1/8 of the toys in a play area are yellow, and 1/4 are green. 3/5 of the remainder are red. The rest of the toys are blue. If there are 100 green toys, how many blue toys are there?
A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To figure out what fraction of the toys are blue, we need to convert all of the fractions to have a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
Looking at the fractions, we can see that there are 3 fractions, \(\frac{1}{8}, \frac{1}{4}\) and \(\frac{3}{5}\).
To solve for the common denominator between \(\frac{1}{8}\) and \(\frac{3}{5}\), we first multiply the denominators, 8 and 5.
8 × 5 = 40We now know that the denominator is going to be 40.
\(\frac{?}{40} \frac{?}{40}\)To get the numerators, we can use these equations:
1 × 5 = 58 × 3 = 24The new fractions look like this:
\(\frac{5}{40} \frac{24}{40}\)To easily convert the last fraction (\(\frac{1}{4}\)) we can multiply the numerator and denominator by 10.
1 × 10 = 104 × 10 = 40Why do we multiply by 10?We multiply by 10 because the denominator, which is 4, can be multiplied by 10 to get our common denominator of 40.
Now, we have our 3 fractions converted to have common denominators.
(\(\frac{5}{40}, \frac{24}{40}\) and \(\frac{10}{40}\))
(Yellow, red, and green)
We can now add these up and see what fraction of blue is remaining.
\(\frac{5}{40}+ \frac{24}{40}+ \frac{10}{40} =\frac{39}{40}\)\(1 - \frac{39}{40} = \frac{1}{40}\)Therefore, the fraction of blue toys compared to the total amount is \(\frac{1}{40}\).
If there are 100 green toys resulting in \(\frac{10}{40}\) of all the toys, we can divide 100 by 10 to get the number of blue toys.
Why do we divide by 10?We divide by 10 because \(\frac{1}{40}\) is only \(\frac{1}{10}\) of \(\frac{10}{40}\), meaning we divide by 10.
100 ÷ 10 = 10Therefore, there are 10 blue toys.
Answer:
1/4=100
10/40=100
40/40=400
1/8=400/8=50
3/5=400/5*3=240
400-100-50-240=10
10 of the toys are blue
Hope this helped!!
Step-by-step explanation:
What expression is equivalent to 1/4(8-6x+12)?
A) 7/2x
B)-13/2x
C)-6x+14
D)-3/2x+5
Simplify (2^3)^–2.
A: -1/64
B: 1/64
C: 2
D: 64
Answer:
B: 1/64
Step-by-step explanation:
2^3 = 8
8^(-2)=1/(8^2)=1/64
Given that
5x:9=7:3
Calculate the value of
x
Answer:
x = 4.2Step-by-step explanation:
Given 5x:9=7:3 To findThe value of xSolution5x:9=7:3 5x = 7*9/35x = 7*35x = 21x = 21/5x = 4.2Answer:
4.2
Step-by-step explanation:
5x:9=7:3
5x/9=7/3
5X×3=7×9
15x=63
X=63/15
X=4.2
So the value of the X is 4.2
HELP PLEASE!!
Quadrilateral CDEF is a rhombus. What is m
Answer:
∠ BDC = 29°
Step-by-step explanation:
the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then
∠ BCD = ∠ BED = 61°
• the diagonals are perpendicular bisectors of each other , then
∠ CBD = 90°
the sum of the 3 angles in Δ BCD = 180°
∠ BDC + ∠ CBD + ∠ BCD = 180°
∠ BDC + 90° + 61° = 180°
∠ BDC + 151° = 180° ( subtract 151° from both sides )
∠ BDC = 29°
A survey asks 184 people "What beverage do you drink in the morning?", and offers choices:
• Coffee only
• Tea only
• Both tea and coffee
• Neither tea nor coffee
Suppose 52 report tea only, 44 report coffee only, and 68 report both.
what is the question?
A bag contains two red marbles, four green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?
There are 2518 sets of five marbles that include either the lavender one or exactly one yellow one, but not both.
To solve this problem, we need to find the number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both colors. Here's one way to approach the problem:
Number of sets of five marbles that include the lavender one: There is only one lavender marble, so we can choose any 4 other marbles to go with it.
There are a total of 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.
This gives us a total of 7 x 6 x 5 x 4 = 840 possible sets of five marbles that include the lavender one.
Number of sets of five marbles that include exactly one yellow one: There are two yellow marbles,
So there are 2 possible choices for the yellow marble. For each choice, we can choose any 4 other marbles to go with it.
As before, there are 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.
This gives us a total of 2 x (7 x 6 x 5 x 4) = 1680 possible sets of five marbles that include exactly one yellow one.
Number of sets of five marbles that include both the lavender one and exactly one yellow one:
We need to subtract these sets from the total number of sets that include either the lavender one or exactly one yellow one.
We have already found that there are 840 sets of five marbles that include the lavender one, and 1680 that include exactly one yellow one.
To find the number of sets that include both, we can choose any one yellow marble and the lavender one.
