Answer:
A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero. It can be shown that a number is rational if and only if its decimal representation is repeating or terminating (i.e. all except finitely many digits are zero). For example, the decimal representation of
1
/
3
becomes periodic just after the decimal point, repeating the single digit "3" forever, i.e. 0.333.... A more complicated example is
3227
/
555
, whose decimal becomes periodic at the second digit following the decimal point and then repeats the sequence "144" forever, i.e. 5.8144144144.... At present, there is no single universally accepted notation or phrasing for repeating decimals.
The infinitely repeated digit sequence is called the repetend or reptend. If the repetend is a zero, this decimal representation is called a terminating decimal rather than a repeating decimal, since the zeros can be omitted and the decimal terminates before these zeros.[1] Every terminating decimal representation can be written as a decimal fraction, a fraction whose divisor is a power of 10 (e.g. 1.585 =
1585
/
1000
); it may also be written as a ratio of the form
k
/
2n5m
(e.g. 1.585 =
317
/
2352
). However, every number with a terminating decimal representation also trivially has a second, alternative representation as a repeating decimal whose repetend is the digit 9. This is obtained by decreasing the final (rightmost) non-zero digit by one and appending a repetend of 9. 1.000... = 0.999... and 1.585000... = 1.584999... are two examples of this. (This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm.[2])
Step-by-step explanation:
what number is not part of the domain of the function: g(x)=x+2/x-1 ? how can you tell?
Answer:
x = 1 is not part of the domain
Step-by-step explanation:
The denominator of g(x) cannot be zero as this would make g(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.
solve
x - 1 = 0 ⇒ x = 1 ← restricted value
The number x = 1 is not part of the domain of the function g(x) = (x+2)/(x-1) because setting x to 1 would result in division by zero, which is undefined. Thus, x = 1 is an asymptotic value and is excluded from the domain.
Explanation:The number that is not part of the domain of the function g(x) = \frac{x+2}{x-1} is x = 1. Knowing that the domain of a function includes all the values that x can take on for which the function is defined, we can identify values that are not in the domain by looking for any values that would cause the function to be undefined. In the case of g(x), since it involves a division by x-1, we need to make sure that the denominator does not equal zero since division by zero is undefined in mathematics.
To find out when the denominator is zero, we set x-1 = 0 and solve for x. The solution is x = 1, which means that x cannot be 1, since it would make the function undefined. Therefore, x = 1 is not part of the domain of g(x).
As described in FIGURE 4.4 from OpenStax under a CC BY 4.0 license, functions like y = \frac{1}{x} have asymptotes or limits that indicate values that are not part of the domain. g(x) has a similar characteristic, where x = 1 is an asymptote.
10 out of every 65 students order pizza for lunch. There are 416 students at her school. How many students will eat pizza at her school?
Answer:
64
Step-by-step explanation:
First, you divide 416 by 65. This gets you 6.4. But it's not 1 in 65 eating pizza, it's 10 out of 65, so then you multiply 6.4 by 10, getting 64.
A movie theater sells student tickets for $6 and adults for $8. The theater sold 140 tickets, generating $990. How many student tickets were sold
65 student tickets were sold
Solution:
Given that movie theater sells student tickets for $ 6 and adults for $ 8
Let "s" be the number of student tickets sold
Let "a" be the number of adult tickets sold
Cost of 1 student ticket = $ 6
Cost of 1 adult ticket = $ 8
Given that theater sold 140 tickets
Number of student tickets sold + number of adult tickets sold = 140
s + a = 140 ------ eqn 1
The theater generated $ 990
number of student tickets sold x Cost of 1 student ticket + number of adult tickets sold x Cost of 1 adult ticket = 990
[tex]s \times 6 + a \times 8 = 990[/tex]
6s + 8a = 990 ------ eqn 2
Let us solve eqn 1 and eqn 2 to find values of "s" and "a"
From eqn 1,
s = 140 - a ----- eqn 3
Substitute eqn 3 in eqn 2
6(140 - a) + 8a = 990
840 - 6a + 8a = 990
2a = 150
a = 75
Substitute a = 75 in eqn 3
s = 140 - 75
s = 65
Therefore 65 student tickets were sold
Question 1
You answer 24 questions on a 100-point test correctly and earn a 96%.
a. All of the questions are worth the same number of points. How many questions are on the test? How many points is each question worth?
There are
questions on the test.
Each question is worth
points.
Question 2
b. Your friend earns a grade of 76% on the same test. How many questions
did your friend answer correctly?
