Answer:
a)-2000
b)-2500
Step-by-step explanation:
Given:
W(t) = 100(t-15)²
applying derivation on both sides
W'(t) = 200(t-15)
->a) At what rate is the water running out at the end of 5 minutes?
Evaluating at t=5
W'(5)= 100(5-15) =>200(-10)
W'(5)=-2000
->b) What is the average rate at which the water flows out during the first 5 minutes?
[tex]\frac{W(5)-W(0)}{5-0} =\frac{100(5-15)^2*100(0-15)^2}{5} =>\frac{10000-22500}{5}[/tex]
=>-2500
Describe in your own words what a hyperbola is.
Answer:
A conic section that can be thought of as an inside-out ellipse
Step-by-step explanation:
Hyperbola is a two-branched open curve-conic section.
What is a hyperbola?Hyperbola is the locus of all those points in a plane such that the difference in their distances from two fixed points in the plane is a constant.
For the given situation,
We need to describe about a hyperbola.
A hyperbola is two curves that are like infinite bows. It is a two-branched open curve, a conic section produced by the intersection of a circular cone and a plane that cuts both nappes of the cone.
The standard equation of hyperbola is
[tex][\frac{x^{2} }{a^{2} }-\frac{y^{2} }{b^{2} }]=1[/tex]
where,[tex]b^2 = a^2 (e^2 -1)[/tex]
a,b are the points on the plane and e is the eccentricity.
Hence we can conclude that hyperbola is a two-branched open curve-conic section.
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Solve the following system of equations {4x−6y=105x+6y=−55
Answer:
31557778998765432
Step-by-step explanation:
is it impossible
what is -4 {2 - y} + 3y = 3 {y - 4}
A bag contains marbles of four different colors listed below. What is the probability of picking a BLUE marble at random out of the bag?
8 blue marbles, 24 red marbles, 16 green marbles, 4 yellow marbles.
~
1) 8/100
2) 2/13
3) 6/13
4) 4/13
Step-by-step explanation:
Total marbles = 24 + 8 + 16 + 4 = 52
Probability of blue marble = 8/ 52 = 4 / 26 = 2 / 13
Option 2 is the correct answer
Which expression represents the volume of a rectangular prism that is not occupied by the cylinder.
Answer:
The volume of the prism not occupied by the cylinder is (150 - 25*pi)*h.
Step-by-step explanation:
In order to calculate the volume of the rectangular prism that is not occupied by the cylinder we need to calculate the total volume of the rectangular prism and subtract it by the volume of the cylinder. We have:
Rectangular prism:
Volume prism = length*height*width
Volume prism = 15*h*10 = 150*h
Cylinder:
Volume cylinder = pi*r²*h = pi*5²*h = 25*pi*h
The volume of the prism that is not occupied by the cylinder is:
volume not occupied = volume prism - volume cylinder
volume not occupied = 150*h - 25*pi*h = (150 - 25*pi)*h
The volume of the prism not occupied by the cylinder is (150 - 25*pi)*h.
Solve
8 - (2x - 9) = 17-24
Answer:
x=12
Step-by-step explanation:
8-(2x-+9)=17-24
8-2x=17-24-9
8-2x=-7+-9
8-2x=-16
-2x=-16-8
-2x=-24
x=-24/-2
x=12
Jackson and Xavier are both solving the multiplication 0.8 x 5. Jackson gets 4 as a solution, and Xavier gets 0.4. Xavier said to Jackson, "Your answer of 4 can't be right for 0.8 x 5. You need a decimal point because a product always has the same number
Answer:
Jackson
0.8×5=4
Xavier
0.8×5=0.4
If Xavier said to Jackson that his answer of 4 can't be right.
Jackson needs a decimal point because a product always have the same answer.
Then,
Xavier is right with his sayings but wrong with the answer of 0.4
The correct answer is 4.0
The decimal point should be counted from the back not from the front as Xavier did
plzzzzzzzzzzzzzzaaaaaaaaaa
Answer:
A
Step-by-step explanation:
[tex]3x^2+5x+2=0[/tex]
[tex]x=\dfrac{-5\pm \sqrt{5^2-4(2)(3)}}{6}=\dfrac{-5\pm 1}{6}=-\dfrac{2}{3}, -1[/tex]
Therefore, the answer is choice A. Hope this helps!