There are 2 choices for the yellow marble and 1 choice for the lavender one,
So there are 2 x 1 = 2 possible sets of five marbles that include both the lavender one and exactly one yellow one.
Number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both:
Finally, we need to subtract the number of sets that include both the lavender one and exactly one yellow one from the total number of sets that include either the lavender one or exactly one yellow one.
The total number of sets that include either the lavender one or exactly one yellow one is 840 + 1680 = 2520. The number of sets that include both is 2,
So the number of sets that include either the lavender one or exactly one yellow one, but not both, is 2520 - 2 = 2518.
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Dewan’s bank account balance is -$16.75. He deposits checks totaling $23.59. What is his new balance? -$1.08
Answer:
$6.84
Step-by-step explanation:
This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.
Original balance: -$16.75Deposit: $23.59New balance: -$16.75 + $23.59 = $6.84
If you could exactly afford either 2 units of x and 7 units of y, or 4 units of x and 3 units of y, then if you spent all of your income on y, how many units of y could you buy?
Answer:
11 units of y
Step-by-step explanation:
Let total income be I
We have the two equations
2x + 7y = I (1) (exactly afford 2 units of x and 7 units of y)
4x + 3y = I (2) (exactly afford 42 units of x and 3 units of y)
Multiply (1) by 2
==> 2(2x + 7y) = 2 x I
==> 4x + 14y = 2I (3)
Subtract (2) from (3)
(3) - (2)
==> 4x + 14y - (4x + 3y) = 2I - I
==> 4x + 14y - 4x - 3y = 2I
==> 14y - 3y = I (x terms cancel)
==> 11y = I
This represents an equation where if you buy 11 units of y, it will be your whole income
Answer: 11 units of y
Which of the following quantities are inversely proportional? WILL GIVE BRAINLIEST AND 25 POINTS
a
The number of hours worked and the amount of money earned, assuming the worker is paid by the hour
b
The height of a rectangular fish tank and the area of its base, if the volume is constant
c
The amount of candy purchased for $25.50 and the price per pound
d
The time it takes to use a 5 lb bag of dry cat food and the number of cats, if each cat eats the same amount of food per same time interval.
Answer:
I believe the answer is D
Step-by-step explanation:
Inverse proportion occurs when one value increases and the other decreases
D is the answer because as each cat eats the same amount of dry cat food, there is less dry cat food in the bag; so this is why D best answers the question.
Hope this helps!
Answer:
a is false, B is true,
Step-by-step explanation:A is false because the more hours you work, the more money you get.
B is true because if the volume is constant, the bigger the length, the smaller the width, or vice versa.
Solve for the percentage in the problem. Round to the nearest tenth of a percent.
$953 is _____% of $1717
Select one:
O a. 0.6
O b. 0.1
O c. 180.2
O d. 55.5
PLZ HURRY GOT 10 MINS LEFT
Answer:
6 units
Step-by-step explanation:
Both units lie on the -5 x-axis, so you only have to look at the difference in the y-axis. Going from -2 to -8 is a 6 unit difference.
Hope this helps :)
Find y' for y = 7x-5 + 2x - 1
y'=
Answer:
9
Step-by-step explanation:
7x-5+2x-1=9x-6
d/dx (9x-6)=9
ALGEBRA please put a very small explanation to the awnser
Certainly! The problem can be solved using the Pythagorean theorem,
which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.
The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.
By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.
Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.
We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.
Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.
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A builder makes drainpipes that drop 1 cm over a
horizontal distance of 30 cm to prevent clogs. See the
diagram below, which is not drawn to scale:
A certain drainpipe needs to cover a horizontal distance
of 700 cm
What is the length l of this drainpipe?
Round your answer to the nearest tenth of a centimeter
cm
Answer:
700.4 cm
Step-by-step explanation:
This involves two similar triangles.
Both triangles are right triangles.
One has legs measuring 1 cm and 30 cm. We can find the hypotenuse by using the Pythagorean theorem.
(1 cm)^2 + (30 cm)^2 = c^2
c^2 = 901 cm^2
c = sqrt(901) cm
The second triangle has one leg with length 700 cm. This leg corresponds to the 30-cm leg in the other triangle. Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [sqrt(901) cm]/x
3/70 = sqrt(901) cm/x
3x = 70 * sqrt(901) cm
x = 70 * sqrt(901) cm/3
x = 700.4 cm
Answer: 700.4 cm
The length of drainpipe is 700.4 cm.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
One has legs measuring 1 cm and 30 cm.
Using Pythagorean theorem.
(1 cm)² + (30 cm)² = c²
c² = 901
c =√901 cm
Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [√(901) cm]/x
3/70 = √(901) cm/x
3x = 70 x √(901) cm
x = 700.4 cm
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Which statement is true?
24 – 15 × 4 – 3 × 2 = 30
24 – 15 × (4 – 3) × 2 = 30
(24 – 15) × 4 – 3 × 2 = 30
(24 – 15) × 4 – 3 × 2 = 66
Answer:
I belive its
24 – 15) × 4 – 3 × 2 = 66, the last one.
If it's wrong please correct me! Hope this can help!
