Answer: Alicia had 3 feet of wood and she used 3 feet, so she has 3 - 3 = 0 feet of wood left.
Since we are asked to estimate the amount of wood, we could round 3 to the nearest whole number and say that Alicia has approximately 0 feet of wood left.
Step-by-step explanation:
A) Find the time tH it takes the projectile to reach its maximum height H.
B) Find tR, the time at which the projectile hits the ground after having traveled through a horizontal distance R.
C) Find H, the maximum height attained by the projectile.
D) Find the total distance R (often called the range) traveled in the x direction; see the figure in the problem introduction.
The Max height H = [tex]\frac{u^{2} sin^{2} }{2g}[/tex] and the range is R = [tex]\frac{u* sin2thetha }{2g}[/tex].
What is projectile?Any object sent into space with only gravity acting on it is considered a projectile. Gravity is the main force working on a projectile. This doesn't necessary imply that the other troops don't affect it; it merely means that their impact is far less than that of gravity. A projectile's route is known as its trajectory. When a particle is hurled obliquely near the surface of the earth, it flows along a curved route with constant acceleration directed towards the planet's center (we assume that the particle stays close to the surface). Such a particle's motion is referred to as projectile motion, and its route is a projectile.
(A) Time taken by the projectile to reach its maximum height which will be given as -
using the equation of motion (1), we get
Vy= V0 + a*t
So the Max height H = [tex]\frac{u^{2} sin^{2} }{2g}[/tex]
And the range is R = [tex]\frac{u* sin2thetha }{2g}[/tex]
Hence the Max height H = [tex]\frac{u^{2} sin^{2} }{2g}[/tex] and the range is R = [tex]\frac{u* sin2thetha }{2g}[/tex].
Learn more about projectile, by the following link
https://brainly.com/question/24216590
#SPJ4
A man holds a note of $4,000 that has an interest rate of 12% annually. The note was made on March 16 and is due November 14. He sells the note to a bank on June 11 at a discount rate of 11% annually. Find the proceeds on the third-party discount note. (Use the banker's rule.)
The proceeds (discounted value) on the third-party discount note are $4,116.90.
What is the discounted value of a note?The discounted value of a note is a value that is less than the maturity value.
The maturity value is the face value of the note plus the accumulated interest.
Face value of the note receivable = $4,000
Annual interest rate = 12%
Note issuance date = March 16
Note due date = November 14
The total number of days = 243 days
Discount date = June 11
Discount rate = 11%
March 16 to June 11 = 87 days
Interest on the note = $320 ($4,000 x 243/365 x 0.12)
Maturity value = $4,320 ($4,000 + $320)
Discount period = 156 days (243 - 87)
Discount on the note = $203.10 ($4,320 x 156/365 x 11%)
Discounted value = $4,116.90 ($4,320 - $203.10)
Thus, the man, who holds a note of $4,000 at 12% interest but sells it at a discount rate of 11%, will receive $4,116.90.
Learn more about discounted notes at https://brainly.com/question/13161668.
#SPJ1
A woman 6 ft tall is standing near a street lamp that is 13 ft tall, as shown in the figure. Find a function that models the length L of her shadow in terms of her distance d from the base of the lamp.
Answer:
Step-by-step explanation:
We can use similar triangles to find the function that models the length of the woman's shadow. If the woman is standing at a distance d from the base of the lamp, the length of her shadow will be proportional to her height, so the ratio of the shadow length to the height will be equal to the ratio of the distance from the base of the lamp to the height of the lamp.
So, if h is the woman's height and L is the length of her shadow, we have:
L/h = d/13
And since h = 6 feet, we can write:
L = (d/13) * 6
So the function that models the length of the woman's shadow in terms of her distance from the base of the lamp is:
L = (d/13) * 6
The given diagram shows the steps for constructing a line parallel to line AB and passing through point P, but an error has occurred in the construction. What needs to be corrected in the diagram to fix the error?
The thing that needs to be corrected in the diagram to fix the error is that the third arc should be drawn centered at F.
How should the error be corrected?
