A bucket contains 72 red, 48 blue, 48 green, and 48 yellow crayons. The art teacher also has 120 pieces of drawing paper. What is the largest number of identical kits the art teacher can make with all of the crayons and all of the paper?
The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.
To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.
The GCD represents the largest number that can divide all the quantities without leaving a remainder.
The GCD of the quantities of crayons can be found by considering the prime factorization:
72 = 2³ × 3²
48 = 2⁴ × 3
48 = 2⁴ × 3
48 = 2⁴ × 3
The GCD of the crayons is 2³ × 3 , which is 24.
Now, we need to find the GCD of the quantity of drawing paper:
120 = 2³ × 3 × 5
The GCD of the drawing paper is also 2³ × 3 , which is 24.
Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.
Each kit would contain an equal distribution of crayons and drawing paper.
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Graph the image of the quadrilateral below
using a scale factor of k= 2/3, using the
origin as the center of dilation.
Thus, the image after the dilation of scale factor of 2/3 with origin for quadrilateral CDEF the are C'(0,0), D'(2, 4), E'(6, 6), F'(15, 3).
Explain about the scale factor:The ratio between comparable dimensions of an object and a representations of that object is known as a scale factor in mathematics. The copy will just be larger if the scaling factor comprises an entire number. A fractional scaling factor means that the duplicate will be smaller.
Scaling up requires a scale factor that is bigger than 1.Scaling down requires a scale factor that is smaller than 1.For the given coordinates quadrilateral CDEF, to find the coordinates of the image after the dilation of 2/3 with origin are-
Multiply each coordinate with 2/3:
C' - C(0*2/3,0*2/3) = C'(0,0)D' - D(3*2/3, 6*2/3) = D'(2, 4)E' - E(9*2/3, 9*2/3) = E'(6, 6)F' - F(15*2/3, 3*2/3) = F'(15, 3)Thus, the image after the dilation of scale factor of 2/3 with origin for quadrilateral CDEF the are C'(0,0), D'(2, 4), E'(6, 6), F'(15, 3).
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(d) State any two(2) properties of a semiconductor material.
Answer:
Semiconductors are somewhere in-between conductors and insulators. This means that they are specific when it comes to conducting electricity meaning that their conduction of electricity varies based on their condition at the time.
For instance, they can conduct electricity when heated.
Properties:
1. Perfect insulator at Absolute Zero.
As mentioned above, semi conductors are better at conducting electricity when they are heated. At Absolute zero - the lowest temperature possible - therefore, these materials would conduct absolutely no electricity thereby making them perfect insulators.
2. More resistance than Conductors but less than Insulators
As mentioned above, they have properties in-between those of insulators and conductors. One of those is their resistance. They can resist more than conductors but less than insulators.
Complete the statement. If a transversal intersects two parallel lines, then ___.
a. Same-side interior angles are complementary,
b. alternate interior angles are congruent
c. Corresponding angles are supplementary
d. none of these
Answer:
alternate interior angles are always congruent.
Step-by-step explanation:
- Consecutive [Same-side] exterior angles are always supplementary.
- Consecutive [Same-side] interior angles are always supplementary.
- Corresponding angles are always congruent.
I am joyous to assist you anytime.
Answer:
B
Step-by-step explanation:
If a transversal intersects two parallel lines, then alternate interior angles are congruent. If a transversal intersects two parallel lines, then same-side interior angles are supplementary. ... If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.
NO LINKS!! Please help me with the Domain and Range part 4ii
Answer:
9) D: (-4, 4]; R: [-6, -4]
10) D: [-5, -5]; R: (-7, ∞)
Step-by-step explanation:
You want the domain and range of the relations shown on the given graphs.
DomainThe domain of a relation is the set of x-values for which it is defined. An open circle indicates that point is not included in either the domain or range.
RangeThe range of a relation is the set of y-values that the relation produces. An open circle indicates the y-value at that point is not in the range.
9)The graph has an open circle at x = -4 on the left, and a solid dot at x = 4 on the right. All of the x-values between these have corresponding y-values.
The domain is (-4, 4].
The bottom (minimum) of the curve lies on the line y = -6, so that is the lowest value in the range. The relation produces all y-values between -6 and -4. The solid dot at (4, -4) means -4 is included in the range.
The range is [-6, -4].
10)The vertical line at x=-5 means -5 is the only value in the domain.
The domain is [-5, -5].
The vertical line extends upward from an open circle at y = -7. The open circle means -7 is not part of the range.
The range is (-7, ∞).
