The required answer is the nearest hundred dollars: $902.09 is approximately $900.
To find the value of the car 20 years after it was purchased, we can use the formula for exponential decay:
Value = Initial value * (1 - Depreciation rate) ^ (time elapsed / time for depreciation)
1. Determine the depreciation rate: The car's value depreciates by one half every 3.5 years, so the depreciation rate is 50% or 0.5.
Depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year as it is used and wears, and second, the allocation in accounting statements of the original cost of the assets to periods in which the assets are used (depreciation with the matching principle).
Depreciation is thus the decrease in the value of assets and the method used to reallocate, or "write down" the cost of a tangible asset (such as equipment) over its useful life span
2. Calculate the number of depreciation periods: Since the car's value halves every 3.5 years, we need to find out how many 3.5-year periods are in 20 years. To do this, divide 20 by 3.5: 20 / 3.5 ≈ 5.71 periods.
3. Use the exponential decay formula:
Value = 29,000 * (1 - 0.5) ^ (5.71)
Value ≈ 29,000 * (0.5) ^ (5.71)
Value ≈ 29,000 * 0.0311
Value ≈ 902.09
4. Round the value to the nearest hundred dollars: $902.09 is approximately $900.
So, the value of the car 20 years after it was purchased is approximately $900.
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Find the slope of the line
Answer:
m = 1/2
Step-by-step explanation:
We Know
The slope of a line is the rise/run
Pick 2 points (0,1) (2,2)
We see the y increase by 1, and the x increase by 2, so the slope of the line is
m = 1/2
Help me with these questions pls
The volume of the cones are;
1. 84. 78 in³
2. 564. 15 ft³
3. 4710 yd³
How to determine the value
The formula for calculating the volume of a cone is expressed as;
V = 1/3 πr²h
Given that;
r is the radius of the cone.h is the height of the coneFrom the information given, we have;
1. Volume = 1/3 × 3.14 × 3² × 9
Multiply the values and find the square
Volume = 254. 34/3
divide the values
Volume = 84. 78 in³
2. Volume = 1/3 × 3.14 × 7² × 11
Multiply the values
Volume = 1692. 46/3
Volume = 564. 15 ft³
3. Volume = 1/3 × 3.14 × 15² × 20
Multiply the values
Volume = 4710 yd³
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Zahra and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags of popcorn and 5 drinks? How much would it cost if they bought
p bags of popcorn and d drinkss
Using basic mathematical procedures, we can determine that the total cost of the 8 bags of popcorn and 5 drinks is $53.
What do math operations entail?An operation, in mathematics, is a mathematical function that transforms zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
The rules that specify the order in which we should carry out the operations required to solve an equation are referred to as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. (from left to right).
The whole price is thus:
Popcorn costs $3.50 for one bag.
One beverage costs $5.
Total cost for 5 beverages and 8 bags of popcorn:
(8 × 3.50) + (5 × 5) 28 + 25 $53
Therefore ,Using basic mathematical procedures, we can determine that the total cost of the 8 bags of popcorn and 5 drinks is $53.
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The appropriate response is provided below:
Zahra is going to the cinema with a few of her friends. A bag of popcorn costs $3.50 and a drink costs $5 at the theatre. How much would it cost if they purchased 5 beverages and 8 bags of popcorn?
What is the process of solving this?
The solution of the trigonometric equation
cos(2x) = cos(x) + 2
is x = 180°
How to solve the trigonometric equation?Here we want to solve the equation:
cos(2x) = cos(x) + 2
First, we know that:
cos(2x) = 2cos(x)² - 1
Then we can rewrite:
2cos(x)² - 1 = cos(x) + 2
We can define:
cos(x)= y
2y² - 1 = y + 2
Then we need to solve the quadratic:
2y² - 1 - y - 2 =0
2y² - y - 3 = 0
Using the quadratic formula we will get:
[tex]y = \frac{1 \pm \sqrt{(-1)^2 - 4*2*2*-3} }{2*2} \\\\y = \frac{1 \pm 5}{4}[/tex]
so the solutions are:
y = (1 + 5)/4 = 6/4
y = (1- 5)/4 = -1
And remember that y = cos(x), then y = 6/4 can be discarded.
Then the solution comes from:
cos(x) = -1
then x = pi = 180°
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Solve for f(-2).
f(x) = -3x + 3
f(-2) = [?]