Given:
Constructing a parallel line to line AB and passing through point P.
To find:
An error occurred in the construction.
The procedure is,
The first arc must be drawn centered at C.The second must be drawn centered at P.Finally, the third arc must be drawn centered at F.However, the third arc is drawn centered at D. This is wrong.
Therefore, the correct step is that the third arc must be centered at F.
Read more about line construction here:
https://brainly.com/question/2302379
#SPJ1
What quadrant is the point (2,-3) in
What is the last one?
The value of the last one is 18.
How to solve equation?The solution of the diagram can be modelled with an equation. Therefore, let's find the last value.
we will use variable to represent the fruit names.
Hence,
yellow fruit = x
red fruit = y
green fruit = z
Therefore,
x + y + z = 29
2y + z = 26
2z + y = 25
Using substitution,
y = 25 - 2z
2(25 - 2z) + z = 26
50 - 4z + z = 26
50 - 3z = 26
-3z = 26 - 50
-3z = -24
z = 8
y = 25 - 2(8)
y = 25 - 16
y = 9
Therefore,
x + 9 + 8 = 29
x = 29 - 17
x = 12
Finally,
x + 1 / 2x = 12 + 1 / 2(12) = 12 + 6 = 18
learn more on equation here: https://brainly.com/question/30066982
#SPJ1
Guys does someone know why are checks debit cards electronic payments all considered cash forms of payment even though the y do not insolvente bills and coins ???
Checks, debit cards, and electronic payments are considered forms of cashless payments because they allow for the transfer of funds between individuals or businesses without the need for physical currency, such as bills and coins.
Checks are considered cash because they are legal tender and can be deposited into a bank account, allowing the funds to be transferred between parties. Debit cards and electronic payments work in a similar way by deducting funds directly from a bank account or transferring funds electronically. While these forms of payment may not involve physical currency, they represent a transfer of value and can be used to purchase goods and services in the same way as cash.
In summary, checks, debit cards, and electronic payments are considered forms of cash because they facilitate the transfer of value between parties, even though they do not involve physical currency.
Answer:
Debit cards account for 28% of all payments, and credit cards account for 23% of all payments. For these payments, payment details are entered manually during a checkout process, or the physical card is processed at a point of sale (POS) system. There’s usually a debit or credit card processing fee, which the business owner needs to pay.
Step-by-step explanation:
pls tell me if wrong thank you have a great night or day
A national diet company markets a special diet plan which requires dieters to use frozen meals prepared by the company. The company advertises that those who follow their plan for 10 weeks will lose, on the average, at least 10 lbs. A consumer group is suspicious of this claim, believing that the weight lose is, on average, much less. If m represents the mean weight loss the population of all American adults would experience after 10 weeks on the plan, what is the appropriate alternative hypothesis that the consumer group wishes to test?a. Ha: mu < 10 b. Ha: mu > 10 c. Ha: mu (notequal)10 d. Ha: mu (notequal) 0
Ha:mu<10 is the appropriate alternative hypothesis that the consumer group wishes to test .
How would you define hypothesis?
An assumption or notion is called a hypothesis when it is put forth with the purpose of debating whether it might be true.
In the scientific process, the hypothesis is developed prior to the completion of any relevant study, other than a brief background review.
Ha:mu<10
Because A consumer group is suspicious of this claim, believing that the weight lose is, on average, much less.
Learn more about hypothesis
brainly.com/question/29519577
#SPJ4
the makers of skittles claim that 20% of skittles candies are orange. suppose this claim is true. you select a random sample of 30 skittles from a large bag. let the proportion of orange skittles in the sample.
The sample size that required to reduce the standard deviation of the sampling distribution to one-half that standard deviation (0.073) is 120.
As per the data given:
The makers of skittles claim that 20% of skittles candies are orange.
20 % = 0.20
Select a random sample of 30 skittles from a large bag.
[tex]\hat p[/tex] = the proportion of orange skittles in the sample.
The standard deviation of the sampling distribution of [tex]\hat p[/tex] = 0.073
The Standard deviation of the Sampling distribution was reduced to [tex]$= \frac{1}{2} \sigma_{\hat{p}}$[/tex].