Your friend answered
questions correctly.
plz help
Answer:
a) There are Total 25 Question on the test.
Each question is worth 4 points.
b) Your friend answered 19 questions correctly.
Step-by-step explanation:
Given:
Question answered =24
Percent earn = 96%
Total point test = 100
We will first solve for part a.
We need to find Total Question on the test and Points worth each question.
Now We know that percent earn is equal to Question answered divided by Total Question on test and ten multiplied by 100.
Framing in equation form we get;
[tex]Percent\ earn = \frac{\textrm{Question Answered}}{\textrm{Total question on test}}\times 100\\ \\\textrm{Total question on test} = \frac{\textrm{Question Answered}}{\textrm{Perecent earned}}\times 100[/tex]
Substituting the given values we get;
Total question on test = [tex]\frac{24}{96}\times 100 =25[/tex]
Hence There are Total 25 Question on the test.
Now we will find each question worth points.
each question worth points can calculated by dividing Total Point test with total number of question on the test.
Framing the equation we get;
each question worth points = [tex]\frac{100}{25} = 4\ points[/tex]
Hence Each question is worth 4 points.
Now Solving for part b.
Given:
Percent earn by friend = 76%
we need to find number of question answered correctly.
question answered correctly = [tex]\frac{\textrm{Percent earned by friend}\times \textrm{Total Number of question}} {100}[/tex]
Substituting the values we get;
question answered correctly = [tex]\frac{76\times 25}{100} = 19[/tex]
Hence Your friend answered 19 questions correctly.
Answer:
a) There are Total 25 Question on the test.
Each question is worth 4 points.
b) Your friend answered 19 questions correctly
Step-by-step explanation:
A football team loses a total of 12 yards in 4 plays. On average how many yards did the team move the ball per play?
The team moved the ball -3 yards per play.
Step-by-step explanation:
Given,
Total yards lost = 12 yards
Total plays = 4 plays
As the yards are lost, therefore, we will use negative sign.
Yards per play = [tex]\frac{Number\ of\ yards}{Number\ of\ plays}[/tex]
Yards per play = [tex]\frac{-12}{4}[/tex]
Yards per play = -3
The team moved the ball -3 yards per play.
Keywords: division, unit rate
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Mariana solved a linear equation and found that it had an infinite number of solutions. Which could have been the final line of her work?
Final answer:
The final line of Mariana's work would show identical sides after simplification, resulting in an equation like 0 = 0 or x = x, indicating an infinite number of solutions.
Explanation:
If Mariana solved a linear equation and found that it had an infinite number of solutions, the final line of her work would show that both sides of the equation are identical after simplification. For instance, if the original equation was 2x + 3 = x + x + 3, upon simplifying both sides, she would end up with x + x = x + x, which is an identity (indicating that any value for x would satisfy the equation). Therefore, the final line could have been a simplified equation that resulted in a statement like 0 = 0 or x = x after all terms cancel out.
The school uses between 300 and 400 sheets of paper per school day. If paper costs the school $2.00 per 100 sheets, approximately how much does the school pay for paper every month? (Remember to only count school days!) A. $140.00 B. $190.00 C. $170.00 D. $90.00
Answer:
Option A. $140.00
Explanation:
1. Using the minimun number of sheets of paper in the interval [300, 400]
a) Cost: $ 2.00 / 100 sheets
b) 300 sheets / day × $ 2.00 / 100 sheets = $ 6.00 / day
c) Approimately 20 school days per month:
$ 6.00 / day × 20 day = $ 120.002. Using the maximum number of sheets of paper in the interval [300, 400]
a) Cost: $ 2.00 / 100 sheets
b) 400 sheets / day × $ 2.00 / 100 sheets = $ 8.00 / day
c) Approimately 20 school days per month:
$8.00 / day × 20 day = $ 160.003. Middle value:
Calculate the middle value between $160.00 and $120.00
[$120.00 + $160.00] / 2 = $140.00Thus, the answer is the option A.
There are 136 people waiting for a river raft ride. Each raft holds 8 people. Silvia used the work below to find the number of rafts needed to hold 136 people. Explain how her work helps to find out how many rafts are needed.
8 % 136
-80
= 56 - 56 =0
Answer:
17 rafts are needed for 136 people.
Step-by-step explanation:
Given:
Total number of people waiting for river raft ride = ?
Number of people the raft holds = 8
To Find:
The number of rafts needed =?
Solution:
Let X be the total number rafts needed to accommodate all the 136 people waiting for the River Raft ride.