Answer:
f(-2) = 9
Step-by-step explanation:
f(x) = -3x + 3 Solve for f(-2).
f(-2) = -3(-2) + 3
f(-2) = 6 + 3
f(-2) = 9
A nearby house requires approximately 52,000 BTUs for heating. If the house is 31 feet long and 25 feet wide, what is the height of the
house? Round your answer to the nearest foot
ft
The height of the house by the given data is 4000ft.
We are given that;
Number of BTUs for heating= 52000
Now,
The time from minutes to hours by dividing by 60:
t=606.24 hr
t≈0.104 hr
Then, we can plug in the values into the heat loss formula and solve for A, which is the surface area of the house:
Q=UAΔTt
52,000=0.25A×50×0.104
A=0.25×50×0.10452,000 ft2
A≈4000 ft2
Therefore, by the algebra the answer will be 4000 ft.
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Answer:3.75 BTUs/ft
height=18 ft
Step-by-step explanation:
If the arch were 32 inches wide but 44 inches tall high, how could you modify your function W to model the new arch
This new function W(x) = 22 - (11/8) * (x - 16)² will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall.
To modify the function W to model the new arch with dimensions of 32 inches wide and 44 inches tall, we need to adjust the formula to reflect the new proportions.
Currently, the function W is defined as:
W(x) = h/2 - h/(2a) * (x - a)²
Where h is the height of the arch and a is half of the width of the arch.
To modify the function for the new arch, we need to adjust the value of a to reflect the new width of 32 inches. Since a is half the width, we have:
a = 32/2 = 16
We also need to adjust the value of h to reflect the new height of 44 inches. Therefore, the new function for the arch would be:
W(x) = 44/2 - 44/(2*16) * (x - 16)²
Simplifying this expression, we get:
W(x) = 22 - (11/8) * (x - 16)²
This new function will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall. The parabolic shape of the function will remain the same, but the specific coefficients in the function have been adjusted to reflect the new proportions of the arch.
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Find the slope of the line
Answer:
m = -2
Step-by-step explanation:
We Know
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-3,2) (-2,0)
We see the y decrease by 2, and the x increase by 1, so the slope is
m = -2
(From Unit 7, Lesson 3. )
The Colorado state flag consists of three horizontal stripes of equal height. The
side lengths of the flag are in the ratio 2 : 3. The diameter of the gold-colored disk is
equal to the height of the center stripe. What percentage of the flag is gold?
The total area of the flag is the sum of the areas of the three stripes and the percentage of the flag that is gold is approximately 0.459%
Let's call this height "h".
We also know that the side lengths of the flag are in the ratio 2:3. This means that if the shortest side is 2x, then the longest side is 3x. Since the three stripes are of equal height, each one must be h/3 in height.
Now we can use this information to find the area of the gold-colored disk and the total area of the flag. The area of a circle is given by the formula A = πr^2, where r is the radius. Since the diameter is equal to the height of the center stripe (which is h/3), the radius of the disk is h/6. So the area of the disk is:
A_disk = π(h/6)^2 = πh^2/36
The total area of the flag is the sum of the areas of the three stripes. Since each stripe is h/3 in height and the shortest side is 2x, the area of each stripe is:
A_stripe = (2x)(h/3) = 2hx/3
So the total area of the flag is:
A_flag = 3(A_stripe) = 6hx
To find the percentage of the flag that is gold, we need to divide the area of the gold-colored disk by the total area of the flag and multiply by 100.
percentage = (A_disk / A_flag) x 100
Substituting our expressions for A_disk and A_flag, we get:
percentage = (πh^2/36) / (6hx) x 100
Simplifying, we can cancel out the factor of h and get:
percentage = (π/216)x100
So the percentage of the flag that is gold is approximately 0.459% (rounded to three decimal places).
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A group of 150 dancers are auditioning for a dance show. 93 of the dancers trying out did not get on the show. What percentage of the dancers didn’t get in the show?
62% of the dancers did not get into the show.
To find the percentage of dancers who did not get into the show.
First, identify the total number of dancers auditioning and the number of dancers who did not get into the show.
In this case, there are 150 dancers in total, and 93 of them did not get in.
Next, divide the number of dancers who did not get into the show by the total number of dancers auditioning.
This will give us the proportion of dancers who did not get in.
Proportion = (Number of dancers who did not get in) / (Total number of dancers)
Proportion = 93 / 150
Finally, to find the percentage, multiply the proportion by 100:
Percentage = Proportion * 100
Percentage = (93 / 150) * 100.
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The model q(t) = 2. 5.00E+00. 0168t predicts the world population, in billions, t years after 1955. What was the population of the world in 1955 based
on this model?
