The given nonhomogeneous equation is:
y'' - y = 17t
To find the general solution, we need to find the complementary solution and particular solution separately.
Complementary Solution:
The associated homogeneous equation is:
y'' - y = 0
The characteristic equation for this is:
r^2 - 1 = 0
Solving for the roots, we get:
r = ±1
So the complementary solution is:
y_c(t) = c1e^t + c2e^(-t)
where c1 and c2 are constants.
Particular Solution:
The particular solution is given as:
y_p(t) = -17t
We can substitute this into the nonhomogeneous equation to find the value of the constant:
y'' - y = 17t
(-17)'' - (-17) = 17t
0 + 17 = 17t
t = 1
Therefore, the constant is -17.
So the particular solution is:
y_p(t) = -17t
General Solution:
The general solution is the sum of the complementary solution and the particular solution:
y(t) = y_c(t) + y_p(t) = c1e^t + c2e^(-t) - 17t
where c1 and c2 are constants.
Therefore, the general solution to the given nonhomogeneous equation y'' - y = 17t with particular solution yp(t) = -17t is:
y(t) = c1e^t + c2e^(-t) - 17t
where c1 and c2 are constants.
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Which type of relationship is indicated by the residual plot?
Onon-linear relationship
linear relationship
exponential relationship
quadratic relationship
cannot be determined
The non-linear relationship is the type of relationship that is indicated by the residual plot.
What is the non-linear relationship?A non-linear relationship denotes a kind of connection between two variables whereby one variable does not consequentially result in a proportional transformation for the other.
To elaborate, instead of delineating a direct line, such an association is generally expressed as a curve, exponential formula, or other convoluted mathematical equations.
Notwithstanding, the rate of difference in these variables isn't fixed and may shift in tandem with changes to either one of their numerical values.
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If x belongs to the interval [0,2π], at which values of x does the tangent to the curve y=cosx have a slope of 1 ? Type answer as x=c, where c is constant. For multiple answers, separate with a comma. For example, x=1. x=2 If x belongs to the interval [0,2π], at which values of x does the tangent to the curve y=cosx have a slope of 21 ? Type answer as x=c, where c is constant. For multiple answers, separate with a comma. For example, x=1, x=2 Note: You can eam partial credit on this problem. You have attempted this problem 0 times. You have 3 attempts left before new version will be requested. You have unlimited attempts remaining.
The value at which x does the tangent to the curve y=cosx have a slope of 1 is x = 3π/2.
To find the values of x at which the tangent to the curve y = cos(x) has a slope of 1, if x belongs to the interval [0,2π], we need to find the points where the derivative of the function is equal to 1. The derivative of y = cos(x) with respect to x is -sin(x). So, we need to solve the equation:
-sin(x) = 1
sin(x) = -1
Now, we want to find the values of x in the interval [0, 2π] that satisfy this equation. The sine function takes the value -1 at x = 3π/2. Therefore, x does the tangent to the curve y=cosx have a slope of 1 is x = 3π/2.
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modeling with mathematics a web browser is open on your computer screen. a rectangular computer screen is shown displaying a rectangular web browser. the length of the computer screen is labeled x plus 7 inches. the length and width of the web browser are labeled x inches and x minus 2 inches respectively. a. the area of the browser window is 24 square inches. find the length of the browser window $x$ . in. b. the browser covers $\frac{3}{13}$ of the screen. what are the dimensions of the screen? length: in. width: in.
