Answer:
1,081 gallons
Step-by-step explanation:
1,119 - 38 = 1,081
Jennifer is thinking about getting an MBA. She will give up making $27,500 a year for the two years it takes to complete the MBA. She will also pay $45,000 in total costs to get the degree. Assume she will make $67,500 a year after she gets her MBA. How long will it take for Jennifer to recover her investment?
Answer:
un year
Step-by-step explanation:
Find the error in the calculations below, if there is one:
Line (1): -5x/4-7/2<-3/8
Line (2): 10x + 28<-3
Line (3): 10x < - 31
Line (4): x < -31/10
Line (5):
The error occurs in the second line, the correct solution is x > -5/2.
What is inequality?The relation between two unequal expressions is defined as inequality.
Given inequality is -5x/4 - 7/2 < -3/8.
The solution of the inequality is:
-5x/4 - 7/2 < -3/8
10x + 28 > 3
10x > -25
x > -25/10
x > -5/2
Hence, the error occurs in the second line, the correct solution is x > -5/2.
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v - 4 > 22 solve the inequality of v and simplify your answer as much as possible. plsssss do this!!!
Answer:
v > 26
Step-by-step explanation:
v > 22 + 4
v > 26
there is no qouificient ( I don't know how to spell that) of v so that's your answer
Find the slope of each line.
1)2x-5y=20
2) 2x-3y=-9
Answer:
1)2/5
2)2/3
Hope this helps!
Answer:
1. m=2/5
2. m-2/3
Step-by-step explanation:
Is the image an example of an angle?
B
65°
A
C
O No; AB and BC intersect in more than one point.
O Yes; AB and BC do not form a line and share an endpoint.
O No; AB and BC form a line.
O Yes; AB and BC are perpendicular to each other.
Yes, the image an example of an angle AB and BC do not form a line and share an endpoint.
What is an angle ?An angle is formed when two lines are extending from a point .
Using this Knowledge it can be deduced from the figure that line BA and BC are extending from point B. Hence forming an angle of 65 degrees
Analyzing the options
option A is wrong as line AB and BC intersected only on one point. formation of a line do not typically say if an angle is formed or not hence making option c incorrect. There is no perpendicular line formed in th figure .
This leaves option B as the correct option
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Given the circle below, find the value of x.251L (9x+26)*
Given the following:
Then:
[tex]a=\frac{b-c}{2}[/tex]In this case, we are given:
a = (9x + 26)
b = 251
To find c, we rest a whole circle (360) and rest angle b:
[tex]c=360-251=109[/tex]And now, we use the formula from above:
[tex]9x+26=\frac{251-109}{2}[/tex]And solve for x:
[tex]\begin{gathered} 9x+26=\frac{142}{2} \\ . \\ 9x=71-26 \\ . \\ x=\frac{45}{9} \\ . \\ x=5 \end{gathered}[/tex]The answer is the last option, x = 5
15. Name the indicated parts of this diagram.AC __________________AE __________________DE __________________AB __________________ADE __________________________ACE = _______°CAB = _______°
SOLUTION:
We want to name the indicated parts on the diagram, their names are;
For the angles, we have;
[tex]\begin{gathered} \measuredangle ADE=22^o\text{ }(Inscribed\text{ }Angle) \\ \measuredangle ACE=44^o\text{ }(Central\text{ }Angle) \\ \measuredangle CAB=90^o\text{ }(Angle\text{ }between\text{ }radius\text{ }and\text{ }tangent) \end{gathered}[/tex]Given the figure below, determine the angle that is an alternate interior angle with respect to. 1. To answer this question, click on the appropriate angle.