Answer:
9) Domain: (-4, 4]
Range: [-6, -4]
10) Domain: [-5]
Range: (-7, ∞)
Step-by-step explanation:
Definitions
An open circle indicates the value is not included in the interval.
A closed circle indicates the value is included in the interval.
An arrow shows that the function continues indefinitely in that direction.
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.
[ or ] : Use square brackets to indicate that the endpoint is included.
Domain & Range
The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 9From inspection of the graph, the minimum x-value is x = -4 and the maximum x-value is x = 4.
There is an open circle at endpoint (-4, -4). Therefore, x = -4 is not included in the domain.
There is an closed circle at endpoint (4, -4). Therefore, x = 4 is included in the domain.
Therefore, the domain of the relation is restricted: (-4, 4]
From inspection of the graph, the minimum y-value is y = -6 and the maximum y-value is y = -4.
This maximum value is included in the range since there is a closed circle at (4, -4).
Therefore, the range of the relation is restricted: [-6, -4]
Question 10From inspection of the graph, the line is a vertical line at x = -5.
Therefore, the domain of the relation is restricted to x = -5: [-5]
From inspection of the graph, the minimum y-value is x = -7.
This minimum value is not included in the range since there is an open circle at (-5, -7).
There is an arrow on the other endpoint of the line, indicating that the line continues indefinitely in that direction.
Therefore, the range of the relation is restricted: (-7, ∞)
stered comsident p43336280840
Save the expression by solating the variable Hemember to balance the equation in each step you take
2
0-6
The result of the expression 20 - 6 is 14.
To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.
Step 1: Start with the given expression, 20 - 6.
Step 2: Evaluate the subtraction operation: 20 - 6 = 14.
Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.
This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.
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A case of woods screws wieghs 18 2/3 pounds.each individual box of woods screws wieghs 1 1/3 pounds. How many individual boxes of wood screws are in the case?
A. 5
B. 9
C. 14
D. 20
17 is what percent of 20?
Answer: 85% or 17/20
Step-by-step explanation: Ok, so 17 being what percent of 20 is 17/20. Then, simply divide from there to get 0.85, also known as 85%.
What the answer for 7 x 44 (62 - 47)?
Based on the data shown below, calculate the correlation coefficient (to three decimal places)
Х
3
4
5
6
7
8
9
10
у
100. 2
93
91. 6
89. 4
86. 6
81. 6
82. 2
82. 4
T=
Question Help: D Post to forum
The correlation coefficient is -0.4124
How to determine the correlation coefficientFrom the question, we have the following parameters that can be used in our computation:
The table of values
Next, we enter these values in a graphing tool, where we have the following summary
X Values
∑ = 52
Mean = 6.5
∑(X - Mx)2 = SSx = 42
Y Values
∑ = 93
Mean = 11.625
∑(Y - My)2 = SSy = 7567.875
X and Y Combined
N = 8
∑(X - Mx)(Y - My) = -232.5
For the coefficient, we have
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -232.5 / √((42)(7567.875)) = -0.4124
Hence, the value is -0.4124
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You had $22 to spend on four raffle tickets. After buying them you $6 left. How much did each raffle ticket cost?$
Answer:
Each raffle ticket costs $5.50.
Step-by-step explanation:
☆We can use proportion to solve this!
\( \frac{22 \: dollars}{4 \: tickets} = \frac{x}{1 \: ticket} \\ \\ \frac{4x}{4} = \frac{22}{4} \\ \\ x = 5.5\)
A piece of material measures 38 inches. Courtney cuts the piece of material into two pieces. One piece measures 19 inches. Write an addition equation that could be used to find the length, m, of the other piece of material.
Answer:
As a whole, the piece first measured 38 inches. No matter how many times you cut it, all of the pieces will still add up to 38 inches. You know that 19 inches is the length of one of the two pieces, so all you need to find is the other unknown piece. Add the two together, with m being the unknown length.
19+m=38
If you want to solve the equation, just subtract 19 from both sides.
19+m=38
m=19
If 10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the
The amount that would be in the savings account after 5 years given the annual interest and the amount deposited is $ 11, 204. 13
How to find the value of the account ?The value of the savings account in 5 years can be found by the future value formula which is :
= Amount deposited x ( 1 + rate ) ^ number of years
Amount deposited = $ 10, 000
Rate = 2. 3 %
Number of years = 5 years
The value in five years is then :
= 10, 000 x ( 1 + 2. 3 % ) ⁵
= 10, 000 x 1.120413075641343
= $ 11, 204. 13
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The full question is:
If 10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the amount in the account be valued in 5 years ?
