Answers
The amount of paper used for the label on the can of tune is 12.57 in²
Here, the shape of the can of can is cylindrical.
The area of the cured surface of cylinder is given by formula,
A = 2πrh
where r is the radius of the cylinder
and h is the height of the cylinder
Here, r = 2 in and h = 1 in
so, the area of the lateral surface of cylinder would be,
A = 2 × π × r × h
A = 2 × π × 2 × 1
A = 4 × π
A = 12.57 sq. in.
Therefore, the required amount of paper = 12.57 in²
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Related Questions
Hannah has a chicken coop with 6 hens. Let X represent the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.
A 2-column table with 7 rows. Column 1 is labeled number of eggs with entries 0, 1, 2, 3, 4, 5, 6. Column 2 is labeled probability with entries 0. 02, 0. 03, 0. 07, 0. 12, 0. 30, 0. 28, 0. 18.
What is the median of the distribution?
3
3. 5
4
4. 2
Answers
1.39 is the median of the distribution
Creating a table:
X :___0 __ 1 __ 2 ___ 3 ____ 4 ___ 5 ___ 6
P(x):0.02_0.03_0.07, 0.12, 0.30_ 0.28_0.18.
The standard deviation = √(Var(x))
Var(x) = Σx²*p(x) - E(x)²
E(x) = ΣX*p(x)
E(x) = (0*0.02) + (1*0.03) + (2*0.07) + (3*0.12) + (4*0.30) + (5*0.28) + (6*0.18) = 4.21
Var(X) :
[tex]((0^2*0.02) + (1^2*0.03) + (2^2*0.07) + (3^2*0.12) + (4^2*0.30) + (5^2*0.28) + (6^2*0.18)) - 4.21^2[/tex]
19.67 - 17.7241
= 1.9459
Standard deviation = √(Var(X))
Standard deviation = √(1.9459)
Standard deviation = 1.3949551
= 1.39
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Full Question ;
Hannah has a chicken coop with 6 hens. Let X be the total number of eggs the hens lay on a randomly chosen day. The distribution for X is given in the table.
A 2-column table with 7 rows. Column 1 is labeled number of eggs with entries 0, 1, 2, 3, 4, 5, 6. Column 2 is labeled probability with entries 0.02, 0.03, 0.07, 0.12, 0.30, 0.28, 0.18.
What is the standard deviation of the distribution?
1.39
1.95
2.16
4.67
Discrete Structures in Mathematics(b) Solve the recurrence relation An = 6an-1 – 9an-2 = with initial conditions ao = 2 and ai = 3. [6 marks]
Answers
First, let me explain some key terms related to the question.
- Discrete: This refers to mathematics that deals with countable or finite sets of numbers, rather than continuous sets. In other words, we're dealing with specific, separate values rather than a continuous range.
- Recurrence: This refers to a mathematical sequence where each term depends on one or more previous terms. In other words, we can use a formula to generate the next term based on previous terms.
- Relation: This refers to a mathematical expression that relates one or more variables. In this case, our recurrence relation relates the sequence An to its previous terms.
With that in mind, let's tackle the question!
We're given a recurrence relation: An = 6An-1 – 9An-2. This means that each term in the sequence An depends on the two previous terms, An-1 and An-2.
We're also given initial conditions: a0 = 2 and a1 = 3. This gives us a starting point for the sequence.
To solve the recurrence relation and find the values of An, we'll use a technique called iteration. Essentially, we'll use the recurrence relation to generate the next term in the sequence, then use that term to generate the next one, and so on.
Here's how it works:
- First, we use the initial conditions to find the first two terms of the sequence: a0 = 2 and a1 = 3.
- Next, we use the recurrence relation to generate the third term: a2 = 6a1 - 9a0 = 6(3) - 9(2) = 0.
- We continue this process, using the recurrence relation to generate each subsequent term. For example, to find a3, we use the formula An = 6An-1 – 9An-2 with n = 3: a3 = 6a2 - 9a1 = 6(0) - 9(3) = -27.
- We can keep going like this to find as many terms as we need.
Here's what the first few terms of the sequence look like:
a0 = 2
a1 = 3
a2 = 0
a3 = -27
a4 = -54
a5 = -162
a6 = -270
...
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There is a bag filled with 3 blue, 4 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?
Answers
The probability of getting exactly 1 blue marble is 9/22 or approximately 0.409.
The probability of getting exactly 1 blue marble can be calculated in two steps:
Step 1: The probability of drawing a blue marble on the first draw is:
P(Blue on first draw) = 3/12
After drawing a blue marble, there will be 2 blue, 4 red, and 5 green marbles left in the bag.
The probability of drawing a non-blue marble on the second draw is:
P(Non-blue on second draw) = 9/11
Alternatively, if a non-blue marble is drawn first, there will be 3 blue, 4 red, and 4 green marbles left in the bag. The probability of then drawing a blue marble on the second draw is:
P(Blue on a second draw after non-blue on the first draw) = 3/11
So the probability of getting one blue and one non-blue marble on the first and second draws in any order is:
P(One blue and one non-blue) = P(Blue on first draw) × P(Non-blue on second draw) + P(Non-blue on first draw) × P(Blue on second draw after non-blue on first draw)
P(One blue and one non-blue) = (3/12) × (9/11) + (9/12) × (3/11) = 27/132
Step 2: There are two possible orders in which we can get exactly 1 blue marble is:
blue on the first draw and non-blue on the second draw, or non-blue on the first draw and blue on the second draw.
The probability of getting exactly 1 blue marble is:
P(Exactly 1 blue) = P(One blue and one non-blue) + P(One non-blue and one blue)
P(Exactly 1 blue) = 27/132 + 27/132 = 54/132
Simplifying, we get:
P(Exactly 1 blue) = 9/22
Therefore, the probability of getting exactly 1 blue marble is 9/22 or approximately 0.409.
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One number is four more than a second number. Two times the first number is 10 more than four times the second number
Answers
Call the first number "x" and the second number "y". So the first number is 3.
From the problem statement, we know:
x = y + 4 (the first number is four more than the second number)
2x = 4y + 10 (two times the first number is 10 more than four times the second number)
Now we can solve for one of the variables in terms of the other, and then substitute that expression into the other equation to solve for the other variable. Let's use the first equation to solve for x:
x = y + 4
Substitute this expression for x into the second equation:
2x = 4y + 10
2(y + 4) = 4y + 10
Distribute the 2:
2y + 8 = 4y + 10
Subtract 2y from both sides:
8 = 2y + 10
Subtract 10 from both sides:
-2 = 2y
Divide both sides by 2:
-1 = y
Now we know that the second number is -1. We can use the first equation to find the first number:
x = y + 4
x = -1 + 4
x = 3
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(a) Determine the equation y = a + mx of the least square line that best fits the given data points. (2,1),(1,1),(3,2). (b) Consider the equation ex + x = 7. Use Newton's method to approximate the solution to 4 significant digits. Make an initial guess of Xo = 2.
Answers
The solution to the equation ex + x = 7 using Newton's method with an initial guess of Xo = 2 is approximately 1.4449.
(a) To determine the equation y = a + mx of the least square line that best fits the given data points (2,1), (1,1), (3,2), we first need to calculate the mean of x and y, and then calculate the slope m and y-intercept a of the line.
Mean of x: (2 + 1 + 3)/3 = 2
Mean of y: (1 + 1 + 2)/3 = 4/3
To calculate the slope m, we need to find the sum of (xi - x-bar)(yi - y-bar) and the sum of (xi - x-bar)^2 for each data point:
(2-2)(1-4/3) + (1-2)(1-4/3) + (3-2)(2-4/3) = -1/3
(2-2)^2 + (1-2)^2 + (3-2)^2 = 6
So, m = (-1/3) / 6 = -1/18
To calculate the y-intercept a, we can use the formula a = y-bar - m(x-bar):
a = (4/3) - (-1/18)(2) = 5/9
Therefore, the equation of the least square line is y = (5/9) - (1/18)x.
(b) We want to solve the equation ex + x = 7 using Newton's method with an initial guess of Xo = 2.
First, we need to find the derivative of the function f(x) = ex + x:
f'(x) = ex + 1
Then, we can use the formula for Newton's method:
Xn+1 = Xn - f(Xn) / f'(Xn)
Plugging in X0 = 2 and using four significant digits:
X1 = 2 - (e^2 + 2) / (e^2 + 1) = 1.574
X2 = 1.574 - (e^1.574 + 1.574) / (e^1.574 + 1) = 1.4633
X3 = 1.4633 - (e^1.4633 + 1.4633) / (e^1.4633 + 1) = 1.445
X4 = 1.445 - (e^1.445 + 1.445) / (e^1.445 + 1) = 1.4449
Therefore, the solution to the equation ex + x = 7 using Newton's method with an initial guess of Xo = 2 is approximately 1.4449.
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For positive constants k and g, the velocity, v, of a particle of mass m at time t is given by v= (mg/k)(1-e^(-kt/m)) At what rate is the velocity is changing at time 0? At t=7? What do your answers tell you about the motion? At what rate is the velocity changing at time 0? rate= At what rate is it changing at t=7? rate =
Answers
This indicates that the particle is accelerating due to gravity. At t=7, the rate at which the velocity is changing depends on the value of k, m, and g. This implies that the particle's acceleration may vary depending on these constants and time.
At time 0, the rate at which the velocity is changing can be found by taking the derivative of the velocity function with respect to time, t.
v(t) = (mg/k)(1-e^(-kt/m))
v'(t) = (mg/k)((ke^(-kt/m))/m)
Plugging in t=0 gives:
v'(0) = (mg/k)((k)/m) = g
Therefore, the rate at which the velocity is changing at time 0 is g.
At t=7, the rate at which the velocity is changing can also be found by taking the derivative of the velocity function with respect to time, t, and plugging in t=7:
v'(7) = (mg/k)((ke^(-7k/m))/m)
This value will depend on the specific values of k, g, and m that are not given in the question.
These rates of change tell us about the motion of the particle. If the rate of change of velocity is positive, the particle is accelerating. If it is negative, the particle is decelerating. If it is zero, the particle is moving at a constant velocity.
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(7) Suppose we have a linear system involving the variables 31.32 -Is. Its augmented matrix has been reduced to (1 62 -5 -2 1 0 0 2-8-1 OOOO 1 (a) Working right to left, use row operations to create z
Answers
Hi! It seems like you have a reduced row echelon form (RREF) matrix and you want to find the solution of the linear system using row operations. Based on the given augmented matrix:
(1 62 -5 | -2)
(0 0 2 | -8)
(0 0 0 | 1)
We can work from right to left, performing row operations to create a variable z.
Step 1: Since the third row has only one non-zero entry (1) in the last column, we can identify it as z:
z = 1
Step 2: Move to the second row and use the equation to solve for y:
2y = -8
y = -8 / 2
y = -4
Step 3: Move to the first row and use the equation to solve for x:
x + 62y - 5z = -2
x + 62(-4) - 5(1) = -2
x - 248 - 5 = -2
x = -2 + 248 + 5
x = 251
The solution to the linear system is x = 251, y = -4, and z = 1.
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Winston has $2,003 to budget each month. He budgets $1,081 for
fixed expenses and the remainder of his budget is set aside for
variable expenses. What percent of his udget is allotted to variable
expenses? Round your answer to the nearest percent if necessary.
Answers
The percentage of budget that is allotted to variable expenses is 46.03%
How to solve for the percentage of budgetWe first have to determine the solution for what the va,riable expenses is supposed to be
$2,003 (total budget) - $1,081 (fixed expenses)
= $922
Next we will have to solve for the percentage that is the budget which is allocated to the variable expenses
This is simply written as
variable expenses / total budget * 100
($922 (variable expenses) ÷ $2,003 (total budget)) × 100 = 46.03%
Hence the percentage of budget that is allotted to variable expenses is 46.03%
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Answer:
46.03%
Step-by-step explanation:
922 ÷ 2003 x 100 which gives you 46.03
Find the mean, median, interquartile range and mean absolute deviation of the set of numbers. Round to the nearest tenth, if necessary. 1, 1, 4, 8, 9, 3, 8 please help
Answers
Answer:
mean- 4.9
median- 4
interquartile range- 7
Step-by-step explanation:
Hope this helps! :)
A rectangle has a width of 14 and a length of 22 find the area
Answers
Answer:
308
Step-by-step explanation:
The area of a rectangle is the length multiplied by the width.
14 x 22 = 308
Hope this helps!
A satellite is in the shape of a cylinder with two hemispheres fitted snugly on either end. If the diameter of the cylinder is 2 m and its length is 12 m, find the volume of the satellite. Express the answer in terms of pi
Answers
The volume of the satellite is,
⇒ V = 12π m³
Given that;
A satellite is in the shape of a cylinder with two hemispheres fitted snugly on either end.
And, The diameter of the cylinder is 2 m and its length is 12 m.
Now, We know that;
Volume of cylinder = πr²h
Hence, We get;
The volume of the satellite is,
⇒ V = π × (2/2)² × 12
⇒ V = 12π m³
Thus, The volume of the satellite is,
⇒ V = 12π m³
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The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.6% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick nine first-time, full-time freshmen from the survey. You are interested in the number that believes that same-sex couples should have the right to legal marital status. What is the standard deviation (σ)?
Answers
The standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.
To find the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students, we need to use the binomial distribution.
Given that 71.6% of all first-time, full-time freshmen believe that same-sex couples should have the right to legal marital status, the probability (p) that a randomly selected student from this population believes this is:
p = 0.716
Since we are interested in the number of students in a sample of nine who believe this, we can model this using the binomial distribution with parameters n = 9 and p = 0.716.
The formula for the standard deviation of a binomial distribution is:
σ = sqrt(n * p * (1 - p))
Substituting in the values of n and p, we get:
σ = sqrt(9 * 0.716 * (1 - 0.716))
σ = 1.168
Therefore, the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.
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Often, there is more than one set of sequences that will take a preimage to an image. Determine one or two other sequences to create FGHIJ from ABCDE.
Answers
The one or two other sequence to create FGHIJ from ABCDE are:
1. F, B+5=G, C+5=H, D+5=I, E+5=J.
2. Reverse ABCDE to get EDCBA
What is a sequence?A sequence refers to an ordered list of items. It may be letters, numbers, or any other objects arranged in a particular order.
A sequence of rigid motions and dilations is a combination of transformations that preserve the original shape and size of a figure, but change its position, orientation, and scale.
To create the sequence FGHIJ from ABCDE, there are many possible sequences that can be used. Here are two:
Sequence 1:
Add 5 to each letter in ABCDE to get FGHIJ: A+5=F, B+5=G, C+5=H, D+5=I, E+5=J.
Sequence 2:
Reverse the order of the letters in ABCDE to get EDCBA.
Add 5 to each letter in EDCBA to get JIHGF: E+5=J, D+5=I, C+5=H, B+5=G, A+5=F.
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What is the probability that a random
point on AK will be on CH?
-10
B
C D E
-8 -6
-4 -2
F G H I I J
K
+++
0 2 4 6 8
P=[?]
10
Enter
Answers
The probability that a random point on AK will be on CH is 1/2
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 and it is equal to 100% in percentage.
probability = sample space /total outcome
The total outcome is the range of AK.
range = highest - lowest
= 10-(-10) = 10+10 = 20
sample space of CH = 4-(-6)
= 4+6 = 10
Therefore probability that a random point on AK will be on CH is 10/20
= 1/2
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What’s the answer for the question please?
Answers
The correct expression is the one in option A; [tex]-3^{15}[/tex]
How to simplify the expression?Here you need to remember two rules for exponents, these are:
[tex]x^n*x^m = x^{n +m}\\\\[/tex]
And:
[tex](x^n)^m = x^{n*m}[/tex]
Now our expression is:
[tex]-(3^2*3^3)^3[/tex]
Using the first rule we will get:
[tex]-(3^2*3^3)^3 = -(3^{2 + 3})^3 = -(3^5)^3[/tex]
Using the second rule:
[tex]-(3^5)^3 = -3^{3*5} = -3^{15}[/tex]
The correct option is a
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Estimate the perimeter and the area of the shaded figure.
Answers
The perimeter and area of the given polygon are:
Perimeter = 22.325 units
Area = 25 square units
How to find the area and perimeter?Using Pythagoras theorem, we can find the length of the sides of the polygon as:
a = √(1² + 3²)
a = √10
b = √(3² + 3²)
b = 2√9
c = √(3² + 3²)
c = 2√9
d = √(1² + 3²)
d = √10
e = 4
Thus:
Perimeter = 2√10 + 4√9 + 4
Perimeter = 22.325 units
Area = 2(¹/₂ * 1 * 3) + 2(¹/₂ * 3 * 3) + (4 * 3)
= 25 square units
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A researcher wanted to estimate the difference between the percentages of users of two toothpaste who will never to switch to another toothpaste. In a sample of 450 users of credit card A taken by this researcher, 90 said they will never switch to toothpaste. In another sample of 550 users of credit card B taken by the same researcher, 80 said that they will never switch to another toothpaste. Construct a 90% confidence interval for the difference between the proportions of all users of the two toothpaste who will never switch.answer briefly
Answers
The 90% confidence interval for the difference between the proportions of all users of the two toothpaste who will never switch is (0.009, 0.101).
To construct a 90% confidence interval for the difference between the proportions of all users of the two toothpaste who will never switch, we can use the following formula:
CI = (p1 - p2) ± Zα/2 * √(p1(1-p1)/n1 + p2(1-p2)/n2)
where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and Zα/2 is the critical value from the standard normal distribution for the desired confidence level.
Plugging in the values given in the problem, we get:
p1 = 90/450 = 0.20
p2 = 80/550 = 0.145
n1 = 450
n2 = 550
α = 0.10 (since we want a 90% confidence interval, which corresponds to a significance level of 0.10)
Zα/2 = 1.645 (from the standard normal distribution table)
Substituting these values into the formula, we get:
CI = (0.20 - 0.145) ± 1.645 * √((0.20 * 0.80 / 450) + (0.145 * 0.855 / 550))
Simplifying, we get:
CI = 0.055 ± 0.046
Therefore, the 90% confidence interval for the difference between the proportions of all users of the two toothpaste who will never switch is (0.009, 0.101).
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An F test with five degrees of freedom in the numerator and seven degrees of freedom in the denominator produced a test statistic who value was 7. 46.
a. What is the P-value if the test is one-tailed?
b. What is the P-value if the test is two-tailed?
Answers
A one-tailed test has a P-value of 0.01 and a two-tailed test has a P-value of 0.053.
We must utilize the F-distribution table or calculator to address this question. The F test follows an F-distribution since it is a ratio of two variances.
a. To calculate the P-value for a one-tailed test, we must first calculate the likelihood that the F-statistic is greater than or equal to 7.46.
Using a table, we can find the area under the F-distribution curve to the right of 7.46 with 5 degrees of freedom in the numerator and 7 degrees of freedom in the denominator.
Assuming an alpha level of 0.05, we reject the null hypothesis if the P-value is less than 0.05.
For the given F-statistic of 7.46, the P-value for a one-tailed F-test with five degrees of freedom in the numerator and seven degrees of freedom in the denominator is approximately 0.01.
b. For a two-tailed test, we must calculate the likelihood of seeing an F-statistic that is 7.46 or more in either direction. This means we must calculate the area under the F-distribution curve in the distribution's two tails.
To find the p-value for a two-tailed F-test with 5 and 7 degrees of freedom and a test statistic of 7.46, we need to use an F-distribution table.
Using a table, we would look for the intersection of the row with 5 degrees of freedom and the column with 7 degrees of freedom, which gives us the critical F-value for a significance level of 0.05 (assuming equal variances in the two populations being compared). The critical F-value is 4.03.
Since the test statistic of 7.46 is greater than the critical F-value of 4.03, the p-value for the two-tailed test is less than 0.05. Specifically, the p-value is the probability of observing an F-statistic as extreme or more extreme than 7.46, which is the probability in the right tail of the F-distribution plus the probability in the left tail:
p-value = P(F > 7.46) + P(F < 1/7.46)
= 0.052 + 0.001
≈ 0.053
Therefore, the p-value for the two-tailed test is approximately 0.053.
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Lourdes Corporation's 13% coupon rate, semiannual payment, $1,000 par value bonds, which mature in 20 years, are callable 5 years from today at $1,075. they sell at a price of $1,327.36, and the yield curve is flat. assume that interest rates are expected to remain at their current level.a) What is the best estimate of these bonds' remaining life? Round your answer to two decimal places.b) If Lourdes plans to raise additional capital and wants to use debt financing, what coupon rate would it have to set in order to issue new bonds at par?
Answers
The best estimate of the remaining life of Lourdes Corporation's bonds is 14.82 years.
Lourdes Corporation would have to set a coupon rate of 10.07% to issue new bonds at par.
To find the remaining life of the bond, we need to use the formula:
Remaining Life = (ln(Par Value/Market Price)) / (2 * ln(1 + Coupon Rate/2))
Substituting the given values, we get:
Remaining Life = (ln(1000/1327.36)) / (2 * ln(1 + 0.13/2)) = 14.82 years
B. To find the required coupon rate for new bonds, we can use the formula:
Coupon Rate = (ln(Par Value/Call Price) + Yield Rate) / (2 * ln(1 + Call Price/Market Price))
Substituting the given values, we get:
Yield Rate = 0.13 (given)
Coupon Rate = (ln(1000/1075) + 0.13) / (2 * ln(1 + 1075/1327.36)) = 0.1007 or 10.07%.
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What is the probability that either event will occur?
A
B
9
9
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = [ ?]
Enter as a decimal rounded to the nearest hundredth.
Answers
The probability that either event will occur is given as follows:
P(A or B) = 0.75.
How to calculate the probability?The formula used to calculate the probability is given as follows:
P(A or B) = P(A) + P(B) - P(A and B).
The total number of events from the Venn's diagram is given as follows:
4 x 9 = 36.
Hence the probability of each outcome is given as follows:
P(A) = (9 + 9)/36 = 0.5.P(B) = (9 + 9)/36 = 0.5.P(A and B) = 9/36 = 0.25.Hence the or probability is given as follows:
P(A or B) = P(A) + P(B) - P(A and B).
P(A or B) = 0.5 + 0.5 - 0.25
P(A or B) = 0.75.
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To encourage a student in his work on rates and ratios, his teacher promises to pay him 70 cents for every correct problem he solves. However, for every problem where he gives an incorrect answer, the teacher will take 40 cents off him! Amazingly, at the end of 33 problems completed, neither owes anything to the other. So how many problems did the student solve correctly? Investigate this fully (give evidence) and clearly show how you arrive at your solution.
Answers only will be awarded O marks
Answers
The student solved 12 problems correctly.
To find out how many problems the student solved correctly, we can use the given information and set up an equation using the terms "correct problems" and "incorrect problems."
Let x represent the number of correct problems and y represent the number of incorrect problems. We know the following:
1. The total number of problems completed is 33, so x + y = 33.
2. The teacher pays 70 cents for correct problems and takes 40 cents for incorrect problems, and neither owes anything to each other. So, 70x - 40y = 0.
Now, we'll solve this system of equations step-by-step:
Step 1: Solve the first equation for x: x = 33 - y.
Step 2: Substitute the expression for x in the second equation: 70(33 - y) - 40y = 0.
Step 3: Simplify and solve for y: 2310 - 70y - 40y = 0 => 2310 - 110y = 0 => y = 21.
Step 4: Substitute the value of y back into the equation for x: x = 33 - 21 => x = 12.
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If fourteen less than the square of a number is 182, what’s the number?
Answers
14^2 = 196
196-14=182
The current that flows through an electrical circuit is inversely proportional to the resistance of that circuit. When the resistance R is 200 ohms, the current I is 1. 2 amperes. Find the current when the resistance is 90 ohms. (Include units in your answer. More information. Round your answer to one decimal place. )
I =
Answers
When current is inversely proportional to the resistance in a circuit, the current when the resistance is 90 ohms is equals to 0.540 Ampere.
In an electrical circuit, the current is inversely proportional to the resistance.
Resistance = 200 ohms
Current = 1.2 ampere
If resistance is 90 ohms then we have to determine the value of current. According to condition, I = kR ,
where, I --> current
k --> constant of Proportionality
R--> resistance
Now, the proportionality constant, k = I/R
=> k = 1.2/200
=> k = 0.006
So, value of current when resistance R = 90 ohms, for this plug in above equation,
=> I = 0.006 × 90
= 0.540
Hence, required value is 0.540 ampere.
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What is the equation of the following line? Be sure to scroll down first to see
all answer options.
O A. y=-¹1-x
OB. y = 2x
OC. y = 4x
O D. y = ¹/x
O E. y = -2x
F. y=x
(-4,8)
-10
10
-10-
(0,0)
10
Answers
The equation of the following line include the following: E. y = -2x .
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (8 - 0)/(-4 - 0)
Slope (m) = 8/-4
Slope (m) = -2.
At data point (-4, 8) and a slope of -2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 8 = -2(x + 4)
y - 8 = -2x - 8
y = -2x
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Armando has a credit card that uses the adjusted balance method. For the first 10 days of one of his 30-day billing cycles, his balance was $2500. He then made a payment of $1600, so his balance decreased to $900, and it remained that amount for the next 10 days. Armando then made a purchase for $1300, so his balance for the last 10 days of the billing cycle was $2200. If his credit card's APR is 33%, how much was Armando charged in interest for the billing cycle?
Answers
Armando was charged approximately $5.08 in interest for the billing cycle.
To calculate the interest charged for the billing cycle, we need to find the average daily balance (ADB) and then multiply it by the daily periodic rate (DPR) and the number of days in the billing cycle. For a credit card that uses the adjusted balance method, the ADB is calculated as the sum of the balances on each day in the billing cycle divided by the number of days in the cycle.
To find the balance on each day in the billing cycle, we need to divide the cycle into three periods: the first 10 days, the next 10 days, and the last 10 days.
During the first 10 days, the balance was $2500, so the total balance for this period was:
10 * $2500 = $25000
During the next 10 days, the balance was $900, so the total balance for this period was:
10 * $900 = $9000
During the last 10 days, the balance was $2200, so the total balance for this period was:
10 * $2200 = $22000
The total balance for the entire billing cycle was:
$25000 + $9000 + $22000 = $56000
The number of days in the billing cycle is 30, so the ADB is:
ADB = $56000 / 30 = $1866.67
The DPR can be calculated by dividing the APR by the number of days in the year:
DPR = 0.33 / 365 = 0.00090411
Finally, we can calculate the interest charged for the billing cycle by multiplying the ADB by the DPR and the number of days in the billing cycle:
Interest = ADB * DPR * Days
Interest = $1866.67 * 0.00090411 * 30
Interest ≈ $5.08
Therefore, Armando was charged approximately $5.08 in interest for the billing cycle.
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46. A factory produces a particular make of flat screen television at a rate of 3 per day on average. The number produced in a week has a Poisson distribution. Find the probability that (a) no flat screen television was produced on a particular day, (b) there are at most nine flat screen televisions produced in 3 days. (c) If the production line only functions 8 hours a day, what is the probability that more than one flat screen television will be produced in 2 hours? (answer: (a) 0.0498, (b) 0.5874, (c) 0.17336)
Previous question
Answers
The probability that more than one flat screen television will be produced in 2 hours is 0.2642.
(a) To find the probability that no flat screen television was produced on a particular day, we can use the Poisson distribution formula:
P(X = 0) = (e^(-λ) * λ^0) / 0!
where λ is the average number of flat screen televisions produced per day, which is 3 in this case.
P(X = 0) = (e^(-3) * 3^0) / 0! = 0.0498 (rounded to four decimal places)
Therefore, the probability that no flat screen television was produced on a particular day is 0.0498.
(b) To find the probability that there are at most nine flat screen televisions produced in 3 days, we can use the cumulative Poisson distribution formula:
P(X ≤ 9) = ∑(k=0 to 9) [(e^(-λ) * λ^k) / k!]
where λ is the average number of flat screen televisions produced per day, which is 3 in this case. To find the probability for 3 days, we need to multiply λ by 3.
P(X ≤ 9) = ∑(k=0 to 9) [(e^(-9) * 9^k) / k!] = 0.5874 (rounded to four decimal places)
Therefore, the probability that there are at most nine flat screen televisions produced in 3 days is 0.5874.
(c) If the production line only functions 8 hours a day, we can adjust λ accordingly. Since there are 24 hours in a day and the production line is functioning for 8 hours, the average number of flat screen televisions produced in 2 hours would be λ/3.
So, the new λ would be 3/3 = 1.
To find the probability that more than one flat screen television will be produced in 2 hours, we can use the Poisson distribution formula:
P(X > 1) = 1 - P(X ≤ 1)
P(X ≤ 1) = (e^(-1) * 1^0) / 0! + (e^(-1) * 1^1) / 1! = 0.7358 (rounded to four decimal places)
P(X > 1) = 1 - 0.7358 = 0.2642 (rounded to four decimal places)
Therefore, the probability that more than one flat screen television will be produced in 2 hours is 0.2642.
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Which of the following problem types can always be solved using the law of sines? Check all that apply.
Answers
Answer:
A, C, E
Step-by-step explanation:
remember to law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
or the "upside-down" version :
sin(A)/a = sin(B)/b = sin(C)/c
with a, b, c being the sides of the triangle, and A, B, C being the corresponding opposite angles in the triangle.
so, as you can clearly see, we always need at least one angle and one side (in fact either 2 angles one side or 1 angle 2 sides) to use the law of sine to solve the rest of the triangle.
therefore, the answer options A, C, E are correct.
for SSS (all 3 sides are known) we need the law of cosine to solve the angles (at least one of them, and then we could continue with either law).
remember :
c² = a² + b² - 2ab×cos(C)
again, a,b,c are the sides, and C is the opposite angle of whatever side we define as "c".
that's why I always call this the extended Pythagoras.
for AAA (all 3 angles are known) we cannot solve the triangle, because dilated triangles all have the same angles. and therefore there are infinitely many triangles with the same angles.
A corporation has 30 manufacturing plants. Of these, 23 are domestic and 7 are located outside of the country. Each year a performance evaluation is conducted for 4 randomly selected plants. What is the probability that the evaluation will include no plants outside the country? What is the probability that the evaluation will include at least 1 plant outside the country? What is the probability that the evaluation will include no more than 1 plant outside the country? The probability is. (Round to four decimal places as needed.) The probability is. (Round to four decimal places as needed.) The probability is. (Round to four decimal places as needed.)
Answers
The probabilities are:
(a) P(X = 0) ≈ 0.3139
(b) P(X ≥ 1) ≈ 0.6861
(c) P(X ≤ 1) ≈ 0.9862
We can model this situation using the hypergeometric distribution.
Let's define:
N = total number of manufacturing plants = 30
D = number of plants outside the country = 7
n = number of plants in the performance evaluation = 4
(a) Probability of including no plants outside the country:
We want to find P(X = 0), where X is the number of plants outside the country in the performance evaluation. This can be calculated using the hypergeometric distribution formula:
P(X = 0) = (C(23, 4) * C(7, 0)) / C(30, 4) = (23 choose 4) / (30 choose 4) ≈ 0.3139
(b) Probability of including at least 1 plant outside the country:
We want to find P(X ≥ 1). We can use the complement rule and find the probability of including no plants outside the country and subtract it from 1:
P(X ≥ 1) = 1 - P(X = 0) = 1 - (C(23, 4) * C(7, 0)) / C(30, 4) ≈ 0.6861
(c) Probability of including no more than 1 plant outside the country:
We want to find P(X ≤ 1). This can be calculated as the sum of P(X = 0) and P(X = 1):
P(X ≤ 1) = P(X = 0) + P(X = 1) = (C(23, 4) * C(7, 0)) / C(30, 4) + (C(23, 3) * C(7, 1)) / C(30, 4) ≈ 0.9862
Therefore, the probabilities are:
(a) P(X = 0) ≈ 0.3139
(b) P(X ≥ 1) ≈ 0.6861
(c) P(X ≤ 1) ≈ 0.9862
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An orange cone has a volume of 376.8 cubin cm and a radius of 6 cm. What is the height?
Answers
Answer:
3.29 cm.
Step-by-step explanation:
The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
Substituting the given values, we get:
376.8 = (1/3)π(6^2)h
Simplifying:
376.8 = 36πh
h = 376.8 / (36π)
h ≈ 3.29 cm
Therefore, the height of the orange cone is approximately 3.29 cm.
18. Suppose that the experimenter uses the sums of squares for all 4 of the interaction terms as an estimate of an error sum of square. The error mean square would then be a. 3.45 b. 2.71 c. 3.00 d. 2.95
Answers
The error mean square would then be given by the term of 2.71 which is option B.
In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally.
The three most often employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to get the mean. When all of the values are organised in ascending order, the Median is the median value of the provided data.
Suppose that the experimenter uses the sums of squares for all 4 of the interaction terms as an estimate of an error sum of square. The error mean square would then be 2.71
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