Answers
Answer:
Nora is correct
Step-by-step explanation:
Sophia used an appropriate method for computing the value of the repeating decimal fraction ...
0.1212_12
Close examination of the given decimal fraction shows that it is non-repeating, so is an irrational number. It cannot be represented by the ratio of integers.
Nora is correct in saying Sophia made a mistake.
___
Sophia depended on 100x -x cancelling some part of the fraction, so the result was a finite decimal. For repeating 2-digit fractions, this works well:
[tex]x=0.12\overline{12}\\100x=12.12\overline{12}\\100x-x=12.12\overline{12}-0.12\overline{12}=12\\x=12/99[/tex]
However, the decimal does not repeat, so this does not work:
100x = 12.1121112
100x -x = 12.1121112 -0.121121112 = 11.99099009900099... non-repeating
That is, the decimal part is not cancelled by Sophia's work, as we said above.
Related Questions
What is the value of each marble?
Answers
Answer:
where
is
the
attachment
bruv?
Answer:
We wouldn't know because we have no information on the marbles.
Step-by-step explanation:
Find the slope of the line tangent to the graph of (x^2)-((xy)^(1/2))=(2y^2)+3x at the point (4,1).
Answers
Compute [tex]\frac{\mathrm dy}{\mathrm dx}[/tex] using implicit differentiation:
[tex]x^2-(xy)^{1/2}=2y^2+3x[/tex]
[tex]\dfrac{\mathrm d(x^2)}{\mathrm dx}-\dfrac{\mathrm d(xy)^{1/2}}{\mathrm dx}=\dfrac{\mathrm d(2y^2)}{\mathrm dx}+\dfrac{\mathrm d(3x)}{\mathrm dx}[/tex]
[tex]2x-\dfrac1{2(xy)^{1/2}}\left(\dfrac{\mathrm dx}{\mathrm dx}y+x\dfrac{\mathrm dy}{\mathrm dx}\right)=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-\dfrac1{2(xy)^{1/2}}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-\dfrac12\left(\dfrac yx\right)^{1/2}-\dfrac12\left(\dfrac xy\right)^{1/2}\dfrac{\mathrm dy}{\mathrm dx}=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-3-\dfrac12\left(\dfrac yx\right)^{1/2}=\left(4y+\dfrac12\left(\dfrac xy\right)^{1/2}\right)\right)\dfrac{\mathrm dy}{\mathrm dx}[/tex]
[tex]4x-6-\left(\dfrac yx\right)^{1/2}=\left(8y+\left(\dfrac xy\right)^{1/2}\right)\right)\dfrac{\mathrm dy}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x-6-\left(\frac yx\right)^{1/2}}{8y+\left(\frac xy\right)^{1/2}}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x(xy)^{1/2}-6(xy)^{1/2}-y}{8y(xy)^{1/2}+x}[/tex]
Plug in x = 4 and y = 1 to find that the tangent line's slope is 19/20.
Irving Manz works for Ben’s Food Mart. He is paid weekly on the basis of a 40-hour week at the rate of $8.95 an hour with time-and-a-half for overtime. During one week he works 49.5 hours. What was Irving’s time-and-a-half pay rate an hour?
Answers
Answer:
Irving earned about $363.00 during the week.
Step-by-step explanation:
Irving’s time-and-a-half pay rate an hour =$485.54
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
Payment for one hour = $8.95
So, paid for 40 hours
=40*$8.95
= $358.00
Now for -a-half overtime
=$8.95*1.5
= $13.425
Now, for extra 9.5 hours
=$13.425*9.5
=$127.5375
Hence, Irving’s time-and-a-half pay rate an hour
=127.5375+358.00
=$485.54
Learn more about unitary method here:
https://brainly.com/question/22056199
#SPJ2
There are 6 black marbles, 14 blue marbles, 8 white marbles,
and 12 clear marbles in a bag. If Andy chooses a second marble
without replacing the first marble, what is P(black, then clear)?
Answers
Answer:
3/65 = 0.046 = 4.6%
Step-by-step explanation:
Notice that the total number of marbles is:
6 + 14 + 8 + 12 = 40
Then , the probability of getting a black marble first is 6/40 = 3/20
Now, since the experiment is without replacing, he is left with a total of 39 marbles in the bag, and the probability of getting a clear one is now 12/39
The total probability is the product of these two:
(3/20) x (12/39) = 3/65 = 0.046 = 4.6%
Mickey used these calculations to find how much he would spend on 7 cartons of eggs, if 12 cartons of eggs cost $22.20. Describe his error.
12 cartons(÷22.20)
$22.22(÷22.20)
Unit price = $0.54
$0.54(7) = $3.78
Answer ; Mickey set up the equivalent rate wrong. The cartons of eggs should be in the denominator, because you need to find the unit price for 1 carton of eggs.
