when the cups of flour increase from 5 to 15, the cups of sugar also increase from 10 to 30, maintaining the constant ratio of 1 : 2.
To find the number of cups of sugar needed when 15 cups of flour are used, let's first determine the constant ratio between cups of flour and cups of sugar.
Given:
- 5 cups of flour are mixed with 10 cups of sugar.
We can set up a ratio:
[tex]\[ \text{Cups of flour} : \text{Cups of sugar} = 5 : 10 \][/tex]
Now, let's simplify this ratio by dividing both parts by their greatest common divisor, which is 5:
[tex]\[ \frac{5}{5} : \frac{10}{5} = 1 : 2 \][/tex]
So, the constant ratio between cups of flour and cups of sugar is 1 : 2.
Now, to find out how many cups of sugar should be used if 15 cups of flour are used, we can use the constant ratio.
[tex]\[ \text{Cups of flour} : \text{Cups of sugar} = 15 : x \][/tex]
Since the ratio is constant, we can use the ratio 1 : 2 to set up a proportion:
[tex]\[ \frac{15}{1} = \frac{x}{2} \][/tex]
Now, let's solve for (x):
[tex]\[ 15 \times 2 = x \times 1 \]\[ 30 = x \][/tex]
So, if 15 cups of flour are used, we will need 30 cups of sugar.
We can also verify this using the constant ratio table:
Cups of flour Cups of sugar
5 10
15 30
As we can see, when the cups of flour increase from 5 to 15, the cups of sugar also increase from 10 to 30, maintaining the constant ratio of 1 : 2.
The probable question maybe:
For a given recipe, 5 cups of flour are mixed with 10 cups of sugar. How many cups of sugar should be used if 15 cups of flour are used? Assuming a constant ratio, fill out the table of equivalent ratios until you have found the value of x.
There are 28 seats in the front row of a theater. Each successive row contains
two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater?
Answer:
28+2*(24-1)= 74
Answer: 74
Step-by-step explanation:
The value Of a painting begins at $12,000 and increases by $500 per year write an equation representing the value V of the painting at the end of any given year y.
Not yet answered Marked out of 100 Flag question
Find the volume of a rectangular prism 3 inches high, 14 inches wide, and 9
inches long,
Barry answered 32 out of 40 questions correctly on his math test. what percent of the questions did he get correct
Answer:it would be 80%
Step-by-step explanation:
Answer:
80%
Step-by-step explanation:
Divide 32/40
you get .80
multiply .80 by 100
The steps Quentin took to evaluate the expression 3m - 3+3 when m = 8
are shown below.
3m - 3 + 3 when m=8
3 x 8 = 24
24 - 3 =21
21 + 3 = 7
What should Quentin have done differently in order to evaluate the
expression?
divided (24-3) by (24x3)
divided (24-3) by (24-3)
subtracted (3 + 3) from 24
subtracted 3 from (24 +3)
Quentin had properly substituted m with 8, but he mistakenly added 3 to 21 rather than subtracting. The right final calculation should provide 24, not 7.
Explanation:In order to correctly evaluate the expression 3m - 3 + 3 when m = 8, Quentin starts off correctly by replacing m with 8, resulting in 24. The mistake happens when Quentin incorrectly adds 3 to 21 instead of subtracting 3 from 21. The correct sequence of steps should be:
3m - 3 + 3 when m=8Replace m with 8. Therefore, 3 * 8 = 24Subtract 3 from 24. Therefore, 24 - 3 = 21Add 3 back to the result of 21 - 3. Therefore, 21 + 3 = 24Learn more about Math Expression Error Correction here:
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How many inches if wooden sticks will be required?
The required amount of wooden sticks would depend on specific measurements for different projects, such as making a Biltmore stick for tree height measurement or spacing vertical studs 16 inches apart, which is equal to 40.64 centimeters. Measurements and conversions would be necessary to determine the exact amount of material needed.
Explanation:The amount of wooden sticks required would depend on the specific project being undertaken. The details provided mention various projects, including constructing a Biltmore stick for measuring tree heights, vertical studs spaced 16 inches apart for lumber usage, and spacing between scaffolds that could be anywhere from 3 to 12 inches. For the Biltmore stick, you would need a stick long enough to reach from your eye level to the ground, as well as additional sticks or markers for the grading. For constructing vertical studs spaced 16 inches apart, you would convert that distance into centimeters, where 16 inches is equal to about 40.64 centimeters. Other examples require sticks of varying sizes, from the barrel of a plastic stick pen cut in half, which would be a few inches, to a list of materials needed for a pyramid structure that changes by 12 inches per level.
how to determine the rate of change by looking at graph?