You pick one card from each set and find the sum. How many different sums are possible?
Answer:
24 possibilities
Step-by-step explanation:
2*2*6=24
24 possibilities
The number of different sums possible is 24 possibilities.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We have been given that pick one card from each set and find the sum.
Therefore, we need to find the number of different sums that are possible;
2 x 2 x 6=24
24 possibilities
Hence, the number of different sums possible is 24 possibilities.
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Given a school supply store sells pencils for $2, pens for $4, and markers for $5. Write an expression for the total cost of 3 pencils, 2 pens, and 3 markers
Answer: 29
Step-by-step explanation:
3x2= 6
4x2=8
3x5=15
6+8+15= 29
hoped I helped you a bit! Good luck! :)
4. A plane was flying at an altitude of 55,000 feet when it began the descent toward the airport. The airplan
descends at a rate of 825 feet per minute.
A. What is the function rule that describes this situation?
B. What is the altitude of the plane after it has descended for 13 minutes? Show your work
C. Use the function in Part A to determine how long it takes for the plane to land if it descends at a
continuous rate.
Answer:
Step-by-step explanation:
A Descent rate,
B 10725ft,
C 25min
Timothy makes reduced copies of a photograph that has an actual length of 8 in. Each time he presses the reduce button on the copier, the copy is reduced by 12%. What formula shows the pattern for the size of each copy of the photograph as it is reduced? What is the length of the photograph’s copy if Timothy presses the reduce button 5 times? Round to the nearest tenth.
Answer:
length of the photograph will be 4.2 in. after pressing the button 5 times.
Step-by-step explanation:
By pressing the button, every time size of the photograph gets reduced by 12%.
Therefore, the sequence formed by the reduced sizes of the photo will be a geometric sequence and the formula for the size of the reduced image will be,
L = [tex]l(1-\frac{12}{100})^{n}[/tex]
Where l = Actual length of the photograph
L = length of the reduced image
n = Number of times the button has been pressed
For l = 8 in. and n = 5
L = [tex]8(1-0.12)^{5}[/tex]
= [tex]8(0.88)^{5}[/tex]
= 4.22 in
L ≈ 4.2 in.
Therefore, length of the photograph will be 4.2 in. after pressing the button 5 times.
The length of the photograph's copy when the button is pressed the 5th times is 4.2 inches
The question is an illustration of an exponential function.
An exponential function is represented as:
[tex]y = ab^x[/tex]
Where:
a represents the initial value i.e. a = 8b = 1 - r; and r represents the rate. i.e. r = 12%.So, the function becomes
[tex]y = 8 \times (1 - 12\%)^x[/tex]
Express 12% as decimal
[tex]y = 8 \times (1 - 0.12)^x[/tex]
This gives
[tex]y = 8 \times 0.88^x[/tex]
When the button is pressed the 5th times, we have:
[tex]y = 8 \times 0.88^5[/tex]
[tex]y = 4.2[/tex]
Hence, the length of the photograph's copy is 4.2 inches
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The art club had an election to select a president. 75% of the 68 members of the club voted in the election. How many members voted?
Answer:
51 members voted of the 68 members
Idk what it is plz help me
Answer:
1) Starting height is 6.25
2) after 20 years it would be 30
1.25(20)=25+5=30
3) 76 years
Answer:
a) 5 feet
b) 30 feet
c) 76 years
Step-by-step explanation:
a) 5 feet. If t is 0, it'll still be 5 feet
b) 30 feet
1.25*20+5=
25+5=
30
c) 76 years
100 = 1.25t+5
1.25t=95
t=76
a knife is 3 times the cost of spoon
9 spoons and 12 knives cost £82.80
Answer:
5 .52
Step-by-step explanation:
do the math. aaaaaaaaaaaaaaaaaaaannnnnnnnnnnnnnnnnddddddd this is the best appppp evvvvver
A copy machine makes 231 copies in 5 minutes and 15 seconds. How many copies does it make per minute?
