A) For 99% confidence, the critical value (from the table) is approximately 2.576.
48 subjects are required for a 99% confidence level. (Round up to the nearest subject)
B) For 90% confidence, the critical value (from the table) is approximately 1.645.
19 subjects are required for a 90% confidence level. (Round up to the nearest subject)
C) Decreasing the confidence level decreases the sample size needed (option B).
What is a Confidence Interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most usual, but other levels, such 90% or 99%, are occasionally used to generate a confidence range.
How to solve
z for 99%=2.58
z for 95%=1.96
a)sample size= [tex](z*s/E)^2=(2.58*12.6/4)^2=66[/tex]
b)sample size= [tex](z*s/E)^2=(1.96*12.6/4)^2=38[/tex]
decreasing the confidence level decreases the sample size required
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If a line has a slope of 3 and contains the point (-1, 4), what is its equation in point-slope form?
A. y+1=3(x-4)
B. y-1=3(x-4)
C. y-4=3(x-1)
D. y-4=3(x+1)
If a line has a slope of 3 and contains the point (-1, 4), its equation in point-slope form include the following: C. y - 4 = 3(x - 1).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (1, 4) and a slope of 3, a linear equation for this line can be calculated or determined by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = 3(x - 1)
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please help me out!! and number the answers with the number of the question please.
Answer:
Question 5 : 10% decay
Question 6 : Amar is right
Step-by-step explanation:
Josh does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 10 hours. He spends at most 8
hours doing cardiovascular work. He spends at most 6 hours on weight training. Let x denote the time (in hours) that Josh spends doing cardiovascular work.
Let y denote the time (in hours) that he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.
11
12-
IN
10
S
Continue
12 13
X
Save For Later
©2023
The figure of the shaded region is shown in graph.
Now, Based on the given information, we can create the following system of inequalities to represent Josh's weekly exercise program:
for he exercises for at least 10 hours;
⇒ x + y ≥ 10
And, When he spends at most 8 hours doing cardiovascular work is,
x ≤ 8
When, he spends at most 6 hours on weight training,
y ≤ 6
Hence, To graph these inequalities, we can start by graphing the three lines that represent each of the above equations.
The first inequality, x + y ≥ 10, represents a line with a y-intercept of 10 and a slope of -1.
The second inequality, x ≤ 8, represents a vertical line at x = 8.
The third inequality, y ≤ 6, represents a horizontal line at y = 6.
Thus, The figure of the shaded region is shown in graph.
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An employee's monthly productivity M, in number of units produced, is found to be a function of the number t of years of service. For a certain product, a productivity function is shown below. Find the maximum productivity and the year in which it is achieved.
M(t)=-3t²+126t+150, 0≤t≤40
The maximum productivity is 2646 units per month and it occurs at 21 years of service.
To find the maximum productivity and the year in which it is achieved, we need to find the vertex of the parabolic function represented by the productivity function.
The vertex of a parabola in the form y = a[tex]x^{2}[/tex] + bx + c is located at the point (-b/2a, c - [tex]b^{2}[/tex]/4a).
In this case, we have:
M(t) = -3[tex]t^{2}[/tex] + 126t + 150
So, a = -3, b = 126, and c = 150.
The year of service, t, is restricted to the interval 0 ≤ t ≤ 40, which means that the maximum productivity will occur at either t = 0 or t = 40, or at the vertex of the parabola.
The x-coordinate of the vertex is given by -b/2a, which in this case is:
t = -b/2a = -126/(2(-3)) = 21
So, the maximum productivity occurs at t = 21 years of service.
To find the maximum productivity, we substitute t = 21 into the productivity function:
M(21) = -3[tex](21)^{2}[/tex] + 126(21) + 150 = 2646
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Which are equivalent to 5-3 × [10x (6-2)]? Select two options.
1. 2 × [10 × (4)]
2. 5-3×[40]
3. 2 × [40]
4. 5 less than 3 times the product of 10 and the difference of 6 and 2
5. the difference of 5 and 3 times the product of 10 and the difference of 6 and 2
Answer:
Option 2 and Option 3 are equivalent to 5-3 × [10x (6-2)]
Step-by-step explanation:
Option 2:
5-3 × [10x (6-2)] = 5-3 × [10x4] = 5-3 × 40 = 5-120 = -115
Option 3:
5-3 × [10x (6-2)] = 5-3 × 40 = 5-120 = -115
F
46°
6.8 yd
E
DE
D
StartFraction n Over 32 EndFraction = StartFraction 1 Over 16 EndFraction a. n = one-half c. n = 2 b. n = 4 d. n = 512
The solution of the fraction is n = 2 (option c).