The population of the world in 1955 based on the model q(t) = 2.500[tex]e^{0.0168t}[/tex] is 2.54 billion.
The model q(t) = 2.500[tex]e^{0.0168t}[/tex] represents the world population in billions
Here, t represents the years after 1955 and e is exponential constant its value is approximately 2.718.
Here the population is growing exponentially means population is growing at faster rate.
To find the population of the world in 1955 we will take
t = 1
on putting the value of t in the given function q(t)
q(t) = 2.500e[tex]e^{0.0168(1)[/tex]
on solving the function q(t) we get
q(t) ≈ 2.54
so, the population of the world in 1955 is 2.54 billion
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Suppose that you are gambling at a casino. Every day you play at a slot machine, and your goal is to minimize your losses. We model this as the experts problem. Every day you must take the advice of one of n experts (i. E. A slot machine). At the end of each day t, if you take advice from expert i, the advice costs you some c t i in [0, 1]. You want to minimize the regret R, defined as:
This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices
In this scenario, we can think of the slot machines as experts providing us with advice on which machine to play each day. The cost of taking advice from each expert, represented by cti, is the amount we lose by playing that particular machine.
To minimize our losses and regret, we want to choose the expert (i.e., slot machine) with the lowest cost each day. However, it's important to note that the cost of taking advice from each expert may change each day, so we need to constantly evaluate and adjust our choices.
To formalize this problem as an optimization task, we can use the concept of regret. Regret measures how much worse off we are by not knowing the best expert in advance. In other words, it's the difference between our cumulative losses if we always chose the best expert versus the losses we actually incur by following different experts each day.
To minimize our regret R, we need to choose the best expert as often as possible. One way to achieve this is by using an online learning algorithm that updates our choice based on the outcomes of each day's play. By continuously monitoring the performance of each slot machine, we can adjust our strategy and minimize our losses over time.
In summary, to minimize our losses while gambling at a casino, we need to treat each slot machine as an expert providing us with advice. We must choose the expert with the lowest cost each day and constantly update our strategy to minimize regret.
This requires an online learning algorithm that adapts to the changing costs of each expert and helps us make optimal choices.
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Hello, pleas help me with this geometry question. It’s about the area of sectors. Thanks :) (question in image below).
Answer:
39.27 square units
Step-by-step explanation:
In circle E with m∠DEF = 70∘ and DE=8, we want to find the area of sector DEF. To do this, we can use the formula for the area of a sector:
A_sector=1/2 r^2⋅
α
where r is the radius of the circle and α is the central angle in radians. In our case, r=8 and α=70 ∘ ⋅ π/180∘ = 7π/18 radians
Now, we can plug these values into the formula:
A_sector = 1/2(8^2) ⋅ 7π/18 = 32 ⋅ 7π/18 ≈ 39.27
So, the area of sector DEF is approximately 39.27 square units, rounded to the nearest hundredth.
The area of sector DEF in circle E is approximately 6.10 square units, rounded to the nearest hundredth.
To find the area of sector DEF in circle E, we need to use the formula for the area of a sector:
Area of sector = (Central angle / 360°) * π * r^2
where "Central angle" is the measure of angle DEF in degrees, "r" is the radius of the circle (DE in this case).
Given that m/DEF = 70° and DE = 8, we can calculate the area of sector DEF as follows:
Area of sector = (70° / 360°) * π * 8^2
Now, perform the calculations step by step:
Area of sector = (70/360) * π * 64
Area of sector = (7/36) * π * 64
Area of sector ≈ 3.14 * (7/36) * 64
Area of sector ≈ 3.14 * 1.9444
Area of sector ≈ 6.10 (rounded to two decimal places)
Therefore, the area of sector DEF in circle E is approximately 6.10 square units, rounded to the nearest hundredth.
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If AM=25CM, MC=20CM, MN=30CM, NC=35CM. What is the scale factor
The scale factor is 7/5 or 1.4.
f AM=25CM, MC=20CM, MN=30CM, NC=35CM.find scale factor
In order to determine the scale factor, we need to compare the corresponding sides of two similar figures. Let's begin by drawing a diagram to represent the given information:
M ------- N
/ \
/ \
A ---------------- C
<-----25cm----->
<-----20cm-----> <-----35cm----->
From the diagram, we see that triangle AMC is similar to triangle CNC, since they share angle C and have proportional sides:
Scale factor = corresponding side length in triangle CNC / corresponding side length in triangle AMC
We can calculate the scale factor by comparing the lengths of the corresponding sides:
Scale factor = NC / AM
Scale factor = 35 cm / 25 cm
Scale factor = 7 / 5
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F(x) =∣x∣ g(x)=∣x+2∣ we can think of g as a translated (shifted) version of f. complete the description of the transformation.
