a) The value of f(x) is 1/51, for 193 ≤ x ≤ 244
b) The mean is 218.5
c) σ = = 17.65
d) P(x > 227) = 0.333
e) P(202 ≤ x ≤ 219) = 0.333
f) P(x ≤ 222) = 0.569
We have,
a)
Since the distribution is uniform, the probability density function (PDF) is constant within the range [193, 244] and zero elsewhere.
The PDF is given by:
f(x) = 1 / (244 - 193) = 1/51, for 193 ≤ x ≤ 244
b)
The mean of a uniform distribution is the average of the minimum and maximum values, so we have:
mean = (193 + 244) / 2 = 218.5
c)
The standard deviation of a uniform distribution is given by:
σ = (b - a) / √12
where a and b are the minimum and maximum values, respectively. Substituting in the values given, we get:
σ = (244 - 193) / √12 = 17.65
d)
The probability of x > 227 is the area under the PDF to the right of x = 227. Since the PDF is constant, this is simply the proportion of the total range that lies to the right of 227:
P(x > 227) = (244 - 227) / (244 - 193) = 17 / 51 ≈ 0.333
e)
The probability of 202 ≤ x ≤ 219 is the area under the PDF between x = 202 and x = 219. This is:
P(202 ≤ x ≤ 219) = (219 - 202) / (244 - 193) = 17 / 51 ≈ 0.333
f)
The probability of x ≤ 222 is the area under the PDF to the left of x = 222. This is:
P(x ≤ 222) = (222 - 193) / (244 - 193) = 29 / 51 ≈ 0.569
Thus,
a) f(x) = 1/51, for 193 ≤ x ≤ 244
b) mean = 218.5
c) σ = = 17.65
d) P(x > 227) = 0.333
e) P(202 ≤ x ≤ 219) = 0.333
f) P(x ≤ 222) = 0.569
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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 53.9 for a sample of size 24 and standard deviation 5.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.
_______ < μ < _________ please teach using calculator method
We can be 90% confident that the true mean reduction in systolic blood pressure for the population is between 51.433 and 56.367.
To estimate the confidence interval for the true mean reduction in systolic blood pressure, we can use the formula:
CI = X ± Zα/2 * (σ/√n)
where X is the sample mean, Zα/2 is the critical value of the standard normal distribution for a given level of confidence (α), σ is the population standard deviation, and n is the sample size.
In this case, X = 53.9, σ = 5.6, n = 24, and we want a 90% confidence interval, so α = 0.1 and Zα/2 = 1.645 (using a standard normal distribution table or calculator).
Substituting the values, we get:
CI = 53.9 ± 1.645 * (5.6/√24)
CI = 53.9 ± 2.467
CI = (51.433, 56.367)
Therefore, we can be 90% confident that the true mean reduction in systolic blood pressure for the population is between 51.433 and 56.367.
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understand subtraction as an unknown-addend problem. for example, subtract 10-8 by finding the number that makes 10 when added to 8.
To understand subtraction as an unknown-addend problem means to view subtraction as finding the missing number in an addition problem.
In the example given, subtracting 10-8 means finding the number that needs to be added to 8 to make 10. This is essentially an addition problem with an unknown addend.
To solve the problem, one needs to think about what number added to 8 will result in 10. This can be done by counting up from 8 until you reach 10, which is a difference of 2. Therefore, 10-8=2, and the missing number is 2.
In general, to subtract any two numbers using this method, you can start with the smaller number and count up until you reach the larger number. The difference between the two numbers is the missing addend. For example, to subtract 15-7, you would start with 7 and count up to 15, which is a difference of 8. So 15-7=8.
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A bag holds 13 marbles. 6 are blue, 2 are green, and 5 are red.
If you select two marbles from the bag in a row without replacing the first marble, what is the probability that the first marble is blue and the second marble is green?
Note: you are not replacing any marbles after each selection.
PLS SHOW ALL WORK!
The probability of selecting blue marble and green marble is 1/13.
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 which is equivalent to 100%.
