Answers
- Small bottles can hold 2/5 L of vinegar
- Containers hold 5 L of vinegar
The question asks us specifically about the case where we have 3 containers; together, their volume totals to 3 x 5 = 15 L of vinegar.
We're asked to find the number of 2/5 L bottles we can make from those 15 L, or in other words, we're being asked to divide the 15 L up into 2/5 L portions. The math question at the core of this is really 15 ÷ 2/5.
If you have much familiarity with division by fractions, you might know that dividing by a fraction is the same as multiplying by its reciprocal. In this case, the reciprocal of 2/5 is 5/2, so 15 ÷ 2/5 is the same as 15 x 5/2. Solving that out, we get:
[tex]15\times \frac{5}{2} = \frac{15\times5}{2}= \frac{75}{2}[/tex]
75/2 as a mixed number is 37 1/2; if we were going for an exact answer, we could stop there and say that the containers fill exactly 37 1/2 bottles, but the question specifically asks how many containers can be completely filled, so we'll have to throw away the fractional part, leaving us with an answer of 37 bottles.
Related Questions
A message center receives calls from 6 p.m. until 6 a.m. Typically, 50% of the calls come in between 6 p.m. and 9 p.m.; 25% of the calls come in between 9 p.m. and midnight; 20% of the calls come in between midnight and 3 a.m.; and 5% of the calls come in between 3 a.m. and 6 a.m.
What is the probability that a call will come in between 6 p.m. and midnight?
Question 5 options:
25%
50%
55%
75%
Answers
3 a.m. to 6 a.m. 5%
Midnight to 6 a.m. = 20% + 5% = 25%
What is the area of rhombus ABCD ?
Enter your answer in the box. Do not round at any steps.
Answers
Answer:
16 units
Step-by-step explanation:
The area of a rhombus is given by the formula A = bh. The base would be CB and the height would be DP. We will use the distance formula to find the length of each:
[tex]d=\sqrt{y_2-y_1)^2+(x_2-x_1)^2}[/tex]
For CB, we have
[tex]d=\sqrt{(2-0)^2+(3--1)^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}[/tex]
For DP we have
[tex]d=\sqrt{(2--1.2)^2+(-5--3.4)^2}=\sqrt{3.2^2+1.6^2}=\sqrt{10.24+2.56}=\sqrt{12.8}[/tex]
This makes the area of the rhombus
[tex]A=bh=\sqrt{20}\times \sqrt{12.8}=\sqrt{20\times 12.8}=\sqrt{256}=16[/tex]
The area of a rhombus can be found using the formula (diagonal1 * diagonal2) / 2. In this case, the area is 24 cm^2.
Explanation:The area of a rhombus can be found using the formula:
Area = (diagonal1 * diagonal2) / 2
where diagonal1 and diagonal2 are the lengths of the two diagonals of the rhombus.
For example, if diagonal1 = 6 cm and diagonal2 = 8 cm, the area of the rhombus is:
Area = (6 * 8) / 2 = 24 cm2
Therefore, the area of rhombus ABCD is 24 cm2.
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Kim's class voted on a location for a field trip. • 5/12 of the class voted for the museum. • 5/24 of the class voted for the zoo. The rest of the class voted for the nature park. What fraction of the class voted for the nature park? The nature park received of the class votes.
Answers
Final answer:
By adding the fractions of votes for the museum (5/12) and zoo (5/24), converting them to a common denominator, and subtracting from the whole, we find that 3/8 of the class voted for the nature park.
Explanation:
To determine what fraction of the class voted for the nature park, we first need to add up the fractions of the class that voted for the museum and the zoo, and then subtract that sum from the whole class, which is represented as 1 (or 12/12). Since 5/12 of the class voted for the museum and 5/24 of the class voted for the zoo, we need to find a common denominator to add these fractions together. The lowest common denominator for 12 and 24 is 24.
