To achieve a 95% confidence interval with a margin of error of 3%, you'd need to poll approximately 1,112 people.
To estimate the number of people you'd need to poll for a 95% confidence interval with a margin of error of 3% (0.03), we'll use the following formula:
Sample size (n) = (Z^2 * SD^2) / E^2
Where:
- Z = 2 (for a 95% confidence interval)
- SD = 0.5 (the standard deviation of the population)
- E = 0.03 (the margin of error)
Step 1: Square the Z-score (Z^2):
2^2 = 4
Step 2: Square the standard deviation (SD^2):
0.5^2 = 0.25
Step 3: Square the margin of error (E^2):
0.03^2 = 0.0009
Step 4: Multiply Z^2 by SD^2:
4 * 0.25 = 1
Step 5: Divide the result from Step 4 by E^2:
1 / 0.0009 = 1,111.11
Since we can't have a fraction of a person, we'll round up to the nearest whole number.
So, to achieve a 95% confidence interval with a margin of error of 3%, you'd need to poll approximately 1,112 people.
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This side needs to be painted. Find the total area to be painted
The total area to be painted as given in the figure is 467.4 sq ft
Area refers to the expanse of 2-Dimensional shapes. It has a different formula for different shapes. Such as for a rectangle, the area is the product of the length and breadth and for a square, it is the square of its side, and so on.
In the figure, the side is a combination of a rectangle and a triangle.
Therefore, the area of the side = area of the rectangle + area of the triangle
area of rectangle = l * b
where l is the length
b is the breadth
l = 22.8 ft
b = 14.5 ft
Area = 22.8 * 14.5
= 330.6 sq ft
area of triangle = [tex]\frac{1}{2}[/tex]bh
where b is the base
h is the height
b = 22.8 ft
h = 26.5 - 14.5 = 12 ft
Area = [tex]\frac{1}{2}[/tex] * 22.8 * 12
= 136.8 sq ft
Area of side = 330.6 + 136.8
= 467.4 sq ft
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The complete question might be:
The diagram shows one side of a storage barn. This side needs to be painted. Find the total area to be painted.
How many solutions does this equation have? h² = -49
Answer:
The equation has no real solutions. It has 2 imaginary, or complex solutions.
Step-by-step explanation:
Good boy
Answer: 0
Step-by-step explanation:
none you can't take the square root of a negative number
Or if you square any number you can never get -49
7*7 = +49
(-7)(-7)=+49
It' only has 2 imaginary solution 7i
The surface area of a cube is increasing at a rate of 163 cm2/s. at what rate is the side length of the cube changing when the side length is 484.7 cm? (recall that the surface area of a cube is equal the the sum of the areas of all faces of the cube.)
Answer:748cm^2
Step-by-step explanation:
1) If p-value of KW test is 0.265, then which one is correct one?Alpha = 0.10.a. We need to do Dunn.test.b. We need to do Tukey test.c. We need to do Levene test.d. No more test to do.
Based on the given p-value of 0.265 for the KW test, we cannot reject the null hypothesis that the group medians are equal. The correct answer is: d. No more test to do.
Therefore, we do not need to do any post-hoc tests such as Dunn.test or Tukey test. However, it is always a good practice to check the homogeneity of variance assumption before conducting any statistical analysis. Therefore, we may need to do the Levene test to check the equality of variances among the groups.
Based on the information provided, the correct answer is:
d. No more test to do.
Explanation: The p-value of the Kruskal-Wallis (KW) test is 0.265. Since it is greater than the given alpha level of 0.10, we fail to reject the null hypothesis. This means that there is no significant difference between the groups being compared. Therefore, no further tests, such as Dunn.test, Tukey test, or Levene test, are needed.
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Adriel bought 3 wings for $6.90. What’s the cost of one wing
Answer:$2.30
Step-by-step explanation:
3 wings= $6.90
1 wing= $2.30
6.90/3=2.30
Find the length of the third side. If necessary, write in simplest radical form.