Answer:
i know if its not the correct one but for me its
(24−15)×4−3×2=30
Choose the best answer to explain whether the question is statistical or not statistical. How far from work does Jeremy live?
Answer:
not statistical
Step-by-step explanation:
Find the coefficients of the polynomial with a leading coefficient of: one, and roots: zero, nine, and nine.
x^3+__x^2 +81x+__
\(zeros \begin{cases} x=0\implies &x=0\\ x=9\implies &x-9=0\\ x=9\implies &x-9=0 \end{cases}\qquad \implies a(x)(x-9)(x-9)=\stackrel{y}{0} \\\\\\ \stackrel{\textit{with a coefficient of 1}}{1(x)(x-9)(x-9)=y}\implies x(x-9)^2=y\implies x(x^2-18x+81)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^3-18x^2+81x=y \end{array}}~\hfill\)
PLS HELP WITH GEOMETRY HW ASAP(show work)
Here
A=B=1 and C=-1Q(2,6) is the pointDistance
\(\\ \rm\Rrightarrow \dfrac{|Ax+By+C|}{\sqrt{A^2+B^2}}\)
\(\\ \rm\Rrightarrow \dfrac{|1(2)+1(6)-4|}{\sqrt{1+1}}\)
\(\\ \rm\Rrightarrow \dfrac{8-4}{\sqrt{2}}\)
\(\\ \rm\Rrightarrow \dfrac{4}{\sqrt{2}}\)
\(\\ \rm\Rrightarrow 2\sqrt{2}units\)
Find the rate of change (slope) for the given table
a -1/4
b -4
c 1/4
d 4
Solve -12 = z3 for z.
Answer:
If you meant -12=3z, then the answer would be -4.
Step-by-step explanation:
Answer:
-4 is z :)
Step-by-step explanation:
Maine has a cold climate in the winter. What is the probability of the temperature falling below 32 Fahrenheit in Maine during the month of January.
The probability is closer to one than zero.
Probability theory is used to analyze and predict the likelihood of events happening in various fields such as statistics, gambling, physics, finance, and more. It allows us to make informed decisions based on the likelihood of different outcomes. In probability theory, the total number of possible outcomes is important to determine the probability of a single event occurring. By comparing the favorable outcomes to the total outcomes, we can calculate the probability of an event happening.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes, i.e {(H, H), (H, T), (T, H), (T, T)}.
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840,000 rounded to the nearest hundred thousand
Answer:
800,000
Step-by-step explanation:
You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
The coordinate of the point after transformation is: (3, -4)
What is the coordinate after moving of point?The coordinate initially is given as (0, -4).
Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:
(0 - 1, -4)
= (-1, -4)
Moving by 4 units to the right means an addition of 4 units to x coordinate to get:
(-1 + 4, -4)
= (3, -4)
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On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance
traveled in miles, d,to the number of hours flying, t,is t=(1/500) d. How many miles did it cover in 2 hours?
A: 200 miles
B: 1 3/5 miles
C:1000 miles
D:10,000 miles
Answer:
I know i am 5 days late but the answer is C: 1000 miles!
Step-by-step explanation:
if the distance traveled in miles was 500 in just 1 hour, this would mean you have to add another 500 to equal to 2 hours.
500+500=1000
Makayla’s local movie theater has a moviegoer club. The charts in the annual registration fee of $25. However movie tickets are discounted remembers at six dollars per ticket instead of the regular nine dollars per ticket. Let him represent the number of movie tickets Makayla’s purchase a need to write a function tomorrow the amount of money Makayla spent going to the movies doing the club
Answer:
m = 25 + 6n
Step-by-step explanation:
To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.
According to the Centers for Disease Control
and Prevention, kids should get
at least 10 minutes of exercise each day
at least 30 minutes of exercise each day
at least 60 minutes of exercise each day
Dat least 3 hours of exercise each day
According to the Centers for Disease Control
and Prevention, kids should get C) at least 60 minutes of exercise each day.
What's exerciseExercise is a movement activity that has an important role for health. With exercise, one's body becomes healthier and stronger. Not only maintaining physical health, exercise also affects spiritual health.
The aim of exercise is to improve one's health. In addition to improving physical fitness, exercise can also improve and improve the performance of the human brain so that it can work more optimally. Therefore, exercise is considered to be able to increase one's self-confidence.
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9. Difference between the place values of "1" in 3116365 is
Which of the following z-scores is NOT outside the middle 68% of the data for a normal distribution?
a.) -0.8
b.) -2.8
c.) 1.8
d.) 3.8
Answer:
Step-by-step explanation:
A, use three_digite rounding arithmetic to compute 13- 6 and determine the absolute,relative ,and percentage errors.
tepeat part (b) using three – digit chopping arithmetic.
PLZ HELP ASAP NO LINKS AND NO STEALING POINTS OR ELSE I WILL REPORT IT HAS TO BE AN IMPROPER FRACTION.
Answer:
Hello Love!
8 ÷ 3/5 = 13 1/3 sense thats a mixed fraction I'll convert it and it converts to 13 x 3 + 1 = 40 so 40/3 is our answer