Answer:
The answer is A) 6 square yards.
Marty has 2 4/5 quarts of juice. He pours the same amount of juice into 2 bottles how much does he pour into each bottle ?
To know how much Marty pours into each bottle, divide the total juice amount by the number of bottles. His total of 2 4/5 quarts became 14/5 when turned into fifths for easier calculation. Dividing 14/5 by 2, we find that Marty pours 1 2/5 quarts into each bottle.
Explanation:Marty has 2 4/5 quarts of juice. He is trying to equally distribute this juice into 2 bottles. To find out how much juice each bottle will contain, we divide the total amount of juice by the number of bottles.
Given that 1 full quart is made up of 5 fifths, 2 quarts are equivalent to 2x5=10 fifths. Marty has 2 full quarts and 4/5 of a quart, which amounts to 10+4=14 fifths of a quart. So, Marty has 14/5 quarts of juice in total.
If he pours the same amount into 2 bottles, then each bottle will contain half of the total amount. To find this out, we divide the total amount by 2, which gives us 14/5 ÷ 2 = 7/5 quarts. Therefore, Marty pours 7/5 quarts or 1 2/5 quarts of juice into each bottle.
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Given the sets
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {0, 1, 4, 7, 9}, and B = {0, 4, 5, 6, 7}, use De Morgan's Laws to find the indicated set. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
(A' ∩ B)'
We used De Morgan's laws to find the complement of the set formed by the intersection of the complement of A and B. We first found the complement of A, then the intersection of this set with B, and finally took the complement of this new set.
Explanation:In set theory, De Morgan's laws relate the intersection and union of sets in a very elegant way. Here, (A' ∩ B)' represents the complement of the set formed by the intersection of the complement of A and B.
First, let's find A'. This is the set of all elements in U that are not in A. U = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } and A = { 0, 1, 4, 7, 9 } So, A' = { 2, 3, 5, 6, 8 }.
Now, let's find the intersection of A' and B, denoted by A' ∩ B. We have B = { 0, 4, 5, 6, 7 } so A' ∩ B = { 5, 6 }.
Finally, let's find the complement of this set, denoted by (A' ∩ B)'. This is the set of all elements in U that are not in A' ∩ B. So, (A' ∩ B)' = { 0, 1, 2, 3, 4, 7, 8, 9 }.
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ms.nenadal write 2×7=7×2 on the board. do you agree or disagree? draw arrays to help explain your thinking
It's accurate to say that 2×7 is not equal to 7×2, and the arrays provide a clear visual explanation of this mathematical concept.
Ms. Nenadal wrote 2×7 on the board, which is not equivalent to 7×2. The order of multiplication, as represented by the commutative property, states that changing the order of the factors does not change the product. In this case, 2×7 means adding 2 seven times, while7×2 means adding 7 two times.
Let's draw arrays to illustrate the difference:
For 2×7:
If we represent this as an array, it would have 2 rows and 7 columns, indicating 2 groups of 7.
Array for 2 × 7:
| * * * * * * * |
| * * * * * * * |
For 7×2:
On the other hand, 7×2 would be represented by an array with 7 rows and 2 columns, indicating 7 groups of 2.
Array for 7 × 2:
| * * |
| * * |
| * * |
| * * |
| * * |
| * * |
| * * |
While the product is the same (14) for both, the grouping and arrangement differ. Therefore, it's accurate to say that 2×7 is not equal to 7×2, and the arrays provide a clear visual explanation of this mathematical concept.
Evaluate cosθ if sinθ = [tex]\frac{ \sqrt{5} }{3} [/tex]
Jason's age is 1 2 of his brother's age. His brother's age can be represented by the expression 12a - 9. Write an expression that can be used to represent the sum of their ages. A) 12a - 5.5 B) 18a - 13.5 C) 18a + 21 Eliminate D) (12a-9) 2
Answer:
[tex]18a - 13.5[/tex]
Step-by-step explanation:
Jason's age is [tex]\frac{1}{2}[/tex] of his brother's age.
Brother age is [tex]12a-9[/tex]
Sum of their ages = Age of Jonson + age of his brother
Jonson's age = half of his brother age
[tex]Jonson's \ age=\frac{12a-9}{2}[/tex]
Sum of their ages =[tex]\frac{12a-9}{2}+12a-9[/tex]
Take common denominator 2
[tex]\frac{12a-9}{2}+\frac{24a-18}{2}[/tex]
[tex]\frac{36a-27}{2} [/tex]
[tex]18a - 13.5[/tex]
In discus competition an athlete threw the discus 63.37meters 62.95 meters and 63.7meters order the distance from least to greatest
which of these is a geometric sequence?
Solve the following system of equations.
4x + 5y = -2
4x + 3y = 10
x=?
y=?
The solution to the system of equations 4x + 5y = -2 and 4x + 3y = 10 is x = 7 and y = -6. This is done by using the elimination method.
Explanation:To solve this system of equations, you can use a method called elimination. The idea is to subtract the second equation from the first to eliminate one of the variables, allowing us to solve for the other.