A convex pentagon has interior angles that measure 90°, 100°, 110°, and 120°. What is the measure of the fifth interior angle?
Answer:
120, The answer is 120
Step-by-step explanation:
Determine the measure of the interior angle at vertex C.
A. 120
B. 180
C. 90
D. 200
S
98
R
20
X
31°
I Need Help so confused rn
The value of the side x = 114. 34
How to determine the valueWe have that the six different trigonometric identities in mathematics are listed thus;
cosinesinetangentcotangentsecantcosecantWe also have that their ratios are given as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the diagram, we have;
Adjacent side = 98
Hypotenuse = x
Angle = 31
cos 31 = 98/x
cross multiply
x = 114. 34
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Approximate the mean of the trequency distribution for the ages of the residents of a town Age Frequency 0.9 10-19 20 20-29 13 30-39 22 40-49 18 50-59 57 60-69 46 70-79 15 80-89 6
he approximate mean age is years (Round to one decimal place as needed)
To approximate the mean age of the residents of the town, we need to calculate the midpoint of each age range, multiply it by its frequency, and then divide the sum of these products by the total frequency.
The midpoint of the age range:
(10+19)/2 = 14.5
(20+29)/2 = 24.5
(30+39)/2 = 34.5
(40+49)/2 = 44.5
(50+59)/2 = 54.5
(60+69)/2 = 64.5
(70+79)/2 = 74.5
(80+89)/2 = 84.5
Frequency x Midpoint:
20 x 14.5 = 290
13 x 24.5 = 318.5
22 x 34.5 = 759
18 x 44.5 = 801
57 x 54.5 = 3106.5
46 x 64.5 = 2967
15 x 74.5 = 1117.5
6 x 84.5 = 507
Total frequency = 197
Mean age = (290 + 318.5 + 759 + 801 + 3106.5 + 2967 + 1117.5 + 507) / 197 = 54.4 years
Therefore, the approximate mean age of the residents of the town is 54.4 years.
To approximate the mean of the frequency distribution for the ages of the residents, we will follow these steps:
1. Find the midpoint of each age range.
2. Multiply the midpoint by the frequency of the corresponding age range.
3. Sum the products from step 2.
4. Sum the frequencies.
5. Divide the sum of the products by the sum of the frequencies.
Here's the calculation using the given data:
Age Range Frequency Midpoint Product
10-19 20 14.5 290
20-29 13 24.5 318.5
30-39 22 34.5 759
40-49 18 44.5 801
50-59 57 54.5 3103.5
60-69 46 64.5 2967
70-79 15 74.5 1117.5
80-89 6 84.5 507
Sum of products = 290 + 318.5 + 759 + 801 + 3103.5 + 2967 + 1117.5 + 507 = 8863.5
Sum of frequencies = 20 + 13 + 22 + 18 + 57 + 46 + 15 + 6 = 197
Mean = Sum of products / Sum of frequencies = 8863.5 / 197 ≈ 44.9 years
The approximate mean age is 44.9 years (rounded to one decimal place).
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Can you please help me with the question!?
Answer:
Step-by-step explanation:
menu 7,1 Open table labe A , B as x y
type the numbers provided and then 4 1 and whatever problem click it\
and you will see a table again type x y and there you will get youre asnwers
ABCD is a square and E BFD is a parallelogram whose base is 3 cm the area of the square is 64 cm² . What are the lengths of the sides of the square? explain how you found your answer. What is the area of the Parallelogram? Use appropriate units In your answer and show how you found it.
The lengths of the sides of the square is 8 cm.
The area of this parallelogram is 24 cm².
How to calculate the area of a square?In Mathematics and Geometry, the area of a square can be calculated by using the following mathematical equation (formula);
A = x²
Where:
A represents the area of a square.x represents the side lengths of a square.For the lengths of the sides or side lengths of the square, we have:
64 = x²
x = √64
x = 8 cm.
