Answer:
The width of the jewelry store is 33 feet.
Step-by-step explanation:
To solve the problem, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W where P is the perimeter, L is the length, and W is the width. Substituting the given values, we get 186 = 2(60) + 2W. Simplifying the right side, we get 186 = 120 + 2W. Subtracting 120 from both sides, we get 66 = 2W. Dividing both sides by 2, we get W = 33.
Therefore, the width of the jewelry store is 33 feet.
DUE TODAY PLEASE HELP!!!!
For which angles is the cosine positive? Select all that apply.
a
0 radians
b
5π/12 radians
c
5π/6 radians
d
3π/4 radians
e
5π/3 radians
Step-by-step explanation:
if it is between 0 and pi/2 (90°), or between 3pi/2 (270°) and 2pi (360°).
for angle = 0, cos = 1. therefore, positive.
0 <= 5pi/12 <= pi/2. therefore, positive.
pi/2 <= 5pi/6 <= pi. therefore, negative.
pi/2 <= 3pi/4 <= pi. therefore, negative.
3pi/2 <= 5pi/3 <= 2pi. therefore, positive.
you do know how to compare fractions, right ?
you need to bring then to the same denominator by multiplying numerator and denominator by the same factor.
e.g. comparing 5pi/12 with pi/2.
to bring them both to .../12, we have to multiply pi/2 by 6/6.
so, we are comparing 5pi/12 and 6pi/12.
and we see, 5pi/12 is smaller.
the others work the same way.
3pi/6 <= 5pi/6 <= 6pi/6
2pi/4 <= 3pi/4 <= 4pi/4
9pi/6 <= 10pi/6 <= 12pi/6
now you see it clearly.
consider the following data for two independent random samples taken from two normal populations. sample 1 sample 2 10 7 13 7 9 8 8 4 6 9 8 7 a. compute the two sample means. b. compute the two sample standard deviations. c. what is the point estimate of the difference between the two population means? d. what is the 90% confidence interval estimate of the difference between the two population means?
a. The sample mean for sample 1 is 9.2, and the sample mean for sample 2 is 7.17.
b. The sample standard deviation for sample 1 is approximately 3.29, and the sample standard deviation for sample 2 is approximately 3.65.
c. The point estimate of the difference between the two population means is 2.03.
d. The 90% confidence interval estimate of the difference between the two population means is [-0.44, 4.50].
a. The sample mean for sample 1 is
(10 + 13 + 9 + 8 + 6) / 5 = 9.2
The sample mean for sample 2 is
(7 + 7 + 8 + 4 + 9 + 8) / 6 = 7.1667 ≈ 7.17
b. The sample standard deviation for sample 1 is:
√[((10-9.2)² + (13-9.2)² + (9-9.2)² + (8-9.2)² + (6-9.2)²) / (5-1)]
= √[10.8] ≈ 3.29
The sample standard deviation for sample 2 is
√[((7-7.17)² + (7-7.17)² + (8-7.17)² + (4-7.17)² + (9-7.17)² + (8-7.17)²) / (6-1)]
= √[13.33] ≈ 3.65
c. The point estimate of the difference between the two population means is:
9.2 - 7.17 = 2.03
d. To calculate the 90% confidence interval estimate of the difference between the two population means, we need to first calculate the standard error of the difference between the sample means:
s.e.(difference between sample means) = √[(s1²/n1) + (s2²/n2)]
= √[(3.29²/5) + (3.65²/6)]
= √[2.60]
≈ 1.61
Next, we can use the t-distribution with degrees of freedom equal to the smaller of n1-1 and n2-1 (in this case, 4) and a 90% confidence level to find the critical value, t*:
t* = 1.533 (from t-distribution table or calculator)
Finally, we can construct the confidence interval estimate:
9.2 - 7.17 ± (t* * s.e.(difference between sample means))
= 2.03 ± (1.533 * 1.61)
= 2.03 ± 2.47
= [ -0.44 , 4.50 ]
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Find the circumference of great circle of sphere whose volume is 36πcm^3
Answer:
The formula for the volume of a sphere is:
V = (4/3)πr^3
where V is the volume and r is the radius of the sphere.
We are given that the volume of the sphere is 36π cm^3, so we can write:
36π = (4/3)πr^3
Simplifying:
r^3 = (36/4) * 3
r^3 = 27
r = 3
Therefore, the radius of the sphere is 3 cm.
