a) The 90% confidence interval is approximately (33.021, 38.979). b) The 95% confidence interval is approximately (32.454, 39.546). c) The 99% confidence interval is approximately (31.340, 40.660).
How to find the confidence intervals for μWe can use the formula:
Confidence Interval = sample mean ± margin of error
where the margin of error is determined by the confidence level and the standard error.
The standard error can be calculated as σ / √n, where σ is the population standard deviation and n is the sample size.
(a) 90 percent confidence interval:
For a 90% confidence level, the critical value (Z) is approximately 1.645.
Standard error = σ / √n = 6 / √11 ≈ 1.809
Margin of error = Z * standard error = 1.645 * 1.809 ≈ 2.979
Lower limit = xbar - margin of error = 36 - 2.979 ≈ 33.021
Upper limit = xbar + margin of error = 36 + 2.979 ≈ 38.979
The 90% confidence interval is approximately (33.021, 38.979).
(b) 95 percent confidence interval:
For a 95% confidence level, the critical value (Z) is approximately 1.96.
Standard error = 6 / √11 ≈ 1.809 (same as in (a))
Margin of error = 1.96 * 1.809 ≈ 3.546
Lower limit = 36 - 3.546 ≈ 32.454
Upper limit = 36 + 3.546 ≈ 39.546
The 95% confidence interval is approximately (32.454, 39.546).
(c) 99 percent confidence interval:
For a 99% confidence level, the critical value (Z) is approximately 2.576.
Standard error = 6 / √11 ≈ 1.809 (same as in (a) and (b))
Margin of error = 2.576 * 1.809 ≈ 4.660
Lower limit = 36 - 4.660 ≈ 31.340
Upper limit = 36 + 4.660 ≈ 40.660
The 99% confidence interval is approximately (31.340, 40.660).
(d) As the confidence level increases, the width of the confidence interval also increases. This means that the range of values that could potentially contain the population mean becomes wider, providing a higher level of confidence in capturing the true population mean.
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Graph the function f(x) = 2x. Which features are correctly stated?
A) x-intercept: none
B) y-intercept: (0, 2)
C) asymptote: x = 0
D) as x → ∞, f(x) → ∞
E) as x → −∞, f(x) → 0
Answer:
a, d, e
Step-by-step explanation:
on usatestprep
The features of the function are given as follows:
Horizontal asymptote: y = 5.
Vertical asymptote: x = 2.
x-intercept: No x-intercept.
y-intercept: (0,-5).
Hole: No holes.
What are the features of the function?The horizontal asymptote is the limit of f(x) as x goes to infinity. To obtain this limit, we consider only the terms with the highest exponent of the numerator and of the denominator, hence:
here, we have,
g(x) = -5x/x -> y = 5 is the horizontal asymptote.
The vertical asymptote is the value of x for which the function is not defined, hence it is the zero of the denominator, thus:
x - 2 = 0 -> x = 2.
The x-intercept is the point (x,0), in which x is found when y = 0, hence:
-5x + 10 = 0
-5x = -10
5x = 10
x = 2.
However, the function is not defined at x = 2, meaning that it has no x-intercept.
The y-intercept is the value of y when x = 0, hence:
y = 10/-2 = -5.
The coordinates are (0,-5).
The entire function can be simplified as follows:
(-5x + 10)/(x - 2) = [-5(x - 2)]/(x - 2) = -5.
Meaning that the function has no holes.
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complete question:
Determine each feature of the graph of the given function.
f(x) = -5+10
2
Horizontal Asymptote: y =
Vertical Asymptote: x =
x-Intercept:
y-Intercept: (0,
Hole: (
,0)
No horizontal asymptote
No vertical asymptote
No x-intercept
No y-intercept
No hole
Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is at least 31 days. Does the claim represent the null hypothesis or the alternative hypothesis? Since the claim (a) How should ! a statement of equality, it represents the ?|
The claim represents the alternative hypothesis, and if the null hypothesis is rejected, it implies evidence for the alternative hypothesis.
The claim "the mean incubation period for the eggs of a species of bird is at least 31 days" represents the alternative hypothesis.
