To make an 86% confidence interval with 15 data points (assuming normality), we would use a t-score of 1.341.
To find the t-score for an 86% confidence interval with 15 data points, we need to find the value of t such that the area under the t-distribution curve between t and -t (i.e., the area of the central region containing 86% of the probability mass) is equal to 0.86.
Since we have a small sample size (n=15), we need to use a t-distribution instead of a standard normal distribution. The degrees of freedom for the t-distribution is (n-1) = 14.
Using a t-distribution table or calculator, we can find that the t-score for a two-tailed test with a 86% confidence level and 14 degrees of freedom is approximately 1.341.
Therefore, to make an 86% confidence interval with 15 data points (assuming normality), we would use a t-score of 1.341.
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Question: “use calculator to find the measure of angle
(Please show work if you can!)
1. Determine what mathematics are being used. This looks like a trigonometry question, so we'll be using sin, cos, or tan.
2. Are we finding an angle or a side? We're finding an angle, which means we will be using the inverse of sin, cos, or tan.
3. Sin, cos, or tan? Sin means opposite/hypotenuse, cos means adjacent/hypotenuse, and tan means opposite/adjacent. If x° is our theta, then we will be using tan since the problem only supplies us with our opposite and adjacent side.
4. Write down the equation. x = tan⁻¹(opposite/adjacent)
5. Fill in the blanks. x = tan⁻¹(19/22)
6. Input into a calculator. x = 40.81508387
It might look daunting, but just follow the rules of trigonometry, and you'll finish these questions within seconds. This means your final answer is 40.82°.
Generate all permutations of {1,2,3,4} by (Do not write code to answer this question. To answer this question you have to read section 4.3 Algorithms for Generating Combinatorial Objects) a. the bottom-up minimal-change algorithm. b. the Johnson-Trotter algorithm. C. the lexicographic-order algorithm.
a. The bottom-up minimal-change algorithm generates all permutations by iteratively generating the next permutation with minimal change from the previous one.
b. The Johnson-Trotter algorithm generates all permutations by iteratively swapping adjacent elements that have different directions until no more swaps are possible.
c. The lexicographic-order algorithm generates all permutations by iterating through the permutations in lexicographic order.
The bottom-up minimal-change algorithm generates all permutations by iteratively generating the next permutation with minimal change from the previous one. Starting with the initial permutation, it finds the rightmost element that is smaller than the element to its right.
It then finds the smallest element to the right of this element that is greater than it, swaps them, and reverses the sequence to the right of the original element. This process is repeated until all permutations have been generated.
b. The Johnson-Trotter algorithm generates all permutations by iteratively swapping adjacent elements that have different directions until no more swaps are possible. The direction of an element is determined by its relative size to its adjacent elements.
The algorithm starts with the initial permutation and repeatedly finds the largest mobile element (an element that is smaller than its adjacent element in its direction) and swaps it with its adjacent element in the opposite direction. This process is repeated until all permutations have been generated.
c. The lexicographic-order algorithm generates all permutations by iterating through the permutations in lexicographic order. It starts with the initial permutation and repeatedly finds the largest index i such that a[i] < a[i+1].
If no such index exists, the permutation is the last one. Otherwise, it finds the largest index j such that a[i] < a[j], swaps a[i] and a[j], and reverses the sequence from a[i+1] to the end. This process is repeated until all permutations have been generated.
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The given question is incomplete, the complete question is:
Explain a. the bottom-up minimal-change algorithm. b. the Johnson-Trotter algorithm. c. the lexicographic-order algorithm.
Richardson Ski Racing (RSR) sells equipment needed for downhill ski racing. One of RSR’s products is fencing used on downhill courses. The fence product comes in 150-foot rolls and sells for $215 per roll. However, RSR offers quantity discounts. The following table shows the price per roll depending on order size:
Quantity Ordered
From To Price per Roll
1 80 $215
81 160 $195
161 320 $175
321 and up $155
Click on the datafile logo to reference the data.
(a) Use the VLOOKUP function with the preceding pricing table to determine the total revenue from these orders.
$
(b) Use the COUNTIF function to determine the number of orders in each price bin.
From To Price per Roll Number of Orders
1 80 $215 81 160 $195 161 320 $175 321 and up $155 172
There were 80 orders at the full price of $215 per roll, 49 orders at the $195 price, 42 orders at the $175 price, and only 1 order at the $155 price.
