Answers
For the 1st fruit drink, 220 pints will be used
For the 2nd fruit drink, 40 pints will be used
Explanation:1st type has concentration = 35% = 0.35
2nd type has concentration = 100% = 1
let the amount for the 35% pure fruit = x
Total amount of fruit juice to be made = 260
amount for the 35% pure fruit + amount for the 100% pure fruit = 260
amount for the 100% pure fruit = 260 - x
concentration of mixture = 45% = 0.45
Amount = 260 pints
concentration for the 1st type (amount) + concentration of the 2nd type (amount) = concentration of mixture (amount)
[tex]0.35(x)\text{ + 1}(260\text{ - x})\text{ = 0.45}(260)[/tex]Solve for x:
[tex]\begin{gathered} 0.35x\text{ + 260 - x = 117} \\ 0.35x\text{ - x + 260 = 117} \\ -0.65x\text{ + 260 = 117} \\ -0.65x\text{ = 117 - 260} \end{gathered}[/tex][tex]\begin{gathered} -0.65x\text{ = - 143} \\ divide\text{ both sides by -0.65:} \\ \frac{-0.65x}{-0.65}\text{ = }\frac{-143}{-0.65} \\ x\text{ = 220} \\ \\ Amount\text{ for 35\% pure fruit = 220pints} \end{gathered}[/tex]Amount for the 100% pure fruit = 260 - x
Amount for the 100% pure fruit = 260 - 220 = 40 pints
For the 1st fruit drink, 220 pints will be used and for the 2nd fruit drink, 40 pints will be used
Related Questions
find the probability:P( z > 1.11 )
Answers
ANSWER
P(Z > 1.11) = 0.1335
EXPLANATION
If we look for the z-score 1.11 in a z-table, we will find the probability that Z is less than 1.11. We can use it to find the probability that Z is greater than 1.11, knowing that,
[tex]P(Z>1.11)=1-P(Z<1.11)[/tex]Let's find this probability in a z-table,
So, the probability is,
[tex]P(Z>1.11)=1-0.8665=0.1335[/tex]Hence, the probability that z is greater than 1.11 is 0.1335.
What is the area, in square meters, of the shape below? 7.6 m 7.6 m
Answers
Question:
Find the area, in swuare meters, of the shape above
Answer:
Remember that the formula for the area of any triangle is:
[tex]\frac{b\times h}{2}[/tex]Where:
• b, is the lenght of the triangle's base
,• h, is the height of the triangle
Using this expression with the triangle in the image, we get:
[tex]\begin{gathered} \frac{b\times h}{2}\rightarrow\frac{7.6\times7.6}{2} \\ \rightarrow28.88m^2 \end{gathered}[/tex]Therefore, the area of the triangle is 28.88 square meters.
can you help me i really ned help one this ques
Answers
As given by the question
There are given that the function
[tex]h(x)=3x^2-7[/tex]Now,
The transformation of the given function is:
vertical shift down, 7 units, and vertical stretched.
So,
The graph vertical stretched and vertical shift down by 7 units.
Hence, option B is correct.
hi how are you? can we work together assignment pls?
Answers
Given
The integers 1, 4, -3.
To locate the given numbers in the given number line.
Explanation:
The numbers 1 and 4 are positive.
Therefore, it is located to the right of zero.
Also, the number -3 is negative.
Therefore, it is located in the left of zero.
That implies,
1. Draw a graph for the scenario below. Remember to label the axes.The level of water in a river rose rapidly during the storm then gradually decreased back to the originallevel.2. A student drew the dashed line on the graph shown and concluded
Answers
ANSWER and EXPLANATION
We want to draw a graph to describe the scenario given.
The x axis will be labelled as time spent by storm.
This is because the time of the storm is the independent variable. The level of water in the river depends on the time by spent by the storm.
The y axis will be laballed as level of water in the river.
This is because it is the dependent the variable.
Since the level of water rises rapidly initially, the graph will go from a low value to a high value in a short span of time.
Then it will gradually go down again since the water level dropped gradually.
The graph will look like that.
for the polynomial below, what is the coefficient of the term with the power of 3[tex] {x}^{2} + \frac{1}{3} {x}^{4} + 6x + 5[/tex]
Answers
We have the polynomial:
[tex]x^3+\frac{1}{3}x^4+6x+5[/tex]The coeficient of the term with the power of 3 is 1, because we have:
[tex]x^3=1\cdot x^3[/tex]The correct answer is B.