The circumference of a great circle on a sphere is given by the formula:
C = 2πr
where r is the radius of the sphere.
So, the circumference of the great circle is:
C = 2π(3) = 6π
Therefore, the circumference of the great circle of the sphere is 6π cm.
What is the minimum value of the function over the interval -5 < x < 5? h(x) = log[(x – 5)2 + 3]
The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].
The minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 can be found through the following.
Recognize that the logarithm function is increasing.
Minimize the argument of the logarithm, i.e., (x - 5)² + 3.
Observe that (x - 5)² is always non-negative since it is a square of a real number.
The minimum value of (x - 5)² occurs when x = 5 (in this case, (x - 5)² = 0).
However, x cannot be equal to 5 because the interval is -5 < x < 5.
Since the interval is open, find the minimum value for (x - 5)² in this interval, which occurs when x is as close to 5 as possible within the given interval. This would be x = 4.999.
Substitute this value of x into the function:
h(x) = log[(4.999 - 5)² + 3] = log[0.001² + 3] ≈ log[3.000001].
Hence, the minimum value of the function h(x) = log[(x - 5)² + 3] over the interval -5 < x < 5 is approximately log[3.000001].
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Pre Alg Need help on this writing Question on both parts
Answer:
a = 2b - x
Step-by-step explanation:
2(x + a) = 4b Divide both sides of the equation by 2
x + a = 2b Subtract x from both sides
a = 2b - x
Helping in the name of Jesus.
Ryan Is in charge of planning a reception for 2600 people. He is trying to decide which snacks to buy. He has asked a random sample of people who are coming to the reception what their favorite snack is. Here are the results.
we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.
How to deal with random sample?
The sample provides information about the favorite snack of a random sample of people, but we need to use this information to make a prediction about the whole population of 2600 people.
First, we can calculate the proportion of the sample who chose pretzels or cookies as their favorite snack:
proportion = (number of people who chose pretzels + number of people who chose cookies) / total number of people in the sample
proportion = (16 + 54) / (30 + 16 + 54 + 64)
proportion = 70 / 164
proportion ≈ 0.4268
Next, we can use this proportion to estimate the number of people who will choose pretzels or cookies as their favorite snack out of the whole population:
predicted number of people = proportion × total number of people in the population
predicted number of people = 0.4268 × 2600
predicted number of people ≈ 1110.8
Rounding to the nearest whole number, we get a predicted number of 1111 people whose favorite snack will be pretzels or cookies at the reception.
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Write f(x) = 5(x - 2)2 - 7 in standard form.
To write f(x) = 5(x - 2)2 - 7 in standard form, we need to expand the squared term first:
f(x) = 5(x - 2)(x - 2) - 7
f(x) = 5(x2 - 4x + 4) - 7
f(x) = 5x2 - 20x + 13
Therefore, the standard form of f(x) = 5(x - 2)2 - 7 is f(x) = 5x2 - 20x + 13.
Answer: f(x)=5x2−20x+13
Step-by-step explanation:
suppose 40% of the people at a large meeting are republican. a sample of 20 is randomly selected to take part in a certain activity. to determine the probability that less than 45% of the sample is republican, what would be the standard deviation used in the z-score calculation?
Given f(x) = 3x2 − 6x − 13, what is the domain of f(x)? all real numbers x ≥ 1 x ≤ −6 x ≥ −13
In summary, the domain of the given function f(x) =[tex]3x^2 - 6x - 13[/tex] is all real numbers.
The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, the function f(x) is a quadratic function, which is given by [tex]f(x) = 3x^2 - 6x - 13.[/tex]
Quadratic functions are defined for all real numbers.
There are no restrictions on the input values of x for this function.
Therefore, the domain of f(x) is all real numbers.
To answer the student question, the correct option is "all real numbers."
The other options, "x ≥ 1," "x ≤ -6," and "x ≥ -13," do not apply in this case as there are no constraints on the values of x for a quadratic function.
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What value of a satisfies the equation -3 (4x - 5) = 2 (1 - 5x)?
Answer:
x = 6.5
Step-by-step explanation:
-3 × ( 4x - 5 ) = 2 × ( 1 - 5x ) -------------> (By multiplying each bracket times its coefficient)
= -12x + 15 = 2 - 10x -------------> (By subtracting "2" from each side)
= -12x + 13 = -10x -------------> (By moving the "-10x" to the other side and the "13" to the right side different signs "-10x becomes +10x and 13 becomes -13")
= -12x + 10x = -13
= -2x = -13 -------------> (Dividing by "-2")
then, x = 6.5
Have any questions? write in the comments
Can anyone please answer this question
The area of shaded part in the figures are
1. 7.07cm²
2. 19.54cm²
What's area of a shape?The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.