Probability = sample space/total outcome
total outcome = 13
The probability of picking blue in the first pick = 6/13
since there is no replacement, the total outcome for the second pick = 12
The probability of picking green in the second pick = 2/12 = 1/6
Therefore the probability of selecting blue and green marble = 6/13 × 1/6
= 1/13
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An online poll asked: "Do you believe the Loch Ness monster exists?" Among 21,466 responses, 62% were "yes." Use a 0.10 significance level to test the claim that most people believe that the Loch Ness monster exists. How is the conclusion affected by the fact that Internet users who saw the question could decide whether to respond?
Identify the null and alternative hypotheses for this test. Choose the correct answer below.
OA H_{0} / p = 0.5 H_{1} / p > 0.5
OB. H_{0} / p = 0.5 H_{1} :p ne0.5
OC. H_{0} / p = 0.5 H_{1} / p < 0.5
OD. H_{0} / p > 0.5 H_{1} / D = 0.5
Who are more likely to respond to an online poll about the Loch Ness monster may not be representative of the general population, and may have different beliefs about its existence.
The correct answer is: H0: p <= 0.5, H1: p > 0.5
Explanation:
The null hypothesis (H0) is that the proportion of people who believe that the Loch Ness monster exists is less than or equal to 0.5. The alternative hypothesis (H1) is that the proportion is greater than 0.5.
This is a one-tailed test, since we are only interested in whether the proportion is greater than 0.5.
The fact that Internet users who saw the question could decide whether to respond may affect the conclusion of the test, as it introduces potential bias into the sample. Those who are more likely to respond to an online poll about the Loch Ness monster may not be representative of the general population, and may have different beliefs about its existence.
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Find the gradient of a line perpendicular to the longest side of the triangle formed by A(-3,4),B(5,2) and C(0,-3)
Find the gradient of a line perpendicular to the longest side of the triangle formed by A(-3,4),B(5,2) and C(0,-3)
NEED HELP ASAP!!!!!
(1)
Abe has $550 to deposit at a rate of 3%.what is the interest earned after one year?
(2)
Jessi can get a $1,500 loan at 3%for 1/4 year. What is the total amount of money that will be paid back to the bank?
(3)
Heath has $418and deposit it at an interest rate of 2%.(What is the interest after one year?)( How much will he have in the account after 5 1/2 years?)
(4)
Pablo deposits $825.50 at an interest rate of 4%.What is the interest earned after one year?
(5)
Kami deposits $1,140 at an interest rate of 6%. (What is the interest earned after one year?) (How much money will she have in the account after 4 years?)
1) Interest amount = $16.5
2) Interest amount = $4.125
3) Interest amount = $8.36
And, After 5 1/2 years;
Interest amount = $22.99
4) Interest amount = $33.02
5) Interest amount = $45.6
Now, We can simplify as;
1) Principal amount = $550
Rate = 3%
Time = 1 year
Hence, We get;
Interest amount = 550 x 3 x 1 / 100
= $16.5
2) Principal amount = $1500
Rate = 3%
Time = 1/4 year
Hence, We get;
Interest amount = 1500 x 3 x 1 / 100 x 4
= $4.125
3) Principal amount = $418
Rate = 2%
Time = 1 year
Hence, We get;
Interest amount = 418 x 2 x 1 / 100
= $8.36
And, After 5 1/2 years;
Interest amount = 418 x 11 x 1 / 100 x 2
= $22.99
4) Principal amount = $825.5
Rate = 4%
Time = 1 year
Hence, We get;
Interest amount = 825.5 x 4 x 1 / 100
= $33.02
5) Principal amount = $1140
Rate = 6%
Time = 1 year
Hence, We get;
Interest amount = 1140 x 6 x 1 / 100
= $68.4
And, After 5 4 years;
Interest amount = 1140 x 4 x 1 / 100
= $45.6
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PLEASE HELP ITS URGENT I INCLUDED THE GRAPH AND WROTE THE PROBLEM DOWN ITS THE IMAGE I HAVE ATTACHED!!!
Answer:
Ive attached a picture
Step-by-step explanation:
Which relationships have the same constant of proportionality between y and x as in the equation y=1/3x?
Therefore, any equation of the form y = kx, where k is a constant, has the same constant of proportionality as the equation y = (1/3)x.
Proportionality, equivalence between two ratios in mathematics. A and B are in the same ratio as C and D in the formula a/b = c/d. When one of a proportion's four quantities is unknown, a proportion is often built up to resolve the word problem.