Edwin deposited money into a savings account that pays a simple annual interestrate of 1.2%. He earned $27 in interest after 3 years. How much did he deposit?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Edwin deposited money into a savings account that pays a simple annual interest rate of 1.2%.
He earned $27 in interest after 3 years.
How much did he deposit?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Simple\text{ Interest = }\frac{Principa\text{l x Rate x Time}}{100} \\ Interest\text{ = \$ 27} \\ Time\text{ = 3 years} \\ Principal\text{ = P} \\ Rate\text{ = 1.2 \%} \end{gathered}[/tex]Making P the subject of the formulae, we have that:
[tex]\begin{gathered} P\text{ =}\frac{100\text{ x Simple Interest}}{Rate\text{ X Time}} \\ P\text{ = }\frac{100\text{ x 27}}{1.\text{ 2 x 3}} \\ P\text{ = }\frac{2700}{3.6} \\ P=\text{ \$ 750} \end{gathered}[/tex]CONCLUSION:
He deposited $ 750
-15•monomial•other polynomial•binomial•trinomial
Answers
Answer
The polynomial given is a monomial.
Explanation
The term used to describe any polynomial depends on how many terms are in the polynomial.
•monomial
A polynomial with only one term.
•other polynomial
A polynomial with more than three terms.
•binomial
A polynomial with only two terms.
•trinomial
A polynomial with only three terms.
For this question,
The polynomial = -15
The polynomial has only one term, hence, this is a monmial.
Hope this Helps!!!
What amount of money will grow to $71,200 in 2 years and 9 months at the interest rate of 6.41% p.a.? compound interestI already solved the problem but I want to see if I’m correct
Answers
Explanation:
We will use the compound interst formula below
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where,
[tex]\begin{gathered} A=71200 \\ r=\frac{6.41}{100}=0.0641 \\ t=2\frac{9}{12}=2.75years \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 71200=P(1+0.0641)^{2.75} \\ 71200=P(1.0641)^{2.75} \\ P=\frac{71200}{(1.0641)^{2.75}} \\ P=60.017.55 \end{gathered}[/tex]Hence,
The final answer is
[tex]\text{ \$}60.017.55[/tex]find the volume of a cube? 8 inches
Answers
A cube has all it sides equal.
The volume of a cube is given by Length x Length x Length
[tex]\begin{gathered} Volume=8X8X8inches^3 \\ \text{Volume = 512 inches }^3 \end{gathered}[/tex]Use algebra to rewrite the following identity in 2 different forms. tan^2(θ) + 1 = sec^2(θ)
Answers
Let's rewrite the identity in two different forms conserving the functions given:
[tex]\tan ^2\theta-\sec ^2\theta=-1[/tex]and
[tex]\tan ^2\theta=\sec ^2\theta-1[/tex]Now, let's find two different identities from this one. To do this let's remember that:
[tex]\begin{gathered} \tan \theta=\frac{\sin \theta}{\cos \theta} \\ \sec \theta=\frac{1}{\cos \theta} \end{gathered}[/tex]Then we have:
[tex]\begin{gathered} \tan ^2\theta+1=\sec ^2\theta \\ \tan ^2\theta-\sec ^2\theta=-1 \\ \frac{\sin^2\theta}{\cos^2\theta}-\frac{1}{\cos^2\theta}=-1 \\ \frac{\sin^2\theta-1}{\cos^2\theta}=-1 \\ \sin ^2\theta-1=-\cos ^2\theta \\ \sin ^2\theta+\cos ^2\theta=1 \end{gathered}[/tex]Therefore, we can write the identity given as:
[tex]\sin ^2\theta+\cos ^2\theta=1[/tex]Let's find a second identity from the one given, to do this we will mutiply it by the cotangent squared of the angle:
[tex]\begin{gathered} \tan ^2\theta+1=\sec ^2\theta \\ \tan ^2\theta\cdot\cot ^2\theta+\cot ^2\theta=\sec ^2\theta\cdot\cot ^2\theta \\ \frac{\sin^2\theta}{\cos^2\theta}\cdot\frac{\cos^2\theta}{\sin^2\theta}+\cot ^2\theta=\frac{1}{\cos^2\theta}\cdot\frac{\cos ^2\theta}{\sin ^2\theta} \\ 1+\cot ^2\theta=\frac{1}{\sin ^2\theta} \\ 1+\cot ^2\theta=\csc ^2\theta \end{gathered}[/tex]Therefore, we can write the identity given as:
[tex]1+\cot ^2\theta=\csc ^2\theta[/tex]what is the circumference? I have to type a exact answer in terms of π.