In hypothesis testing, the null hypothesis (H0) is the statement that is assumed to be true or the statement of no effect or no difference. The alternative hypothesis (Ha) is the statement that contradicts or opposes the null hypothesis and represents the possibility of an effect or a difference.
If a hypothesis test is performed and it rejects the null hypothesis (H0), it means that there is sufficient evidence to support the alternative hypothesis (Ha). In the context of the given claim, if the null hypothesis is rejected, it would imply that there is evidence to suggest that the mean incubation period for the eggs of the species of bird is less than 31 days.
On the other hand, if the hypothesis test fails to reject the null hypothesis (H0), it means that there is not enough evidence to support the alternative hypothesis (Ha). In the given claim, if the null hypothesis is not rejected, it would imply that there is not enough evidence to conclude that the mean incubation period for the eggs of the species of bird is less than 31 days.
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the function \:h=-0.01x^2+0.9x models the height in feet, h, of a soccer ball as it travels a horizontal distance in feet, x. What is the maximin height of the soccer ball and how long does it take for the ball to reach this height
Answer:
Nice!
Step-by-step explanation:
A box contains three cards. On one card there is a question mark (Upper Q), on another card there is a pear (Upper P), and on the third card there is a moon (Upper M). Two cards are to be selected at random with replacement. Complete parts (a) through (e) below. a) Determine the number of sample points in the sample space.
Complete question :
Determine the probability that two pears are selected The probability is(Simplity your answer.)
d) Determine the probability that a card containing a PEAR and then a card containing a question mark are selected
Answer:
(QQ, QP, QM, QP, PP, MP, QM, PM, MM) ;
Step-by-step explanation:
Given :
Marking on card :
Question mark = Q
Pear = P
Moon = M
Selecting two cards with replacement :
Sample space :
_____ Q ____ P _____ M
Q ___QQ ___QP ___ QM
P ___QP ____PP ___ MP
M__ QM ____PM ___MM
(QQ, QP, QM, QP, PP, MP, QM, PM, MM) ;
1/9 ;
2/9
P(selecting 2 pears) = (PP)
P(p) = required outcome / Total possible outcomes = 1 / 9
Card containing a pear and then a question mark ;
(PQ or QP).
P(p) = 1/3 ; P(Q) = 1/3
P(PQ) + P(QP)
(1/3 * 1/3) + (/3 * 1/3)
1/9 + 1/9
(1 + 1) / 9
= 2/9
Will mark brainliest if correct.
Answer:
b
Step-by-step explanation:
Answer:
i am pretty sure the answer is d
Step-by-step explanation:
let me know if this is wrong
A teacher is correcting a student's homework
assignment, but she cannot read one line of the
student's work. The student's work is shown
below, with a blank space representing the
missing line.
Step 1:
- 2x + 11 = -5
Step 2: -2x + 11 – 11 = -5 – 11
Step 3:
-2x = -16
Step 4:
Step 5:
1x = 8
Step 6:
x= 8
Which of the following represents the correct
Step 4 and the property that would be used to
justify the step?
Answer without Explanation:
B
Find the area of the surface.
The part of the surface
z = xy
that lies within the cylinder
x² + y² = 64.
The area of the surface is 2π(3√3 - 1). The surface area integral is given by A = ∬D √(1 + (dz/dx)² + (dz/dy)²) dA.
To find the area of the surface that lies within the cylinder x² + y² = 64 and is defined by z = xy, we can use the surface area integral.
The surface area integral is given by:
A = ∬D √(1 + (dz/dx)² + (dz/dy)²) dA
where D represents the region on the xy-plane that corresponds to the surface.
In this case, the region D is the circle with radius 8 (which is obtained by solving x² + y² = 64). To evaluate the integral, we need to determine the partial derivatives dz/dx and dz/dy.
Taking the partial derivative of z with respect to x:
∂z/∂x = y
Taking the partial derivative of z with respect to y:
∂z/∂y = x
Substituting these values into the surface area integral formula:
A = ∬D √(1 + y² + x²) dA
Since D is a circle with radius 8, we can express the integral in polar coordinates. The limits of integration for r are 0 to 8, and the limits of integration for θ are 0 to 2π.