[tex]$ \sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=0.073$[/tex]
Divide both sides by 2
We get:
[tex]$\sqrt{\frac{p(1-p)}{n}}=\frac{0.073}{2}[/tex]............... (1)
Now it should become be one - half.
Let [tex]$n_1[/tex] be the new sample size.
[tex]$\sqrt{\frac{p(1-p)}{n_1}}=\frac{0.073}{2}[/tex] ..................2
From (1) and (2) RHS of both equations is equal.
Then equate both equations
[tex]$\frac{1}{2} \sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{p(1-p)}{n_1}}$[/tex]
Squaring on both sides
We get:
[tex]$\Rightarrow\left(\frac{1}{2}\right)^2 \frac{p(1-p)}{n}=\frac{p(1-p)}{n_1}\end{aligned}$[/tex]
[tex]$\Rightarrow \frac{1}{4 n}=\frac{1}{n_1}$[/tex]
[tex]$\Rightarrow n_1=4 n$[/tex]
[tex]$n_1-[/tex] The new sample size required = 4n
n-The old sample size.
The sample size that required = 4n
= 4 (30)
= 120
For more questions on random sample
https://brainly.com/question/5431978
#SPJ4
The makers of skittles claim that 20% of skittles candies are orange. Suppose this claim is true. You select a random sample of 30 skittles from a large bag. Let p-hat = the proportion of orange skittles in the sample. The standard deviation of the sampling distribution of p-hat = .073
What sample size would be required to reduce the standard deviation of the sampling distribution to one-half that standard deviation (.073)
In Exercises 1 and 2, determine which matrices are in reduced echelon form and which others are only in echelon form.a. 1 1 0 10 0 1 10 0 0 0b. 1 1 0 00 1 1 00 0 1 1c. 1 0 0 01 1 0 00 1 1 00 0 1 1d. 0 1 1 1 10 0 2 2 20 0 0 0 30 0 0 0 0
In the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.
What is echelon form and reduced echelon form?Row echelon form suggests that: Each row's leading (first) entry must be
Each following row's first entry must be on a new column to the right.
All rows with zero entries are listed below rows with non-zero items.
If the leading entry in each column is the only nonzero element in that column, reduced echelon form also results from echelon form conditions.
According to the definitions we see that, in the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.
Learn more about matrix here:
https://brainly.com/question/28180105
#SPJ4
Six oranges cost R18,00. how much will 5 oranges and 15 oranges cost?
The costs of 5 oranges and 15 oranges are R15 and R45
How to determine the costsFrom the question, we have the following parameters that can be used in our computation:
Six oranges cost R18,00
This means that the unit rate is
Unit rate = R18,00/6 = R3.00
For 5 oranges, we have
Cost = 5 * R3.00 = R15.00
For 15 oranges, we have
Cost = 15 * R3.00 = R45.00
So, the costs are R15.00 and R45.00
Read more about unit rate at
https://brainly.com/question/19493296
#SPJ1
Why does a reflection make my phone look like theres a scratch when there is none on my phone? answer asap for vrainlist
Do u have a screen protector cuz if u do thats probably why
Step-by-step explanation:
Answer:
light diffraction and a dirty phone screen.
It’s multi step word problems divide and multiply
The number of adults who attended the concert is 824.
Linear Equation:
The equation is said to be linear if the greatest power of a variable always equals 1. It is also known as a one-degree equation. The usual form of a linear equation with one variable is Ax + B = 0. In this case, the variables x and A are variables while the variable B is a constant.
It is given in the question that the number of adults are twice the number of children.
then,
Suppose there were x children present at the concert.
Then number of adults will be 2x.
According to the given question,
x + 2x = 1236
3x = 1236
dividing both sides by 3, we get
x= 412
therefore, number of children who attended the concert is 412.
Then the number of adults will be,
2x = 2 x 412 = 824
therefore, the number of adults who attended the concert is 824.
