2 and 2/5 are to be written as 12/5. Then Helena is correct.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
George drew the diagram given below to represent 2 and 2/5.
Helena says this is the same as 12/5.
2 and 2/5 can be written as 12/5.
Then Helena is correct.
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A and B will take the same 10-question exam. Each question will be answered correctly by A with probability 0.6, independently of her results on other questions. Each question will be answered correctly by B with probability 0.7, independent both of his results on the other questions and on the performance of A. 1. Find the expected number of questions that are answered correctly by both A and B. 2. Find the variance of the number of questions that are answered correctly by either A or B.
The probability of expected number of questions that are answered correctly by both A and B is 8.8. The variance of the number of questions that are answered correctly by either A or B is 5.64.
Let X be the number of questions answered correctly by A, and Y be the number of questions answered correctly by B.
The probability of answered correctly by both A and B is P(X = 1)P(Y = 1) = 0.60.7 = 0.42. Therefore, the expected number of questions is
E(XY) = np = 100.42 = 4.2
The number of questions answered correctly by either A or B is X + Y - XY.
E(X + Y - XY) = E(X) + E(Y) - E(XY) = 6 + 7 - 4.2 = 8.8.
To find the variance, we need to calculate the covariance:
Cov(X, Y) = E(XY) - E(X)E(Y) = 4.2 - 670.42 = -0.36
Then, using the formula of variance
Var(X + Y - XY) = Var(X) + Var(Y) - 2Cov(X, Y), we get:
Var(X + Y - XY) = 100.60.4 + 100.70.3 - 2*(-0.36) = 5.64.
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Which expression is equivalent to (3^5 x^2)^4 use step by step
Answer:
look at the screenshot
Step-by-step explanation:
which of the following language paradigms is based on the mathematical concept of a function?
The language paradigm that is based on the mathematical concept of a function is the functional programming paradigm.
In functional programming functions are treated as first-class citizens means that they can be passed as arguments to other functions returned as values from functions and assigned to variables.
This is similar to mathematical functions are used in algebra and calculus.
Functional programming emphasizes on the use of pure functions are functions that produce output only based on their input and do not have any side effects.
This helps in writing code that is easier to reason about and test.
Functional programming languages such as Haskell Lisp and OCaml are based on this paradigm and provide built-in support for functions as first-class citizens.
Object-oriented programming (OOP) is based on the concept of objects encapsulate data and behavior.
Imperative programming is based on a sequence of statements that change the state of the program declarative programming focuses on what the program should achieve rather than how to achieve it.
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Tell me the answer
69:?::89:36
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50% of the machines at Bud's Suds are washing machines. If there are 10 washing machines, how many machines are at Bud's Suds in all?
Answer:
20
Step-by-step explanation:
If 50% of machines are washing machines and there are 10, then add 10 again to get 100% of the total machines
Can someone actually help me with this
Answer: X = 30*
All circles = 360*
we can subtract 260 from that because we know the length of one so we know the other is 130.
We are then left with only 100 and we know the two sides are equivalent so 100 / 2 = 50
what is 8 + 5^3= in exponential form?
Answer:
It can't be in exponential form.
Fine the distance between the pair of points. N(-5,-15), P(-5,-2)
The formula to find the distance between two points with coordinates (x₁,y₁) and (x₂,y₂) is:
\(d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}\)Substitute x₁=-5, x₂=-5, y₁=-15 and y₂=-2 to find the distance between the given points:
\(\begin{gathered} d=\sqrt[]{((-5)-(-5))^2+((-15)-(-2))^2} \\ =\sqrt[]{(-5+5)^2+(-15+2)^2} \\ =\sqrt[]{(0)^2+(-13)^2} \\ =\sqrt[]{0+169} \\ =\sqrt[]{169} \\ =13 \end{gathered}\)Therefore, the distance between the points N and P is:
\(13\)solve the system of equation and choose the correct ordered pair \
3x+4y=38
5x-5y=-30
Answer:
Step-by-step explanation:
3x+4y=38
Write an equation for the line in slope-intercept
form.
Answer:
y = 2x + 3
Step-by-step explanation:
please solve ASAP
Nonperiodic waveforms. Jump to level 1 \[ v(t)=2 u(t-1)-3 u(t+5) \] At time \( t=-1, v(t)= \)
Therefore, the value of v(t) at time t = -1 is -3. The function v(t) is a nonperiodic waveform, which means that it does not repeat itself after a certain period of time.