A = ∫₀²π ∫₀⁸ √(1 + r²sin²θ + r²cos²θ) r dr dθ
Simplifying the expression under the square root:
A = ∫₀²π ∫₀⁸ √(1 + r²) r dr dθ
Now we can evaluate the integral:
A = ∫₀²π [(1/3)(1 + r²)^(3/2)]⁸₀ dθ
A = ∫₀²π (1/3)(9√3 - 1) dθ
A = (1/3)(9√3 - 1) ∫₀²π dθ
A = (1/3)(9√3 - 1)(2π - 0)
A = 2π(3√3 - 1)
The area of the surface is 2π(3√3 - 1).
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write two inequalities to
compare -12 and -6
write two inequalities to compare 8 and -10
Answer:
First one: -12 < -6
-6 > -12
Second one:
-8 > -10
-10 < -8
Step-by-step explanation:
Well you just compare them with greater then or less then signs.
what is the slope and y intercept of the line with equation 3x-6y=7
Answer:
x intercept = (7/3, 0)
y intercept = (0, -7/6)
slope = 1/2
Step-by-step explanation:
Let W = {(0,x, y, z); x – 3y + 92 = 0} be a subspace of R*. Then a basis for W is: {(0,6.1,0), (0,-9,0,1)) None of the mentioned {(0,-6,1,0), (0,9,0,1)) {(0,3,1,0), (0,-9,0,1)) -4 12 -1 -1 Let k be a real number and A = k 2 lo 7 1 Then A is a singular matrix if None of the mentioned k=15/2 k=10 k=5
A basis for W is {(0,-6,1,0), (0,9,0,1)}.
Matrix A is a singular matrix when k = 1.
To find the basis for the subspace W and determine the value of k for matrix A, let's go through each part separately.
Part 1: Basis for W
The subspace W is defined by the equation x – 3y + 92 = 0. In order to find a basis for W, we need to find two linearly independent vectors that satisfy this equation.
From the given options, the vectors {(0,6.1,0)} and {(0,-9,0,1)} do not satisfy the equation x – 3y + 92 = 0.
However, the vectors {(0,-6,1,0)} and {(0,9,0,1)} satisfy the equation x – 3y + 92 = 0. Therefore, a basis for W is {(0,-6,1,0), (0,9,0,1)}.
Part 2: Singular Matrix A
Matrix A = [k 2 10 7 1].
To determine if A is a singular matrix, we need to check if its determinant is equal to zero.
Calculating the determinant of A:
det(A) = k(21 - 710) - 2(27 - 101) + 10(27 - 101)
= k(-68) - 2(-14) + 10(4)
= -68k + 28 + 40
= -68k + 68
A is a singular matrix if det(A) = -68k + 68 = 0.
Solving the equation -68k + 68 = 0, we find k = 1.
Therefore, A is a singular matrix when k = 1.
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What would u do to find the missing value plz helpp ASAP plz I’ll give brainliest!
Answer:
23 [tex]\frac{1}{24}[/tex]
Step-by-step explanation:
you subtract 82 [tex]\frac{2}{3}[/tex] by 59 [tex]\frac{5}{8}[/tex] and you'll get the answer
match the range of the function f(x)=x^2+2x-1 to its domain
2
-2
3
-3
Answer:
See solutions below
Step-by-step explanation:
Match the range of the function f(x)=x^2+2x-1 to its domain
Domains of the function are the input values x i.e 2, -2, 3 and 3
corresponding f(x) for each values are the range
when x = 2
f(2)=2^2+2(2)-1
f(2) = 4 + 4 - 1
f(2) = 7
when x = -2
f(-2)=(-2)^2+2(-2)-1
f(-2) = 4 - 4 - 1
f(-2) = -1
when x = 3
f(3)=3^2+2(3)-1
f(3) = 9 + 6 - 1
f(3) = 14
when x = -3
f(-3)=(-3)^2+2(-3)-1
f(-3) = 9 -6 - 1
f(-3) = 2
A genetic experiment with peas resulted in one sample of oping that consisted of 443 green peas and 10 yelow peas a. Construct a 50% confidence intervallo state of the percentage of b. Based on the confidence interval do the results of the experiment appear to control the expectation that 20% of the ring peas won Construct a son contence terva Express the percentages in conform
a) Therefore, the 50% confidence interval for the percentage of yellow peas in the population is approximately (0.47%, 3.93%).
b) Since the confidence interval does not contain the value of 20%, we can say that the results of the experiment do not support the expectation that 20% of the peas should be yellow.
c) The 90% confidence interval for the percentage of green peas in the population is approximately (95.87%, 99.53%).