The transformation of f(x) to g(x) involves a horizontal shift and a reflection. The function g(x) is a transformed version of f(x) obtained by translating f(x) to the left by 2 units along the x-axis.
Specifically, to obtain g(x) from f(x), we first shift f(x) two units to the left, and then we take the absolute value of the result.
This means that the graph of g(x) will be the same as the graph of f(x) for all values of x greater than or equal to -2, but will be reflected across the y-axis for all values of x less than -2.
In other words, the transformation of f(x) to g(x) involves a horizontal shift and a reflection.
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A cereal company packages their granola in cylindrical containers that have a diameter of 20 cm and a height of 17. 4 cm. Approximately how much granola will a container hold?
The volume of granola a cylindrical container can hold 5451.6 cubic centimeters if containers have a diameter of 20 cm and a height of 17. 4 cm.
The number of unit cubes (cubes of unit length) that can fit inside a cylinder determines its volume.
Identifying the radius (r) and height (h)
r = 10 cm
h = 17.4 cm
Calculating the volume (V) using the formula V = πr²h
V = π × (10 cm)² × 17.4 cm
V ≈ 3.14 × 100 cm² × 17.4 cm
V ≈ 5451.6 cm³
Approximately, a container will hold 5451.6 cubic centimeters of granola.
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Your brother traveled 115 miles in 2. 52 hours to come home for school break. What’s the average speed that he was traveling?
The average speed that your brother was traveling is approximately 45.63 miles per hour
The average speed is the total distance traveled divided by the total time taken. So we have:
Average speed = total distance ÷ total time
We are given the total distance as 115 miles and the total time as 2.52 hours. Therefore, the average speed is:
Average speed = 115 miles ÷ 2.52 hours
Average speed = 45.63 miles per hour
So, the average speed that your brother was traveling is approximately 45.63 miles per hour.
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In the figure, AABC and ADEF are similar. what’s the scale factor from AABC to ADEF?
Answer:
3
Step-by-step explanation:
We can see that in figure ABC, line segment AB is 5 ft.
We can also see that in figure DEF, line segment DE is 15 ft.
How did we get from 5 to 15?
We multiplied by 3, so the scale factor is 3.
Hope this helps! :)
Help Please
Show your work so I can understand to get brainly
The maximum value represents (b) the point where most profits are made
What the maximum value representsGiven that the graph is the graph of a company's profit
The maximum value represents (b) the point where most profits are made
What the x-intercept representsGiven that the graph is the graph of a company's profit
The x-intercept is when the profit = 0
So
The x-intercept represents (b) the price per pen where no profit is made
The approximate average rateThis is calculated as
Rate = [f(6) - f(3)]/[6 - 3]
So, we have
Rate = [0 - 120]/[6 - 3]
Rate = -40
The domain in this contextThe domain of this graph given the situation is (0, 6] because the values do not makes sense beyond those points
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Part A: Using computer software, a correlation coefficient of r = 0. 01 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
If the scatter plot shows no discernible relationship between the variables and the points appear randomly scattered, then the r-value of 0.01 is accurate. However, if there is a visible relationship, the value of r may need to be recalculated or checked for errors in data input or analysis.
To find whether a correlation coefficient of r = 0.01 is an accurate value for the data based on the scatter plot, it's essential to consider the following factors:
1. Visual inspection of the scatter plot: Observe the overall pattern of data points in the scatter plot. If the points seem randomly scattered with no discernible pattern, then a correlation coefficient close to 0, such as r = 0.01, would be accurate. However, if there is a clear linear or non-linear relationship between the variables, the value of r = 0.01 may not be accurate.
2. Strength of the relationship: The correlation coefficient r ranges from -1 to 1, where -1 represents a strong negative relationship, 0 represents no relationship, and 1 represents a strong positive relationship. An r-value of 0.01 indicates a very weak or no relationship between the variables. Confirm that this is consistent with the scatter plot pattern.
To determine if the r-value of 0.01 is accurate for the data, carefully examine the scatter plot and consider these factors. If the scatter plot shows no discernible relationship between the variables and the points appear randomly scattered, then the r-value of 0.01 is accurate. However, if there is a visible relationship, the value of r may need to be recalculated or checked for errors in data input or analysis.