To know more about Linear Equations, visit:
https://brainly.com/question/29739212
#SPJ1
2.9. Consider the following nonstochastic models (i.e., models without the stochastic error term). Are they linear regression models? If not, is it possible, by suitable algebraic manipulations, to convert them into linear models? a Y₁ = A. Y₁ = Bi 1 + P₂X₂ X₂ B₁ + A₂X₁ 1 c. Y₁ = 1 + exp(-B₁ - B2X₁)
The first and second models are linear regression models as it follow the general form, while the third model is not a linear regression model
What are linear regression modelLinear Regression is a statistical method used to model the relationship between a dependent variable (also known as the response or output variable) and one or more independent variables (also known as predictor or input variables). It assumes that there is a linear relationship between the independent variables and the dependent variable.
A linear regression model takes the form:
Y = β0 + β1X1 + β2X2 + ... + βnXn + ε
Where Y is the dependent variable, X1, X2, ..., Xn are the independent variables, β0, β1, β2, ..., βn are the coefficients that represent the slope of the line for each independent variable, and ε is the error term. The goal of linear regression is to estimate the coefficients β0, β1, β2, ..., βn so that the model can be used to make predictions about the dependent variable.
a. Y₁ = A + B₁X₁ + B₂X₂
This is a linear regression model, as the relationship between Y₁ and X₁, X₂ is linear, with the coefficients A, B₁, and B₂.
b. Y₁ = B₁X₁ + A
This is also a linear regression model, as the relationship between Y₁ and X₁ is linear with the coefficients A and B₁.
c. Y₁ = 1 + exp(-B₁ - B2X₁)
This is not a linear regression model, as the relationship between Y₁ and X₁ is not linear. It is not possible to convert it into a linear regression model by suitable algebraic manipulations.
Learn more on linear regression model here;
https://brainly.com/question/2235989
#SPJ1
25. Mr. Polar Bear asks if dilations will result in similar figures that differ by a scale factor.
Do you tell him "yes" or "no"?.
Answer:
Yes
Step-by-step explanation:
Dilations shrink or expand a figure. If the scale factor is one, the two figures will be identical.
Two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post. If the worker wants to stake both ropes in the ground at the same point, where should the stake be laced to use the least amount of rope?
The ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.
What are similar triangle?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
Given that, two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post, we need to find where should the stake be laced to use the least amount of rope,
Let rope of the 16 ft high pole be at x ft and that of 24 ft high pole at (30-x)
The structure of rope and poles are making a set of similar triangles, (refer to figure attached)
We know that, the corresponding sides of the similar triangle are in same ratio,
Therefore,
16 / x = 24 / (30-x)
2 / x = 3 / (30-x)
60 - 2x = 3x
5x = 60
x = 12
30-12 = 18
Hence, the ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.
Learn more about similar triangles, click;
https://brainly.com/question/29731302
#SPJ1
Solve the system of equations below. You may want to use the method by substitution starting with the second equation.
3x−2y
=34
5x+10y
=−10
Answer:
(8,-5)
x=8
y=-5
Step-by-step explanation:
What did Nixon's visit to China prove to the US?
A. If you can deal with one communist nation, others will likely join in
B. The Soviet Union was close to falling apart and communism would leave Eastern Europe
C. Most communist nations actually practice capitalism and have free elections
D. The communist world was not a single entity, and had many different positions
According to the information, it can be inferred that US President Nixon's visit to China proved that the communist world was not a single entity and had many different positions.
What was Nixon's visit to China?The visit of the President of the United States Richard Nixon to the People's Republic of China is an important event in the political and foreign relations sphere of the United States because it was a way to establish a formal relationship between the United States and the People's Republic of China.
This was significant because it was the first time a US President had visited the PRC, who at the time considered the US one of his main enemies. Additionally, this allowed him to verify to the other states that there were different ways of proposing communism. In this case, Chinese communist thought was moderated, so the relationship with the United States was allowed.
Learn more about China in: https://brainly.com/question/9695945
#SPJ1
i need this by today please
Which team has the best record? Explain how you know.
The team that has the best record when compared to the other teams would be = team High - 5s which has the least number of losses.