The data given in the problem is:
Sample size (n) = 443 + 10 = 453
Number of yellow peas (x) = 10
Number of green peas (n-x) = 443
Since the sample size is very large (n > 30), we can use the normal distribution to find the confidence interval.
a) To construct a 50% confidence interval for the percentage of yellow peas in the population, we use the following formula:
Lower limit = p - z(α/2)√(p(1-p)/n)
Upper limit = p + z(α/2)√(p(1-p)/n)
where: p = x/n = 10/453 = 0.022 (proportion of yellow peas in the sample)
z(α/2) = z(0.25) = 0.674 (z-value for a 50% confidence level)
Plugging in the values, we get:
Lower limit = 0.022 - 0.674√(0.022(1-0.022)/453) ≈ 0.0047
Upper limit = 0.022 + 0.674√(0.022(1-0.022)/453) ≈ 0.0393
Therefore, the 50% confidence interval for the percentage of yellow peas in the population is approximately (0.47%, 3.93%).
b) Since the confidence interval does not contain the value of 20%, we can say that the results of the experiment do not support the expectation that 20% of the peas should be yellow.
c) To construct a 90% confidence interval for the percentage of green peas in the population, we can use the same formula as before with x = 443:
Lower limit = p - z(α/2)√(p(1-p)/n)
Upper limit = p + z(α/2)√(p(1-p)/n)where:
p = x/n = 443/453 = 0.977 (proportion of green peas in the sample)
z(α/2) = z(0.05) = 1.645 (z-value for a 90% confidence level)
Plugging in the values, we get:
Lower limit = 0.977 - 1.645√(0.977(1-0.977)/453) ≈ 0.9587
Upper limit = 0.977 + 1.645√(0.977(1-0.977)/453) ≈ 0.9953
Therefore, the 90% confidence interval for the percentage of green peas in the population is approximately (95.87%, 99.53%).
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I need help ASAP
How do I find the radius of a cone even if they don’t give the diameter
Who ever can answer this gets 30 points!!!
Answer:
dowload the link up the other one answer
Determine whether there is a significant difference in the pattern of rankings for the 26 American and 41 European male tennis players included in the top-100 seeded players on the pro-tennis tour.
To determine whether there is a significant difference in the pattern of rankings for the 26 American and 41 European male tennis players included in the top-100 seeded players on the pro-tennis tour, a statistical analysis can be conducted.
Statistical analysis would include a two-sample t-test or an ANOVA test to compare the means of the two groups (American and European players). If the p-value obtained is less than the level of significance (usually 0.05), then there is a significant difference between the pattern of rankings of the two groups.The rankings of players will also be taken into account. If there is a significant difference between the two groups, then further analysis can be done to determine the cause of the difference. Possible factors that could contribute to the difference include training regimes, genetics, playing surfaces, and mental preparation, among others.
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There is no significant difference in the pattern of rankings between these two groups of players.
To determine whether there is a significant difference in the pattern of rankings for the 26 American and 41 European male tennis players included in the top-100 seeded players on the pro-tennis tour, we need to perform a statistical analysis using appropriate tests such as the t-test or ANOVA (Analysis of Variance).
The null hypothesis for this test would be that there is no significant difference in the pattern of rankings between the American and European male tennis players included in the top-100 seeded players on the pro-tennis tour.
The alternative hypothesis would be that there is a significant difference in the pattern of rankings between these two groups of players.
If the p-value obtained from the test is less than the chosen level of significance (usually 0.05), then we can reject the null hypothesis and conclude that there is a significant difference in the pattern of rankings for the American and European male tennis players included in the top-100 seeded players on the pro-tennis tour.
On the other hand, if the p-value is greater than the level of significance, we fail to reject the null hypothesis and conclude that there is no significant difference in the pattern of rankings between these two groups of players.
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3 of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?
Answer:
97/100
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one ids attached to the event. If it doesn't a value of zero is attached to the event.
