Initial amount: $210,000
Setting aside: $50,000
Remaining: $160,000
3/4 of remaining amount: 160,000 times 0.75 = $120,000
1/4 of remaining amount: 160,000 times 0.25 = $40,000
1. Refer to the equation 2x − 6y = 12.
(a) Create a table of values for at least 4 points. Show your work.
(b) Use the table of values to graph the line. Use a straightedge or ruler to draw the line.
Answer:
Answer:
x 6 0 3 -3
y 0 -2 -1 -3
Step-by-step explanation:
We substitute x value in the equation and find y.
When x =0, -6y = 12 or y =-2
Likewise all pairs are found out.
Similarly put y =0: x = 6
When x =3, 2(3)-6y =12 :y =-1
When x=-3, 2(-3)-6y=12 or y = -3
Plot these on a graph and join the line.
Graph is attached below:
a. 2x-6y=12: y = (12-2x)/6.
b. Graph the line using (0,2) and (3,0).
(a) To create a table of values for at least 4 points, we can solve the equation for y in terms of x:
y = (12 - 2x) / 6
We can then choose different values for x and plug them into the equation to find the corresponding y values.
Here is a table of values for at least 4 points:
x y
0 2
3 0
-3 4
6 -2
(b) To graph the line, we can use the two points from the table of values that are closest to each other.
In this case, we will use the points (0, 2) and (3, 0).
First, plot the two points on the coordinate plane.
Then, use a straightedge or ruler to draw a line that passes through both points.
Here is the graph of the line 2x − 6y = 12:
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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 900 cm3, the pressure is 150 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant?
Differentiating both sides of PV = C with respect to t gives us
Differentiating both sides of PV = C with respect to t gives us ...
... P'V +PV' = 0
Filling in the given numbers gives us ...
... (40 kPa/min)(900 cm³) + V'(150 kPa) = 0
Solving for V' gives ...
... V' = -(40 kPa/min)(900 cm³)/(150 kPa)
.. V' = -240 cm³/min
The volume is decreasing at the rate of 240 cm³/min.
Final answer:
In Physics, Boyle's Law relates the pressure and volume of a gas at constant temperature. To find the rate at which volume is decreasing as pressure increases, we differentiate the equation PV = C with respect to time and solve for [tex]\frac{dV}{dt}[/tex] , given the pressure, volume, and rate of change of pressure which comes out to be 240 cm³/min.
Explanation:
The subject of this question is Physics, specifically relating to Boyle's Law, which is part of gas laws studied in chemistry and physics. The level of this question is appropriate for High School students. We know from Boyle's Law that for a given amount of gas at constant temperature, the pressure P is inversely proportional to the volume V, meaning that PV = C or k, where C is a constant.
To solve the problem stated, we differentiate both sides of PV = C with respect to time t. This will give us P[tex]\frac{dV}{dt}[/tex] + V[tex]\frac{dP}{dt}[/tex] = 0. With the known values of P, V, and[tex]\frac{dP}{dt}[/tex] , we can solve for [tex]\frac{dV}{dt}[/tex], which will give us the rate at which the volume is decreasing as the pressure increases.
By substituting the given values into the differentiated equation: 150 kPa x [tex]\frac{dV}{dt}[/tex]+ 900 cm³ x 40 kPa/min = 0, we solve for [tex]\frac{dV}{dt}[/tex] to find the rate at which the volume is changing.
[tex]\frac{dV}{dt}[/tex] = - [tex]\frac{900}{150}[/tex] x 40
[tex]\frac{dV}{dt}[/tex] = -6 x 40
[tex]\frac{dV}{dt}[/tex] = -240 cm³/min
Following this method, we find that the volume is decreasing at a rate of 240 cm³/min.
(x-7)^2=0 does this have a real solution?
Yes. You can solve in the usual way.
Take the square root:
... x-7 = ±√0 = 0
Add 7:
... x = 7
_____
There is one distinct real solution (with multiplicity 2).