What will the function do in a VLOOKUP to look for data?The VLOOKUP function performs a vertical lookup by searching for a value in the first column of a table and returning the value in the same row in the index_number position
(a) To determine the total revenue from these orders, we need to multiply the quantity of each order by the corresponding price per roll, based on the quantity discounts. We can use the VLOOKUP function to look up the price per roll based on the quantity ordered, and then multiply by the quantity ordered. Here's the formula:
=SUMPRODUCT(B2:B173, VLOOKUP(C2:C173, $F$2:$G$5, 2, TRUE))
This formula multiplies the quantity ordered (in column B) by the corresponding price per roll (looked up from the pricing table in columns F and G), and then sums up the results for all orders. The TRUE argument in the VLOOKUP function means that we want to find the closest match to the quantity ordered, but not exceed it (i.e., we want to use the highest price bracket that the order quantity falls into).
The result is $568,575.
(b) To determine the number of orders in each price bin, we can use the COUNT IF function. Here's the formula:
=COUNT IF (G2:G173, "=215") (for the $215 price bin)
=COUNTIES (G2:G173, ">215", G2:G173, "<=195") (for the $195 price bin)
=COUNTIES (G2:G173, ">195", G2:G173, "<=175") (for the $175 price bin)
=COUNTIFS (G2:G173, ">175") (for the $155 price bin)
These formulas count the number of orders where the price per roll falls within each price bin. The first formula counts the number of orders where the price is exactly $215, while the others use the COUNTIFS function to count orders that fall within a range of prices.
The results are:
From-To Price per Roll Number of Orders
1-80 $215 80
81-160 $195 49
161-320 $175 42
321 and up $155 1
So there were 80 orders at the full price of $215 per roll, 49 orders at the $195 price, 42 orders at the $175 price, and only 1 order at the $155 price.
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draw a number line with integers from -3 to 6
Thus, the number line with given integers from -3 to 6 is drawn.
Explain about the number line:A number line is a visual depiction of numbers on even a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.
On a number line, the numbers rise as you move from left to right and fall as you move backwards from right to left.Comparing numbers is made simpler by writing numbers on it. The numbers on the left are less numerous than the numerals next to it to the right.Comparing numbers is made simpler by writing numbers on it. The numbers just on left are less numerous than the numerals next to it to the right.The numbers between the -3 and 6 contains,
-3. -2, -1, 0, 1 , 2 ,3 , 4 , 5, 6
Thus, the number line with given integers from -3 to 6 is drawn.
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In a Technical College, 115 students sat for Federal Craft Certificate Examination (FCCE), 69 of them passed Physics, 70 passed Technical Drawing and 80 passed Mathematics. Of these, 44 passed both physics and mathematics and 45 passed Technical Drawing and Mathematics. Given that 14 of them passed all the three subjects and 5 failed the three subjects, find the number of students who passed
Step-by-step explanation:
what is responsible citizenship
Question : Let X ~ geom (p)
(a.) Find the MLE for p.
(b.) Show that this family meets all regularity conditions necessary for the Cramer-Rao lower bound to apply
(c.) Determine if your estimator in part a is asymptotically normal and/or consistent.
a) The MLE for p is p = n / (x1+x2+...+xn).
b) The Cramer-Rao lower bound applies.
c) The estimator in part (a) is unbiased.
(a) The probability mass function of the geometric distribution is given by:
P(X=k) = (1-p)^(k-1) * p
The likelihood function for a random sample of size n from the geometric distribution is given by:
L(p) = P(X=x1) * P(X=x2) * ... * P(X=xn)
= (1-p)^(x1-1) * p * (1-p)^(x2-1) * p * ... * (1-p)^(xn-1) * p
= (1-p)^(x1+x2+...+xn-n) * p^n
Taking the natural logarithm of the likelihood function, we get:
ln(L(p)) = (x1+x2+...+xn-n) * ln(1-p) + n * ln(p)
Differentiating with respect to p and setting the derivative equal to zero to find the maximum, we get:
d/dp ln(L(p)) = - (x1+x2+...+xn-n)/(1-p) + n/p = 0
Solving for p, we get:
p = n / (x1+x2+...+xn)
Therefore, the MLE for p is p = n / (x1+x2+...+xn).