First, we convert 5/12 to a fraction with a denominator of 24, which would be 10/24 (since 5 × 2 = 10 and 12 × 2 = 24). Now we can add the two fractions:
10/24 (votes for the museum)
5/24 (votes for the zoo)
Therefore, 10/24 + 5/24 = 15/24. After that, we subtract the sum from the whole to find out what fraction voted for the nature park:
12/12 - 15/24 = 24/24 - 15/24 = 9/24.
Hence, 9/24 of the class voted for the nature park. However, we can simplify 9/24 by dividing the numerator and the denominator by their greatest common divisor, which is 3, giving us 3/8.
Therefore, 3/8 of the class voted for the nature park.
What is the eccentricity of a completely flat ellipse
Answers
The eccentricity of a completely flat ellipse ranges from one (1) to zero (0).
What is eccentricity of flat ellipse?Eccentricity of an ellipse is the measure of how 'out of round' an ellipse is.
The eccentricity of an ellipse ranges from 0 to 1.
If the eccentricity is 0, it is not squashed at all and it will remain a circle.
However, if the eccentricity is 1, it is completely squashed and looks like a straight line.
Thus, the eccentricity of a completely flat ellipse ranges from one (1) to zero (0).
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The subtraction property of equality let's you say that if 5x+6=21, then ____ = 15
Answers
Divide.
8.64÷(−0.27)
Enter your answer in the box.
Answers
32 is your answer hope it helped :) welcome
Which statement is true about the difference 2 square root of 7 − square root of 28? It is rational and equal to −2. It is rational and equal to 0. It is irrational and equal to −2square root of 7. It is irrational and equal tosquare root of 7.
Answers
What is the value of m?
0.61m−1.51m=9
Answers
9/-.9
m=-10
The value of m from the given expression would be; -10.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We have been given the expression as
0.61m - 1.51m = 9
Combine Like Terms;
-0.9m = 9
Divide -0.9 To Both Sides;
-0.9m/-0.9 = 9/-0.9
Simplify;
m = -10
Hence, m equals to -10.
The value of m from the given expression would be; -10.
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Line segment ab has a length of 4 units. it is translated 1 unit to the right on a coordinate plane to obtain line segment a prime b prime. what is the length of a prime b prime? 1 unit 4 units 5 units 6 units
Answers
Answer:
The length of A'B' is 4 unit.
Step-by-step explanation:
Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size,
That is, if the measurement of segment AB is 4 unit then after translation by any factor its measurement will not change,
So, the measurement of segment A'B' would be 4 unit.
Verification :
Let the coordinates of A and B are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively,
Also, the rule of translation 1 unit right is,
[tex](x,y)\rightarrow (x+1, y)[/tex]
By the distance formula,
The measure of segment AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Thus, if A'B' is the transformed segment of segment AB,
Then, coordinates of A' and B' are [tex](x_1+1, y_1)[/tex] and [tex](x_2+1, y_2)[/tex]
So, the measure of segment A'B' = [tex]\sqrt{(x_2+1-x_1-1)^2+(y_2-y_1)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence, the measure of AB = measure of A'B'
Darius and Matthew have 3 fruit bars. They are both hungry after playing football and decide to split the fruit bars evenly.How much fruit bars will reach boy get.
Answers
If you divide three by two you get 1.5, which translates to 1 1/2 fruit bars per boy if they split it evenly. Hope this helps!
You deposit $5000 in an account earning 7.5% simple interest. How long will it take for the balance of the account to be $6500?
Answers
Final answer:
It will take 4 years for the balance of an account to grow from $5000 to $6500 at a 7.5% simple interest rate. The formula for simple interest I = P × r × t is used, and after rearranging to solve for t, we find t = 4 years.
Explanation:
To calculate how long it will take for the balance of an account to reach a certain amount with simple interest, we can use the formula for simple interest: I = P × r × t, where I is the interest earned, P is the principal amount (initial deposit), r is the annual interest rate, and t is the time in years. In this case, we want to find out when the account balance will be $6500 after depositing $5000. The total interest earned to reach $6500 will be $6500 - $5000 = $1500.