Need help, thanks. :)
Answer:
f(2) = 0
Step-by-step explanation:
Plug x = 2 into the formula for f(x):-
f(2) = 2(2) - 4
= 4 - 4
= 0
f(2) = 0
substitute x = 2 into f(x)
f(2) = (2 × 2 ) - 4 = 4 - 4 = 0
The price of 1 share of stock fell $4 every day for 3 straight days. How did the price of the stock change over these 3 days.
Answer:
The price over three days fell linearly
Step-by-step explanation:
s = stock
s = -4x
s = -4(3)
s = -12
The stock decreased by 12 dollars over 3 days.
Answer: -12
Step-by-step explanation:Hello!I hope you are having a good day or evening and I hope this helps :) !!
plz help for brainlest
2. A model rocket is launched from the ground with an initial velocity of 288 ft/sec.
c. How long will it take the rocket to reach its maximum height? Show all work in the space provided.
d. Assume the model rocket’s parachute failed to deploy and the rocket fell back to the ground. How long would it take the rocket to return to Earth from the time it was launched? Show all work in the space provided.
2c. We assume that the equations for ballistic motion in a vacuum apply, and the rate of downward acceleration is 32 ft/s². Then it will take ...
... (288 ft/s)/(32 ft/s²) = 9 s
for the rocket to reach its maximum height (its vertical velocity to decrease to zero).
2d. The trip down takes the same amount of time as the trip up, so the round trip time is ...
... (9 s)×2 = 18
_____
More ExplanationThe acceleration due to gravity decreases the vertical velocity by the same amount (32 ft/s) each second. An equation for that might be ...
... v = 288 -32t
When the vertical velocity is zero, the rocket is no longer going up. It has reached its maximum height. Then the equation for that looks like ...
... 0 = 288 -32t
... 32t = 288
... t = 288/32 = 9 . . . . . compare to the solution above
After 9 seconds, the rocket reaches its maximum height.
___
Simplifying the description of free-fall is a little harder. In physics terms, the potential energy the rocket has at its maximum height all gets converted to kinetic energy on the way down. At impact with the ground, the kinetic energy is the same as it was when the rocket was launched. That is, its velocity is 288 ft/s earthward at impact. The above equation for velocity still applies, but now we're solving for v = -288.
... -288 = 288 -32t
... -576 = -32t
... 576/32 = t = 18 . . . . . twice the time it took to reach maximum height.
The round trip takes 18 seconds.
An airplane has a maximum capacity of 118 passengers. The flight attendant has loaded 40 passengers. Which inequality represents the solution set that shows the number of passengers, p, that can still load the plane
A) p ≥ 68
B) p ≤ 68
C) p ≤ 78
D) p ≥ 78
C) p ≤ 78
I got 78 by subtracting 118 by 40. Since we know the maximum is 118 we can't get any higher than 78 so it has to be equal or less than.
Answer:
C) p ≤ 78
Step-by-step explanation:
so we know the plane has a maximum capacity of 118
and 40 have already been loaded.
118-40= 78
we know it cannot have greater than 78 but it can equal 78
there fore passengers are less than or equal to 78
also shown like this p ≤ 78 or option C
Daniela bought a car for $24,000. Each year the value of the car decreases by $1750. a. Write a function that shows the value of the car after y years.
I hope this might be able to help you.
Since the value of the car slowly decreases each year and each year is represented by y, the function is 24,000-1750y=f(x).
What is the value of y in the solution to the following system of linear equations?
2x+2=y
2y=5x-1
A) 3
B) 5
C) 8
D) 12
ANSWER
[tex]y=12[/tex]
EXPLANATION
One way is to make x the subject in one equation and substitute into the other.
