Answers
We have a mixture of 300 ml with 15% alcohol content, this means that in this mixture we have an alcohol total of:
[tex]\text{alcohol}=300\cdot\frac{15}{100}=45\text{ ml}[/tex]And we want to obtain a 60% alcohol solution by mixing a 90% mixture with the 15% one we have.
[tex]\begin{gathered} \text{volume 90 \%}=v \\ \text{ alcohool content}=0.9\cdot v \end{gathered}[/tex]When we add this volume to what we already have, we will obtain:
[tex]\begin{gathered} \text{ final mixture}=300+v \\ \text{alcohool content}=45+0.9\cdot v \end{gathered}[/tex]And what we want is that the alcohol content must be equal to 60% of the final mixture, so we have:
[tex]\begin{gathered} 60\text{ \%}\cdot\text{ final mixture}=\text{ alcohol content} \\ \frac{60}{100}\cdot(300+v)=45+0.9\cdot v \\ 0.6\cdot(300+v)=45+0.9\cdot v \\ 180+0.6\cdot v=45+0.9\cdot v \\ \text{0}.9\cdot v-0.6\cdot v=180-45 \\ 0.3\cdot v=135 \\ v=\frac{135}{0.3}=450\text{ ml} \end{gathered}[/tex]This means that we need to add 450 ml of the 90% solution to obtain the desired final mixture.
Related Questions
what are the partial products of 35 x7
Answers
For 35 x 7 the partial products would be: 7 x 30 and 7 x 5.
In this question, we need to find the partial products of 35 x 7.
We know that, when we multiply numbers together, the answer is called as the product.
The partial product method is one way to multiply numbers is to use.
For 35 x 7, the partial products would be: 7 x 30 and 7 x 5.
7 x 30 = 210.
7 x 5 = 35.
When we have the partial products, to find the answer to the problem, we add them together.
210 + 35 = 245.
So, 35 x 7 = 245.
Therefore, for 35 x 7 the partial products would be: 7 x 30 and 7 x 5.
Learn more about the product here:
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A lot is in the shape of a triangle. One side is 100 ft longer than the shortest side, while the third side is 700 ft longer than the shortest side. The perimeter of the lot is 2900 ft. Find the lengths of the lot.The lengths of the sides of the lot are ___,___, and ___ (ft, ft^2, or ft^3.)
Answers
We have the next information
x= the shortest side measure
y= the second side measure
y=x+100
z= the third side measures
z=x+700
We know also that the perimeter is 2900 ft
Therefore the equation for the perimeter of the triangle will be
[tex]P=x+y+z[/tex][tex]2900=x+x+100+x+700[/tex]we sum like terms
[tex]2900=3x+800[/tex]then we isolate the x
[tex]3x=2900-800[/tex][tex]3x=2100[/tex][tex]x=\frac{2100}{3}=700[/tex]therefore
x=700ft
y=700+100=800ft
z=700+700=1400ft
The lengths of the sides of the lote are 700 ,800, and 1400 ft,
help please !!! i’m trying to graduateplease refer left box as “box a” and the right as “box b” :)
Answers
Given:
There are given the two-equation:
[tex]\begin{gathered} f(x)=-0.3(x-2)^2+5...(1) \\ f(x)=0.2(x+2)^2-5...(2) \end{gathered}[/tex]Explanation:
According to the question, we need to find the values of vertex, the axis of symmetry, and focus.