At boarding school, students spend 1/4 of their time eating and sleeping, 3/5 of their time in class, and 1'12 studying. The rest of the time is considered free time, which the student can spend doing activities of their own choosing. What fraction is considered free time?
Answer:
1/15 of their time is free time.
Step-by-step explanation:
To find the answer to this 2-step problem, we have to add all the fractions up, then find how much of that time is not part of the fraction.
So to add all the fractions, you have the equation:
1/4 + 3/5 + 1/12
The first thing we have to do is to find a common denominator.
4, 5, and 12 are each able to multiply into 60.
So we can make the equation now with a common denominator.
15/60+36/60+5/60=56/60.
We now can simplfy this.
56/60=14/15
Now that we know how long it is to do all the other activities, it tells us that the rest of the time is free time. To find the rest of the time, we have to do:
1-14/15=1/15
So 1/15 of their time is free time.
The total time spent is 14/15 and the free time is 1/15 if students spend 1/4 of their time eating and sleeping, 3/5 of their time in class, and 1'12 studying.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
We have:
At boarding school, students spend 1/4 of their time eating and sleeping, 3/5 of their time in class, and 1/12 studying
Add all the fractions:
= 1/4 + 3/5 + 1/12
= 14/15
Free time = 1 - 14/15
= 1/15
Thus, the total time spent is 14/15 and the free time is 1/15 if students spend 1/4 of their time eating and sleeping, 3/5 of their time in class, and 1'12 studying.
Learn more about the fraction here:
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What is the volume of the figure
Answer:
96 cubic cm.
Step-by-step explanation:
Area= Length*Width*Height
Area= 6*4*4
Area= 96
Answer:
D
Step-by-step explanation:
Because Volume = length x width x height
4 x 4 x 6=
16 x 6
96
Can someone answer this question please answer it correctly if it’s corect I will mark you brainliest
Answer:
2012
Step-by-step explanation:
Based on the graph, you can tell that private residence needed 6000 liters of cleaner in 2012 and only 2000 in 2016
Started at 15 degrees and dropped 1/2 degrees each minute
Answer:
7.5 should be the answer sorry if its wrong i don't have all of the information
Estimate the perimeter of the figure to the nearest whole number.
Answer:
See Explanation Below
Step-by-step explanation:
The question is incomplete (because the figure to calculate the perimeter is missing).
However from the comment attached to your question, I understand that the figure looks like a plus sign.
The perimeter of a plane shape is calculated by adding the length of each side of the shape.
Take for instance;
A square of length 5cm.
We know that a square has 4 equal sides; meaning that the length of the other sides are also 5cm
So, the perimeter of the square will be calculated as 5cm + 5cm + 5cm + 5cm = 20cm
Similarly, the perimeter of a triangle whose sides are 4ft, 3ft and 5ft will be calculated by adding up the length of the three sides.
Perimeter of the triangle = 4ft + 3ft + 5ft
Perimeter = 12ft.
Having explained how the perimeter of a plane shape is calculated; take for example, the attachment below.
(The sides are measured in centimetres)
The plus sign has 12 sides; Its perimeter is calculated by adding up the length of the 12 sides.
Perimeter = 3 + 7 + 7 + 5 + 5 + 5 + 5 + 2 + 2 + 4 + 4 + 3
Perimeter = 52cm
Answer:
stop tryna cheat and figure it out
Step-by-step explanation:
The shape on the left is transformed to the shape on the right. Which of the following statements describes the transformation?
A. MNOP → M'N'O'P'
B. M'N'O'P' → MNOP
C. P'O'M'N' → MOPN
D. MNOP → O'P'M'N'
The shown transformation is described by the statement:
MNOP → M'N'O'P'
So the correct option is A.
How to define a transformation?
Here we have a transformation that enlarges and rotates our original rectangle, with vertices M, N, O, and P.
Transformations do not act only on figures, they act on every point on the plane, so we could apply the same transformation to each one of the vertices, in such a way, we will get:
M → M'N → N'O → O'P → P'.Writing all of these together, we just get:
MNOP → M'N'O'P'
So the correct option is A.
If you want to learn more about transformations, you can read:
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Rewrite as a simplified fraction.
0.2 = ?
Answer:
1/5
Step-by-step explanation:
When changing a decimal to a fraction, think of the decimal "out of 1." In mathematical terms, "out of" generally means division.
For example on this question, think of 0.2 as 0.2 out of 1, which would be shown as 0.2/1
To more easily simplify this, multiply both the top and bottom by 10
0.2/1 x 10/10
You are able to do this because 10/10 is equal to 1 and multiplying by a number and 1 results in the same number.
