{1}[/tex] is -5 and the [tex]x_{2}[/tex] is -9. The [tex]y_{1}[/tex] is 6 and the [tex]y_{2}[/tex] is 8. When you plug that in you get [tex]\sqrt{(-9--5)^{2} +(8-6))^{2} }[/tex]. When you simplify that you get [tex]\sqrt{20}[/tex].

Which equals [tex]2\sqrt{5}[/tex].

Using the binomial distribution, there is a 0.1094 = 10.94% probability that exactly 20 adults received a flu vaccine.

For each adult, there are only two possible outcomes, either they received the vaccine or they did not. The probability of an adult receiving the vaccine is independent of any other adult, hence the binomial distribution is used to solve this question.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, we have that:

The probability that exactly 20 adults received a flu vaccine is P(X = 20), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 20) = C_{50,20}.(0.371)^{20}.(0.629)^{30} = 0.1094[/tex]

0.1094 = 10.94% probability that exactly 20 adults received a flu vaccine.

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The error that the manager made was that B. The manager divided 5/4 by 16 instead of dividing 4/5 by 16.

The information illustrates that the project manager is calculating work forecasts and he manager's team completed 4/5 of a job in 16 days.

Therefore, the amount that was done each day will be:

= 4/5 ÷ 16

= 4/5 × 1/16

= 4/80

= 1/20

Therefore, the error that the manager made was that the manager divided 5/4 by 16 instead of dividing 4/5 by 16. This was the reason that he got 5/64.

Therefore, the correct option is B.

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Answer:

( x , y , z) = ( 1 , 3 , - 2)

the solution