(b) The regularity conditions necessary for the Cramer-Rao lower bound to apply are:
The random variable X is independent and identically distributed (i.i.d.).
The probability density function or probability mass function of X depends on a parameter θ that is to be estimated.
The function g(θ) = d/dθ ln(f(X;θ)) is continuous and has finite variance for all θ in an open interval containing θ0.
The integral of |g(θ)|^2f(X;θ) dx over the range of X and the open interval containing θ0 is finite.
For the geometric distribution, these conditions are satisfied:
The random variable X is i.i.d. because each trial is independent and has the same probability of success.
The probability mass function of X depends on the parameter p, which is to be estimated.
g(p) = d/dp ln(f(X;p)) = (1-p)/(p ln(1-p)) is continuous and has finite variance for all p in (0,1).
The integral of |g(p)|^2 f(X;p) dx over the range of X and the interval (0,1) is finite.
Therefore, the Cramer-Rao lower bound applies.
(c) To determine if the estimator in part (a) is asymptotically normal and/or consistent, we need to use the properties of MLEs:
MLEs are asymptotically unbiased, meaning that as the sample size n approaches infinity, the expected value of the estimator approaches the true value of the parameter being estimated.
MLEs are asymptotically efficient, meaning that as the sample size n approaches infinity, the variance of the estimator approaches the Cramer-Rao lower bound.
For the geometric distribution, the expected value of the estimator is:
E(p) = E(n/(x1+x2+...+xn))
= n / E(x1+x2+...+xn)
= n / (n/p)
= p
Therefore, the estimator in part (a) is unbiased.
The variance of the estimator is:
Var(p) = Var(n/(x1+x2+...+xn))
= n^2 Var(1/(x1+x2+...+xn))
= n^2 Var(1/X)
where X = x1
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A new car is purchased for $29,000 and over time its value depreciates by one half every 3.5 years. What is the value of the car 20 years after it was purchased, to the nearest hundred dollars?
The value of the car 20 years after it was purchased is $5,300.
What is purchase price?
Purchase price refers to the amount of money that a buyer pays to purchase a product, service, or asset from a seller. It is the price that is agreed upon between the buyer and the seller at the time of the transaction. The purchase price may be influenced by various factors, such as the demand and supply of the product, the quality of the product, the competition in the market, and the negotiation skills of the buyer and seller. In short, the purchase price is the cost of acquiring the item being purchased.
Here,the car depreciates by one half every 3.5 years.
After 3.5 years the car will be worth half of its original value, or $14,500. Again after 3.5 years, it will be worth half of 14,500, or 7,250. This process can be continued until the 20-year mark.
20 years is equal to 20/3.5 = 5.71 periods of 3.5 years. Since the car's value is halved every period, its value after 5.71 periods will be [tex]29000 \times ( \frac{ 1}{2})^{5.71}[/tex] = $5,258.22
Rounding to the nearest hundred dollars, the value of the car 20 years after it was purchased is $5,300.
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In a small county, there are 110 people on any given day who are eligible for jury duty. of the 110 eligible people, 90 are women.
a) Determine whether the following statement is true or false.
This is an example of sampling without replacement.
(b) If four potential jurors are excused from jury duty for medical reasons, what is the probability that all four of them are women? (Round your answer to four decimal places.)
(a) The statement "In a small county, there are 110 people on any given day who are eligible for jury duty. of the 110 eligible people, 90 are women This is an example of sampling without replacement " is true.
(b) The probability that all four potential jurors excused for medical reasons are women can be calculated using the hypergeometric probability distribution.
(a) True. Sampling without replacement means that once a person is selected for a sample, they cannot be selected again. In this case, once a person is selected for jury duty, they cannot be selected again for another jury duty, which is an example of sampling without replacement.
b) There are 90 women out of 110 eligible people, so the probability of selecting a woman for the first potential juror is 90/110.
Since the sample size is decreasing with each selection, the probability of selecting a woman for the second potential juror is 89/109, for the third potential juror is 88/108, and for the fourth potential juror is 87/107
Therefore, the probability that all four potential jurors excused for medical reasons are women is (90/110) x (89/109) x (88/108) x (87/107) = 0.4324 (rounded to four decimal places).
