Write the number 0.21212121.. as a fraction let x=
We know that numbers with periodic decimals (there are decimals that repeat infinitely) can be written as a fraction of two integer numbers.
Here we have the number:
0.212121...
Where the decimals "21" are repeating decimals, and we want to write this as a fraction.
And we will find that the fraction form of this number is: 21/99
To find it, first let's define:
x = 0.212121...
Now we need to multiply this by 10^n, where n is the number of repeating decimals, here we have two (2 and 1) then n = 2.
Now we need to multiply:
x×10^2 = x×100 = (0.2121...)×100 = 21.212121...
Now we can subtract the original number so we get:
x×100 - x = x×99 = 21.212121... - 0.212121... = 21
Then we just found that:
x×99 = 21
Solving for x, we get:
x = 21/99 = 0.212121...
Then the fraction that we want to find is 21/99
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Write each number in standard form 600 + 90 + 3
A pet store has 9 puppies and 48 kittens.
What is the ratio of kittens to puppies?
Enter your answer in simplest fractional form in the box.
The ratio of kittens to puppies is [tex]\dfrac{16}{3}[/tex].
Given:
The number of puppies is 9.
The number of kittens is 48.
To find:
The ratio of kittens to puppies.
Explanation:
The ratio of kittens to puppies is the fraction of the number of kittens and the number of puppies. So,
[tex]\text{Ratio}=\dfrac{\text{Number of kittens}}{\text{Number of puppies}}[/tex]
[tex]\text{Ratio}=\dfrac{48}{9}[/tex]
[tex]\text{Ratio}=\dfrac{16}{3}[/tex]
Therefore, the ratio of kittens to puppies is [tex]\dfrac{16}{3}[/tex].
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Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value.
At a boating and sports store, the cost of renting a personal watercraft is $53 per half hour, which includes a 6% sales tax. Determine the cost of a half hour rental before tax.
The equation is ?. The cost of a half hour rental is $? Per half hour.
Type an equation using x as the variable.
Which equation is a point slope form equation for line AB ?
A.y−2=34(x−1)
B.y−1=34(x−2)
C.y−5=34(x−6)
D.y−6=34(x−5)
The required equation is C.) y−5 = 3/4(x−6)
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (6,5) and, (-2,-1)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>(y-5)/(x-6)=(-1-5)/(-2-6)
=>4y-20=3x-18
=>y-5=3/4(x-6)
Hence, the required equation is, C.) y−5 = 3/4(x−6)
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find the new amount given the original amount and the percent of change. 29,000; 4% decrease
5x + 6y = 18 and 18x -15y =36
// Solve equation [1] for the variable x
// Plug this in for variable x in equation [2]
// Plug this in for variable x in equation [3]
// Solve equation [2] for the variable y
// Plug this in for variable y in equation [3]
// Solve equation [3] for the variable z
// By now we know this much :
x = -6y-3z-18 y = -2 z = -1// Use the y and z values to solve for x
x = -6(-2)-3(-1)-18 = -3
math question down below
Match the equation with its corresponding solution for x. 4x + 7 = 35
Mr. Smith spent 6 hours hiking along a trail and back. He walked out at the rate of 4 miles per hour and walked back at the rate of 2 miles per hour. How long did it take Mr. Smith to get to the end of the trial?
Linear equations are algebraic equations which represents the value of variables. These equations have unique solutions or sometimes there may be a number of solutions. Linear equation may contain n number of variables.
Given:
[tex]\begin{aligned}\rm\:Total\: time\: taken\: by \:MR. Smith \: &= 6 hours\\\\\rm\:Speed\:while\:going &= 4 \:miles\:per\:hour.\\\\\rm\:Speed \:while\:coming\:back &= 2\: miles\:per \:hour \end[/tex]
CalculationsLet time taken to walk out be [tex]x[/tex] and time taken to walk back be [tex]2x[/tex]. The total time taken will be the summation of [tex]x[/tex] and [tex]2x[/tex] .
[tex]\begin{aligned}\rm\:Total\:time&= 6\:hours\\\\x+2x&= 6\: hours\\\\3x&=6\:hours\end[/tex]
Continuing further,
[tex]x=\dfrac{6}{3}\:hours \\\\x=2\:hours[/tex]
Therefore it can be said that the time taken by Mr. Smith to reach the end of the trial is 2 hours.