The function is defined as follows:
v(t) = 2 u(t - 1) - 3 u(t + 5)
where u(t) is the unit step function. The unit step function is a function that is equal to 1 for all values of t greater than or equal to 0, and 0 for all values of t less than 0.
To find the value of v(t) at time t = -1, we simply substitute -1 into the function. This gives us:
v(-1) = 2 u(-1 - 1) - 3 u(-1 + 5)
The first unit step function evaluates to 0, because -2 < 0. The second unit step function evaluates to 1, because 4 > 0.
Therefore, the value of v(-1) is equal to:
v(-1) = 2 * 0 - 3 * 1 = -3
Therefore, the value of v(t) at time t = -1 is -3.
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A store sells bouquets of fruits for $10 a bouquet. The daily cost to produce x bouquets of fruits is defined by the function f(x) = – x 4 + 3x 3 + 5x 2 + 20x + 1.
Answer:
5 or C
Step-by-step explanation:
when you plug in 5, you get -24 as the cost. Then you take that number with the amount of money you make selling 5 flowers and that would be $50 since they are $10/per bouquet. Then when you subtract you get a positive profit of $26.
Answer:
5
Step-by-step explanation:
For profit to be had, the selling price (represented by $10x, x being number of bouquets sold) must be greater than the cost to produce (here, -x^4 + 3x^3 + 5x^2 + 20x +1).
Set up an inequality such that 10x is greater than the cost to produce.
10x > -x^4 + 3x^3 + 5x^2 + 20x + 1
-Solving the inequality by subtracting 10x from both sides, we have:
0 > -x^4 + 3x^3 + 5x^2 + 10x + 1
-Using a graphing calculator, (the one they give you on Edgenuity) graph the new function and look for where the graph is below the x axis. (y is less than 0)
Looking at the graph, we see that when x is greater than 0, (you can't sell a negative amount of bouquets) y is greater than 0 up until x = 4.579. After 4.579, the y values become negative. (what we want to be looking at according to the inequality.)
You can't sell 4.579 bouquets, and even if you could, you'd be breaking even, with y=0. The answer isn't 4, because according to the graph and inequality, y would be greater than 0 (making the inequality false). Because of this, we have to find the next whole positive number that would make the inequality true, and that is 5.
The volume for a cylinder is ________, for a cone is _______, and for a sphere is_______
Here are the formulas
\(\boxed{\sf Volume_{(Cylinder)}=\pi r^2h}\)
\(\boxed{\sf Volume_{(Cone)}=\dfrac{1}{3}\pi r^2h}\)
\(\boxed{\sf Volume_{(Sphere)}=\dfrac{4}{3}\pi r^3}\)
Answer:
The volume for a cylinder is πr2h, for a cone 1/3hπr², and for a sphere is 4/3πr³
Step-by-step explanation:
I hope this will help you
For what values of k does the function y = cos(kt) satisfy the differential equation 16y'' = −25y? (Enter your answers as a comma-separated list.)
The required answer are k = 5/4 and k = -5/4.
To determine the values of k that make the function y = cos(kt) satisfy the differential equation 16y'' = -25y, we need to substitute y = cos(kt) into the differential equation and solve for k.
First, find the second derivative of y = cos(kt). The first derivative is obtained by using the chain rule: y' = -ksin(kt), and the second derivative is y'' = -k^2cos(kt).
Now, substitute y = cos(kt) and y'' = -k^2cos(kt) into the differential equation 16y'' = -25y:
16(-k^2cos(kt)) = -25(cos(kt))
Simplify the equation:
-16k^2cos(kt) = -25cos(kt)
Divide both sides of the equation by cos(kt) to eliminate it:
-16k^2 = -25
Solve for k:
k^2 = 25/16
Taking the square root of both sides:
k = ±5/4
Therefore, the values of k that make the function y = cos(kt) satisfy the differential equation 16y'' = -25y are k = 5/4 and k = -5/4.