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Briefly discuss the difference between indefinite integral and definite integral. Give an example to provide emphasis. *
A definite integral is defined as the signed area under a function between certain limits (bounds) of integration.
An indefinite integral represents the family of antiderivatives of a function and is also known as its general integral or antiderivative.
The difference between the integralsAn indefinite integral represents the family of antiderivatives of a function and is also known as its general integral or antiderivative. An indefinite integral does not have specific limits of integration; its result includes a constant of integration (usually denoted +C), which accounts for all possible constant shifts within its antiderivative.
A definite integral is defined as the signed area under a function between certain limits (bounds) of integration. The real number that represents its net area between it and x-axis during an interval.
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HELPPPPPPP
I have zero idea of what to do!
Answer:
72 + 7x + 24 = 180
7x + 96 = 180
7x = 84
x = 12
Sam has a box shaped like a rectangular prism. It measures 1/6 inches in height, 1/3 in. Wide and 1/2 in. Long. What is the volume of the box? Leave your answer as an improper fraction
A rectangular prism is a three-dimensional shape with six faces, all of which are rectangles. The volume of a rectangular prism can be found by multiplying the length, width, and height of the prism.
In this case, Sam's box has a height of 1/6 inches, a width of 1/3 inches, and a length of 1/2 inches. To find the volume, we need to multiply these three dimensions:
(1/6) x (1/3) x (1/2) = 1/36 cubic inches.
Therefore, the volume of Sam's box is 1/36 cubic inches, which is an improper fraction because the numerator is greater than the denominator.
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A satellite orbiting Earth travels 4.95×10^7 meters for each orbit. It takes 6,600 seconds to make one orbit. What is the speed of the satellite in meters per second? Give your answer in standard form.
The value of the speed of the satellite in meters per second is,
⇒ Speed = 7.5 x 10³ m /sec
We have to given that;
A satellite orbiting Earth travels 4.95×10⁷ meters for each orbit.
And, It takes 6,600 seconds to make one orbit.
Hence, the speed of the satellite in meters per second is,
⇒ Speed = Distance / Time
⇒ Speed = 4.95×10⁷/ 6,600
⇒ Speed = 0.00075 x 10⁷
⇒ Speed = 7.5 x 10⁻⁴ x 10⁷
⇒ Speed = 7.5 x 10³ m /sec
Thus, The value of the speed of the satellite in meters per second is,
⇒ Speed = 7.5 x 10³ m /sec
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Simplify 3y(y^2-3y+2)
Answer:
3y^3-9y^2+6y
Step-by-step explanation:
= 3y^3-9y^2+6y
A random sample of 18 observations taken from a normally distributed population produced the following data:
28. 4 27. 3 25. 5 25. 5 31. 1 23. 0 26. 3 24. 6 28. 4
37. 2 23. 9 28. 7 27. 9 25. 1 27. 2 25. 3 22. 6 22. 7
What is the point estimate of μ?
Make a 99% confidence interval for μ.
What is the margin of error of estimate for μ in part b?
Point estimate of μ [tex]26.15[/tex]
99% confidence interval: [tex](24.213, 28.087)[/tex]
Margin of error:[tex]1.437[/tex]
How to estimate μ and create a 99% confidence interval ?The point estimate of (population mean) is calculated by finding the sample mean , which is the average of the given sample data. Adding up all the observations and dividing by the sample size (18), we get:
To make a 99% confidence interval for we can use the t-distribution and the sample mean. Since the sample size is 18, we have (18 - 1) = 17 degrees of freedom. Using a t-distribution table or a calculator, we find the critical value for a 99% confidence level and 17 degrees of freedom to be approximately 2.898.
Next, we calculate the standard error (SE) using the sample standard deviation (s) divided by the square root of the sample size .Assuming the population standard deviation is unknown, we estimate it using the sample standard deviation, which is approximately 3.858.
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u = 28.8
The 99% confidence interval for μ is (27.01, 30.59).
How to solve the data28.4 + 27.3 + 25.5 + 25.5 + 31.1 + 23.0 + 26.3 + 24.6 + 28.4 + 37.2 + 23.9 + 28.7 + 27.9 + 25.1 + 27.2 + 25.3 + 22.6 + 22.7 = 518.3
The sample mean (or the point estimate of μ) is:
518.3 / 18 = 28.8
Calculate each data point's deviation from the mean, square it, and then sum up these values.
