Answer
Option C is correct.
There are roughly 4 liters in 1 gallon
And the estimate (4 liters in 1 gallon) is greaster then the exact number of liters in a gallon (3.79 liters in 1 gallon).
Explanation
We are given some parameters
33.8 fluid ounces = 1 liter
128 fluid ounces = 1 gallon
We are then told to find the amount of liters that are roughly in a gallon.
To do this, we will put the parameters that are equivalent as fractions on each other
[tex]\begin{gathered} \frac{33.8\text{ fluid ounces}}{1\text{ liter}}=1 \\ \frac{128\text{ fluid ounces}}{1\text{ gallon}}=1 \end{gathered}[/tex]We can write the first relation as an inverse and we will still have the same thing
[tex]\begin{gathered} \frac{1\text{ liter}}{33.8\text{ fluid ounces}}=1 \\ \frac{128\text{ fluid ounces}}{1\text{ gallon}}=1 \\ \text{ Since, 1 }\times1=1 \\ We\text{ can find the relation betw}een\text{ liter and gallon by saying} \\ \frac{1\text{ liter}}{33.8\text{ fluid ounces}}\times\frac{128\text{ fluid ounces}}{1\text{ gallon}} \\ \frac{128}{33.8}\frac{\text{liter}}{\text{gallon}} \\ =\frac{3.79\text{ liters}}{1\text{ gallon}} \end{gathered}[/tex]3.79 liters = 1 gallon
A right approximation will be that
1 gallon = 4 liters
We can then see that the estimate is greater than the exact number of liters in a gallon.
Hope this Helps!!!
15. A beekeeper estimates that his bee population will triple each year.
Answer:
[tex]P\mleft(x\mright)=150(3^x)[/tex]Explanation:
The initial number of bees = 150
[tex]P(0)=150[/tex]The beekeeper estimates that his bee population will triple each year. Thus, after 1 and 2 years:
[tex]\begin{gathered} P(1)=150\times3 \\ P(2)=150\times3\times3=150\times3^2 \end{gathered}[/tex]Continuing in like manner, after x years:
[tex]P(x)=150(3^x)[/tex]P(x) is the required function.
Multiple the binomials (simplify) (y-4)(y-8)
Given
[tex](y-4)(y-8)[/tex]Simplify as shown below
[tex]\begin{gathered} (y-4)(y-8)=y(y-8)-4(y-8)=y^2-8y-4y+(-4)(-8)=y^2-12y+32 \\ \Rightarrow(y-4)(y-8)=y^2-12y+32 \end{gathered}[/tex]The answer is y^2-12y+32
If the two expressions are equivalent, find value of x
1. Subtract 1/x in both sides of the equation:
[tex]\begin{gathered} \frac{5}{x}-\frac{1}{x}-\frac{1}{3}=\frac{1}{x}-\frac{1}{x} \\ \\ \frac{4}{x}-\frac{1}{3}=0 \end{gathered}[/tex]2. Add 1/3 in both sides of the equation:
[tex]\begin{gathered} \frac{4}{x}-\frac{1}{3}+\frac{1}{3}=0+\frac{1}{3} \\ \\ \frac{4}{x}=\frac{1}{3} \end{gathered}[/tex]3. Multiply both sides of the equation by x:
[tex]\begin{gathered} x\cdot\frac{4}{x}=x\cdot\frac{1}{3} \\ \\ 4=\frac{x}{3} \end{gathered}[/tex]4. Multiply both sides of the equation by 3:
[tex]\begin{gathered} 4\cdot3=\frac{x}{3}\cdot3 \\ \\ 12=x \\ \\ \text{ Rewrite} \\ x=12 \end{gathered}[/tex]Then, the value of x is 12Solve the following system of linear equations by graphing:4.Ex+3y54 9- 5858615+cilo=Answer 2 PointsKeypadKeyboard ShortcutsGraph the linear equations by writing the equations in slope-intercept form:y =Ixty =IxtIdentify the appropriate number of solutions. If there is a solution, give thepoint:O One SolutionO No SolutionO Infinite Number of Solutions
We have a system of equations:
[tex]\begin{gathered} -\frac{4}{5}x+3y=-\frac{58}{5} \\ \frac{4}{3}x+\frac{9}{5}y=\frac{86}{15} \end{gathered}[/tex]We have to write the equations in slope-intercept form.