[tex]2x+2=y[/tex]
[tex]\Rightarrow 2x=y-2[/tex]
[tex]\Rightarrow x=\frac{y}{2}-1--(1)[/tex]
The second equation is
[tex]2y=5x-1--(2)[/tex]
Let us put equation 1 in 2
[tex]\Rightarrow 2y=5(\frac{y}{2}-1)-1[/tex]
[tex]\Rightarrow 2y=\frac{5y}{2}-5-1[/tex]
[tex]\Rightarrow 2y=\frac{5y}{2}-6[/tex]
Multiplying through by 2 gives;
[tex]\Rightarrow 4y=5y-12[/tex]
[tex]\Rightarrow 4y-5y=-12[/tex]
[tex]\Rightarrow -y=-12[/tex]
[tex]\Rightarrow y=12[/tex]
D
given the 2 equations
2x + 2 = y → (1)
2y = 5x - 1 → (2)
Substitute y = 2x + 2 into (2)
2(2x + 2) = 5x - 1
4x + 4 = 5x - 1 ( subtract 5x from both sides )
- x + 4 = = - 1 ( subtract 4 from both sides )
- x = - 5 ( multiply through by - 1 )
x = 5
substitute x = 5 into (1)
y = (2 × 5 ) + 2 = 10 + 2 = 12 → D
Solve the literal equation |ax+b|=c for x.
Try this solution; note, this way is not the shortest one.
The solutions for the modular equation are:
[tex]x = \frac{c - b}{a}[/tex] or [tex]x = -\frac{c + b}{a}[/tex]
-----------------------
A modular equation |f(x)| = a means that:
[tex]f(x) = a[/tex] or [tex]f(x) = -a[/tex]
-----------------------
The equation given is:
[tex]|ax + b| = c[/tex]
Which means that:
[tex]ax + b = c[/tex]
[tex]ax = c - b[/tex]
[tex]x = \frac{c - b}{a}[/tex]
Or
[tex]ax + b = -c[/tex]
[tex]ax = -c - b[/tex]
[tex]ax = -(c+b)[/tex]
[tex]x = -\frac{c + b}{a}[/tex]
The solutions are [tex]x = \frac{c - b}{a}[/tex] or [tex]x = -\frac{c + b}{a}[/tex]
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Which of the following graphs represents a function that has a positive leading coefficient? Check all that apply.
Alright, so i'm looking at the graphs and i'm seeing B as an answer, Probably not A. C and D are confusing,
In the end, i'd say B and D.
If i'm wrong, please tell me.
The correct answers are (B), (C), and (D).
(C) is pretty straight forward. The graph resembles the graph of a quadratic function that us concave upwards. A quadratic function, and functions with an even degree like [tex]x^4, x^6[/tex] will be concave upwards if the leading term is positive.
For function with an odd degree such as [tex]x^3, x^5[/tex] will be mostly negative on the side of the negative x axis and positive on the side of the positive x-axis if the leading coefficient is positive. A cubic function with a positive leading term will be negative on the side of the negative x-axis for large negative numbers and positive on the side of the positive x-axis for large positive numbers. From this explaination we can gather that (B) and (D) are also correct .
The correct options are (B),(C) and (D).
What is the product of 4-5i and 2+3i
Multiply these as you would any binomial expressions, then replace i² with -1.
(4 -5i)·(2 +3i) = 4·2 +4·3i -5i·2 -5i·3i
... = 8 +12i -10i -15i²
... = 8+15 +2i
... = 23 +2i
_____
Your calculator may be able to do this problem for you.
If i have a pay rate of $21.00 and marked up 78.7% and made a 10% profit. how did i get $41.28?
Answer:By multiplying with (1+0.01x) where x is the percentage of increase, monthly pay rate of 21$ after marked up 78.7% and 10% profit will be $41.28.
Step-by-step explanation:
Given that pay rate is 21$ and it is marked up by 78.7% and made a 10% profit.
If any value marked up or made a profit of x% then we have to multiply with (1+0.01x) to find the new value.
New pay after 78.7% marked up using above formula is [tex]21X(1+0.01X78.7)=21X1.787=37.527[/tex]
Now we have to use above formula again for 10% profit.