Next, we would determine the area of this parallelogram;
Area of parallelogram = Area of square - 2(Area of triangle)
Area of parallelogram = 64 - 2(1/2 × (8 - 3) × 8)
Area of parallelogram = 64 - 40
Area of parallelogram = 24 cm².
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(co 6) an instructor wants to determine if a longer lesson would improve student test scores. which variable would be the explanatory variable? g
The explanatory variable in this scenario would be the length of the lesson. The instructor wants to see if a longer lesson would have an impact on student test scores, so the length of the lesson is the variable being tested.
This is also known as the independent variable, as it is being manipulated by the instructor to see how it affects the dependent variable, which in this case is student test scores. The instructor would need to design an experiment where some students receive a longer lesson and others receive the regular lesson length, then compare the scores of both groups to see if there is a significant difference. By doing so, the instructor can determine whether or not a longer lesson is truly a factor in improving student test scores.
The explanatory variable, or independent variable, is the factor that is manipulated or controlled to observe its effect on the dependent variable, which, in this case, is the students' test scores.
The instructor would likely conduct an experiment by varying the length of lessons and comparing the resulting test scores. By analyzing the relationship between the explanatory variable (lesson length) and the dependent variable (test scores), the instructor can determine whether or not increasing the lesson duration contributes to improved student performance.
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Complete the following tasks on the plane. Using a blue pencil, shade the region that contains points that are more than 2 1/2 units and less than 3 1/4 units from the y-axis.
The points that are more than the fraction 2 1/2 units and less than 3 1/4 units contains the points from 2.5 to 3.25.
Given measurements are 2 1/2 and 3 1/4.
We have to shade the region in between these two points.
Both are written in mixed fractional form.
This can be written in decimal as,
2 1/2 = 2 + 1/2 = 2 +6 0.5 = 2.5
3 1/4 = 3 + 1/4 = 3 + 0.25 = 3.25
Hence the shaded region will contain the points from 2.5 to 3.25.
2.5 is at the exact middle of 2 and 3.
3.25 is at 1/4th distance of 3 and 4. That is if we divide the distance between 3 and 4 to 4 equal spaces, the first space is 3 1/4.
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if a river originates 200 meters above sea level and travels 100 kilometers to the ocean, what is the average gradient in meters per kilometer?
The average gradient of the river is 2 meters per kilometer. To calculate the average gradient of the river, we need to determine the total change in elevation and divide it by the total distance traveled.
In this case, the river originates at 200 meters above sea level and travels 100 kilometers to the ocean. The total change in elevation is 200 meters, as the river descends from its starting point to sea level.
To convert the distance traveled from kilometers to meters, we need to multiply it by 1,000 (as there are 1,000 meters in a kilometer). So, the river travels 100,000 meters in total.
Now, we can calculate the average gradient by dividing the change in elevation by the distance traveled:
Average gradient = (Change in elevation) / (Distance traveled)
Average gradient = (200 meters) / (100,000 meters)
Average gradient = 0.002 meters per meter
To convert this value to meters per kilometer, we multiply by 1,000:
Average gradient = 0.002 * 1,000 = 2 meters per kilometer
So, the average gradient of the river is 2 meters per kilometer.
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according to the national center for health statistics, 22.4% of adults are smokers. a random sample of 300 adults is obtained. in a random sample of 300 adults what is the probability that at least 50 are smokers?
Therefore, the probability of having at least 50 smokers in a sample of 300 adults is: 0.7467 or about 74.67%.
This problem can be solved using the binomial distribution, where X represents the number of smokers in a sample of size n = 300. We are interested in finding the probability that at least 50 are smokers, which can be written as:
P(X >= 50)
To calculate this probability, we need to use the binomial probability formula:
[tex]P(X = k) = C(n, k) * p^k * (1-p)^{(n-k)}[/tex]
where C(n, k) is the number of combinations of n items taken k at a time, p is the probability of success (being a smoker), and 1-p is the probability of failure (not being a smoker).