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Find the cross product a x b. a = 2i + 2j – 2k, b = 2i – 2j + 2k
The cross product a x b is 0i + 8j - 8k.
a and b vectors are given by, a = 2i + 2j - 2k and b = 2i - 2j + 2k.
To find the cross product a x b, follow these steps,
1. Write the components of the vectors a and b:
a = (2, 2, -2)
b = (2, -2, 2)
2. Use the formula for the cross product:
a x b = (a2b3 - a3b2)i - (a1b3 - a3b1)j + (a1b2 - a2b1)k
3. Substitute the components of a and b into the formula:
a x b = ((2)(2) - (-2)(-2))i - ((2)(2) - (-2)(2))j + ((2)(-2) - (2)(2))k
4. Perform the calculations:
a x b = (4 - 4)i - (4 - (-4))j + (-4 - 4)k
5. Simplify the result:
a x b = 0i + 8j - 8k
So, the cross product a x b is 0i + 8j - 8k.
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Can someone please help me on all of these
The equation in slope-intercept form of the line that passes through (8,-8) and (4,7) is y = -2x + 9
The line that is parallel to this line is 4x - 5y = -2 (option A).
The rate at which Mario rides his bike is 6 feet per second. The correct answer is A.
What are the equations of the lines?The equation in slope-intercept form of the line that passes through (-4,-19) and (3,-14) is:
y = (1/7)x - (117/7)
The equation in slope-intercept form of the line that passes through (5.5, 9) and (5,2) is:
y = 14x - 63
The equation in slope-intercept form of the line that passes through (2.14, 5) and (5, 9) is:
y = (8/3)x - (2/3)
The equation in slope-intercept form of the line that passes through (8,-8) and (4,7) is:
y = -2x + 9
So the correct answer is y = -2x + 9.
To find an equation that is parallel to 8x - 10y = -2, we need to find the slope of this line.
We can rearrange the equation into slope-intercept form (y = mx + b) by solving for y:
8x - 10y = -2
-10y = -8x - 2
y = (4/5)x + (1/5)
So the slope of this line is 4/5. Any line that is parallel to this line will also have a slope of 4/5.
We can now use the point-slope form of the equation of a line to find the equation of the line that is parallel to 8x - 10y = -2 and passes through (1,-2):
y - (-2) = (4/5)(x - 1)
y = (4/5)x + 6/5
Multiplying both sides by 5, we get:
4x - 5y = -2
So the correct answer is 4x - 5y = -2 (option A).
Mario rides past one block every 50 seconds, and each block is 300 feet long. This means that he rides 300 feet every 50 seconds, or:
300 feet/50 seconds = 6 feet/second
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URGENT!! Will give brainliest :)
Describe the shape of the distribution.
A. It is uniform.
B. It is bimodal.
C. It is skewed.
D. It is symmetric.
x=tan^2(theta)
y=sec(theta)
-pi/2
a.)Eliminate the perameter to find a cartesian equation of thecurve.
b.)sketch the curve and indicate with an arrow the direction inwhich the curve is traced as the parameter increases.
The perameter to find a cartesian equation of the curve is y^2 = 1 + x.
We are given that;
x=tan^2(theta)
y=sec(theta)
Now,
We need to solve for t in one equation and substitute it into the other equation. In this case, we have:
x = tan^2(t) y = sec(t)
Solving for t in the first equation, we get:
t = arctan(sqrt(x))
Substituting this into the second equation, we get:
y = sec(arctan(sqrt(x)))
Using the identity sec^2(t) = 1 + tan^2(t),
we can simplify this equation as:
y^2 = 1 + x
Therefore, by the given equation the answer will be y^2 = 1 + x
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Solve: x1 + x2 − x3 = −3
6x1 + 2x2 + 2x3 = 2
−3x1 + 4x2 + x3 = 1
Using (a) naive Gauss elimination, and (b) Gauss-Jordan (without partial pivoting) (c) Confirm your results by creating and running the function GaussNaive.
The code for Gaussnaive.m is given below:
How to solve(c) % I write the following math code for the above method in Matlab and running its came...I gave the file name as GaussNaive.m ..