The solution is 44 copies
The number of copies the copy machine makes in one minute is 44 copies
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The number of copies the copy machine makes = 231 copies
Time required by the to make 231 copies = 5 minutes 15 seconds
5 minutes = 5 x 60 seconds
5 minutes = 300 seconds
5 minutes 15 seconds = 300 + 15 seconds
5 minutes 15 seconds = 315 seconds
So , Time required by the to make 231 copies = 315 seconds
Now , number of copies in 1 minute = 60 x ( The number of copies the copy machine makes / Time required by the to make 231 copies )
Substituting the values in the equation , we get
Number of copies in one minute A = 60 x ( 231 / 315 )
Number of copies in one minute A = 60 x 0.733
Number of copies in one minute A = 44 copies
Therefore , the value of A is 44 copies
Hence , the number of copies is 44 copies
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What is the slope of the line that passes through (1,-19) and (-2,-7)?
The formula for the slope of a line is m = (y2 - y1) / (x2 - x1).
Point 1 = (1, -19)
Point 2 = (-2, -7)
m = (-7 - -19) / (-2 - 1)
m = (-7 + 19) / (-2 - 1)
m = 12 / -3
m = -4
Hope this helps! :)
Melissa needs to wrap a gift box that is shaped like a rectangular prism. The length is 6 inches, the width is 6 inches and the height is 8 inches. How much wrapping paper does she need to cover the whole box
Answer:
A=264
Step-by-step explanation:
In ΔHIJ, the measure of ∠J=90°, IJ = 47 feet, and HI = 68 feet. Find the measure of ∠H to the nearest degree.
Answer:
44
Step-by-step explanation:
VX
Does choosing a blue marble represent the complement
event of choosing a red marble? Explain.
B
Р
В
Answer:
red marble
Step-by-step explanation:
i did this yw
The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both 25 2525 kilometers long. The population in Las Pythagoras is 100 , 000 100,000100, comma, 000 people. What is the population density of Las Pythagoras?
320
Step-by-step explanation:
The area of a circle is 4π x 2 + 12πx + 9π.
a. What is an expression for the radius of the circle?
b. What is the least possible integer value of x for the circle to exist? Explain.
Answer:B D
Step-by-step explanation:
I just got it right
DESPERATE GEOMETRY HELP!!!
Answer:
b. 3
Step-by-step explanation:
pi * r^2 * h = 162 pi
plug in 18 ft for h
pi * r^2 * (18) = 162 pi
simplifies to r^2 = 9
r=3
Tue or False? The first distribution shown below had a smaller mean than does the second distribution
Answer:
the answer id true
i hope that helps
2. Express as a unit rate.
a) Betty drives her car 150 km in 2 h.
150 km/2 =
Answer:
75 km per hour.Step-by-step explanation:
150km/2hr divided by two is 75 km/hr
James has g amount of games. Samuel, his friend, has 4 times as many games as James. Write an algebraic expression to represent how many games James has and how many games Samuel has in terms of g.
Answer: The answer is given below
Step-by-step explanation:
From the question, we are told that James has a lot of games and his friend Samuel, has 4 times as many games as James.
So let the number of games that James has be denoted by g.
Since Samuel has 4 times as the number of games that James has, then Samuel's game will be
= 4 × g
= 4g
Therefore, the expression for James will be g and the expression for the number of games Samuel has is 4g.
can someone help? 25 points
Answer:
8 hours
Step-by-step explanation:
HE has to pay $7 an hour.
8*7=56
He has a descount of $3, so
$56-$3=$53.
Which is the exat amount of money that Tony has.
Answer:
The answer is 46
Because he wants to spend less so you would do
7x7=49
He could only rent the boat for 7 hours because that would be less than 53$
Now you do 49-3=46
Because he had a discount
So the answer is 46
Step-by-step explanation:
Hope this helped!
what is the percent change between 6 to 3?
Answer:
50% = percent chang
Step-by-step explanation:
6 ÷ 50%
6 × .50 = 3
3 ÷ .50 = 6
What are the roots of the graph below?
Answer:
-2,-1,1,2
Step-by-step explanation:
The term root is just another name for the x intercept so just look at where your line crosses the x axis and you will have your answer. Remember the y axis is not involved so it cannot be a co-ordinate.
how do I simplify this algebraic expression 3x+2a-4x
Start by changing the -4x to + -4x.
So we have 3x + 2a + -4x.
To simplify, we can only combine what are called our like terms and in this problem, we have a pair of like terms in our x terms.
3x + -4x simplifies to -x.
So our answer is -x + 2a.
Note that if you wrote your answer as -1x + 2a, it means the same thing. However, as we move farther into math, we usually tend to drop the -1 or 1 that is in front of a variable since it's implied