According to the principle of proportionality, any incidental human casualties and property damage must not outweigh the tangible benefits to the military that may be expected from the destruction of a military objective.
The equation y = (1/3)x represents a proportional relationship between y and x with a constant of proportionality of 1/3.
Any equation of the form y = kx, where k is a constant, represents a proportional relationship between y and x with a constant of proportionality of k.
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What is the value of M?
70 is the answer
Step-by-step explanation:
A restaurant serves 10 different entrees, 6 of which contain meat. What is the ratio of vegetarian to non-vegetarian items?
Answer:
4/6 which is 2:3
Explanation:
the vegterian is 10-6=4
the non vegterian or eat meat is 6
and their ratio is 4/6
2:3
Determine Q(Q), where Q is the cubic defined by the polynomial: (1) F(X,Y,Z) = X3 + 2Y3 – 423 € Q[X,Y,Z). (2) F(X,Y,Z) = (Y + Z)3 - 2X3 € Q[X,Y,Z). 9 Hint: For (1), study the divisibility by powers of 2 of an eventual solution, once assumed to be given by integral coordinates. For (2), note that Q is not geomet- rically irreducible and study the Galois action on the irreducible components. F(X, Y, Z) = X3 + 2Y3 – 423 € Q[X, Y, Z] F(X, Y, Z) = (Y + 2)3 – 2X3 E Q[X, Y, Z].
The Q(Q) = {(a,b,c,√2a+b+c) | a,b,c ∈ Q} ∪ {(-a,b,c,-√2a+b+c) | a,b,c ∈ Q}, where Q is the cubic.
To determine Q(Q), we need to find the set of solutions to the cubic equations defined by the polynomials F(X,Y,Z) in Q[X,Y,Z].
For F(X,Y,Z) = X3 + 2Y3 – 423 € Q[X,Y,Z], we can use the fact that any integer cube is congruent to either 0, 1, or -1 modulo 9. Thus, if we assume that there exists a solution with integral coordinates, we must have X and Y both congruent to 3 modulo 9 (since 423 is congruent to 6 modulo 9). However, this leads to a contradiction when we consider the parity of Z (odd), so there are no solutions with integral coordinates. Therefore, Q(Q) = {}.
For F(X,Y,Z) = (Y + Z)3 - 2X3 € Q[X,Y,Z], we note that Q is not geometrically irreducible since the polynomial (Y+Z)3 - 2X3 can be factored as (Y+Z-√2X)(Y+Z+√2X)(Y+Z) in Q(√2X)[Y,Z]. Thus, we need to study the Galois action on the irreducible components.
The Galois group of Q(√2X)/Q is generated by the automorphism σ(√2X) = -√2X, which fixes Q and interchanges the two roots of the irreducible polynomial Y+Z-√2X. Therefore, there are two irreducible components of Q(Q), given by Y+Z-√2X = 0 and Y+Z+√2X = 0.
To find the solutions on each component, we substitute either Y+Z-√2X or Y+Z+√2X into the original equation F(X,Y,Z) = (Y + Z)3 - 2X3 € Q[X,Y,Z] and solve for X. We obtain:
- For Y+Z-√2X = 0, we have X = (Y+Z)√2/∛2. Thus, we can express the solutions as (X,Y,Z) = (a,b,c,√2a+b+c) where a, b, and c are arbitrary rational numbers.
- For Y+Z+√2X = 0, we have X = -(Y+Z)√2/∛2. Thus, the solutions can be expressed as (X,Y,Z) = (-a,b,c,-√2a+b+c) where a, b, and c are arbitrary rational numbers.
Therefore, Q(Q) = {(a,b,c,√2a+b+c) | a,b,c ∈ Q} ∪ {(-a,b,c,-√2a+b+c) | a,b,c ∈ Q}.
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define a method that recieves 2 ints as input parameters and returns true or false depending on whether or not the first nubmer is twice the second
Python Program to Find Whether a Number is a Power of Two. The function power of two is defined. It takes a number n as an argument and returns True if the number is a power of two. If n is not positive, False is returned. If n is positive, then n & (n – 1) is calculated.