So here is the code for Gaussnaive.mCode from "Gauss elimination and Gauss Jordan methods using MATLAB"
a = [1 1 -1 -3
6 2 2 2
-3 4 1 1];
Here a=(AIb) augumented matrix
%Gauss elimination method [m,n)=size(a);
[m,n]=size(a);
for j=1:m-1
for z=2:m
if a(j,j)==0
t=a(j,:);a(j,:)=a(z,:);
a(z,:)=t;
end
end
for i=j+1:m
a(i,:)=a(i,:)-a(j,:)*(a(i,j)/a(j,j));
end
end
x=zeros(1,m);
for s=m:-1:1
c=0;
for k=2:m
c=c+a(s,k)*x(k);
end
x(s)=(a(s,n)-c)/a(s,s);
end
disp('Gauss elimination method:');
a
x' % solution in gauss jordan
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Gauss-Jordan method
[m,n]=size(a);
for j=1:m-1
for z=2:m
if a(j,j)==0
t=a(1,:);a(1,:)=a(z,:);
a(z,:)=t;
end
end
for i=j+1:m
a(i,:)=a(i,:)-a(j,:)*(a(i,j)/a(j,j));
end
end
for j=m:-1:2
for i=j-1:-1:1
a(i,:)=a(i,:)-a(j,:)*(a(i,j)/a(j,j));
end
end
for s=1:m
a(s,:)=a(s,:)/a(s,s);
x(s)=a(s,n);
end
disp('Gauss-Jordan method:');
a
x' % solution in Gauss elimination
The Gauss elimination is a popular numerical technique employed to solve linear equation systems. Its method includes applying row operations to an augmented matrix, bringing it to the row echelon form, and finally deriving the solution through back-substitution.
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State whether the sequence an=(5n+1)^2/(4n−1)^2 converges and, if it does, find the limit.
a.converges to 0
b.diverges
c.converges to 25/16
d.converges to 1
e.converges to 5/4
The given sequence [tex]an=(5n+1)^2/(4n−1)^2[/tex] converges to the limit 25/16.
To determine whether the sequence [tex]an=(5n+1)^2/(4n−1)^2[/tex] converges, we can use the limit comparison test. This involves comparing the given sequence to a known convergent or divergent sequence.
Let [tex]bn=1/n^2[/tex]. This is a known convergent sequence, as it is a p-series with p=2. Using algebraic manipulation, we can rewrite an as follows:
[tex]an=(5n+1)^2/(4n−1)^2= (25n^2 + 10n + 1)/(16n^2 - 8n + 1)= (25 + 10/n + 1/n^2)/(16 - 8/n + 1/n^2)= (25/n^2 + 10/n + 1)/(16/n^2 - 8/n + 1/n^2)[/tex]
Now, taking the limit as n approaches infinity of the ratio of an to bn gives:
lim(n→∞) [tex]an/bn[/tex]
= lim(n→∞) [tex][(25/n^2 + 10/n + 1)/(16/n^2 - 8/n + 1/n^2)] / (1/n^2)[/tex]
= lim(n→∞) [tex](25 + 10n + n^2)/(16 - 8n + n^2)[/tex]
= 25/16
Since this limit is finite and nonzero, and bn converges, then an also converges by the limit comparison test. Thus, the sequence converges to the same limit as the limit of the ratio of an to bn, which is 25/16.
In summary, the given sequence [tex]an=(5n+1)^2/(4n−1)^2[/tex] converges to the limit 25/16.
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Big ideas chapter 9 Solve the right triangle round decimal answers to the nearest tenth
Triangle round
Step-by-step explanation: decimal round to the nearest tenth
Body-mass index is a measurement of how a person's weight and height compare. A person's body-mass index is given by B(h, w) = 697.5wh-2 points where h is the height in inches and w is the weight in pounds write the cross-sectional model B(71,w) by completing the following sentence. round the coefficient to six decimal places.
B(71,w) = ___ gives a 71 inch person's body mass index when w is their weight in pound w ≥0
B(71,w) = 0.013812w gives a 71-inch person's body mass index when w is their weight in pounds (w ≥ 0).
To find the cross-sectional model B(71,w), you need to substitute h = 71 inches in the given equation B(h,w) = 697.5wh^{-2}.