We start with the first equation:
[tex]\begin{gathered} -\frac{4}{5}x+3y=-\frac{58}{5} \\ 3y=-\frac{58}{5}+\frac{4}{5}x \\ 5\cdot3y=4x-58 \\ 15y=4x-58 \\ y=\frac{4}{15}x-\frac{58}{15} \end{gathered}[/tex]For the second equation we get:
[tex]\begin{gathered} \frac{4}{3}x+\frac{9}{5}y=\frac{86}{15} \\ \frac{9}{5}y=\frac{86}{15}-\frac{4}{3}x \\ y=\frac{5}{9}\cdot\frac{86}{15}-\frac{5}{9}\cdot\frac{4}{3}x \\ y=\frac{86}{9\cdot3}-\frac{20}{27}x \\ y=-\frac{20}{27}x+\frac{86}{27} \end{gathered}[/tex]To graph the equations we need two points. We can easily identify the y-intercept from the equations, but we have to identify one more point for each equation.
We can give a value to x and find the corresponding value of y.
Then, for example we can calculate y for x = 1 in the first equation:
[tex]\begin{gathered} y=\frac{4}{15}(1)-\frac{58}{15} \\ y=\frac{4}{15}-\frac{58}{15} \\ y=-\frac{54}{15} \end{gathered}[/tex]Then, for the first equation we know the points (0, -58/15) and (1, -54/15).
For the second equation we can do the same, by giving a value of 1 to x (NOTE: we can give any arbitrary value to x, it does not have to be the same for both equations) and calculate y:
[tex]\begin{gathered} y=-\frac{20}{27}(1)+\frac{86}{27} \\ y=-\frac{20}{27}+\frac{86}{27} \\ y=\frac{66}{27} \end{gathered}[/tex]Now we know the points of the second equation: (0, 86/27) and (1, 66/27).
With such fractions we can not make an accurate graph in paper, as they don't match the divisions of the grid.
We can use approximate decimals values for the fractions and graph the points.
The approximations for the first equation are:
[tex]\begin{gathered} (0,-\frac{58}{15})\approx(0,-3.9) \\ (1,-\frac{54}{15})=(1,-3.6) \end{gathered}[/tex]and for the second equation:
[tex]\begin{gathered} (0,\frac{86}{27})\approx(0,3.2) \\ (1,\frac{66}{27})\approx(1,2.4) \end{gathered}[/tex]We can then graph the equations as:
If we graph the equations with the exact points, we get an intersection point at (7,-2).
This intersection is the unique solution to both equations at the same time, so it is the only solution to the system of equations.
Answer:
The equations in slope-intercept form are:
y = 4/15 x + (-58/15)
y = -20/27 * x + 86/27
The system has only one solution: (7, -2).
Tickets to a play cost $10 at the door and $8 in advance.
The theatre club wants to raise at least $800 from the sale of the tickets from the play. Write and
graph an inequality for the number of tickets the theatre club needs to sell. If
the club sells 40 tickets in advance, how many does it need to sell at the door to
reach its goal? Use x to represent the number of tickets sold at the door. Use y
to represent the number of tickets sold in advance.
The system of linear inequality is solved to determine that they need to sell at least 48 door ticket. The graph of the problem is attached below
System of Linear InequalityA system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.
To solve this problem, we have to write out a system of linear inequality and solve.
x = number of tickets sold at doory = number of tickets sold in advance10x + 8y ≥ 800 ...eq(i)
y = 40 ...eq(ii)
put y = 40 in eq(i)
10x + 8(40) ≥ 800
10x + 320 ≥ 800
10x ≥ 800 - 320
10x ≥480
x ≥ 48
They need to sell at least 48 door tickets to meet the target.
The graph of the inequality is attached below
Learn more on system of linear inequality here
https://brainly.com/question/23093488
#SPJ1
The coordinates of the midpoint of GH are M(-2,5) and the coordinates of one endpoint are H(-3, 7).