Now,
First, find all values for the first equation:
So,
From the equation (1):
[tex]\begin{equation*} f(x)=-0.3(x-2)^2+5 \end{equation*}[/tex]Then,
From the standard form of the equation of parabola:
[tex]y=a(x-h)^2+k[/tex]Where,
[tex]\begin{gathered} vertex:(h,k) \\ Axis\text{ of symmetry:x=h} \end{gathered}[/tex]Now,
The values for the equation (1) are:
[tex]\begin{gathered} vertex:(2,5) \\ Axis\text{ of symmetry: x=2} \\ focus:(2,4.166) \end{gathered}[/tex]Now,
For the equation (2):
[tex]\begin{equation*} f(x)=0.2(x+2)^2-5 \end{equation*}[/tex]Then,
[tex]\begin{gathered} vertex:(-2,-5) \\ focus:(-2,-3.75) \\ Axis\text{ of symmetry: x=-2} \end{gathered}[/tex]Final answer:
Hence, the all values for both box are shown below:
So,
For the first box:
[tex]\begin{gathered} \begin{equation*} f(x)=-0.3(x-2)^2+5 \end{equation*} \\ vertex:(2,5) \\ focus:(2,4\frac{1}{6}) \\ Ax\imaginaryI s\text{ofsymmetry: x=2} \end{gathered}[/tex]And,
For the second box:
[tex]\begin{gathered} \begin{equation*} f(x)=0.2(x+2)^2-5 \end{equation*} \\ vertex:(-2,-5) \\ focus:(-2,-3\frac{3}{4}) \\ Axis\text{ of symmetry:x = -2} \end{gathered}[/tex]A bank features a savings account that has an annual percentage rate of r = 3.6% with interest compoundedquarterly. Haley deposits $10,000 into the account.The account balance can be modeled by the exponential formula Ale) = a(1+)*,, where A is accountvalue after t years, a is the principal (starting amount), r is the annual percentage rate, k is the number oftimes each year that the interest is compounded.(A) What values should be used for a, r, and k?a =10000T0.036 ok=4(B) How much money will Haley have in the account in 9 years?Answer = $ 13800Round answer to the nearest penny.(C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effectiveannual percentage rate which includes all compounding in the year).APY =Round answer to 3 decimal places.
Answers
The answer to the part C:
Part C asking for APY ( Annual percentage yield )
APY is giving by the formula:
[tex]\text{APY}=(1+\frac{r}{k})^k-1[/tex]Where: r is the annual percentage rate.
k is the number of times each year that the interest is compounded.
Given: r = 3.6% = 0.036 , k = 4
Substitute with (r) and (k) into the formula of APY
So,
[tex]\text{APY}=(1+\frac{0.036}{4})^4-1=1.0364889-1=0.0364889=3.64889\%[/tex]Rounding to 3 decimal places.
So, the answer will be APY = 3.649%
XOSelect the correct answer.Rosa is working on the electrical wiring for a community theater. She creates a diagram of the conduits joining different areas of thetheater on a coordinate grid and uses the line y=-4x+3 to represent the conduit between the stage and the dressing room. Thecondult between the ticket window and the security office passes through the point (4,7) on the grid and is perpendicular to the condultbetween the stage and dressing room.What is the equation of the line representing the conduit between the ticket window and the security office?
Answers
The product of the slopes of the perpendicular lines is -1
That means if the slope of one of them is m, then the slope of the other is -1/m
(we reciprocal it and change its sign)
The given equation is
[tex]y=-4x+3[/tex]The slope of the line of the equation y = mx + b is m
Then the slope of the given line is -4
To find the slope of the perpendicular line to it, reciprocal it and change its sign
Then the slope of the perpendicular line is
[tex]m_P=\frac{1}{4}[/tex]Substitute it in the form of the equation
[tex]y=\frac{1}{4}x+b[/tex]To find b we will use the given point (4, 7) which lies on the perpendicular line
Substitute x by 4 and y by 7 in the equation
[tex]\begin{gathered} 7=\frac{1}{4}(4)+b \\ 7=1+b \\ 7-1=1-1+b \\ 6=b \end{gathered}[/tex]Substitute the value of b in the equation
[tex]y=\frac{1}{4}x+6[/tex]The answer is y = 1/4x + 6
[tex]y=\frac{1}{4}x+6[/tex]The answer is the last choice
A brownie recipe for class 3 1/2 cups of sugar took one cup of chocolate chips. If one and three-quarter cups of sugar issues, but quantity of chocolate chips will be needed, according to the recipe?
