Let V be the volume of the tank. The tap fills the tank at a rate of V/(4 hours), or V/4 per hour. The hole empties the tank at a rate of V per hour. If both the tap and hole work together, the net rate of water flow is V/4 - V or -3V/4 per hour.
Starting with a full tank, the volume v of water at time t is given by the function
v(t) = V + (-3V/4) t
Solve v(t) = 0 to find the time it takes to empty:
V - 3V/4 t = 0
V = 3V/4 t
t = V / (3V/4) = 4/3
So it takes 4/3 hours = 80 minutes to empty a full tank.
2- Answer the following question:
a. What are the four different ways to solve a quadratic function? (5 points)
b. Solvex² - 4x - 11 = 0 using completing the square. You must show all the steps. (10 points)
c. Solve 2x² + 16x + 24 = 0 using the quadratic formula. You must show all the steps. (10 points)
A. Four ways to solve a quadratic equation
---Factoring
---Completing the square
---Quadratic equation
---Graphing
B. Solve the equation by completing the square
x^2 - 4x - 11 = 0
x^2 - 4x = 11
x^2 - 4x + 4 = 11 + 4
(x - 2)^2 = 15
x - 2 = +/- 15
x - 2 = 15 || x = 17
x - 2 = -15 || x = -13
C. Solve the equation using the quadratic formula
Quadratic formula = [tex]\frac{-b +/-\sqrt{b^2 - 4ac} }{2a}[/tex]
Equation = 2x^2 + 16x + 24 = 0
a = 2
b = 16
c = 24
[tex]\frac{-16 +/- \sqrt{16^2 - 4(2)(24)} }{2(2)}[/tex]
[tex]\frac{-16 +/- \sqrt{256 - 192} }{4}[/tex]
[tex]\frac{-16 +/- \sqrt{64} }{4}[/tex]
[tex]\frac{-16 +/- 8 }{4}[/tex]
[-16 + 8] / 4 = -2
[-16 - 8] / 4 = -6
x = -6, -2
Hope this helps!
Persevere with Problems The table shows the highway fuel economy of various popular vehicles.
The mean absolute deviation of highway fuel economy of various popular vehicles is 4.9
How to find mean absolute deviation?Find the mean of the data set
= (38 + 48 + 25 + 35 + 33 + 37 + 32 + 34 + 23 + 30) / 10
= 335 / 10
= 33.5
Mean deviation of each set;
38 - 33.5 = 4.5
48 - 33.5 =14.5
25 - 33.5 = -8.5
35 - 33.5 = 1.5
33 - 33 .5 = -0.5
37 - 33.5 = 3.5
32 - 33.5 = -1.5
34 - 33.5 = 0.5
23 - 33.5 = -10.5
30 - 33.5 = -3.5
Absolute deviation of each value
|4.5| = 4.5
|14.5| = 14.5
|8.5| = 8.5
|1.5| = 1.5
|-0.5| = 0.5
|3.5| = 3.5
|-1.5| = 1.5
|0.5| = 0.5
|-10.5| = 10.5
|-3.5| = 3.5
Total absolute deviation = 4.5 + 14.5 + 8.5 + 1.5 + 0.5 + 3.5 + 1.5 + 0.5 + 10.5 + 3.5
= 49
Mean absolute deviation = Total absolute deviation / mean
= 49/10
= 4.9
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6)( b)write down the ratio of white chocolates to milk chocolates 3/8
Answer:
white chocolates = 3
milk chocolates = 8
ratio= 3:8
[tex] \frac{3}{8} [/tex]
0.375
A price is divided into 1:11. If the difference between the shares is £180, what is the total prize
Answer:
£216
Step-by-step explanation:
The total prize will be the sum of the divisions of the prize. The difference of those divisions is given.
__
divisionsLet P represent the value of the prize. The 1:11 ratio of the parts tells us there are 1 +11 = 12 total parts, and their ratio is P/12 : 11P/12. The sum of these divisions is the whole prize:
P/12 +11P/12 = 12P/12 = P
differenceThe difference of the two divisions of the prize is ...
11P/12 -P/12 = £180
10P = £2160 . . . . . . . . multiply by 12 and simplify
P = £216 . . . . . . . . divide by 10
The total prize is £216.
_____
Additional comment
The divisions of the prize are
£216/12 = £18 and 11×£18 = £198
The sum of those divisions is the total prize: £18 +198 = £216.
The total price (prize)the difference between the shares is £180 is £216.
How to determine the total prizeLet's represent the total price as "P." According to the information given, the price is divided into a ratio of 1:11.
The total number of parts in the ratio is 1 + 11 = 12 (1 part for the first share and 11 parts for the second share).
Let the first share be "x" and the second share be "11x" (since the ratio is 1:11).
Now, the difference between the shares is £180:
11x - x = £180
Simplifying:
10x = £180
Now, divide both sides by 10 to find the value of "x":
x = £180 / 10
x = £18
Now, we can find the total price "P" by adding the shares together:
P = x + 11x
P = £18 + £198
P = £216
So, the total price (prize) is £216.
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the measure of one interior angle of a regular polygon is 60 degree mote the twice the measure of an exterior angle at the same vertex how many sides does this polygon have
Answer:
3 sides
Step-by-step explanation:
If the interior angle measures 60 degrees, this means the exterior angle measures 120 degrees.
The exterior angle of a regular polygon is given by 360/n, where n is the number of sides, so setting this equal to 120, we get that n=3 sides
PLEASE HELP ME ASAP
Does the series converge or diverge? If it converges, what is the sum? Show your work
The series is a convergence series and the sum of the series is -8/3
The type of the seriesThe series is given as:
[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]
The above series has the following properties:
First term; a = -4Common ratio, r = -1/2Start by calculating the absolute value of the common ratio
Absolute value = |-1/2|
This gives
Absolute value = 1/2
The above value is less than 1.
It means that the series converges.
The sum of the seriesThis is calculated using:
[tex]S_{\infty} = \frac{a}{1 -r}[/tex]
So, we have:
[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]
Evaluate the sum
[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]
Evaluate the quotient
[tex]S_{\infty} = \frac{-8}{3}[/tex]
Hence, the sum of the series is -8/3
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PLEASE HELP Which statement about the answer to this problem is most accurate?
5/6−3/8=19/24
The answer 19/24 is reasonable because both fractions are closer to 1/2 than they are to 1, making the difference close to 0.
The answer 19/24 is reasonable because 5/6 and 3/8 are both closer to 1 than to 1/2, making the difference close to 0.
The answer 19/24 is not reasonable because 5/6 is closer to 1 than to 1/2, and 3 is close to 1/2, making the difference close to 1/2.
The answer 19/24 is not reasonable because 5/6 is closer to 1/2 than to 1, and 3/8 is closer to 0 than to 1/2, making the difference close to 1/2.
The answer 19/24 is not reasonable because 5/6 is closer to 1 than to 1/2, and 3 is close to 1/2, making the difference close to 1/2.
Step-by-step explanation:
the third answer.
5/6 is almost 1, 3/8 is almost 1/2, so their difference is close to 1 - 1/2 = 1/2.
and 19/24 is much bigger than 1/2 (which would be 12/24).
in real numbers
5/6 - 3/8 = 5×4/24 - 3×3/24 = 20/24 - 9/24 = 11/24.
which is indeed very close to 1/2 (or 12/24).
The maximum possible correspondence or correlation between two variables is represented by a Pearson product-moment coefficient of:
Correlation analysis is meant to determine the strength of a linear
relationship between variables.
A true statement of correlation analysis is that; The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.The complete question is as below:-
Which of the following statements is true of the correlation analysis? The null hypothesis for the Pearson correlation coefficient states that there is always a strong association between two variables. The larger the correlation coefficient, the weaker the association between two variables. The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero. The Pearson correlation coefficient measures the degree of linear association that ranges from 1.0 to 10.0. The Pearson correlation coefficient measures the degree of linear association between three variables.
What is correlation analysis?Correlation analysis is a test to determine the presence and or amount of relationship that exists between variables.
During a hypothesis test aimed at determining the existence of a correlation between variables, the null and alternative hypotheses are as follows;
The null hypothesis, H₀: There are no relationships between the variables
H₀: r = 0
The alternative hypothesis, Hₐ: The variables have an association
Hₐ: r ≠ 0
Therefore, the true statement of the correlation analysis is; The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.
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(-17,-5), (15,-13)
Slope of the line through each pair of points
PLEASE HELP!
Martha and Emily had to sew dresses with beads. Emily had 20% more beads than Martha. Then Emily gave 25% of her beads to Martha. Now Martha has 80 beads more than Emily. How many beads did each dressmaker had at the start?
Answer:
Emily has about 73 beads and Martha has about 62
Step-by-step explanation:
E = M · 1.2
M + ( .25 · E ) = m
m = 80
Now work backwards to find the answer.
Note that to find the answer you must get rid of the variable E, so you must use the expression M · 1.2 to represent E.
M + ( .25 · M · 1.2 ) = 80
M + .3M = 80
1.3M = 80
Divide both sides by 1.3
M = 61.5
Round to the nearest one
M = 62
Now use this to find E
E = 62 · 1.2
E = 74.4
Round to nearest one
E = 73
This might be confusing but I hope it was helpful!
Also, can I get brainliest because this took a lot of work to figure out.
What is the distance to the earth’s horizon from point P?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
The distance to the earth’s horizon from point P is 281.6 miles
How to determine the distance to the earth’s horizon from point P?The tangent line from P meets the radius of the earth at a right angle.
This means that the triangle is a right triangle.
The length of x is then calculated as:
(3959 + 10)^2= 3959^2 + x^2
Rewrite as:
x^2 = (3959 + 10)^2- 3959^2
Evaluate
x^2 = 79280
Take the square root of both sides
x = 281.6
Hence, the distance to the earth’s horizon from point P is 281.6 miles
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Answer:
Answer above is wrong. See answer below.
Step-by-step explanation:
help me I need the answer on paper help me now
Answer:
x = 144
Step-by-step explanation:
Angle sum of heptagon = 900
5x + 90 + 90 = 900
5x + 180 = 900
5x + 180 - 180= 900 - 180
5x = 720
Divide both sides by 5
x = 144
The UAE has very specific guidelines set out for the use and display of the UAE flag. One of
the rules regards the dimensions of the flag. The rule is that the ratio of the length of the flag
to the width must be 2: 1.
The length and width of the flag is 37 cm and 18.5 cm
It is divided into four rectangular parts. The first is red in colour, its length being equivalent to
the height of the flag, while its width is 0.25 of the length of the entire flag. The other three
parts constitute the remaining area of the flag which are in the shape of three equal horizontal
rectangles, width of these rectangles should be 0.33 of the width of the entire flag . The top
most rectangle part is green, the middle is white and the lower is black in colour.
[tex]\sf\large\green{\underbrace{\red{Question*}}}:[/tex]
[tex] \mathbb\blue{SOLVE} [/tex]
[tex] \pink{1. \: \: \: \: \: \: (3 - x)(x + 2) = 0}[/tex]
[tex] \pink{2. \: \: \: \: \: {(q + 2)}^{2} - 40}[/tex]
[tex]\large{\underline{\underline{\pmb{\sf{\color {red}{Solve:}}}}}}[/tex]
[tex] \sf \red{1. \: (3x - x) (x + 2) = 0}[/tex]
[tex] \sf \red{2. \: (q + 2)^{2} - 40}[/tex]
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
2.soln:
(q + 2)² - 40
=> (q)² + 2.q.2 + (2)² - 40
=> q² + 4q + 4 - 40
=>q² + 4q - 36
Here, a = 1, b = 4 and c = - 36
By, using Quadratic formula
See the attachment
Alice is playing checkers against a computer and has won 8 games out of the 12 she's played so far.
Alice must win the next consecutive games to reach a winning percentage of 80%. After that, losing
consecutive games
will bring her winning percentage down to 50%.
Answer:
Step-by-step explanation:
[tex]\frac{8+x}{12+x} =\frac{80}{100} =\frac{4}{5} \\40+5x=48+4x\\5x-4x=48-40\\x=8[/tex]
so she wins next 8 consecutive games to reach winning percentage of 80%.
let she loses next y games to reach winning percentage of 50 %.
[tex]\frac{16}{12+8+y} =\frac{50}{100} =\frac{1}{2} \\\frac{16}{20+y} =\frac{1}{2} \\32=20+y\\y=32-20=12y=12[/tex]
Hence she loses next 12 games to reach winning percentage of 50 %.
The weights of packs of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation 2.4 grams. The weight of a randomly selected pack of gum has a z-score of 3.11. Which of the following statements is the best interpretation of the z-score?
The weight of this pack of gum is lighter than the mean weight by 3.11 standard deviations.
The weight of this pack of gum is heavier than the mean weight by 3.11 standard deviations.
The weight of this pack of gum is lighter than the mean weight by 2.4 standard deviations.
The weight of this pack of gum is heavier than the mean weight by 2.4 standard deviations.
The weight of this pack of gum is heavier than the mean weight by 3.11 standard deviations.
Why is the above statement appropriate ?The supplied z-score of 3.11 can be best translated as "This pack of gum weighs 3.11 standard deviations more than the mean weight." A z-score indicates how many standard deviations an observation is from the population mean. When an observation has a positive z-score, it is above the mean; when it has a negative z-score, it is below the mean. The selected pack of gum weighs more than the population's mean weight because the specified z-score is positive. Furthermore, a z-score of 3.11 means that the pack of gum weighs 3.11 standard deviations more than the population's mean weight.
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5x-4y=10
slope intercept form
Answer:
5x-4y=10
solution
first find x intercept is the graph cross x-axis.to find the x intercept,we set y¹=0 and the Solve x.
5x-4y=10
5x-4(0)=0
x¹ =2 y¹=0
y intercept
5x-4y=10
5(0)-4y=10
y²=2.5 x²=0
If Cyrus knows that △ABC∼△EDC and AB¯¯¯¯¯¯¯¯∥ED¯¯¯¯¯¯¯¯, how can he prove that line m passing through AB¯¯¯¯¯¯¯¯ has the same slope as line l passing through ED¯¯¯¯¯¯¯¯?
Brainliest and 5 Stars to Best Answer and Explanation!
As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.
calculate the angles marked with letters
Answer:
I think m is 70 and n is 40 because I did a bunch of adding and subtracting
Circle O has secant lines AB and BD intersects circle O at points C and D. if AD=40 degrees and BC=120 degrees, find
Answer:
Angle AED: 40
Angle BEC: 105
Explanation:
1) To find Angle AED, you have to do arc BC minus arc AD then divide by 2.
120 - 40 = 80.
80 / 2 = 40
2) To find Angle BEC, you have to do arc BA + CD then divide by 2. But that's only angle CED. You'll have to double the number because BEA is vertical; then minus 360.
62 + 88 = 150
150 / 2 = 75
75 times 2 = 150
360 - 150 = 210
210 / 2 = 105
- You'll divide 210 by 2 because of the vertical angles of AED and BEC.
Satoranaing
19100
Points C, D, and G lie on plane X. Points E and F lie on
plane Y.
X
B
A
Y
Intro
E
D
G
F
Which statements are true? Select three options.
There are exactly two planes that contain points A,
B, and F.
There is exactly one plane that contains points E, F,
and B.
The line that can be drawn through points C and G
would lie in plane X.
The line that can be drawn through points E and F
would lie in plane Y.
The only points that can lie on plane Y are points E
and F.
Done
The statements that are true about the given points on the line are; Options B, C and D
How to identify points on a Plane?
A plane is defined by a line and a point outside of it. Meanwhile, a line is defined by two points. Thus, whenever we have 3 non-collinear points, we can define a plane.
Let us check each of the given options;
A) There are exactly two planes that contain points A, B, and F;
If these points are collinear, they can't make a plane and If they are not collinear, they define a plane.
Since we can't make two planes with them, then the statement is false.
B) There is exactly one plane that contains points E, F, and B;
Due to the same reasoning in part A, the statement is true assuming the points are not collinear.
C) The line that can be drawn through points C and G would lie in plane X;
The statement is true because both points C and G lie on plane X, and as such the line that connects them also should lie on the same plane.
D) The line that can be drawn through points E and F would lie in plane Y; Similar to above, this statement is true.
E) The only points that can lie on plane Y are points E and F.
This statement is false because infinite points can lie on a plane.
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Find the measure of angle VOQ
Answer:
124
.........................
If LN = 12x + 16, what is the length of Line segment L N in units?
Answer:
LN = 64 units
Step-by-step explanation:
Given M lies on LN, so LN = LM + MN --------------(1)
LN = 12x + 16
LM = 10x + 8
MN = 5x - 4
Substituting the values in equation 1, we get:
12x + 16 = (10x + 8) + (5x - 4)
12x + 16 = 15x + 4
15x - 12x = 16 -4
3x=12
Therefore x=4
LN= 12(4) + 16 = 64 units
The Broad Street subway line express train stops at city hall every 9 minutes. The local train stops at the station every 12 minutes. If you arrived at the station just as both trains left, how long will you have to wait until they both arrive at the same time again?
