Answer:
7 hours.
Step-by-step explanation:
This is a rate problem. We can start by using the formula: Rate x Time = Quantity.
The rate at which the cistern is filled is the quantity of water in the cistern divided by the time it takes to fill it. So, the rate at which the cistern is filled is 1 (the cistern is full) / 6 hours = 1/6 cistern/hour.
Similarly, the rate at which the cistern is emptied by the leak is 1 (the cistern is full) / the time it takes to empty it. So, the rate at which the cistern is emptied by the leak is 1 (the cistern is full) / 7 hours = 1/7 cistern/hour.
Since we know the rate at which the cistern is filled and the rate at which it is emptied, we can find the time it takes for the cistern to be emptied by dividing 1 (the cistern is full) by the rate at which it is emptied.
Therefore, the cistern will be emptied in 1 / (1/7 cistern/hour) = 7 hour.
use log. 16＾k ＋4＾（k＋1）＝1/4＾3
which of the following scenarios contain biased samples? select all that apply. select all that apply: to estimate the mean project completions of technicians in his company, donald collects data by recording completions from the warehouse area. kenneth wants to estimate the mean market shares of his company. he collects data by selecting a random group of coworkers within one department. to estimate the male to female ratio of the residents of her city, janice collects data by recording the sex of every 50th resident after selecting a random starting point on a list of residents. amy wants to estimate the mean accidents of coworkers at her company. she collects data by recording the accidents of every 25th coworker on the list of coworkers after a randomly selecting first coworker.
The scenarios that contain biased samples is Kenneth wants to estimate the mean market shares of his company. he collects data by selecting a random group of coworkers within one department. to estimate the male to female ratio of the residents of her city, janice collects data by recording the sex of every 50th resident after selecting a random starting point on a list of residents.
What is bias in sampling?When some members of a population are systematically more likely to be chosen in a sample than others, this is known as sampling bias. the thing that makes sampling bias significant is that Sampling bias poses a risk to external validity since it restricts the applicability of your findings to a larger population.
The market shares only reflect one department, and no other employees have an equal chance of being chosen to represent all sales in the company, hence the sample from option B is skewed.
Therefore, option B is correct.
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In ΔOPQ, p = 9.7 inches,
�
m∠Q=93° and
�
m∠O=82°. Find the length of q, to the nearest 10th of an inch.
Answer:
To find the length of q, we can use the Law of Cosines formula:
q = sqrt(p^2 + o^2 - 2 * p * o * cos(Q))
where p and o are the lengths of sides PQ and PO, and Q is the measure of the included angle between them.
Since we know that p = 9.7 inches and ∠Q = 93°, we can use the Law of Sines to find o:
sin(Q) = o/q
=> o = q * sin(Q)
=> o = 9.7 * sin(93)
Using this formula and rounding to the nearest tenth, we can find that o = 11.7 inches.
Now we can use the Law of Cosines to find q:
q = sqrt(p^2 + o^2 - 2 * p * o * cos(Q))
=> q = sqrt(9.7^2 + 11.7^2 - 2 * 9.7 * 11.7 * cos(93))
Rounding to the nearest tenth, we get that q = 17.2 inches.
Answer:
111.1
Step-by-step explanation:
problem 6. a population of bacteria, growing according to the malthusian model, doubles itself in 10 days. if there are 1000 bacteria present initially, how long will it take the population to reach 10,000?
Here the population growth is as per the Malthusian model. As per the calculations, the bacterial population will reach 10000 after 33 days.
Here the bacterial growth is as per the exponential growth curve. So the equation is,
[tex]P_{t} = P_{0} e^{rt}[/tex]
[tex]P_{t}[/tex] is the population at n
[tex]P_{0}[/tex] is the initial population
r is the time
t is the rate
Population doubles after 10 days.
So, [tex]2000 = 1000e^{r*10} \\\\\frac{2000}{1000} = e^{10r}\\\\ 2 = e^{10r\\}\\\\[/tex]
Taking logarithms on both sides
[tex]ln(2) = lne^{10r}\\\\10r = 0.693\\ \\r = 0.0693[/tex]
So the rate is 0.0693.