Answers
The problem says "3 1/2 cups of sugar took one cup of chocolate chips"
The ratio is: 3 1/2 sugar for each cup of chocolate.
We want to find the quantity of chocolate chips for "one and three-quarter cups of sugar"
First, let's convert 3 1/2 into an improper fraction:
[tex]3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot2}{1\cdot2}+\frac{1}{2}=\frac{6}{2}+\frac{1}{2}=\frac{7}{2}[/tex]Now, we want to find an expression for "one and three-quarter". We can write:
[tex]1\frac{3}{4}=1+\frac{3}{4}=\frac{4}{4}+\frac{3}{4}=\frac{7}{4}[/tex]And now, we can use cross multiplication. If 7/2 of sugar needs 1 cup of chocolate, how many of chocolate if 7/4 of sugar is used? If we call x to the quantity of chocolate needed, we can wirte:
[tex]\frac{\frac{7}{2}}{\frac{7}{4}}=\frac{1}{x}[/tex]Now take the reciprocal on both sides:
[tex]\frac{\frac{7}{4}}{\frac{7}{2}}=x[/tex]And solve:
[tex]x=\frac{7}{4}\cdot\frac{2}{7}=\frac{2}{4}=\frac{1}{2}[/tex]Thus, the answer is: According to the recipe, the quantity of chocolate needed is 1/2 cup.
A person chooses 2 different vowels from the alphabet. What is the sample space in this experiment?
Answers
Given
A person chooses 2 different vowels from the alphabet.
Procedure
Space
[tex]\mleft\lbrace AE,AI,AO,AU,EI,EO,EU,IO,IU,OU\mright\rbrace[/tex]If AE = x + 2 and BD = 4x – 16, then the length of ACI is A6 B. 10 C. 12 D. 24
Answers
Remember that
the diagonals in a rectangle are congruent and bisect each other
that means
AE=BD/2
substitute the given values
x+2=(4x-16)/2
solve for x
2x+4=4x-16
4x-2x=4+16
2x=20
x=10
AC=BD=4(10)-16=24
answer is option DState the type of random sampling that requires that the population be organized into groups. Randomly groups are chosen and all members in the chosen groups are surveyed. A: simpleB: clusteredC: systematicD: stratified
Answers
Recall that the clustered random sample is split into groups and the overall sample consists of every member of some groups it means all members in groups are surveyed. randomly groups are chosen
Hence the required type of random sampling is clustered.
Option B is correct.
A building in a city has a rectangular base. The length of the base measures 75 ft less than three times the width. The perimeter of this base is 890 ft. What are the dimensions of the base?
Answers
The building has a rectangular base .
let
w = width
L= length
Therefore,
L = 3w - 75
perimeter = 890 ft
The dimensions are calculated below
[tex]undefined[/tex]Type a word problem that you need to use addition to solve Use the scaffold if you need help.
Answers
An example of a word problem that we will need to use addition to solve is:
• The sum of 5 and the product of 4 and 2.
This can be interpreted mathematically as:
[tex]=5+(4\times2)[/tex]mm6. Which of the following is not a characteristic of the figure with vertices at coordinates A(1, 3), B(1,5), C(8,5), andD(8,3)F. two sets of parallel linesG. four right anglesH. four verticesI. four equal side lengths
Answers
Consider the diagram ABCD corresponding to the given figure,
Once the figure ABCD is obtained, it is observed that it is a rectangle.
The opposite sides of a rectangle are always equal, so F is the correct choice.
All the internal angles of a rectangle are 90 degree, so G is also correct.
A rectangle definitely has 4 vertices, so H is also correct.
But observe that the length of the rectangle is much more than its width. So it cannot have all four sides equal. Therefore, I is False for the given figure.