(28.4-28.8)² + (27.3-28.8)² + (25.5-28.8)² + (25.5-28.8)² + (31.1-28.8)² + (23.0-28.8)² + (26.3-28.8)² + (24.6-28.8)² + (28.4-28.8)² + (37.2-28.8)² + (23.9-28.8)² + (28.7-28.8)² + (27.9-28.8)² + (25.1-28.8)² + (27.2-28.8)² + (25.3-28.8)² + (22.6-28.8)² + (22.7-28.8)²
= 116.4
Divide by (n - 1), where n is the number of observations. In this case, n = 18, so n - 1 = 17.
So, the variance (s²) is 116.4 / 17 = 6.85 (approximately)
s = √6.85 = 2.62
CI = x ± (t * (s/√n))
CI = 28.8 ± (2.898 * (2.62/√18))
CI = 28.8 ± 1.79
So, the 99% confidence interval for μ is (27.01, 30.59).
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Complete the relative frequency table based on the total number of people surveyed.
Type the correct answer in each box. Round your answers to the nearest hundredth.
Coffee
Tea
Total
Relative Frequency for the Whole Table
Early Bird
Night Owl
0.19
0.44
0.6
Total
0.35
1
The complete relative frequency table include the following missing values:
Early bird Night Owl Total
Coffee. 0.21 0.44 0.65
Tea. 0.19. 0.16. 0.35
Total. 0.4. 0.6. 1
How to determine and complete the given relative frequency table?The total of each column is being determined from the grand total which can then be use to fill in the various missing parts of the relative frequency table.
For coffee;
To determine the total = 1-0.35 = 0.65
Coffee early Bird = 0.65-0.44 =0.21
For tea ;
Tea night owl = 0.35-0.19 = 0.16
For grand total = 1-0.6 = 0.4
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The ratio of m angle wxz to m angle zxy is 11:25. what is m angle zxy
The measure of angle zxy is 125 degrees.
To solve the problem, we can use the fact that the sum of the measures of two adjacent angles is 180 degrees. Let's call the measure of angle zxy "x".
We know that the ratio of m angle wxz to m angle zxy is 11:25, which means that:
m angle wxz : m angle zxy = 11 : 25
We can write this as an equation:
m angle wxz / m angle zxy = 11/25
We also know that the two angles are adjacent, so their measures add up to 180 degrees:
m angle wxz + m angle zxy = 180
Now we can use these two equations to solve for x:
m angle wxz / x = 11/25
m angle wxz = (11/25)x
Substituting this into the second equation:
(11/25)x + x = 180
(36/25)x = 180
x = (25/36) * 180
x = 125
Therefore, the measure of angle zxy is 125 degrees.
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The first floor of a tiny house has has a length of 11 feet. The width of the kitchen if is 7 feet and the width of the bathroom is 4 feet. The expression 11(7+4) represents the total area in square feet. Write an expression to represent the total area as the sum of the areas of each room
The total area of the first floor of the tiny house is 121 square feet
The total area of the first floor of the tiny house can be expressed as the sum of the areas of each room. The area of a rectangle is calculated by multiplying the length by the width. Therefore, we can write:
Total area = Area of kitchen + Area of bathroom
The area of the kitchen is given by the product of the length and the width of the kitchen, which is 11 feet and 7 feet, respectively. Therefore, the area of the kitchen can be written as:
Area of kitchen = 11 x 7 = 77 square feet
Similarly, the area of the bathroom is given by the product of the length and the width of the bathroom, which is 11 feet and 4 feet, respectively. Therefore, the area of the bathroom can be written as:
Area of bathroom = 11 x 4 = 44 square feet
Substituting these expressions into the equation for the total area, we get:
Total area = Area of kitchen + Area of bathroom
= 77 + 44
= 121 square feet
Therefore, the total area of the first floor of the tiny house is 121 square feet, which can also be expressed as the sum of the areas of the kitchen and bathroom.
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a study of 90 randomly selected families, 40 owned at least one television. find the 95% confidence interval for the true proportion of families that own at least one television.
The 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542).,
How do we calculate ?The formula for the confidence interval of a proportion:
CI = p ± z* (√(p*(1-p)/n))
where:
p is the sample proportion (40/90 = 0.4444)
z* is the critical value of the standard normal distribution at the 95% confidence level (1.96)
n is the sample size (90)
Substituting the values, we have
CI = 0.4444 ± 1.96 * (√(0.4444*(1-0.4444)/90))
CI = 0.4444 ± 1.96 * (√(0.00245))
CI = 0.4444 ± 1.96 * 0.0495
CI = 0.4444 ± 0.097
Hence, the 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542) when rounded to three decimal places.
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