DIRECTIONS: Use this information to answer Parts A and B.
A faucet supplies water at a constant rate. After 3 minutes, the faucet supplies 12 liters of water.
Part A
Use the Line Tool to graph the proportional relationship that gives the number of liters of water the facet supplies, y, after x minutes.
The graph of the proportional relationship is added as an attachment
How to determine the graph of the scenarioFrom the question, we have the following parameters that can be used in our computation:
Time = 3 minutes
Supply of water = 12 litres
Using the above parameters, we have the following ordered pairs
(0, 0) and (3, 12)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (0, 0) and (3, 12)
The gradient of the line is then calculated using the following slope equation
gradient = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 0) and (3, 12)
Substitute the known values in the above equation
So, we have the following equation
gradient = (12 - 0)/(4 - 0)
Evaluate
gradient = 3
The equation of the line is then calculated as
y = gradient * x
Substitute the known values in the above equation
So, we have the following equation
y = 3 * x
Evaluate the products
y= 3x
Hence, the line equation is y= 3x
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find the missing number so that the equation has infinitely many solutions. 2x + _ = 2x - 4
Answer:
The missing number is -4.---------------------------------
For the equation to have infinitely many solutions, the variables and constants should cancel and should end up with 0 = 0. It means for any value of the variable the equation is true, i.e. both sides are equal.
Given equation:
2x + ? = 2x - 4If we solve it for ? we'll get:
? = - 4Let R be the relation defined on P({1,……,100}) by A R B , if and only if |A n B| is even.
Is R reflexive? Is R symmetric? Is R anti-symmetric? Is R transitive?
Only the transitive relation is true for the provided relation for (x, y) R if x y defined on the set of positive integers.
Step-by-step explanation:Assuming (x, y), R
To determine whether or not a relation is transitive, symmetric, antisymmetric, reflexive, or a partial order:
If (x, x)R for all x R x x for all x R, which is false.
b. Symmetric: For all (x, y) R, if "x" and "y" are related, then "y" is also related to "x."
In this case, x y y x for all (x, y) R, which is false.
c. Antisymmetric: If "x" and "y" are related, then "x" equals "y" for all (x, y) R.
In this case, x y and y x x = y are false.
not in opposition.
c. Transitive: If "x" and "y" are related, then
For all values of x, y, and z R, 'x' is connected to 'z'.
For any x, y, and z R, x y, y z x z.
True.
Therefore, only the transitive relation for the given relation for (x, y) R if x y defined on the set of positive integers is true.
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12. Carly's family is going to buy cell phones for the entire family. After some research they have narrowed their choices
down to 2 companies. AT&T charges a monthly rate of $100 plus $15 for each phone on the account. Their competitor,
Sprint, charges a flat monthly fee of $200 and they will receive an unlimited number of phones on the account.
a. Write an equation for the cost of each cell phone provider and then graph the equations.
AT&T:
Sprint:
b. Use any method to determine which company would be cheaper if Carly's family consists of Carly, mom, dad, two brothers, and one sister. Explain your reasoning
a) The linear functions each cell phone provider are given as follows:
AT&T: 100 + 15x.Sprint: 200.The graph with these functions is given by the image shown at the end of the answer.
b) The cheaper companies are given as follows:
Less than 7 phones: AT&T.7 or more phones: Sprint.How to define the linear functions?The linear functions in this problem are defined in slope-intercept format as follows:
y = mx + b.
In which the coefficients and their meaning are given as follows:
m is the slope, representing the cost per phone.b is the intercept, representing the fixed cost, before considering the costs per phone.Hence the cost functions for this problem are given as follows:
AT&T: 100 + 15x.Sprint: 200.The functions intersect at x = 6.67, hence the cheaper plans are given as follows:
Less than 7 phones: AT&T. (cheaper initially due to the lower intercept).7 or more phones: Sprint. (cheaper for more phones due to the lower slope).More can be learned about linear functions at https://brainly.com/question/24808124
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Which statements about the cylinder are true? Select two options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is 1÷4π.x²
The area of the cylinder's base is 1÷2π.x²
The height of the cylinder is 2x units
The height of the cylinder is 4x units
The area of the cylinder's base is 1÷4π.x² is the correct option
What is a cylinder?