When population reaches 10000,
[tex]10000 =1000e^{0.0693t}[/tex]
[tex]\frac{10000}{1000} =e^{0.0693n}[/tex]
[tex]10 = e^{0.0693*t}\\ \\ln(10) = ln(e^{0.0693t}\\ \\2.3 = 0.0693t\\\\t = 2.3/0.0693\\= 33.18[/tex]
So the number of days to reach population of 10000 is 33.18≈ 33 days.
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Please help. Consider x0y0z as 100000x+100y+10z or 100000x+100y+z
Answer:
To determine if the expression 100000x+100y+10z or 100000x+100y+z is divisible by 3, 7, 13, and 37, you can use the divisibility rules for each number.
Divisibility by 3: To check if a number is divisible by 3, you can add up the digits of the number, then check if the sum is divisible by 3.
Divisibility by 7: To check if a number is divisible by 7, you can subtract twice the last digit from the remaining number, then check if the result is divisible by 7.
Divisibility by 13: To check if a number is divisible by 13, you can subtract 10 times the last digit from the remaining number, then check if the result is divisible by 13.
Divisibility by 37: To check if a number is divisible by 37, you can subtract 30 times the last digit from the remaining number, then check if the result is divisible by 37.
By applying these divisibility rules to the expression 100000x+100y+10z or 100000x+100y+z, you can determine if it is divisible by 3, 7, 13, and 37.
Solve the system of equations by using substitution
x=3y
2x+4y=10
Answer:
(3, 1 )
Step-by-step explanation:
x = 3y → (1)
2x + 4y = 10 → (2)
substitute x = 3y into (2)
2(3y) + 4y = 10
6y + 4y = 10
10y = 10 ( divide both sides by 10 )
y = 1
substitute y = 1 into (1)
x = 3y = 3(1) = 3
solution is (3, 1 )
5. The area of a rectangular plot 50m long is 1500 sqm. Find the width of the rectangular plot.
Answer:
area = length * width
1,500 = 50 m * width
width = 1,500 / 50
width = 30 meters
Step-by-step explanation:
Which of the following points lies on the graph of the function y = 2 times 3 Superscript x?
The point lies on the graph of the function will be (2, 18). Then the correct option is A.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The exponent equation is given below.
y = 2(3)ˣ
At x = 2, the value of the variable 'y' is given as,
y = 2(3)²
y = 2(9)
y = 18
The point lies on the graph of the function will be (2, 18). Then the correct option is A.
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The missing options are given below.
A. (2, 18)
B. (2, 11)
C. (2, 8)
D. (2, 12)
a pool drained at a rate of 15 gallons every 2 minutes.How many cups of water drained out of the pool each second?
Answer: The answer is 0.125 cups.
Step-by-step explanation:
First, you need to find the unit rate of the draining.
7.5 gallons = one minute
Divide 7.5 by 60 seconds
After dividing, you should get 0.125 cups of water per second.
Therefore, the pool drained at a rate of 0.125 cups every second.
Hope this helps! :)
Fifteen solid spheres are made by melting a solid metallic cone of base diameter 2cm
and height 15cm. The radius of each sphere is:
The radius of each of the sphere is 1.1 centimetres.
How to find the radius of the sphere?Fifteen solid spheres are made by melting a solid metallic cone of base diameter 2cm and height 15cm. Therefore, let's find the volume of the cone to know the radius of the sphere.
Hence,
volume of a cone = 1 / 3 πr²h
where
h = height of the coner = radiusTherefore,
volume of the cone = 1 / 3 × π × 1² × 15
volume of the cone = 5π cm³
Therefore, let's find the radius of the sphere.
volume of a sphere = 4πr³
where
r = radius5π = 4 × π × r³
r³ = 5 / 4
r = ∛5 / 4
r = 1.07721734502
Therefore,
radius of each sphere = 1.1 cm
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On Monday, the balance in your checking account is -$149. The bank charges you a $15 fee for having a negative balance. The next day you make two deposits of $117 and $59. What is your new balance?