The dimensions of the screen are:
length = L = 12 inches
width = W = (13L - 182) / 3 = (13*12 - 182) / 3 = 2 inches
a. The area of the browser window is given by:
area = length * width
24 = x(x-2)
Simplifying and solving for x, we get:
[tex]x^2[/tex] - 2x - 24 = 0
(x - 6)(x + 4) = 0
Since the length cannot be negative, we take x = 6. Therefore, the length of the browser window is x = 6 inches.
b. Let L and W be the length and width of the computer screen, respectively. We are given that:
length of browser = x inches = L - 7 inches
width of browser = x - 2 inches
The area of the browser is:
area of browser = x(x-2) = (L-7)(L-9)
We are also given that the browser covers 3/13 of the screen, so:
area of browser = (3/13) * area of screen
x(x-2) = (3/13) * L * W
Substituting x = L - 7 and simplifying, we get:
(L-7)(L-9) = (3/13) * L * W
Expanding and simplifying, we get:
13L[tex]^2[/tex] - 182L + 546 = 3LW
Since L and W are positive, we can divide both sides by 3L to get:
W = (13L - 182) / 3
We also know that the browser covers 3/13 of the screen, so:
area of browser = (3/13) * area of screen
x(x-2) = (3/13) * L * W
6(4) = (3/13) * L * ((13L-182)/3)
24 = (L/3) * (13L-182)
8 = L(13L-182)/3
24 = L(13L-182)
13L^2 - 182L - 24 = 0
(L - 12)(13L + 2) = 0
Since the length cannot be negative, we take L = 12. Therefore, the dimensions of the screen are:
length = L = 12 inches
width = W = (13L - 182) / 3 = (13*12 - 182) / 3 = 2 inches
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find the value of y. round to the nearest tenth, if necessary
Answer:
8.9
Step-by-step explanation:
according to the Pythagorean theorem:
c^2=a^2+b^2
Where c is the longest side, the hypotenuse, and a and b are the sides.
Substitute the numbers in:
12^2=8^2+y^2
144=64+y^2
144-64=y^2
80=y^2
Y= square root of 80
Y= 8.944
After rounding to the nearest tenth, that would be 8.9
T/F : The solution set of the linear system whose augmented matrix [a1a2a3b] is the same as the solution set of the equation x1a1+x2a2+a3x3=b
True.
the solution set of the linear system whose augmented matrix [a1 a2 a3 | b] is the same as the solution set of the equation x1a1 + x2a2 + a3x3 = b.
The augmented matrix [a1 a2 a3 | b] corresponds to the system of linear equations:
a1x1 + a2x2 + a3x3 = b
The solution set of this system is the same as the solution set of the vector equation:
[x1, x2, x3] * [a1, a2, a3] = b
which can be written as:
x1a1 + x2a2 + x3a3 = b
Therefore, the solution set of the linear system whose augmented matrix [a1 a2 a3 | b] is the same as the solution set of the equation x1a1 + x2a2 + a3x3 = b.
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pls help ASAPP v(if u dont know the answer then dont GUESS the answer. and no links please)
the answer is b or the second one
Answer:
Step-by-step explanation:
first do Pemdas and thats it
can Someone please help me answer this? i really don't know what to do for this one and it due tmr and I got a bunch of questions lefttt ty for whoever helps :D
Health Club B costs $8 less in monthly membership fees than Health Club A.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.For Club A, the monthly cost is given as follows:
$60.
For Club B, we have that each 4 months, the cost increases by $208, hence the monthly cost is given as follows:
208/4 = $52.
Which is $8 less than Club A.
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need help on number 15 and 16 pleasee
Answer:
15) Let n = 1 be the first term of each sequence.
[tex] - 65536 \times - 4 = 262144[/tex]
[tex]a(n) = 262144( - { \frac{1}{4}) }^{n} [/tex]
[tex]a(9) = ( {4}^{9} ) {( - \frac{1}{4} )}^{9} = {( - 1)}^{9} = - 1[/tex]
16)
[tex] 6 \div (- 3 )= - 2[/tex]
[tex]a(n )= ( - 2) ({( - 3)}^{n} )[/tex]
[tex]a(9) = - 2(( { - 3)}^{9} ) [/tex]
[tex]a(9) = - 2 \times - 19683 = 39366[/tex]
f the series is convergent, use the alternating series estimation theorem to determine the minimum number of terms we need to add in order to find the sum with an error less than 0.00005. (if the quantity diverges, enter diverges.)
To use the alternating series estimation theorem, we need to check that the series alternates in sign and that the absolute value of the terms decreases monotonically.
