Answers
We have the next information
4 cups of water
1 cup lemon concentrate
in total, we have 5 cups of lemonade
5 ----- 100%
1 ------ x
x is the percentage of lemon concentrate
[tex]x=\frac{100}{5}=20[/tex]the percentage of lemon concentrate in the lemonade is 20%
Related Questions
The percentage of students in the school that attended the talent show for the years 2008 to 2013 are shown.This Year, the school had a total of 360 students. How many students do you expect to attend the talent show this year? Explain.
Answers
Considering this year as the last year in the table which is 2013
[tex]\text{the total number of students in 2013=360}[/tex][tex]\text{The percentage of students attendance in 2013=95\%}[/tex]Therefore,
The number of students to attend this year's talent show will be calculated by
[tex]A\text{ttendance}=\text{percentage of students}\times total\text{ number of students}[/tex][tex]\begin{gathered} \text{Attendance}=95\text{ \%}\times360 \\ \text{Attendance}=\frac{95}{100}\times360 \\ \text{Attendance}=\frac{34200}{100} \\ \text{Attendance}=342\text{ students} \end{gathered}[/tex]Hence.
The attendance for this year is 342 students
How do I know which score is the highest frequency? how do I figure the scores had a frequency of 2?
Answers
To determine the score which presents the highest frequency, we need to check the last column, the frequency one, and find the highest value among them. The score which is in the same row that this value will be the score with the highest frequency.
In the present problem, there are values of frequency equal to 1, 2, 3, and 4. The one with frequency 4 is the one with the highest frequency. (8th row). And the Score related to it is Score 8.Once we check the frequency column once again, we see that the 2nd, the 4th, and the 7th rows have a frequency equal to 2.
Checking the Scores of the related rows, we are able to say that the scores with frequency 2 are: 2, 4, and 7.how can you obtain the points for the log below from its inverse?
Answers
Answer
Check Explanation
Explanation
The laws of logarithms will come in handy in helping to obtain the points for the log from its inverse.
Before we commence, the two laws of logarithms that we will be using is that
log₄ 4ᶜ = c (log₄ 4)
And
log₄ 4 = 1
So, no matter the value of inverse given, a simple mathematical evaluation will give the log points.
when x = 1
f(x) = log₄ x
f(1) = log₄ 1 = log₄ 4⁰ = 0 log₄ 4 = 0 × 1 = 0
when x = 4
f(x) = log₄ x
f(4) = log₄ 4 = log₄ 4¹ = 1 (log₄ 4) = 1 × 1 = 1
when x = 16
f(x) = log₄ x
f(16) = log₄ 16 = log₄ 4² = 2 (log₄ 4) = 2 × 1 = 2
when x = 64
f(x) = log₄ x
f(64) = log₄ 64 = log₄ 4³ = 3 (log₄ 4) = 3 × 1 = 3
Hope this Helps!!!
Michael withdraws $40 from his checking account each day how long will it take him to withdraw $680
Answers
Solution
- The amount Michael withdraws every day is $40.
- The number of days it takes to withdraw $680 is given by:
[tex]\frac{\text{Total Amount Withdrawn}}{\text{Amount Withdrawn per day}}[/tex]- Using the formula above, we have:
[tex]\frac{\text{Total Amount Withdrawn}}{\text{Amount Withdrawn per day}}=\frac{680}{40}=17\text{ days}[/tex]Final Answer
The answer is 17 days
How else can you write 6p in mathematic terms?
Answers
In mathematic terms, the expression 6p is written as 6 times p.
Mathematic terms
Mathematic terms means a single mathematical expression. The terms may be a single number, a single variable, several variables multiplied but never added or subtracted. Some of the terms contain variables with a number in front of them. Those number in front of a term is called a coefficient.
Given,
Here we have the expression 6p.
Now, we have to write it as a mathematic term.
While we looking into the expression 6p.
The only operation word in this expression is p which is multiplied with the constant that is the number 6.
So, in the verbal phrase it can be written as 6 times p.