Probability that the DVRs is not faulty = total number of faulty videos / total number of videos
total number of faulty videos = 100 - 3 = 97
total number of videos = 100
97/100
A ja ja ja ibsnisbisnobs
Answer:
20
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
Please I need help with this for better understanding and clarity. Thank you. (e Three different Mathematics books,four different French books and two different Physics books are to be arranged on a shelf.How many different arrangements are possible if
i. the books in each particular subject must all stand together only the French books must be in the first position on the shelf whilst the others
ii. must also always be together but not in the first position
iii. all the three subject matters can be arranged anyhow.
The required number of arrangements when all the three subject matters can be arranged anyhow is given by:
9! = 362880
i. The required number of arrangements when French books are in the first position is given by:
3! * 2! * 4! = 1728
ii. the required number of arrangements is given by:
3! * 4! * 2! = 3456
iii. the required number of arrangements when all the three subject matters can be arranged anyhow is given by:
9! = 362880
Given that there are e = 3
Mathematics books,
f = 4 French books, and
p = 2 Physics books to be arranged on a shelf.
The problem requires to calculate the number of different arrangements are possible in the following ways:
i. If the books in each particular subject must all stand together only the French books must be in the first position on the shelf whilst the others
ii. Must also always be together but not in the first position.
All the three subject matters can be arranged anyhow.
i. If the books in each particular subject must all stand together only the French books must be in the first position on the shelf whilst the others:
If the French books are always in the first position of the shelf, then the remaining 8 books can be arranged in 8! ways as they all have different titles. But there are 3! ways to arrange the mathematics books and 2! ways to arrange the physics books.
Therefore, the required number of arrangements when French books are in the first position is given by:
3! * 2! * 4! = 1728
ii. Must also always be together but not in the first position
If all the books of the same subject must be kept together, then there are 3! ways to arrange the mathematics books, 4! ways to arrange the French books, and 2! ways to arrange the physics books.
Therefore, the required number of arrangements is given by:
3! * 4! * 2! = 3456
iii. All the three subject matters can be arranged anyhow.
If all the three subject matters can be arranged anyhow, then the total number of books to be arranged is 9.
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22:13 progress 87 percent shift changes you created the following labor plan for truck unloading and box storage during an 8-hour shift. task boxes processed per worker per hour
A labor plan was created for truck unloading and box storage during an 8-hour shift, with the productivity measured in boxes processed per worker per hour.
To fully answer the question, it is necessary to provide the details of the labor plan, including the specific productivity rates for each task and the number of workers assigned to each task. Without this information, it is not possible to provide a comprehensive explanation. However, the labor plan aims to optimize the efficiency of truck unloading and box storage within the given 8-hour shift. It likely involves assigning workers to different tasks based on their productivity levels and the estimated time required for each task.
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Jack and Andrea want to create a right triangle together using values of x and y and the polynomial identity to generate Pythagorean triples. If Andrea picks a value of x = 2, and the hypotenuse of the resulting right triangle is 5, what natural number value of y did Jack pick?
y = 1
y = 4
y = 2
y = 3
Answer:
I think the answer could be y=3 or y=2
it could be something else tho im sorry
Answer:
y=2
Step-by-step explanation:
The student council had a cupcake fundraiser. The cupcakes were donated, but the icing, plates and candy were purchased for $50. The
student council sold the cupcakes for $1.50 each.
Which equation shows the relationship between the profit, p, and the number of cupcakes sold, n?
eight thousand eight and eight tenths in standard form help plz
Answer:
8,088.8
Step-by-step explanation:
A segment in the complex plane has a midpoint at -1+i. If the segment has an endpoint at -5-7i, what is the other endpoint? -9-15i
Given that a segment in the complex plane has a midpoint at -1+i. If the segment has an endpoint at -5-7i, we need to find the other endpoint.
To find the other endpoint, we can use the midpoint formula which states that the midpoint of a segment is the average of the endpoints of the segment. Let the other endpoint be represented by the complex number z. Then, we have:-1 + i = (-5 - 7i + z)/2Multiplying both sides by 2, we get:-2 + 2i = -5 - 7i + zSimplifying the equation by moving the known values to the left-hand side, we have:z = -2 + 2i + 5 + 7iCombining like terms, we get:z = 3 + 9iTherefore, the other endpoint is 3 + 9i. Thus, the correct option is (D) 3 + 9i.