How to calculate the team that has the best record?The team with the best score can be calculated by finding the difference between the games and the losses.
The difference between games and losses of team Jule's Rules = 36-12 = 24.
The difference between games and losses of Pink Sox= 68-17 = 51
The difference between games and losses Go-Girls =
52-13 = 51
The difference between games and losses High-5s = 72-8 = 64
Therefore the team with the best record = team High - 5s which has the least number of losses.
Learn more about subtraction here:
https://brainly.com/question/28467694
#SPJ1
In Problems 31 and 32 find values of m so that the function y = xm is a solution of the given differential equation. xy'' + 2y' = 0
m = -2, 0. The function y = xm is a solution when m = -2 or 0.
For the differential equation xy'' + 2y' = 0, the function y = xm is a solution if m = -2 or 0. This can be seen by substitution and solving the resulting equation. When m = -2, the equation simplifies to 0 = 0, which is true. When m = 0, the equation simplifies to 0 = 2y', which is true when y' = 0. Therefore, the function y = xm is a solution when m = -2 or 0.
To solve for m, first substitute the function y = xm into the differential equation, giving xm'' + 2mx' = 0. Then move all terms containing m to one side of the equation, leaving 0 on the other side. This gives m'' + 2m' = 0, which is a second-order linear differential equation. This equation can be solved using the characteristic equation, which is found by setting the discriminant of the equation equal to 0. The discriminant for this equation is 4 - 4(1)(0) = 4, which is greater than 0. Thus, the equation has two distinct real solutions, which are m = -2 and m = 0. Therefore, the function y = xm is a solution when m = -2 or 0.
Learn more about function here
https://brainly.com/question/29633660
#SPJ4
This is a variation of problem 10 on page 141 of our textbook. You may want to solve this problem only after you solve the next one, which is the general version of this one. On the other hand, you also may want to solve this one first, and when solving the general one compare your evolving solution against your results in this problem.
A child is flying a kite. If the kite is 105 feet above the child's hand level and the wind is blowing it on a horizontal course at 6 feet per second, the child is paying out cord at _____________ feet per second when 165 feet of cord are out. Assume that the cord remains straight from hand to kite. (If you have ever flown a kite you know that this is an unrealistic assumption.)
For a solution of this problem (after the set closes) see the next problem.
The child is paying out the cord at a rate of 0 feet per second when 165 feet of cord are out.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The distance between the kite and the child's hand level "d". Then, using the Pythagorean theorem, we can write:
d² + 105²= (165)²
d² = 165² - 105²
d = 129.1 ft
The length of the cord is increasing at a rate of 6 feet per second
Let us consider the length of the cord "L".
d² + L² = (165)²
Differentiating both sides with respect to time (t), we get:
2d(dd/dt) + 2L (dL/dt) = 0
We want to find (dL/dt) when L = 165 and d = 129.1.
(dL/dt) = -d × (dd/dt) / L
Substituting in the values we found for d and L, we get:
(dL/dt) = -(129.1 ft) × (0 ft/s) / (165 ft) = 0 ft/s
Therefore, the child is paying out the cord at a rate of 0 feet per second when 165 feet of cord are out.
To learn more on Differentiation click:
https://brainly.com/question/24898810
#SPJ1
Translate the following verbal statement into an algebraic equation and then solve:
Use x for your variable.
The quotient of four more than a number and seven is ten.
the quotient of four (4) more than a number (x) and seven (7) is ten (10) equals (x +4)/7 = 10.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given The quotient of four is more than a number and seven is ten.
also given Use x for your variable.
In Mathematics, quotient literally means dividing a particular number by another number i.e the division of two (2) numbers.
Next, we would translate the word problem (sentence) into an algebraic expression as follows;
=> (x +4)/7 = 10
In conclusion, the algebraic expression for the quotient of four (4) more than a number (x) and seven (7) is ten (10) equals (x +4)/7 = 10.
Learn more about algebraic Expression here:
https://brainly.com/question/953809
#SPJ1
Question 1 of 10
If AABC= ADBC, then BC bisects the angle ZACD.