After making the deposits, your new balance will be $12
2.6. Consider the machine described in Conceptual Problem 2.8. Suppose the ma- chine is initially up. Compute the probability that the machine is up at times n = 5, 10, 15, and 20. (Assume p = .95.) 2.8. Consider a machine that works as follows. If it is up at the beginning of a day, it stays up at the beginning of the next day with probability p and fails with probability 1 - p. It takes exactly 2 days for the repairs, at the end of which the machine is as good as new. Let Xn be the state of the machine at the beginning of day n, where the state is 0 if the machine has just failed, 1 if 1 day's worth of repair work is done on it, and 2 if it is up. Show that {Xn, n >0} is a DTMC, and display its transition probability matrix.
The probability that the machine is up at times n = 5, 10, 15, and 20 can be calculated as n = 5: 0.773797, n = 10: 0.60653065, n = 15: 0.47000363 and n = 20: 0.35831814.
For the machine described in Conceptual Problem 2.8, the probability that the machine is up at times n = 5, 10, 15, and 20 can be calculated using the formula:
P(machine is up at time n) = P(machine was up at time n-1) * p
Given that the machine is initially up and p = 0.95, the probabilities are as follows:
n = 5: P(machine is up at time 5) = 0.95 * 0.95 * 0.95 * 0.95 * 0.95 = 0.773797n = 10: P(machine is up at time 10) = [tex]0.95^{10[/tex] = 0.60653065n = 15: P(machine is up at time 15) = [tex]0.95^{15[/tex] = 0.47000363n = 20: P(machine is up at time 20) = [tex]0.95^{20[/tex] = 0.35831814As for the transition probability matrix of the DTMC {Xn, n > 0}, the possible transitions are:
Xn = 0 to Xn+1 = 1 (1 day's worth of repair work is done) with a probability of 1 Xn = 1 to Xn+1 = 2 (machine is up) with probability pXn = 0 to Xn+1 = 0 (machine fails again) with probability 1 - pXn = 2 to Xn+1 = 2 (machine stays up) with probability pXn = 2 to Xn+1 = 0 (machine fails) with probability 1 - pThus, the transition probability matrix and the transition probability matrix of the DTMC {Xn, n > 0} can be represented as attached in the below image:
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A rhombus is a quadrilateral with 4 congruent sides.
Explain why quadrilateral ACBD is a rhombus.
Answer: It is because the length of the diagonals are not equal.
Step-by-step explanation: Note: The diagonals of a square are equal
Express d² - 8d + 9 in completed square form.
Answer:
(d - 4)² - 7
Step-by-step explanation:
Formula for completing the square: x² + ax + b = (x + [tex]\frac{a}{2}[/tex])² - ([tex]\frac{a}{2}[/tex])² + b
d² - 8d + 9 = (d - [tex]\frac{8}{2}[/tex])² - ([tex]\frac{8}{2}[/tex])² + 9
= (d - 4)² - 4² + 9
= (d - 4)² - 16 + 9
= (d - 4)² - 7
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. The other side is 13 more than 4 times the length of the bottom of the triangle. The last side is 8 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
Answer:
The perimeter of the triangle is the distance around the triangle.
We need to apply our ability to convert word problems in to mathematical expressions.
we were told that the bottom of the triangle is units.
From the diagram perimeter
Four times the length of the bottom will be .
12 more than 4 times the bottom will be
Hence another side of the triangle is
Finally we were told that the last side is 3 more than the bottom, that will be
Step-by-step explanation:
solve the initial value problem. (9ye^9xy-5/y)dx (9xe^9xy 5x/y^2)dy=0, y(3)=3 the implicit solution is:
The initial value problem [tex](9ye^9xy-5/y)dx (9xe^9xy 5x/y^2)dy=0, y(3)=3[/tex] can be approximated using numerical methods such as the Euler method.
To find the initial value problem is a differential equation of the form:
[tex](9ye^(9xy) - 5/y) dx + (9xe^(9xy) - 5x/y^2) dy = 0[/tex]
with the initial condition y(3) = 3.
Since this is an implicit solution, we cannot find an explicit solution for y in terms of x. However, we can use numerical methods to find approximate solutions for y. One such method is the Euler method.