The area of a sector is expressed as:
A= tetha/360 × πr²
Area of the shaded part = area of big sector - area of small sector.
1. area of big sector = 90/360 × 3.14 × 5²
= 7065/360
= 19.63cm²
area of small sector = 90/360 × 3.14 × 4²
= 12.56cm²
area of shaded part = 19.63 - 12.56
= 7.07cm²
2. Area of big sector = 40/360 × 3.14 × 9²
= 28.26cm²
area of small sector = 40/360 × 3.14 × 5²
= 8.72
area of shaded part = 28.26-8.72
= 19.54cm²
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three relationships are described below: i. the amount of fuel used on a trip increases as the size of the car increases and as the distance traveled increases. ii. as the number of people helping mow a lawn increases, the time it takes to mow the lawn decreases. iii. the cost of having a house painted increases as the size of the house increases. what type of variation describes each relationship? i is joint, ii is direct, and iii is inverse. i is direct, ii is inverse, and iii is joint. i is direct, ii is joint, and iii is inverse. i is joint, ii is inverse, and iii is direct.
The described point iii is joint variation.
In the given question,
Three relationships are described.
They are:
i. The amount of fuel used on a trip increases as the size of the car increases and as the distance traveled increases.
ii. As the number of people helping mow a lawn increases, the time it takes to mow the lawn decreases.
iii. The cost of having a house painted increases as the size of the house increases.
Type of variation that describes each relationship:
Direct variation describes the relationship i between the amount of fuel used on a trip and the size of the car and distance traveled.
This is because the amount of fuel used is directly proportional to the size of the car and distance traveled. As the size of the car and distance traveled increases, the amount of fuel used also increases.
Hence,
i is direct variation.
Inverse variation describes the relationship
ii between the number of people helping mow a lawn and the time it takes to mow the lawn.
This is because the number of people helping is inversely proportional to the time it takes to mow the lawn.
As the number of people helping increases, the time it takes to mow the lawn decreases.
Hence, ii is inverse variation.Joint variation describes the relationship iii between the cost of having a house painted and the size of the house.
This is because the cost of having a house painted is jointly proportional to the size of the house. As the size of the house increases, the cost of having it painted also increases.
Hence, iii is joint variation.
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PR is tangent to circle Q at Point R. PS is tangent to circle Q at Point S. Find m
Answer:
142
Step-by-step explanation:
∠P + ∠Q = 180
38 + ∠Q = 180
Subtract 38 from both sides
∠Q = 142 degrees
A scientist is studying bacterial growth over time. Her research is conducted by placing 10 strep bacteria in a petri dish containing enough food for the bacteria to live and thrive for the course of the research. She records the number of bacteria present every two hours for 6 hours. The collected data is shown in the table below and on the given graph.
a. What function, linear or exponential, do you think would be the best choice to model this data? Explain why you think your choice is the best-fit.
b. Explain how to determine which function is the best choice mathematically, without using a graph.
Demonstrate your method.
c. Think of an example of at least 4 data points that would be best modeled by the function you did NOT choose in part a. Explain how you set up the data so that it worked with this type of function.
This is reflected in the data as the number of bacteria doubles every two hours, which is a characteristic of exponential growth.
What do you mean by exponential data ?Data that changes or grows at an exponential rate over time is referred to as exponential data. This indicates that the data changes quickly, either increasing or decreasing, and that the pace of change quickens over time. Exponential data frequently consists of numbers that rise steadily over time, with the rate of rise accelerating over time.
a.) exponential function would be the ideal option to model this data. An exponential curve is produced as the quantity of bacteria multiplies at an ever-increasingly rapid rate.
b. One way to determine which function is the best choice is to examine the rate of change of the data. In this case, we may calculate the average rate of change for each time period and see if it is constant. If the rate of change is constant, the data can be represented by a linear function. However, if the rate of change increases or decreases, an exponential or quadratic function might be a better fit.