Then you get 2 /10 . Both 2 and 10 are divisible by 2
2 /2 = 1 and 10 /2 = 5
So the final answer is 1/5
combining like terms
-7r-9+8+5r
show how you got the answer
Answer:
-2r - 1
Step-by-step explanation:
The like terms here are -7r and 5r,
The like terms for constants are -9 and 8
so add -7r + 5r = -2r
and add -9 + 8 = -1
Determine the following for the transformed cosine function shown whose period is 1,080 degrees.
Frequency:
b in the equation:
Answer:
Frequency: 1/1080
b in the equation: 1/3
Step-by-step explanation:
The frequency is 1/1080 and the value of b is 1/3
How to determine the values of frequency and b?The period is given as;
T = 1080
The frequency is calculated using:
f = 1/T
So, we have:
f = 1/1080
The value of b is calculated using:
2π/b = T
This gives
2π/b = 1080
Make b the subject
b = 2π/1080
Express 2π as degrees
b = 360/1080
Divide
b = 1/3
Hence, the frequency is 1/1080 and the value of b is 1/3
Read more about cosine functions at:
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If a triangle has one angle that measures 62.5o and another angle that measures 77o , then what is the measurement of the last angle?
Answer:
40.5 degrees
Step-by-step explanation:
A triangle's angles all add up to 180 degrees, so to solve this all you need to do is add the two numbers you have and subtract them from 180.
62.5+77+x=180
139.5+x=180
-139.5 -139.5
x=40.5
To find the measurement of the last angle in a triangle, subtract the sum of the known angle measurements from 180 degrees. Given angles of 62.5° and 77°, the measurement of the last angle is 40.5°.
The question involves finding the measurement of the last angle in a triangle given the measurements of the other two angles. In Euclidean geometry, it is established that the sum of the angles in a triangle equals 180 degrees. Given that one angle measures 62.5° and another measures 77°, we can find the last angle by subtracting the sum of these two angles from 180 degrees.
Step 1: Add the measurements of the two known angles: 62.5° + 77° = 139.5°.
Step 2: Subtract this sum from 180°: 180° - 139.5° = 40.5°.
Therefore, the measurement of the last angle in the triangle is 40.5°.
Dante bought a new graduated cylinder for his chemistry class. It holds 662.7 milliliters of liquid. If the cylinder has a radius of 4.7 cm, then how tall is the cylinder? (Note: 1 milliliter is equal to 1 cubic centimeter)
A.
141 cm
B.
19,881 cm
C.
30 cm
D.
70.5 cm
Given:
Dante bought a new graduated cylinder for his chemistry class.
Volume of the cylinder = 662.7π milliliters of liquid
Converting to cubic centimeter, we get;
Volume of the cylinder = 662.7π cm³
Radius of the cylinder = 4.7 cm
We need to determine the height of the cylinder.
Height of the cylinder:
The height of the cylinder can be determined using the formula,
[tex]V=\pi r^2 h[/tex]
Substituting the values, we have;
[tex]662.7 \pi=\pi (4.7)^2h[/tex]
[tex]662.7 \pi=\pi (22.09)h[/tex]
Dividing both sides by 22.09π, we get;
[tex]30=h[/tex]
Therefore, the height of the cylinder is 30 cm.
Hence, Option C is the correct answer.
The calculated height of the graduated cylinder is approximately 30 cm, which is option C.
To determine how tall Dante's graduated cylinder is, given it holds 662.7π milliliters (mL) of liquid, we should use the formula for the volume of a cylinder, V = πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height.
Since 1 milliliter is equivalent to 1 cubic centimeter (cm³), we have V = 662.7π cm³, and the radius 'r' is given as 4.7 cm. Inserting these values into the formula and solving for 'h' gives us:
V = πr²h
662.7π cm³ = π × (4.7 cm)² × h
662.7π cm³ = π × (22.09 cm²) × h
662.7π cm³ = 22.09π × h
h = 662.7 cm³ /22.09
h ≈ 30cm
Therefore, the height of the cylinder is approximately option c. 30 cm.
The above question is incomplete, the complete question is:
Dante bought a new graduated cylinder for his chemistry class. It holds 662.7π milliliters of liquid. If the cylinder has a radius of 4.7 cm, then how tall is the cylinder? (Note: 1 milliliter is equal to 1 cubic centimeter)
A.
141 cm
B.
19,881 cm
C.
30 cm
D.
70.5 cm
Is the answer -165° -125° 125° or 165° pleas help quickly
Answer:
125
Step-by-step explanation:
mark me brainliest pls? brainliest for brainliest
Answer:
165 I just did it
Step-by-step explanation:
What is the sum of (6p^2+3) and (6-5p^3+3p^2)
the sum of (6p^2+3) and (6-5p^3+3p^2) is
[tex](6p^2+3)+(6-5p^3+3p^2)= 6p^2+3+6-5p^3+3p^2=-5p^3+9p^2+9[/tex]
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
P.S. Hello from Russia :^)
\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/
Answer:
9 P ^ 2 + 9 - 5 p ^ 3
Step-by-step explanation:
6p^ 2 + 3 + 6 - 5p ^ 3 + 3p ^ 2
Solve 5x=125.