Answers
The sloth travels 1/3 meters in 1/10 minute. What is the sloth's running speed? Include the unit of measure.
Answers
Fractions
We are given the distance traveled by a sloth as d=1/3 meters and the time it took of t=1/10 minute.
The speed can be calculated as
[tex]v=\frac{d}{t}[/tex]Substituting values:
[tex]v=\frac{\frac{1}{3}}{\frac{1}{10}}[/tex]To divide the fractions, we multiply by the reciprocal of the denominator:
[tex]v=\frac{1}{3}\cdot\frac{10}{1}=\frac{10}{3}[/tex]Since the distance was given in meters and the time was given in minutes, the speed is calculated in m/min.
The sloth's running speed is 10/3 m/min
Solve each equation Show steps for credit 6.6=n-47.r-2=58.6=m+6
Answers
Answer:
• n=10
,• r=7
Explanation:
No 6
Given the equation:
[tex]6=n-4[/tex]To solve for n, add 4 to both sides of the equation:
[tex]\begin{gathered} 6+4=n-4+4 \\ 10=n \end{gathered}[/tex]The value of n is 10.
No 7
Given the equation:
[tex]r-2=5[/tex]To solve for r, add 2 to both sides of the equation:
[tex]\begin{gathered} r-2+2=5+2 \\ r=7 \end{gathered}[/tex]The value of r is 7.
6. A hot air balloon rises from the ground. Does the height of the balloon vary directly with the time it has been in the air? How do you know? Time (minutes) 5 7 10 15 Height (feet) 70 98 140 210
Answers
yes, it vary directly with the time, because:
[tex]\begin{gathered} \text{let:} \\ h=\text{height} \\ t=\text{time} \\ h(t)=kt \\ \text{Where:} \\ k=\text{constant of proportionality} \end{gathered}[/tex]For t = 5 , h = 70
so:
[tex]\begin{gathered} 70=k\cdot5 \\ k=\frac{70}{5} \\ k=14 \end{gathered}[/tex]If:
[tex]\begin{gathered} t=7\colon \\ h(7)=14\cdot7=98 \\ t=10\colon \\ h(10)=14\cdot10=140 \\ t=15\colon \\ h(15)=14\cdot15=210 \end{gathered}[/tex]Since there is a constant of direct proportionality for each of the values, the function varies directly
Given the unit circle what is the value of x
Answers
The equation of the unit circle is
[tex]x^2+y^2=1[/tex][tex]\text{ The point (x,}\frac{3}{4})\text{ lies on the given unit circle.}[/tex]Replace x=x and y=3/4 in the equation, we get
[tex]x^2+(\frac{3}{4})^2=1[/tex][tex]x^2+\frac{9}{16}=1[/tex]Subtracting 9/4 from both sides, we get
[tex]x^2+\frac{9}{16}-\frac{9}{16}=1-\frac{9}{16}[/tex][tex]x^2=\frac{16}{16}-\frac{9}{16}[/tex][tex]x^2=\frac{16-9}{16}[/tex][tex]x^2=\frac{7}{16}[/tex]Taking square root on both sides, we get
[tex]x=\pm\sqrt[]{\frac{7}{16}}[/tex][tex]x=\pm\frac{\sqrt[]{7}}{4}[/tex][tex]x=\frac{\sqrt[]{7}}{4}\text{ or }x=-\frac{\sqrt[]{7}}{4}\text{ }[/tex]Hence the required value of x is
[tex]\text{ }x=-\frac{\sqrt[]{7}}{4}\text{ }[/tex](2, -3) and (3, -2)Find the slope.
