Giving 80 points to the person who answers correctly
The function f(t) represents water going into a swimming pool with respect to the number of hours(t) water is flowing in where(t) represents time. f(t)=t squared +8t+9 There is a leak in the pool and it’s losing water at a rate represented by d(t). d(t)=t squared +11t+4
a.Write a function w(t) to represent the amount of water in the pool using the two functions.
b. Use the new function to determine if the pool will leak all of the water
c. If the pool will drain of all water, how much time will it take?
d.Will f(t) and d(t) intersect on a graph? Explain what it means if they do.
e. What is the domain of f(t), d(t), and w(t)? Explain your answer.
Answers
Using operations with functions, we have that:
a) w(t) = -3t + 5.
b) The pool will leak all the water in 1.67 hours.
c) 1.67 hours.
d) Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.
e) The domain of the function is 0 ≤ t ≤ 1.67.
What is the amount of water in the pool?The amount of water in the pool is determined by the subtraction of the amount flowing into the pool by the amount being drained out the pool.
For this problem, these following functions are given:
Flowing: f(t) = t² + 8t + 9.Draining: d(t) = t² + 11t + 4.Hence the amount of water in the pool is given by:
w(t) = f(t) - d(t)
w(t) = t² + 8t + 9 - t² - 11t - 4
w(t) = -3t + 5.
Hence:
The function is: w(t) = -3t + 5.
The pool will have leaked all the water when:
w(t) = 0.
Hence:
-3t + 5 = 0.
3t = 5
t = 1.67.
The pool will leak all the water in 1.67 hours.
Equaling f(t) and d(t), we have that:
t² + 8t + 9 = t² + 11t + 4.
3t = 5.
t = 1.67.
Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked.
The domain of a function is the set that contains all input values of the function. For this problem, the input is the time, hence:
Time cannot be negative, hence t ≥ 0.When all the water has been drained, everything stops, hence t ≤ 1.67.Hence:
The domain of the function is 0 ≤ t ≤ 1.67.
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Related Questions
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 3 to 2.If there were 1773 yes votes, what was the total number of votes?
Answers
Answer:
2955
Step-by-step explanation:
The ratio of yes votes to no votes is 3:2.
The total ratio is:
3 + 2 = 5
Let the total number of votes be x.
The number of yes votes was 1773. This means that:
3/5 * x = 1773
3x = 1773 * 5
x = (1773 * 5) / 3
x = 2955 votes.
There were 2955 votes in total.
Write an expression for the function g(t) whose graph is the graph of -100(1.05) shifted to the right 5, and up 50 units. Pick a number below.
1. 0-100(1.05+5)' + 50
2. 0-100(1.05) +50
3. 0-100(1.05)
4. -100(105) + 50
Answers
The correct expression is option 1: 0-100(1.05+5)' + 50.
What is expression?Expression in math is a combination of numbers, symbols and operations used to represent a value or a mathematical relationship. Examples of expressions include algebraic expressions, polynomials, matrices, and trigonometric functions. They are often used to solve equations or solve for a certain value. Expressions are used to express relationships between variables, and can be used to describe real-world problems or situations.
This expression translates to the following: take the result of -100 multiplied by 1.05, then add 5 to it, then take the result and multiply it again by -100. Finally, add 50 to the result.
This expression is used to describe the graph of -100(1.05) shifted to the right 5, and up 50 units. This is because when the graph is shifted to the right 5, it is essentially adding 5 to the result of -100 multiplied by 1.05. When the graph is shifted up 50 units, it is adding 50 to the result. Therefore, the expression 0-100(1.05+5)' + 50 accurately expresses the function g(t) whose graph is the graph of -100(1.05) shifted to the right 5, and up 50 units.
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a. If p is an even number, then p + 12 is even.
Answers
Answer:
True???
Step-by-step explanation:
Is this a true or false question?
P+12=even number
Examples...
12+12=24
16+12=28
66+12=78
Answer:
YES
Step-by-step explanation:
even + even = even
always and forever
an optimal solution to a linear programming problem must lie part 2 a. somewhere in the interior of the feasible region. b. at the intersection of at least two constraints. c. somewhere outside of the feasible region. d. somewere on the line between two corner points.
Answers
The correct option is b which tells that an optimal solution to a linear programming problem must lie at the intersection of at least two constraints.
Linear programming is an optimization technique that is fine for the purpose of getting the best solution such as maximizing profit or certain 4th-era quantities.