X=25
x=3
Answer: X = 25
Step-by-step explanation: 5 * 25 = 125
Artaud noticed that if he takes the opposite of his age and adds 38 he gets the number 27. How old is
Artaud?
Answer:
11
Step-by-step explanation:
Let his age be x then the opposite of his age is - x, then
- x + 38 = 27 ( subtract 38 from both sides )
- x = - 11 ( multiply both sides by - 1 )
x = 11
Thus he is 11 years old
Can somebody help me
Answer:
B
Step-by-step explanation:
Simplify the expression x^3+125/x+5 and then evaluate the resulting expression of x=-5
Answer:
[tex]-145[/tex]
Step-by-step explanation:
Step 1: Set x to -5
[tex]x^3+125/x+5[/tex]
[tex](-5)^3 + 125/-5 + 5[/tex]
[tex]-125 - 25 + 5[/tex]
[tex]-145[/tex]
Answer: [tex]-145[/tex]
Can anyone answer this like really quickly I’m being timed
Answer:
48%
Step-by-step explanation:
12 = 48
25 100
Answer:
Step-by-step explanation:
i dont know the answer but how to solve is by adding up all the numbers and dividing by 12
(2+76+1+9)+4-3x9
Hi I’m doing homework right now and I don’t really get order of operations.
Answer:
65
Step-by-step explanation:
You should follow the PEMDAS rule. You first solve what is in the parenthesis, followed by the multiplication and division, then addition or subtraction. However depending on your equation you can switch the order of addition and subtraction
Answer:
65
Step-by-step explanation:
(2+76+1+9)+4-3x9
Parentheses first
(2+76+1+9)
88
Replace it in the equation
88+4-3x9
The exponents (we dont have any)
The multiply and divide
88+4-27
Then add and subtract
65
James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1 length: 12 in. width: 15 in. diagonal: 20 in. Parallelogram 2 length: 16 in. width: 30 in. diagonal: 34 in. Parallelogram 3 length: 20 in. width: 21 in. diagonal: 29 in. Parallelogram 4 length: 18 in. width: 20 in. diagonal: 26 in. James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle. 4 parallelograms are put together so that one vertex from each paper exists on a point. Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply. The quadrilaterals can be placed such that each occupies one-quarter of the circle. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 2 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 3 do not form right angles. The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.
Answer:
the answer is b and e
Step-by-step explanation:
Answer:
B and E
Step-by-step explanation:
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.
The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.
Find the area of the circle below
You can find the area of a circle by using this formula:
[tex]y = \pi r^2[/tex]
Knowing that a circle's diameter is double its radius, we know that the radius of this circle is 12.5 yards. Substitute this for r in the equation to find the area:
[tex]y = \pi *12.5^2\\y=156.25*\pi \\y=490.87[/tex]
Answer:
The area of the circle is 490.8738521 yards or if your rounding 490.87 yards.
Step-by-step explanation:
Area of circle = πr²
r = half of diameter
r = 25 ÷ 2
r = 12.5
A = π(12.5)²
A = π(156.25)
A = 490.8738521
A ≈ 490.87 yards
Hope I helped ya.
< Sarah >
answer to be named brainliest get a thank you and a 5 star vote
Meagan was given 20 math problems and she has completed 14 of them. What percentage of the problems does she have left to do?
Question 5 options:
3%
30%
70%
7%
Answer:
30%
Step-by-step explanation:
Meagan completed 14/20 math problems. 14÷20 is 0.7
So she completed 70% of those math problems. The question is How many does she have left?
So she has 30% left to complete.
The Deep Creek State Forest is a 380-acre state forest located 11 miles north of St. Augustine, Florida. The cottontail rabbit population in this forest grows at the rate of 5% monthly. If there are 175 rabbits in forest in September, find how many rabbits should be expected by next September. Use the formula: y=175(2.7)0.05t y = 175 ( 2 . 7 ) 0 . 05 t . Round your answer to the nearest whole number. The cottontail rabbit population next September is expected to be rabbits. (Round your answer to the nearest whole number)
Answer:
By next September, the estimated population would be 284 cottontail rabbits
Step-by-step explanation:
The formula that express the growth of the rabbits is
Y = 175(2.7)0.05t
Y = number of rabbits
Where t = time in months.
The growth of the rabbits in 12 months would be. Since from one September to another equal 1 year which is 12 months.
Y = 175(2.7)0.05(12)
Y = 283.5 = 284 rabbits
The estimated population of cottontail rabbits by next September is 284 rabbits