Assuming these conditions are met, the alternating series estimation theorem tells us that the error in approximating the sum of the series by the sum of the first n terms is bounded by the absolute value of the (n+1)th term.
To determine the minimum number of terms we need to add in order to find the sum with an error less than 0.00005, we can set the absolute value of the (n+1)th term to be less than or equal to 0.00005 and solve for n. If such an n exists, then we know that adding n terms will give us an approximation with the desired level of accuracy. If no such n exists, then the series diverges and we cannot find an approximation with the desired level of accuracy.
Note that the alternating series estimation theorem only applies to alternating series, so if the given series is not alternating, then we cannot use this theorem to determine the minimum number of terms needed for a desired level of accuracy.
The Alternating Series Estimation Theorem states that for a convergent alternating series with decreasing positive terms, the error in the partial sum is less than the first omitted term.
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help i need help with the question
The angle which is supplemental to the 6 is the angle 8, which makes option a correct.
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.
Supplementary angles are a pair of angles that add up to 180 degrees. The angles 6 and 8 lie on a straight line which implies they are supplementary as the sum of angles on a straight line is also 180°
Therefore, the angle which is supplemental to the 6 is the angle 8, which makes option a correct.
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Points A and B are 80km apart on a highway. A car starts from A and another car starts from B at the same time. If they travel in the same direction, they meet in 8 hours, but if they travel in opposite directions, they meet in 1 hour 20 mins. What are their speeds in km/hr?
The speeds of the car are 35 km/hr and 25 km/hr, if a car starts from A and another car starts from B at the same time. If both cars travel in the same direction, they cross in 8 hours, but if these cars travel in opposite directions, they meet each other in 1 hour 20 mins. A and B have a distance of 80 km.
Let the speed of the car at A be [tex]v_1[/tex]
the speed of the car at B be [tex]v_2[/tex]
In the first case, they travel in the same direction, the relative velocity is given by [tex]v_1-v_2[/tex]
[tex]v_1-v_2[/tex] = [tex]\frac{80}{8}[/tex]
[tex]v_1-v_2[/tex] = 10 -----(i)
In the second case, they travel in the opposite direction, the relative velocity is given by [tex]v_1+v_2[/tex]
[tex]v_1+v_2[/tex] = [tex]\frac{80}{1\frac{1}{3} }[/tex]
[tex]v_1+v_2[/tex] = [tex]\frac{80*3}{4}[/tex]
[tex]v_1+v_2[/tex] = 60 ------(ii)
Add equations (i) and (ii)
[tex]2v_1[/tex] = 70
[tex]v_1[/tex] = 35 km/hr
From equation (i)
[tex]v_2[/tex] = 25 km/hr
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Solve x^2-4x+4=0 by graphing. Select all solutions that apply.
Answer:
−
x
2
−
4
x
−
4
=
0
Graph each side of the equation. The solution is the x-value of the point of intersection.
x
=
−
2
image of graph
Step-by-step explanation:
−
x
2
−
4
x
−
4
=
0
Graph each side of the equation. The solution is the x-value of the point of intersection.
x
=
−
2
image of graph
You have 7 different video games. How many different ways can you arrange the games side by side on a shult? You can arrange the 7 different video games in different ways
There are 5,040 different ways to arrange the 7 video games side by side on a shult.
To calculate the number of different ways you can arrange the 7 different video games on a shult, you can use the formula for permutations, which is n!/(n-r)!. In this case, n is the total number of games (7) and r is the number of games being arranged at once (also 7, since you are arranging all of them).
So the calculation would be:
7! / (7-7)! = 7! / 0! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040
Therefore, there are 5,040 different ways you can arrange the 7 different video games side by side on a shult.
To arrange the 7 different video games side by side on a shult, you can use the concept of permutations. In this case, there are 7 video games, and you want to arrange all of them. So, the number of ways to arrange the video games can be calculated using the formula:
Number of arrangements = 7! (7 factorial)
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
Therefore, there are 5,040 different ways to arrange the 7 video games side by side on a shult.
