Denise needs to buy 25/3 gallons of 85% ethanol and 35/3 gallons of 25% ethanol to have 20 gallons of 50% ethanol.
x | y | 20 gal
use x and y because you don't know how much she needs.
0.85x | 0.25y | 20(0.5)
85% is 85/100 or 0.85, and you need that much of x, same goes for the 25% and 50% mixtures
so now you can make up 2 equations
1) x + y = 20
2) 0.85x + 0.25y= 10 (you get 10 when you multiply 20 by 0.5)
now you can solve for x or y using substitution. first rewrite 1) in terms of x or y:
x+ y= 20 ----> y= 20 - x
now you can substitute 20- x for y in the second equation..
0.85x + 0.25y= 10
0.85x + 0.25(20-x)= 10 distribute here..(0.25 * 20 and 0.25 * (-x) )
0.85x + 5 - 0.25x = 10 combine like terms
0.6x +5 = 10 move the 5 over to the other side
0.6x= 10 -5
0.6x = 5 divide both sides by 0.6
x= 25/3 or 8.3 now you know the amount of x so you can substitue this back into the first equation to find y.
0.85x + 0.25y= 10
0.85(25/3) +0.25y= 10
85/12 + 0.25y= 10
0.25y = 10- 85/12
0.25y= 35/12
y= 35/3 or 11.6
you can check by putting these values into the euations:
1) x+ y= 20
25/3 + 35/3 =20
20= 20 good so far
2) 0.85x + 0.25y= 10
0.85(25/3) + 0.25(35/3)=10
10 = 10 so our values for x and y work
I have to describe and correct th error in rewriting the equation 2x-y=5
To correct the rewritten equation 2x-y=5, isolate y on one side by moving the 2x term to the other side, resulting in y = 2x - 5.
Explanation:
To correct the rewritten equation 2x-y=5, we need to isolate y on one side of the equation. So, let's start by moving the 2x term to the other side, which requires subtracting 2x from both sides of the equation. This gives us -y = -2x + 5. Now we need to solve for y by multiplying both sides of the equation by -1 to get y = 2x - 5.
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Please please please help me :((
What is the solution to the inequality?
-2/3 (2x - 1/2)<= 1/5x - 1
Question: What is the solution to the inequality?
Answer: [[tex][\frac{20}{23} ,[/tex]∞)
How many 1/4 pounds of patties can be made from 5 pounds of ground turkey?
20 becuase 1/4 needs 4 to be 1 and multiply it by 5 and you get 20
You can make 20 patties. Hope this helped.
8x^3 ÷ 9x^4 someone pls answer
The answer would be
8/9x^7
Because all your doing is adding the exponents together and you get 7
Four friends went to cd music store. Lana purchased for CDs for $36.68 troy purchased five CDs for $40.55 Juanita purchased five CDs for $47.15 Alex purchased six CDs for $54.42 what was the average cost of the CDs each friend bought
name the property for the given statement 2+4=2+4
it is the identity property because it states that 2+4=2+4 and 2+4 will always equal itself, 2+4
another example of this would be 5=5
The correct option is A.
The property for the given statement "2 + 4 = 2 + 4" is the Addition Property of Equality.
The property demonstrated in the given statement "2 + 4 = 2 + 4" is the addition property of equality. Here's why:
A. **Addition Property of Equality**: This property states that if you add the same number to both sides of an equation, the equality remains true. In the given equation, both sides are identical, with 2 + 4 on each side. Therefore, adding the same quantity (in this case, zero) to both sides keeps the equation true.
B. Distributive property involves multiplication and addition, which is not applicable here.
C. Multiplication Property of Equality involves multiplication, which is not present in the given equation.
D. Subtraction Property of Equality is not relevant since there is no subtraction involved in the given equation.
So, the correct option is A. Addition Property of Equality.
The complete question is here:
Name the property for the given statement.
2 + 4 = 2 + 4
A. addition property of equality
B. distributive property
C. multiplication property of equality
D. subtraction property of equality
label each number as rational or irrational
A. 7.23
B. π
C. √2
D. -5
how do u calculate these no from least to greatest 4.2, 3.10, 4 1/8, 3.01, 2.3, 2 4/5 , 3.017
Answer:
2.3, 2.8, 3.01, 3.017, 3.10, 4.125, 4.2
Or [tex]2.3, 2\frac{4}{5}, 3.01, 3.017, 3.10, 4\frac{1}{8}, 4.2[/tex]
Step-by-step explanation:
The given numbers are [tex]4.2, 3.10, 4\frac{1}{8}, 3.01, 2.3, 2\frac{4}{5}, 3.017[/tex]
To arrange them we will covert the fractions into decimals first.