The coordinates of the other endpoint are(
).
Echeck
? Help
< PREV - 1 2 3 4 5 6
-
NEXT >
What are the coordinates of the other endpoint
EXPLANATION :
From the problem, we have segment GH and the midpoint is M(-2, 5).
One of the endpoints has coordinates of H(-3, 7)
and we need to find the coordinates of G(x, y)
The midpoint formula is :
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) are the coordinates of G
(x2, y2) = (-3, 7) are the coordinates of H
and (-2, 5) are the coordinates of the midpoint.
Then :
[tex](-2,5)=(\frac{x+(-3)}{2},\frac{y+7}{2})[/tex]We can equate the x coordinate :
[tex]\begin{gathered} -2=\frac{x+(-3)}{2} \\ \\ \text{ cross multiply :} \\ -2(2)=x-3 \\ -4=x-3 \\ -4+3=x \\ -1=x \\ x=-1 \end{gathered}[/tex]then the y coordinate :
[tex]\begin{gathered} 5=\frac{y+7}{2} \\ \\ \text{ cross multiply :} \\ 5(2)=y+7 \\ 10=y+7 \\ 10-7=y \\ 3=y \\ y=3 \end{gathered}[/tex]Now we have the point (-1, 3)
ANSWER :
The coordinates of the other endpoint are G(-1, 3)
Mr. Eric’s business class has 91 students, classified by academic year and gender, As illustrated in the following table. Mr. Eric randomly chooses one student to collect yesterday’s work. What is the probability that he selects a female, given that he chooses randomly from only the juniors? Express your answer as a fraction.
Given:
Eric’s business class has 91 students
Mr. Eric randomly chooses one student to collect yesterday’s work
We will find the probability that he selects a female, given that he chooses randomly from only the juniors
As shown from the table:
The number of females from the juniors = 6
The number of juniors = 6 +13 = 19
So, the probability will be =
[tex]\frac{6}{19}[/tex]How to find the diagonal side one triangle like the measure with the Pythagorean Theorem
How to find the diagonal side one triangle like the measure with the Pythagorean Theorem
see the attached figure to better understand the p
Does the point (2, 6) satisfy the inequality 2x + 2y ≥ 16?
yes
no
help me please asap!!!
The slope of the function is 1/2 and the y - intercept is 2
The standard form of slope-intercept form of line is y = mx + b
where , m is slope of line
and b is y-intercept.
Observing the graph ,
we can say Linear function also passes through two points
At (4,0) on x-axis and at (0,2) on y-axis and
also , the graph is making right angles triangle at (0,0)
Slope of the function = m = Tan∅
Tan∅ = Perpendicular of right triangle / base of triangle
Perpendicular of triangle = 2 unit
and base = 4 unit
Tan∅ = 2/4 = 1/2
Therefore , slope of line = 1/2
equation of line : y = 1/2 x + b
This line is passing through (0,2)
2 = 1/2(0) + b
b = 2
Therefore , the y-intercept = 2
Hence , the equation of line = y = 1/2 x + 2
To know more about Slope of the line here ,
https://brainly.com/question/14511992
#SPJ1
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = -9p2 + 18,000p. What unitprice should be established for the dryer to maximize revenue? What is the maximum revenue?
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = -9p2 + 18,000p. What unit
price should be established for the dryer to maximize revenue? What is the maximum revenue?
we have the quadratic equation
[tex]R(p)=-9p^2+18,000p[/tex]this is a vertical parabola, open downward
the vertex represents a maximum
Convert to factored form
Complete the square
factor -9
[tex]R(p)=-9(p^2-2,000p)[/tex][tex]R(p)=-9(p^2-2,000p+1,000^2-1,000^2^{})[/tex][tex]\begin{gathered} R(p)=-9(p^2-2,000p+1,000^2)+9,000,000 \\ R(p)=-9(p^{}-1,000)^2+9,000,000 \end{gathered}[/tex]the vertex is the point (1,000, 9,000,000)
therefore
the price is $1,000 and the maximum revenue is $9,000,000Problem N 2
we have the equation
[tex]C(x)=0.7x^2+26x-292+\frac{2800}{x}[/tex]using a graphing tool
the minimum is the point (8.58,308.95)
therefore
Part a
the average cost is minimized when approximately 9 lawnmowers ........
Part b
the minimum average cost is approximately $309 per mower
which of the following gives the line of symmetry
To be able to reflect the trapezoid to itself, the reflection must be at the point where the figure will be divided symmetrically.
For a trapezoid, it must be reflected at the center of its base.
In the given figure, the center of the base of the trapezoid falls at x = 4.
Thus, to reflect it by itself, it must be reflected at x = 4.
The answer is letter B.
A new cell phone costs $108.99 in the store. What would your total cost be if the sale tax is 7.5% ? Round your answer to the nearest cent, if necessary.
to calculate the tax we need to multiply the % by the price of the cellphone
7.5%=0.075
108.99*0.075=8.17
and the total cost is:
$108.99 + $8.17= 117.16
So the answer is: $
4. Find the midpoint of DK, given the coordinates D (-10, -4) and K is located at the origin.m:|| m:1 m:Midpoint:Equation of the line:
The midpoint between two coordinates can be calculated using the equation
[tex]m=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Point D has the coordinates (-10, -4). The problem stated that point K is located at the origin, hence, we can say that its coordinates are (0, 0).
Using the formula stated above to solve the coordinates of the midpoint, we get
[tex]\begin{gathered} m=(\frac{-10+0}{2},\frac{-4+0}{2}) \\ m=(\frac{-10}{2},-\frac{4}{2}) \\ m=(-5,-2) \end{gathered}[/tex]Answer: The midpoint of the line segment DK is located at (-5,-2).
turn the expression from radical form to exponential expression in fractional form. No need to evaluate just be out in simplest form
To answer this question, we need to remember the next property of radicals:
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]In this case, we have that:
[tex]\sqrt[3x]{5}[/tex]And we can see that the exponent for 5 is m = 1. Therefore, we can rewrite the expression as follows:
[tex]\begin{gathered} \sqrt[3x]{5}=5^{\frac{1}{3x}} \\ \end{gathered}[/tex]In summary, therefore, we can say that the radical form to an exponential in fractional form is:
[tex]undefined[/tex]Find the distance between (-4, 2) and (10, 2) c. -14d. 14
The distance between two points (a, b) and (c, d) is given by:
[tex]\sqrt[]{(c-a)^2+(d-b)^2}[/tex]For points (-4, 2) and (10, 2), we have:
a = -4
b = 2
c = 10
d = 2
Thus, the distance between those points is
[tex]\sqrt[]{\lbrack10-(-4)\rbrack^2+(2-2)^2}=\sqrt[]{(10+4)^2+0}=\sqrt[]{14^2}=14[/tex]Therefore, the answer is 14.
A circular arc has measure of 4 cm and is intercepted by a central angle of 73°. Find the radius r of the circle. Do not round any intermediate computations, and round your answer to the nearest tenth.r= __ cm
The arc lenghr is given by:
[tex]s=r\theta[/tex]where s is the arc lenght, r is tha raidus and theta is the angle measure in radians. Since in our problem the angle is given in degrees we have to convert it to radians, to do this we have to multiply the angle by the factor:
[tex]\frac{\pi}{180}[/tex]Then:
[tex]\theta=(73)(\frac{\pi}{180})[/tex]Plugging the value of the arc lenght and the angle in the first formula, and solving for r we have:
[tex]\begin{gathered} 4=r(73)(\frac{\pi}{180}) \\ r=\frac{4\cdot180}{73\cdot\pi} \\ r=3.1 \end{gathered}[/tex]Therefore, the radius of the circle is 3.1 cm.
I will give brainliest if you help me with this problem not joking
Answer: 9+6+-6+-7
Step-by-step explanation:
im not sure thats my guess tho
2(3x + 8) = 6x + 16How many solutions does this equation have
Answer:
The equation has infinite number of solutions
Explanation:
Given the equation:
2(3x + 8) = 6x + 16
To know how many solutions this equation has, we need to solve it and see.
Remove the brackets on the left-hand side
6x + 16 = 6x + 16
The expression on the left-hand side is exactly the same as the one on the right-hand side, this reason, there is infinite number of solutions that would satisfy this.
Evaluate the expression when x = 32 and y = 2.
x/14 A. 1/16
B.16/21
D.2
C.4
Answer:
I think its 16/21
Step-by-step explanation:
Answer:
2Step-by-step explanation:
Given x = 14, y = 2x/14
Void "y" because it is not in this equation.= x/14
32/14
= 2.2
≈ 2
⦁ It takes the earth 24 h to complete a full rotation. It takes Mercury approximately 58 days, 15 h, and 30 min to complete a full rotation. How many hours does it take Mercury to complete a full rotation? Show your work using the correct conversion factors.
Answer:
Answer:
58 days, 15 h, and 30 min
Step-by-step explanation:
I’m stuck on how to verify number 7 and how to find the possible value for sin theta
Given:
There are given the trigonometric function:
[tex]sec^2\theta cos2\theta=1-tan^2\theta[/tex]Explanation:
To verify the above trigonometric function, we need to solve the left side of the equation.
So,
From the left side of the given equation:
[tex]sec^2\theta cos2\theta[/tex]Now,
From the formula of cos function:
[tex]cos2\theta=cos^2\theta-sin^2\theta[/tex]Then,
Use the above formula on the above-left side of the equation:
[tex]sec^2\theta cos2\theta=sec^2\theta(cos^2\theta-sin^2\theta)[/tex]Now,
From the formula of sec function:
[tex]sec^2\theta=\frac{1}{cos^2\theta}[/tex]Then,
Apply the above sec function into the above equation:
[tex]\begin{gathered} sec^2\theta cos2\theta=sec^2\theta(cos^2\theta-s\imaginaryI n^2\theta) \\ =\frac{1}{cos^2\theta}(cos^2\theta-s\mathrm{i}n^2\theta) \\ =\frac{(cos^2\theta-s\mathrm{i}n^2\theta)}{cos^2\theta} \end{gathered}[/tex]Then,
[tex]\frac{(cos^{2}\theta- s\mathrm{\imaginaryI}n^{2}\theta)}{cos^{2}\theta}=\frac{cos^2\theta}{cos^2\theta}-\frac{sin^2\theta}{cos^2\theta}[/tex]Then,
From the formula for tan function:
[tex]\frac{sin^2\theta}{cos^2\theta}=tan^2\theta[/tex]Then,
Apply the above formula into the given result:
So,
[tex]\begin{gathered} \frac{(cos^{2}\theta- s\mathrm{\imaginaryI}n^{2}\theta)}{cos^{2}\theta}=\frac{cos^{2}\theta}{cos^{2}\theta}-\frac{s\imaginaryI n^{2}\theta}{cos^{2}\theta} \\ =1-\frac{s\mathrm{i}n^2\theta}{cos^2\theta} \\ =1-tan^2\theta \end{gathered}[/tex]Final answer:
Hence, the above trigonometric function has been proved.
[tex]sec^2\theta cos2\theta=1-tan^2\theta[/tex]Find the restricted values of x for the following rational expression. If there are no restricted values of x,indicate "No Restrictions".x² +8x² - x - 12AnswerHow to enter your answer (opens in new window)Separate multiple answers with commas.KeypadKeyboard ShortcutsSelecting a radio button will replace the entered answer value(s) with the radio button value. If the radiobutton is not selected, the entered answer is used.
Answer:
To find the restricted values of x for the given rational expression,
[tex]\frac{x^2+8}{x^2-x-12}[/tex]The above expression is defined only when x^2-x-12 not equal to 0.
x values are restricted for the solution of x^2-x-12=0
To find the values of x when x^2-x-12=0.