Here p take any valid number in the real numbers.
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A small company produces baseball and racquetball by the function B(x)=-6x^2+2,556x-106,878. The profit made from the racquetball products can be represented by the function R(x)=-x^2+293x-16,770. If x is the total number of products made, which function best describes P(x), the profit the company makes from these two products?
Answers
profit made from the baseball products
[tex]B(x)=-6x^2+2556x-106878[/tex]Profit made from the racquetball products
[tex]R(x)=-x^2+293x-16770[/tex]Profit made from those 2 products is
[tex]\begin{gathered} P(x)=-6x^2-x^2+2556x+293x-106878-16770 \\ P(x)=-7x^2+2849x-123648 \end{gathered}[/tex]A triangle has two sides of length 13 and 17. What is the largest possible whole numberlength for the third side?
Answers
Given two sides of a triangle, x, and z, such that
[tex]x\le z[/tex]then the third side y must satisfy the following condition
[tex]z-xIn our case,x =13, and z = 17
Then, the third side y
lies in
17-13 < x < 17 +13
4 < x < 30
Hence the largest possible whole number of the third side is 29
A portion of $ 100,000 (x) is invested with a 3% after one year. The rest of the investment (and) obtained a return of 1%. The total return on investment was $ 1,800. 1) What equation shows the return on investment? 2) What equation shows how the $ 100,000 was divided?3) how much money was invested at a 3% rate of return?4) how much money was invested at a rate of return of 1%
Answers
We can write a system of equations that describe our problem.
Since we don't know how the original $100,000 was divided, we call the two parts X and Y
So we know that X + Y = 100000
Then we know the Combined Interest coming from the accounts.
We use the Interest formula for return on investment:
I = P * r * t
were P is the principal, r is the percent rate (in decimal form), and t is the number of years (in our case 1)
Then the interest from the 3% account (let's call it I1) (if X amount of money was deposited there) is:
I1 = X * 0.03 * 1 = 0.03 X
Similarly, the interest I2 coming from the 1% account (if Y amount of money was deposited there) is given by:
I2 = Y * 0.01 * 1 = 0.01 Y
Then, the addition of these two interest is our total return of $1800:
0.03 X + 0.01 Y = 1800
Then our system of equations is:
X + Y = 100000
0.03 X + 0.01 Y = 1800
which we solve by substituting for example for Y in the first equation:
Y = 100000 - X
and replacing the Y by this expression in our second equation:
0.03 X + 0.01 (100000 - X) = 1800
use distributive property to eliminate parenthesis:
0.03 X + 1000 - 0.01 X = 1800
combine like terms
0.02 X + 1000 = 1800
subtract 1000 from both sides
0.02 X = 800
divide both sides by 0.02 to completely isolate X:
X = 800 / 0.02
X = $40000
This is the amount deposited on the 3% account
Then we easily calculate the amount deposited in the other account by replacing x with $40000 in the equation we use for substitution:
Y = $100000 - $40000 = $60000
Then, the amount deposited in the 1% account was $60000
and the amount deposited in the 3% account was $40000.
What is the solution to 4x-8=12 please explain
Answers
Given the equation 4x-8=12 you need to clear the value of x.
First step is to leave the value of x in one side of the equation and the integers in the other side, to do so you have to add 8 to both sides of the equation
[tex]\begin{gathered} 4x-8=12 \\ 4x-8+8=12+8 \\ 4x=20 \end{gathered}[/tex]Next you have to divide both terms of the equation by 4 to get the value of x
[tex]\begin{gathered} 4x=20 \\ \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]The value of x=5
There is a 40% chance that it will be cloudy tomorrow.
If it is cloudy, there is a 79% chance that it will rain.
What is the probability that it will rain?
Answers
Answer:
3.16%
Step-by-step explanation:
a*(79/100)*40/100
3.16a/100
3.16%
Answer:
O. 316
Step-by-step explanation:
40/100 × 79/100 =0.316
a turtle swims 15 kilometers in 9 hours how long does it take the turtle to swim 18 kilometers?