Answers
Given the points:
(x1, y1) ==> (2, -3)
(x2, y2) ==> (3, -2)
To find the slope, use the formula below:
[tex]\text{Slope}=\frac{y2-y1}{x2-x1}[/tex]Thus, we have:
[tex]\text{Slope = }\frac{-2-(-3)}{3-2}=\frac{-2+3}{1}=\frac{1}{1}=1[/tex]The slope of the line is 1
ANSWER:
1
V640 A.580 B.C.go B3O D.
Answers
Answer: C.
Ravi’s chocolate bar is 62% cocoa. if the weight of the chocolate bar is 61 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Answers
Recall that the x% of y can be computed using the following expression:
[tex]y\cdot\frac{x}{100}\text{.}[/tex]Now, since Ravi's chocolate bar is 62% cocoa, and the weight of the chocolate bar is 61 gr, then the chocolate bar contains:
[tex]61\cdot\frac{62}{100}[/tex]grams of cocoa.
Simplifying the above result we get:
[tex]61\cdot0.62=37.82\approx37.8.[/tex]Answer: Ravi's chocolate bar contains 37.8 grams.
how do I find the following answer to parts A ?
Answers
Given that DE is the midsegment of ΔABC, then:
[tex]\frac{1}{2}BC\text{ = }DE[/tex]BD = DA
AE = EC
Option A is true because:
AC = AE + EC
AC - AE = EC
Option B is true because:
AD + DB = AB
AD + AD = AB (BD = DA)
2AD = AB
AD = 1/2AB
Option C is true because:
1/2BC = DE
BC = 2DE
Given that ΔABC is scalene, then AB ≠ AC ≠ BC, in consequence, AD ≠ AE. Then option D is the correct option
Gabby worked 60 hours in 7 days. Determine the rate for a ratio of the two different quantities.
Answers
As per the data, Gabby worked 60 hours in 7 days , the required rate for a ratio of the two different quantities is equal to (60 /7) hours per day.
As given in the question,
Number of days Gabby worked = 7 days
Number of hours Gabby worked = 60 hours
Then the required rate for a ratio of the two different quantities that is hours and days is equal to
60 hours in 7 days
In worked done in 1 day is equal to
7 days = 60 hours
1 day = ( 60 / 7 ) hours per day
Therefore, as per the data, Gabby worked 60 hours in 7 days , the required rate for a ratio of the two different quantities is equal to
(60 /7) hours per day.
Learn more about ratio here
brainly.com/question/13419413
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I don't understand how to find the quotient of 2.8√68.32
Answers
Answer:
The quotient is;
[tex]24.4[/tex]Explanation:
We want to find the quotient;
[tex]\frac{68.32}{2.8}[/tex]Solving, we have;
Therefore, the quotient is;
[tex]\frac{68.32}{2.8}=24.4[/tex]y = f(x)The graph of the linear function f is shown in thexy-plane above. The graph of the linear function g(not shown) is perpendicular to the graph offand passes throu the point (1,3). What is thevalue of g(0)?
Answers
Answer:
g(0) = 5/2
Step-by-step explanation:
The equation of a line is given by:
y = ax + b
In which a is the slope, which is given by the variation in y divided by the variation in x.
If two lines are perpendicular, the multiplication of their slopes is -1.
Line f:
Passes through the points (0,3) and (1,1).
Variation in y: 1 - 3 = -2
Variation in x: 1 - 0 = 1
Slope = -2/1 = -2.
Line g:
Perpendicular to g, so the slope is:
-2*a = -1
2a = 1
a = 1/2
So the line g has an equation given by:
y = (1/2)*x + b
Passes through the point (1,3).
This means that when x = 1, y = 3. We use this to find b.
3 = (1/2)*1 + b
b = 3 - 1/2
b = 5/2
So:
g = y(x) = (1/2)*x + 5/2
g(0) = (1/2)*0 + 5/2 = 5/2
g(0) = 5/2
Answer : its c
Explanation
what is -44 a rational number an integer or a whole number
Answers
integer and rational
Whole numbers have no decimals. (no negatives)
Rational numbers can be represented as a ratio: -44/1
Integers are negative and positive counting numbers.
Translate point A 9units right and 3 units up.Drag and place the BLUE dot to show the location of A where is the location of A'?