When there are just two choice variables, the graphic method of solving a linear programming issue can be employed.
It is fine by modelling real-life problems into mathematical models that have linear relationships or constraints such as in the form of objective functions.
In linear programming, an objective function defines the formula for quantity optimization and the goal from this is to determine variable values that maximize or minimize the objective function depending on the problem robbery solved.
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Sarah is sitting blindfolded before a plate holding 3 apples and 1 pear. What is the probability that Sarah will select the pear? Write your answer as a fraction.
Answers
Answer:
3/1
Step-by-step explanation:
3/1 the ratio is 3:1
PLEASE HELP
given the value f(x)= 4x-7 , find f(-2)
Answers
if you can answer all questions that would amazing but if not it’s okkk, if you do can you number the question so i know where each answer go
Answers
The solution to all parts is given below.
1. The midpoint between (10, 2) and (2, -4) is
x= (10+2)/2 = 12/2 = 6
and, y= (2-4)/2 = (-2)/2= -1
2. The distance between the point (2, -6) and (7,3) is
= √(7-2)² + (3+6)²
= √5² + 9²
= √25 + 81
= √106 unit
3. The equation of circle with radius 9 and Center (-3, 5)
(x-h)² + (y-k)² = r²
So, (x+3)² + (y-5)² = 9²
4. M(2, 1) is the midpoint of segment AB
B is located at (6, 3)
Using the midpoint formula:
(2 + x₂)/2 = 6 => 2 + x₂ = 12 => x₂ = 10
(1 + y₂)/2 = 3 => 1 + y₂ = 6 => y₂ = 5
Therefore, point A is located at (10, 5).
5. (x - 3)² + (y + 1)² = 49
Substituting the values of (0, 5):
(0 - 3)² + (5 + 1)² = 49
(-3)² + 6² = 49
9 + 36 = 49
45 = 49
Since 45 is not equal to 49, the point (0, 5) does not lie on the circle.
Therefore, the point (0, 5) lies outside the circle.
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What value of x makes the equation true?
3 (4x – 5) + = 10
Answers
Answer:
do you mean :3(4x-5)=10
if so then your answer is 2.08
Step-by-step explanation:
12x = 25
x = 2.08
hope this helps and please mark brainliest!
Solve by completing a square x(2)-8×+15=0
Answers
Answer:
2x -8x+15=0
-6x+15=0
-6x= 15
x= 5/2
Step-by-step explanation:
Answer:
x=2.5
Step-by-step explanation:
x(2)-8×+15=0 combine like terms
-6x+15=0 subtract 15 from both sides
-6×=-15 divide by -6 on both sides
x=2.5
a filing cabinet measures 5 feet high 18 inches wide and 2 feet deep. what is the volume of the filing cabinet
Answers
Answer:
Volume of the filling cabinet = 15ft^3
Step-by-step explanation:
volume = d * b * h
and the filling cabinet is
height = 5ft
width = 18 inch
depth = 2ft
we will first convert the width from inches to feet
where 1 ft -------- 12 inches
(x) ft ---------18 inches
therefore by cross multiplying
12 * (X) = 18 * 1
12 (X) = 18
X = 18 / 12
X = 1.5 ft
so Volume = 2 * 1.5 * 5 = 15 cubic feet or 15ft^3
During the rebuilding after World War II, we were short of tractors. The machine and tractor stations would lend each other equipment as needed. Three machine and tractor stations were neighbors. The first lent the second and third as many tractors as they each already had. A few months later, the second lent the first and third as many as they each had. Still later, the third lent the first and second as many as they each already had. Each station now had 24 tractors.
How many tractors did each station originally have?
Answers
The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;
The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors
What are simultaneous equations?Simultaneous equations are a set of two or more equations that have common variables.
Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station
According to the details in the question, after the first transaction, we get
Number of tractors at the first station = x - y - z
Number of tractors at the second station = y + y = 2·y
Number of tractors at the third station = z + z = 2·z
After the second transaction, we get;
Number of tractors at the first station = 2·x - 2·y - 2·z
Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z
Number of tractors at the third station = 2·z + 2·z = 4·z
After the third transaction, we get;
Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z
Number of tractors at the second tractor station = 6·y - 2·x - 2·z
Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y
The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)
6·y - 2·x - 2·z = 24...(2)
7·z - x - y = 24...(3)
Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;
12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24
16·y - 8·x = 24...(4)
Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;
14·z - 2·x - 2·y = 48
42·y - 14·x - 14·z = 168
42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168
40·y - 16·x = 216...(5)
Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;
40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168
8·y = 168
y = 168/8 = 21
The number of tractors initially at the second station, y = 21
16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24
8·x = 16 × 21 - 24 = 312
x = 312 ÷ 8 = 39
The number of tractors initially at the first station, x = 39
7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24
7·z = 24 + 39 + 21 = 84
z = 84/7 = 12
The number of tractors initially at the third station, z = 12
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Find the median, mean, and range.