Thus, it concludes that option I is the correct choice.
Homework help. Roger uses his truck to plow parking lots when it snows. He wants to find a model to predict the number if service calls he can expect to receive based on the amount of snow will fall. Based on the data he uses the linear model C(s)=0.8s+0.29. According to this model, how many service calls will roger have if 4.7 inches of snow fall
Answers
Step 1
Given the function;
[tex]\begin{gathered} C(s)=0.8s+0.29 \\ \text{where; } \\ s=amount\text{ of snow in inches} \\ C(s)=service\text{ calls} \end{gathered}[/tex]Required; To find how many services calls Roger will have if 4.7 inches of snowfalls
Step 2
Substitute for s=4.7inches
[tex]\begin{gathered} C(4.7)=0.8(4.7)+0.29 \\ C(4.7)=4.05 \\ C(4.7)\approx4\text{ service calls to the nearest whole number} \end{gathered}[/tex]Hence, he will receive approximately to the nearest whole number 4 service calls.
what number would come next in the sequence? 3,11,19,27,35,
Answers
what number would come next in the sequence? 3,11,19,27,35
we have
a1=3
a2=11
a3=19
a4=27
a5=35
so
a2-a1=111-3=8
a3-a2=19-11=8
a4-a3=27-19=8
a5-a4=35-27=8
This is an arithmetic sequence and the common difference d is equal to 8
the next term is
a6=a5+d
a6=35+8=43
answer is 43
Part 2
if Victoria were to put in his school at(0;0) on a coordinate plane her house house would be located at(6,8) if each unit is equal to half of a mile how many miles away from is Victoria house?
Find out the distance
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]substitute the given values
[tex]\begin{gathered} d=\sqrt[]{(8-0)^2+(6-0)^2} \\ d=\sqrt[]{64+36} \\ d=\sqrt[]{100} \\ d=10\text{ units} \end{gathered}[/tex]Remember that
each unit is equal to half of a mile
so
10(1/2)=5 miles
the answer is 5 miles
Suppose that the velocity v(t) (in m/s) of a sky diver falling near the Earth’s surface is given by the following function, where time t is measured in seconds.
Answers
The expression is given as,
[tex]v(t)=53(1-e^{-0.26t})[/tex]Substitute the value t=3 in the above expression and obtain the velocity corresponding to 3 seconds,
[tex]\begin{gathered} v(3)=53(1-e^{-0.26(3)}) \\ v(3)=53(1-e^{-(0.78)}) \\ v(3)\approx53(0.54159) \\ v(3)\approx28.7045 \\ v(3)\approx29 \end{gathered}[/tex]Thus, the velocity of the skydiver is 29 m/s after 3 seconds.
Substitute the value t=5 in the above expression and obtain the velocity corresponding to 5 seconds,
[tex]\begin{gathered} v(5)=53(1-e^{-0.26(5)}) \\ v(5)=53(1-e^{-1.3}) \\ v(5)\approx53(0.727) \\ v(5)\approx38.5558 \\ v(5)\approx39 \end{gathered}[/tex]Thus, the velocity of the skydiver is 39 m/s approximately after 5 seconds.
Solve the inequality and express your answer in interval notation using decimal forms for the numeric value.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Solve the inequality and express your answer in interval notation using decimal forms for the numeric value.
Step 2:
The details of the solution are as follows:
CONCLUSION:
The final answer is:
[tex]Interval\text{ notation: \lparen -}\infty\text{ , 2. 2 \rparen}[/tex]Am I just connecting the points? Or is there something else I have to do?
Answers
It's important to know when the letters have a bar on top like (a), that means you have to draw a segment, as the image below shows.
When the letters have an arrow on top and this arrow as no ending points, that means you have to draw a line which must be infinite.
At last, when the letters have an arrow with one endpoint, then you have to draw a ray that has one ending point and the other extreme is infinite.
There you have them, all the corresponding representations.
Find the length of WXExpress your answer as a fraction times (All info in figure)
Answers
Given:
VW = 5
m∠WVX = 60 degrees
Let's find the length of arc WX.
To find the length of arc WX, apply the formula below.
Apply the formula:
[tex]L=2\pi r\times\frac{\theta}{360}[/tex]Where:
r is the radius = 5
θ is the measure of the central angle = 60 degrees.
Hence, we have:
[tex]\begin{gathered} L=2\pi\times5\times\frac{60}{360} \\ \\ L=10\pi\times\frac{1}{6} \\ \\ L=\frac{10}{6}\pi \\ \\ L=\frac{5}{3}\pi \end{gathered}[/tex]Therefore, the length of arc WX is:
[tex]\frac{5}{3}\pi[/tex]ANSWER:
[tex]\frac{5}{3}\pi[/tex]Decide whether the information defines a function . If it does, state the domain of the function .
Answers
We can remember that a function is a relation between two variables in such a way that the independent variable has EXACTLY one dependent variable.
In this case, we have that:
a ---> 0
b ---> 1
c ---> 0
d ---> 1
We do not find that the variable has other value. It has only a value of 0.
It does not matter that the other values have the same output.
Thus, this information 'tells us' that the relation is a function.
Additionally, the domain of the function, in this case, are all the elements in the input row, that is:
Domain: {a, b, c, d}
Solve for x:2 (x+5) = (x - 4) ?
Answers
Solving for x :
[tex]\begin{gathered} 2(x+5)=(x-4) \\ \rightarrow2x+10=x-4 \\ \rightarrow2x-x=-4-10 \\ \rightarrow x=-14 \\ \\ \Rightarrow x=-14 \end{gathered}[/tex]Thereby, x = -14
A cylinder has a height of 15 feet in a diameter of 14feetFind the volume for each problem used 3.14 for pi in round your answer to the nearest tenth
Answers
In general, the volume of a cylinder is given by the formula below
[tex]\begin{gathered} V_{cylinder}=\pi r^2h \\ \pi=3.14 \\ r\rightarrow\text{ radius, one half of the diameter} \\ h\rightarrow\text{ height} \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} V_{cylinder}=3.14*(\frac{14}{2})^2*15=3.14*49*15=2307.9 \\ \Rightarrow V_{cylinder}=2307.9 \end{gathered}[/tex]The answer is 2307.9ft^3
Line f is graphed on the coordinate grid shown. What is the slope of a line perpendicular to Line f?
Answers
From the property of lines :
If two lines are perpendicular then, the product of the slope of both the lines are equal to ( - 1)
where slope of line is express as :
[tex]\text{ Slope=}\frac{y_2-y_1}{x_2-x_1}[/tex]For the slope of the given line,
consider any two coordinates : (-2, 0) & (0,4)
Substitute the coordinates in the expression of the slope,
[tex]\begin{gathered} \text{ Slope=}\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope}=\frac{4-0}{0-(-2)} \\ \text{Slope}=\frac{4}{2} \\ \text{Slope}=2 \end{gathered}[/tex]Slope = 2
Let the slope of the given line is express as m i.e. m = 2
Consider the slope of the line which is perpendicular to given line f is n
Apply the property of line :
Product of slope = (- 1 )
m x n = ( - 1)
Substitute the values :
2 x n = ( -1)
n = (- 1) /2
Slope of the line which is perpendicular to the line f is (-1/2)
Answer : Slope of the line which is perpendicular to the line f is (-1/2)
How many feet did the grasshopper travel after hopping twice? A. 25 B. D. 45 9 C. 2 9 14 9 Ο Α OB O OD
Answers
Explanation:
If the grasshopper travels a distance of 5 feet in 9 equal hops, then in each hops it travels 5/9 feet.
Now we want to know how many feet does it travel after 2 hops. It will be twice one hop:
[tex]\frac{5}{9}\times2=\frac{10}{9}=1\frac{1}{9}[/tex]Answer:
The grasshopper traveled 1 1/9 feet after hopping twice
Last week, Rose Petropolis earned gross pay of $820. Her employer deducted $109 in federal withholding taxes, 6.2% in Social Security taxes, 1.45% in Medicare taxes, $74 in health insurance, and $45 in union dues. What was Rose's net pay?
Answers
Explanation:
We have to substract the amounts her empoyer deducted from her gross pay:
First we have to find the percentages:
Social security: 6.2%:
[tex]820\times\frac{6.2}{100}=820\times0.062=50.84[/tex]Medicare 1.45%:
[tex]820\times\frac{1.45}{100}=820\times0.0145=11.89[/tex]In total:
[tex]820-109-50.84-11.89-74-45=529.27[/tex]Answer:
Rose's net pay was $529.27
fill in the table using this function rule y = 25 - 2x
Answers
Answer
x | y
1 | 23
2 | 21
5 | 15
6 | 13
Explanation
We can solve each of these by inserting the values for x
y = 25 - 2x
when x = 1
y = 25 - 2x
y = 25 - 2(1)
y = 25 - 2
y = 23
when x = 2
y = 25 - 2x
y = 25 - 2(2)
y = 25 - 4
y = 21
when x = 5
y = 25 - 2x
y = 25 - 2(5)
y = 25 - 10
y = 15
when x = 6
y = 25 - 2x
y = 25 - 2(6)
y = 25 - 12
y = 13
Hope this Helps!!!
what is the pattern for 6, 1, 8, 4, 2, 7 please explain
Answers
Let's begin by identifying key information given to us:
[tex]6,1,8,4,2,7[/tex]The series has no convergence since the differences between the numbers don't converge
A food pantry gave away a total of 200 turkeys on Monday and continued to give out 25 turkeys each day of the rest of the week. Which explicit equation represents this situation?
Answers
hello
since this question request we solve for the explicit formula, we are going to assume that the sequence is an arithmetic progression and the formula of explicit formula is given as
[tex]\begin{gathered} f(n)=a+(n-1)d \\ a=\text{ first term } \\ n=\text{nth term} \\ d=common\text{ difference} \end{gathered}[/tex]in this case, we can define our values as
[tex]\begin{gathered} a=200 \\ d=25 \\ n=n \end{gathered}[/tex][tex]\begin{gathered} f(n)=200+(n-1)25 \\ n=\text{ number of days} \end{gathered}[/tex]what’s the area of the kite?area= __ m squared simply your answer
Answers
Answer:
40 m^2
Explanation:
Given:
To find:
Area of a kite
Note that the area(A) of a kite can be determined by taking half the product of the lengths of the diagonals as seen below;
[tex]\begin{gathered} A=\frac{(3+7)*(4+4)}{2} \\ =\frac{10*8}{2} \\ =\frac{80}{2} \\ =40\text{ m}^2 \end{gathered}[/tex]So the area of the given kite is 40 m^2
The price of a Math Book after discount of 25% off is $36 what is the original price of the math book
Answers
$48
Explanation:Discount = 25% = 0.25
The final price = $36
Percentage of the original price = 100% -25% = 75%
Percentage of the original price = 0.75
let the original price = y
Percentage of the original price × original price = 36
0.75 × y = 36
0.75y = 36
[tex]\begin{gathered} y\text{ = }\frac{36}{0.75} \\ y\text{ = 48} \end{gathered}[/tex]The original price of the math book = $48
Which of the following integers is a solution to x > -2?-5-3-4-1
Answers
Given:
The inequality is x>-2.
Required:
Choose the correct option for the solution to the inequality.
Explanation:
The given inequality is x>-2.
The solution to the inequality is the points that are greater than -2.
From the given options the point that is greater than -2 is -1.
So -1 is the solution to the inequality x>-2.
Final Answer:
The last option is the correct answer.