In the Euler method, we start with an initial estimate for y(x), and then use the derivative information to find y(x + h), where h is a small step size. We then use the new estimate to find the next value, and so on.
To apply the Euler method to this problem, we start with the initial condition y(3) = 3, and then use the following formula to estimate y(x + h):
y(x + h) = y(x) + h * f(x, y(x))
where f(x, y) is the derivative information from the differential equation:
[tex]f(x, y) = -(9xe^(9xy) - 5x/y^2) / (9ye^(9xy) - 5/y)[/tex]
Using the Euler method, we can iteratively estimate y(x) for increasing values of x, until we reach a desired value of x or the accuracy is within an acceptable limit.
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Please answer asap! I need answer for the blank spaces ! Thanks!
Answer: 1 quarter or 0.25 cents.
Step-by-step explanation: According to the illustration shown, we can infer that the coin we are looking for is for 1 value. So, if we subtract the amount shown (total) from the other coins (pennies in this case), 0.27 - 0.02 = 0.25 which is equivalent to the coin of the quarter (worth $0.25 USD) So, the blanks would look like this:
1 quarters
0 dimes
0 nickles
2 pennies
I hope this helped!
Given :
ray TV bisects ZUTW
ray TV is an altitude in A TUW
Prove:
Δ TUW is isosceles
Answer:
To prove that triangle TUW is isosceles, we can use the fact that ray TV bisects angle ZUT and is an altitude in triangle TUW.
Since ray TV bisects angle ZUT, it splits the angle into two congruent angles, ZTV and TVU. This means that angle ZTV is congruent to angle TVU.
Since ray TV is an altitude in triangle TUW, it forms a right angle with the base of the triangle, which is line segment TU. This means that angle TVU is a right angle, and therefore, angle ZTV is a right angle as well.
Since angle ZTV and angle TVU are congruent right angles, we know that the two sides that form these angles, UT and TU, are congruent. This means that side UT is congruent to side TU, and therefore, triangle TUW is isosceles.
Given points F(3, 1), G( 8, 2), H(2, 4), and J(1, 6).
a. Find the slope of FG and the slope of HJ.
b. Explain if FG and HJ are parallel, perpendicular or neither.
The slope of FG is equal to 1/5 while the slope of HJ is equal to -2.
Lines FG and HJ are neither parallel nor perpendicular because their slopes are different and not an inverse of each other.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
For the slope of line FG, we have the following:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (2 - 1)/(8 - 3)
Slope (m) of line FG = 1/5.
For the slope of line HJ, we have the following:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (6 - 4)/(1 - 2)
Slope (m) of line HJ = -2/1.
Slope (m) of line HJ = -2.
In Mathematics, a condition that must be met for two lines to be perpendicular is given by m₁ × m₂ = -1 while m₁ = m₂ for an two lines that are parallel.
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A produce tore offer red and green apple. In one morning they old 48 apple total. If 20 of the apple they old were red, what i the ratio of green apple old to red apple old?
The ratio of green apples sold to red apple old is:
7:5
If the store sold a total of 48 apples and 20 of them were red, then the number of green apples sold is:
48 apples - 20 red apples = 28 green applesTo find the ratio of green apples to red apples, we divide the number of green apples by the number of red apples and express the result as a fraction:
28 green apples / 20 red apples = 7/5So the ratio of green apples to red apples is 7:5, or written as a fraction, 7/5. This means for every 5 red apples sold, the store sold 7 green apples.
The ratio of green apples to red apples is a way of comparing the number of green apples to the number of red apples sold in a specific time period.
It provides a way to understand the proportion of green apples relative to red apples, and can be useful for the store to track the popularity of different types of apples.
Complete Question:
"A produce store offer red and green apple. In one morning they sold 48 apple total. If 20 of the apple they sold were red, what is the ratio of green apple sold to red apple sold?"