The given annual interest rate is 7.5% (or 0.075 when converted to decimal form). We will rearrange the simple interest formula to solve for t:
t = I / (P × r)
Now, substituting the given values:
t = $1500 / ($5000 × 0.075)
t = $1500 / $375
t = 4 years
Therefore, it will take 4 years for the balance of the account to be $6500 at a 7.5% simple interest rate.
A golfer has 4 different hats, 3 gloves, and 2 pairs of shoes to pick from for his round of golf. In how many ways can he make his choices?
Answers
The number of ways the golfer can make his choices is 4 hats times 3 gloves times 2 shoes, resulting in 24 different combinations.
Explanation:The student is asking about the number of different ways a golfer can choose from 4 hats, 3 gloves, and 2 pairs of shoes. To find the total number of combinations, we multiply the number of choices for each category. Thus, the number of ways the golfer can make his choices is:
4 (hats) × 3 (gloves) × 2 (shoes) = 24 combinations.
This is not an instance where factorial calculation (4!) is necessary, since the golfer does not need to select one of each item in a specific order but simply needs to choose one from each category.
To calculate the number of ways the golfer can make his choices, we can use the concept of permutations.
For the hats, there are 4 choices. For the gloves, there are 3 choices. And for the shoes, there are 2 choices.
To find the total number of combinations, we multiply the number of choices for each category together: 4 hats * 3 gloves * 2 pairs of shoes = 24 different ways the golfer can make his choices.
Final answer:
The golfer can choose his accessories in 24 different ways by selecting 1 out of 4 hats, 1 out of 3 gloves, and 1 out of 2 pairs of shoes, and multiplying the choices together (4 × 3 × 2).
Explanation:
The question asks us to calculate the total number of ways the golfer can choose his outfit accessories assuming he chooses one of each type. To do this, we need to consider each type of accessory independently and multiply the number of choices for each type.
The golfer has 4 different hats, 3 pairs of gloves, and 2 pairs of shoes to choose from. Since these choices are independent of each other, we simply multiply the number of options for each type of accessory:
4 options for hats,3 options for gloves,2 options for shoes.Thus, the total number of combinations is 4 hats × 3 gloves × 2 shoes = 24 different ways the golfer can choose his accessories for the round of golf.
This is an example of a fundamental counting principle problem, where we multiply the number of choices in each step to get the total number of combinations.
State whether the triangles are similar.
Answers
Solve x2 + 8x − 3 = 0 using the completing-the-square method
Answers
How do you solve a quadratic formula
Answers
how many times can 32 go into 64
Answers
hope this helps
Triangle ABC is located at A (−2, 2), B (−2, 4), and C (0, 0). The triangle is then transformed using the rule (x+3, y− 2) to form the image A'B'C'. What are the new coordinates of A', B', and C'?
Answers
find (f•g) when f(x)=x^2-7x+12 and g(x)=3/x^2-16
Answers
1) g(x) = 3 / (x^2 - 16),
2) f(x) = x^2 - 7x + 12, and
3) (f•g)(x) = the product of the two functions f(x) * g(x)
The solution is found by factoring the two polynomilas f(x) and g(x):
f(x) = x^2 - 7x + 12 = (x - 4) (x -3)
g(x) = x^2 - 16 = (x - 4) (x + 4)
=> (f•g) (x) = (x - 4) (x - 3) / [ (x - 4)(x + 4) ] = (x - 3) / (x + 4)
Answer: (x - 3) / (x + 4)
A car travels 308 miles in 5 hours and 30 minutes. how many miles does it travel per hour?
Answers
which expression is equal to the expression below?
(2x6)^4
A 4 x (2x6)
B 8^4
C 2 x (6)^4
D 2^4 x 6^4
Answers
Hey there!