To define a function that receives two numbers as input parameters and returns true or false depending on whether or not the first number is twice the second, follow these steps:
1. Define the function with a name, e.g., "is_twice," and specify the two input parameters, e.g., "num1" and "num2."
2. Inside the function, check if the first number is equal to twice the second number.
3. Return True if the condition is met; otherwise, return False.
Here's the function definition:
```python
def is _ twice (num1, num2):
if num1 == 2 * num2:
return True
else:
return False
```
Now you can call this function with two numbers as input parameters, and it will return true or false based on the condition mentioned.
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In a flower garden, there are 6 tulips for every 7 daisies. If there are 48 tulips, how many daisies are there?
Answer:
56, There are 56 daisies.
Step-by-step explanation:
Please help me with this my quiz. Thank you :)
Due tomorrow
Answer: yello
Step-by-step explanation:
Write the equation of the line perpendicular to the tangent line through (2,3)
Note that the equation of the line perpendicular to the tangent to the curve y = x³ − 3x+1 is y = (-1/9)x + 7/3.
Why is this so ?To find the equation of the line perpendicular to the tangent of the curve at the point (2, 3):
Get the slop of the tangent at that point.
To do this, we take derivative of the function y = x³ - 3x + 1 and evaluating it at x = 2:
y' = 3x² - 3
y '(2) = 3 (2) ² - 3 = 9
So the slope of (2, 3) = 9.
Since the line we are looking for is perpendicular to this tangent, its slope will be the negative reciprocal of 9, which is -1/ 9.
Next, use the point-slope form of a line to write the equation of the line
y - 3 = (-1/9) ( x - 2)
⇒ y = (-1/9)x + 7/3
So the equation of the lie perpendicular to the tangent to the curve at the point (2,3) is y = (-1/9)x + 7/3.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Find equation to the line perpendicular to the tangent to the curve y=x³−3x+1 , at the point (2,3)
.
If X is an exponential random variable with parameter λ, and c>0, show that cX is exponential with parameter λ/c.CDF Method:Let X be a continuous random variable and let Y=g(X)be a function of that random variable, where g(X) is some function of X. Let fX(x) be the probability density function (PDF) of X and fY(y) be the PDF of Y. Recall that the cumulative distribution function (CDF) of X is defined as the probability that X is less than or equal to some value x, for any real value of x. Mathematically,FX(x)=P(X≤x)Similarly, FY(y)=P(Y≤y).To find the distribution of Y, we can use the CDF method. We start by expressing the CDF of Y (FY(y)) in terms of X. We do this by using the fact that Y=g(X)and then solving the resulting inequality for X. Mathematically,FY(y)=P(Y≤y)=P(g(X)≤y)=⋯=P(X ???⋯)We isolate X in the inequality and we get an inequality which can be changed into CDF terms (the CDF of X).After we find the CDF of Y, we can differentiate it to get the PDF of Y. Recall that for any random variable, the first derivative of its CDF is equal to its PDF. In mathematical terms,fY(y)=ddyFY(y)We do this using the CDF of Y we obtained earlier. After completing this step, you will have the PDF of Y.
We have shown that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.
To show that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ, and c>0, we will use the CDF method:
1. Define the transformation: Let Y = cX be a function of the random variable X, where c > 0.
2. Find the CDF of Y: We want to find P(Y ≤ y), which is equal to P(cX ≤ y) or P(X ≤ y/c).
3. Express CDF of Y in terms of X: Since P(X ≤ y/c) is the CDF of X at y/c, we have FY(y) = FX(y/c).
4. Find the PDF of X: The exponential distribution has the PDF fX(x) = λ * exp(-λx) for x ≥ 0.
5. Differentiate the CDF of Y to find its PDF: To find fY(y), we differentiate FY(y) with respect to y. Using the chain rule, we have:
fY(y) = d(FX(y/c))/dy = fX(y/c) * (1/c)
6. Substitute the PDF of X: Now, we replace fX(y/c) with its exponential form λ * exp(-λ(y/c)):
fY(y) = (λ * exp(-λ(y/c))) * (1/c)
7. Simplify the expression: fY(y) = (λ/c) * exp(-λ(y/c))
This is the PDF of an exponential distribution with parameter λ/c. Therefore, cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.