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Solving Systems and Missing Angles
*Show your work and write the rule used to solve each problem
4. The magnitude of angle S is 40°. Answer A.
5. The value of x is 48°. Answer B.
6. The true conclusion is Trevor is correct because the point (4 , 0) satisfies both equations. Answer B.
7. The system of equations has infinitely many solutions. Answer D.
Two parallel lines cut by a transversal form several angles. Look at the top image on the left. Two types of alternate angles have the same magnitude of the angle
Alternate interior anglesThe tangent line of two parallel lines is equals
Line equation number 1 : ax + by = c4. From the picture
PQ and RS are parallel∠Q and ∠S are alternate interior angles ∠S = ∠Q5. Look at the top image on the right.
∠B = 42°∠A and ∠B are alternate exterior angles ∠A = ∠B6. Solve the system of equations with the substitution method
x - 2y = 4 and y = 4 - xTrevor (4 , 0)Joey (0 , - 2)x - 2y = 47. The system of equations
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prove that sum of angles of a convex plygon of n sides is (n-2)pi, where n>3
The IH states that the sum of the angles in convex polygon C(which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A.
Using induction all convex polygons with n vertices have angles that add to (n - 2)·π, therefore let P(n) be that. We will demonstrate that P(n), where n≥3, holds for every n ∈ N. We demonstrate P(3), which states that any convex polygon with three vertices has an angle total of 180 degrees. Any triangle formed by such a polygon has angles that add up to 180°.
Assume that P(n) holds for some n ≥ 3 and that all convex polygons with n vertices have angles that add to (n-2) 180° for the inductive step. We demonstrate P(n+1), which states that each convex polygon with n+1 vertices has an angle sum of (n-1)·π. Let A represent any n+1-vertex convex polygon.
The IH states that the sum of the angles in convex polygon C (which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A. As a result, the total angle in A is (n-1) 180°. Thus, the induction is complete and P(n + 1) holds.
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In the diagram below, ST is parallel to PQ. If SR = 2.4, PQ = 1.8, RQ = 3,
and ST = 1.2, find the length of PR. Figures are not necessarily drawn to scale.
P
R
T
Answer:
PR is equal to 3
Step-by-step explanation:
line QR is 0.6 bigger than line SR. So I did SR + 0.6 = 2.4 + 0.6 = 3
Therefore, our answer is 3
write a real world deseription for the Algebraic expression 4.95x + 3
Answer:
You are paying 3$ already for a drink and for each sandwich (x) you buy is 4.95$
Step-by-step explanation:
You are paying 3$ already for a drink and for each sandwich (x) you buy is 4.95$
So you pay 4.95x + 3 for your drink and x sandwiches
The algebraic expression 4.95x + 3 can be described as the total cost of a product that has a fixed price of 3 dollars, and an additional price of 4.95 dollars per unit of the product. In this case, x represents the number of units purchased, and the expression represents the total cost of the purchase.
let f(x) = 1 x if x < −1 x2 if −1 ≤ x < 1 2 − x if x ≥ 1 . sketch the graph of f.
The function that best represented by this graph is f(x) = −x² + 1.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
A graph of a function is given in the image.
The parent function of the graph is g(x) = x².
And the graph is negative of the parent function.
And shifted upwards to 1 point.
That means, the function is f(x) = −x² + 1.
Therefore, the function is f(x) = −x² + 1.
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tell whether each equation has one zero or infinitely many solutions.
2. 1/2n + 7 = (n+14)/2
Answer:
n/2 + 7 is always equal to (n + 14)/2
Step-by-step explanation:
Both equations are the same, re-written.
Simplify the following:
n/2 + 7
Put each term in n/2 + 7 over the common denominator 2: n/2 + 7 = n/2 + 14/2:
n/2 + 14/2
n/2 + 14/2 = (n + 14)/2:
Answer: (n + 14)/2
how does each inverse function from part a relate to its original function? describe the relationship in terms of the context for each situation.
The inverse function is the reverse of the original function and relationship between the two functions is determined by the mapping between the inputs and outputs of the original function.
In mathematics, the inverse function is a inverse function of a function is the reverse of the original function.
To understand the relationship between an inverse function and its original function, consider the following example. Suppose we have a function that maps the height of an object to its weight.