Answers
Answer:
10.8 hours or 648 minutes
Step-by-step explanation:
1. Find a factor of 15 and 18 kilometers. A similar factor is 3.
2. Find how long it will take the turtle to swim 3 kilometers.
3. Divide 9 by 5 which is how long it takes to swim three hours. (Keep it in a fraction for now)
4.Multiply 9/5 by 6 to get 18 hours; which is 10.8 hours.
name each angle pair as corresponding, alternate interior, alternate exterior, consecutive interior angle, or no relationship. identify the transversal that connects each angle pair.
Answers
Graph the linear equation.
x=-2/12/12
X=
Use the graphing tool to graph the linear equation.
Click to
enlarge
graph
3
10
8
6
2
d
4
6
8
40
Answers
The graph of (3, 2) is located 3 units to the right of the y-axis and 2 units above the x-axis, while the graphs of (-3, 2), (-3, -2) and (3, -2) are located 3 units to the left of the y-axis and 2 units below the x-axis, 3 units to the right of the y-axis, and 3 units to the bottom of the x-axis, respectively.
What is linear equations?The ordinate of the point is the distance from the x-axis that it is placed at, and the abscissa of the point is the distance from the y-axis that it is located at. An algebraic equation of the type known as a linear equation.
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Find x when the f(x) = 350 - 125x ; when f(x) = 0.
Answers
ANSWER
x = 2.8
EXPLANATION
The function given is:
f(x) = 350 - 125x
We want to find the value of x when f(x) = 0.
This means that:
[tex]\begin{gathered} f(x)\text{ = 350 - 125x} \\ \Rightarrow\text{ 0 = 350 - 125x} \\ \Rightarrow\text{ 125x = 350} \\ \frac{125x}{125}\text{ = }\frac{350}{125} \\ x\text{ = 2.8} \end{gathered}[/tex]That is the value of x
Pep Boys Automotive paid $208.50 for a pickup truck bed liner. The original selling price was $291.90, but this was marked down 35%. If operating expenses are 28% of the cost, find the absolute loss
Answers
Step 1: State the given in the question
THe following were given:
[tex]\begin{gathered} \text{Amount Paid (}A_{\text{paid}})=208.50 \\ (Originalsellingprice)SP_{ORIGINAL}=291.90 \\ \text{Marked Percentage=35\%} \\ \text{Operating expenses=28\%} \end{gathered}[/tex]Step 2: State what is to be found
We are to find the absolute loss
Step 3: Calculate the selling price
Please note that the selling price is the marked down price
The marked down price would be
[tex]\begin{gathered} P_{\text{MARKED DOWN}}=(100-35)\text{ \% of original selling price} \\ P_{\text{MARKED DOWN}}=65\text{ \% of }SP_{ORIGINAL} \\ P_{\text{MARKED DOWN}}=\frac{65}{100}\times291.90=189.74 \end{gathered}[/tex]The selling price is the marked down price which is $189.74
Step 4: Calcualte the operating expenses
Please note that the cost price is amount paid. Therefore, the operating expenses would be as calculated below:
[tex]\begin{gathered} E_{\text{OPEARATING}}=28\text{ \% of Amount Paid} \\ E_{\text{OPERATING}}=28\text{ \% of }A_{\text{paid}}=\frac{28}{100}\times208.50 \\ E_{\text{OPERATING}}=0.28\times208.50=58.38 \end{gathered}[/tex]Hence, the operating expenses is $58.38
Step 5: Calculate the total cost price
The total cost price is the addition of the cost price and the operating expenses. This is as calculated below:
[tex]\begin{gathered} C_{\text{TOTAL COST PRICE}}=E_{OPERATING}+A_{PAID} \\ C_{\text{TOTAL COST PRICE}}=58.38+208.50=266.88 \end{gathered}[/tex]Hence, the total cost price is $266.88
Step 6: Calculate the absolute loss
The absolute loss is the difference between the total cost price and the marked down price (or the actual selling price). This is as calculated below:
[tex]\begin{gathered} L_{\text{ABSOLUTE LOSS}}=C_{TOTAL\text{ COST PRICE}}-P_{MARKED\text{ DOWN}} \\ L_{\text{ABSOLUTE LOSS}}=266.88-189.74=77.14 \end{gathered}[/tex]Hence, the absolute loss is $77.14
The Consumer Price Index (CPI), which measures the cost of a typical package of consumer goods, was 202.9 in 2011 and 233.2 in 2016. Let x=11 correspond to the year 2011 and estimate the CPI in 2013 and 2014. Assume that the data can be modeled by a straight line and that the trend continues indefinitely. Use two data points to find such a line and then estimate the requested quantities. Let y represent the CPI. The linear equation that best models the CPI is____ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to the nearest hundredth as needed.)