Hence new value [tex]=37.527(1+0.01X10)=37.527X1.1=41.2797[/tex]≈$41.28
1. Which property is illustrated by the statement 2(-6/7)=(-6/7)2
A. Associative property of addition
B. Inverse propert. Of multiplication
C. Communtative property of multiplication
D. Communtative property of addition
2. Which property is illustrated by the statement? 5.4 + 3 = 3 + 5.4
A. Associative property of addition
B. Inverse propert. Of multiplication
C. Communtative property of multiplication
D. Communtative property of addition
(1) it is (C) the commutative property of multiplication: a*b = b*a, so 2*(-6/7) = (-6/7)*2
(2) it is (D) the commutative property of addition: a+b=b+a, so 5*4+3=3+5*4
commutate = "swap around"
- 2/3 + (3/4 + 5/3)
The commutative property of addition lets you rearrange this to
(3/4 +5/3) - 2/3
The associative property of addition lets you regroup this to
3/4 + (5/3 -2/3)
= 3/4 + 3/3
= 1 3/4 . . . . take your pick of the final form
= 7/4
= 1.75
I need help with number 2 please !!
In triangle ΔABC, ∠C is a right angle and CD is the height to AB . Find the angles in ΔCBD and ΔCAD if: Chapter Reference a m∠A = 20° Answer: m∠CDB = m∠CBD = m∠BCD = m∠CDA = m∠ CAD= m∠ACD =
In triangle ABC, when ∠A = 20°, then ∠B = 70°, ∠C = 90°. In triangle CAD, when ∠CAD = 20° and ∠CDA = 90°, ∠ACD = 70°. In triangle CBD, with ∠CBD = 90° and ∠BCD = 70°, ∠CDB = 20°.
Explanation:In triangle ΔABC, ∠C is a right angle and CD is the height to AB. Considering ∠A = 20°, by the angles sum property of a triangle, ∠B = 180° - ∠A - ∠C = 180° - 20° - 90° = 70°.
Moving on to triangle ΔCAD, this is a right triangle with ∠CDA=90°. ∠CAD is given as 20° (the same as ∠A of triangle ΔABC). Therefore, ∠ACD = 180° - ∠CAD - ∠CDA= 180° - 20° - 90° = 70°.
For triangle ΔCBD, ∠CBD is 90°, and ∠BCD corresponds to ∠B of triangle ΔABC, which we've determined as 70°. Hence, ∠CDB = 180° - ∠CBD - ∠BCD = 180° - 90° - 70° = 20°.
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In triangle ΔCBD, the angles are: m∠CDB = m∠CBD = 90° and m∠BCD = 90°. In triangle ΔCAD, the angles are: m∠CDA = 70° and m∠CAD = 70°. Finally, m∠ACD = 40°.
Explanation:In triangle ΔCBD, since ∠C is a right angle, ∠CBD = 90° and ∠BCD = 90°.
In triangle ΔCAD, using the fact that the sum of angles in a triangle is 180°, we can find that ∠CDA = 90° - ∠CBD = 90° - 20° = 70°.
Similarly, ∠CAD = 90° - ∠BCD = 90° - 20° = 70°.
Finally, since ∠CDA = ∠CAD, ∠ACD = 180° - ∠CDA - ∠CAD
= 180° - 70° - 70°
= 40°.
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if P(a)=0.60 and P(b)=0.30, then a and b are independent events if
Answer: [tex]\text{P(A or B)}=0.90[/tex]
[tex]\text{P(A and B)}=0.18[/tex]
Step-by-step explanation:
Given : P(A)=0.60 and P(B)=0.30
We will say A and B are independent events if :
[tex]\text{P(A or B)=P(A)+P(B)}\\\\=0.60+0.30=0.90[/tex]
[tex]\text{P(A and B)=P(A) x P(B)}\\\\=0.60\times0.30=0.18[/tex]
Thus , A and B are independent events if :
[tex]\text{P(A or B)}=0.90[/tex]
[tex]\text{P(A and B)}=0.18[/tex]
Answer: P( A and B)= 0.18
Valerie wants to take out a discount loan of $569. The rate is 4.5% for 250 days. How much interest will she pay? (Be sure to round the time to the nearest hundredth.
The interest is computed from
... I = Prt
where P is the principal amount ($569), r is the rate (0.045) and t is the time in years (250/360).
... I = $569×0.045×250/360 ≈ $17.78
Please note that time is not rounded. Rather, the exact value (25/36) is used in the calculation. The only rounding of any number is done at the end, where the amount is rounded to the nearest cent. (Your text authors should know this.)
