A hair company makes three batches of scented shampoo using the recipe shown. Each batch contains a different total amount of shampoo. 1/2 is pineapple, 1/5 is banana, 3/10 is coconut.
Batch 1:
Pineapple
Banana
Coconut is 2 1/10
Batch 2:
Pineapple
Banana is 3 1/5
Coconut
Batch 3:
Pineapple is 2 1/2
Banana
Coconut
Answer:
Batch 1: Pineapple = 3 1/2; Banana = 1 2/5
Batch 2: Pineapple = 8; Coconut = 4 4/5
Batch 3: Banana = 1; Coconut = 1 1/2
Step-by-step explanation:
For Batch 1:
We know that coconut is 3/10 of the mixture, and we have 2 1/10 coconut:
3/10x = 2 1/10
Converting 2 1/10 to an improper fraction, we have
3/10x = 21/10
Divide both sides by 3/10:
3/10x ÷ 3/10 = 21/10 ÷ 3/10
To divide fractions, flip the second one and multiply:
x = 21/10 × 10/3 = 210/30 = 7
This means we have 7 total of the mixture.
1/2 of this is pineapple: 1/2(7) = 7/2 = 3 1/2
1/5 is banana: 1/5(7) = 7/5 = 1 2/5
For Batch 2:
1/5 of the total is banana; we have 3 1/5 banana:
1/5x = 3 1/5
Convert the second fraction to an improper fraction:
1/5x = 16/5
Divide both sides by 1/5:
1/5x÷1/5 = 16/5÷1/5
Flip the second fraction and multiply:
x = 16/5×5/1 = 80/5 = 16
We have 16 of the total shampoo.
Pineapple is 1/2 of this:
1/2(16) = 8
Coconut is 3/10 of the total:
3/10(16) = 48/10 = 4 8/10 = 4 4/5
For Batch 3:
Pineapple is 1/2 of the total. We have 2 1/2 pineapple:
1/2x = 2 1/2
Convert the fraction on the right to improper:
1/2x = 5/2
Divide both sides by 1/2:
1/2x÷1/2 = 5/2÷1/2
Flip the second fraction and multiply:
x = 5/2×2/1 = 10/2 = 5
We have 5 total shampoo.
Banana is 1/5 of this:
1/5(5) = 1
Coconut is 3/10 of this:
3/10(5) = 15/10 = 1 5/10 = 1 1/2
The gray area is the sidewalk. The area of the sidewalk is ___________ square units.
A) 48
B) 56
C) 72
D) 84
Answer: 72
Step-by-step explanation: i did it a got it right
I need help on number 11 please explain thanks! :)
what is equivalent to ^3√8^x
Which expression is equal to 5p? p + p + p + p + p 4p + 1 p + 5 p3 + p2
The expression equal to 5p is Option A: p + p + p + p + p. Other options do not correctly represent the sum of five instances of p.
The correct expression that is equal to 5p is A. p + p + p + p + p. Let's break it down:
A. p + p + p + p + p adds the variable p five times, which by definition equals 5p.
B. 4p + 1 simplifies to 4p + 1, which is not equal to 5p because it includes an additional constant term.
C. p + 5 represents the variable p plus the number 5, which is not the same as multiplying p by 5.
D. p3 + p2 is a polynomial with different powers of p and does not simplify to 5p.
Therefore, option A is the correct answer.
Which expression is equal to 5p?
A. p + p + p + p + p
B. 4p + 1
C. p + 5
D. p3 + p2
Find the value of x. Round to the nearest tenth of the right triangle. hypotenuse is x, side leg is 12, and angle is 47
Definition of classic probability
Probability is the likelihood, or chance, that a certain event will occur. The easiest way to understand probability is with coin tosses. Probability can also be applied in various fields such as medicine and stock market.
Explanation:Probability is the likelihood, or chance, that a certain event will occur. The easiest way to understand probability is with coin tosses.
When you toss a coin, the chance of a head turning up is 50 percent. This is because a coin has only two sides, so there is an equal chance of a head or tail turning up on any given toss.
Probability can also be applied in various fields. For example, doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent.
Stockbrokers use probability to determine the rate of return on a client's investments. In statistics, we study populations and use a sample to gain information about the larger population. Data are the result of sampling from a population.
The area of rectangle A is 11/12 square meters.The area of rectangle B is 8/12 square meters.How much larger is rectangle A?
relay race. To start, you must run 20 yards to Checkpoint A. You then must turn and run 12 yards to Checkpoint B. Last, you must turn and run back to the starting line. What is the distance from Checkpoint B to the starting line?
The distance from checkpoint B to the starting line for the given right-angle triangle will be 16 yards.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
In a triangle, the sum of all three angles is 180°
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
As per the given right angle triangle,
Suppose the missing length is x.
By Pythagoras' theorem,
x = √(20² - 12²)
x = √(400 - 144) = √256 = 16
Hence "The distance from checkpoint B to the starting line for the given right-angle triangle will be 16 yards".