To find the other endpoint of the segment in the complex plane, we can use the midpoint formula. The midpoint formula states that the midpoint between two complex numbers, z₁ and z₂, is given by:
Midpoint = (z₁ + z₂) / 2
We are given that the midpoint is -1 + i and one endpoint is -5 - 7i. Let's denote the other endpoint as z₂. Using the midpoint formula, we can write:
-1 + i = (-5 - 7i + z₂) / 2
To isolate z₂, we can multiply both sides of the equation by 2:
2(-1 + i) = -5 - 7i + z₂
To simplifying, we have:
-2 + 2i = -5 - 7i + z₂
Now, let's isolate z₂ by subtracting -5 - 7i from both sides:
-2 + 2i + 5 + 7i = z₂
Combining like terms, we get: 3 + 9i = z₂
Therefore, the other endpoint of the segment in the complex plane is given by -9 - 15i.
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The given information is that in the complex plane, a segment has its midpoint at -1+i. The segment has an endpoint at -5-7i. It is asked to find the other endpoint of the segment.
Thus, the other endpoint of the segment is -9 + 9i.
The midpoint of the segment is given as follows:
Midpoint = (endpoint1 + endpoint2) / 2
-1+i = (-5-7i + endpoint2) / 2
Multiplying both sides of above equation by 2, we get:
-2 + 2i = -5 - 7i + endpoint2
endpoint2 = -2 + 2i + 5 + 7i
endpoint2 = -9 + 9i
Therefore, the other endpoint of the segment is -9 + 9i.
Thus, the answer for this question is -9+9i.
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Please Help! Draw the graph of an absolute value function that has these key features:
vertex: (2,-3)
increasing: (2, ∞)
decreasing: (-∞, 2)
domain: all real numbers
range: [-3, ∞)
end behavior: As x approaches negative infinity, f(x) approaches positive infinity. As x approaches positive infinity, f(x) approaches positive infinity.
Answer:edmentum
Step-by-step explanation:
Dexamethasone 12 mg IV push Drug available: Dexamethasone 4 mg/5 mL How many milliliters would be needed to be drawn up for one dose?
A. 3 ml
B. 2.4 ml
C. 10 ml
D. 15 ml
The correct answer is option B) 2.4 ml. The 2.4 milliliters would be needed to be drawn up for one dose.
To calculate the amount of Dexamethasone 4 mg/5 mL needed for a 12 mg dose, we can use a simple proportion:
4 mg / 5 mL = 12 mg / x
Cross-multiplying, we get:
4 mg * x = 60 mg
x = 60 mg / 4 mg/mL
x = 15 mL
Therefore, to administer a 12 mg dose of Dexamethasone using the available drug concentration of Dexamethasone 4 mg/5 mL, we need to draw up only 2.4 mL.
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(a) y = 5z + x simplify x
Answer:
x=y−5z
Step-by-step explanation:
y=5z+x
Step 1: Flip the equation.
x+5z=y
Step 2: Add -5z to both sides.
x+5z+−5z=y+−5z
x=y−5z
Answer:
x=y−5z
plz mark me as brainliest
Answer:
x = ay - 5z
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Melissa and Matt both started a card collection at the same time. Melissa started her card collection with 100 cards and added 13 cards to her collection each week. Matt started his card collection with 130 cards and added 8 cards to his collection each week. After how many weeks did Melissa and Matt have the same number of cards in their collections?
Answer:
a few weeks
Step-by-step explanation:
What’s the answer???
Answer:
$50, 100
Step-by-step explanation:
In a population,weights of females are normally distributed with mean 52kg and standard deviation 6kg. Weights of males are normally distributed with mean 75kg and standard deviation 8kg. One male and one female are chosen at random. (a) What is the probability that the male is heavier than 81kg? [3marks] (b) What is the probability that the female is heavier than the male? Hint: If X and Y are independent Normal random variables then, for every ab e R,aX+bY has a Normal distribution. [3marks] (c If the male is above average weight(75kg),what is the probability that he is heav than 81kg?
The probability that he weighs more than 81 kg given that he is above the average weight is 0.4532.
