Answer:
We know that Steve hikes at a steady pace, from this we can assume that he hikes at a constant velocity, then we can model this situation with a linear relationship:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
where y represents the position and x the time.
Then first let's define our system.
Let's define the waterfall as the 0mi in the position axis.
Let's define the moment when he starts hiking (from the campground) as the 0h in the time axis.
now we know that:
"After two hours he’s 13 miles from the waterfall"
This can be modeled with the point (2h, 13mi)
"After four hours he’s 6 miles from the waterfall"
This can be modeled with the point (4h, 6mi)
Now we have the two points we wanted, with this we can find the slope, that in this case, represents the hiking speed of Steve:
a = (6mi - 13mi)/(4h - 2h) = -3.5mi/h
We have a negative quantity, this is because we defined the waterfall as the zero in the position axis, so he is moving towards the zero, that's why we have a negative slope.
Then the position can be written as:
y = (-3.5mi/h)*x + b
Now to find the value of b, we can replace one of our points in the equation, for example with the first point we have:
x = 2h, y = 13mi
13mi = (-3.5mi/h)*2h + b
13mi = -7mi + b
13mi + 7mi = b
20mi = b.
Then the equation is:
y = (-3.5mi/h)*t + 20mi
From this, we know that the campground (the initial position of Steve) is 20 miles away from the waterfall.
And with this, we also can find the time that Steve needs to get to the waterfall.
Remember that the waterfall was the zero in the position, then when we have:
y = 0 = (-3.5mi/h)*t + 20mi
-20mi/(-3.5mi/h) = t
5.7h = t.
This means that Steve will get to the waterfall 5.7 hours after he lefts the campground.
4) Eric bought a canoe for $333.75. He bought a life vest for $134.87 and an ore paddle for $67.89
The sales tax was 5.25%. What was his total cost?
Answer:
His total cost is $564.68
Step-by-step explanation:
333.75 + 134.87 + 67.89 = 536.51
536.51 x 0.0525 = 28.17
536.51 + 28.17 = 564.68
let a = {a,b,c,d,e} and b = {a,b,c,d,e,f,g,h}. Match the given sets in the left to their corresponding values in the right.
a = a, b = b, c = c, d = d, e = e, f = no corresponding value, g = no corresponding value, and h = no corresponding value.
let a = {a,b,c,d,e} and b = {a,b,c,d,e,f,g,h}. To match the given sets in the left to their corresponding values in the right, we need to compare the elements in each set and determine which ones are the same.
The set a = {a,b,c,d,e} has the elements a, b, c, d, and e. The set b = {a,b,c,d,e,f,g,h} has the elements a, b, c, d, e, f, g, and h.
Comparing the two sets, we can see that the elements a, b, c, d, and e are the same in both sets. Therefore, the corresponding values for these elements are a = a, b = b, c = c, d = d, and e = e.
The elements f, g, and h are only present in the set b, so there are no corresponding values for these elements in the set a.
So the final matching of the given sets in the left to their corresponding values in the right is: a = a, b = b, c = c, d = d, e = e, f = no corresponding value, g = no corresponding value, and h = no corresponding value.
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find the slope (m) and y -intercept (b) of the equation in standar form 2x-3y=6
Answer:
m = \(\frac{2}{3}\) , b = - 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Given
2x - 3y = 6 ( subtract 2x from both sides )
- 3y = - 2x + 6 ( divide all terms by - 3 )
y = \(\frac{2}{3}\) x - 2 ← in slope- intercept form
with slope m = \(\frac{2}{3}\) and y- intercept b = - 2
Answer:
y- intercept is (0, -2)
slope is 2/3
Step-by-step explanation:
find 2 points on the line:
2x-3y=6
1/2*(6+3y) =x
if y is 2, x is 6 ((6,2))
if y is 4, x is 9 ((9, 4))
y-intercept is when x = 0.
0-3y=6
y=-2
slope is (y2-y1)/(x2-x1): choose y2 and the corresponding x-coordinate is x2. then the others are the 1's. let's use 4 as y2 which means:
x2 = 9
x1 = 6
y1 = 2
then plug in and solve.
(4-2)/(9-6)
= 2/3
m = 2/3
Hope this helps!
what is the slope of the line through (6, 3) (7, -4)
Answer:
m= -7
Step-by-step explanation:
Select three expressions equivalent to 28xy + 16x.
The three equivalent expressions to 28xy + 16x are:
4x(7y + 4)2(14xy + 8x)4xy(7 + 4).What are three equivalent expressions to 28xy + 16x?These expressions can be obtained by factoring out common terms from the original expression, resulting in equivalent expressions with the same values when evaluated.
For example, 4x(7y + 4) can be simplified to 28xy + 16x by using the distributive property. Similarly, 2(14xy + 8x) and 4xy(7 + 4) can also be obtained by factoring out common terms and rearranging the expression. Therefore, all three expressions are equivalent to the original expression, 28xy + 16x.
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Answer:
There are many expressions that are equivalent to 28xy + 16x, but here are three possible examples:
4x(7y + 4)
4(7xy + 4x)
8(3.5xy + 2x)
All three of these expressions follow the distributive property of multiplication over addition and simplify to 28xy + 16x.
Step-by-step explanation:
If someone work 48.5 hours in a week, they would get how many amount of overtime hours?
If someone works 48.5 hours in a week and their regular work week is 40 hours, then they would have worked 8.5 hours of overtime.
What is meant by a week?
A week is a unit of time equal to seven days, usually beginning on Monday and ending on Sunday. It is commonly used to measure and organize time.
What is meant by hours?
Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.
According to the given information
In most cases, overtime pay is calculated as 1.5 times the employee’s regular hourly rate.
If someone works 48.5 hours in a week and their regular workweek is 40 hours, then they would have worked 8.5 hours of overtime.
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One unit of A is composed of two units of B and three units of C. Each B is composed of one unit of F. C is made of one unit of D, one unit of E, and two units of F. Items A,B,C, and D have 20,50,60, and 25 units of on-hand inventory, respectively. Items A,B, and C use lot-for-lot (L4L) as their lot-sizing technique, while D,E, and F require multiples of 50,100 , and 100 , respectively, to be purchased. B has scheduled receipts of 30 units in period 1. No other scheduled receipts exist. Lead times are one period for items A, B, and D, and two periods for items C,E, and F. Gross requirements for A are 20 units in period 1,20 units in period 2, 60 units in period 6, and 50 units in period 8. Find the planned order releases for all items.
The planned order releases for each item are as follows: A: 20 units in period 1, B: 10 units in period 1, C: 40 units in period 3, D: No planned order release, E: 100 units in period 5, F: 100 units in period 5
To determine the planned order releases for all items, we need to calculate the net requirements for each period based on the given information. We will start with the highest-level item and work our way down the bill of materials.
Item A:
Period 1: Gross requirement of 20 units.
Since A uses lot-for-lot (L4L) as the lot-sizing technique, we release an order for 20 units of A.
Item B:
Item B is a component of A, and each A requires 2 units of B.
We need to calculate the net requirements for B based on the planned order release for A.
Period 1: Gross requirement of 20 units * 2 (requirement multiplier for B) = 40 units.
B has a scheduled receipt of 30 units in period 1.
Net requirement for B in period 1: 40 units - 30 units = 10 units.
Since B also uses L4L as the lot-sizing technique, we release an order for 10 units of B.
Item C:
Item C is a component of A, and each A requires 3 units of C.
We need to calculate the net requirements for C based on the planned order release for A.
Period 1: Gross requirement of 20 units * 3 (requirement multiplier for C) = 60 units.
C has a lead time of two periods, so we need to account for that.
Net requirement for C in period 3: 60 units - 20 units (scheduled receipt for A in period 1) = 40 units.
Since C uses L4L as the lot-sizing technique, we release an order for 40 units of C.
Item D:
Item D is a component of C, and each C requires 1 unit of D.
We need to calculate the net requirements for D based on the planned order release for C.
Period 3: Gross requirement of 40 units * 1 (requirement multiplier for D) = 40 units.
D has a lead time of one period, so we need to account for that.
Net requirement for D in period 4: 40 units - 60 units (scheduled receipt for C in period 3) = -20 units (no requirement).
Since the net requirement is negative, we do not release any planned order for D.
Item E:
Item E is a component of C, and each C requires 1 unit of E.
We need to calculate the net requirements for E based on the planned order release for C.
Period 3: Gross requirement of 40 units * 1 (requirement multiplier for E) = 40 units.
E has a lead time of two periods, so we need to account for that.
Net requirement for E in period 5: 40 units - 0 units (no scheduled receipt for E) = 40 units.
Since E requires a multiple of 100 to be purchased, we release an order for 100 units of E.
Item F:
Item F is a component of B and C, and each B requires 1 unit of F, while each C requires 2 units of F.
We need to calculate the net requirements for F based on the planned order releases for B and C.
Period 1: Gross requirement for B = 10 units * 1 (requirement multiplier for F) = 10 units.
Period 3: Gross requirement for C = 40 units * 2 (requirement multiplier for F) = 80 units.
F has a lead time of two periods, so we need to account for that.
Net requirement for F in period 5: 10 units + 80 units - 0 units (no scheduled receipt for F) = 90 units.
Since F requires a multiple of 100 to be purchased, we release an order for 100 units of F.
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Gina wilson homework I need help fast it’s due tomorrow
ok so for whatw e do is mulitpy the numbers
A computer with a regular price of $650 is on sale for 25% off.
What is the discount amount?
When solving this equation I got the price $487.5
Because 75% of 650 is $487.5
And 25% of 650 is 162.5
And to check my work I add them together to see if I get 650.
487.5+162.5= 650, meaning that I was correct.
So the correct answer to your problem is $487.5
an ambulance is traveling north at 46.1 m/s, approaching a car that is also traveling north at 36.2 m/s. the ambulance driver hears his siren at a freq
The frequency of the sound heard by the ambulance driver is approximately 1.05 times the frequency of the sound emitted by the siren.
We can use the Doppler effect equation to find the frequency of the sound heard by the ambulance driver.
The Doppler effect describes the change in frequency of a wave (such as sound or light) due to the relative motion of the source and the observer.
The equation for the Doppler effect for sound is:
f' = f (v + vo) / (v + vs)
where f is the frequency of the sound emitted by the siren (in Hz), f' is the frequency of the sound heard by the observer (in Hz), v is the speed of sound in air (approximately 343 m/s at room temperature), vo is the velocity of the observer (in m/s), and vs is the velocity of the source (in m/s).
In this case, the ambulance is the observer and the car is the source. Both are traveling north, so we can take their velocities as positive. Plugging in the given values, we get:
f' = f (v + vo) / (v + vs)
= f (v + 46.1) / (v + 36.2)
= f (343 + 46.1) / (343 + 36.2)
≈ 1.05 f.
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As the ambulance and car are approaching each other. The frequency heard by the driver is approximately 1.05 times the frequency of the siren.
To calculate the frequency of the sound heard by the ambulance driver, we can use the Doppler effect equation. The Doppler effect describes the change in frequency of a wave, such as sound or light, due to the relative motion of the source and the observer.
In this case, the ambulance is the observer, and the car is the source. Both are travelling north, so we can take their velocities as positive. We are given that the ambulance is travelling at a speed of 46.1 m/s, and the car is travelling at a speed of 36.2 m/s.
We also need to know the speed of sound in air, which is approximately 343 m/s at room temperature. With this information, we can use the Doppler effect equation for sound:
f' = f (v + vo) / (v + vs)
where f is the frequency of the sound emitted by the siren, f' is the frequency of the sound heard by the observer (in this case, the ambulance driver), v is the speed of sound in air, vo is the velocity of the observer (in this case, the ambulance), and vs is the velocity of the source (in this case, the car).
Plugging in the given values, we get:
f' = f (v + vo) / (v + vs)
= f (v + 46.1) / (v + 36.2)
= f (343 + 46.1) / (343 + 36.2)
≈ 1.05 f
Therefore, the frequency of the sound heard by the ambulance driver is approximately 1.05 times the frequency of the sound emitted by the siren.
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Draw the image of quadrilateral ABCD under a translation by 2 units to the left and 6 units down.
Answer:
Step-by-step explanation:
Find the value of p^3 - q^3 if
(a) p-q=- 7 and pq=10
(b) P-9=5/7 and pq=7/3
Answer:
Here is the solution...hope it helps:)
Simplify.
√12 . √20
The simplified value of √12 . √20 is 4√15.
To calculate this, we can break down the numbers under the square roots into their prime factors.
The prime factorization of 12 is 2^2 * 3, and the prime factorization of 20 is 2^2 * 5.
Taking the square root of 12, we can simplify it as √(2^2 * 3), which becomes 2√3.
Similarly, the square root of 20 can be simplified as √(2^2 * 5), which becomes 2√5.
Now, we can multiply the simplified values together: 2√3 * 2√5.
When multiplying two square roots, we can combine the numbers outside the square root and the numbers inside the square root separately.
Multiplying the numbers outside the square root, we have 2 * 2 = 4.
Multiplying the numbers inside the square root, we have √3 * √5 = √(3 * 5) = √15.
Therefore, the final simplified value is 4√15
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Example A marksman takes 10 shots at a target and has probability 0.2 of hitting the target with each shot, independently of all other shots. Let X be the number of hits. (a) Calculate and sketch the PMF of X (b) Whai is the probabillity of scoring no hits? (c) What is the probability of scoring more hits than misses? (d) Find the expectation and the variance of X. (e) Suppose the marksman has to pay $3 to enter the shooting range and he gets $2 for each hit. Let Y be his profit. Find the expectation and the variance of Y (f) Now let's assume that the marksman enters the shooting range for free and gets the number of dollars that is equal to the square of the number of hits. let Z be his profit. Find the expectation of Z
a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
b) The probability of scoring no hits is the probability of X being 0.
c) The probability of scoring more hits than misses is the probability of X being greater than 5
d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).
e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3
The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)
f) The expectation of Z: E(Z) = E(X²)
What is probability?
Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.
(a) To calculate the Probability Mass Function (PMF) of X, we can use the binomial distribution formula. Since the marksman takes 10 shots independently with a probability of 0.2 of hitting the target, the PMF of X follows a binomial distribution with parameters n = 10 (number of trials) and p = 0.2 (probability of success):
PMF of \(X(x) = C(n, x) * p^x * (1 - p)^{(n - x)}\)
Where C(n, x) represents the number of combinations or "n choose x."
Let's calculate the PMF for each value of X from 0 to 10:
PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰
PMF of X(1) = C(10, 1) * (0.2)¹ * (0.8)⁹
PMF of X(2) = C(10, 2) * (0.2)² * (0.8)⁸
...
PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
(b) The probability of scoring no hits is the probability of X being 0. So we calculate PMF of X(0):
PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰
(c) The probability of scoring more hits than misses is the probability of X being greater than 5. We need to calculate the sum of PMF of X from X = 6 to X = 10:
PMF of X(6) + PMF of X(7) + PMF of X(8) + PMF of X(9) + PMF of X(10)
(d) The expectation (mean) of X can be found using the formula:
E(X) = n * p
where n is the number of trials and p is the probability of success. In this case, E(X) = 10 * 0.2.
The variance of X can be calculated using the formula:
Var(X) = n * p * (1 - p)
In this case, Var(X) = 10 * 0.2 * (1 - 0.2).
(e) To calculate the expectation and variance of Y, we need to consider the profit from each hit. Each hit earns $2, and since X represents the number of hits, Y can be calculated as:
Y = 2X - 3
The expectation of Y can be calculated as:
E(Y) = E(2X - 3) = 2E(X) - 3
To calculate the variance of Y, we can use the property Var(aX + b) = a²Var(X) when a and b are constants:
Var(Y) = Var(2X - 3) = 4Var(X)
(f) Similarly, for Z, each hit earns a dollar amount equal to the square of the number of hits:
Z = X²
The expectation of Z can be calculated as:
E(Z) = E(X²)
Hence, a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
b) The probability of scoring no hits is the probability of X being 0.
c) The probability of scoring more hits than misses is the probability of X being greater than 5
d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).
e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3
The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)
f) The expectation of Z: E(Z) = E(X²)
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a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
b) The probability of scoring no hits is the probability of X being 0.
c) The probability of scoring more hits than misses is the probability of X being greater than 5
d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).
e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3
The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)
f) The expectation of Z: E(Z) = E(X²)
What is probability?
Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.
(a) To calculate the Probability Mass Function (PMF) of X, we can use the binomial distribution formula. Since the marksman takes 10 shots independently with a probability of 0.2 of hitting the target, the PMF of X follows a binomial distribution with parameters n = 10 (number of trials) and p = 0.2 (probability of success):
PMF of
Where C(n, x) represents the number of combinations or "n choose x."
Let's calculate the PMF for each value of X from 0 to 10:
PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰
PMF of X(1) = C(10, 1) * (0.2)¹ * (0.8)⁹
PMF of X(2) = C(10, 2) * (0.2)² * (0.8)⁸
......
PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
(b) The probability of scoring no hits is the probability of X being 0. So we calculate PMF of X(0):
PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰
(c) The probability of scoring more hits than misses is the probability of X being greater than 5. We need to calculate the sum of PMF of X from X = 6 to X = 10:
PMF of X(6) + PMF of X(7) + PMF of X(8) + PMF of X(9) + PMF of X(10)
(d) The expectation (mean) of X can be found using the formula:
E(X) = n * p
where n is the number of trials and p is the probability of success. In this case, E(X) = 10 * 0.2.
The variance of X can be calculated using the formula:
Var(X) = n * p * (1 - p)
In this case, Var(X) = 10 * 0.2 * (1 - 0.2).
(e) To calculate the expectation and variance of Y, we need to consider the profit from each hit. Each hit earns $2, and since X represents the number of hits, Y can be calculated as:
Y = 2X - 3
The expectation of Y can be calculated as:
E(Y) = E(2X - 3) = 2E(X) - 3
To calculate the variance of Y, we can use the property Var(aX + b) = a²Var(X) when a and b are constants:
Var(Y) = Var(2X - 3) = 4Var(X)
(f) Similarly, for Z, each hit earns a dollar amount equal to the square of the number of hits:
Z = X²
The expectation of Z can be calculated as:
E(Z) = E(X²)
Hence, a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
b) The probability of scoring no hits is the probability of X being 0.
c) The probability of scoring more hits than misses is the probability of X being greater than 5
d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).
e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3
The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)
f) The expectation of Z: E(Z) = E(X²)
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Suppose a political advisor is interested in the proportion of the vote an opponent will receive. If he samples voters randomly and tests hypotheses regarding p, the population proportion, what should he do to reduce his risk of making a Type II error
This will increase the probability of rejecting a false null hypothesis and accepting a true alternative hypothesis.The political advisor should ensure proper sampling, increase the alpha level, and have a larger sample size to reduce the risk of making a Type II error. A type II error is when a null hypothesis is accepted when it is false.
Suppose a political advisor is interested in the proportion of the vote an opponent will receive. If he samples voters randomly and tests hypotheses regarding p, the population proportion, he should do the following to reduce his risk of making a Type II error:To reduce the risk of making a Type II error, a political advisor interested in the proportion of the vote an opponent will receive, if he samples voters randomly and tests hypotheses regarding p, the population proportion should ensure that he has a larger sample size for testing. A larger sample size can help in making his results statistically significant and that the results are a true representation of the population.Proper sampling can also help to reduce the risk of a Type II error. Random sampling of the voters ensures that there is no bias in the selection process, which can skew the results. A random sample of voters is a fair representation of the population, and results obtained from a random sample are more likely to be accurate. This reduces the likelihood of a Type II error.The advisor should also increase the alpha level to reduce the risk of a Type II error. By increasing the alpha level, he is lowering the rejection region, which will reduce the likelihood of a Type II error. This will increase the probability of rejecting a false null hypothesis and accepting a true alternative hypothesis.The political advisor should ensure proper sampling, increase the alpha level, and have a larger sample size to reduce the risk of making a Type II error. A type II error is when a null hypothesis is accepted when it is false.
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(4+5)(4-51) =
please help i don’t feel like doing math rn
Answer:
423
Step-by-step explanation:
Answer:
-423
Step-by-step explanation:
Hope This Helps!
Plz Mark Brainliest!
What is a complex root of a polynomial?
The roots of a polynomial are the values of x for which the polynomial evaluates to 0.
A complex root is a root for which the real and imaginary parts are not both 0. If a polynomial has a complex root, that means that there is at least one value of x for which the polynomial evaluates to 0.
This can happen in two ways: either the polynomial has a real root and an imaginary root, or it has two complex roots. In either case, the complex roots must be found in order to determine the polynomial's factorization.
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michael is running for president. the proportion of voters who favor michael is 0.8. a simple random sample of 100 voters is taken. (a) what is the expected value of the sampling distribution of p?
The expected value of the sampling distribution of p is 0.8.
A statistic's probability distribution is called a sampling distribution when it is calculated from a larger number of samples taken from a particular population. The distribution of frequencies for a variety of outcomes that could possibly occur for a statistic of a population is known as the sampling distribution of that population.
The normal distribution, which is also known as the Gaussian distribution, is symmetric about the mean. It demonstrates that data close to the mean occur more frequently than data far from the mean. The normal distribution is depicted graphically as a "bell curve."
the sampling distribution of sample proportion will be a normal distribution with mean
\(\mu_{p}\) = p = 0.8
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What’s the median of this set of data 71,37,22,81,65,54,52,41,48,71
Answer:
I'm glad you asked!
Step-by-step explanation:
Step 1:Order the numbers from least to greatest.
\(22,37,41,48,52,54,65,71,71,81\)
Step 2:Now find the middle number.
\(22,37,41,48\),52,54\(,65,71,71,81\)
Step 3:Since there are two numbers,we add them together then divide by 2.
\(52+54 =106\)
\(106/2=53\)
The median is 53.
Answer:
53
Step-by-step explanation:
Clark Company manufactures a product with a standard direct labor cost of two hours at $18 per hour. During July, 1200 units were produced using 2500 hours at $18.30 per hour. The labor quantity variance was O $1110 U. O $1800 U. $1830 U. O $1830 F.
The labor quantity variance of Clark Company is $1800 U (Unfavorable). Option b is correct.
Compare the actual labor hours used with the standard labor hours allowed and multiply the difference by the standard labor rate.
Standard labor hours allowed = Standard hours per unit × Number of units produced
Standard labor hours allowed = 2 hours × 1200 units = 2400 hours
Actual labor hours used = 2500 hours
Labor quantity variance = (Actual labor hours used - Standard labor hours allowed) * Standard labor rate
Labor quantity variance = (2500 hours - 2400 hours) × $18 per hour
Labor quantity variance = 100 hours × $18 per hour
Labor quantity variance = $1800
Since the actual labor hours used exceeded the standard labor hours allowed, the labor quantity variance is unfavorable. Therefore, the labor quantity variance is $1800 U (Unfavorable).
Option b is correct.
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Explain two procedures that you can use to draw two adjacent complementary angles. Then draw a pair of adjacent complementary angles so that one angle has a measure of 30°.
Answer:
Complementary angle of 30° is 60°.
Step-by-step explanation:
The complementary angles are the angles whose sum is 90.
If one angle is x then the other angle is 90 - x, they both are complementary to each other.
One angle is 30°, so the other angle is 90° - 30° = 60°
33. The influent total suspended solids (TSS) concentra-
tion to a primary clarifier is 300 milligrams per liter
(mg/L) and the effluent TSS concentration is 100
mg/L. What is the efficiency of the primary clarifier
in removing TSS (as a percentage)?
1. 50% TSS removal
2. 67% TSS removal
3. 60% TSS removal
dsera
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4. 55% TSS
The primary clarifier is removing 67% of the TSS from the influent wastewater, resulting in an effluent with a TSS concentration of 100 mg/L. This is a significant reduction in TSS and is an important step in the overall wastewater treatment process.
The efficiency of the primary clarifier in removing total suspended (TSS) is 67%, based on the given influent and effluent TSS concentrations.
Primary clarifiers are used in wastewater treatment plants to remove settleable solids from wastewater. The TSS concentration is a measure of the amount of suspended solids present in the wastewater.
The efficiency of a clarifier in removing TSS is calculated as the percentage reduction in TSS concentration from the influent to the effluent.
In this case, the influent TSS concentration to the primary clarifier is 300 mg/L, and the effluent TSS concentration is 100 mg/L. Therefore, the TSS removal efficiency of the primary clarifier is calculated as follows:
TSS removal efficiency = [(influent TSS concentration - effluent TSS concentration) / influent TSS concentration] x 100%
= [(300 mg/L - 100 mg/L) / 300 mg/L] x 100%
= 67%
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4) Angles 3 and 6 are congruent. What would you use to prove those lines parallel? (pic below)A. Converse of Same-Side Interior Angles Theorem
B. Alternate Interior Angles Theorem
C. Converse of the Corresponding Angles Postulate
D. Converse of Alternate Interior Angles Theorem
Answer:
B?
Step-by-step explanation:
Please quickly help me figure this out
The final expression of the simplified version is 28x + 8y + 2.
What is the simplified version?We know that, to simplify means to obtain the lowest possible form of the of the expression. The expression is written in its simplest form when there are no more ambiguities left in the way that it is written.
Given the expression;
-2(3x + 12y - 5 - 17x - 16y + 4)
We can now expand the expression to have;
-6x - 24y + 10 + 34x + 32y - 8
This could further simplify to
-6x + 34x - 24y + 32y + 10 - 8
To obtain the final simplified expression, we have;
28x + 8y + 2
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What statements describe the properties of a plane? select three options. a plane is one dimensional. a plane has length and width. a plane extends infinitely in all directions. a plane is precisely defined. a plane is a flat surface.
The correct options for defining a plane are-
2)A plane has length and width.3)A plane extends infinitely in all directions5)A plane is a flat surface.What is a plane?A plane is a flat, 2-dimensional surface which extends indefinitely in mathematics. Planes can appear as infinitely expanded subspaces from some multidimensional space, such as one of the room's walls, or they can exist independently, as in the configuration of Euclidean geometry.
Some key properties of the plane are-
If two distinct planes exist, they either are parallel to one another or intersect in a line.A line either runs parallel to the a plane, intersects it at a specific point, or exists within the plane.If two distinct lines are perpendicular to same plane, they has to be parallel to one another.Two planes that are perpendicular to same line must be parallel.Parallel planes & intersecting planes are the two types of planes. Parallel planes are two non-intersecting planes, and intersecting planes are planes that intersect along a line.To know more about the plane, here
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The correct question is -
What statements describe the properties of a plane? Select three options.
1)A plane is one dimensional.
2)A plane has length and width.
3)A plane extends infinitely in all directions.
4)A plane is precisely defined.
5)A plane is a flat surface.
Can someone help me with this question, its timed...
Answer:
Where is the question???
A firm has a loss level EBIT of $175m and an expected EBIT of $200m with a standard deviation of $50m. What is the z-score? What is the probability that the firm WILL have a negative EPS? A z-score of -1.20 would be entered as - 1.20. A probability of 37.25% should be entered as 37.25.
The required z-score is -0.5 and the probability that the firm WILL have a negative EPS is 30.85%.
Firm has a loss level EBIT of $175m and an expected EBIT of $200m with a standard deviation of $50m.
Z-score = (EBIT - Expected EBIT) / Standard deviation= (175 - 200) / 50= -0.5
Probability of having a negative EPS:
To find the probability that the firm will have a negative EPS, we need to find the area to the left of Z-score. As the Z-score is negative, we will be finding the left-tail probability using the standard normal table from the link below:
The area to the left of Z-score (0.5) is 0.3085 or 30.85%.
Therefore, the probability that the firm WILL have a negative EPS is 30.85%.
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find an equation of the plane passing through that is orthogonal to the planes xyz and xyz.
The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.
We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.
A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.
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Question correction:
Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0
Lou has 2 sets of numbers .The first set starts with 3 and follows a pattern increase by 5 .The second set starts with 39 and follows a pattern increase by 6 How many numbers do the 2 sets have in conmen
Answer:
2
Step-by-step explanation:
Let, Lou's set = x
g(x) = 3 + 5x
x = 0,..
3, 8, 13, 18, 23, 28, 33
set y:
g(y) = 39 - 6x
x = 0,...
(39, 33, 27, 21, 15, 9, 3)
Numbers in common :
(3, 33)
= 2
Talisa says that she has 34 colored pencils in her art box. her friend jaime has 58 colored pencils in her box. about how many more colored pencils does jaime have than talisa ? use rounding to help you decide.
The colored pencils does jaime have more than talisa is 24
what is arithmetic operator?An arithmetic operator is a mathematical function that takes two operands and performs a calculation on them.
They are used in common arithmetic and most computer languages contain a set of such operators that can be used within equations to perform a number of types of sequential calculation. Basic arithmetic operators include:
:-Addition (+)
:-Subtraction (-)
:-Multiplication (×)
:-Division (÷)
so;
A.T.Q:-
The colored pencils does talisa have are 34
The colored pencils does jaime have are 58
∴ by using arithmetic operator Subtraction (-) , we conclude that how more colored pencils does jaime have than talisa
∵ jaime's colored pencils - talisa's colored pencils
⇒ 58- 34
⇒24
hence; jaime have 24 pencils more than talisa
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