A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centres of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.
The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centres of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centres.
The cylinder seems to be a rectangle from the side perspective and a circle from the top view.
Since a cylinder has a curved form and no straight lines, it lacks vertices in contrast to cones, cubes, and cuboid shapes. Two of its faces are round.
According to the question volume of the cylinder is
1. πr^2h = πr^3
h=r=x/2
2.
The radius of cylinder is
= x/2
3.
The area of the cylinder's base is
= πr^2
= (π x^2)/4
4.
The height of the cylinder is =
radius= height =x/2
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Which of the following is a true proportion of the figure based on the triangle proportionality theorem?
A) i/j=h/k
B) j/k=j/i
C) h/i=h/k
D) k/i=j/i
A true proportion of the figure based on the triangle proportionality theorem is: A) i/j = h/k.
What is a triangle?In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is the triangle proportionality theorem?The triangle proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
Since side TU is parallel to side QR, side TU will divide both sides QS and RS proportionally in accordance with the triangle proportionality theorem as follows;
RU/QT = SU/ST ≡ i/j = h/k
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Which of the following statements is true regarding that equation |x+3|-2=k?
There are no solutions when k=-1 or when k=-3.
If k=-1 there are solutions, but if k=-3 there are no solutions.
If k=-3 there are solutions, but if k=-1 there are no solutions.
There are solutions when k=-1 and when k=-3.
There are solutions when k = -1 and when k = -3
What is Linear Equation in One Variable?
A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.
Solution:
|x + 3| - 2 = k
Removing the modulus sign
x + 3 - 2 = k -----(i) = x + 1 = k
-x - 3 - 2 = k -----(ii) -x - 5 = k
Putting k = -1
(i) x = -2 and (ii) x = -4
Putting k = -3
(i) x = -4 and (ii) x = -2
Since, x has solution on both the values of k
We can say that,
There are solutions when k = -1 and when k = -3
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Design An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 12 more than three times the length of the
bottom of the triangle. The last side is 4 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
Answer:
[tex]P_t=5x+16[/tex]
Step-by-step explanation:
The perimeter of the triangle will be the sum of all the sides,
[tex]P_t=a+b+c[/tex]
For this problem, let a=x, b=3x+12, and c=4+x. So,
[tex]P_t=(x)+(3x+12)+(4+x)\\P_t=x+3x+12+4+x\\P_t=x+3x+x+12+4\\P_t=5x+16[/tex]
An artist is building a pedestal out of wood that will be used to display a piece of sculpture. She plans to cover the pedestal with tile. How much tile will it take to cover the pedestal, including the bottom?
224 square feet
192 square feet
144 square feet
288 square feet
tile will it take to cover the pedestal, including the bottom is 288 square feet
How much tile will it take to cover the pedestal, including the bottom?It depends on how big the pedestal is and how big the tiles are that are being used. It would require 192 square feet of tile to cover the pedestal, including the bottom, if the tiles were one foot square and the pedestal was four feet tall.To cover the pedestal, however, would require 224 square feet of tile if it were five feet tall and the chosen tiles were two feet square.Similar to this, 144 square feet of tile would be required to cover a pedestal that is three feet tall and two feet square. The pedestal would require 288 square feet of tile to cover it, including the bottom, assuming the tiles were one foot square and the pedestal was five feet tall.As you can see, the size of the pedestal and the tiles being used both affect how many tiles are needed to completely cover the pedestal.To learn more about a tiling project refer to:
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solve the following expression when t=6 and d=8. t+d divided by 8-6. help
Match each equation on the left with its solution on the right. No answer on the right will be used twice.
The correct match the following is shown below:
2x + 3 (x - 2) = 6 (x + 1) + x → x = -6
2x + 3 (x - 2) = 6 (x - 1) - x → All real numbers
2x + 3 (x - 2) = 6 (x - 1) + x → x = 0
2x + 3 (x - 1) = 6 (x - 1) - x → No solution.