(a) Probability that male is heavier than 81 kg can be found using the z-score formula;
z = (x - μ) / σ = (81 - 75) / 8 = 0.75P(z > 0.75) = 1 - P(z < 0.75)
Now referring to z-tables, we find that P(z < 0.75) = 0.7734
Therefore, P(z > 0.75) = 1 - P(z < 0.75) = 1 - 0.7734 = 0.2266
Thus, the probability that the male is heavier than 81 kg is 0.2266.
(b) Let X be the weight of female and Y be the weight of male. We know that X ~ N(52, 6) and Y ~ N(75, 8)
Let Z = X - Y then, Z ~ N(52 - 75, sqrt(6^2 + 8^2)) = N(-23, 10)
Now, we need to find the probability that X > Y. i.e P(X - Y > 0)P(X - Y > 0) can be written as P(Z > -23/10)
Now, referring to the z-tables, we can find that P(Z > -2.3) = 0.9893
Therefore, P(X > Y) = P(X - Y > 0) = 0.9893.
(c) Given that male weight is above average weight, we need to find the probability that he weighs more than 81 kg i.e. P(Y > 81 | Y > 75)
This is conditional probability and can be found using Bayes' Theorem:
P(Y > 81 | Y > 75) = P(Y > 75 | Y > 81) * P(Y > 81) / P(Y > 75)
Now, P(Y > 75 | Y > 81) = 1, P(Y > 81) can be found as:
P(Y > 81) = P(Z > (81 - 75) / 8) = P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.7734 = 0.2266
Also,P(Y > 75) = P(Z > 0) = 0.5Therefore,P(Y > 81 | Y > 75) = 1 * 0.2266 / 0.5 = 0.4532
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The given information is that weights of females are normally distributed with mean 52kg and standard deviation 6kg. Weights of males are normally distributed with mean 75kg and standard deviation 8kg. One male and one female are chosen at random.
The probability that the male is heavier than 81kg is 0.2266.
The probability that the female is heavier than the male is 0.0107.
If the male is above average weight(75kg),then the probability that he is heavy than 81kg is 0.2266.
a) The weight of males is normally distributed with a mean of 75kg and a standard deviation of 8kg. The probability that the male is heavier than 81kg can be calculated as follows: z = (81 - 75) / 8
= 0.75P(Z > 0.75)
= 0.2266
Therefore, the probability that the male is heavier than 81 kg is 0.2266.
b) If X and Y are independent Normal random variables, then, for every ab e R, aX + bY has a Normal distribution. The weights of males and females are independent, normally distributed random variables with means of 75kg and 52kg and standard deviations of 8kg and 6kg respectively. Therefore, the difference in weights of the male and the female is a normally distributed random variable with mean μ = 75 - 52 = 23kg and standard deviation σ = √(8² + 6²) = √(100) = 10kg. Let Z be a standard normal variable. The probability that the female is heavier than the male can be calculated as follows:
P(X < Y) = P(X - Y < 0) = P[(X - Y - μ)/σ < (-23)/10] = P(Z < -2.3) = 0.0107
Therefore, the probability that the female is heavier than the male is 0.0107.
c) If the male is above average weight, then we can assume that he weighs 75 kg. The probability that he is heavier than 81 kg can be calculated as follows:
z = (81 - 75) / 8 = 0.75P(Z > 0.75) = 0.2266
Therefore, the probability that the male is above average weight and heavier than 81 kg is 0.2266.
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dr. ellison says that the equation y = -3x 7 has a solution of (2, 13). is dr. ellison right or wrong
Dr. Ellison is wrong.
To determine if the equation y = -3x + 7 has a solution of (2, 13), we can substitute the values of x and y into the equation and check if it holds true.
Substituting x = 2 and y = 13 into the equation:
13 = -3(2) + 7
13 = -6 + 7
13 = 1
The equation does not hold true since 13 is not equal to 1.
Therefore, (2, 13) is not a solution to the equation y = -3x + 7.
Hence, Dr. Ellison is incorrect in stating that (2, 13) is a solution to the equation.
An equation is a mathematical statement that indicates that two expressions are equal. It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. Equations are used to represent relationships between quantities and to solve problems in various branches of mathematics and science.
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