14, 1, 16, 6, 15, 2
Answers
Answer:
Median: 10
Mean: 9
Range: 15
Step-by-step explanation:
Have a good day :)
Evaluate:
-1 + 8(-9) -|-3-7
Answers
Answer:
-63
Step-by-step explanation:
A family of four goes out to dinner. The total price for their food and drink purchases is $54.88. The sales tax is 5%. How will the waitress determine the amount of tax to add to the bill?
Answers
Answer:
Multiple the total by .10 or 10% (move the decimal place one to the left). Doing that gives 10% of the total or $5.48. To get 5%, divide that number in half for $2.74.
Step-by-step explanation:
This is the same for determining a tip of 20%. Move the decimal one to the left and double that number. For 15%, move the decimal place one to the left. There's 10%, half that, and add the two numbers together for 15%.
10 times a number, x, is 1/2 the sum of the number and three which answer represents this situation
10x+1/2x+3
10x=1/2(x+3)
10x=1/2x+3
10x+1/2(x+3)
Answers
Answer:
10x=1/2(x+3)
Step-by-step explanation:
option b is the answer
4. A pizza shop has 12" pizzas with 6 slices and 16" pizzas with slices. Which pizza has bigger slices?
Answers
PLEASE HELP!! Which variable is most important to the following problem?
The Top Shoppe orders 85 shirts for each of its 22 stores from a clothing
manufacturer. The manufacturer has 3000 shirts in stock. The Top Shoppe pays $20 for each shirt. How much does the Top Shoppe pay for the shirts?
A. The total cost of the shirts
B. The number of shirts the manufacturer has left after the order
C. The sizes of the shirts ordered
D. The number of shirts the Top Shoppe orders
Answers
Answer:
ok so we know that it order 85 shirts for each of its 22 stores so we can multiply 22 by 85 which is 1870. so the company order 1870 shirts and they pay 20$ for each so we can multiply 1870 by 20 which is 37400. so top shoppe pays 37400 for the shirts.
A=37400
B=I don't know what the order was so i dont know
C= also there is nothing about the size of the shirts
D=1870
so the most important variable is probity A but there could be an argument made about the importance of D.
Your Welcome
BIFFY OUT!!!
What is 71% of $1120? *
Answers
Answer:
$795.20
Step-by-step explanation:
0.71 × $1,120 = $795.20
Hope this helps! :)
Answer:
$ 795,20
Step-by-step explanation:
71%×$1120 =
= 71×$1120/100
= $79520/100
= $ 795,20
Help me with this problems
Answers
Answer:
its easy
Step-by-step explanation:
you should change all into degrees
The image of the A(2, -3) after a transformation by the mapping (x,y) to ( 2x, y+2) is the point: *
3 points
A) (4, 1)
B) (4,-1)
C (4, 5)
(D (4,5)
Answers
Answer:
Step-by-step explanation:
B
rewrite (3x + 2)(x - 3) in standard form
Answers
Answer: 3x^2 − 7x − 6
Evaluate (3.1 x 10^4)
Answers
Answer:
31,000
Step-by-step explanation:
3.1 x 10,000
When calculating a loan’s effective interest rate, if the nominal rate is 8.5%, what value of i do you plug into your equation? a. 8.5 b. 0.85 c. 0.085 d. 1.85 please select the best answer from the choices provided a b c d
Answers
The nominal interest rate to plug in will be 0.085.
What is interest rate?
An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.Given to us, the nominal rate is 8.5%,
The value to plug into your equation,
The equation can be simple interest or compound interest in both cases the value of the nominal rate to the plugin will be the same.
Thus, the nominal rate is 8.5% can be written as
Nominal rate = 8.5%
= 85/100 = 0.085
Hence, the nominal rate to plug in will be 0.085.