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Help me find the volume! PLEASE ITS IMPORTANT!!!!
The volume of the given pyramid is approximately 780.975 cubic kilometers.
Given information:
The provided shape is a pyramid with a triangular base.
And the width of the base is 11.7 kilometers and the length of the base is 26.7 kilometers.
And the height of the pyramid is 15 kilometers.
To find the volume of a pyramid with a triangular base, we use the formula:
V = (1/3)Bh
where V is the volume, B is the area of the base, and h is the height of the pyramid.
In this case, we are given that the base of the pyramid is a triangle with a width of 11.7 kilometers and a length of 26.7 kilometers.
To find the area of this triangle, we use the formula for the area of a triangle:
B = (1/2)bh
where b is the width and h is the length of the base of the triangle.
Substituting the given values, we get:
B = (1/2)(11.7)(26.7)
B = 156.195 km²
Now, we substitute the values of B and h into the formula for the volume of a pyramid:
V = (1/3)(156.195)(15)
V = 780.975 km³.
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Describe any patterns or trends you noticed when finding the products in part C.
Generalize the patterns you noticed in part D to create a rule or identity to describe those patterns. For example, if you notice that every time you multiply a negative number by another negative number the result is positive, we can
generalize this by saying (-a)(-b) = c, where a, b, and c are all positive real numbers.
Edmentum
This equation generalizes the patterns seen in part D, where a and b represent real numbers:
(a + bi)(a − bi) = a2 + b2.
What is an Equation?An equation expresses the equivalence of two mathematical expressions utilizing an equal sign to separate its two sides. Each side, comprising one or more terms, is a distinct entity conveying a specific value, variable or operator.
Equations represent essential components used to express linear relationships between variables as well as for problem-solving purposes in various domains including science and math. The resolution of equations involves discovering values of variables that establish both aspects of the equation to be held equal by equating them with solutions deemed valid.
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An angle measures 4° more than the measure of its supplementary angle. What is the measure of each angle?
The measure of the angle is 92 degrees, and its supplementary angle measures 88 degrees.
Given information:
An angle measures 4° more than the measure of its supplementary angle.
Let x be the measure of the angle in degrees.
Then, its supplementary angle measures 180° - x degrees.
According to the problem, we have:
x = (180 - x) + 4
Simplifying and solving for x, we get:
2x = 184
x = 92
Therefore, the measure of the angle is 92 degrees, and its supplementary angle measures 180 - 92 = 88 degrees.
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find three consecutive integers, the sum of whose squares is 65 more than three times the square of the smallest.
The three consecutive integers are 10, 11, and 12.
To find three consecutive integers, the sum of whose squares is 65 more than three times the square of the smallest, follow these steps:
1. Let the smallest integer be x. Then, the other two consecutive integers are x + 1 and x + 2.
2. The sum of their squares is x^2 + (x + 1)^2 + (x + 2)^2.
3. The given condition is that this sum is 65 more than three times the square of the smallest integer: x^2 + (x + 1)^2 + (x + 2)^2 = 3x^2 + 65.
4. Simplify the equation:
x^2 + (x^2 + 2x + 1) + (x^2 + 4x + 4) = 3x^2 + 65
5. Combine like terms:
3x^2 + 6x + 5 = 3x^2 + 65
6. Subtract 3x^2 from both sides to eliminate the x^2 terms:
6x + 5 = 65
7. Subtract 5 from both sides:
6x = 60
8. Divide by 6:
x = 10
So, the three consecutive integers are 10, 11, and 12.
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a sailfish can travel as fast as 68 miles per hour. at that rate, how far would a sailfish travel in 45 minutes
Therefore, a sailfish would travel 51 miles in 45 minutes if it maintained a speed of 68 miles per hour in the equation.
To calculate the distance traveled in a given time, we can use the formula distance = rate x time, where rate refers to the speed of travel and time refers to the duration of travel. In this scenario, we are given a rate of 68 miles per hour and a time of 45 minutes.