Which sum or difference is modeled by the algebra tiles
Answer:
i believe the answer that you picked is right ....i think ^^
10 liters to quarts (Round answer to the nearest hundredth)
Answer:
10.56 quarts
Step-by-step explanation:
10.5669 quarts
10.56 quarts
Which statement is true about the algebraic expression 450 −15t?
A student has 450 marbles. Each of their t friends gives them 15 marbles. The expression represents the total marbles the student has.
A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
A student has 450 marbles. They give t marbles to one of their friend and 15 marbles to another. The expression represents the total marbles the student is left with.
A student has 450 marbles. One of their friends gives them t marbles and another friend gives them 15 marbles. The expression represents the total marbles the student has.
PLEASE HELP I'M SOOO CONFUSED
The statement that is true about the algebraic expression 450 −15t is B. A student has 450 marbles. They give t marbles to each of their 15 friends. The expression represents the total marbles the student is left with.
What is the definition of an algebraic expression?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
In this case, when a student has 450 marbles. They give t marbles to each of their 15 friends.
The expression represents the total marbles the student is left with will be:
= 450 - (15 × t)
= 450 - 15t
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400 Suppose a particular surveillance system has a 99% chance of correctly identifying a future terrorist and a 99.8% chance of correctly identifying someone who is not a future terrorist. If there are 1,000 future terrorists in a population of 400 million, and one of these 400 million is randomly selected, scrutinized by the system, and identified as a future terrorist, what is the probability that he/she actually is a future terrorist
Answer:
1.236 × 10^(-3)
Step-by-step explanation:
Let A be the event that the person is a future terrorist
Let B the event that the person is identified as a terrorist
We are told that there are 1,000 future terrorists in a population of 400 million. Thus, the Probability that the person is a terrorist is;
P(A) = 1000/400000000
P(A) = 0.0000025
P(A') = 1 - P(A)
P(A') = 1 - 0.0000025
P(A') = 0.9999975
We are told that the system has a 99% chance of correctly identifying a future terrorist. Thus; P(B|A) = 0.99
Thus, P(B'|A) = 1 - P(B|A)
P(B'|A) = 1 - 0.99
P(B'|A) = 0.01
We are told that there is a 99.8% chance of correctly identifying someone who is not a future terrorist. Thus; P(B'|A') = 0.998
Hence: P(B|A') = 1 - P(B'|A')
P(B|A') = 1 - 0.998
P(B|A') = 0.002
We want to find the probability that someone who is identified as a terrorist, is actually a future terrorist. This is represented by: P(A|B)
We can find it from bayes theorem as follows;
P(A|B) = [P(B|A) × P(A)]/[(P(B|A) × P(A)) + (P(B|A') × P(A')]
Plugging in the relevant values;
P(A|B) = [0.99 × 0.0000025]/[(0.99 × 0.0000025) + (0.002 × 0.9999975)]
P(A|B) = 0.00123597357 = 1.236 × 10^(-3)
Rewrite the expression without using a negative exponent.
Hello!
Recall the Properties of Exponents:
\(\bold{a^{-m}\displaystyle\frac{1}{a^m}}\)
Solve:
\(\bold{\displaystyle\frac{1}{2y^{-2}}}\)
Flop it over:
\(\bold{2y^2}\)
And we're done! :-)
Hope everything is clear.
Let me know if you have any questions!
#KeepOnLearning
Hey there!
Answer:
\( \rightarrow \: \boxed{ \sf{ \frac{1}{2y {}^{ - 2}} } } \: \sf{ \rightarrow \frac{y {}^{2} }{2}} \\ \)
Solving steps
\( \rightarrow \: \boxed{\sf{ \frac{1}{2 {y}^{ - 2} } }} \rightarrow \sf{ \frac{1}{2 \times \frac{1}{ {y}^{2} } } } \: \rightarrow \: \sf{ \frac{1}{ \frac{2}{y {}^{2} } } } \rightarrow \sf{ \frac{ {y}^{2} }{2} }\)
Please help with this equation:
4.5(8-x)+36=102-2.5(3x+24)
answer
x=14
Step-by-step explanation:
4.5(8-x)+36=102-2.5(3x+24)
36-4.5x+36=102-7.5x-60
-4.5x=42-7.5x
7.5x-4.5x=42
3x=42
x=42/3
x=14
Solve the inequality below
-8x + 4 > 20
Include x and number in answer
Answer:
x<-2
Step-by-step explanation:
You first subtract 4 from both sides. Then you divide both sides by -8 (note: when you multiply or divide by a negative the sign flips. Then you get your answer
I need help with this question
Let:
\(\begin{gathered} B=(3,2) \\ B^{\prime}=(-2,-2) \\ \end{gathered}\)After a translation 5 units left
\(B\to(3-5,2)\to(-2,2)\)and after a reflection across the x-axis:
\(B\to(x,-y)\to(-2,-2)\)3. Higher Order Thinking The
lengths of the pencils are
given at the right.