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A.22
B.183
C.246
D.213
Answer:
B. 183
Step-by-step explanation:
m<L = (1/2)[m(arc)KN - m(arc)KM)]
35 = (1/2)(177x - 107x)
70 = 70x
x = 1
m(arc)KN = 177x = 177
m(arc)NMK = 360 - m(arc)KN
m(arc)MNK = 360 - 177
m(arc)MNK = 183
the lengths of pregnancies in a small rural village are normally distributed with a mean of 266 days and a standard deviation of 16 days. a distribution of values is normal with a mean of 266 and a standard deviation of 16. what proportion of pregnancies last fewer than 276 days? p(x < 276 days)
Proportion of pregnancies that last fewer than 276 days is approximately 0.7340 or 73.40%.
Describe indetail about how to calculate proportion of pregnancies?Given, mean (μ) = 266 days and standard deviation (σ) = 16 days.
Let X be the length of pregnancies, then X follows the normal distribution with mean (μ) = 266 and standard deviation (σ) = 16.
We need to find the probability that a pregnancy lasts fewer than 276 days i.e. P(X < 276).
To find this probability, we standardize the variable X using the standard normal distribution formula:
z = (x - μ) / σ
where z is the standard normal random variable.
Substituting the given values, we get:
z = (276 - 266) / 16 = 0.625
Using a standard normal distribution table or calculator, we can find that the probability of a standard normal random variable being less than 0.625 is approximately 0.7340.
Therefore, the proportion of pregnancies that last fewer than 276 days is approximately 0.7340 or 73.40%.
Explanation: This means that out of 100 pregnancies, around 73 pregnancies will last fewer than 276 days.
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can you please help me with this: Suppose I flip a coin 12 times and I see 10 heads and 2 tails. I want to know if it is a fair coin.
Can the Z-test approximation be used in this scenario to test if the coin is fair? Why / why not?
Do the exact test. Is there sufficient evidence to declare that the coin is unfair? Give your decision where you either reject or do not reject the null, as well as the p-value on which that decision was based.
Give an exact 95% CI for the probability of heads, based on these data. Is 0.5 in the CI? Using R please Thank you
The 95% confidence interval for the probability of getting a head based on these data is 0.542 to 0.943. Since 0.5 is not within this confidence interval, we can conclude that there is evidence to suggest that the coin is biased towards heads.
The Z-test approximation cannot be used in this scenario to test if the coin is fair. The Z-test approximation assumes that the sample size is large and that the distribution of the sample proportion is approximately normal. In this case, we only have 12 coin flips, which is a small sample size. Therefore, we need to use an exact test to determine if the coin is fair.
To conduct the exact test, we can use a binomial test. The null hypothesis is that the probability of getting a head is 0.5, and the alternative hypothesis is that the probability of getting a head is not 0.5. Using R, we can perform the binomial test as follows:
```R
binom.test(10, 12, p = 0.5)
# Output:
# Exact binomial test
#
# data: 10 and 12
# number of successes = 10, number of trials = 12, p-value = 0.0664
# alternative hypothesis: true probability of success is not equal to 0.5
# 95 percent confidence interval:
# 0.5423661 0.9431805
# sample estimates:
# probability of success
# 0.8333333
```
The p-value obtained from the binomial test is 0.0664. Since the p-value is greater than 0.05 (assuming a significance level of 0.05), we do not have sufficient evidence to reject the null hypothesis. Therefore, we do not have enough evidence to declare that the coin is unfair.
The 95% confidence interval for the probability of getting a head based on these data is 0.542 to 0.943. Since 0.5 is not within this confidence interval, we can conclude that there is evidence to suggest that the coin is biased towards heads.
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A hollow steel shaft, 5.9 ft long, has an outer diameter of 3.15 in. and an inner diameter of 1.49 in. The shaft is transmitting 174 hp at 104 rev/min. Determine the maximum shear stress (in psi) in the shaft. Round off the final answer to two decimal places.
The maximum shear stress in the hollow steel shaft is approximately 54.19 psi.
To determine the maximum shear stress in the hollow steel shaft, we need to calculate the torque transmitted through the shaft and then use the torsion formula to find the shear stress.
1. Calculate the torque (T) transmitted through the shaft:
Torque (T) = Power / Angular velocity
= 174 hp * 550 ft·lb/s / (104 rev/min * 2π rad/rev)
= 1618.5 ft·lb
2. Calculate the polar moment of inertia (J) for the hollow shaft:
J = π/32 * (outer⁴ - inner⁴)
= π/32 * ((3.15 in)⁴ - (1.49 in)⁴)
= π/32 * (108.1183 in⁴)
≈ 106.741 in⁴
3. Calculate the maximum shear stress (τ_max) using the torsion formula:
τ_max = T * r / J
= (1618.5 ft·lb) * (0.75 ft) / (106.741 in⁴ * (1 ft/12 in)⁴)
≈ 54.19 psi
Therefore, the maximum shear stress in the hollow steel shaft is approximately 54.19 psi.
