The length of the third part of the rope is 4 feet.
Given that A 48-feet rope is cut into three length. The second length of the rope is twice the first length. The third length of rope is one-fifth the first length
Let's assume the length of the 1st part is "x".
Then the length of the second part is "2x". and the length of the third part is "[tex]\frac{x}{5}[/tex]".
The total length of rope is 48 feet
⇒x+2x+[tex]\frac{x}{5}[/tex]= 48 feet
⇒3x+[tex]\frac{x}{5}[/tex]= 48 feet
⇒[tex]\frac{16x}{5}[/tex]= 48 feet
⇒ x= 20 feet.
Therefore, The length of the third part of the rope is 4 feet.
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What is the solution to the equation below? Round your answer to two
decimal places.
log₂ x = 2.5
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:
log x+ log y= log x ylog x - log y= log(x/y)log xⁿ=n log xThe 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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Han made some hot chocolate by mixing 4 cups of milk with 6 tablespoons of cocoa
how many cups of milk is that
how many cups of cocoa is that
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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What is 6 over 9 times 6 over 8 equal
Answer:
0.5
Step-by-step explanation:
Answer: the answer is 0.5 or 1/2
Step-by-step explanation:
6 inches more than 2 times the height, 54 square inches what’s the base and height
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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Jon placed a ladder 24 feet long against the side of his house. The base of the ladder was 10 feet from the house. What angle did the ladder make with the ground, to the nearest degree.
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
A house has decreased in value by 35% since it was purchased. If the current value is $104,000, what was the value when it was purchased?
The value when it was purchased is $160,000 in linear equation.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.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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NO LINKS! Please help me
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:
θ is the angle.O is the side opposite the angle.A is the side adjacent the angle.H is the hypotenuse (the side opposite the right angle).[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]
PLEASE HELP ASAP WILL GIVE BRAINLIST
Question 3(Multiple Choice Worth 2 points)
(Multiplying and Dividing with Scientific Notation LC)
Find the product of (3 x 10^9) and (2 x 10^9). Write the final answer in scientific notation.
6 x 1081
6 x 10018
6 x 1018
6 x 109
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)
x+y-z= 6
3x - 2y + z = -5
x + 3y - 2z = 14
Answer:
( x , y , z) = ( 1 , 3 , - 2)
the solution
A project manager is calculating work forecasts. The manager's team completed of a job in 16 days. At this rate, the
manager says that the team completed of the project each day.
What was the manager's error?
O The manager is correct. There was no error.
O The manager divided by 16 instead of dividing
by 16.
O The manager divided 16 by
instead of dividing
by 16.
O The manager divided 16 by
instead of multiplying 16 by
O The manager divided by 16 instead of multiplying 16 by
The error that the manager made was that B. The manager divided 5/4 by 16 instead of dividing 4/5 by 16.
How to calculate the value?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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0.39 x 10^9
Put in scientific notation and explain how it works.
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]
Given the following composite figure, d = 7.5 cm and w = 15.1 cm.
What is the area of the figure?
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
How much money (in dollars) should be invested in an account that earns 5% interest, compounded quarterly, to yield $10,000 in 4 years? Round your answer to the nearest cent.
[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]
Which lines are parallel if the m<2 = m<6? Lines r & s or lines l & m
(Click document to see image)
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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I was
following a recipe to make punch for a party. The rect cakks for 2 cups of juice for every 3 cups o
f seltzer. If I have 12 cups of seltzer, how many cups of juice do I need?
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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graph the following. x= -1. y= 5
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:
x to the power of 2 - x + 6
X²-X+6
X²-X¹:there's a invisible ¹ on the variable/XX+6
6XFind the domain y=1-7x/8-|3x-15|
Using set builder notation, the domain of the given function is;
{x | x ≠ 5}
How to find the Domain of a Function?
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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When a vehicle is in motion, it has _____.
Answer:
Kinetic energy
Step-by-step explanation:
because when something is in motion it gains kinetic energy
Ashley received a $22 discount on a radio she bought for $96.00. What is the percent of discount she saved?
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
what is the answer to this equation 21 x ___=7
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
4.)
Find the area of the polygon with the given vertices:
E(3, 1), F(3,-2), G(-2,-2)
Perimeter EFG =____
last year 30 people went on a family trip to universal this is 5 times as many people that went the year before. how many people went the uear before?
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 :)
When converted to millimeters, the distance 360,000,000 meters is expressed as millimeters in scientific notation.
Answer:
360 million written in scientific notation is 3.6 × 108.
Step-by-step explanation:
Geoffrey buys 48 shares of Deegan Pharmaceuticals at $6.15.each, and his broker charges him a commission of $81. How
much did Geoffrey pay for his stock?
a. $376.20
b. $295.20
C. $450.30
d. $219.60
Answer:
A
Step-by-step explanation:
He paid $376.20
If a linear function has the points (−5,4) and (−2,−2) on its graph, what is the rate of change of the function?
The rate of change of the linear equation that has the given points on its graph is; -2.
How to Find the Rate of Change of a Linear Function?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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list 5 multiples of 9
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
According to data from the CDC, about 37.1% of adults (individuals 18 years of age or older) in the United States and 57.9% of children (individuals between 6 months and 17 years of age) in the United States received a flu vaccine during the 2017-2018 flu season.
a) Consider a random sample of 50 adults.
i. Calculate the probability that exactly 20 adults received a flu vaccine.
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.
What is the binomial distribution formula?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:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, we have that:
There is a random sample of 50 adults, hence n = 50.37.1% of adults received the flu vaccine, hence p = 0.371.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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(FIRST ANSWER WITH EXPLANATION GETS BRAINLIEST)
Daisy is studying an ant population. On the first day, there are 10 ants. A week later, there are 100 ants. After the third week, there are 1,000 ants. Assuming the ant growth continues at this rate, how many ants would there be after 5 weeks?
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!!
Please help I will give brainliest
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].