Now, let's consider the equation n/32 = 1/16, where n is a variable that we want to solve for. This equation tells us that the ratio of n to 32 is equal to the ratio of 1 to 16. In other words, if we divide n by 32, we get the same result as if we divide 1 by 16.
To solve for n, we can use algebraic techniques to isolate the variable on one side of the equation. One way to do this is to multiply both sides of the equation by 32, which gives us:
n = (1/16) * 32
We can simplify the right-hand side of this expression by multiplying 1/16 by 32, which gives us:
n = 2
Therefore, the answer to this problem is n = 2. (option c).
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Complete Question:
n/32 = 1/16. Fine the value of n.
a. n = one-half
b. n = 4
c. n = 2
d. n = 512
i need the answer asap
Answer: -4, -2 and 5, 7
Step-by-step explanation:
A food critic collected data on the lengths of time customers waited for their food
1/2, 1/4, 3/4, 1/2,1/4, 1/2, 1
What is the difference between the longest time and the shortest time that customers waited?
Answer:
Hi
You can identify which is the shortest and longest by converting the fractions to decimal or by finding the L.C.M
The longest time is 1
and the shortest is 1/4
The difference would be 1-1/4= 3/4
The radius of a cylindrical construction pipe is 1.5ft. If the pipe is 16ft long, what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
If the radius of a cylindrical construction pipe is 1.5ft, the volume of the construction pipe is approximately 452 cubic feet.
To find the volume of a cylinder, we use the formula V = πr²h, where r is the radius of the base, h is the height, and π is a constant approximately equal to 3.14.
In this problem, the radius is given as 1.5ft and the height is given as 16ft. Therefore, we can plug in these values to get:
V = π(1.5ft)²(16ft)
Simplifying this expression, we get:
V = 9π(16ft)
Using the value 3.14 for π, we can approximate the volume as:
V ≈ 9(3.14)(16ft) ≈ 452ft³
It's important to include the correct unit in the answer, which in this case is cubic feet.
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im just gonna give a image of the questions i give up on typing
Answer:
The answer is 43°
Step-by-step explanation:
137+137+x+43=360°
x+317=360
x=360-317
x=43°
Find the standard deviation
of the given data.
First, find the mean, X, of the data.
5, 6, 8, 13
The standard deviation of the given data is approximately 3.08.
To find the standard deviation of the given data (5, 6, 8, 13), we first need to find the mean (X) of the data.
Mean (X) = (5 + 6 + 8 + 13) / 4 = 32 / 4 = 8
Next, we calculate the deviations from the mean for each data point:
Deviation from the mean = Data point - Mean
For 5: 5 - 8 = -3
For 6: 6 - 8 = -2
For 8: 8 - 8 = 0
For 13: 13 - 8 = 5
Then, we square each deviation:
(-3)^2 = 9
(-2)^2 = 4
0^2 = 0
5^2 = 25
Next, we calculate the sum of the squared deviations:
Sum of squared deviations = 9 + 4 + 0 + 25 = 38
To find the variance, we divide the sum of squared deviations by the number of data points:
Variance = Sum of squared deviations / Number of data points = 38 / 4 = 9.5
Finally, we take the square root of the variance to find the standard deviation:
Standard deviation = √Variance = √9.5 ≈ 3.08
Therefore, the standard deviation of the given data is approximately 3.08.
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Write an equation of the line using function notation.
Slope 0; through (−3,−2)
The equation of the line is f(x)=
The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.
Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.
This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.
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3/8=4/7x what is x please help me omg
The value of the variable x = 21/32
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.
These expressions are also made up of certain arithmetic or mathematical operations.
These operations includes;
SubtractionDivisionAdditionMultiplicationBracketParenthesesFrom the information given, we have that;
3/8=4/7x
cross multiply the values, we have;
7x(3) = 8(4)
multiply the values and expand the brackets, we get the values;
21x = 32
Divide both sides by the coefficient of the variable x, we get;
x = 32/21
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The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5.
a. What is the point estimate of the population mean?