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draw the graph of polynomial function
The graph of the polynomial function that passes through the points P(−2,2) and Q(1,0) is added as an attachment
Drawing the graph of polynomial functionFrom the question, we have the following parameters that can be used in our computation:
The graph passes through the points P(−2,2) and Q(1,0)
Assuming the graph is a linear function
So, we have
y = mx + c
Where
c = y when x = 0 and m = slope
This gives
-2m + c = 2
m + c = 0
Subtract the equations
So, we have
-3m = 2
m = -2/3
Solving for c, we have
-2/3 + c = 0
Evaluate
c = 2/3
So, the equation is f(x) = -2/3x + 2/3
See attachment for the graph
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Complete question
Draw the graph of polynomial function f(x) containing the points P(−2,2) and Q(1,0)
A serving of crackers has 1. 5 grams of fat. How many grams of fat are in 3. 85 servings
The approximately grams is 5.78 of fat in 3.85 servings of crackers. The nutritional information on food packages typically lists the amount of nutrients, including fat, in grams per serving.
We used grams in this calculation to measure the amount of fat in the serving of crackers and in the total number of servings.
To determine the grams of fat in 3.85 servings of a food item, you would need to know the amount of fat in one serving of that food and multiply it by 3.85.
For example, if one serving of the food contains 10 grams of fat, then the total amount of fat in 3.85 servings would be:
10 grams of fat/serving x 3.85 servings = 38.5 grams of fat
So, there would be 38.5 grams of fat in 3.85 servings of that food item. Please note that the actual amount of fat may vary depending on the specific food item and its nutritional content.
It's always best to refer to the nutrition label or consult a reliable source for accurate and up-to-date nutritional information
To calculate the total grams of fat in 3.85 servings of crackers, you can multiply the amount of fat in one serving by 3.85.
One serving of crackers has 1.5 grams of fat.
Total grams of fat in 3.85 servings of crackers = 1.5 grams of fat per serving x 3.85 servings
= 5.78 grams of fat.
Therefore, there are approximately 5.78 grams of fat in 3.85 servings of crackers.
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Which is a factor !!! See picture below
Answer: A: (x+3)
Step-by-step explanation:
Lets simplify this first:
[tex]2x^2 + 2x - 12[/tex]
[tex]2(x^2 + x - 6)[/tex]
we can factor this into:
[tex]2(x+3)(x-2)[/tex]
so, from the options, we can see that option A is correct.
Help me solve this please and thanks!
Answer:
9 x 9 x 9
Step-by-step explanation:
its obvious
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 3
2 3
3 10
4 9
5 6
6 3
Determine the probability that a student studied for exactly 5 hours. Round to the nearest hundredth.
0.83
0.21
0.17
0.14
The probability that a student studied for exactly 5 hours is 0.17. (third option)
What is the probability?Probability calculates the chances that an event would happen. The probability the event occurs with certainty is 1 and the probability that the event would not occur with certainty is 0. The more likely the event is to happen, the closer the probability value would be to 1.
Probability that a student studied for exactly 5 hours = number of students that studied for 5 hours / total students surveyed
= 6 / 35 = 0.17
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The length of a cell phone is
1.4
1.4 inches and the width is
4.4
4.4 inches. The company making the cell phone wants to make a new version whose length will be
1.96
1.96 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
The width of the new phone is 6.16 inches.
How to find the width of the new phone?The length of a cell phone is 1.4 inches and the width is 4.4 inches. The company making the cell phone wants to make a new version whose length will be 1.96 inches.
The side length of the new phone are proportional to the old phone. Therefore, the width of the new phone can be calculated as follows:
let
x = width of the new phone
1.4 / 1.96 = 4.4 / x
cross multiply
1.4x = 4.4 × 1.96
1.4x = 8.624
divide both sides by 1.4
x = 8.624 / 1.4
x = 6.16
Therefore,
width of the new phone = 6.16 inches
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The weekly sales of Honolulu Red Oranges is given by
q = 1040 - 20р.
Calculate the price elasticity of demand when the price is $32 per orange
The price elasticity of demand when the price is $32 per orange is 2
To calculate the price elasticity of demand, we need to use the formula:
E = (%Δq / %Δp) x (p/q)
where E is the price elasticity of demand, %Δq is the percentage change in quantity demanded, %Δp is the percentage change in price, and p/q is the average price-quantity ratio.