From 0 to 2 hours: (25-10)/(2-0) = 7.5
From 2 to 4 hours: (50-25)/(4-2) = 12.5
From 4 to 6 hours: (100-50)/(6-4) = 25
c. The distance travelled by an automobile at a constant pace is an illustration of data that would be best characterised by a linear function. Imagine a car driving for four hours at a speed of 60 mph. Below is a list of the distance covered each hour:
After 1 hour: 60 miles
After 2 hours: 120 miles
After 3 hours: 180 miles
After 4 hours: 240 miles
In this case, the distance traveled is directly proportional to the time, so a linear function would be the best fit.
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I need help with these questions
please help, i do not understand. thank you!
Answer: it's 1
Step-by-step explanation:
The x in the numerator determines that the x is in absolute value, meaning only positive integers.
That wouldn't matter anyway, because since any value of x would have to be greater than 0 (meaning only positive values), and both x's are the same x, the equation would have to equal one.
For example, you could plug in 2 to both x's. 2/2 is 1.
Or you could plug in 289 to both x's, in which 289/289 is 1.
No matter what number, as long as it's positive, will be 1.
Find the equation of the line joining Q(-1/2, 3.5) and midpoint AP [A(4, 1) P(3, 7).
Answer:
The equation of the line joining Q(-1/2, 3.5) and midpoint AP [A(4, 1) P(3, 7)] is y = (-5/19)x + (117/38)
The equation of the line joining Q(-1/2, 3.5) and the midpoint of AP (4, 1) and P(3, 7) is y = 0.125x + 3.5625. This is found using the two-point form of the equation of a line and the midpoint formula.
Explanation:First, find the midpoint, M, of AP using the formula M = [(x1+x2)/2, (y1+y2)/2]. Plugging in the coordinates given for A(4,1) and P(3,7), M = [(4+3)/2, (1+7)/2] = [7/2, 8/2] = [3.5, 4]. Now, use the two-point form of the equation of a line to find the equation of the line QM: (y - y1) = m(x - x1), where m is the slope of the line. The slope is found by the formula (y2-y1)/(x2-x1). Substituting Q(-1/2, 3.5) and M(3.5, 4), you get m = (4 - 3.5)/(3.5 - (-1/2)) = 0.5/4 = 0.125. Now substitute Q(-1/2, 3.5) and m = 0.125 into the formula to get the equation of the line: (y - 3.5) = 0.125(x +1/2). This can be simplified as: y = 0.125x + 3.5625. So the
equation of the line
joining Q(-1/2, 3.5) and the midpoint of AP is y = 0.125x + 3.5625.
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Mr James works a basic week of 40 hours at a rate of $16 an hour. His overtime rate
is $4 per hour MORE than his basic rate.
Calculate:
(a) his total wage for a basic week,
(b) his wage for a week in which he worked 47 hours,
(c) the number of hours he worked during one week if he was paid a wage of $860.
Answer:
Sure, I can help you with that. (a) His total wage for a basic week can be calculated as follows: Total wage for a basic week = Basic rate per hour x Number of hours worked in a basic week Total wage for a basic week = $16 x 40 Total wage for a basic week = $640 Therefore, his total wage for a basic week is $640. (b) His wage for a week in which he worked 47 hours can be calculated as follows: Wage for a week with overtime = (Basic rate per hour + Overtime rate per hour) x Number of overtime hours worked + Total wage for a basic week Overtime rate per hour = Basic rate per hour + $4 Overtime rate per hour = $16 + $4 Overtime rate per hour = $20 Wage for a week with overtime =$16
Find g(x), where g(x) is the translation 5 units left of f(x)=x2.
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
The function g(x) in the form a(x - h)² + k is g(x) = (x + 5)² + 0, where a = 1, h = -5, and k = 0.
What is the function?
Starting with the function f(x) = x², a translation 5 units left can be achieved by replacing x with (x + 5), since (x + 5) is 5 units to the left of x. Therefore, we have:
g(x) = f(x + 5)
g(x) = (x + 5)²
g(x) = x² + 10x + 25
This is the equation of the parabola obtained by translating the graph of y = x² five units to the left. We can write this equation in the desired form of a(x - h)² + k by completing the square:
g(x) = x² + 10x + 25
g(x) = 1(x² + 10x) + 25
g(x) = 1(x² + 10x + 25 - 25) + 25
g(x) = 1((x + 5)² - 25) + 25
g(x) = 1(x + 5)² - 1(25) + 25
g(x) = (x + 5)² + 0
Therefore, the function g(x) in the form a(x - h)² + k is g(x) = (x + 5)² + 0, where a = 1, h = -5, and k = 0.