[tex]4.2, 3.10, 4.125, 3.01, 2.3, 2.8, 3.017[/tex]
Let's understand which number is greater among 2.3 and 2.8.
Here 2 is common in both the numbers but after decimal one number has 2 and other 8.
So number having greater number after decimal will be greater than the other one.
Therefore, out of 2.3 and 2.8, 2.8 will be greater.
Now we will arrange all the numbers from least to greatest.
2.3, 2.8, 3.01, 3.017, 3.10, 4.125, 4.2
if p q is true and q is true then p is _____ true
Never
Always
Sometimes
A film student wants to capture a shot of a satellite dish placed at the top of a building. The line of sight between the ground camera and top of the building is 51 feet, and the angel of the camera with respect to the ground is 43 degrees. What is the height of the building?
Answer:
34.78 feet
Step-by-step explanation:
1) using the cosine function, I did cos(43)=x/51
This is because cosine is equal to adjacent over hypotnuse
Once I found x, I used the pythagorean theorem to get 34.78 feet
does the table represent a function? why or why not?
Answer:
No it doesn't represent a function since x = 5 produces y = 2 and y = 3
So the answer is B. No, because one x-value corresponds to two different y-values.
For each value of v, determine whether it is a solution to -52=4-8v. I was given a -9 for the value of v. Please help
In isosceles triangle the length of the base is twice shorter than the length of a leg. The perimeter of this triangle is 50 cm. Find the lengths of all sides.
The length of the base is 10 and the length of each leg is 20.
In order to find this, we can start by making the length of the base x. Now we know that the legs are twice as long, which would make them 2x. Since there are two of them, we can add x + 2x + 2x and set equal to 50 to find the value of x.
x + 2x + 2x = 50
5x = 50
x = 10
Now we can plug this in for our leg length as well to find that.
2x = Leg
2(10) = Leg
20 = leg
A hair care company makes three batches of scented shampoo using the recipe shown. Each batch contains a different total amount of shampoo. Drag numbers to show how much of each scent should be used in each batch of shampoo. 1/2 of the scent is pineapple. 1/5 of the scent is banana. 3/10 of the scent is coconut.
i think there is 5 total units in the shampoo; 2 1/2 units of pineapple; 1/5(5) = 1 unit of banana; and 3/10(5) = 1 1/2 units of coconut. im not fully sure
so if im wrong correct me but have a blessed day/night
=)
The scents for each batch of shampoo are divided as follows: 1/2 pineapple, 1/5 banana, and 3/10 coconut. The real quantities will correlate with the total amount of shampoo in each batch.
Explanation:To determine how much of each scent should be used in the shampoo, we will need to apply fractions. Here's a step-by-step guide:
Pineapple scent: It's given that 1/2 of the scent is pineapple. This simply means that if the total amount of scent used is represented as a whole or '1', then half of it would be pineapple.Banana scent: It's also stated that 1/5 of the scent is banana. This signifies that, a fifth of the total scent used would be banana.Coconut scent: Lastly, 3/10 of the scent is coconut. Thus, slightly less than one third of the total scent would be coconut.The actual amount of each scent will vary depending on the total quantity of shampoo per batch.
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The first term of an arithmetic sequence is 5. The eleventh term is 125. What is the common difference?
Final answer:
The common difference of the arithmetic sequence with the first term of 5 and the eleventh term of 125 is found to be 12, using the formula for the nth term of an arithmetic sequence.
Explanation:
The student is asking how to find the common difference in an arithmetic sequence where the first term is 5 and the eleventh term is 125. To solve this, we can use the formula for the nth term of an arithmetic sequence, which is given by:
Tn = a + (n - 1)d
where Tn is the nth term, a is the first term, n is the term number, and d is the common difference. In this case, we know that a = 5 and T11 = 125, and we want to find d.
So we can set up the equation 125 = 5 + (11 - 1)d, which simplifies to 125 = 5 + 10d. Solving for d, we get d = (125 - 5)/10 = 120/10 = 12. Hence, the common difference of the arithmetic sequence is 12.
Maria bought 4 tops and a pair of pants that cost a total of $96.20 .each top cost the same amount of Money and the pair of pants cost $36.96 . What was the cost of each top ?