[tex]\bold{(2\times6)^4}[/tex][tex]\bold{2\times6=12}[/tex][tex]\bold{12\times12\times12\times12}[/tex][tex]\bold{12\times12=144}[/tex][tex]\bold{144\times144=20,736}[/tex][tex]\bold{A.\downarrow}[/tex]
[tex]\bold{4\times(2\times6)}[/tex][tex]\bold{2\times6=12}[/tex][tex]\bold{4\times12=48}[/tex][tex]\bold{48\neq20,736}[/tex][tex]\boxed{\bold{incorrect}}[/tex][tex]\bold{B.\downarrow}[/tex]
[tex]\bold{8^4}[/tex][tex]\bold{8\times8\times8\times8}[/tex][tex]\bold{8\times8=64}[/tex][tex]\bold{64\times64=4,096}[/tex][tex]\bold{4,096\neq20,736}[/tex][tex]\boxed{\bold{incorrect}}[/tex]
[tex]\bold{C.\downarrow}[/tex]
[tex]\bold{2\times(6)^4}[/tex][tex]\bold{6^4=1,296}[/tex][tex]\bold{2\times1,296=2,592}[/tex][tex]\bold{2,592\neq20,736}[/tex][tex]\boxed{\bold{incorrect}}[/tex][tex]\bold{D\downarrow}[/tex]
[tex]\bold{2^4\times6^4}[/tex][tex]\bold{2^4=16}[/tex][tex]\bold{6^4=1,296}[/tex][tex]\bold{16\times1,296=20,736}[/tex][tex]\bold{20,736=20,736}[/tex][tex]\boxed{\boxed{\bold{correct}}}[/tex][tex]\boxed{\boxed{\bold{Answer:D.2^4\times6^4}\checkmark}}[/tex]
Good luck on your assignment and enjoy your day!
~[tex]\bold{LoveYourselfFirst:)}[/tex]
Which equation is a trigonometric identity?
Answers
The real identity that looks similar to them is
sin^2 x + cos^2 x = 1
Options A and D are both incorrect and are not identities.
From options B and C, option B is the correct one.
By definition we have:
sin x = opp/hyp
cos x = adj/hyp
tan x = opp/adj
If you divide sin x by cos x and simplify, you get opp/adj, which is exactly what the tangent is.
The answer is B.
A ferris wheel is drawn on a coordinate plane so that the first car is located at the point (0,40). What are the coordinates of the first car after a rotation of 270 degrees° counterclockwise about the origin?
Answers
After a 270-degree counterclockwise rotation, the first car on the ferris wheel originally located at (0, 40) will be at (40, 0).
Explanation:If the first car of a ferris wheel is located at the point (0, 40) on a coordinate plane and undergoes a rotation of 270 degrees counterclockwise about the origin, the new coordinates of the first car can be determined by applying a rotation transformation. To perform a 270-degree counterclockwise rotation, we rotate the point 90 degrees clockwise. This equivalent action simplifies the calculation, as rotating (0, 40) 90 degrees clockwise results in the point moving to (40, 0). Therefore, after a 270-degree counterclockwise rotation (which is equivalent to a 90-degree clockwise rotation), the new coordinates of the first car on the ferris wheel are (40, 0).
A plane traveled from California and back. It took one hour longer on the way out than it did on the way back. The plane's average speed out was 300 mph. The average speed on the way back was 350 mph. How many hours did the trip out take? A. 7 hours B. 6 hours C. 13 hours D. 8 hours
Answers
300t = 350(t-1)
300t = 350t-350
-50t=-350
t = -350 /-50
t = 7 hours
Is △RWS ~ △QWT?
yes
no
Answers
Answer: Yes ΔRWS≈ΔQWT.
Step-by-step explanation:
We know that when two chords intersect each other inside a circle, the products of their segments are equal.
Therefore, [tex]QW\times WS=TW\times RW\\\Rightarrow\frac{QW}{RW}=\frac{TW}{WS}[/tex]
Now in triangle QWT and triangle RWS
∠QWT=∠RWS [Vertically opposite angles]
[tex]\frac{QW}{RW}=\frac{TW}{WS}[/tex]
Therefore, By SAS similarity rule
ΔRWS≈ΔQWT
Therefore, yes ΔRWS≈ΔQWT.
How do I solve this literal equation
Answers
au=k
2. Now divide both sides by u
a=k/u
The diameter of a circular clock is 12 inches. what is the approximate length of the outer edge of the clock between the numbers 3 and 6?