Answer:
36 Minutes
Step-by-step explanation:
You have to find the lowest common multiple which you can do by listing the times tables for each number.
9,18,27,36,45,54
12,24,36,48,60,72
and finding the lowest multiple that matches.
Both the train will meet after 36 minutes.
Concept:To find when both the train will meet again at the same time, we need to find the LCM of the frequency.How to solve the given question?Frequency of express train = 9 minutes = 3 × 3Frequency of local train = 12 minutes = 2 × 2 × 3LCM = 2 × 2 × 3 × 3 = 36Thus, both the train will meet after 36 minutes.
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Sanjay has ordered 30 slices of pizza for 7 people, including himself. If everyone gets an equal share, how many slices will each person get and what is the remainder? Choose the answer in the form (quotient)r (remainder).
please help i'm retaking a test because i don't have my head in the game! :C
Answer:
Each person get 4 slice of pizza and 2 is remaining
a data set has a mean of 5.3 and a mean absolute deviation of 2. which data points fall within the mean absolute deviation?
select all the correct answers.
2.9
3.1
4.5
6.8
07.3
The data points that fall within the mean absolute deviation are 2.9 and 3.1.
What is the mean absolute deviation?The mean absolute deviation is the mean average distance between every data point and the mean of the data set.
From the information given:
Mean of the data set = 5.3Mean absolute deviation = 2The mean absolute deviation is:
= (|5.3 - 2|)/1
= 3.3
Thus, the data points that fall within the mean absolute deviation are 2.9 and 3.1.
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will give 25 points for a short answer
No, to be parallel the two given angles would need to be the same(corresponding angles)
The two lines are not parallel.
MODELING WITH MATHEMATICS Three tennis balls are stored in a cylindrical container with a height of 8 inches and a radius of 1.43 inches. The circumference of a tennis ball is 8 inches. Round your answers to the nearest hundredth.
I just need help with part b
A picture shows three tennis balls placed one above another in a cylindrical container.
a. Find the volume of a tennis ball. Round your answer to the nearest hundredth.
The volume of a tennis ball is about
cubic inches.
Answer is about 8.65
b. Find the amount of space within the cylinder not taken up by the tennis balls. Round your answer to the nearest hundredth.
The volume of the space within the cylinder not taken up by the tennis balls is about
cubic inches.
The volume of a tennis ball is about 8.65 cubic inches
The volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches
Calculating volumeFrom the question, we are to determine the volume of a tennis ball
From the given information,
The circumference of a tennis ball is 8 inches
That is,
C = 2πr (C is circumference)
8 = 2πr
∴ r = 8/2π
r = 4/π inches
This the radius of a tennis ball
Now, for the volume of a tennis ball
Using the formula for calculating the volume of a sphere
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
Then, the volume of a tennis is
[tex]V = \frac{4}{3}\pi \times (\frac{4}{\pi})^{3}[/tex]
[tex]V = \frac{4}{3}\pi \times \frac{64}{\pi^{3}}[/tex]
[tex]V = \frac{256}{3\pi^{2}}[/tex]
V = 8.64607 cubic inches
V ≅ 8.65 cubic inches
Hence, the volume of a tennis ball is about 8.65 cubic inches
b. To find the amount of space within the cylinder not taken up by the tennis balls
First, we will calculate the volume of the cylinder
Using the formula for calculating the volume of a cylinder
V = πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
r = 1.43 inches
h = 8 inches
Putting the parameters into the formula, we get
V = π × 1.43² × 8
V = 16.3592π
V = 51.39 cubic inches
This is the volume of the cylinder
Now, for the amount of space within the cylinder not taken up by the tennis balls
Since there are three tennis balls,
The amount of space not taken up will be
51.39 cubic inches - 3(8.65 cubic inches)
51.39 cubic inches - 25.95 cubic inches
= 25.44 cubic inches
Hence, the volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches
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what is the mean median and mode of 201,201,200,199,199
Answer:
the median will be 200.
the mode will be 402 n 398.
the mean will be 400.
10 fish are swimming in the ocean, 6 of them drown, how many are left?
Answer:
10
Step-by-step explanation:
Fish can't drown.