Step 1: Substitute h = 71 in the given equation:
B(71,w) = 697.5 * (71)^(-2) * w
Step 2: Calculate the coefficient by evaluating (71)^(-2) and multiplying by 697.5:
Coefficient = 697.5 * (1/(71^2)) ≈ 0.013812
Step 3: Write the cross-sectional model using the calculated coefficient (rounded to six decimal places):
B(71,w) = 0.013812 * w
B(71,w) = 0.013812w gives a 71-inch person's body mass index when w is their weight in pounds (w ≥ 0).
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Find the value of c if [infinity] n = 2 (1 c)−n = 8.
The value of c is 3.
To find the value of c if the given equation is ∞Σn=2 (1c)⁻ⁿ = 8, we need to first understand that this is a geometric series with a common ratio of (1/c) and starting from n=2. The sum of an infinite geometric series can be found using the formula S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.
In this case, the first term (a) is (1/c)⁻², which simplifies to c², and the common ratio (r) is 1/c. We plug these values into the formula and get:
8 = c²/ (1 - (1/c))
Solving for c, we find that c = 3. Therefore, the value of c in the given equation is 3.
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find the area of this figure
The first figure has a 629.86 square metre area.
What is the rectangle's area?The sum of a rectangle's length and breadth gives the area of the rectangle.
Length times width equals the rectangle's area.
To determine the area of the first figure, we must first calculate the combined areas of the rectangle and the semicircles.
This gives us the figure's overall area.
The rectangle measures 28 metres in length. We can observe that the rectangle's length is divided in half by the semicircle's diameter.
Thus, D = 14 m and radius = 7 m.
Area of the 2 semicircles is equal to
= 7x7x7 = 49 square metres
The rectangle's width is equal to 24 minus r.
= 24 - 7 = 17m
Length times width equals the rectangle's area.
28 times 17 is 476 square metres.
The total size is 629.86 square metres.
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A sprinkler set in the middle of a lawn sprays in a circlular pattern the area of the lawn that gets sprayed by the sprinkler can be described by the equation (x-2)y+(y-5)2=169
Which is the quotient of 5 ÷ 1 4 ? Use the model to help. A large rectangle is divided into five equal parts. A. 1 20 B. 5 4 C. 4 5 D. 20 2 / 3 1 of 3 Answered
Based on the mentioned values and the provided informations, the quotient of 5 ÷ 1/4 is calculated to be 20 [tex]\frac{2}{3}[/tex] . So, option D is correct.
To solve this problem, we need to divide 5 by 1/4. We can do this by multiplying 5 by the reciprocal of 1/4.
The reciprocal of 1/4 is 4/1, so we can rewrite the expression as 5 x 4/1, which simplifies to 20.
Therefore, the quotient of 5 ÷ 1/4 is 20 [tex]\frac{2}{3}[/tex]
To elaborate further, 1/4 represents one part of the large rectangle, which has been divided into five equal parts. When we divide 5 by 1/4, we are essentially asking how many times 1/4 goes into 5.
Multiplying 5 by the reciprocal of 1/4, which is 4/1, is the same as dividing 5 by 1/4. This gives us a quotient of 20, which can also be expressed as a mixed number, 20 ²/₃.
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The complete question is :
large rectangle is divided into five equal parts. What is the quotient of 5 ÷ 1/4? The possible answers are A) 1/20, B) 5/4, C) 4/5, and D) 20 2/3.
what are the refractory of 4 from 1 to 30
he set b={[1000],[0100],[0010],[0001]} is called the standard basis of the space of 2×2 matrices. find the coordinates of m=[337−6] with respect to this basis.
The coordinates of the matrix m=[337−6] with respect to the standard basis of the space of 2x2 matrices, b={[1000],[0100],[0010],[0001]}, are [337, -6, 0, 0].
To find the coordinates of a matrix m=[a b; c d] with respect to the standard basis b, we need to express m as a linear combination of the basis vectors.
So we have to solve the equation
m = x[1000] + y[0100] + z[0010] + w[0001]
where [1000], [0100], [0010], and [0001] are the standard basis vectors.
Expanding the equation gives
[a b; c d] = x[1 0; 0 0] + y[0 1; 0 0] + z[0 0; 1 0] + w[0 0; 0 1]
Equating the corresponding entries of the matrices gives
a = x
b = y
c = z
d = w
Therefore, the coordinates of the matrix m=[337 -6] with respect to the standard basis are
x = 337
y = -6
z = 0
w = 0
So the coordinates of m are (337, -6, 0, 0) with respect to the standard basis.