Write and solve a two-step
problem about the pencils.
6 cm
8 cm
10 cm
The lengths of the three pencils form a right-triangle, and the two-step problem is:
6^2 + 8^2 = 10^2100 = 100How to write the two-step problemThe lengths of the pencils are given as:
6cm, 8cm and 10cm
Using the Pythagoras theorem, we have:
6^2 + 8^2 = 10^2
Evaluate the exponents
100 = 100
Hence, the lengths of the three pencils form a right-triangle
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find all the zeros in the indicated finite field of the given polyomial with coefficients in that field x^5 3x^3 x^2 2x
Answer:
The answer is "Zeros are 0 and 4".
Step-by-step explanation:
Given equation:
\(\to x^5+3x^3+x^2+2x\)
applying the by direct verification:
\(\to \phi_{0} (x^5+3x^3+x^2+2x) =0^5+3 \cdot 0^3+0^2+2 \cdot 0 \\\\\)
\(= 0 \ mod \ 5 \\\\\)
\(\to \phi_{1} \ (x^5+3x^3+x^2+2x) =1^5+3 \cdot 1^3+1^2+2 \cdot 1 \\\\\)
\(= 1+3+1+2 \ mod \ 5 \\\\ = 2 \ mod \ 5\)
\(\to \phi_{2} \ (x^5+3x^3+x^2+2x) =2^5+3 \cdot 2^3+2^2+2 \cdot 2 \\\\\)
\(= 2+4+4+4 \ mod \ 5 \\\\ = 4 \ mod \ 5\)
\(\to \phi_{3}\ (x^5+3x^3+x^2+2x) =3^5+3 \cdot 3^3+3^2+2 \cdot 3 \\\\\)
\(= 3+1+4+1 \ mod \ 5 \\\\ = 4 \ mod \ 5\)
\(\to \phi_{4} \ (x^5+3x^3+x^2+2x) =4^5+3 \cdot 4^3+4^2+2 \cdot 4 \\\\\)
\(= 4+2+1+3 \ mod \ 5 \\\\ = 0 \ mod \ 5\)
Latoya took a piece of wood 13 - inches long and sawed off a piece measuring a inch. what is the length remaining.
Answer: 12 Inches
Step-by-step explanation: If the wood is originally 13 inches and the piece sawwed off was one inch, then 13-1=12 Inches.
x^2=-28 square root method
Answer:
2i\(\sqrt{7}\),-2i\(\sqrt{7}\)
how do I solve this screen shot
Answer:
add me as a friend and give me thanks
Step-by-step explanation:
the answer is A for sure
3/4 + (1/3 divide 1/6) - (- 1/2)=
Answer:
Step-by-step explanation:
3.25 or 13/4
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. Which statement best describes the meaning of one of the bars in the histogram? O 110 snacks have between 100 and 120 mg of sugar O 110 snacks have 7 mg of sugar. O 7 snacks have about 110 mg of sugar. O The largest number of snacks have 12 mg of sugar
The correct answer is option A. 110 snacks have between 100 and 120 mg of sugar.
A bar in a histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar. So, the statement that best describes the meaning of one of the bars in the histogram is: 110 snacks have between 100 and 120 mg of sugar.
In summary, the bar in the histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar.
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Please help quick I need it
The area of the composite figure is 122.24 units².
How to find the area of a composite figure?The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.
Hence,
area of the composite figure = area of the rectangle + 2(area of semi circle)
Therefore,
area of the composite figure = 9 × 8 + 2(1 / 2 πr²)
area of the composite figure = 72 + πr²
where
r = 8 / 2 = 4 units
Therefore,
area of the composite figure = 72 + 3.14 × 4²
area of the composite figure = 72 + 3.14 × 16
area of the composite figure = 72 + 50.24
area of the composite figure = 122.24 units²
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What is the area of a rectangle
7 inches long and 3 inches wide?
Answer:
21
Step-by-step explanation:
you do 7x3