Answers
Answer: you would divide the total price of $22.20 by the amount of cartons, which is 12, giving you the unit rate of $1.85 per carton. the unit rate, $1.85 multiplied by 7 is $12.95, so it would cost $12.95 for 7 cartons of eggs
Step-by-step explanation:
Answer:
Step-by-step explanation:
the person up is right
The school athletic director had a budget of $500 to purchase 164 items
for the soccer team. She purchased vests for $2.50 each, soccer balls for
$9.25 each, and cones for $0.75 each. She purchased 40 more cones than
balls. How many of each item can purchase?
Answers
Answer: She purchased 72 cones, 32 balls, and 60 vests.
Step-by-step explanation:
The total number of items is 164.
The price of the vests is $2.50 each.
The price of the soccer balls is $9.25 each.
The price of the cones is $0.75 each.
The total budget was $500.
If V is the number of vests, B the number of balls, and C the number of cones, we have that:
V + B + C = 164.
V*$2.50 + B*$9.25 + C*$0.75 = $500.
and:
"She purchased 40 more cones than balls."
C = B + 40.
Then we have a system of 3 equations and 3 variables:
V + B + C = 164.
V*$2.50 + B*$9.25 + C*$0.75 = $500.
C = B + 40.
Here the first step is to replace the third equation into the other two, in this way we eliminate one variable and one equation:
V + B + (B + 40) = 164
V*$2.50 + B*$9.25 + (B + 40)*$0.75 = $500.
Now we want to isolate one variable in one of the equations, i will isolate V in the first equation:
V = 164 - 2*B - 40 = 124 - 2*B
Now i can replace this into the other equation:
(124 - 2*B)*$2.50 + B*$9.25 + (B + 40)*$0.75 = $500
Now let's solve this for B.
$310 - $5*B + B*$9.25 + B*$0.75 + $30 = $500
B*( $9.25 - $5 + $0.75) = $500 - $310 - $30
B*$5 = $160
B = 160/5 = 32
Now we know the value of B.
And by the equations above:
V = 124 -2*B = 124 - 2*32 = 60
C = B + 40 = 32 + 40 = 72.
Then:
She purchased 72 cones, 32 balls and 60 vests.
what is the smallest number that rounds to 30,000 why
Answers
Answer:
25000
Step-by-step explanation:
Because you round in thousands since the 5 is in the thousandths place.
To calculate 4 % tax on $63.78, multiply 4.2 times 63.78.
T
F
It’s true
Answers
Answer
False
Step-by-step explanation:
Cause i got it right on edge :)
Answer:
False
Step-by-step explanation:
you multiply .042 to 63.79 because 4.2 is the percentage.
Which of the following inequalities is graphed on the coordinate plane?
Answers
Answer: A
Step-by-step explanation:
This picture is very blurry, but the line appears to be a solid line. Since it is a solid line, it tells us that the inequality is ≤ or ≥. We can eliminate C and D. Now, the difference between A and B is the shading. Since the shading is showing that the numbers are increasing, we know that the inequality is ≥. Therefore, A is the correct answer.
Question 7
2 pts
If you bought something in Wyoming for $54, you would be charged $3.56 in state sales tax. What is the
state sales tax rate in Wyoming?
Insert your answer as a percentage to the tenth WITHOUT the % symbol.
Question 8
2 pts
Answers
Answer:
6.6
Step-by-step explanation:
The way to do this is to find the tax as a decimal. Worry about the 100 later.
54 * x = 3.56
Divide by 54
x = 3.56/54
x = .06593
Now use the 100
0.06592 * 100 = 6.593
But you want it rounded to the 1/10
So you should get 6.6 %
0.0605 in standard form?
Answers
Step-by-step explanation:
Actually 0.0605 is already in standard form and it can be expressed in scientific notations as given below.
[tex] \huge0.0605 = 6.05 \times {10}^{ - 2} \\ [/tex]
1.) (-18, -20) (18, 16)
2.) (-7, 14) (-11, 4)
3.) (-5, -4) (3, 9)
4.) (13, -8) (-9, -1)
Answers
1.) (-18, -20) (18, 16)
m= 1
2.) (-7, 14) (-11, 4)
m= 5/2
3.) (-5, -4) (3, 9)
m= 13/8
4.) (13, -8) (-9, -1)
m= -7/22
. Which table does NOT show y as a function of x?
I 름
4
1
A.
7
Х
10
14
9
9
11
y
18
17
15
16
110
90
B.
14
х
100
80
100
y
-0.2
1.0
-0.9
8.1
-1.3
4.4
C.
0.6
-3.7
Х
-0.2
5.8
y
29
24
21
-27
2.5
2.5
D.
- 24
Х
2.7
2.8
2.7
Y У
o
Answers
Katy is deciding which charity to donate to. She is going to donate fifty dollars to each charity chosen, and she can donate to a women's shelter (abbreviated B), a charity for rescue animals (abbreviated R), and a children's foundation (C). The dots in the Venn diagram below show the combinations that she can donate to. Let X be the event of donating fifty dollars each to two charities for a total of one hundred dollars. Let Y be the event of donating to the charity for rescue animals. Move the dots on the Venn diagram to place the dots in the correct event, X, Y,or X AND Y. Note that you might not use all of the dots.