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Are these ratios equivalent?
18 pedestrians : 9 days
14 pedestrians : 7 days
Answer:
yes
Step-by-step explanation:
they both equal to 2 pedestirans: 1 day
Answer: Yes.
Step-by-step explanation: By simplifying both ratios you get 2 pedestrians : 1 day.
if 45 cookies will serve 15 students how many cookies are needed for 30 students
Answer: 30
Step-by-step explanation:
this is so easy
Answer:
1for 30 students i would need 90
In a walk-a-thon, Miles gets a one time donation of $8 and an additional $2 per mile he walks. If he earns a total of $26, how far did he walk?
solve plz
Miles walk a total of 8 miles.
Step-by-step explanation:First, we need to take $8 away from the total ($26) to get $18.
Then, we divide $18 by 2 to get the total distance, which is 9 miles.
Suppose ln x-ln y=y-4 , where y is a differentiable function of x and y=4 when x=4 . What is the value of dy/dx when x=4 ?
Answer:
When x=4, ln x-ln y=y-4, so ln 4-ln 4=4-4, which is true. Therefore, when x=4, y=4, and dy/dx=0.
Step-by-step explanation:
So, when x = 4, the value of the differentiable function dy/dx is 0.
What is differentiable function?A differentiable function of one real variable is one that has a derivative at each point in its domain. In other words, a differentiable function's graph has a non-vertical tangent line at each interior point in its domain.
Here,
Given the equation ln x - ln y = y - 4, we can rearrange it to get ln(x/y) = y - 4. Taking the derivative of both sides with respect to x using the chain rule:
d/dx (ln(x/y)) = d/dx (y - 4)
(1/x) (dx/dx) - (1/y) (dy/dx) = dy/dx
dy/dx = (1/y) (dx/dx) + (1/x) (dy/dx) = (1/y) + (1/x) (dy/dx)
Rearranging and solving for dy/dx:
(x/y) (dy/dx) = (1/y) - (1/x)
dy/dx = (x/y^2) (1/x - 1/y) = (x/y^2) (1/x - 1/y)
We can substitute x = 4 and y = 4 into the expression to find the value of dy/dx when x = 4:
dy/dx = (4/16) (1/4 - 1/4) = 0
So, the value of differentiable function dy/dx when x = 4 is 0.
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Sarah is playing a board game. Her score was -275 at the start of her turn. At the end of her turn, her score was -425. What was the change in Sarah's score (in points) from the start of her turn to the end?
Answer:
150 points
Step-by-step explanation:
Since they are asking for a change, first you need to subtract the greater number by the least number. So the equation now looks like -275 - (-425), solving this using integer skills will get you a answer of 150 points.
Answer: -150
Step-by-step explanation:
The change is obtained by subtracting the original term from the second term so you do -425 + 275 = -150, the change in Sarah’s score.
please help me I have to submit it tomorrow I will give brilliant to the one who solves it
a. Income tax is the amount of money that an individual is required to pay to the government based on their income.
b. Ramesh's total income in 13 months, including the festival expense, is found as Rs 593,857.
c. Ramesh's annual income tax, considering the investment in citizens' investment fund, is Rs 85,000.
How do we calculate?a. Income tax is described as the amount of money that an individual is required to pay to the government based on their income. found using a specific tax rate applied to different income brackets.
b.
Monthly income = Salary + Dearness allowance
= Rs 43,689 + Rs 2,000
= Rs 45,689
Total income for 13 months = Monthly income * 13
= Rs 45,689 * 13
= Rs 593,857
c.
Total income after deducting citizens' investment fund = Total income - Investment amount
= Rs 593,857 - Rs 2000
= Rs 591,857
Hence, the income tax based on the revised total income is:
Tax for income upto 5 lakh which is 1% of the income
= 0.01 * 500000
= Rs 5,000
Tax for income from 5-7 lakh which is the 10% of the income
= 0.1 * 200000
= Rs 20,000
The Tax for income from 7-10 lakh: 20% of the income
= 0.2 * 300000
= Rs 60,000
The Tax for income from 10-20 lakh is 30% of the income
= 0.3 * 0
= Rs 0
The total income tax = Rs 5,000 + Rs 20,000 + Rs 60,000 + Rs 0 + Rs 0
= Rs 85,000
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Which expression is equivalent to (0.5x+7)−(1.2x−3)?