Subtracting the second equation from the first gives you:
4x + 5y - (4x + 3y) = -2 - 10
This simplifies to: 2y = -12
So, y = -12 / 2 = -6
Then, substitute y = -6 into the first equation:
4x + 5(-6) = -2
This simplifies to 4x - 30 = -2, or 4x = 28
So, x = 28 / 4 = 7
So the solution to the system of equations is x =7, y = -6
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An open top box with a square base has a surface area of 100 square inches. express the volume of the box as a function of the length of the edge of the base. what is its domain?
Given:
An open-top box with a square base has a surface area of 100 square inches.
Question:
Express the volume of the box as a function of the length of the edge of the base. What is its domain?The Process:
Let the length of the edge of the base = x Let height = hPart-1: The surface area
Let us arrange the equation to get the surface area of the box with a square base. Recall that the box is without a lid and its surface area is 100 square inches.
[tex]\boxed{ \ Surface \ area = area \ of \ base + (4 \times area \ of \ rectangle) \ }[/tex]
[tex]\boxed{ \ x^2 + (4 \cdot x \cdot h) = 100 \ }[/tex]
[tex]\boxed{ \ x^2 + 4xh = 100 \ }[/tex]
From the above equation, we set it again so that "xh" is the subject on the left.
Both sides are subtracted by x².
[tex]\boxed{ \ 4xh = 100 - x^2 \ }[/tex]
Both sides are divided by 4.
[tex]\boxed{ \ xh = \frac{100 - x^2}{4} \ }[/tex] ... (Equation-1)
That is the strategy we have prepared.
- - - - - - - - - -
Part-2: The volume
[tex]\boxed{ \ Volume \ of \ the \ box = length \times width \times height \ }[/tex]
[tex]\boxed{ \ Volume = x \cdot x \cdot h \ }[/tex]
[tex]\boxed{ \ Volume = x^2h \ }[/tex] ...(Equation-2)
Substitution Equation-1 into Equation-2.
[tex]\boxed{ \ Volume = x(xh) \ }[/tex]
[tex]\boxed{ \ Volume = x \bigg( \frac{100 - x^2}{4} \bigg) \ }[/tex]
[tex]\boxed{ \ Volume = \frac{100x - x^3}{4} \ }[/tex]
[tex]\boxed{ \ Volume = 25x - \frac{1}{4}x^3 \ }[/tex]
Thus, an expression of the volume of the box as a function of the length of the edge of the base is [tex]\boxed{\boxed{ \ Volume = 25x - \frac{1}{4}x^3 \ }}[/tex]
- - - - - - - - - -
Part-3: The domain of volume
The value of volume must always be positive, i.e., V > 0.
[tex]\boxed{ \ 25x - \frac{1}{4}x^3 > 0 \ }[/tex]
Both sides are multiplied by 4.
[tex]\boxed{ \ 100x - x^3 > 0 \ }[/tex]
Both sides are multiplied by -1, notice the change in the sign of the inequality.
[tex]\boxed{ \ x^3 - 100x < 0 \ }[/tex]
[tex]\boxed{ \ x(x^2 - 100) < 0 \ }[/tex]
[tex]\boxed{ \ x(x - 10)(x + 10) < 0 \ }[/tex]
We get [tex]\boxed{ \ x = 0, \ x = 10, \ and \ x = - 10 \ }[/tex].
Since the values of x cannot be negative, x = -10 are promptly rejected. For x = 0 can be used as one of the domain limits.Consider the test of signs:
x(x - 10) (x + 10) is negative to the left of x = 10, and positive to the right of x = 10 on the number line.
Examples of tests:
[tex]\boxed{ \ for \ x = 2 \rightarrow 2(2 - 10)(2 + 10) < 0 \ }[/tex][tex]\boxed{ \ for \ x = 11 \rightarrow 11(11 - 10)(11 + 10) > 0 \ }[/tex]Remember this form above, [tex]\boxed{\ x(x - 10)(x + 10) < 0 \ }[/tex], the value of the test result must be negative (because < 0).
Thus, the domain of the volume is [tex]\boxed{ \ 0 < x < 10 \ }[/tex] or [tex]\boxed{ \ (0, 10) \ }[/tex]
Learn moreFind out the area of a cube https://brainly.com/question/12613605What is the volume of each prism? https://brainly.com/question/414021The volume of a rectangular prism https://brainly.com/question/11613210Keywords: an open-top box, with, a square base, has a surface area, 100 square inches, express, the volume, as a function, the length, edge, base, what, its domain, test of signs, substitution
The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $ 6 per pound with some Orange Pekoe tea that sells for $ 4 per pound to get 300 pounds of the new blend. The selling price of the new blend is to be $ 4.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?
The large rectangle's dimensions are three times the dimensions of the small rectangle. It is #60
A.)
B.)
C.)
D.)