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5) A sample of men is found to be normally distributed with an average height of 70.5 inches and a standard deviation of 2.5 inches. Where do 95% of the men fall?
A) Between 63 inches and 70.5 inches
B) Between 65.5 inches and 75.5 inches
C) Between 68 inches and 73 inches
D) Between 63 inches and 78 inches
For the given information of standard deviation, the correct answer is option B) Between 65.5 inches and 75.5 inches.
What is standard deviation?
Standard deviation is a statistical measure that measures the amount of variation or dispersion of a set of data values from the mean. It tells how much the data deviates from the average of the data set.
We can use the z-score formula to solve this problem. If we assume a normal distribution, we can find the z-score associated with the 95th percentile (or 0.95 probability) using a standard normal distribution table or calculator. The z-score is approximately 1.96.
Then we can use the formula:
z = (x - μ) / σ
where z is the z-score, x is the height we want to find, μ is the mean height, and σ is the standard deviation.
Solving for x:
1.96 = (x - 70.5) / 2.5
Multiplying both sides by 2.5:
4.9 = x - 70.5
Adding 70.5 to both sides:
x = 75.4
So 95% of the men fall between 65.5 inches and 75.5 inches (option B).
Therefore, the correct answer is option B) Between 65.5 inches and 75.5 inches.
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Someone please help me answer this question correctly
The equation of the linear function that fits the given data is y = 10x - 2.
EquationsTo find the equation of a linear function in slope-intercept form, we need to determine the slope (m) and y-intercept (b).
m = (y2 - y1) / (x2 - x1)
(x1, y1) = (0, -2)
(x2, y2) = (4, 38)
m = (38 - (-2)) / (4 - 0)
= 40 / 4
= 10
y = mx + b
To find the y-intercept, we can use any point on the line. Let's use (0, -2):
-2 = 10(0) + b
b = -2
So,
y = 10x - 2
We can check that this equation satisfies all the given data points:
When x = 0, y = 10(0) - 2 = -2
When x = 1, y = 10(1) - 2 = 8
When x = 2, y = 10(2) - 2 = 18
When x = 3, y = 10(3) - 2 = 28
When x = 4, y = 10(4) - 2 = 38
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whats the answer plss hurryy upp plss
If A=1+r+7r^2 and B=1-r^2, find an expression that equals A+3B in standard form.
Answer:
To find A+3B, we need to first find A and B. A = 1 + r + 7r^2 B = 1 - r^2 Now we can substitute these expressions into A+3B: A+3B = (1 + r + 7r^2) + 3(1 - r^2) Simplifying this expression, we get: A+3B = 1 + r + 7r^2 + 3 - 3r^2 A+3B = 4 + r + 4r^2 So the expression that equals A+3B in standard form is 4 + r + 4r^2.
I'm stressing really bad because I don't know how to solve this math time series question. IF SOMEONE COULD PLEASE LEND ME THEIR EXPERTISE AND GENIUSNESS, I HOPE YOU ARE UNCEASINGLY BLESSED!
The predicted sales for week 10 is 30.143.
What is median?Median is a measure οf central tendency that represents the middle value in a dataset when the values are arranged in οrder οf magnitude.
Tο remοve the aberrant values frοm the time series data, we can replace them with dummy values. We can use the mean οr median οf the remaining values in the series tο replace the aberrant values.
Using mean as the replacement value, we get:
Week 1 2 3 4 5 6 7
Sales 26 28 27 30 23 23 38
Now we can use a regression model to predict the sales for week 10. Let's assume a linear regression model:
Sales = a + b*Week
where a is the intercept and b is the slope of the regression line.
To fit the model, we can use the sales data for weeks 1-7:
Week 1 2 3 4 5 6 7
Sales 26 28 27 30 23 23 38
The least squares estimates for the model parameters are:
b = 1.6429
a = 14.7143
Using these parameter estimates, we can predict the sales for week 10:
Sales(10) = a + b10
= 14.7143 + 1.642910
= 30.143
Therefore, the predicted sales for week 10 is 30.143.
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PLEASE HELP ME PLEASE SHOW EXPLANATION WHEN SOLVING IT OR I WILL REPORT YOUUU
Answer:
[tex]x {}^{2} - 5[/tex]
What is the range of the function f(x) = -3x - 4 when the domain is {-1, 0, 1}
Step-by-step explanation:
For: x=-1
f(x)= -3*-1 -4 =-1
For: x=0
f(x)= -3*0-4 =-4
For: x=1
f(x)= -3*1 -4 =-7
Therefore, the range of f(x)= [-1, -4, -7]
10. A piece of cardboard is 12 x 15 inches. What is the max volume of an open-roof box that can be formed by folding up the sides to create a height of x? ROUND ANSWER TO THE NEAREST WHOLE NUMBER
Answer:
180 fr
Step-by-step explanation:
its too hard
3. Classify each of the given sets of measurements
as one unique triangle, multiple triangles, or no A.