To use the formula, we first need to convert the time to hours since the rate is given in miles per hour. We do this by dividing the time by 60, since there are 60 minutes in an hour. In this case, 45 minutes divided by 60 minutes per hour gives us 0.75 hours.
Now, we can plug in the values for rate and time into the formula and solve for distance. Multiplying 68 miles per hour by 0.75 hours gives us a distance of 51 miles.
45 minutes / 60 minutes per hour = 0.75 hours
Then, we can use the formula: distance = rate x time
distance = 68 miles per hour x 0.75 hours
distance = 51 miles
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Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3
7
8
,
5
1
4
,
4
,
6
1
8
,
4
1
2
,
5
1
4
,
3
1
2
,
5
3
8
,
4
3
4
,
5
Part A
How many dots will the line plot have in all?
A.
2
B.
6
C.
7
D.
10
Part B
The students will make the line plot using one fractional unit. What fractional unit should the students use so that all of the data can be plotted above a label?
A.
tenths
B.
eighths
C.
fourths
D.
halves
HELP MEEEE
Answer: I don't know, sorry!
Step-by-step explanation:
if each complete revolution of the pedals moves the bike 5.20 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. neglect work done by friction and other losses. the pedals turn in a circle of diameter 34.4 cm.
Average force ≈ 0.208 times the total force exerted in a revolution.
To calculate the average force exerted on the pedals tangent to their circular path, we need to first find the circumference of the pedal circle and then determine the force exerted per revolution.
1. Calculate the circumference of the pedal circle:
Circumference = π * diameter
Circumference = π * 0.344 m (converted 34.4 cm to meters)
Circumference ≈ 1.081 m
2. Calculate the force exerted per revolution:
We are given that each complete revolution moves the bike 5.20 m along its path. The force exerted per revolution is directly proportional to the work done.
Work done = Force * distance
Force = Work done / distance
Force = Work done / (5.20 m / 1.081 m)
Since the work done by friction and other losses is neglected, we only need to know the ratio of distances to determine the average force exerted on the pedals tangent to their circular path. Therefore,
Average force = 1.081 m / 5.20 m
Average force ≈ 0.208 times the total force exerted in a revolution.
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a study of two kinds of photocopying equipment shows that 61 failures of the first kind of equipment took on the average 80.7 minutes to repair with a standard deviation of 19.4 minutes, whereas 41 failures of the second kind of equipment took on the average 88.1 minutes to repair with a standard deviation of 18.8 minutes. construct a 98% confidence interval for the ratio of the variances of the two populations sampled.
To construct a confidence interval for the ratio of the variances of the two populations sampled, we can use the F-distribution. The formula for the F-statistic is: F = (s1^2 / s2^2) / (n1 - 1) / (n2 - 1) Where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Using the given data, we have:
s1 = 19.4
s2 = 18.8
n1 = 61
n2 = 41
The F-statistic is then:
F = (19.4^2 / 18.8^2) / (61 - 1) / (41 - 1) = 1.399
To find the confidence interval, we need to look up the critical values of the F-distribution with degrees of freedom (df) of (n1 - 1) and (n2 - 1) at the 1% level of significance.
Using a table or calculator, we find that the critical values are 0.414 and 2.518.
Thus, the confidence interval for the ratio of the variances is:
1 / (2.518 / sqrt(F)) < σ1^2 / σ2^2 < 1 / (0.414 / sqrt(F))
1 / (2.518 / sqrt(1.399)) < σ1^2 / σ2^2 < 1 / (0.414 / sqrt(1.399))
0.266 < σ1^2 / σ2^2 < 2.083
Therefore, we can be 98% confident that the ratio of the variances of the two populations sampled lies between 0.266 and 2.083.
To construct a 98% confidence interval for the ratio of the variances of the two populations sampled, we will use the F-distribution and the following formula:
CI = (s1^2 / s2^2) * (1 / Fα/2, df1, df2, F1-α/2, df1, df2)
Here, s1 and s2 are the standard deviations of the first and second kinds of equipment, and df1 and df2 are the degrees of freedom for each sample. Fα/2 and F1-α/2 are the F-distribution critical values at the α/2 and 1-α/2 levels, respectively.