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PLEASE PLEASE MATH HELP WILL GIVE BRAINLIEST!!!
Angle K in △MKL is a right angle.
What is the value of tan M ?
8/15
8/17
15/8
15/17
dividing fractions I don't know what it is and nits 6th grade divide fraction
what is the answer to 2/3(5x+6)=34
What is 4(0.5x + 2.5y - 0.7y - 1.3y + 4) simplified?
Suppose you have to use right-triangle trigonometry to find the apothem of a regular polygon. Which is greater, the apothem or the radius of the polygon?
In a regular polygon, the apothem is the distance from the center to the midpoint of a side, whereas the radius is the distance from the center to a vertex. Because the radius is the hypotenuse in a right triangle formed within the polygon, as per the Pythagorean theorem, it is always longer than the apothem.
Explanation:In the context of a regular polygon, the apothem is defined as the distance from the center of the polygon to the midpoint of any side. The radius, on the other hand, is defined as the distance from the center to any of the vertices. Since a regular polygon's sides and angles are equal, one can observe that its apothem is always smaller than its radius.
In order to illustrate this, consider a right triangle formed by the radius, the apothem, and half the length of a side. By using the Pythagorean theorem (a² + b² = c²), we know that the radius (or hypotenuse) is the longest side, and therefore greater than the apothem (one of the perpendicular sides).
Simply put, the radius is always greater than the apothem in a regular polygon.
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The radius of a regular polygon is always greater than the apothem.
To determine if the apothem or the radius of a regular polygon is greater, we can use a right-triangle trigonometry approach. Here's a step-by-step explanation:
Consider a regular polygon with n sides inscribed in a circle. The circle's radius is r, and this radius is the hypotenuse of a right triangle formed by the radius, the apothem a, and half the length of one side of the polygon.The apothem is the perpendicular distance from the center of the polygon to the midpoint of one of its sides.Since the hypotenuse of a right triangle is always the longest side, the radius (r) is always greater than the apothem (a) according to the Pythagorean theorem.For example, in a regular hexagon, the radius is twice the apothem, clearly illustrating this relationship.Therefore, in any regular polygon, the apothem is always less than the radius, as the hypotenuse (radius) is the longest side in the right triangle formed by the apothem and half the length of a side of the polygon.
3 + d < 3 – d. Solve
list of all the dimensions you can make for rectangular prisms with 12cm linking cubes
Draw Three triangles One equilateral one isosceles and one scalene label Each and explain how you classified each triangle
I’m not sure what the answer is
how to solve this cause I was gone for 1/2 of my class and missed stuff.
To find y, first find the measure of the third interior angle. We'll call it x.
The triangle angle sum theorem allows us to create an equation to find x. Set the interior angle values equal to 180 and solve.
180 = 28 + 30 + x
Add the constants.
180 = 58 + x
Subtract 58 from both sides.
122 = x
Now, ∠x (which we now know measures 122°) is supplementary to ∠y. Set them equal to 180 and solve for y.
180 = 122 + y
Subtract 122 from both sides.
58 = y
Answer:m∠y = 58°
Solve 8n + 2 – 6n = 9 + 2n – 13, and interpret the results.
no solutions
infinitely many solutions
only one solution, n = 2
two solutions, n = 2 or n = - 4
The equation 8n + 2 - 6n = 9 + 2n - 13 has only one solution, n = -3.
Explanation:To solve the equation 8n + 2 - 6n = 9 + 2n - 13, we need to simplify both sides and combine like terms.
Starting with the left side of the equation, 8n - 6n can be simplified to 2n. And on the right side, 9 - 13 is -4.
So, we have 2n + 2 = -4. We can now subtract 2 from both sides to isolate the variable n. This gives us 2n = -6. To solve for n, divide both sides of the equation by 2: n = -3.
Therefore, the equation 8n + 2 - 6n = 9 + 2n - 13 has only one solution, n = -3.
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a line with a slope of 1/8 passes through the points (u, -9) and (6, -8). what is the value of u?
The surface area of a prism is Square units all measurements in the image below input whole number only
Please do either 1,2,3 or 4
Am I doing these right? Are these correct?
The population of a city is 451,400. The population is expected to decrease at a rate of 3.2% each year. Which function equation represents the population of the city after t years?
Answer:
This was the correct answer, I even provided proof from my own test. Hope this helps!
Step-by-step explanation:
A student wrote this statement “a triangular prism has a height of 15 inches and a base area of 20 square inches. The volume of the prism is 300 square inches.” Identify and correct the error
PLEASE HELP ME I BEG YOU BRAINLIEST ALWAYS!!!!!
there is a line whose slope is 1/6 and whose y-intercept is 4. what is its equation in slope intetecept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
y= x +
The unit rate in kilometers per minute for 18.25km in 1 h 45 minute
nicks telephone company charges 0.05 per min for weekend calls and $0.09 per minute for calls made on weekdays this month Nick was bailed 622 minutes these charges were 45.94 how many minutes did he talk on weekends and how many minutes did he talk on weekdays