So now X will be
X= [tex]\frac{\text{Total number of people}}{\text{number of people a raft can hold}}[/tex]
X= [tex]\frac{136}{8}[/tex]
X = 17
Please Help!
A function is represented by the values in the table.
x y
22 26
20 22
16 20
14 18
10 14
Choose from the drop-down menu to complete the statement. The function represented in the table (Is or is not) linear.
Pick one: Is or is not.
A function is a relationship between inputs where each input is related to exactly one output.
The coordinates of the table are: (22, 26), (20, 22), (16, 20), (14, 18),
(10, 14).
The graph of the coordinates formed from the table must show a linear graph.
This means a straight line.
The graph is shown below and it is not a straight line.
The function represented in the table is not linear.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function is represented by the values in the table.
x y
22 26
20 22
16 20
14 18
10 14
Now,
We can find the coordinates of the given function.
(22, 26)
(20, 22)
(16, 20)
(14, 18)
(10, 14)
The graph of these coordinates must show a linear graph.
This means a straight line.
The graph is shown below and it is not a straight line.
Thus,
The function represented in the table is not linear.
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You get 15 points for this question :) can you please explain step by step or do it in the 2 step equation format please? Thank you.
QUESTION: what is the value of t? (equation: 25 + 6t - 7 = 36)
Answer:
t=3
Step-by-step explanation:
6t= 36+7-25
t=18/6
2 years is what percent of 11 years
Answer:
2 years are the 18.2% of 11 years.
Step-by-step explanation:
For calculating what percentage of 11 years is 2 years, we have to do the following calculations:
Fraction used to represent the question = 2/11
Now, we divide 2 by 11, where 2 is the dividend and 11 the divisor:
2/11 = 0.1818....
Converting 0.1818 to percentage:
0.1818 * 100 = 18.2% (Rounding to the nearest tenth)
2 years are the 18.2% of 11 years.
Sophia has completed 80% of the problems on her math test. She has completed 32 problems. What is the total number of problems on the test?
Answer:
40
Step-by-step explanation:
80% of the test = 32 questions
100% of the test = x questions
Cross multiply
80*x = 100 * 32 Combine the right
80x = 3200 Divide by 80
x = 3200/80
x = 40
There are 40 questions on the test.
HELP ASAP. Gotta get this done.
Answer:
C
Step-by-step explanation:
The ratio of frames : containers can be calculated using values from table.
3 : 12 = 7 : 28 = 9 : 36 = 1 : 4 ← in simplest form, thus
Number of containers is 4 times the number of frames
Thus for 5 picture frames the number of containers = 5 × 4 = 20 → C
NEED HELP ASAP!!!!!
Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y = seven divided by square root of quantity eight x plus ten.
Answer:
B
Step-by-step explanation:
To find [tex]y=f(g(x))[/tex], substitute the value of [tex]g(x)[/tex] into the the function f(x) instead of x.
Consider option B:
Given
[tex]f(x)=\dfrac{7}{\sqrt{x}}\\ \\g(x)=8x+10[/tex]
So,
[tex]f(g(x))\\ \\=f(8x+10)\ [\text{Expression } 8x+10\text{ has a role of }x]\\ \\=\dfrac{7}{\sqrt{8x+10}}[/tex]
This is exactly what you need as answer.