Answers
The first thing we have to identify in our problem are the variables
[tex]\begin{gathered} x\to\text{time} \\ y\to\text{CPI} \end{gathered}[/tex]Now we see the points (x,y) that gives us the problem
[tex]\begin{gathered} 2011\to(11,202.9) \\ 2016\to(16,233.2) \end{gathered}[/tex]Since behavior can be modeled by a straight line, we use the general equation of the straight line
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the y-intercept.
Taking this into account and with the 2 points that they give us, we proceed to calculate the equation of the line starting with the slope:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{233.2-202.9}{16-11} \\ m=\frac{30.3}{5} \\ m=6.06 \end{gathered}[/tex][tex]\begin{gathered} y=6.06x+b \\ 202.9=6.06(11)+b \\ b=202.9-66.66 \\ b=136.24 \end{gathered}[/tex]The equation that models the behavior of the CPI is
[tex]y=6.06x+136.24[/tex]Now we calculate the CPI values for the years 2013 and 2014
[tex]\begin{gathered} 2013\to x=13 \\ y=6.06(13)+136.24 \\ y=78.78+136.24 \\ y=215.02 \end{gathered}[/tex][tex]\begin{gathered} 2014\to x=14 \\ y=6.06(14)+136.24 \\ y=84.84+136.24 \\ y=221.08 \end{gathered}[/tex]make a table of values then graph the following quadratic functions, label atleast 5 points
Answers
Given the function below:
[tex]f(x)=\frac{-4(x-3)^2}{9}+4[/tex]Substituting each value of x in the table in the function above, we get
[tex]\begin{gathered} f(0)=\frac{-4(0-3)^2}{9}+4\text{ = }\frac{-4(-3)^2}{9}+4 \\ \\ f(0)=\frac{-4\times9}{9}+4\text{ =-4+4 = 0} \end{gathered}[/tex][tex]f(1)=\frac{-4(1-3)^2}{9}+4\text{ =}\frac{-4\times4}{9}+4=\frac{-16}{9}+4=\frac{20}{9}[/tex][tex]f(6)=\frac{-4(6-3)^2}{9}+4\text{ = }\frac{-4(3^2)}{9}+4\text{ =-4+4 = 0}[/tex]How is the input force different from the output force?
Responses
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is all of the energy applied to the situation, and the output force is the result.
The input force is applied to the problem, and the output force is the movement that results.
The input force is applied to the problem, and the output force is the movement that results.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The output force is applied to the simple machine, and the input force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object.
Answers
The input force different from the output force is D. The input force is applied to the simple machine, and the output force is the force the simple machine applies to an object."
What is a simple machine?A simple machine is a mechanical device that alters the magnitude or direction of a force. In general, they are the most basic systems that exploit mechanical advantage to multiply force.
A simple machine is a mechanical device that adjusts the direction or amplitude of a force. According to Newton's third law, if object A exerts a force on object B, object B will exert a force of same size and opposite direction on object A.
In that situation, the input force is done by object A, and the output force is done by object B as a reaction.
With this in mind, we can see that the proper answer is: "The input force is applied to the simple machine, and the output force is the force applied to an item."