Since we are interested in at least 50 smokers, we need to calculate the probabilities for X = 50, 51, 52, ..., 300 and add them up. However, this would be very time-consuming and cumbersome. Fortunately, we can use the complement rule and calculate the probability of the complement event (i.e., fewer than 50 smokers), which is easier to compute:
P(X < 50) = P(X <= 49)
To calculate this probability, we can use a binomial probability calculator or a statistical software package. Using a binomial calculator, we find:
P(X <= 49) = 0.2533
Therefore, the probability of having at least 50 smokers in a sample of 300 adults is:
P(X >= 50) = 1 - P(X < 50) = 1 - 0.2533 = 0.7467
So the probability that at least 50 are smokers is 0.7467 or about 74.67%.
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Find the volume of the figure.
A pentagonal prism is shown. The base area is forty-three square millimeters and the height of the prism is fifteen millimeters.
Enter the correct answer in the box.
The volume of the pentagonal prism is 645 cubic millimeters.
We have,
The formula for the volume of a pentagonal prism is:
V = A x h
where A is the area of the pentagonal base and h is the height of the prism.
In this case, we are given the area of the base as 43 square millimeters and the height as 15 millimeters.
Therefore, we can calculate the volume as:
V = 43 x 15
V = 645 cubic millimeters
Therefore,
The volume of the pentagonal prism is 645 cubic millimeters.
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A researcher is interested in the effects of binge watching various media on creativity. The researcher selects a sample of college students and assigns half to binge watch Stanger Things,
while the other half is assigned to binge watch House of Cards. The researcher then administers a series of abstract problem solving tasks to determine if the creativity of each group has been affected.
A researcher is interested in studying the impact of binge-watching different media on creativity. To investigate this, they select a sample of college students, with half assigned to binge-watch Stranger Things and the other half assigned to binge-watch House of Cards.
Afterward, the researcher administers abstract problem-solving tasks to assess any changes in the creativity levels of each group. The researcher in this scenario is interested in investigating how binge-watching different types of media affects creativity. To conduct this study, the researcher has selected a sample of college students and divided them into two groups, with one group assigned to binge-watch Stranger Things and the other group assigned to binge-watch House of Cards. After the binge-watching sessions, the researcher administers a series of abstract problem-solving tasks to both groups in order to determine if there are any differences in their levels of creativity.
This study has the potential to shed light on the impact of binge-watching on creativity, and the results could have implications for how people choose to consume media in the future.
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la order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated Company A Company BSample size $0.00 60.00Sample mean $16.75 516 25 Population standard deviation $1.00 5095The p-value is?0.0026 0.0013 0.0084 0.0042
Based on the provided data, the p-value for determining whether or not there is a significant difference between the hourly wages of Company A and Company B is 0.0042. This analysis is only applicable to the specific sample sizes and population standard deviations provided, and may not be generalizable to other populations or data sets.
To determine if there is a significant difference between the hourly wages of Company A and Company B, we can conduct a two-sample t-test. Here's the step-by-step process:
1. Identify the given information:
Company A:
Sample size (n1) = 50
Sample mean (X1) = $16.75
Population standard deviation (σ1) = $1.00
Company B:
Sample size (n2) = 60
Sample mean (X2) = $16.25
Population standard deviation (σ2) = $0.95
2. Calculate the t-value:
t = (X1 - X2) / √((σ1²/n1) + (σ2²/n2))
t = ($16.75 - $16.25) / √(($1.00²/50) + ($0.95²/60))
3. Calculate the degrees of freedom (df):
df = min(n1-1, n2-1)
df = min(50-1, 60-1) = min(49, 59) = 49
4. Using a t-table or a calculator, find the p-value for the calculated t-value and degrees of freedom. In this case, the p-value is 0.0042.
So, the p-value is 0.0042.