Answers
So to find the length of the outer edge between 3 and 6 = 2 x Pi x 6 = 37.7. And then divide 37.7 by 4 which equals to 9.425 inches
Determine the equation of the graph, and select the correct answer below.
Courtesy of Texas Instruments
y = (x + 4)^2 + 1
y = (x + 4)^2 − 1
y = (x − 4)^2 + 1
y = (x − 4)^2 − 1
Answers
Equation is ..
Y = (x -h)^2 + k
Put in vertex (-4,-1) gives the equation
Y = (x+4)^2 - 1
The equations provided represent parabolas that have been translated or reflected from the standard form y = x^2. Without a given graph or additional details, we can't definitively determine which equation is correct.
Explanation:Without a graph or specific details regarding the shape, position, and characteristics of the graph, we can't definitively choose one of the given equations. However, each equation represents a parabolic function that is translated and/or reflected from the standard form, y = x².
The equation y = (x + 4)² + 1 represents a parabola that is shifted 4 units to the left and 1 unit up from the origin.
The equation y = (x + 4)² − 1 is a parabola that is shifted 4 units to the left and 1 unit down.
For the equation y = (x − 4)² + 1, the parabola is shifted 4 units to the right and 1 unit up.
And lastly, the equation y = (x − 4)² − 1 describes a parabola that is shifted 4 units to the right and 1 unit down.
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A rancher needs to enclose two adjacent rectangularâ corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 180 yd of fencing isâ available, find the largest total area that can be enclosed.
Answers
Let L = Length parallel to the river,
Here, L + 3B = 180 yd
So, L = 180 - 3B
We know that the area of the rectangle,
A = L × B
= (180 - 3B) × B
= 180 B - 3[tex] B^{2} [/tex]
We know that quadratic equation has symmetry,
So, For maximum area Breadth B = [tex] \frac{-2a}{b} [/tex]
Here, a = -3 & b 180
So, B = [tex] \frac{-180}{2(-3)} [/tex]
= 30 yd
So, L = 180 - 3B
= 180 - 3(30)
= 180 - 90
= 90
So, Maximum Area = L × B
= 90 × 30
= 2700 square yards
Therefore, the correct answer is 2700 square yards.
x = the width of each rectangular area.
y = the length of each rectangular area.
The amount of fencing available is 180 yards, therefore
4x + 2y = 180
or
2x + y = 90
y = 90 - 2x (1)
The total enclosed area is
A = 2xy
= 2x(90 - 2x)
A = 180x - 4x² (2)
In order to maximize A,
A'(x) = 180 - 8x = 0
x = 180/8 = 22.5 yd
y = 90 - 2x = 45.0 yd
To verify that A will be maximum, A''(x) should be negative.
A'' = -8 (verified).
The maximum area is
Amax = 2*22.5*45.0 = 2025.0 yd²
Answer: 2025 yd²
(Please help) Which answer describes the polynomial?
[tex]3x^3+4x^2-7[/tex]
A) quatric trinomial
B) cubix trinomial
C) quadratic trinomial
D) cubic binomial
Answers
notice, there are three terms, therefore is a trinomial.
the term that has the highest degree, has a degree of 3, therefore the degree of the polynomial as a whole is 3, or a cubic degree.
so, is a cubic trinomial.
In a class of 80 students, 42 received a grade of
a. what fraction of the class did not receive an a? reduce to the lowest terms.
Answers
42 received an A
so 40-42 = 38 did not
the fraction would be 38/80, divide both numbers by 2
38/80 reduces to 19/40 did not receive an A
Out of 80 students, 38 did not receive an A, resulting in the fraction who did not receive an A being 19/40 after simplifying.
Explanation:In a class of 80 students, if 42 received a grade of A, then the number of students who did not receive an A is the total number of students minus the number who did receive an A. So, 80 students − 42 students = 38 students. The fraction of the class that did not receive an A is 38 out of 80, which can be simplified by dividing both the numerator and the denominator by their greatest common factor, which is 2.
Therefore, the reduced fraction is 19/40.
The fraction of the class that did not receive an A is 19/40 which, if we converted into a percentage, would be 47.5%.