What is 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.
Given:
The equation is, 2x + 3 (x - 2) = 6 (x + 1) + x, 2x + 3 (x - 2) = 6 (x - 1) - x, 2x + 3 (x - 2) = 6 (x - 1) + x, and 2x + 3 (x - 1) = 6 (x - 1) - x
Solve the above equations as shown below,
2x + 3 (x - 2) = 6 (x + 1) + x
2x + 3x - 6 = 6x + 6 + x
5x - 6 = 7x + 6
7x - 5x = -6 - 6
x = -6
2x + 3 (x - 2) = 6 (x - 1) - x
2x + 3x - 6 = 6x - 6 - x
5x - 6 = 5x - 6
Infinity solutions,
2x + 3 (x - 2) = 6 (x - 1) + x
2x + 3x - 6 = 6x - 6 + x
5x - 6 = 7x - 6
x = 0
2x + 3 (x - 1) = 6 (x - 1) - x
2x + 3x - 3 = 6x - 6 - x
5x - 3 = 5x - 6
Parallel line, hence, no solution.
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Find (fog)(x).
f(x) = 5x
g(x) = 6x
Write your answer as a polynomial in simplest form.
(fog)(x) =
Answer: (fog)(x) = f(g(x)) = f(6x) = 5(6x) = 30x
So (fog)(x) = 30x, which is a polynomial in simplest form
find f^-1(x) for the function f(x)=x/2-4.
Answer:
f(x)=x/2-4
-f(x)=a
a=x/2-4
x=a/2-4
a/2-4=x /×2
a-8=2x
a=8+2x -> f^-1(x)=8+2x
standard form. (x+8)(x−6)
Answer:
x^2-2x-48
Step-by-step explanation:
FOIL
Firsts = x*x = x^2
outside = x*-6 = -6x
inside = 8*x = 8x
lasts = 8*-6 = -48
add all together x^2-6x+8x-48 = x^2-2x-48
Answer:
x² + 2x - 48
Step-by-step explanation:
( x + 8 ) ( x - 6 )
= x ( x - 6 ) + 8 ( x - 6 )
= x*x - 6*x + 8*x + 8*( - 6 )
= x² - 6x + 8x - 48
= x² + 2x - 48
A football club sells, on average, 23000 tickets per match. In one season they play, on average, 46 matches.How many tickets do they sell, on average, each season?
Answer:
the football team sells 805,000 tickets each season
Step-by-step explanation:
average number of tickets sold per match=23,000
the average number of games played each session=35
the number of tickets sold on average each session = 23,000 x 35 which equals 805,000
so the average football club sells 805,000 tickets each season
What is the end behavior of f(x)=−x^4−2x^3+2x^2−5?
Using the Leading Coefficient Test the end behavior of the given function f(x) = −x⁴ − 2x³ + 2x² − 5 is
x tends to -∞, f(x) tends to -∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of functionThe given function is:
f(x) = −x⁴ − 2x³ + 2x² − 5
The end behavior is determined by the leading Coefficient = −x⁴ and it is described as
x ⇒ ∞ f(x) ⇒ ∞
x ⇒ -∞ f(x) ⇒ -∞
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The graph represents the journey of a bus from the bus stop to different locations:
The title for the graph is Bus Journey. The label on the y-axis is Distance in miles, and the label on the x-axis is Time in hours. The graph shows 5 parts. The part labeled 1 is a smooth curve going up from the origin. The part labeled 2 is a straight horizontal line. The part labeled 3 is a smooth curve going up. The part labeled 4 is a straight horizontal line. The part labeled 5 is a smooth curve going down that touches the x-axis.
Part A: Use complete sentences to describe the motion of the bus in parts 1, 2, 3, 4, and 5 of the journey. (4 points)
Part B: In which parts of the graph is the function increasing, decreasing, and constant? (4 points)
Part C: Is the graph linear or non-linear? Explain your answer. (2 points)
Answer:
Part A is 100
Part B is 50
Part C is 25
all of it goes down by 15 so just keep subtracting
Step-by-step explanation:
I used common since and a sheet of paper
At the halfway point of a telethon, a charity has only raised one quarter of its
target amount. If its total amount raised doubles each of the next two hours,
what percentage of its target amount will it have raised?