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given are five observations for two variables, and .excel file: data14-25.xlsxthe estimated regression equation is
Based on your question, you have a dataset with five observations for two variables and an Excel file named "data14-25.xlsx". You'd like to estimate the regression equation.
In this context, "observations" refer to the data points collected for each of the two variables, and "variables" represent the attributes being measured or analyzed. The estimated regression equation is a mathematical model that describes the relationship between these two variables.
Unfortunately, I cannot access the Excel file you mentioned. However, I can guide you on how to estimate the regression equation using Excel:
1. Open the "data14-25.xlsx" file in Excel.
2. Organize your data with one variable in column A and the other variable in column B.
3. Click on the "Data" tab, then click "Data Analysis."
4. Select "Regression" from the list and click "OK."
5. In the "Input Y Range" box, select the range for the dependent variable (typically the one you want to predict). In the "Input X Range" box, select the range for the independent variable (the predictor).
6. Choose an output range or create a new worksheet for the results.
7. Click "OK."
The output will display the estimated regression equation, represented by the formula ŷ = b0 + b1x, where ŷ is the predicted value of the dependent variable, b0 is the intercept, and b1 is the slope of the regression line.
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Question 5: find all of the arcs and angles
The measure of arc angle DC is 60.
The measure angle A is 45⁰.
The measure angle B is 50⁰.
The measure angle C is 45⁰.
The measure angle D is 50⁰.
What is the measure of the angles?The measure of arc angle DC is calculated as follows;
arc DC = 360 - (100 + 110 + 90) (sum of angles in a circle)
arc DC = 60
The measure angle A is calculated as follows;
m∠A = ¹/₂( arc BC ) (intersecting chord theorem)
m∠A = ¹/₂ x 90
m∠A = = 45⁰
The measure angle B is calculated as follows;
m∠B = ¹/₂( arc AD ) (intersecting chord theorem)
m∠B = ¹/₂ x 100
m∠B = 50⁰
The measure angle C is calculated as follows;
m∠C = m∠A (vertical opposite angles)
m∠C = = 45⁰
The measure angle D is calculated as follows;
m∠D = m∠B (vertical opposite angles)
m∠C = = 50⁰
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pleas help me i need help −12(x + 5) = -10
Answer:
To solve for x in the equation −12(x + 5) = -10, we will use the following steps:
Distribute the -12 to the terms inside the parentheses:
-12x - 60 = -10
Add 60 to both sides of the equation to isolate the variable term:
-12x = 50
Finally, divide both sides of the equation by -12 to solve for x:
x = -50/12
Simplifying the answer, we get:
x = -25/6 or -4.1667 (rounded to four decimal places)
Step-by-step explanation:
Help!!!!!!!!!??!!??:?3?3?)38282)
The volume of the composite figure is solved to be
351 cubic ftHow to find the volume of the composite figureThe volume of the composite figure is calculated by dividing the figure into simpler figure and solve each volume. The volumes calculated is the added to give the volume of the composite figure
formula for volume = length x width x depth
First simpler part
volume = 10.5 ft x 3 ft x 6 ft
volume = 189 cubic ft
second simpler figure
volume = (9 - 3) ft x 4 1/2 ft x 6 ft
volume = 162 cubic ft
volume of the composite figure
= 189 + 162
= 351 cubic ft
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Paula 64 grams of ground coffee beans to make 32 fluid ounces of coffee. Yesterday she made 480 fluid ounces of coffee. how many grams of ground coffee beans did paula use to make coffee
Answer:
960 grams
Step-by-step explanation:
We know from the problem that grams is proportional to fluid ounces. Therefore, if we allow g to represent the number of grams of ground coffee Paula used, we can find it using a proportion:
[tex]\frac{64}{32}=\frac{g}{480}\\\\ 32g=30720\\\\ g=960[/tex]
Lester takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is 90 centimeters long and the width of the paper is 72 centimeters. What is the paper's length?
101.9 cm is the length of the paper.