Step one: 96.20-36.96=59.24
Step two: 59.24÷4=14.81
Answer: Each top cost $14.81
Can someone help me with this
25t = 5( 5t + 1)
That equation has no solutions.
A scientist measured the energy of a system and found that it was increasing. The data shown represent the energy taken every billionth of a second. Time (nanoseconds) 0 1 2 3 Energy (Joules) 2.654 6.290 14.909 35.335 Classify the type of growth the scientist observed. 1)linear 2)quadratic 4)exponential 5)logarithmic
At start ( t = 0 nanoseconds ) :
E ( t = 0 ) = 2.645 J
E ( t = 1 ) = 6.290 J
E ( t = 1 ) : E ( t = 0 ) = 6.290 : 2.645 = 2.37
Also:
E ( t = 2 ) : E ( t = 1 ) = 14.909 : 6.290 = 2.37
E ( t = 3 ) ; E ( t = 2 ) = 35.335 : 14.909 = 2.37
Therefore, the formula for calculating the energy of the system is:
E ( t ) = 2.645 * 2.37 ^ t
The answer is 4) exponential growth.
At start ( t = 0 nanoseconds ) :
E ( t = 0 ) = 2.645 J
E ( t = 1 ) = 6.290 J
E ( t = 1 ) : E ( t = 0 ) = 6.290 : 2.645 = 2.37
Also:
E ( t = 2 ) : E ( t = 1 ) = 14.909 : 6.290 = 2.37
E ( t = 3 ) ; E ( t = 2 ) = 35.335 : 14.909 = 2.37
E ( t ) = 2.645 * 2.37 ^ t
The answer is 4) exponential growth.
A motorcycle can travel 15 miles on 3/8 of a gallon of gasoline. How far can the motorcycle travel on one gallon of gasoline.
i believe the answer would be 40 miles
the easy way to do it is to look at it as 5 miles for 1/8 gallon of gas and 1 whole gallon is 8/8 so multiply 5 *8=40
40 miles on 1 gallon of gas
Samuel was the last prophet of Israel. True OR False
im going to say true hope this helps
Find the difference of -12, 19
In this scenario, plus 12 and 19 to find 31 therefore the difference is 31
It takes 24 people to pull a 50 ton iron rod. How many people it take to pull a 150 ton iron rod?
72 people.
50 x 3 = 150
24 x 3 = 72
A 2-gallon jug of water costs $9.92. What is the price per cup?
The price per cup for a 2-gallon jug of water costing $9.92 is $0.31.
The question asks us to find the price per cup for a 2-gallon jug of water costing $9.92. First, we need to determine how many cups are in 2 gallons of water.
There are 16 cups in a gallon, so in 2 gallons, there would be 32 cups (16 cups/gallon x 2 gallons = 32 cups). Next, we calculate the price per cup by dividing the total cost by the number of cups.
Total cost of 2 gallons = $9.92
Number of cups in 2 gallons = 32 cups
Price per cup = Total cost / Number of cups
Price per cup = $9.92 / 32 cups
Price per cup = $0.31
B is the midpoint of AC. If AB = 3x + 2 and BC = 5x - 10, find AC
If B is the midpoint of AC, then |AB| = |AC|.
|AB| = 3x + 2
|BC| = 5x - 10
Therefore we have the equation:
3x + 2 = 5x - 10 |subtract 2 from both sides
3x = 5x - 12 |subtract 5x from both sides
-2x = -12 |divide both sides by (-2)
x = 6
The measure of line segment AC is 40 units.
Given that, B is the midpoint of AC.
What is the midpoint of a line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.
Since, B is the midpoint of AC, we get
AB=BC
⇒ 3x + 2 = 5x - 10
⇒ 5x-3x=2+10
⇒ 2x=12
⇒ x=6
So, AC=AB+BC
= 3x + 2 + 5x - 10
= 8x-8
= 8(x-1)
= 8(6-1)
= 40 units
Therefore, the measure of line segment AC is 40 units.
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How to do this question?
Remark
Drawing that diagram was a very good idea. If you can picture something happening, you are half way there. I tend to use a table, but the diagram will come to the same thing.
Olivia Dawn
Start 176 80
Donate x x Subtract
What's left 176 - x 80 - x
Equation
176 - x = 5*(80 - x) Olivia had 5 times as many books as Dawn did. Remove the brackets.