It is also observed that the speed while coming back was half of the speed of walking out. So it can be said that the time taken to walk back was twice the time Mr. Smith took to reach the end of the trail.
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The angles of a quadrilateral are 140, 80, 60, and 80
What type of quadrilateral could it be?
A farmer had 1,000 horses and cows. After selling some of them, he had 550 horses and 350 cows left. How many horses and cows did he sell altogether?
A cylinder has a volume of 320 pi cu. in. and a height of 5". Find the radius of the cylinder.
Answer:
The radius of cylinder is 8 inches.
Step-by-step explanation:
We have given,
Volume of cylinder = 320π cubic inches
Height of cylinder = 5 inches
We know, Formula for volume of cylinder as : V =πr²h
where r is radius of cylinder and h is the height of cylinder.
So, We can plug values for V and h to get radius of cylinder.
i.e V = πr²h
320π = πr²* 5
Solving for r.
We get,
320 = r² * 5
320/5 = r²
64 = r²
or r = ±8 , Since radius of cylinder can not a negative number so we neglect -8.
Hence the radius of cylinder is 8 inches.
The formula f= n/4 + 37 estimates the temperature F in degrees Fahrenheit when crickets chirp n times per minute. Use the formula to estimate the
temperature when n = 75 chirps/min. Round to the nearest whole number, if necessary.
a) 52mc009-4.jpg
b) 53mc009-3.jpg
c) 56mc009-5.jpg
d)58mc009-2.jpg
Answer:
56°F
Step-by-step explanation:
Given : The formula[tex]F = \frac{n}{4} + 37[/tex]estimates the temperature F in degrees Fahrenheit when crickets chirp n times per minute.
To Find: Use the formula to estimate the temperature when n = 75 chirps/min.
Solution:
Formula : [tex]F = \frac{n}{4} + 37[/tex]
Where F in degrees Fahrenheit when crickets chirp n times per minute.
Now we are supposed to substitute n = 75
So, [tex]F = \frac{75}{4} + 37[/tex]
[tex]F = 55.75[/tex]
Hence the temperature is 56°F when n = 75 chirps/min.
the tempura temperature halfway to the sun from mercury is aproxamently 1,800 Celsius and scientist theorize that it may be 26,000 times hotter at the center of the sun. aproxamently how hot is the center of the sun
Final answer:
Using the given approximation, the temperature at the Sun's core would be 46,800,000 degrees Celsius. However, scientific data indicates that the accurate temperature is 15 million degrees Celsius, due to nuclear fusion processes occurring at the core.
Explanation:
If the temperature halfway to the Sun from Mercury is approximately 1,800 Celsius and scientists theorize that it may be 26,000 times hotter at the center of the Sun, we can calculate the temperature at the center by multiplying 1,800 Celsius by 26,000. This gives us an estimated temperature of the sun's core at 46,800,000 degrees Celsius. However, according to scientific data, the temperature near the center of the Sun is thought to be around 15 million degrees Celsius (1.5 ×[tex]10^7[/tex] °C) or kelvin, which is much more accurate than the extrapolation from the original question.
Mercury's proximity to the Sun accounts for its high surface temperatures, but without a significant atmosphere, the temperatures fluctuate dramatically between day and night. At the Sun's core, however, the temperatures reach extremes due to nuclear fusion, which releases vast amounts of energy and maintains the central temperature around 15 million degrees Celsius.
17 times 59 distributive property
In the diagram, m CD = 128° and m DA = 76°. What is m∠ABC?
Answer: The value of m∠ABC is 102° .
Step-by-step explanation:
Since we have given that
m CD = 128°
m DA = 76°
We need to find the m∠ABC, Angle subtended at the center is half of the sum of the measure of the arc intercepted by it.
[tex]\frac{m\ CD+m\ DA}{2}=\angle ABC\\\\\frac{128^\circ+76^\circ}{2}=\angle ABC\\\\102^\circ=m\angle ABC[/tex]
The value of m∠ABC is 102° .
A dolphin dove 31 meters below the surface of the water to reach a fish. It traveled 16% of the total distance every second.
What was the depth of the dolphin after 3 seconds?
A. –19.84 meters
B. –4.96 meters
C. –7.44 meters
D. –14.88 meters
Give the other person Brainliest, please...