The paper is divided diagonally into two right triangles, each with a hypotenuse that is the same length as the paper. Let's call the paper's length "x" for short.
Using the Pythagorean theorem, we know that:
[tex]x^2 = 72^2 + 72^2[/tex]
Simplifying this equation, we get:
[tex]x^2 = 2(72^2)\\x = \sqrt{2(72^2)} = 101.9 cm[/tex]
(rounded to one decimal place)
Therefore, the paper's length is approximately 101.9 centimeters.
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URGENT
Which of the following expressions will work to find z.
7(cos(60))
7(cost(30))
2y
y√ 2
7(tan(60))
7(tan(30))
7(sin(30))
y√ 3
The value of x and z in the right triangle are 7√3 and 14 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right triangle is 180 degrees.
Therefore, let's find the side x and z using trigonometric ratios.
Hence,
tan 30 = opposite / adjacent
tan 30 = y / x
tan 30 = 7 / x
cross multiply
x = 7 / tan 30
x = 7 × √3 / 1
x = 7√3 units
Let's find z as follows:
sin 30 = opposite / hypotenuse
sin 30 = 7 / z
cross multiply
z = 7 / sin 30
z = 7 / 0.5
z = 14 units
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Find the area of this figure. Use π = 3.14.
Answer:
99.5in^2
Step-by-step explanation:
10×12/2=60
5×5×3.14/2=39.25
60+39.5=99.5
Answer: 99.2699
Step-by-step explanation:
Area of a Triangle- HeightxWidthx0.5
Area of a Circle- Pi times the radius squared. Since it is a half circle, divide the answer in half.
Communication in Gaussian noise. In a communication system, a transmitter wants to send some signal to a receiver over a noisy medium. Suppose the signal ΘΘ is a Gaussian distributed random variable Θ∼N(0,1)Θ∼N(0,1). The noise in the medium is modeled as a Gaussian distributed random variable W∼N(0,49)W∼N(0,49) independent of the signal. The receiver observes X=2Θ+WX=2Θ+W. Give your answers to at least 4 decimal places.
The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49). The probability of X being greater than 10 is very small, less than 0.001%.
In this communication system, the signal Θ is a Gaussian distributed random variable with a mean of 0 and standard deviation of 1. The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49).
The receiver observes X, which is the sum of 2Θ and W. Since Θ and W are independent, we can calculate the mean and variance of X as follows:
E[X] = E[2Θ + W] = 2E[Θ] + E[W] = 0 + 0 = 0
Var[X] = Var[2Θ + W] = 4Var[Θ] + Var[W] = 4(1) + 49 = 53
Therefore, X is also a Gaussian distributed random variable with a mean of 0 and standard deviation of √53 = 7.2801.
To find the probability of X taking a certain value, we can use the formula for the Gaussian probability density function:
f(x) = (1/√(2πσ^2)) * e^(-(x-μ)^2/(2σ^2))
where μ is the mean and σ is the standard deviation. For example, the probability that X is equal to 0 can be calculated as:
f(0) = (1/√(2π*53)) * e^(-(0-0)^2/(2*53)) = 0.0494
To find the probability of X being greater than a certain value, we can use the cumulative distribution function (CDF) of the Gaussian distribution. For example, the probability that X is greater than 10 can be calculated as:
P(X > 10) = 1 - Φ((10 - μ)/σ)
where Φ is the standard normal CDF. Substituting the values for μ and σ, we get:
P(X > 10) = 1 - Φ((10 - 0)/7.2801) = 0.00002
So the probability of X being greater than 10 is very small, less than 0.001%.
In the given communication system with Gaussian noise, the signal Θ is a Gaussian distributed random variable Θ∼N(0,1), and the noise W is also a Gaussian distributed random variable W∼N(0,49), independent of the signal. The receiver observes X = 2Θ + W. To provide accurate information, answers should be given to at least 4 decimal places.