In this case, the alternate interior angles are for example angles 6 and 3 because they are on the inner side of each of the lines (m and l) but on opposite sides of the transversal (t).
m∠6 = m∠3
or
m∠4 = m∠5
Solve the multiple-angle equation. (Enter your answers as a comma-separated list. Use n as an arbitrary integer. Enter your response in radians.)2 cos 2x − 1 = 0
Given:
The function is:
[tex]2\cos2x-1=0[/tex]Find-:
The value of "x"
Explanation-:
The value of x is:
[tex]\begin{gathered} 2\cos2x-1=0 \\ \\ 2\cos2x=1 \\ \\ \cos2x=\frac{1}{2} \\ \end{gathered}[/tex]Solve for x is:
[tex]\begin{gathered} \cos2x=\frac{1}{2} \\ \\ 2x=\cos^{-1}(\frac{1}{2}) \\ \\ 2x=\frac{\pi}{3}+2\pi n\text{ and }2x=\frac{5\pi}{3}+2\pi n \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} 2x=\frac{\pi}{3}+2\pi n \\ \\ x=\frac{\pi}{2\times3}+\frac{2\pi n}{2} \\ \\ x=\frac{\pi}{6}+\pi n \end{gathered}[/tex]Another value of "x" is:
[tex]\begin{gathered} 2x=\frac{5\pi}{3}+2\pi n \\ \\ x=\frac{5\pi}{3\times2}+\frac{2\pi n}{2} \\ \\ x=\frac{5\pi}{6}+\pi n \end{gathered}[/tex]So, the answer is:
[tex]x=\frac{\pi}{6}+\pi n,\frac{5\pi}{6}+\pi n[/tex]Use the equation one sixth plus s equals 21 over 30 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
(Its due in 45 minutes so help answer it plsss)
s is 4/15 of the equation one sixth plus s equals 21 over 30.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is
one sixth plus s equals 21 over 30
This can be written as
one sixth can be written as 1/6.
21 over 30 can be written as 21/30.
so the equation is 1/6+s=21/30.
Let us separate the variable s to find the value of s.
s=21/30-1/6
The LCM of 30 and 6 is 30
s=21-5/30
s=16/30=4/15
Hence s is 4/15 of the equation one sixth plus s equals 21 over 30.
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Determine if the equation is linear. If so graph the function (x+y=1)
Answer:
The equation is linear
Step-by-step explanation:
Make the equation in y=mx+b form
which is y=-x+1 and because the x is not the first power it must be linear
Graph:
A bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. What would be the height of the 7th bounce of the ball? Round to the nearest tenth (if necessary).
If a bouncy ball is dropped such that the height of its first bounce is 3.75 feet and each successive bounce is 79% of the previous bounce's height. The height of the 7th bounce of the ball is 0.7.
Determining the height of the ballGiven data:
First bounce = 3.75 feet
Successive bounce = 79% or 0.79%
Bounce = 7
Now let determine the height of thee 7th bounce of the ball using this formula
Height = First bounce × (Successive bounce) ^ Number of bounce
Let plug in the formula
Height = 3.75 × (0.79 ) ^7
Height = 0.7
Therefore the height is 0.7.
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HELP ASAP, IM DUE IN 4 HOURS
Rotate DEF 90° clockwise around the origin. Then translate D'E'F' to the right 5units and down 2 units. What are the coordinates of D''E''F''? Show and explain how you arrived at your answer.
Answer below and in attached graph Step by stepShow and explain:1) The rule for a rotation by 90° around the origin is (x,y)→(−y,x) so I moved the y to x and changed the sign, I moved x to y position. 2) to translate 5 units right and 2 units down, you add (+5, -2) to your current coordinates of D’ E’ and F’ giving D’’ E’’ F’’. Pre Image ➡️ D’ E’ F’ ➡️. D’’ E’’ F’’ (+5, -2)D (-5, -2) ➡️ (2, -5) ➡️ (7, -7)E (0, -2) ➡️ (2, 0). ➡️ (7, -2)F (-4, -6) ➡️ ( 6, -4). ➡️ (11, -6)Attached graph of pre image and transformations
Write an equation of the line through (-3,- 6) having slope17/16Give the answer in standard form.The equation of the line is
The equation of a line in Standard form is:
[tex]Ax+By=C[/tex]Where "A", "B" and "C" are Integers ("A" is positive).