I need help please
The large rectangle's dimensions are 3 times the dimensions of the small rectangle. If the small rectangle's dimensions are W for width and L for length, then the large rectangle's dimensions are 3W and 3L.
Explanation:The subject of this question is Mathematics, specifically relating to geometry and ratios. You're asked to compare two rectangles: a large one and a small one. The large rectangle's dimensions (both the width and length) are three times the dimensions of the small rectangle. Let's assume the dimensions of the small rectangle are W (width) and L (length). Then, the dimensions of the large rectangle would be 3W and 3L, respectively. This is because the large rectangle is three times the size of the small rectangle in both width and length.
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257.673 rounded to the nearest hundreth
what is the complement to a 32 angle
Solve for x. −23(3x−4)+3x=56
Answer: 6/11
Step-by-step explanation:
Open bracket
-69x+92+3x=56
Collect like term
-66x=-36
Divide both side by -66
x=6\11
If you interchange the coordinates of any point in Quadrant 2, in which quadrant would the new point be located?
The selling price for a classic car is $14000, which is $2500 less than three times its original price. What was the original price of the car?
The original price of the car was $5,500, which is derived from the mathematical equation based on the given information in the question.
Explanation:The subject of this question is algebra, a branch of mathematics. The question gives us the selling price of a classic car and tells us that this price is $2500 less than three times its original price. We're asked to find the original price. Let’s denote the original price by x.
According to the problem, 3x (three times the original price) minus $2500 equals the selling price ($14,000). So, if we set this up as an equation, it looks like this: 3x - $2500 = $14,000.
To solve for x (the original price), we first need to add $2500 to both sides of our equation, giving us 3x = $16,500. Then, we divide each side by 3 to solve for x, arriving at x = $16,500 ÷ 3 = $5,500. Therefore, the original price of the car was $5,500.
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Clarence solved the equation 3x + 15 = 33 and showed the following work. 3x + 15 = 33 3x + 15 - 15 = 33 3x = 33 = x = 11 Which of the following is true? x is 11. x should be 6. x should be 16. x should be 99.
Answer:
x=6
Step-by-step explanation:
Can someone help figure out how to solve this equation? Thank you!
There 20 people competing in a contest if first place earns $100, second place earns $50 and third place earns $25, How many ways can the three winners be selected?
a grain of sand has a diameter of 0.049 millimeters how do I write that in words
A bird of species A, when diving, can travel 6 times as fast as bird of species B top speed. if the total speeds for these to birds 231 miles per hour, find the fastest speed of the birds of species A and the fastest speed of the bird of species B
Renee hiked for 3 and 3/ 4 miles. After resting, Renee hiked back along the same route for 2 and 1 /4 miles. How many more miles does Renee need to hike to return to the place where she started? Represent your answer as a simplified mixed number, if necessary.
Which equation correctly applies the distributive property?
A.70+2.028=(70⋅2)+(70⋅0.02)+(70⋅0.008)
B.−2.5⋅0.6⋅5.8=−2.5⋅5.8⋅0.6
C. −1.5⋅(6⋅1.25)=(−1.5⋅6)⋅1.25
D.(0.7⋅0.7)+(0.7⋅0.9)+(0.7⋅0.2)=0.7⋅(0.7+0.9+0.2)
It's C.!!! hope this helps :D!
At a harvest 16 ears of corn are being picked for every 18 peppers if 9 peppers have been picked how many ears of corn have been picked(I need the actual math)
One third of the candidates for a job were 25 years old or younger. Two sevenths of the candidates were at least 50 years old. If 84 people applied for the job, how many were between 25 and 50?
1/3 * 84 = 28 were under 25
2/7 * 84 = 24 were at least 50
28 + 24 = 52
84-52 = 32 were between 25 and 50
Answer:
32 candidates are between 25 and 50.
Step-by-step explanation:
84 people applied for the job. [tex]\frac{1}{3}[/tex] of the candidates for a job were 25 years old or younger.
[tex]\frac{1}{3}[/tex] of 84 candidates = [tex]\frac{1}{3}[/tex] × 84 = 28 candidates
[tex]\frac{2}{7}[/tex] of the candidates were at least 50 years old.
[tex]\frac{2}{7}[/tex] of 84 candidates = [tex]\frac{2}{7}[/tex] × 84 = 24 candidates
age 25 and below + age 50 above = 28 + 24 = 52 candidates
Candidates between 25 and 50 = 84 - 52 = 32 candidates
32 candidates are between 25 and 50.
what is the slope of the line that passes through each pair of points A(-2, -4), B(2,4)
Prime factorization practice all factors 1.- 25 2.- 49 3.- 7 4.- 13 5.- 24 6.- 48 7.- 168
the absolute value of a number can be positive or negative true or false
Answer: False
Step-by-step explanation:
it’s just false I need points
g(x) = x3 + 6x2 + 12x + 8
Determine the function’s value when x = −1.
Imagine a sphere. if the sphere is cut three times at right angles, the resulting pieces would be what fraction of the original sphere?
How to write 5x923 in expanded form