Solution
176 - x = 400 - 5x Add 5x to both sides
176 + 5x - x = 400 Combine terms on the left
176 + 4x = 400 Subtract 176 from both sides
4x = 400 - 176 Combine terms on the right.
4x = 224 Divide by 4
x = 224/4
x = 56 Answer
A savings account at Bank A pays 5% simple interest. An account at Bank B pay 2% compound interest. The table shows the balance in each account after an initial deposit $1000.
Which describes the balance after a long period of time?
The answer is B. The balance in bank b will be greater
Answer:
option B.
Step-by-step explanation:
given,
Bank A pays 5% simple interest
Bank B pays 2% compound interest
both Bank has initial deposit of $1000.
when we look at the table the growth in the 5 years are given.
but when we look for long period of time
company B will be have balance more than company A after long period of time.
hence, the correct answer is option B.
What is the average rate of change for the sequence shown below? a coordinate plane showing the points negative 1, 4. 1, 3. 3, 2. 5, 1.
Answer: - 1/2 = - 0.5
Explanation:
1. Make the sequence clear. These are the given points (x,y):
(-1, 4)(1, 3)(3, 2)(5, 1)2. The average rate of change only takes into account the last and the first pairs of your intervals, those are (5, 1) and (-1, 4).
Average rate of change = [change in y] / [change in x] = [1 - 4] / [5 - (-1) ] =
= - 3 / 6 = - 1/2 = - 0.5 ← answer
The averate ratre of change is the slope of the line that joins the first and last points. The fact that the result is negative means that there was a net decrease of the values.
Michelle has a recipe that asks for 2 1/2 cups of vegetable oil. She wants to use 2/3 that amount of oil use applesauce to replace the rest. How much will she use
To find out how much vegetable oil Michelle will use, you need to multiply 2 1/2 by 2/3, giving us approximately 1 2/3 cups. The rest will be substituted with applesauce which is approximately 5/6 cups.
Explanation:In this scenario, Michelle has a recipe that requires 2 1/2 cups of vegetable oil. She wants to use only 2/3 of the total vegetable oil, and use applesauce for the rest. To find out how much vegetable oil she will use, you need to multiply 2 1/2 by 2/3.
But before that, you need to convert 2 1/2 into an improper fraction, where 2 1/2 is equivalent to 5/2. So, the total amount of vegetable oil Michelle will use can be calculated as follows: (5/2) *(2/3) = 10/6 = 5/3 cups.
This means Michelle will use approximately 1 2/3 cups of vegetable oil. To find out the rest of the substitute in applesauce, simply subtract 1 2/3 from 2 1/2. This equals to approximately 5/6 cups of applesauce.
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Michelle will use 1 2/3 cups of vegetable oil for her recipe and replace the remaining amount with 5/6 cup of applesauce.
Michelle needs to calculate the amount of vegetable oil to use if she wants to use 2/3 of the amount specified in the recipe, and then find how much applesauce to replace the rest of the oil. The original recipe calls for 2 1/2 cups of oil. Firstly, calculate 2/3 of 2 1/2 cups:
Convert 2 1/2 to an improper fraction, which is 5/2.
Multiply 5/2 by 2/3 to find 2/3 of the mixture, which equals (5/2) × (2/3) = 5/3, or 1 2/3 cups.
This is the amount of vegetable oil Michelle will use. Now for the applesauce:
Subtract 1 2/3 cups from 2 1/2 cups to find the amount to replace with applesauce: 2 1/2 - 1 2/3 = 5/2 - 5/3 = 15/6 - 10/6 = 5/6.
Michelle will use 1 2/3 cups of vegetable oil and 5/6 cup of applesauce.
Obtuse, right, acute, scalene, isosceles, equilateral, and equiangular are classifications of
it classifys triangles
a triangle? Is it a shape? If it is then it is a triangle.
seven increased by the product of two numbers
Seven increased by the product of two numbers
The answer would be 7+x*x the variables stand for the 2 unknown numbers and the product is the * symbol. Increased stands as the plus symbol. Hope this helps!
Answer: The expression for the given statement is [tex]7+(x\times y)[/tex]
Step-by-step explanation:
We are given a statement:
Seven increased by the product of two numbers
Let the first number be considered as 'x' and second number be considered as 'y'
'Increased' in the above statement means addition operation.
'Product' in the above statement means multiplication operation.
Hence, the expression for the given statement is [tex]7+(x\times y)[/tex]