10
b. What is the point estimate of the population standard deviation (to 3 decimals)?
3.240
c. With 95% confidence, what is the margin of error for the estimation of the population mean (to 1 decimal)?
d. What is the 95% confidence interval for the population mean (to 1 decimal)?
*
The point estimate of the population mean is 10.5.
The point estimate of the population standard deviation is 3.240, rounded to 3 decimals.
The margin of error for the estimation of the population mean with 95% confidence is 3.1
The 95% confidence interval for the population mean is [7.4, 13.6]
a. The point estimate of the population mean is the sample mean.
We can calculate it by adding up all the sample values and dividing by the sample size:
(10 + 8 + 12 + 15 + 13 + 11 + 6 + 5) / 8 = 10.5
Therefore, the point estimate of the population mean is 10.5.
b. The point estimate of the population standard deviation is the sample standard deviation. We can calculate it using the following formula:
s = √Σ(xi - x)² / (n - 1) ]
Plugging in the sample values, we get:
x = 10.5
s = √((10-10.5)² + (8-10.5)² + (12-10.5)² + (15-10.5)²+ (13-10.5)² + (11-10.5)²+ (6-10.5)² + (5-10.5)²) / (8 - 1) ]
s = 3.240
c.
margin of error = t-value × (sample standard deviation / √(sample size))
Plugging in the values we found, we get:
margin of error = 2.365 × (3.240 / √(8))
margin of error=3.067
d. Finally, we can use the following formula to find the 95% confidence interval for the population mean:
confidence interval = sample mean ± margin of error
confidence interval = 10.5 ± 3.067
confidence interval = [7.4, 13.6]
Therefore, the 95% confidence interval for the population mean is [7.4, 13.6]
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araceli renta un local rectangular de 4.2 metros de frente y 7.3 metros de largo para su panaderia, ¿cuantos metros cuadrados tiene el local que rento?
The number of square meters that the space that Araceli rents is, is 30. 66 square meters.
How to find the area ?The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.
The given width is 4. 2 meters and the length is 7. 3 meters.
The area of the space in square meters is therefore :
Area = Length × Width
Area = 7. 3 meters × 4. 2 meters
Area = 30. 66 square meters
In conclusion, the space that Araceli rents has an area of 30. 66 square meters.
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Se compra un lote de CD´s de tres marcas diferentes: 500 CD´s de la marca A, 400 de la marca B y 100 de la marca C. Se sabe que el porcentaje de CD´s defectuosos para cada una de las marcas es del 1% para A, el 1.5% para B y el 2% para la marca C. Si se toma un CD al azar del lote: a) Calcular la probabilidad de que el CD elegido sea defectuoso
Entonces, la probabilidad de que el CD elegido al azar sea defectuoso es del 1.3%.
Para calcular la probabilidad de que el CD elegido al azar sea defectuoso, debemos considerar la proporcion de CD's defectuosos para cada marca y su cantidad en el lote total.
En primer lugar, podemos calcular el número total de CD's en el lote:
500 (marca A) + 400 (marca B) + 100 (marca C) = 1000 CD's
Luego, podemos calcular el número de CD's defectuosos para cada marca:
Marca A: 1% de 500 CD's = 5 CD's defectuosos
Marca B: 1.5% de 400 CD's = 6 CD's defectuosos
Marca C: 2% de 100 CD's = 2 CD's defectuosos
Por lo tanto, el numero total de CD's defectuosos en el lote es:
5 (marca A) + 6 (marca B) + 2 (marca C) = 13 CD's defectuosos
Finalmente, la probabilidad de que el CD elegido al azar sea defectuoso es simplemente la proporción de CD's defectuosos en el lote total:
P(CD defectuoso) = 13/1000 = 0.013 o 1.3%
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please help and show work
Answer:
A
Step-by-step explanation:
0.15 × 12 = 1.8
ps : i'm not sure if it's true or not, but i think this is the answer. i'm sorry if i get you wrong
A drama department is building the set for an upcoming play. They want to build a tree line from the corner of the castle to the back corner of the stage. The dimensions of the stage and castle are shown. What is the length of the tree line, t, to the nearest foot? Show your work.