Place the letter in the correct box.
a) 52, 63, 65°
b) 31°, 102°, 46°
c) 70.6°, 47.4°, 62°
e)
f)
7.9 cm, 2.4 cm, 2.9 cm
12% in, 6 % in, 5 % in
124 mm, 432 mm, 385 mm
The Classify each of the given sets of measurements is given below:
How to Classify each of the given sets of measurementsa) 52, 63, 65°: These measurements form a unique triangle. This is a right-angled triangle, also known as a Pythagorean triple.
b) 31°, 102°, 46°: These measurements do not form a triangle. The sum of the angles in a triangle is always 180°, but in this case, the sum is 179°, which is less than 180°.
c) 70.6°, 47.4°, 62°: These measurements do not form a unique triangle. There are multiple possible triangles that can be formed with these measurements.
d) 3 cm, 4 cm, 5 cm: These measurements form a unique triangle. This is another example of a Pythagorean triple.
e) 7.9 cm, 2.4 cm, 2.9 cm: These measurements do not form a triangle. The sum of the two smaller sides is less than the length of the largest side, which violates the triangle inequality.
f) 12% in, 6% in, 5% in: These measurements do not form a triangle. The sum of the two smaller sides is less than the length of the largest side, which violates the triangle inequality.
g) 124 mm, 432 mm, 385 mm: These measurements form a unique triangle.
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An experiment consists of drawing a card and recording its color, then rolling a die and recording its value.
Is the following tree diagram correct based on the describes situation AND explain how you know.
thx
The probabilities of rolling each number on the die are 1÷6, which is correctly represented by the branching probabilities from each die-rolling node.
What is an experiment ?
In science and statistics, an experiment is a controlled procedure designed to test a hypothesis or to investigate the effect of one or more factors or variables on an outcome of interest. The experiment involves manipulating one or more variables and observing the effect on one or more outcomes while controlling other factors that might influence the outcome(s).
Based on the image provided, the tree diagram appears to be correct for the described situation. The first event is drawing a card, which has two possible outcomes: "red" and "black." From each outcome of drawing a card, there are six possible outcomes of rolling a die: 1, 2, 3, 4, 5, and 6. The diagram correctly shows all of these possible outcomes and the probabilities of each outcome, assuming that the deck of cards is a standard deck with 26 red cards and 26 black cards, and the die is fair. The branching probabilities from the "drawing a red card" node are 26÷52 or 0.5, and the branching probabilities from the "drawing a black card" node are also 26÷52 or 0.5.
Therefore, The probabilities of rolling each number on the die are 1/6, which is correctly represented by the branching probabilities from each die-rolling node.
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a programmer plans to develop a new software system. in planning the operating system, he needs the estimate the % of computers that use a new operating system. how many computers must be surveyed in order to be 95% within 4% margin of erro
To be 95% confident within a 4% margin of error, the programmer must survey at least 601 computers.
To estimate the percentage of computers that use a new operating system with a 95% confidence level and a 4% margin of error, you must first determine the required sample size. Here's a step-by-step explanation:
Identify the confidence level and margin of error: In this case, the confidence level is 95% and the margin of error is 4%.
Determine the standard value (Z-score) for the desired confidence level: For a 95% confidence level, the Z-score is 1.96. This value can be found using a Z-score table or an online calculator.
Use the formula for sample size calculation:
n = (Z^2 * p * (1-p)) / E^2
Where n is the required sample size, Z is the Z-score, p is the estimated proportion of computers using the new operating system, and E is the margin of error.
Since we do not have an estimate for the proportion (p), we will assume the worst-case scenario (p=0.5) to ensure the largest possible sample size:
n = (1.96^2 * 0.5 * 0.5) / 0.04^2
Calculate the sample size:
n ≈ (3.8416 * 0.25) / 0.0016
n ≈ 0.9604 / 0.0016
n ≈ 600.25
Round up to the nearest whole number: Since we cannot survey a fraction of a computer, we will round up to the next whole number, which is 601.
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