Answers
Answer:
Step-by-step explanation:
A negative number divided by a negative number will result in a _ Quotient
Answers
Answer:
Positive
Step-by-step explanation:
Two negatives make a positive.
Six more than the product of three and a number
Answers
Answer:
6+3x
Step-by-step explanation:
A number will be given the variable x
So:
6+(3x)Answer:
3x + 6.
Step-by-step explanation:
The number is x.
Calculate the average speed between 0 s and 20 s
Answers
Answer:
2 m/s
Step-by-step explanation:
Notice that the slope of the time period from 0s to 20s is linear. This means we can simply look at the distance traveled over the amount of time. So the distance and time both start at 0. At 20s, the distance is 40m.
So we can say the following to find the slope:
(40m - 0m) / (20s - 0s) == 40m / 20s == 2 m/s
Hence, the average speed between 0s and 20s is 2m/s.
Cheers
After a 90% reduction, you purchase a new soft drink machine on sale for $64. What was the original price of the soft drink machine?
Answers
Answer:
$640
Step-by-step explanation:
Let [tex]x[/tex] equal the original price of the machine.
We know that $64 is 10% of [tex]x[/tex] because $64 is left of [tex]x[/tex] after the 90% reduction.
Set up an equation:
[tex].10x=64[/tex]
Divide by the coefficient of [tex]x[/tex], which in this case is [tex].10[/tex]
[tex]x=640[/tex]
13times the difference of a number n and 20 is 322. Write as an equation.
Answers
Answer:
13(n-20)=322
Step-by-step explanation:
13 times n-20 equals 322
Your friend says that in the number 45,951, one 5 is 10 times as great as the other 5. Is your friend correct? Expain.
Answers
Answer:
No.
Step-by-step explanation:
The friend is not correct because in this case one five is 100 times greater than the other, not 10.
Estimate the difference.
858.9 - 172
Use rounding to estimate the difference.
Answers
Answer:
can u answer my question plz
Step-by-step explanation: A kitchen wall tile is shaped like a parallelogram. The base of the tile is two times the height of the tile. The height of the tile is 2 in. The length of the other side of the tile is 3 in. What is the area of the tile?
A middle school has 2 girls for every 1 boy in seventh grade. The seventh-grade class
has 28 fewer students than the eighth-grade class, which has 298 students. How many
girls are in seventh grade?
Answers
Answer:
180 girls
Step-by-step explanation:
298-28=270
270 divided by 3 = 90
90+90 = 180
so there are 180 girls and only 90 boys
As a cube what is -1/64 ________ to the power of ^3
Answers
Answer:
(-1/64)= (-1/4)^3
Explanation:
[tex]\sqrt[3]{-\frac{1}{64} }=-\frac{1}{4}[/tex]
[tex](-\frac{1}{4})^3=-\frac{1}{64}[/tex]
¿Cuántas libras de café “La Finca” que se vende a $5 la libra debe mezclarse con 80 libras decafé común que se vende a $2 la libra, para hacer una mezcla que se venda a $3 la libra?
Answers
Answer:
Necesitamos agregar 40 libras del café La Finca
Step-by-step explanation:
Sea x el número de libras de café de La Finca a mezclar.
Entonces, la cantidad total de libras que obtendremos en la mezcla será (x + 80) libras.
Ahora trabajemos con los precios; Tenemos x libras de La Finca a $ 5 por libra, con 80 libras de café a $ 2 por libra para dar una mezcla de (x + 80) a $ 3 Así, sumaremos el precio de La Finca más la otra variante para llegar al costo de la nueva mezcla.
Matemáticamente;
5 (x) + 2 (80) = 3 (x + 80)
5x + 160 = 3x + 240
5x -3x = 240-160
2x = 80
x = 80/2 x = 40
I need help please
Answers
Answer:
Equal 15
Step-by-step explanation:
2+588(357)
4-136
Write an expression that is equivalent to 5(x + 2) - 7(x + 2)?
Answers
Answer:
-2x-4
Step-by-step explanation:
Just simplify
-2+10-14
-2x-4
work out the difference in minutes between 1 hour 25 minutes and 1 1/4 hours step by step please :)
Answers
[tex]\huge\boxed{\boxed{\bold{10\ \bftext{minutes}}}}[/tex]
[tex]\hrulefill[/tex]
First, let's change both of these times into just minutes. (We know that one hour is sixty minutes.)
[tex]\text{First time: } 1*60+25=60+25=85[/tex]
[tex]\text{Second time: } 1*60+\frac{1}{4}*60=60+15=75[/tex]
Now, just subtract:
[tex]85-75=\large\boxed{10}[/tex]
Define alternate interior angles
Answers
All lines parallel to y = 5x - 7 have a slope of
Answers
Answer:
5
Step-by-step explanation:
[tex]y = 5x - 5 \\ equating \: it \: with \\ y = mx + b \\ slope \: (m) = 5[/tex]
Parallel lines have same slope.
So, slope of required line = 5
Which pound bag is the lowest price per pound of dog food?
They are all the same cost per pound.
30
8
22