The original function would take the height as an input and output the corresponding weight. The inverse function, on the other hand, would take the weight as an input and output the corresponding height.
It is important to note that not all functions have an inverse. A function is only considered to have an inverse if it is a one-to-one mapping, meaning that each input has a unique output.
In summary, If the original function is a one-to-one mapping, then it has an inverse function that can be found by swapping the inputs and outputs.
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the pka’s for carbonic acid and bicarbonate at 37°c are 3.83 and 10.25, respectively. o i. write the equation for each of these equilibria.
The equation for the equilibrium of carbonic acid (H2CO3) and bicarbonate (HCO3-) is: H2CO3 ⇌ H+ + HCO3- and equation for the equilibrium of bicarbonate (HCO3-) and carbon dioxide (CO2) is: HCO3- ⇌ H+ + CO2.
The equation for the equilibrium of carbonic acid (H2CO3) and bicarbonate (HCO3-) is: H2CO3 ⇌ H+ + HCO3-
The equation for the equilibrium of bicarbonate (HCO3-) and carbon dioxide (CO2) is: HCO3- ⇌ H+ + CO2
At 37°C, the pKa for carbonic acid (H2CO3) is 3.83, which means that the concentration of H+ in the first equation will be 10^-3.83 = 0.000195 M. The concentration of HCO3- in the first equation will be 0.000195 M.
The pKa for bicarbonate (HCO3-) is 10.25, which means that the concentration of H+ in the second equation will be 10^-10.25 = 0.00000007 M. The concentration of CO2 in the second equation will be 0.00000007 M.
Therefore, The equation for the equilibrium of carbonic acid (H2CO3) and bicarbonate (HCO3-) is: H2CO3 ⇌ H+ + HCO3- and equation for the equilibrium of bicarbonate (HCO3-) and carbon dioxide (CO2) is: HCO3- ⇌ H+ + CO2.
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Select the correct answer.
Which stock bar chart represents the stock data in the table?
Stock Z
April 4, 2018, Daily
Data
Open
Close
High
Low
Volume (M)
OA.
Price
13.54
13.51
13.65
13.41
50.00
13.71
13.66
13.61
Stock Z Chart
For each period, the stock price or trade volume is shown on the vertical axis. There are numerous chart types that can be employed in technical analysis.
What do stock bar charts show?A bar chart shows the open, high, low, and closing prices of a security or asset over a predetermined amount of time. A price bar's vertical line depicts the high and low prices for the specified time period. Each price bar's left and right horizontal lines stand in for the open and closing prices.
Bar graphs display the frequency counts of values for various levels of a nominal or categorical variable. Other statistics, including percentages, are occasionally displayed on bar charts. Figure 1 shows an illustration of a bar chart showing survey response data.
For each period, the stock price or trade volume is shown on the vertical axis. There are numerous chart types that can be employed in technical analysis.
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The complete question is "
jacknyrox18
05/19/2020
Chemistry
High School
answered
Look at the chart showing the daily stock data for WebTrend Inc.’s stock over the past month, and read this stock analyst’s view of the stock:
Stock analyst: There is a downward trend of the data with the peak price achieved on March 13. Investors are interested in WebTrend Inc. as demonstrated by the increase in trading volume.
Which statement is a fair conclusion based on the chart and the analyst’s comments about the WebTrend stock?
A.
The stock price increased and volume decreased on April 3.
B.
One month is not enough time to determine whether the price is at a low.
C.
The price has been falling, so an investor can assume it will begin to rise again soon.
D.
When the price change is negative for the day, an investor can assume the trading volume will decrease.
"
a partial identification on an nc license plate reveals that it contains only vowels(aeiou) and digits can only be even. how many nc plates could meet this requirement?
The number of ways that NC license plates meet the requirement is 78125
There are 7 places to be filled in the number plate
The NC license plate can be represented as below.
Since there are 5 vowels. So, each of the first three places can be filled in 5 ways. and also each of the last four places can be filled in 5 ways.
So, each place looks like the below:
5 ways 5 ways 5 ways 5 ways 5 ways 5 ways 5 ways
So, the number of possible NC license plates that meets the requirement is
5^7 = 78125
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