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case you know that:
[tex]m=\frac{17}{16}[/tex]And knowing that the line passes through the point
[tex]\mleft(-3,-6\mright)[/tex]You can substitute values and solve for "b":
[tex]\begin{gathered} y=mx+b \\ -6=(\frac{17}{16})(-3)+b \\ \\ \\ -6=-\frac{51}{16}+b \\ \\ -6=-\frac{51}{16}+b \\ \\ -6+\frac{51}{16}=b \\ \\ b=-\frac{45}{16} \end{gathered}[/tex]Then, the equation of this line in Slope-Intercept form is:
[tex]y=\frac{17}{16}x-\frac{45}{16}[/tex]Now that you have this equation, you can write it in Standard form as following:
[tex]\begin{gathered} y+\frac{45}{16}=\frac{17}{16}x \\ \\ \frac{45}{16}=\frac{17}{16}x-y \\ \\ \frac{17}{16}x-y=\frac{45}{16} \end{gathered}[/tex]The answer is:
[tex]\frac{17}{16}x-y=\frac{45}{16}[/tex]5. Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts
are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three
complete sentences, explain how the graphs of the functions for the two months are similar
and how they are different.
The function exists
Last month: 2x + 3y = 1,470
Next month: 2x + 3y = 1,593
What is meant by functions?An expression, rule, or law in mathematics that establishes the link between an independent variable and a dependent variable (the dependent variable)
Given: Profit of every sandwich = $2
Profit of every wrap = $3
Let x be the number of sandwich and
y be the number of wrap
Last month: 2x + 3y = 1,470
Next month: 2x + 3y = 1,593
Both still have the same profit. $2 for sandwiches and $3 for wraps.
The only reason why there exists a difference in the total amount exists the change in the number of sandwich or wrap sold in a given month.
Therefore, the next month's total sale exists higher than last month's total sale, it exists safe to assume that the sale of sandwich or wrap exists higher than last month's sale.
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Can you help me with my math problem. im not sure where i got it wrong
Answer:
The value of k is;
[tex]k=-7.1842[/tex]Explanation:
Given the equation:
[tex]-3\cdot16^{-k-7}+8=3[/tex]To solve, let us subtract 8 from both sides;
[tex]\begin{gathered} -3\cdot16^{-k-7}+8-8=3-8 \\ -3\cdot16^{-k-7}=-5 \end{gathered}[/tex]then, we can then divide both sides by -3;
[tex]\begin{gathered} \frac{-3\cdot16^{-k-7}}{-3}=\frac{-5}{-3} \\ 16^{-k-7}=\frac{5}{3} \end{gathered}[/tex]To solve further we need to take the logarithm of both sides;
[tex]\begin{gathered} 16^{-k-7}=\frac{5}{3} \\ \log 16^{-k-7}=\log \frac{5}{3} \\ (-k-7)\log 16=\log \frac{5}{3} \\ \text{dividing both sides by log 16, we have;} \\ \frac{(-k-7)\log 16}{\log 16}=\frac{\log\frac{5}{3}}{\log16} \\ -k-7=\frac{\log\frac{5}{3}}{\log16} \end{gathered}[/tex]finding the value of the log;
[tex]-k-7=0.1842\text{ (to 4 decimal place)}[/tex]solving for k;
[tex]\begin{gathered} -k-7=0.1842 \\ -k=0.1842+7 \\ -k=7.1842 \\ k=-7.1842 \end{gathered}[/tex]Therefore, the value of k is;
[tex]k=-7.1842[/tex]5-52: the first card selected from a standard 52-card deck is a king. a. if it is returned to the deck, what is the probability that a king will be drawn on the second selection? b. if the king is not replaced, what is the probability that a king will be drawn on the second selection? c. in part (b), are we assuming the card selections are independent? justify your answer.
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability.
The probability of getting a king card is 1/13 or 0.077.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: Total number of probability - 52
Now, the first selected card is king and it is returned to the deck.
So it contains no effect on the second selection card.
Then, we have to estimate probability to obtain a king
probability = favourable outcomes for a king / total possible outcomess
= 4 king cards / 52 cards in total
= 4 / 52 = 1 / 13
The probability of getting a king card is 1 / 13 or 0.077
Therefore, the correct answer is option B. 1/13, or 0.077.
The complete question is:
The first card selected from a standard 52-card deck was a king. It isreturned to the deck, what is the probability that a king will be drawn on the second selection?
A. 1/4 or 0.25
B. 1/13, or 0.077
C. 12/13, or 0.923
D. 1/3 or 0.33
E. None of the above
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solving one step inequalities using addition subtraction multiplication and division
To begin with
we have the inequality
[tex]4>x-2[/tex]To solve
Step 1: we will collect like terms
[tex]4+2>x[/tex]simplify the inequality above
[tex]\begin{gathered} 6>x \\ \text{Re}-\text{arranging} \\ x<6 \end{gathered}[/tex]Hence, the answer is
[tex]x<6[/tex]To draw the shape
Part B is correct
(7, 8) and (-1, 0)find the distance between the two points?
The distance (d) between two points is computed as follows:
[tex]d\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}^{}[/tex]where (x1, y1) and (x2, y2) are the points of interest. In this case, the points are (7, 8) and (-1, 0). Replacing into the equation:
[tex]d\text{ = }\sqrt{(-1-7)^2+(0-8)^2\text{ }}[/tex][tex]d\text{ = }\sqrt{(-8)^2+(-8)^2}=\sqrt{128}[/tex]4x^2+10x-4 divided by 2x-1
The division of 4 · x² + 10 · x - 4 by 2 · x - 1 is equal to (2 · x + 6) + 2 / (2 · x - 1).
How to divide a polynomial by algebra properties
In this problem we find a second grade polynomial, also known as quadratic function, being divided by a first grade polynomial, also known as linear function. The complete procedure is shown below:
4 · x² + 10 · x - 4 Given4 · x² - 2 · x + 12 · x - 4 Definition of subtraction / Distributive property(4 · x² - 2 · x) + (12 · x - 6) + 2 Existence of additive inverse / Modulative, commutative and associative property2 · x · (2 · x - 1) + 6 · (2 · x - 1) + 2 Definition of power / Definition of multiplication / Distributive property(2 · x + 6) · (2 · x - 1) + 2 Distributive and commutative properties(2 · x + 6) + 2 / (2 · x - 1) Dividing (5) by (2 · x - 1) / ResultThe resulting polynomial is (2 · x + 6) + 2 / (2 · x - 1).
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In the diagram below line FG is // to line HI, and line segments BC and AD intersect at E.
The measure of angle GBE = 3x+20, and the measure angle ECD = x.
The values of the angle x in the line segments is 40 degrees.
How to find the measure of angle?When parallel lines are are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the line FG is parallel to line HI. The line segment BC and AD are the transversal lines that cut across the parallel lines FG and HI.
Therefore,
3x + 20 + x = 180 (Same interior angles)
Same interior angles are supplementary. That is the angles sum up to 180 degrees.
Therefore,
3x + 20 + x = 180
4x + 20 = 180
4x = 160
divide both sides by 4
x = 160 / 4
x = 40 degrees
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You have discovered another alien. Find the correct rescue path before answering this question.
When the spaceship starts from a point on the y axis, what is the y-intercept of the line of travel?
the x-coordinate of the spaceship
the y-coordinate of the spaceship
the y-coordinate of the alien
the distance from the spaceship to the alien
From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
Given,
You have discovered another alien. Find the correct rescue path .
When the spaceship starts from a point on the y axis, we have to find the y intercept of the line of travel.
y-intercept;
A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
Here,
From the problem we can get that the y intercept of the line of travel is the y coordinate of the spaceship.
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PLEASE HELP URGENT HELP PLEASE!!!!!!!!!!!!!!!!
Answer:
[tex]y = \frac{w}{h - 5c^{3}}[/tex]
Step-by-step explanation:
separate y from everything
[tex]w = y(h - 5c^{3})[/tex]
now divide everything by the thing in the parenthesis
[tex]\frac{w}{h - 5c^{3}} = y[/tex]
now flip it
[tex]y = \frac{w}{h - 5c^{3}}[/tex]
that is your answer
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A (4, 5), B (12,9); 3 to 1 The coordinates of P are:
By applying line ratio, the coordinates of P are: [10, 8].
How to determine the coordinates of P?Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Given the following parameters:
Point A (4, 5)Point B (12, 9)m:n = 3:1Substituting the given parameters into the formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(3(12) + 1(4))/(3 + 1)], [(3(9) + 1(5))/(3 + 1)]
P(x, y) = [(36 + 4)/4], [(27 + 5)/4]
P(x, y) = [40/4, 32/4]
P(x, y) = [10, 8].
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POSSIBLE POINTS
Write and solve the given inequality: twice the difference of three times a number and five is at most the sum of four times a number and six.
O [8,00)
O (8,00)
O(-0,8)
O(-0,8]
The inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]
Let the number be x,
Twice the difference of three times a number and five = 2(3x - 5)
The sum of four times a number and six is (4x + 6)
2(3x - 5) ≤ (4x + 6)
6x - 10 ≤ 4x + 6
6x - 4x ≤ 6 + 10
2x ≤ 16
x ≤ 8
x can be any positive number less than or equal to 8.
Therefore, the inequality is 2(3x - 5) ≤ (4x + 6) and the solution of the inequality is (-0, 8]
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Remington purchased a new cell phone for $350 and added an annual warranty plan that cost him $35 per year. In what year will Remington's average annual cost of owning the phone be $122.50? Type your answer....
Answer:
3 years and 6 months
Step-by-step explanation:
35 × 3= 105 + 17 = 122
2.916 a month × 6 = 17. 496. And round to the nears while number = 17.50 = 105 + 17.50 = 122.5 or 122.50 zero fir place holder.
Solve the system using linear combination.
41
(5x + 3y
3x - 6y = 9
=
We want to eliminate the variable y. What number should we multiply times the first
equation, so that when we add the two equations, we can eliminate the variable y?
The solution of system of equation is x = 2 and y = 7. We should multiply first equation with 2 so that when we add the two equations, we csystem of equation an eliminate the variable y.
What is system of equation?
Two or more equations that share variables are said to be .
For instance, consider two equations where x and y are shared:
x + y = 6
3x + y = 2
We might be able to solve equations that have the same number of variables. Where the lines intersect in this case is the answer (1,5)
Given system of equation:
5x + 3y = 41,
3x - 6y = 9
Lets multiply the first equation with 2, we get
10x + 6y = 82
Adding these equation with second given equation we get,
10x +6y +(3x - 6y) = 82 + 9
13x = 91
x = 91/13
x = 7
putting the value of x in any one equation
3(7) -6y = 9
y = 2
Therefore, the x and y in the given system of equation are 7 and 2 respectively.
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assume that movement of a molecule is limited. it can move to the opposite side of the container or stay where it is. if the movement is random, what is the probability (0-100%) that the molecule will move to the opposite side?
The Probability that that the molecule will move to the opposite side is 50% .
In the question ,
it is given that
there a molecule is free to move to the opposite side of the container , or stay where where it is ,
As per the given information
the molecule can move to opposite side or stay where it is ,
and the movement of the molecule is random
as the container had two sides ( shown in figure given below )
the probability that the molecule moves to the opposite side is 1/2 ,
in percent it can be written as 50% .
the correct option is (c) .
Therefore , The Probability that that the molecule will move to the opposite side is 50% .
The given question is incomplete , the complete question is
Assume that movement of a molecule is limited. it can move to the opposite side of the container or stay where it is. if the movement is random, what is the probability (0-100%) that the molecule will move to the opposite side?
(a) 0%
(b) 25%
(c) 50%
(d) 100%
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Solve the following equation for y, simplifying all fractions: 6x + 10y = - 80 a) y = 3 X - 8 5 3 X 8 b) y alw c) y -x + 8 w л | о л | d) y = x – 8
Solving a linear equation with 2 variables
First isolate y term
10 y = -6x - 80
Now divide by 10
y = (-6/10)x -(80/10)
y = (-3/5)x - 8
Jodi bough a new car with 14 gallon gas tank. Around the town she is able to drive 336 miles on one tank of gas. on her first trip traveling on highways, she drives 448 on one tank of gas.A: Write a compound inequality in compact from the represents how many miles Jodi can drive on a tank of gas. Let m represent the number of miles per gallon.B: Rewrite the compound inequality as two simply inequalities separate by either and or, or.C: Solve each simple inequality. Then write the solution in compact form.
We have the following:
A.
Let m represent the number of miles per gallon, the inequality would be as follows
[tex]\frac{336}{14}\leq m\leq\frac{448}{12}[/tex]B. In two simple inequalities we have this
[tex]m\ge\frac{336}{14}\text{ or }m\leq\frac{448}{14}[/tex]C.
[tex]\begin{gathered} m\ge24\text{ or }m\leq32 \\ 24\leq m\leq32 \end{gathered}[/tex]