Consider, x^2-x-12=0
we get,
[tex]x^2-x-12=0[/tex][tex]x^2-4x+3x-12=0[/tex][tex]x\left(x-4\right)+3\left(x-4\right)=0[/tex]Taking x-4 as common we get,
[tex]\left(x-4\right)\left(x+3\right)=0[/tex]we get, x=4,x=-3
The restricted values of x are 4,-3.
we get,
[tex]x\ne4,-3[/tex]Answer is:
[tex]x\ne4,-3[/tex]Ed earns a $100 commission on each computer he sells plus a base salary of $50,000 . His total income last year was 75,000 . Which equation can be used to find how many computers Ed sold last year ? A. 50,000 + 100x = 75,000 B. 50,000 - 100 x = 75,000 C. 75,000 + 100x = 50,000
ANSWER
50,000 + 100x = 75,000
STEP-BY-STEP EXPLANATION:
Given parameters
• Ed base salary = $50, 000
,• Commission on each computer sells = $100
,• Total income = $75,000
Let x be the number of computers sold
Total income = base salary + commission * number of cars sold
75000 = 50000 + 100* x
50,000 + 100x = 75, 000
Hence, the equation that can be used to find the number of cars sold is
50,000 + 100x = 75,000
the ratio of isabella's money to Shane's money is 5:10.if Isabelle has $55 how much money do Shane have?what about they have together?
Write the percent as decimal 49%
Solution;
Given: The given number in percentage is 49 %
Required: Decimal value of given percentage.
Explanation:
Convert percentage into decimal as follows:
[tex]49\text{ \%=}\frac{49}{100}[/tex][tex]49\text{ \%=0.49}[/tex]Therefore, the required answer is 0.49
Final answer: The de
Translate into proportion 16.4 is 45% of what number ?
Given:
16.4 is 45%
[tex]\begin{gathered} 16.4\times\frac{45}{100}=\frac{b}{1} \\ \frac{16.4}{b}=\frac{100}{45} \end{gathered}[/tex]Hence, the required option is D.
How do I find the restrictions on x if there are any? [tex] \frac{1}{x - 1} = \frac{5}{x - 10} [/tex]
We have the expression:
[tex]\frac{1}{x - 1}=\frac{5}{x - 10}[/tex]When we have rational functions, where the denominator is a function of x, we have a restriction for the domain for any value of x that makes the denominator equal to 0.
That is because if the denominator is 0, then we have a function f(x) that is a division by zero and is undefined.
If we have a value that makes f(x) to be undefined, then this value of x does not belong to the domain of f(x).
Expression:
[tex]\begin{gathered} \frac{1}{x-1}=\frac{5}{x-10} \\ \frac{x-1}{1}=\frac{x-10}{5} \\ x-1=\frac{x}{5}-\frac{10}{5} \\ x-1=\frac{1}{5}x-2 \\ x-\frac{1}{5}x=-2+1 \\ \frac{4}{5}x=-1 \\ x=-1\cdot\frac{5}{4} \\ x=-\frac{5}{4} \end{gathered}[/tex]Answer: There is no restriction for x in the expression.
using the rule of s-14 - (-2) = -12
We will have:
[tex]-14-(-2)=-12\Rightarrow-14+2=-12\Rightarrow-12=-12[/tex]Given f(x)=2x-1 and g(x) =x^2 -2A) f(5)B) f(g(3))C) f(a+1) - f(a)D) g(2f(-1))E) g(x+h) -g(x)/h
2x + h
Explanation:
Given the following functions
f(x) = 2x - 1
g(x) = x^2 - 2
We are to simplify the expressionn:
[tex]\frac{g(x+h)-g(x)}{h}[/tex]Substitute the given functions into the expression and simplify
[tex]\begin{gathered} \frac{\lbrack(x+h)^2-2\rbrack-(x^2-2)}{h} \\ \frac{\lbrack\cancel{x^2}^{}+2xh+h^2-\cancel{2}-\cancel{x^2}^{}+\cancel{2}}{h} \\ \frac{2xh+h^2}{h} \end{gathered}[/tex]Factor out "h" from the numerator to have:
[tex]\begin{gathered} \frac{\cancel{h}(2x+h)}{\cancel{h}} \\ 2x+h \end{gathered}[/tex]Hence the simplified form of the expression is 2x + h