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the humane society reports that of 428 animals at their local animal shelter, 376 are household pets and the remaining 52 are wildlife animals. over the weekend, 29 of the household pets were adopted and 10 of the wildlife animals were released back into the wild. is there sufficient evidence to indicate a difference in the number of animals leaving the shelter over the weekend for the two types (household pets and wildlife animals)? use the p-value approach at the 1% level of significance.
Answers
There is sufficient evidence to believe that the number of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.
How to prove it there's sufficient evidenceTo determine if there's sufficient evidence,
Let us define the null and alternative hypotheses for this test as follows:
Null hypothesis (H0): The proportion of household pets leaving the shelter over the weekend is the same as the proportion of wildlife animals leaving the shelter over the weekend.
Alternative hypothesis (Ha): The proportion of household pets leaving the shelter over the weekend is different from the proportion of wildlife animals leaving the shelter over the weekend.
The test statistic for two sample test is given by:
z = (p1 - p2) / sqrt(p * (1 - p) * (1/n1 + 1/n2))
where
p1 and p2 are the proportions of household pets and wildlife animals leaving the shelter over the weekend, respectively,
p is the pooled proportion,
n1 and n2 are the sample sizes for household pets and wildlife animals, respectively.
Pooled proportion is
p = (x1 + x2) / (n1 + n2)
where x1 and x2 are the number of household pets and wildlife animals leaving the shelter over the weekend, respectively.
Given
-n1 = 376, n2 = 52, x1 = 29, x2 = 10
p = (29 + 10) / (376 + 52) = 0.091
The observed proportions are:
p1 = x1 / n1 = 29 / 376 = 0.0771
p2 = x2 / n2 = 10 / 52 = 0.1923
The test statistic value
z = (0.0771 - 0.1923) / sqrt(0.091 * (1 - 0.091) * (1/376 + 1/52)) = -3.04
By using a standard normal distribution table,
The p-value is 0.00238.
Since the p-value (0.00238) is less than the level of significance (0.01), we reject the null hypothesis and conclude that there is sufficient evidence to indicate a difference in the number of animals leaving the shelter over the weekend for household pets and wildlife animals.
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.. The solution of which quadratic Inequality is shown on the number line?
O (3+6) (3 – 4) <0
O (2-6) (2 - 4) > 0
O (30 – 6)(+4) <0.
O (30 – 6) (x – 4) <0
Answers
Explanation:
If you graphed (x-6)(x+4) on the xy plane, then you'll see a parabola forming. This parabola has roots at x = -4 and x = 6. Between these roots, the curve is below the x axis. This visually shows that (x-6)(x+4) is negative when -4 < x < 6.
Furthermore, we can say that (x-6)(x+4) is negative or zero when \(-4 \le x \le 6\) which corresponds directly to the number line graph your teacher gave you. The endpoints being closed circles mean "include this as part of the shaded solution set".
Amy scores 7760 points on a new game, to the nearest 10.
Bill scores 7700 points to the nearest 100.
Who did better?
Amy
Bill
Can't tell
Answers
Answer:Bill
Step-by-step explanation:
Because Bill scored to the nearest 100
Explanation: Bill’s score has to be 7749-7700 for it to be rounded by the nearest hundred and get 7700. While Amy’s would have to be anywhere from 7755-7760 for it to be rounded by the nearest ten and get 7760.
The average of 16 numbers is 70. If the average of 15 of these numbers is 17, then the 16th number is?
Answers
Answer:
865
Step-by-step explanation:
16*70=1120
15*17=255
1120-255=865
im confused on how to do this
Answers
Answer:
150
Step-by-step explanation:
Surface area is the area of all the surfaces (or sides). To find the surface area, find the area of one side of the cube. Since a side of a cube is a square, all the lengths are the same. So, 5*5= 25. There are 6 sides to a cube, so multiply 6 by one of the faces 's area (aka sides), so 6*25=150.
2. Finance Planners recommend no more than 30% of your income should be your rent.
1. How much should Hagatha spend on rent if she brings home $2,000 per month?
2. If the average rent for a one-bedroom in Portland is $1,743, how much does Hagatha need to earn per month to have her rent total 30% of his income?
Answers
She needs to make $5810 a month to have her 1743$ rent be 30% of her income because 30/100 = 1743/x
x= 5810
Find the value of x.
Answers
Answer:
x = 35°
Step-by-step explanation:
These two angles are alternate angles so they both are equal.
5x - 54 = 3x + 16
5x - 3x = 16 + 54
2x = 70
x = 70 ÷ 2
x = 35°