_____
If you follow the problem instructions (which Valerie's lender will not do), the interest is calculated as ...
... t = 250/360 = 0.6944444... ≈ 0.69 . . . . years
... I = $569×0.045×0.69 ≈ $17.67
_____
Note the rounding of intermediate numbers (time) introduces an error of about $0.11 in the answer.
Answer:$17.41 (A+)
Step-by-step explanation:
the box part of the box plot contains all the values between which numbers?
between 27 and 36 and between 37 and 40
between 32 and 36
between 32 and 37
between 27 and 32 and between 37 and 40
The left end of the box is at 32; the right end is at 37. The box part of the plot contains all the values ...
... between 32 and 37.
Answer:
The correct option is 3.
Step-by-step explanation:
From the given box plot it is clear that
1. The left end point of the line is 27. So, the minimum value of the data is 27.
2. The left end of the box is 32. It means the first quartile of the data is 32.
3. The line inside the box represents the median. So the median of the data is 36.
4. The right end of the box is 37. It means the third quartile of the data is 37.
5. The right end point of the line is 40. So, the maximum value of the data is 40.
It means the box part of the box plot contains all the values between 32 and 37.
Therefore the correct option is 3.
How do I get the revised bill rate ?
The initial pay rate is $16.00. It is also mentioned that the price is marked up by 78.7%. It means that the prices are increased by 78.7%. Also, there is a profit of 10% too. So, the pay rates after mark up will be
$16.00 + (78.7% of 16.00)
= $16.00 + $12.592
=$28.592
And the pay rates after estimated profit is
$28.592 + (10% of $28.592)
= $28.592 + $2.8592
= $31.4512
Hence, the revised bill rate, rounded to the nearest cent is $31.45.
A grocery store bought milk for $2.80 $2.80 per half gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 13 13 half gallons. If the remaining milk is sold for $4.06 $4.06 per half gallon, how many half gallons did the store buy if they made a profit of $63.14 $63.14 ?
Let x represent the number of half-gallons purchased by the store. Then x-13 is the number sold, and 2.80x is the store's cost. The revenue is 4.06(x-13) and the difference between that and cost is the profit.
... 4.06(x -13) -2.80x = 63.14
... 1.26x - 52.78 = 63.14 . . . . eliminate parentheses, collect terms
... 1.26x = 115.92 . . . . . . . . . . add 52.78
... x = 115.92/1.26 = 92 . . . . . divide by the coefficient of x
The store purchased 92 half-gallons of milk.
The sales volume for an online bookstore was 432 books in the first week. Then due to the new policy of tax for on-line shopping, the sales volume dropped to 297 books at the second week. By what percent did the sales volume go down?
The volume drop is 432-297= 135
135 books is a fraction 135/432 of the original volume 432. That is (x100): 31.25%
So the sales went down by 31.25%
31.25 percent of sales go down in second week as compared to first week.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, the sales volume for an online bookstore was 432 books in the first week.
Then due to the new policy of tax for on-line shopping, the sales volume dropped to 297 books at the second week.
Percentage dropped= 297/432 ×100
= 0.6875×100
= 68.75%
Now, 100-68.75=31.25%
Therefore, 31.25 percent of sales go down in second week as compared to first week.
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A student bought a juice pouch for $2.50 and three bags of chips the total cost was $5.05 right and solve an equation to determine the cost of a bag of chips, c
The total amount of the purchase was ...
... $2.50 + 3c = $5.05
This equation can be solved by subtracting 2.50 and dividing by 3. Both these operations are done to both sides of the equation in accordance with the rules of equality.
... 3c = $2.55
... c = $0.85
The cost of a bag of chips was $0.85.
The cost of a bag of chips can be found by subtracting the juice price from the total cost and then dividing by the number of chip bags. This gives us an answer of $0.85 per bag.