PS: I know this question was asked back in 2017, but just want the other person to get brainliest :D
If d = 20 and C = 20π
If d = 26 and C = 26π
If r = 12 and C = π
If r = 18 and C = 14π
If r = 6 and C = 12π
If r = 50 and C = 100π
^Matches w
then d = 1
then d = 100
then d = 12
then d = 14
then r = 10
then r = 13
What goes w what!
A frozen yogurt shop weighs customers' cups on a scale to determine how much they will pay for their yogurt. The scale rounds weights to the nearest tenth of an ounce. A weight of 10 ounces or more costs at least $3.
Final answer:
Leslie can find out which yogurt gives her more by converting pounds to ounces. A 2-pound container is equivalent to 32 ounces, which is more than the total of 30 ounces from five 6-ounce containers.
Explanation:
Comparing Yogurt Quantities
To determine which yogurt option provides more quantity, Leslie needs to convert the weights into the same units. This means converting pounds to ounces, or ounces to pounds. In this case, converting pounds to ounces is more straightforward because we deal with whole numbers.
There are 16 ounces in 1 pound, so a 2-pound container of yogurt is equivalent to 32 ounces (2 x 16 = 32). On the other hand, five 6-ounce containers of yogurt total 30 ounces (5 x 6 = 30). Therefore, the 2-pound container gives more yogurt since 32 ounces is more than 30 ounces.
What number goes on top and how do you solve it.
A water tank holds 18,000 gallons. How long will it take for the water level to reach 6000 gallons if the water is used at an average rate of 450 gallons per day?
Dr. McDonald thinks that his group of earth science students is particularly special (in a good way), and he is interested in knowing if their class average falls within the boundaries of the average score for the larger group of students who have taken earth science over the past 20 years. Because he has kept good records, he knows the means and standard deviations for both his group of 36 students and the larger group of 1,000 past enrollees. Here are the data he has, and the values for which you will need to compute the z-test
Circle P has a diameter of 20 feet. Circle Q has a diameter of 30 feet. What is the ratio of the circumference?
Answer:
The ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]
Explanation:
The circumference of a circle is given by the formula \(C = \pi \times d\), where [tex]\(d\)[/tex] is the diameter.
For Circle P with a diameter of 20 feet, the circumference is:
[tex]\[ C_P = \pi \times 20 \][/tex]
For Circle Q with a diameter of 30 feet, the circumference is:
[tex]\[ C_Q = \pi \times 30 \][/tex]
To find the ratio of the circumferences of Circle P to Circle Q, we divide the circumference of Circle P by the circumference of Circle Q:
[tex]\[ \text{Ratio} = \frac{C_P}{C_Q} = \frac{\pi \times 20}{\pi \times 30} \][/tex]
[tex]\[ \text{Ratio} = \frac{20}{30} = \frac{2}{3} \][/tex]
So, the ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]
If 3/4 of the sections on a different spinner have stripes and there are 24 sections how many sections have stripes
Need the complete Answer of this problemssssss.
What is the sum of the geometric sequence −4, 24, −144, … if there are 7 terms?-159,964
−26,661
26,661
159,963
Answ
-159,964
Step-by-step explan
I got it right on the test
Cindy has 26 nickels. She is getting rolls of nickels from the bank. She has enough money to get up to 10 rolls of nickels and each roll contains 40 nickels. The bank will not give partial rolls. The function that models the number of nickels Cindy will have after leaving the bank is f(r)=40r+26, where r is the number of rolls of nickels she gets. What is the practical domain of the function?
A) all real numbers
B) r>1
C) {66, 106, 146, 186, 226, 266, 306, 346, 386, 426}
D) all integers from 1 to 10, inclusive
Answer: Option D is the right answer. The practical domain of the function=all integers from 1 to 10, inclusive.
Step-by-step explanation:
Given function f(r)=40r+26, where r is the number of rolls of nickels she gets.
as it is already mentioned that she can get up to 10 rolls of nickels.
Therefore domain of function contains r ≤10,such that r is a natural number.
i.e.Domain of f(r)=all integers from 1 to 10, inclusive.
Domain of a f(x) is a set of values of x which make function f(x) well defined.
Benjamin solved the equation 3+/2=10 and justified each step as shown. Identify Benjamin’s error and fix his mistake.
3+x/2=10 GIVEN
x/2=7 MULTIPLICATION PROPERTY OF EQUALITY
x=14 SUBTRACTION PROPERTY OF EQUALITY
Calculate the rounding error when 7.69 is rounded to 1 decimal place