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Answer the statistical measures and create a box and whiskers plot for the following set of data.
Answers
Solution
The picture below is the solution to the problem
Brief explanantion
From the data given, It is obvious that:
Minimum = 2
Maximum =
The total number of the data is 3, so the number 7th term is the median
Thus,
Median = 8
To find Q1
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)th\text{ term} \\ Q_1=\frac{1}{4}(13+1)=\frac{14}{4}=3.5 \end{gathered}[/tex]Q1 is between the third and fourth term
Therefore, Q1 is
[tex]Q_1=0.5(4)+0.5(6)=5[/tex]Similarly, to find Q3
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_3=\frac{3}{4}(13+1)=3\times\frac{14}{4}=3\times3.5=10.5 \end{gathered}[/tex]Q3 is between the tenth and the eleventh term
Therefore, Q3 is
[tex]Q_3=0.5(11)+0.5(11)=11[/tex]the math club has 18 members and 50% are sixth graders.The science club has 25 members and 40% are sixth graders. The principal wants to know which club has more sixth graders.
Answers
The science club had more sixth graders.
How to calculate the value?The math club has 18 members and 50% are sixth graders. The number of sixth graders will be:
= Percentage × Number of members
= 50% × 18
= 0.5 × 18
= 9
The science club has 25 members and 40% are sixth graders. The number of sixth graders will be:
= Percentage × Number of members
= 40% × 25
= 0.4 × 25
= 10
Since 10 is more than 5, the science class has higher number.
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Write a mathematical sentence that expresses the information given below. Use b as your variable name. If necessary:
type < = to mean
or > = to mean .
If you need to show multiplication, do not use the letter x. Use the asterisk ( * ) symbol instead, or simplify your answer.
Emily has 300 books. If Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
Answers
The number of books owned by frank is represented as b < 150
What is inequality?Inequality represents the form of writing expressions where the left hand side of the expression is not exactly equal to the right hand side of the expression
How to represent the required expressionInformation gotten from the data include
Emily has 300 books
Frank were to double the number of books that he now owns, he would still have fewer than Emily has.
Let the number of books owned by frank be b and from the information we have that:
2b < 300
b < 150
hence the number of books owned by frank, b less than 150
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A coin is tossed nine times what is the probability of getting all tails express your answer as a simplified fraction or decimal rounded to four decimal places
Answers
The probability of getting a tail on each toss is:
[tex]\frac{1}{2}[/tex]Since there is only one way of getting all tails, it follows that the required probability is given by:
[tex](\frac{1}{2})^9\approx0.0020[/tex]Hence, the required probability is approximately 0.0020
For each ordered pair, determine whether it is a solution to 7x - 4y = -5.(x,y)(-2,6) it is a solution yes or no(1,3) it is a solution yes or no(-3,4) it is a solution yes or no(4,2) it is a solution yes or no
Answers
If x=1, then:
[tex]\begin{gathered} 7(1)-4y=-5 \\ \Rightarrow-4y=-5-7=-12 \\ \Rightarrow y=\frac{-12}{-4}=3 \\ \\ y=3 \end{gathered}[/tex]therefore, a solution to the equation 7x-4y=-5 is (1,3)
If the cost of a car is $6,345.00, and the tax rate is 6%, how much is the total cost of the car?