75%
80%
87.5%
93%
100%
Answer:75%
Step-by-step explanation:
Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $900
Total amount = $1800
Compounded monthly,
so formula becomes,
Total amount = amount (1+r/1200)^12t
T = A[tex](1+r/1200)^{12t}[/tex]
1800 = 900 (1+6/1200)^12t
2 = (1+1/200)^12t
2 = 1.005^12t
taking log on both sides
log 2 = 12t *log 1.005
0.3/0.002 = 12t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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One side of a rectangle is 8 cm and the perimeter is 48 cm. Find the area.
Answer: 128 square centimeters
Step-by-step explanation:
If the perimeter is 48 cm, then the sum of the lengths of any two adjacent sides must be 24 cm.
Since the length of one of these sides is given to be 8 cm, it follows the length of the corresponding adjacent side is 16 cm.
Thus, using the formula for the area of a rectangle, the area is 128 square centimeters.
There are two shapes on the coordinate plane shown. Which statement about the shapes is true? A. Shape A can be matched to shape B by reflecting it about the x-axis, then about the y-axis, and then shifting 1 on the x-axis and –3 on the y-axis. B. Shape A can be matched to shape B by reflecting about the origin and then shifting –3 on the x-axis and 1 on the y-axis. C. Shape A can be matched to shape B by reflecting it about the y-axis, then about the x-axis, and then dilating it from the origin by a factor of 2. D. Shape A can be matched to shape B by reflecting it about the y-axis, then about the x-axis, and then dilating it from the origin by a factor of .
Answer:
B. Shape A can be matched to shape B by reflecting about the origin and then shifting –3 on the x-axis and 1 on the y-axis.
Step-by-step explanation:
A decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller. What is the average class size currently?
The average class size of Newton middle school is 21.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller.
The average class size will be calculated as,
Average class size = 30 x (70%)
Average class size = 30 x 0.7
Average class size = 21
Therefore, the average class size at Newton middle school is 21.
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How many nine-letter words can be formed from the letters of hyperbola, using each letter once per
word? The words do not have to actually spell anything, of course.
The letters of "hyperbola" can be combined into 40,320 different nine-letter words by using each letter just once.
What are the Combinations?Combinations are the procedures used in mathematics to pick k things from n different items without replacement.
The following formula computes the combinations of k items from n:
(n, k) = n! / k!×(n-k)!
There are 8 letters in the word "hyperbola",
So, there are 8 choices for the first letter, 7 choices for the second letter, and so on, down to 1 choice for the last letter.
This means that there are :
⇒ 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
Therefore, 40,320 possible nine-letter words can be formed from the letters of "hyperbola" using each letter once per word.
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How many solutions does this system of equations have? 2x+y=1 4x+2y=2 O Exactly two None O Exactly one Infinitely many
Answer:
Infinitely many
Step-by-step explanation:
2x+y=1
4x+2y=2
Divide both sides of the second equation by 2.
2x + y = 1
This is the same as the first equations. Both equations are the same equation. Since you have only one equation and two variables, there is an infinite number of solutions.
Answer: Infinitely many
At noon, ship A is 130 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?
√5 km/h fast is the distance between the ships changing at 4:00 PM .
What is the Pythagorean theorem ?
The Pythagorean theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.
This is represented by the equation a2 + b2 = c2 in common algebraic notation.
Ship A is sailing 25 km/h east and Ship B is sailing 15 km north. They are giving us the time frame, which is 4 hours ( t = 4). Recall that Distance = Rate * time. Let us find the distance for each ship after 4 hours
Ship A Ship B
d=25*4 = 100 km d=15*4= 60 km
the Pythagorean theorem.
a2+b2=c2
(30)2+(60)2=c2
c=30√(5)
From the question, "How fast" is asking us for a rate. The rate on the hypotenuse side. We have to take the derivative of the pythagorean theorem with respect to time.