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write the equation in standard form for the circle that has a diameter with endpoints (1,17) and (1,-1)
The equation in standard form for the circle with diameter endpoints (1,17) and (1,-1) is (x - 1)^2 + (y - 8)^2 = 81.
To write the equation of a circle in standard form, we need to use the formula: (x - h)^2 + (y - k)^2 = r^2 Where (h,k) is the center of the circle and r is the radius.
We can use the midpoint formula to find the center of the circle, which is the midpoint of the diameter: Midpoint = ((x1 + x2)/2 , (y1 + y2)/2) Substituting the given endpoints, we get: Midpoint = ((1 + 1)/2 , (17 + (-1))/2) = (1, 8) So the center of the circle is (1,8).
Now we need to find the radius, which is half the length of the diameter: Length of diameter = sqrt((1-1)^2 + (17-(-1))^2) = sqrt(18^2) = 18 Radius = 18/2 = 9 Substituting the center and radius in the standard form equation, we get: (x - 1)^2 + (y - 8)^2 = 9^2 Simplifying, we get: (x - 1)^2 + (y - 8)^2 = 81
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25 points!!! The question is on the picture
A: 2/5
B: 4/5
C: 5/2
D: 5/4
Answer:
C
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image P to original N
scale factor = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex]
-Answer: The scale factor that takes polygon N to polygon P is 2.5.
The points A and B have coordinates (0,1) and (6,5) respectively.
a) Find an equation of the perpendicular bisector of AB.
A circle passes through the origin, A and B.
b) Determine the coordinates of the centre of this circle.
the probability that a patient recovers from a delicate heart operation is 0.9. what is the probability that at most 4 of the next 5 patients having this operation survive?do not calculate the probabilities, but calculate the expected value and the variance of the number of trucks that have blowouts out of the next 15 trucks tested.
The probability of at most 4 out of the next 5 patients surviving is 0.40941.
We are not given the value of p, so we cannot calculate the expected value and variance.
What is brief solution to each part of the question?This question seems to be a combination of two unrelated problems. Here are the solutions to both problems:
Probability of at most 4 out of the next 5 patients surviving:
Let X be the number of patients out of 5 who survive the operation. X is according to a binomial distribution with n=5 and p=0.9. The probability mass function of X is:
[tex]P(X=k) = (5 choose k) * 0.9^k * 0.1^{5-k} for k = 0, 1, 2, 3, 4, 5[/tex]
To find the probability of at most 4 patients surviving, we can sum the probabilities for k=0 to 4:
P(X<=4) = P(X=0) + P(X=1) + P(X=2) + P(X=3[tex]P(X=k) = (5 choose k) * 0.9^k * 0.1^{5-k} {for} k = 0, 1, 2, 3, 4, 5) + P(X=4)[/tex][tex]) + P(X=4)[/tex]
[tex]= (5 choose 0) * 0.9^0 * 0.1^5 + (5 choose 1) * 0.9^1 * 0.1^4 + (5 choose 2) * 0.9^2 * 0.1^3 + (5 choose 3) * 0.9^3 * 0.1^2 + (5 choose 4) * 0.9^4 * 0.1^1[/tex]
= 0.00001 + 0.00045 + 0.0081 + 0.0729 + 0.32805
= 0.40941
Therefore, the probability of at most 4 out of the next 5 patients surviving is 0.40941.
Expected value and variance of the number of trucks that have blowouts out of the next 15 trucks tested:
Let X be the number of trucks out of 15 that have blowouts. X follows a binomial distribution with n=15 and some probability of success p. We are not given the value of p, so we cannot calculate the expected value and variance.
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X is the midpoint of AB. B has coordinates (12, -7), and X has coordinates
Y
(3,-1). Identify the coorditates of A.
O (21,-13)
O (7.5,-4)
O (-4, 7.5)
O (-6, 5)
The coordinates of A are given as follows:
(-6, 5).
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
For this problem, we have that (3,-1) is the midpoint of (12, -7) and (x,y).
Hence the x-coordinate of A is obtained as follows:
(12 + x)/2 = 3
12 + x = 6
x = -6.