Answers
Given:
Cost of Car is $6,345
Tax rate is 6%
[tex]\begin{gathered} \text{Tax Amount=6345}\times\frac{6}{100} \\ \text{Tax Amount= \$380.70} \end{gathered}[/tex][tex]\begin{gathered} \text{Total cost of the car =6345+380.70} \\ \text{Total cost of the car = \$6725.70} \end{gathered}[/tex]Determine a third pair of congruent parts to establish congruence between the triangles. Give the congruence postulate involved
Answers
In this problem, we have that
mYO ≅ XO
The third pair of congruent parts is
m by vertical angles
therefore
triangle YOT ≅ triangle XOB ----> by ASA congruence postulate
r is the midpoint of op and qr is perpendicular to op in the diagram below find the the length of qr
Answers
Given:
OP = 20 in
QP = 26 in
Since R is the midpoint of OP, then, OR = RP
Thus
[tex]OR=RP=\frac{OP}{2}=\frac{20}{2}=10\text{ in}[/tex]To find the length of QR, use pythagoras theorem below:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \\ RP^2+QR^2=PQ^2 \end{gathered}[/tex]Input values into the formula:
[tex]10^2+QR^2=26^2[/tex]Subtract 10² from both sides:
[tex]\begin{gathered} 10^2-10^2+QR^2=26^2-10^2 \\ \\ QR^2=26^2-10^2 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{QR^2}=\sqrt[]{26^2-10^2} \\ \\ QR=\sqrt[]{676-100} \\ \\ QR=\sqrt[]{576} \\ \\ QR=24 \end{gathered}[/tex]Therefore, the length of QR is 24 in
5x^2+2x-3 and x+4 how do I find the area
Answers
You have a rectangle with the followinf expressions for its sides:
w: width = 5x² + 2x - 3
h: height = x + 4
In order to calculate the area of the rectangle, you use the following formula for the area:
A = w*h
By replacing w and h by the given algebraic expressions you have:
A = (5x² + 2x - 3)(x + 4) use distribution property
A = 5x²(x) + 5x²(4) + 2x(x) + 2x(4) - 3(x) - 3(4) simplify
A = 5x³ + 20x² + 2x² + 8x - 3x - 12 simplify similar terms
A = 5x³ + 22x² + 5x - 12
Hence, the total area of the figure is 5x³ + 22x² + 5x - 12
Question 2 (7 points)Match the fractions and decimals to the corrects percentage.
Answers
we can change a fraction to a percentage multiplying the fraction by 100
also, we can change a decimal number to a percentage multiplying by 100
for example
1. 1/5
[tex]\frac{1}{5}\cdot100=20[/tex]In this case, 1/5 represent 20%
4. .625
[tex]0.625\cdot100=62.5[/tex]In this case, 0.625 represent 62.5%
If we do the same process to all the next numbers we will obtain the next solutions.
1. 1/5 ------ a. 20%
2. 8/10 ------ f. 80%
3. 0.08 ------ d. 8%
4. .625 ---- g. 62.5%
5. 32/100 ---- b. 32%
6. 1/2 ------ c. 50%
7. 1.25 ---- e. 125%
Which of the following is a proportion?8/10=6/83/4=12/154/6=9/126/9=8/12
Answers
To be able to determine which among the choices is a proportion, you check if each side has the same common ratio.
A. 8/10 = 6/8
Ratio: 0.80 = 0.75 (Not Proportional)
B. 3/4 = 12/15
Ratio: 0.75 = 0.80 (Not Proportional)
C. 4/6 = 9/12
Ratio: 0.67 = 0.75 (Not Proportional)
D. 6/9 = 8/12
Ratio: 0.67 = 0.67 (Proportional)
Since the ratio of each side of letter D is equal, Letter D is the one that is in Proportion.
Find the exact length of the arc intercepted by a central angle on a circle of radius . Then round to the nearest tenth of a unit.
Answers
Given:
Angle subtended at the center = 135 degrees
radius (r) = 4 yd
Solution
The formula for the length (l) of an arc is given as:
[tex]\begin{gathered} l\text{ = }\frac{\phi}{360^0}\text{ }\times\text{ 2}\pi r \\ \text{where }\phi\text{ is the angle subtend}ed\text{ at the center} \end{gathered}[/tex]When we substitute the given parameters, we can find the length (l) of the arc:
[tex]\begin{gathered} l\text{ = }\frac{135}{360}\text{ }\times\text{ 2 }\times\text{ }\pi\text{ }\times\text{ 4} \\ =3\pi \\ \approx\text{ 9.4 yd (nearest tenth)} \end{gathered}[/tex]Answer: 9.4 yd or 3.0 pi