Samantha is measuring the snowfall in a snow Gog for her science project. The first week she measured 3 3/4 inches of snow the second week she measured twice as much snow, and the third weekShe measured half as much snow as the first week. It did not snow at all in the fourth week. How much snowfall did Samantha measure for the entire month? Explain
Samantha measured [tex]13\frac{1}{8}[/tex] inches for the entire month
Step-by-step explanation:
Samantha is measuring the snowfall in a snow Gog for her science project
The first week she measured 3 3/4 inches of snowThe second week she measured twice as much snow, and the third week she measured half as much snow as the first weekIt did not snow at all in the fourth weekWe need to find how much snowfall Samantha measured for the entire month
∵ She measured [tex]3\frac{3}{4}[/tex] inches of snow in the 1st week
- Change the mixed number to improper fraction
∵ [tex]3\frac{3}{4}=\frac{(3)(4)+3}{4}=\frac{12+3}{4}=\frac{15}{4}[/tex]
∴ She measured [tex]\frac{15}{4}[/tex] inches of snow in the 1st week
∵ She measured twice as much snow as the 1st week in the 2nd week
- Multiply the value of the 1st week by 2
∵ [tex]\frac{15}{4}[/tex] × 2 = [tex]\frac{30}{4}[/tex]
∴ She measured [tex]\frac{30}{4}[/tex] inches of snow in the 2nd week
∵ She measured half as much snow as the 1st week in the 3rd week
- Multiply the value of the 1st week by 1/2
∵ [tex]\frac{15}{4}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{15}{8}[/tex]
∴ She measured [tex]\frac{15}{8}[/tex] inches of snow in the 3rd week
∵ It did not snow at all in the fourth week
- Add the values of the three weeks above to find the amount
of snowfall she measured for the entire month
∵ The amount of snowfall = [tex]\frac{15}{4}+\frac{30}{4}+\frac{15}{8}[/tex]
- To add the fraction you must make all the denominator same number
so multiply the 1st and 2nd fractions by 2 up and down to make all
the denominator equal 8
∴ The amount of snowfall = [tex]\frac{30}{8}+\frac{60}{8}+\frac{15}{8}[/tex]
- Add the numerators and put the sum over 8
∴ The amount of snowfall = [tex]\frac{105}{8}[/tex]
- You can change the improper fraction to mixed number by divide
105 by 8 and put the reminder over 8
∵ 105 ÷ 8 = 13 and 1/8
∴ The amount of the snowfall = [tex]13\frac{1}{8}[/tex] inches
Samantha measured [tex]13\frac{1}{8}[/tex] inches for the entire month
Learn more:
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Is p = 6m + 9m a proportional relationship?
Answer:
yes
Step-by-step explanation:
the local music activities coordinator sold 300 tickets to the orchestra concert. student tickets were $4 and adult tickets were $6. if the total sales were $1,600 how many student tickets were sold
100 children tickets and 200 adult tickets were sold.
Step-by-step explanation:
Given,
Cost of one student ticket = $4
Cost of one adult ticket = $6
Total sales = $1600
Number of tickets sold = 300
Let,
x represent the number of children tickets sold.
y represent the number of adult tickets sold.
According to given statement;
x+y=300 Eqn 1
4x+6y=1600 Eqn 2
Multiplying Eqn 1 by 4
[tex]4(x+y=300)\\4x+4y=1200\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](4x+6y)-(4x+4y)=1600-1200\\4x+6y-4x-4y=400\\2y=400[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{400}{2}\\y=200[/tex]
Putting y=200 in Eqn 1
[tex]x+200=300\\x=300-200\\x=100[/tex]
100 children tickets and 200 adult tickets were sold.
Keywords: linear equation, elimination method
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In ΔABC, m∠ACB = 90°, CD ⊥ AB and m∠ACD = 45°. Find: AC, if CD = 6√2 in.
Answer:
AC = 12 units.
Step-by-step explanation:
Δ ACD is right-angled. ( as CD ⊥ AB).
cos 45° = CD / AC = 6√2 / AC
AC = 6√2 / cos 45°
AC = 6√2 / 1 /√2
= 6√2 *√2
= 6 * 2
= 12 (answer)
HOPE THIS HELPED ;3
an exponential function has an
Answer:
Step-by-step explanation:
Exponential functions have the form
f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.
Answer:
Exponential functions have the form
Step-by-step explanation:
Whats the range of y=2x-7
Answer:
(-∞,∞) or {y|y∈R}
Step-by-step explanation:
Devin inveated $750 in a CD that pays 6% simple interest, calculated quarterly. How much money will Devin earn in 3 years?
Answer:
$896.70
Step-by-step explanation:
Amount( A) Devi earned can be calculated from the formula below
[tex]A =P ({ 1 + \frac{r}{m} })^{mt}[/tex]
Where,
P= principal=$750
r=rate=6%=0.06
m=compounding frequency=4
t=time=3yrs
[tex]A =750 ({ 1 + \frac{0.06}{4} })^{(4 \times 3)}[/tex]
[tex]A =750 ({ 1 + 0.015)}^{12}[/tex]
[tex]A =750 \times ({ 1.015)}^{12}[/tex]
[tex]A =750 \times 1.1956[/tex]
[tex]A = 896.70[/tex]
Answer:
135
885-750 is 135 on financial literacy
What the product to (-3q+3)+7(8q+1)
Answer:
53q+10
Step-by-step explanation:
(-3q+3)+7(8q+1)
-3q+3+56q+7
53q+3+7
53q+10
Answer:
[tex] - 3q + 3 + 56q + 7 \\ 53q + 10[/tex]
Good luck!