Answers
we have that
Part 1
Point A(-7,-7)
The rule to translate point A is
(x,y) -------> (x+9, y+3)
so
A(-7,-7) -------> A'(-7+9,-7+3)
A'(2, -4)
Part 2
The rule to translate point B is
(x,y) ------> (x-5, y+6)
we have
B(7,-3)
so
B(7,-3) ------- B'(7-5,-3+6)
B'(2,3)
Write the equation of the parabola in vertex form, factored form, and general form.
Answers
The vertex form of the parabola is
[tex]y=(x-1)^2-4[/tex]the general form is
[tex]y=x^2-2x-3[/tex]and the factored form is
[tex]y=(x+1)(x-3)[/tex]To solve this, we look at the graph and see that the vertex coordinates are (1,-4)
the vertex form is
[tex]y=a(x-h)^2+k[/tex]where h is the x coordinate of the vertex and k is the y coordinate. now we have to find the value of a
the factor form is
[tex]y=a(x-x_1)(x-x_2)[/tex]where x1 and x2 are the roots of the parabola. we know the coordinates of the roots: (-1,0) (3,0)
now, we can use this to find the value of a
[tex]y=a(x+1)(x-3)[/tex]now we plug the coodinates of the vertex (1,-4) in the equation before and solve for a
[tex]-4=a(1+1)(1-3)[/tex][tex]\frac{-4}{-4}=1=a[/tex]now we just add the value of a to the factor and vertex forms. the only thing remaining is the general form. for this we need to apply the distributive property in the factor form
[tex]y=(x+1)(x-3)=x^2-2x-3[/tex]and thus, we have all three forms calculated
1. Max had $36.06. He spent $14.60 on a new shirt and $4.95 on a pack of socks. How much money did Max have left? type
Answers
$16.51
Explanation
to solve this we can use a subtraction
make
Max had $36.06 (positive)
He spent $14.60 on a new shir(negative)
$4.95 on a pack of socks(negative)
so, the money he left is
Money he left0 money he had- money he spent
Step 1
add to final the total money he spent
[tex]\begin{gathered} \text{money spent=new shirt+a pack of socks} \\ \text{replace} \\ \text{money spent=14.60+4.95=19.55} \end{gathered}[/tex]Step 2
find the money left
money left=money he had-money he spent
replace
[tex]\text{money left}=36.06-19.55=16.51[/tex]so, the answer is $16.51
I hope this helps you
Write the word sentence as an equation. Then solve the equation.A number multiplied by 2/5 is3/20Equation:Solution: x=
Answers
Answer: x=0.375
Explanation:
The sentence we have is:
"A number multiplied by 2/5 is 3/20"
We can call that number x, and we get the following equation:
[tex]\frac{2}{5}x=\frac{3}{20}[/tex]that is the first part.
Now we need to solve that equation for x.
Step 1: Multiply the left side and right side by 20 (to cancel the 20 in the right side)
[tex]20(\frac{2}{5}x)=3[/tex]Step 2: Solve the operations on the left
[tex]\begin{gathered} \frac{40x}{5}=3 \\ 8x=3 \end{gathered}[/tex]Step 3: Divide both sides of the equation by 8
[tex]\begin{gathered} x=\frac{3}{8} \\ x=0.375 \end{gathered}[/tex]Answer: x=0.375
A band is receiving $650.00 for playing at a festival. Their manager takes 15% of the money received for each show, and the band pays their sound technician 10% of all profit. How much money is left for the band to split?
Answers
We have the following:
To find the answer we must subtract the percentages as follows
[tex]\begin{gathered} 650-\frac{15}{100}\cdot650-\frac{10}{100}\cdot650 \\ 650-97.5-65=487.5 \end{gathered}[/tex]Therefore to distribute among the band $487.5
after filling a gas tank the odometer read 42,911.8. after the next filling it resd 43,373.8. it took 17.5 gal to fill the tank. how many miles per gallon did the driver get?
Answers
26.4 miles per gallon
Explanantion:We need to find the difference in the odometer reading. This will give the number miles it covered.
Initial = 42,911.8
Next raeding = 43,373.8
difference = 43373.8 - 42911.8 = 462
Distance = 462 miles
Number of gallons = 17.5gal
Miles per gallon = distance/number of gallons
Miles per gallon = 462/17.5
Miles per gallon = 26.4 miles per gallon