The length of the tree line, t, to the nearest foot, is 20 ft.
We have,
From the figure,
t can be considered as the hypotenuse.
And,
The other two sides are::
15 - (7 + 5) = 15 - 12 = 3
30 - 10 = 20
Now,
Applying the Pythagorean theorem,
t² = 3² + 20²
t² = 9 + 400
t² = 409
t = 20
Thus,
The length of the tree line, t, to the nearest foot, is 20 ft.
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20 POINTS MARKING BRAINLIST PLEASE HELP!!
The probability that a point falls in the red-shaded square is given as follows:
p = 9/16.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The probability that a point falls in the red shared square is then given by the division of the area of the red shaded square by the division of the area of the larger square.
The area of the red-shaded square is given as follows:
3² = 9.
The area of the larger square is given as follows:
4² = 16.
Hence the probability is given as follows:
p = 9/16.
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What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer:
(4,0) & (9,5)
Step-by-step explanation:
Where the equations cross are the solutions!
Hope this Helps! :)
Happy Studies
10) Se invierten $8,000 a una tasa de interés compuesta continua del 4%, por lo que se puede usar la fórmula v(t)=8,000e.c para encontrar el valor de la inversión después de t años. ¿Después de cuántos 0.041 años se duplicará el valor de la inversión?
The number of years that it would take for the investment to double, given a continuous compounding rate, is 17. 33 years.
How to find the time to double ?The formula for continuous compound interest is given by:
[tex]A = Pe ^{rt}[/tex]
We are given $ 8, 000 and want to know how long it would take for this amount to double and become $ 16, 000.
The formula would be:
[tex]16,000 = 8, 000 e ^{0.04 t}2 = e ^{0.04t}[/tex]
ln ( 2 ) = 0 .04t
t = ln ( 2 ) / 0. 04
= 17. 33 years
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After running 5/6 of an hour konner is 1/3 of the way
The number of hours that Konner is left with till they can reach their destination is 1 ¹ / ₃ hours
How to find the number of hours ?We can start by using a proportion to set up an equation to solve for the time needed to arrive:
Distance traveled / total distance = time traveled / total time
Using a ratio, we infer that 5 / 6 of an hour is equivalent to 1 / 3 of the way.
This means that if there are 2 / 3 of the way left, the hours left till Konner reaches is:
= 5 / 6 x 2
= 10 / 6
= 5 / 3
= 1 ¹ / ₃ hours
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Question is:
How much longer till he arrives ?
If D = 2w? - w - 7 and C = 3w - 6, find an expression that equals D + 3C in
standard form.
The expression is equivalent to 10w - 25 = 0
How to determine the expressionIt is important to note that algebraic expressions are described as expressions that are made up of terms, variables, coefficients, factors and constants.
These expressions are also made up of arithmetic operations. These operations are;
BracketParenthesesSubtractionMultiplicationAdditionFrom the information given, we have that;
D = 2w - w - 7
C = 3w - 6
To determine the value of the expression D + 3C
substitute the expression
2w - w - 7 + 3(3w -6)
expand the bracket
2w - w - 7 + 9w - 18
collect the like terms and add
10w - 25 = 0
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2. A sphere has a great circle with a circumference of 10 pie meters. Find the radius. If the sphere is
cut in half, find the surface area of the closed hemisphere and its volume. Give exact answers in
terms of pie
The surface area of the two hemispheres combined is 100π square meters, and the volume of the two hemispheres combined is (500/3)π cubic meters.
The circumference of a great circle on a sphere is given by the formula C = 2πr, where r is the radius of the sphere.
In this case, we are given that the circumference of the great circle is 10π meters, so we can set up an equation:
10π = 2πr
Dividing both sides by 2π, we get:
r = 5
So the radius of the sphere is 5 meters.
When the sphere is cut in half, we get two equal hemispheres. The surface area of a closed hemisphere is given by the formula A = 2πr^2, where r is the radius of the hemisphere.