OA. True
OB. False
D
SUBMIT
Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = (x − y)2, y(0) = 0.6; y(0.5) y(0.5) ≈ (h = 0.1) y(0.5) ≈ (h = 0.05)
Using Euler's method, y(0.5) ≈ 0.7052 when h = 0.1 and y(0.5) ≈ 0.6803 when h = 0.05.
What is Euler's method?
Ordinary differential equations (ODE) can be solved using the Euler's method, a first-order numerical technique, with a specified beginning value.
We are given an equation y' = f(x,y), a point ([tex]x_{o} ,y_{o}[/tex]) and a step value h.
We have
f(x,y) = (x − y)^2
Point is (0,0.6)
We need to find y(0.5).
So, using Euler's method with step h = 0.1, we get
⇒[tex]x_{1}[/tex] = [tex]x_{o}[/tex] + h
⇒[tex]x_{1}[/tex] = 0 + 0.1 = 0.1
⇒[tex]y_{1}[/tex] = [tex]y_{o}[/tex] + h * f([tex]x_{o} ,y_{o}[/tex])
⇒[tex]y_{1}[/tex] = 0.6 + 0.1 * (0 - 0.6)^2
⇒[tex]y_{1}[/tex] = 0.636
⇒[tex]x_{2}[/tex] = [tex]x_{1}[/tex] + h
⇒[tex]x_{2}[/tex] = 0.1 + 0.1 = 0.2
⇒[tex]y_{2}[/tex] = [tex]y_{1}[/tex] + h * f([tex]x_{1} ,y_{1}[/tex])
⇒[tex]y_{2}[/tex] = 0.636 + 0.1 * (0.1 - 0.636)^2
⇒[tex]y_{2}[/tex] = 0.6647296
⇒[tex]x_{3}[/tex] = [tex]x_{2}[/tex] + h
⇒[tex]x_{3}[/tex] = 0.2 + 0.1 = 0.3
⇒[tex]y_{3}[/tex] = [tex]y_{2}[/tex] + h * f([tex]x_{2} ,y_{2}[/tex])
⇒[tex]y_{3}[/tex] = 0.6647296 + 0.1 * (0.2 - 0.6647296)^2
⇒[tex]y_{3}[/tex] ≈ 0.6863
⇒[tex]x_{4}[/tex] = [tex]x_{3}[/tex] + h
⇒[tex]x_{4}[/tex] = 0.3 + 0.1 = 0.4
⇒[tex]y_{4}[/tex] = [tex]y_{3}[/tex] + h * f([tex]x_{3} ,y_{3}[/tex])
⇒[tex]y_{4}[/tex] ≈ 0.6863 + 0.1 * (0.3 - 0.6863)^2
⇒[tex]y_{4}[/tex] ≈ 0.7012
⇒[tex]x_{5}[/tex] = [tex]x_{4}[/tex] + h
⇒[tex]x_{5}[/tex] = 0.4 + 0.1 = 0.5
⇒[tex]y_{5}[/tex] = [tex]y_{4}[/tex] + h * f([tex]x_{4} ,y_{4}[/tex])
⇒[tex]y_{5}[/tex] ≈ 0.7012 + 0.1 * (0.5 - 0.7012)^2
⇒[tex]y_{5}[/tex] ≈ 0.7052
So, y(0.5) ≈ 0.7052
Similarly, with step h = 0.5, we will calculate the values till [tex]x_{10}[/tex] and [tex]y_{10}[/tex]
On doing this, we get y(0.5) ≈ 0.6803
Hence, using Euler's method, y(0.5) ≈ 0.7052 when h = 0.1 and y(0.5) ≈ 0.6803 when h = 0.05.
Learn more about Euler's method from the given link
https://brainly.com/question/14286413
#SPJ4
EASY POINTS!
Two runners are training for their next competitions. Each runner is able to run a certain
distance in proportion to the time. The table on the left displays the distance Runner A
can run in relation to the time. Meanwhile, the graph on the right displays the distance
Runner B can run in relation to time.
What are the unit rates for the two runners? Which runner can run faster?