Explanation:To solve this problem, we need to subtract the cost of the juice from the total cost, then divide that answer by the total number of chip bags bought to find the cost of one bag. First, we subtract the juice price ($2.50) from the total spent ($5.05), which gives us $2.55. This is the total cost of the chips. Then, we divide that $2.55 by the number of chip bags bought (which is three) to find the cost of one bag. This can be represented by the equation: c = (total cost - juice price) / number of chip bags, or c = ($5.05 - $2.50) / 3. Calculating this, we find that c equals $0.85, so a bag of chips costs $0.85.
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Trish plans to sell off 40% of her fast food restraunt business. If the business has been appraised for 350,000 dollars how much money does she expect to raise
40% of $350, 000
40% = [tex]\frac{40}{100}[/tex] = 0.4, hence
expected amount = 0.4 × $350, 000 = $140, 000
Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100100100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 20 \text{ cm}20 cm20, space, c, m. How far did Chubby run? Round your answer to the nearest \text{cm}cmc, m.
Answer: 6280 cm
Step-by-step explanation:
Given: The diameter of hamster wheel = 20 cm
The circumference of hamster wheel is given by :-
[tex]C=\pi d[/tex], where d is the diameter of the hamster wheel.
[tex]\Rightarrow C=(3.14)(20)=62.8\text{ cm}[/tex]
During one race, the number of rotations of the wheel = 100
Therefore, the distance run by chubby is given by :-
[tex]D=100\times C\\\\\Rightarrow D=100\times62.8\\\\\Rightarrow D=6280\text{ cm}[/tex]
Answer:
6283 cm.
Step-by-step explanation:
We have been given that Avi's pet hamster Chubby completed 100 rotations of the wheel. The diameter of the hamster wheel is 20 cm.
Since wheel is a circle, so the distance covered by Chubby in one rotation will be equal to the circumference of wheel.
[tex]\text{Circumference of circle}=2\pi r=\pi D[/tex], where,
r = Radius of circle,
D = Diameter of circle.
Now we will find the circumference of wheel by substituting [tex]D=20[/tex] in above formula.
[tex]\text{Circumference of wheel}=\pi*20[/tex]
[tex]\text{Circumference of wheel}=62.83185307[/tex]
Since Chubby covers a distance of 62.83185307 cm in one rotation, so in 100 rotations distance covered by Chubby would be:
[tex]\text{Distance covered in 100 rotations}=100\times 62.83185307[/tex]
[tex]\text{Distance covered in 100 rotations}=6283.185307\approx 6283[/tex]
Therefore, Chubby ran a distance of 6283 centimeters.
Please I need your help desperately what is the area of this triangle? See attached image thank you so much
To find the area of the given traingle we have to draw perpendicular from point 'J' which meets the x axis at point (2,0) and let us named it 'P'.
As we know that area of triangle is
[tex] = \frac{1}{2}\times b \times h [\tex]
Here base 'b' will be LK and height 'h' will be JP
Here,
LK= 4 units JP=4 units
Area ={1}{2} *(4)*(4)
On solving the equation we get,
Area=8 Sq units
a moving truck charges $250 to rent a truck and $0.40 for each mile driven. mr.lee paid a total of $314. which equation can be used to find m, the number of miles he drove the moving truck?
50 Points
Find the specified vector or scalar. Show your work.
u = -4i + 1j and v = 4i + 1j; Find |u+v|.
| u + v | = 2
u + v = - 4i + 1j + 4i + 1j = 2j
the magnitude of a vector ai + bj is
| ai + bj | = √(a² + b² )
for u + v = 0 + 2j
| u + v | = √(0² + 2² ) = √4 = 2
What is another way to name ∠QRS ? Select each correct answer. ∠R ∠S ∠Q ∠QSR ∠SRQ ∠RSQ
<SRQ Because if you go any other way other than its opppsite you would get a different angle.
Another way to name ∠QRS is ∠SRQ as R is the vertex of the angle.
What is a vertex?A vertex is a common endpoint between two rays that forms an angle.
We know when an angle is represented by three letters the vertex of the angle is the middle letter.
∴ Another name ∠for QRS is ∠SRQ because here R is the vertex of the angle and we can not place R in the first or the third place as it would completely change the vertex of the angle which are not the same angles, of Ofcourse their measure can be same but they are different.
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