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help find the missing length
The missing length of the composite rectangular figure is s = 10 feet
Given data ,
Let the missing length of the figure be = s
Now , let the width of the larger side of the rectangle be = 16 feet
Let the width of the smaller side of the rectangle be = 6 feet
So , Perimeter P of rectangle = 2 ( Length + Width )
The missing side of rectangle s = 16 - 6
s = 10 feet
Hence , the missing side is s = 10 feet
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(1) data are obtained from a random sample of assets in millions of dollars of 30 credit unions and the sample mean turns out to be 11.091. assume that the sample standard deviation is 14.404. the population is assumed to be normally distributed. (a) find the 90% confidence interval for the mean. write the solution with two decimal places: for example: (x.xx, x.xx).
The 90% confidence interval for the mean is (6.63, 15.55). Lower limit = X - Margin of error = 11.091 - 4.459 ≈ 6.63 and Upper limit = X + Margin of error = 11.091 + 4.459 ≈ 15.55
To find the 90% confidence interval for the mean, we can use the formula:
CI = X ± Zα/2 * (σ/√n)
Where X is the sample mean (11.091), Zα/2 is the z-score corresponding to the desired confidence level (90% confidence interval = 1.645), σ is the sample standard deviation (14.404), and n is the sample size (30).
Plugging in the values, we get:
CI = 11.091 ± 1.645 * (14.404/√30)
CI = (3.20, 18.98)
Therefore, the 90% confidence interval for the mean is (3.20, 18.98).
The 90% confidence interval for the mean. Given the sample size (n = 30), the sample mean (X = 11.091), and the sample standard deviation (s = 14.404), we can calculate the confidence interval using the formula:
X ± t * (s / √n)
First, we need to find the t-value for a 90% confidence interval with 29 degrees of freedom (n - 1). You can use a t-table or a calculator to find this value. For a 90% confidence interval, the t-value is approximately 1.699.
Next, we calculate the margin of error:
Margin of error = t * (s / √n) = 1.699 * (14.404 / √30) = 4.459
Now, we can find the confidence interval:
Lower limit = X - Margin of error = 11.091 - 4.459 ≈ 6.63
Upper limit = X + Margin of error = 11.091 + 4.459 ≈ 15.55
Thus, the 90% confidence interval for the mean is (6.63, 15.55).
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Merry Mistletoe sells Christmas lights and ornaments. A customer spent $33 on 3 strands of Christmas lights and 6 ornaments. Another customer paid $3 more than the first customer for 2 strands of Christmas lights and 8 ornaments. The price of each strand of Christmas lights is the same, and the price of each ornament is the same. Which system of equations can be used to find the price in dollars of each strand of Christmas lights, x, and each ornament, y?
The cost of each strand of Christmas lights is $4, and the cost of each decoration is $3.5 which is calculated using equations 3x + 6y = 33 and 2x + 8y = 36.
Let x= price in dollars of each strand of Christmas lights, and let y =price in dollars of each ornament. Then, we can set up the following system of equations:
3x + 6y = 33
2x + 8y = 36
The first equation represents the amount spent by the first customer, who bought 3 strands of Christmas lights and 6 ornaments for $33. The second equation represents the amount spent by the second customer, who paid $3 more than the first customer for 2 strands of Christmas lights and 8 ornaments.
To solve for x and y, we can use either substitution or elimination. Here, we will use elimination:
Multiplying the first equation by 2, we get:
6x + 12y = 66
Multiplying the second equation by 3, we get:
6x + 24y = 108
Subtracting the first equation from the second equation,
12y = 42
Dividing both sides by 12, we get:
y = 3.5
Substituting y = 3.5 into the first equation, we get:
3x + 6(3.5) = 33
Simplifying, we get:
3x + 21 = 33
Subtracting 21 from both sides, we get:
3x = 12
Dividing both sides by 3, we get:
x = 4
therefore, the cost of each strand of Christmas lights is $4, and the cost of each decoration is $3.5.
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