Since we are dealing with a radius of 5 meters, the surface area of one hemisphere is:
A = 2π(5^2) = 50π
Therefore, the surface area of the two hemispheres combined is:
2A = 2(50π) = 100π
The volume of a closed hemisphere is given by the formula V = (2/3)πr^3. Again, since we are dealing with a radius of 5 meters, the volume of one hemisphere is:
V = (2/3)π(5^3) = (2/3)π125 = (250/3)π
Therefore, the volume of the two hemispheres combined is:
2V = 2(250/3)π = (500/3)π
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please solve this ixl sucks
Filled box will be:
Box 1: Sum of angles on starlight line is 180°.
Box 2: m ∠LQR + m ∠MQR = 180°
Box 3: m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR
Box 4: m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR
Box 5: If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel.
From the given figure we have to prove that LM ∥ NP.
m ∠LQR + m ∠QRN = 180° [Given]
m ∠LQR + m ∠MQR = 180° [Sum of angles on starlight line is 180°]
m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR [Transitive property of Equality]
m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR [Subtraction property of Equality]
m ∠QRN = m ∠MQR [Definition of Congruence]
LM ∥ NP [If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel]
Hence it is proved that, LM ∥ NP.
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hi would like some help asap
Answer:
B. quadratic
Step-by-step explanation:
You want to know the kind of function that would best fit the points shown on the graph.
SlopeThe points on the graph demonstrate a slope that starts out positive and decreases through 0 to a slope with a negative value.
A linear function has a constant slope.
An exponential function has a continuously increasing or continuously decreasing slope.
A quadratic function has a slope that changes sign, matching the slope of the curve joining the given points.
The equation that best fits the given data will be quadratic.
<95141404393>
Two friends went to get ice cream sundaes. They each chose a flavor of ice cream from a list of vanilla and chocolate and toppings from a list of hot fudge, strawberries, sprinkles, peanuts, and whipped cream. Use the sets below describing their choices and find C'.
Let A = {vanilla, chocolate, hot fudge, strawberries, sprinkles, peanuts, whipped cream}
Let B = {vanilla, hot fudge, sprinkles, whipped cream}
Let C = {chocolate, hot fudge, peanuts, whipped cream}
a
{vanilla, strawberries, sprinkles}
b
{chocolate, hot fudge, peanuts, whipped cream}
c
{vanilla, hot fudge, sprinkles, whipped cream}
d
{chocolate, strawberries, sprinkles}
The complement of a set C, denoted by C', contains all the elements of the universal set that are not in C. In this case, the universal set is A, which contains all the flavors and toppings available.
Given data ,
a) {vanilla, strawberries, sprinkles}
This set contains vanilla, strawberries, and sprinkles but does not contain any elements from C. Therefore, C' = A - {vanilla, strawberries, sprinkles} = {chocolate, hot fudge, peanuts, whipped cream}.
b) {chocolate, hot fudge, peanuts, whipped cream}
This set contains all the elements of C but does not contain any elements from A that are not in C. Therefore, C' = A - C = {vanilla, strawberries, sprinkles}.
c) {vanilla, hot fudge, sprinkles, whipped cream}
This set contains hot fudge, sprinkles, and whipped cream but does not contain any elements from C. Therefore, C' = A - {hot fudge, sprinkles, whipped cream} = {vanilla, chocolate, strawberries, peanuts}.
d) {chocolate, strawberries, sprinkles}
This set contains strawberries and sprinkles but does not contain any elements from C. Therefore, C' = A - {strawberries, sprinkles} = {vanilla, chocolate, hot fudge, peanuts, whipped cream}.
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6
Select the correct answer.
What is the domain of y = cos(z)?
O A. [0, 00)
OB.
2T
O C. (-00,00)
O D. [-1, 1]
Reset
Next
3) Fairview and Union are 9 cm apart on a map
that has a scale of 1 cm: 10 km. How far
apart are the real cities?
Answer:
Fairview and Union are 9 cm apart on the map, and the scale is 1 cm: 10 km. So, to figure out the actual distance between the two cities, we need to use some math.
If 1 cm on the map represents 10 km in real life, then 9 cm on the map represents 90 km in real life. Therefore, Fairview and Union are actually 90 km apart.
Hope that helps!
Step-by-step explanation:
Answer:
90 km
Step-by-step explanation:
The scale of the map is
1 cm : 10 km
The scale of a map is a ratio. We can use a proportion to solve this problem.
1 cm is to 10 km as 9 cm is to x km
1/10 = 9/x
1 × x = 10 × 9
x = 90
Answer: 90 km