2a(da/dt) + 2b(db/dt) = 2c(dc/dt)
Solve for dc/dt
dc/dt = [a(da/dt) + b(db/dt)] / c
dc/dt = [30(-25) + 60(15)] / 30√5 ****Note: we have -25 as time increases, the distance is smaller
dc/dt = √5 km/h
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A vehicle uses 1 gallons of gasoline to travel 13 miles. At this rate, how many miles can the vehicle travel per gallon of gasoline?
You may find the answer to this question in the statement of the problem, if the vehicles uses 1 gallon to travel 13 times, then it is traveling at a rate of 13 miles per gallon.
I don’t remember how to do this. Help
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. H0: P=0.93 versus H1:p≠0.93 n=500, x=450, a=0.05 Is np0(1-P0) ≥10? Select the correct choice below and fill in the answer box to complete your choice. A. No because np0(1-P0) equals__ B. Yes, because np0(1-P0) equals__
Using the Central Limit Theorem, it is found that these conditions are required to avoid the high variability associated with small samples.
What does the Central Limit Theorem states?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean and standard deviation , as long as[tex]np\geq 10[/tex] and [tex]n(1-p)\geq 10[/tex]From the equation of the standard error, we could see that if one of the conditions is not respected, the standard error would be very high, indicating a low accuracy of the estimate, hence it is found that these conditions are required to avoid the high variability associated with small samples.[tex]s=\sqrt{p(1-p)/n}[/tex]
If we compare the p value and using the significance level given [tex]\alpha=0.05[/tex] we have[tex]pv > \alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.[tex]p v=2*p(z < -0.531)=0.595[/tex]
1) Data given and notation
n=500 represent the random sample taken
X=380 represent the number of people with some characteristic
estimated proportion of adults that said that it is morally wrong to not report all income on tax returns
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is 0.7 .:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1) The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value Check for the assumptions that he sample must satisfy in order to apply the test
a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.
b) The sample needs to be large enough
3) Calculate the statistic
[tex]z=\frac{0.76 - 0.77}{\sqrt{\frac{0.77(1-77)}{500} } =0.531}[/tex]
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha =0.05[/tex]The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]pv=2*p(z < -0.0531)=0.595[/tex]
If we compare the p value and using the significance level given we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion is not significantly different from 0.77.
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A certain quadratic function has x-intercepts at 2 and 3. What are the x-coordinates of its vertex?
a) 5/2 because by symmetry, both x-intercepts should be the same vertical distance from the vertex point which is at x = 5/2 or 2.5.
b) 7/2 because by symmetry, both x-intercepts should be the same vertical distance from the vertex point which is at x = 7/2 or 3.5.
c) 5/2 because by symmetry, both x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5.
d) 7/2 because by symmetry, both x-intercepts should be the same horizontal distance from the axis of symmetry at x = 7/2 or 3.5.
Because both of its x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5 according to symmetry, the vertex's x-coordinates are 5/2.
What is coordinates?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
Here,
The parabola is symmetric around its vertex. This means that the roots are the same horizontal distance away from the vertex. Furthermore, we can apply the midpoint formula on the given roots to find the x coordinate of the vertex.
Find the midpoint of 2 and 3 to get
(2+3)/2 = 5/2
The x-coordinates of its vertex is 5/2 because by symmetry, both x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5.
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In triangle ABC, m∠B = (13x − 16)° and the measure of the exterior angle to ∠B is (8x − 14)°. Find m∠B.
10°
66°
49°
114°
The measure of angle B is (d) 114 degrees
How to determine the measure of angle B?From the question, we have the following parameters that can be used in our computation:
B = 13x - 16
Exterior of B = 8x - 14
As a general rule, the sum of an angle and its exterior is 180 degrees
This means that
13x - 16 + 8x - 14 = 180
Evaluate the like terms
So, we have
21x = 210
Divide both sides
x = 10
Recall that
B = 13x - 16
So, we have
B = 13 x 10 - 16
Evaluate
B = 114
Hence, the measure is 114 degrees
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Answer:
The measure of angle B is (d) 114 degrees
Step-by-step explanation: