1. Write a linear equation of the form y1 = mx + b for your first set of data.2. Write a linear equation of the form y2 = mx + b for the other equation in your system. 3. Graph and explain the solution.
Answers
Given:
Company A: transport 56 people in one hour for $40 per person in 30 minutes
Company B:
Related Questions
A baker has 85 cups of flour to make bread. She uses 6 1/4 cups of flour for each loaf of bread. How many loaf of bread can she make
Answers
Answer;
The number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]Explanation:
Given that a baker has 85 cups of flour to make bread.
[tex]A=85\text{ cups}[/tex]And for each bread she uses 6 1/4 cups of flour.
[tex]r=6\frac{1}{4}\text{ cups}[/tex]The number of loaf of bread she can make can be calculated by dividing the total amount of flour by the amount of flour per bread;
[tex]\begin{gathered} n=\frac{A}{r}=\frac{85}{6\frac{1}{4}}=\frac{85}{6.25} \\ n=13.6 \end{gathered}[/tex]Since it will not complete the 14th loaf of bread.
So, the number of loaf of bread she can make is;
[tex]13\text{ loaves}[/tex]Help me out please I don’t understand what I’m doing
Answers
Since we have the value for selling each shirt, the earnings that came from the hats sold and the total earnings we can complete equation using a linear equation in which the cost of each shirt will represent the slope and the y-intercept will be the earnings that came from the hats, like this:
[tex]5x+40=125[/tex]then clear the equation for x in order to find how many shirts were sold
[tex]\begin{gathered} 5x=125-40 \\ 5x=85 \\ x=17 \end{gathered}[/tex]Show all five steps of the hypothesis test. You can either type them in here, or write them out on paper and send me a scan/picture of your work.The average movie ticket in 2010 cost $7.89. A random sample of 15 movie tickets from the suburbs of a large U.S. city indicated that the mean cost was $11.09 with a standard deviation of $4.86. At the 0.01 level of significance, can it be concluded that the mean in this area is higher than the national average?
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Step 1
State the null and alternative hypothesis
[tex]\begin{gathered} H_o=7.89 \\ H_a>7.89 \end{gathered}[/tex]Step 2
State the p-value of the significance level.
[tex]\begin{gathered} \alpha=0.01 \\ p=\frac{\alpha}{2}=\frac{0.01}{2}=0.005 \end{gathered}[/tex]Step 3
Calculate the statistical test
[tex]\begin{gathered} n=15 \\ \mu(\operatorname{mean})=11.09 \\ \sigma(s\tan dard\text{ deviation)=4.86} \end{gathered}[/tex]The t-test formula is given as
[tex]t=\text{ }\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Where
[tex]\begin{gathered} \bar{x}=\operatorname{mean} \\ \mu=theoretical\text{ }value \\ \end{gathered}[/tex][tex]\begin{gathered} t=\frac{7.89-11.09}{\frac{4.86}{\sqrt[]{15}}} \\ t=\frac{7.89-11.09}{1.254846604} \\ t=\frac{-3.2}{1.254846604} \\ t=-2.550112492 \end{gathered}[/tex]Step 4
Find the p-value from the t-test.
[tex]\text{The p-value from the t-test is 0.01}209[/tex]Step 5
Conclusion
The result is not significant at p<0.01. Therefore, the null hypothesis is rejected. It cannot be concluded that the mean in this area is higher than the national average because the p-value is greater than 0.01t
what is a unit rate for meter per second if a car travels 274 m in 17 seconds
Answers
The rate is 274m/17s = 16.1176m/s
The Ruiz family took a summer trip.
In 4 days, they drove 1,600 miles. If they drove an equal
number of miles each day, how many miles did they drive
each day? Describe the basic fact you use to find your
answer and how many zeros you add from the dividend.
Answers
Answer:
400 miles each day
Step-by-step explanation:
You have 1600 miles divided into four days.
1600 / 4
We can use the basic fact that multiplying a number by ten simply means shifting everything to the left, for example 2 x 10 = 20, we just shifted 2 to the left and inserted a 0.
So for this problem, we can do the same. Divide 1600 by 100, or 10 x 10, then divide by 4.
1600/16 = 100
16/4 = 4.
Now, since we divided by ten twice before, we can get the right answer by multiplying by ten twice.
4 x 10 = 40
40 x 10 = 400
F(x) = 5-7x find f(-3)
Answers
Answer:
26
Step-by-step explanation:
Just plug -3 in where ever you see x
[tex]f(x)=5-7x\\f(-3)=5-7(-3)\\f(-3)=5+21\\f(-3)=26[/tex]
Which points are included in the solution Set of the systems of equations graphed below?
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Given:
Required:
We need to find the points are included in the solution
Explanation:
Recall that the solution of the system of inequalities is the intersection region of all the solutions in the system.
The points G and F lie inside the intersection.
The points in the solution are G and F.
Final answer:
Points F and G.
What is the sequence that has a recursive formula A(n)= A(n-1)+4 where A(1)=3
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1) Considering that, let's find each term:
[tex]\begin{gathered} a_1=3 \\ a_n=a_{n-1}+4 \\ a_2=a_1+4\Rightarrow a_2=3+4=7 \\ a_3=a_2+4\Rightarrow a_3=7+4\text{ =11} \\ a_4=11+4\text{ }\Rightarrow a_4=15 \end{gathered}[/tex]2) So the sequence is
[tex](3,7,11,15,\ldots)[/tex]As each term, from the 2nd one is 4 units more that's why we can make it using a recursive formula
Solve each word problem using a system of equations. Use substitution or elimination. 1. One number added to three times another number is 24. Five times the first number added to three times the other number is 36.
Answers
ANSWER
The first number is 3 and the second number is 7
EXPLANATION
Let the first number be x.
Let the second number be y.
The first line of the word problem is:
One number added to three times another number is 24.
This means that:
x + 3(y) = 24
=> x + 3y = 24 ______(1)
The second line of the word problem is:
Five times the first number added to three times the other number is 36.
5(x) + 3(y) = 36
5x + 3y = 36 ______(2)
Now, we have a system of equations:
x + 3y = 24 ____(1)
5x + 3y = 36 ___(2)
From the first equation, we have that:
x = 24 - 3y
Substitute that into the second equation:
5(24 - 3y) + 3y = 36
120 - 15y + 3y = 36
Collect like terms:
-15y + 3y = 36 - 120
-12y = -84
Divide through by -12:
y = -84 / -12
y = 7
Recall that:
x = 24 - 3y
=> x = 24 - 3(7) = 24 - 21
x = 3
Therefore, the first number is 3 and the second number is 7.
Add these fractions using fraction bars after choosing a common denominator Use the fraction bar inactivate to find the difference
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The fractions you have to add are 1/3 and -5/6
[tex]\frac{1}{3}+(-\frac{5}{6})[/tex]The denominators are "3" and "6"
The common denominator between both numbers is 6.
6*1=6
3*2=6
Multiply 1/3 by factor 2 so that both fractions will have the same denominator
[tex]\frac{1}{3}\cdot2=\frac{1\cdot2}{3\cdot2}=\frac{2}{6}[/tex]Now you can add both fractions
[tex]\frac{2}{6}+(-\frac{5}{6})=\frac{2}{6}-\frac{5}{6}=\frac{2-5}{6}=-\frac{3}{6}[/tex]The result is not in its most reduced form, to siplify the fraction divide both the numerator and denominator by 3
[tex]-\frac{3}{6}\div3=-\frac{1}{2}[/tex]The result is -1/2, in the number line:
What is the solution to14h + 6 = 2(5 + 7h) - 4 ?
Answers
14h + 6 = 2(5 + 7h) - 4
First , apply distributive porperty to solve the parentheses:
14h+6 =2(5)+2(7h)-4
14h+6 = 10+14h-4
Move the "h " terms to the left:
14h-14h = 10-4-6
0 = 0
h has infinite solutions.
distance of (-5,-3) and (-9,4)
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Answer:11
Step-by-step explanation:
12 = - 2/5 yI got -30 I want to see if I did the correct steps
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Solution
[tex]12=-\frac{2}{5}y[/tex]Step 1: Simplify the expression
[tex]\begin{gathered} 12=-\frac{2}{5}y \\ \text{cross multiply} \\ 12(5)=-2y \\ 60=-2y \end{gathered}[/tex]Step 2: Divide the both side by -2
[tex]\begin{gathered} 60=-2y \\ \frac{60}{-2}=-\frac{2y}{-2} \\ y=-30 \end{gathered}[/tex]Therefore the correct value of y = - 30
What is a stem and leaf plot? How is it used and how exactly do i solve one? (an example would be great)
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A stem and leaf plot is a table where each of the data is divided into two parts. The stem, that is the first digit and the leaf is the last digits. Let's say that we have the following set of data.
[tex]10,\text{ 12, 25, 28, 29, 35, 38, 40, 44}[/tex]If we want to make a stem and leaf plot of that data, we first write a column where we place the first digit of each number without repetition, like this:
[tex]\begin{gathered} 1 \\ 2 \\ 3 \\ 4 \end{gathered}[/tex]These are the stems. Now the leaves are the last digit of each number put in order next to the corresponding first digit, like this:
[tex]\begin{gathered} 1\parallel\text{ 0 2} \\ 2\parallel\text{ 5 8 9} \\ 3\text{ }\parallel\text{5 8} \\ 4\text{ }\parallel\text{0 4} \end{gathered}[/tex]Find the coordinates of point p that partition AB in the ratio 1: 4,
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Given:
[tex]A(1,-1)\text{ ; B(}4,4)\text{ m:n =1:4}[/tex][tex](x,y)=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex][tex](x,y)=(\frac{4+4}{1+4},\frac{4-4}{1+4})[/tex][tex](x,y)=(\frac{8}{5},0)[/tex]Therefore the point P be ( 1.6 ,0)
consider the graph of the function f(x)= 10^x what is the range of function g if g(x)= -f(x) -5 ?
Answers
SOLUTION
So, from the graph, we are looking for the range of
[tex]\begin{gathered} g(x)=-f(x)-5 \\ where\text{ } \\ f(x)=10^x \\ \end{gathered}[/tex]The graph of g(x) is shown below
[tex]g(x)=-10^x-5[/tex]The range is determined from the y-axis or the y-values. We can see that the y-values is from negative infinity and ends in -5. So the range is between
negative infinity to -5.
So we have
[tex]\begin{gathered} f(x)<-5\text{ or } \\ (-\infty,-5) \end{gathered}[/tex]So, comparing this to the options given, we can see that
The answer is option B
3. An equation that crosses the y-axis at -5 and crosses the x-axis at 24. An equation that crosses the y-axis at -5 and crosses the x-axis at -65. An equation that crosses the y-axis at -5 and crosses the point (2,3)
Answers
We need to find the equation of the line which:
• crosses the y-axis at -5
,• crosses the x-axis at 2
The y-axis cutting point is (0,-5)
The x-axis cutting point is (2,0)
The equation of line is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-axis cutting point
m is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
y_2 = 0
y_1 = -5
x_2 = 2
x_1 = 0
So, slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0--5}{2-0}=\frac{0+5}{2}=\frac{5}{2}[/tex]We got m, we also know b.
The y cutting point is -5, so b = -5
The equation is:
[tex]y=\frac{5}{2}x-5[/tex]The graph would look like:
More clear version:
Consider the quadratic f(x)=x^2-x-30Determine the following ( enter all numerical answers as integers,fraction or decimals$The smallest (leftmost) x-intercepts is x=The largest (rightmost)x-intercepts is x=The y-intercept is y=The vertex is The line of symmetry has the equation
Answers
ANSWER
Smallest x-intercept: x = -5
Largest x-intercept: x = 6
y-intercept: y = -30
The vertex is (1/2, -121/4)
Line of symmetry x = 1/2
EXPLANATION
Given:
[tex]f(x)\text{ = x}^2\text{ - x - 30}[/tex]Desired Results:
1. Smallest x-intercept: x =
2. Largest x-intercept: x =
3. y-intercept: y =
4. The vertex is
5. Equation of Line of symmetry
1. Determine the x-intercepts by equating f(x) to zero (0).
[tex]\begin{gathered} 0\text{ = x}^2-x-30 \\ x^2-6x+5x-30\text{ = 0} \\ x(x-6)+5(x-6)=0 \\ (x-6)(x+5)=0 \\ x-6=0,\text{ x+5=0} \\ x\text{ = 6, x = -5} \end{gathered}[/tex]The smallest and largest x-intercepts are -5 and 6 respectively.
2. Determine the y-intercept by equating x to 0
[tex]\begin{gathered} y\text{ = \lparen0\rparen}^2-0-30 \\ y\text{ = -30} \end{gathered}[/tex]y-intercept is -30
3a. Determine the x-coordinate of the vertex using the formula
[tex]x\text{ = -}\frac{b}{2a}[/tex]where:
a = 1
b = -1
Substitute the values
[tex]\begin{gathered} x\text{ = -}\frac{(-1)}{2(1)} \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]3b. Determine the y-coordinate of the vertex by substituting x into the equation
[tex]\begin{gathered} y\text{ = \lparen}\frac{1}{2})^2-\frac{1}{2}-30 \\ y\text{ = }\frac{1}{4}-\frac{1}{2}-30 \\ Find\text{ LCM} \\ y\text{ = }\frac{1-2-120}{4} \\ y\text{ = -}\frac{121}{4} \end{gathered}[/tex]4. Determine the line of symmetry
In standard form the line of symmetry of a quadratic function can be identified using the formula
[tex]\begin{gathered} x\text{ = -}\frac{b}{2a} \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]Consider the following functions round your answer to two decimal places if necessary
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Solution
Step 1:
[tex]\begin{gathered} f(x)\text{ = }\sqrt{x\text{ + 2}} \\ \\ g(x)\text{ = }\frac{x-2}{2} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} (\text{ f . g\rparen\lparen x\rparen = }\sqrt{\frac{x-2}{2}+2} \\ \\ (\text{ f . g\rparen\lparen x\rparen }=\text{ }\sqrt{\frac{x\text{ +2}}{2}} \end{gathered}[/tex]Step 3
Domain definition
[tex]\begin{gathered} The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values \\ \:for\:which\:the\:function\:is\:real\:and\:defined. \\ \mathrm{The\:function\:domain} \\ x\ge \:-2 \\ \\ \:\mathrm{Interval\:Notation:}\text{ \lbrack-2, }\infty) \end{gathered}[/tex]Final answer
The crew knows the amount of dirt the truck can hold each trip in cubic yards.
Answers
Given:
Measurements of hole are 48ft 39ft and and 9ft
Required:
Volume in cubic yd
total number of trip
total cost of trip
Explanation:
First we need to convert given measurements from ft to yd
[tex]\begin{gathered} 3ft=1yd \\ 48ft=16yd \\ 39ft=13yd \\ 9ft=3yd \end{gathered}[/tex]
A)
[tex]V=lhw=16*13*3=624yd^3[/tex]B)
11 cubic yd in 1 trip
then
624 cubic yd in x trip
[tex]x=\frac{624}{11}=56.7\approx57[/tex]C)
cost for 1 trip is $1175
then
cost for 57 trip is y
[tex]y=57*1175=66975[/tex]Final answer:
Volume in cubic yd is 624
total number of trips is 57
total cost of trip $66975
helppppppppppppppppppppppppppp
Answers
Step-by-step explanation:
make the fractions decimals and put them on the plot
Find a degree 3 polynomial with real coefficients having zeros 3 and 1 - 32 and a lead coefficient of 1.
Write Pin expanded form. Be sure to write the full equation, including P(x)
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The polynomial function of least degree with only real coefficients will be; y = x³ - 8 · x² + 22 · x - 20.
What is polynomial ?Algebraic expressions called polynomials include constants and indeterminates. Polynomials can be thought of as a type of mathematics.
The statement indicates that the polynomial has real coefficients having zeros 3 and 1 - 32 and a lead coefficient of 1.
By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then we get;
y = 1 · (x - 3) · (x - 3 - i) · (x - 3 + i)
y = (x - 3) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]
y = (x - 3) · (x² - 6 · x + 9 - i²)
y = (x - 3) · (x² - 6 · x + 10)
y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20
y = x³ - 8 · x² + 22 · x - 20
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Answer:
[tex]p(x)=x^3-5x^2+16x-30[/tex]
Step-by-step explanation:
Given information:
Degree 3 polynomial with real coefficients.Zeros: 3 and (1 - 3i).Lead coefficient of 1.For any complex number [tex]z = a+bi[/tex] , the complex conjugate of the number is defined as [tex]z^*=a-bi[/tex].
If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.
Therefore, if p(x) is a polynomial with real coefficients, and (1 - 3i) is a root of p(x)=0, then its complex conjugate (1 + 3i) is also a root of p(x)=0.
Therefore, the polynomial in factored form is:
[tex]p(x)=a(x-3)(x-(1-3i))(x-(1+3i))[/tex]
As the leading coefficient is 1, then a = 1:
[tex]p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]
Expand the polynomial:
[tex]\implies p(x)=(x-3)(x-(1-3i))(x-(1+3i))[/tex]
[tex]\implies p(x)=(x-3)(x-1+3i)(x-1-3i)[/tex]
[tex]\implies p(x)=(x-3)(x^2-x-3xi-x+1+3i+3ix-3i-9i^2)[/tex]
[tex]\implies p(x)=(x-3)(x^2-x-x-3xi+3ix+1+3i-3i-9i^2)[/tex]
[tex]\implies p(x)=(x-3)(x^2-2x+1-9(-1))[/tex]
[tex]\implies p(x)=(x-3)(x^2-2x+10)[/tex]
[tex]\implies p(x)=x^3-2x^2+10x-3x^2+6x-30[/tex]
[tex]\implies p(x)=x^3-2x^2-3x^2+10x+6x-30[/tex]
[tex]\implies p(x)=x^3-5x^2+16x-30[/tex]
Instructions: Factor 2x2 + 252 + 50. Rewrite the trinomial with the c-term expanded, using the two factors. Answer: 24 50
Answers
Given the polynomial:
[tex]undefined[/tex]How to draw the graphs of the following non-linear functions?y=x^2 + 1y=3^x + 1
Answers
The first step is to substitute values of x into each equation.
For y = x^2 + 1,
if x = - 2, y = (- 2)^2 + 1 = 4 + 1 = 5
if x = - 1, y = (- 1)^2 + 1 = 1 + 1 = 2
if x = 0, y = (0)^2 + 1 = 0 + 1 = 1
if x = 1, y = (1)^2 + 1 = 1 + 1 = 2
if x = 2, y = (2)^2 + 1 = 4 + 1 = 5
We would plot the corresponding values of x and y on the graph as shown below
For y = 3^(x + 1),
if x = - 2, y = 3^(-2 + 1) = 3^-1 = 0.33
if x = - 1, y = 3^(-1 + 1) = 3^0 = 1
if x = 0, y = 3^(0 + 1) = 3^1 = 3
if x = 1, y = 3^(1 + 1) = 3^2 = 9
if x = 2, y = 3^(2 + 1) = 3^3 = 27
We would plot the corresponding values of x and y on the graph as shown below
You have an investment account that has a balance of $50,000. If the account iscompounded daily and has an interest rate of 4%, how much did you originally depositinto the account 10 years ago?
Answers
Since we know the future alue of the account, using the formula for the compounded interest with n = 365 (since the account is compounded daily), t=10, r = 4% and A=50000 in the following equation:
[tex]A=P(1+\frac{r}{n})^{n\cdot t}[/tex]using these values and solving for P, we get:
[tex]\begin{gathered} 50000=P(1+\frac{0.04}{365})^{365\cdot10} \\ \Rightarrow P=\frac{50000}{(1+\frac{0.04}{365})^{3650}}=33516.74 \\ P=33,516.74 \end{gathered}[/tex]therefore, the original amount deposited 10 years ago is $33,516.74
The table shows a proportional relationship.
x 12 8 24
y 3 2 6
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (3, 12).
A line passes through the point (0, 0) and continues through the point (2, 8).
A line passes through the point (0, 0) and continues through the point (6, 24).
A line passes through the point (0, 0) and continues through the point (12, 3).
Answers
The graph of the proportional relationship would look like A line passes through the point (0, 0) and continues through the point (12, 3).
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.
The given table is
x 12 8 24
y 3 2 6
The graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (12, 3).
In the ordered pair the first value represents the x axis value and second value represents the y value. The ordered pair (12, 3) is coordinated with the values of x and y in the table.
Hence the graph of the proportional relationship would look like A line passes through the point (0, 0) and continues through the point (12, 3).
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solve the system by addition method x + 4y = 34x + 5y = - 10
Answers
y = 2
so,
x + 4 * 2 = 3
x = 3 - 4 * 2 = 3 - 8 = -5
so,
x = -5 and y = 2
NAMEDATEPERIOD21. Clare has a 1/2 liter bottle full of water. A cone-shaped paper cup has diameter 10 cmand slant height 13 cm as shown. Can she pour all the water into one paper cup, or willit overflow? Explain your reasoning. (3 pts.)(The volume of a cone ismerhand liter = 500 cubic centimeters)10cm13 cm
Answers
We have the following:
The first thing is to calculate the volume of the cone
[tex]\begin{gathered} V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h \\ \end{gathered}[/tex]where r is the radius and h is the height
the radius is half the diameter, like this
[tex]r=\frac{d}{2}=\frac{10}{2}=5[/tex]The radius is 5 cm.
Now, for the height, we calculate it by means of the Pythagorean theorem that says the following
[tex]\begin{gathered} c^2=a^2+b^2 \\ c=13 \\ a=5 \\ b=h \\ \text{replacing:} \\ 13^2=5^2+h^2 \\ h^2=13^2-5^2 \\ h=\sqrt[]{169-25} \\ h=\sqrt[]{144}=12 \end{gathered}[/tex]The height is 12 cm
The volume is:
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot5^2\cdot12 \\ V=314 \end{gathered}[/tex]The water bottle has a total of 500 cubic centimeters, while the cone is 314 cubic centimeters, therefore it cannot pour out all the water and it would overflow
Tank A contains a mixture of 10 gallons of water and 5 gallons of pure alcohol tank b has 12 gallons of what and 3 gallons of alcohol how many gallons should be taken from each tank and combiend in order to obtain 8 gallons of a solution countaning 25% alcohol
Answers
The volume from tanks A and B are taken as 3 and 5 gallons respectively.
Here,
Let the volume taken from tank A and tank B be x and y.
According to the question,
x + y = 8 - - - - - (1)
And
Composition of the alcohol in Tank A = 1/3
Composition of the alcohol in tank B = 1 /5
x / 3 + y / 5 = 8 / 4
5x + 3y = 30
From equation 1
5(y8 - y) + 3y = 30
-5y + 40 + 3y = 30
-2y = -10
y = 5
Now, put y in equation 1
x = 8 - 5
x = 3
Thus, the Volume from tanks A and B are taken as 3 and 5 gallons respectively.
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Which is closest to the circumference of the earth if it's diameter is 7926.41 miles?
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ANSWER
24901.55 miles
EXPLANATION
We have to find the circumference of the earth using the diameter given.
The formula for circumference is:
[tex]C=\pi\cdot D[/tex]where D = diameter
Therefore, the circumference is:
[tex]\begin{gathered} C=\pi\cdot7926.41 \\ C=24901.55\text{ miles} \end{gathered}[/tex]