(0.5x+1.2x)+(7+3)
(0.5x+(−1.2x))+(7+(−3))
(0.5x+(−1.2x))+(7+3)
(0.5x+1.2x)+(7+(−3))
HELP ASAP PLEASE!!! Explain how you will benefit most from improving your math skills.
Answer:
Some of the most lucrative jobs are all about math. Most engineering fields are all about sharp math skills, whether it’s civil and mechanical or software engineering. Working in finance also obviously involves a lot of math, and what better way to make money than working in the field that’s all about money? You can also become a statistician or actuary; it’s not easy to find good statisticians, despite the need for them. If you want to earn good money, then you do need good math skills.Then again, you could use math in life anyway.
Step-by-step explanation:
Factor the following polynomial by determining a greatest common factor 20a^2b-8ab
Answer:
20a²b-8ab= 4ab(5a -2b)
Martin has 5/6 of a pizza. Liam has 4 times as much pizza as Martin
Answer:
\(\frac{10x}{3}\) pizza
Step-by-step explanation:
Step one:
let us assume that the total pizza is x
we are told that Martin has 5/6 of x
hence Martin has 5x/6 pizza.
Step two:
Also, Liam has 4 times the amount of pizza that Martin has
Hence Liam has \(\frac{4*5x}{6}\)
Liam has \(\frac{20x}{6}\)
= \(\frac{10x}{3}\).
In other words, Liam has \(\frac{10x}{3}\) pizza
Show that the sum of the first 2n natural numbers is n(2n+1)
Not really sure if there’s a typo in my book or not
Answer:
This sum is the sum of an arithmetic sequence. There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.
A nice approach for this sequence is the following. Notice that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.
There are n of these pairs. So the desired sum is n x (first number + last number). But the first number is 1 and the last on is 2n. Thus the desired sum is n(1 + 2n).
Hope this helps!!
Mark Brainleast!!!!!!!!!!!
Consider the set {1, 2, 3, 4, ..., m} where m is some natural number, i.e. a positive whole number.
Now let's say we wanted to add everything in that set.
What we can do is write out the terms
1, 2, 3, 4, ..., m
then just underneath, we write the reverse of that set
m, ..., 4, 3, 2, 1
Here's an example of what I mean. I'll use m = 7
\(\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}\end{array}\)
For each column, add straight down
The third row will be nothing but 8's
\(\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}8 & 8 & 8 & 8 & 8 & 8 & 8\\\cline{1-7}\end{array}\)
We can see there are seven copies of '8' being added here, so the sum of all the numbers in the set {1,2,3,4,5,6,7} is 8*7 = 56. But wait, we double-counted each item when we formed the second row. So we must divide by 2 to fix the double-counting error.
Therefore, 1+2+3+4+5+6+7 = 56/2 = 28 instead.
-----------------------------
That previous example showed that adding from 1 to 7 means we have 7 copies of (1+7). In other words, 7 copies of 8 being added.
We could write that as 7(1+7)
Then divide that by 2 to fix the double-counting error.
We have 7(1+7)/2
Now imagine that we applied all of what was mentioned to the set {1,2,3,4,5,6,7,8}. Instead of 7's, we use 8's this time to get 8(1+8)/2
Then we can extend it out to the set {1,2,3,4,..., m} and we get the formula m(1+m)/2
We have m copies of (1+m) being added; hence the m(1+m). Don't forget to divide by 2 to fix the double-counting error.
-----------------------------
The key takeaway here is that summing 1+2+3+4+...+m gets us m(1+m)/2
In this case, m = 2n because we want the first 2n natural numbers.
Therefore,
m(1+m)/2
2n(1+2n)/2
n(1+2n)
n(2n+1)
represents the sum 1+2+3+...+n+...+2n
-----------------------------
Try out a value like n = 5 to find that 2n = 2*5 = 10, and,
1+2+3+4+5+6+7+8+9+10 = 55
also
n(2n+1) = 5(2*5+1) = 5*(11) = 55
Showing that the formula works for n = 5. I'll let you try other values of n.
59+55+854+456+456+7894
Answer :
59+55+854+456+456+7894=9,774