Answer:
12 / 1 and runner B
Step-by-step explanation:
at 13 seconds runner a had only run 156 ft, however runner b had run 200 ft.
A lot of 1000 components contains 300 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Answer the following questions: a. Find P(A)= b. Find P(B|A)= c. Find P(A∩B)= d. Find P( Ac∩B)= e. Find P(B)=
The probability of A is 0.3, P(B|A) is 0.299, P(A∩B) is 0.3, P(Ac∩B) is 0.3 and P(B) is 0.3.
a. P(A) = The probability that the first component drawn is defective = Number of defective components/Total number of components
= 300/1000 = 0.3
b. P(B|A) = The probability that the second component drawn is defective given the first component is defective = Number of defective components remaining/Total number of components remaining
= (300-1)/(1000-1) = 0.299
c. P(A∩B) = The probability that both components are defective = Number of defective components/Total number of components
= 300/1000 = 0.3
d. P(Ac∩B) = The probability that the first component is not defective and the second component is defective = Number of defective components/Total number of components
= 300/1000 = 0.3
e. P(B) = The probability that the second component drawn is defective = Number of defective components/Total number of components
= 300/1000 = 0.3
The probability of A is 0.3, P(B|A) is 0.299, P(A∩B) is 0.3, P(Ac∩B) is 0.3 and P(B) is 0.3.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
A CFL player has an annual salary of $305,000. The player donates 1/8 of his salary to charity. What amount is this?
Answer:
The player has an annual salary of $305,000, and they have decided to donate 1/8 of their salary to charity. To calculate this, we simply divide their salary by 8.
305,000 / 8 = $38,125
So, the player is donating $38,125 to charity every year. This is calculated by taking 1/8 of their annual salary.
The fraction 1/8 represents one out of eight equal parts of the player's salary, and when this fraction is multiplied by the player's salary, it gives the exact amount that they are donating to charity.
Camille took a friend for a birthday dinner. The total bill for dinner was $31.09 (including tax and a tip). If Camille paid a 20.7% tip, what was her bill before adding the tip?
Answer: Let's call the bill before the tip "x".
The tip was 20.7% of the bill, so the amount of the tip can be expressed as:
tip = 0.207 * x
The total bill, including the tip, was $31.09, so we can write an equation to represent this:
x + tip = 31.09
Substituting the expression for the tip into this equation, we get:
x + 0.207x = 31.09
Expanding and solving for x, we get:
1.207x = 31.09
x = 31.09 / 1.207
x = 25.76
So the bill before adding the tip was $25.76.
Step-by-step explanation:
The coffee variety Arabica yields about 750kg of coffee beans per hectare while Robusta yields about 1200kg/hectare. Suppose that a plantation has hectares of Arabica and r hectares of Robusta. On August 14th, 2003, the world market price of coffee was $1.42/kg for Arabica and $0.73 kg for Robusta.
Please show your work
Write an equation relating A and R if the plantation produces coffee worth $1,200,000.
Step-by-step explanation:
a)
Arabica coffee = 750a
Robusta coffee = 1200r
The total amount coffee beans 750a + 1200r = 1000000 kg
b)
The total amount of market price
1.42*750a +0.73*1200r 1000000
1065a + 876r = 1000000 dollars
step by step reading
The coffee variety Arabica yields about 750 kg of coffee beans per hectare, while
Robusta yields about 1200 kg per hectare. Suppose that a plantation has a
hectares of Arabica and r hectares of Robusta.
a. Write an equation relating a and r if the plantation yields 1,200,000 kg of coffee.
b. On August 14, 2003, the world market price of coffee was $1.42 per kg of Arabica
and $0.73 per kg of Robusta. Write an equation relating a and r if the plantation
produces coffee worth $1,200.000. what does that answer that means it would be
ANSWER
a
Arabica coffee = 750a
Robusta coffee = 1200r
The total amount coffee beans
750a + 1200r = 1.200,000 kg
b)
The total amount of market price
1.42*750a + 0.73*1200r = 1,200.000 ⇒
1065a + 876r = 1,200.000 dollar!!!!!!