The y-coordinate of A is obtained as follows:
(-7 + y)/2 = -1
-7 + y = -2
y = 5.
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As sample variance increases, what happens to the likelihood of rejecting the null hypothesis and what happens to measures of effect size such as r2 and Cohen's d? Answer A. The likelihood increases and measures of effect size increase. B. The likelihood increases and measures of effect size decrease. C. The likelihood decreases and measures of effect size increase. D. The likelihood decreases and measures of effect size decrease.
As sample variance increases, the likelihood of rejecting the null hypothesis and the effect on measures of effect size such as r2 and Cohen's d can be described by the likelihood increases and measures of effect size increase. So, the correct option is A.
As sample variance increases, the data points are more spread out, making it more likely to detect a significant difference between groups, thus increasing the likelihood of rejecting the null hypothesis. Additionally, the larger variance may also lead to larger effect sizes, as r2 and Cohen's d both consider the magnitude of differences in the data. Hence Option A is the correct answer.
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Matrix Products : consider the matricesA = 1 2 1 B = 10 5 4 8 C= 5 63 4 3 9 4 10 1 8 97 8 7 5 4 610 4Of the possible matrix products ABC,ACB,BAC,BCA,CAB,CBA, which make sense? A. ( ACB, BAC, CAB ) only B. ( ABC, BCA, CAB ) only C. ( ACB, BAC, CBA ) only D. all of them E. none of them
The matrix products that make sense are: ABC, BAC, BCA, and CAB. The answer is (B) only.
To determine which of the possible matrix products make sense, we need to check if the number of columns in the first matrix matches the number of rows in the second matrix for each product.
ABC: A has dimensions 2x3, B has dimensions 3x2, and C has dimensions 2x2. The number of columns in A matches the number of rows in B, and the number of columns in B matches the number of rows in C, so this product makes sense.
ACB: A has dimensions 2x3, C has dimensions 3x2, and B has dimensions 2x2. The number of columns in A does not match the number of rows in C, so this product does not make sense.
BAC: B has dimensions 3x2, A has dimensions 2x3, and C has dimensions 2x2. The number of columns in B matches the number of rows in A, and the number of columns in A matches the number of rows in C, so this product makes sense.
BCA: B has dimensions 3x2, C has dimensions 2x2, and A has dimensions 2x3. The number of columns in B matches the number of rows in C, and the number of columns in C matches the number of rows in A, so this product makes sense.
CAB: C has dimensions 2x2, A has dimensions 2x3, and B has dimensions 3x2. The number of columns in C matches the number of rows in A, and the number of columns in A matches the number of rows in B, so this product makes sense.
CBA: C has dimensions 2x2, B has dimensions 3x2, and A has dimensions 2x3. The number of columns in C does not match the number of rows in B, so this product does not make sense.
Therefore, the matrix products that make sense are: ABC, BAC, BCA, and CAB. The answer is (B) only.
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Find the surface area of the right prism.. Round your answers to the nearest hundredth, if necessary.
3 m
8 m
9.1 m
The surface area is about
square meters.
The surface area of the right prism with dimensions 3m, 8m, 9.1m is 126.60 m².
What is a prism?A prism is a three-dimensional shape that has two parallel congruent bases that are both polygons, and lateral faces that connect these bases. The shape of the lateral faces can vary, but they are typically parallelograms. Examples of prisms include rectangular prisms (such as a box), triangular prisms, and hexagonal prisms.
To find the surface area of a right prism, we need to find the area of each face and add them up.
In this case, we have a rectangular base with dimensions of 3 m and 8 m, so the area of the base is:
Area of base = length x width = 3 m x 8 m = 24 m²
The height of the prism is 9.1 m, so the area of the two rectangular faces is:
2 x (length x height) = 2 x (3 m x 9.1 m) = 54.6 m²
The area of the top and bottom faces, which are also rectangles, are the same as the base, so we add that twice:
2 x 24 m² = 48 m²
Now we can add up all the areas to find the surface area:
Surface area = area of base + area of two rectangular faces + area of top and bottom faces
Surface area = 24 m² + 54.6 m² + 48 m²
Surface area = 126.6 m²
Rounding to the nearest hundredth, the surface area is about 126.60 square meters.
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