Given that the weekly sales of Honolulu Red Oranges is given by q = 1040 - 20p, we can find the derivative of q with respect to p as follows:
dq/dp = -20
This tells us that for every $1 increase in price, the quantity demanded will decrease by 20 units.
At a price of $32 per orange, the quantity demanded is:
q = 1040 - 20(32) = 424
If the price were to increase to $33 per orange, the new quantity demanded would be:
q' = 1040 - 20(33) = 404
Using these values, we can calculate the percentage changes in price and quantity demanded as:
%Δp = [(33 - 32) / 32] x 100% = 3.125%
%Δq = [(404 - 424) / 424] x 100% = -4.72%
The average price-quantity ratio is:
(p+ p')/2q = [(32 + 33)/2]/424 = 0.015
Now we can calculate the price elasticity of demand as:
E = (%Δq / %Δp) x (p/q) = (-4.72 / 3.125) x 0.015 = -0.023
Since the price elasticity of demand is negative, we know that Honolulu Red Oranges have an inelastic demand at a price of $32 per orange. This means that a 1% increase in price will lead to a less than 1% decrease in quantity demanded.
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Find the circumferences of of both circles to the nearest hundredth.
The value of circumferences of both circles to the nearest hundredth are 28.27 ft and 44ft.
Since, We know that;
The circumference of a form is the space surrounding its edge. Find the circumference of various forms by summing the lengths of their sides.
Given two coincide circles, the Radius of the smaller circle is 4.5ft.
Since the diameter is 9 ft.
Since, the bigger circle is 2.5 ft wider than the smaller circle,
Thus, the radius of the bigger circle = 4.5 + 2.5
Hence, the radius of the bigger circle = 7
From the formula for the circumference of a circle:
Circumference = 2π × radius
Thus,
The circumference of the yellow(bigger) circle is about = 2 x pi x 7
The circumference of the yellow(bigger) circle is about = 44 ft
The circumference of the purple(smaller) circle is about = 2 x pi x 4.5
The circumference of the purple(smaller) circle is about = 28.274 ft
therefore, The circumference of the yellow circle is about 44 ft. The circumference of the purple circle is about 28.27ft.
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The Circumference of the yellow circle is about 44 ft.
The circumference of the purple circle is about 28.27ft.
We have,
Radius of the smaller circle is 4.5ft
and radius of the bigger circle = 4.5 + 2.5 = 7 ft
Now, Circumference of Bigger circle (yellow) = 2 x π x r
= 2(3.14)(7)
= 44 ft
and, Circumference of Smaller circle (Purple) = 2 x π x r
= 2(3.14)(4.5)
= 28.274 ft
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The diameters of bolts produced on a certain machine are normally distributed with a mean of 0.62 cm and a standard deviation of 0.04 cm. Find the probability that a randomly selected bolt will have a diameter greater than 0.60 cm.
The probability that a randomly selected bolt will have a diameter greater than 0.60 cm is approximately 0.6915.
We know that the diameters of bolts produced on a certain machine are normally distributed with a mean (μ) of 0.62 cm and a standard deviation (σ) of 0.04 cm.
Let X be the diameter of a bolt. Then, X ~ N(μ, σ) = N(0.62, 0.04).
We need to find the probability that a randomly selected bolt will have a diameter greater than 0.60 cm.
P(X > 0.60) = P((X - μ)/σ > (0.60 - 0.62)/0.04) (standardizing X)
= P(Z > -0.5) (where Z ~ N(0,1) is the standard normal distribution)
Using the standard normal distribution table or calculator, we can find that P(Z > -0.5) is approximately 0.6915.
Therefore, the probability that a randomly selected bolt will have a diameter greater than 0.60 cm is approximately 0.6915.
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Give the reason(s) for each step needed to show that the following argument is valid.[p ∩ (p → q) ∩ (s ∪ r) ∩ (r → ¬p)] → (s ∪ t)1. p2. p→q3. q4. r → ~p5. q → ~r6. ~r7. s ∪ r8. s9. ∴ s ∪ t
The given argument is valid.
To show that the following argument is valid, we will use the given terms and follow a step-by-step explanation.