Intelligent Muslim,
From Uzbekistan.
The population of a town went from 100000 to 137000 in 5 years. What was the percent increase in the town's population over that time?
Answer: 37%
Step-by-step explanation:
Initial Population = 100,000
Population after 5 years = 137,000
Population increase = 137,000 - 100,000
= 37,000
Therefore % increase = 37,000/100,000 x 100
= 37%
What is the length of the side opposite
3 units
4 units
5 units
6 units
Answer:
It's 6 units
Step-by-step explanation:
i took the test
the ratio of the point (-3,k) divides the line segment joining the points (-5,-4) and (-2,3) also find the value of k
Answer:
Step-by-step explanation:
midpoint theorem : (mx₂+nx₁/m+n , my₂+ny₁/m+n)
(-3, k) = ( -3*-2 + k*-5/-3+k , -3*3 + k*-4/-3+k)
(-3, k) = (6-5k/-3+k , -9-4k/-3+k)
Compare x values of both side ;
-3 = 6-5k/-3+k
-3 *( -3+k) = 6-5k
-3*-3 +k *-3 = 6-5k
9 -3k = 6- 5k
5k -3k = 6 - 9
2k = -3
k= -3/2
Factor each polynomial expression and explain the factoring process used.
Answers:
b) [tex]x(25x-1)[/tex]
c) [tex]x^{2}-4(x-3)[/tex]
d)[tex]4x(x-5)+25[/tex]
e)[tex]2(3x^{2}+11x+14)[/tex]
Step-by-step explanation:
b) We have the following expression:
[tex]25x^{2}-x[/tex]
Applying common factor [tex]x[/tex]:
[tex]x(25x-1)[/tex]
c) We have the following expression:
[tex]x^{2}-4x+12[/tex]
Applying common factor [tex]4[/tex]:
[tex]x^{2}-4(x-3)[/tex]
d)We have the following expression:
[tex]4x^{2}-20x+25[/tex]
Applying common factor [tex]4x[/tex]:
[tex]4x(x-5)+25[/tex]
e)We have the following expression:
[tex]6x^{2}+22x+28[/tex]
Applying common factor [tex]2[/tex]:
[tex]2(3x^{2}+11x+14)[/tex]
Answer this pic please and explain how to do it
Balancing of equations as shown in the attached document requires that the number of atoms, of an element, on the left of the equation is equivalent to the number of the atoms of the same element on the right of the equation. This is in observation of the conservation of mass rule of thermodynamics. Mass and energy cannot be destroyed nor created, it can only be transformed from one form to another. In this case, mass remains the same in the system since this is a chemical reaction- only the bonds between atoms are being rearranged.
This rectangle has a perimeter of 120
centimeters. If the width is 20 cm, what is
measure of the length?
20 cm
x cm
The length of the rectangle, given a perimeter of 120 cm and a width of 20 cm, is 40 cm.
Explanation:This question pertains to the calculation of the dimensions of a rectangle given its perimeter and one side. In a rectangle, the perimeter is given by the formula 2(Length + Width). In this case, the perimeter is 120 cm, and the width is 20 cm. We can set up the following equation based on the given information: 120 = 2(Length + 20). After simplifying, we get 120 = 2*Length + 40, which leads to 2*Length = 120 - 40 or 2*Length = 80. Finally, solving for Length gives Length = 80 / 2 = 40 cm. Therefore, the length of the rectangle is 40 cm.
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jordan can swim to laps in 4 1/2 minutes
select the correct unit rate for the given situation.
Answer:
Step-by-step explanation:
4 1/2 minutes = 4.5 minutes
2 / 4.5 = 0.44 laps per minute
OR
4.5 / 2 = 2.25 minutes per lap
not sure which one ur looking for...but both are unit rates
The unit rate of Jordan's swimming speed is approximately 0.44 laps per minute. This is calculated by dividing the number of laps (2) by the total time (4.5 minutes).
Explanation:To identify the unit rate in this scenario, we first need to understand what we are finding. The unit rate means how much of something is done in one unit of time, in this case, how many laps Jordan can swim in one minute. Since Jordan can swim two laps in 4 1/2 minutes, we want to find out how many laps he can swim in one minute. We divide the total laps (2) by the total time (4.5). This will compute to approximately 0.44. Hence, Jordan can swim around 0.44 laps in one minute.
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Chad earns $8.60 per hour. What is his gross pay for working 24 hours?
Answer:
$206.4
Step-by-step explanation:
8.6*24=206.4