Step 1: Calculate the variances (s1^2 and s2^2).
Variance1 = (19.4)^2 = 376.36
Variance2 = (18.8)^2 = 353.44
Step 2: Calculate the degrees of freedom (df1 and df2).
df1 = n1 - 1 = 61 - 1 = 60
df2 = n2 - 1 = 41 - 1 = 40
Step 3: Find the F-distribution critical values (Fα/2, df1, df2, F1-α/2, df1, df2) for a 98% confidence interval (α = 0.02).
F0.01, 60, 40 = 0.4611
F0.99, 60, 40 = 2.1080
Step 4: Calculate the confidence interval using the formula.
CI = (376.36 / 353.44) * (1 / 0.4611, 2.1080)
Lower limit = (376.36 / 353.44) * 0.4611 = 0.5925
Upper limit = (376.36 / 353.44) * 2.1080 = 2.2444
The 98% confidence interval for the ratio of the variances of the two populations sampled is (0.5925, 2.2444).
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A drawer contains 12 brown socks and 12 black socks, all unmatched. A man takes socks out at random in the dark. Answer the following questions. Question 7 Select the least number of socks that he must take out to be sure that he has at least two socks of the same color. 12 4 Question 8 Select the least number of socks that he must take out to be sure that he has at least two black socks. 3
For Question 7, the man must take out 4 socks to be sure that he has at least two socks of the same color. This is because he could potentially take out 3 brown socks and 3 black socks before getting a matching pair, but with 4 socks, there must be at least two of the same color.
For Question 8, the man must take out 3 socks to be sure that he has at least two black socks. This is because he could potentially take out all 12 brown socks before getting a black one, but with 3 socks, there must be at least one black sock and then a potential for a second.
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Use the given information to find the minimum sample sizerequired to estimate an unknown population mean mu.Margin of error: $130, confidence level: 99%, sigma = $544
The minimum sample size required to estimate the unknown population mean mu with the given margin of error and confidence level is 117.
To find the minimum sample size required to estimate an unknown population mean with a margin of error of $130 and a confidence level of 99% while assuming a known population standard deviation (sigma) of $544, we can use the following formula:
n = (Z^2 * sigma^2) / E^2
Where:
n = sample size
Z = z-score for the given confidence level (99%) = 2.576
sigma = population standard deviation ($544)
E = margin of error ($130)
Substituting the given values, we get:
n = (2.576^2 * $544^2) / $130^2
n = 208.10
Rounding up to the nearest whole number, the minimum sample size required is 209. Therefore, we would need to sample at least 209 individuals from the population to estimate the population mean with a margin of error of $130 and a confidence level of 99%, assuming a known population standard deviation of $544.
To find the minimum sample size required to estimate an unknown population mean mu, we need to use the formula for margin of error (E) in a normal distribution:
E = Z * (sigma / sqrt(n))
Here, E is the margin of error, Z is the z-score corresponding to the desired confidence level, sigma is the population standard deviation, and n is the sample size. We are given E = $130, confidence level = 99%, and sigma = $544.
First, find the z-score corresponding to the 99% confidence level. Since we want 99% of the area under the curve, we need to find the z-score that leaves 1% (100% - 99%) in the tails. We split the 1% into two tails, which gives 0.5% in each tail. From the z-table, we find the z-score that corresponds to 99.5% (since we want 0.5% in the right tail) is approximately 2.576.
Now, we can plug in the values into the formula:
130 = 2.576 * (544 / sqrt(n))
To solve for n, we need to follow these steps:
1. Divide both sides by 2.576:
130 / 2.576 = (544 / sqrt(n))
50.465 = 544 / sqrt(n)
2. Rearrange the equation to isolate the square root of n:
sqrt(n) = 544 / 50.465
sqrt(n) ≈ 10.78
3. Square both sides to find n:
n ≈ (10.78)^2
n ≈ 116.20
Since we cannot have a fraction of a person in the sample, we round up to the nearest whole number. Therefore, the minimum sample size required to estimate the unknown population mean mu with the given margin of error and confidence level is 117.