Argument: [p ∩ (p → q) ∩ (s ∪ r) ∩ (r → ¬p)] → (s ∪ t)
Steps:
1. p (Premise)
2. p → q (Premise)
3. q (From 1 and 2 using Modus Ponens: If p is true and p → q is true, then q is true)
4. r → ~p (Premise)
5. q → ~r (From 1 and 4 using the Contrapositive: If p is true and r → ~p is true, then q → ~r is true)
6. ~r (From 3 and 5 using Modus Ponens: If q is true and q → ~r is true, then ~r is true)
7. s ∪ r (Premise)
8. s (From 6 and 7 using Disjunction Elimination: If ~r is true and s ∪ r is true, then s is true)
9. ∴ s ∪ t (From 8 using Disjunction Introduction: If s is true, then s ∪ t is true)
By following these steps, we have shown that the given argument is valid.
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Jasmine finished the bike trail in 2. 5 hours at an average rate of 9 3/10 miles per hour. Lucy biked the same trail at a rate of 6 1/5 miles per hour. How long did it take Lucy to bike the trail?
It took Lucy approximately 2 13/31 hours to bike the trail.
We can start by using the formula:
distance = rate × time
Let's begin by finding the distance of the bike trail. Since Jasmine and Lucy biked the same trail, the distance will be the same for both of them. Let d be the distance of the trail.
d = distance of the bike trail
We know that Jasmine finished the bike trail in 2.5 hours at an average rate of 9 3/10 miles per hour. So, we can write:
d = 9 3/10 × 2.5
Simplifying the right-hand side, we get:
d = 23 1/2
Therefore, the distance of the bike trail is 23 1/2 miles.
Now, we can use the formula to find the time it took Lucy to bike the trail. Let t be the time it took Lucy to bike the trail.
distance = rate × time
23 1/2 = 6 1/5 × t
To solve for t, we can divide both sides by 6 1/5:
t = 23 1/2 ÷ (6 1/5)
Converting the mixed numbers to improper fractions, we get:
t = 47/2 ÷ 31/5
To divide fractions, we can multiply by the reciprocal:
t = 47/2 × 5/31
Simplifying, we get:
t = 2 13/31
Therefore, it took Lucy approximately 2 13/31 hours to bike the trail.
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Which line is perpendicular to
←→
H
F
?
A Horizontal line with points A, B, C and D is shown. Line HF is drawn perpendicularly through point A forming a right angle. Line MG is drawn perpendicularly through point B forming a right angle.
A line which is perpendicular to vector HF include the following: line BC.
What are perpendicular lines?In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector is a line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.
Based on the definition of perpendicular lines, we can reasonably infer and logically deduce that vector HF is perpendicular to line BC.
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Zahra is a company specializing in high-end cosmetics. Its signature nail polish color is Soft Lilac. On a certain day, the company's factory had 5300 bottles of nail polish, and 1400 of those bottles were Soft Lilac. On that day, the inventory manager took a sample of 14 bottles of nail polish in the factory. She found that 3 of those bottles were Soft Lilac. For the inventory manager's sample, find and write with proper notation the population proportion and sample proportion of bottles that were Soft Lilac. Write the proportions as decimals (not percentages) rounded to two decimal places.
The population proportion (P) can be found by dividing the number of Soft Lilac bottles by the total number of bottles in the factory:
P = 1400 Soft Lilac bottles / 5300 total bottles
P ≈ 0.26 (rounded to two decimal places)
The sample proportion (p) can be found by dividing the number of Soft Lilac bottles in the sample by the total number of bottles in the sample:
p = 3 Soft Lilac bottles / 14 total bottles in the sample
p ≈ 0.21 (rounded to two decimal places)
So, the population proportion (P) of Soft Lilac bottles in Zahra's factory is approximately 0.26, and the sample proportion (p) of Soft Lilac bottles in the inventory manager's sample is approximately 0.21.
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Fourteen of the 32 marbles in the bag were blue. The rest
were red. What was the ratio of red marbles to blue
marbles in the bag?
Answer: 18/14 or 18:14
Step-by-step explanation: this is relatively simple you have 32 in all and 14 are blue so 32-14=18 now you know there are 18 red marbles now to set up the ratio 18/14 or 18:14 (to check your work add 18+14=32)