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the statistical power of a test is the probability that the test will correctly reject a false null hypothesis. that is, if a null hypothesis is false at the population level, the statistical power of a test is the probability that a researcher rejects the null hypothesis in his or her sample too. group of answer choices true false
The statement provided in the question is true. The statistical power of a test is the probability of correctly rejecting a false null hypothesis. It is the ability of a statistical test to detect a true effect, given that one exists. In other words, it is the likelihood that a study will be able to detect a difference or relationship between variables if such a difference or relationship truly exists in the population being studied.
The statistical power of a test depends on several factors, including the sample size, the effect size, and the level of significance chosen for the test. A larger sample size, a larger effect size, and a smaller level of significance all increase the power of a test. A low statistical power may indicate that the sample size is too small or that the test is not sensitive enough to detect the true effect.
Therefore, it is important to consider statistical power when designing and interpreting studies.
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15 The line plot shows the weights of ten eggs laid by one hen. EGGS LAID BY ONE HEN
THE PICTURE
what is the total weight, in onces, of the four heaviest eggs?
A 4
B 7
C 8 1/2
D 8 3/4
Pls tell me the answer again!
Answer:
I believe its 8 3/4
Step-by-step explanation:
Sarah was mixing up some lemonade to sell for her lemonade stand. The recipe calls for 3 scoops of lemonade mix to make 2 gallons of lemonade.
If she has 21 scoops of lemonade mix in the container, how many gallons of lemonade can she make?
*
Sarah can make 14 gallons of lemonade with 21 scoops of lemonade mix.
Given information:
Sarah was mixing up some lemonade to sell for her lemonade stand.
The recipe calls for 3 scoops of lemonade mix to make 2 gallons of lemonade.
If 3 scoops of lemonade mix are needed to make 2 gallons of lemonade, then one scoop of lemonade mix can make 2/3 of a gallon of lemonade.
As per the multiplication,
So, with 21 scoops of lemonade mix, Sarah can make:
21 scoops x (2/3 gallon/scoop) = 14 gallons
Therefore, Sarah can make 14 gallons of lemonade with 21 scoops of lemonade mix.
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Someone please help me with this question.
The value of the angle x of the regular octagon is: x = 112.5°
How to find the interior angle of a polygon?The formula for the Interior angle of a Polygon is:
θ = 180(n - 2)/n
We are given that the polygon has 8 sides. Thus:
θ = 180(8 - 2)/8
θ = 135°
Sum of angles in a triangle is 180° and as such, the base angles of the Isosceles triangle formed is:
base angle = (180 - 135)/2
= 22.5°
Thus:
x = 135 - 22.5
x = 112.5°
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(-3,6) (-2,9) write the equation in slope intercept form
Answer:
y = 3x + 15
Step-by-step explanation:
The slope-intercept form is y = mx + b
m = the slope
b = y-intercept
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-3,6) (-2,9)
We see the y increase by 3 and the x increase by 1, so the slope is
m = 3
Y-intercept is located at (0,15)
So, the equation is y = 3x + 15
Evaluate the equation. 2 + n=8 1/3
Answer: n= 6 1/3
Step-by-step explanation:
2+n=8 1/3
-2 -2
n=6 1/3
you just subtract 2 from both sides
What is the surface area of a rubik's cube in cm² with side that measures 14cm?
The surface area of the Rubik's cube is 1176 cm².
Surface area is a measurement of the overall space occupied by an object's surface. Often, it is expressed in terms of square measurements like square meters (m²) or square feet (ft²).
A Rubik's cube has six faces, each of which is a square with sides equal to the length of a side of the cube. Therefore, the surface area of a Rubik's cube is six times the area of one of its faces.
The area of one face of the cube with a side of 14 cm is:
14 cm x 14 cm = 196 cm²
So, the total surface area of the Rubik's cube is:
6 x 196 cm²= 1176 cm²
Hence, the area will bed 1176 cm².
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