To show that the series Σα) f(n)/2n^3 - 1 n converges regardless of the rule for f, we can use the Comparison Test. Let's choose a series that is easier to compare to, such as Σ(1/2n^3).
First, note that 0 ≤ f(n) ≤ 1 for all n, since f is a function that is not negative and bounded by 1. Thus, we have: 0 ≤ f(n)/2n^3 - 1 n ≤ 1/2n^3, Now, we can compare the given series to the series Σ(1/2n^3) using the Comparison Test. Since 0 ≤ f(n)/2n^3 - 1 n ≤ 1/2n^3 for all n, we know that: 0 ≤ Σα) f(n)/2n^3 - 1 n ≤ Σ(1/2n^3), The series Σ(1/2n^3) is a convergent p-series with p = 3 > 1, so by the Comparison Test, the given series Σα) f(n)/2n^3 - 1 n also converges. Therefore, we have shown that the series Σα) f(n)/2n^3 - 1 n converges regardless of the rule for f.
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Can someone how to use a TI-84 Plus to do the following:
Normal Distribution: Finding Values
Normal Distribution: Finding Probibilities
Sampling Distributions and the Central Limit Theorem
!!!!I have a test on this tmr please help!!!!
Normal Distribution: Finding Values
Press the "2nd" key, then press the "vars" key to access the DISTR menu.
Scroll down to "Normalcdf" and press enter.
Enter the lower bound, upper bound, mean, and standard deviation. For example, if you want to find the probability that X is between 60 and 70, given that the mean is 65 and the standard deviation is 5, you would enter "60, 70, 65, 5".
Press enter to get the result. The calculator will give you the probability that X falls between the two values you entered.
Normal Distribution: Finding ProbabilitiesPress the "2nd" key, then press the "vars" key to access the DISTR menu.
Scroll down to "InvNorm" and press enter.
Enter the probability you want to find. For example, if you want to find the z-score that corresponds to the 90th percentile, you would enter "0.9".
Enter the mean and standard deviation. For example, if the mean is 65 and the standard deviation is 5, you would enter "65, 5".
Press enter to get the result. The calculator will give you the z-score that corresponds to the probability you entered.
Sampling Distributions and the Central Limit Theorem: Press the "2nd" key, then press the "vars" key to access the DISTR menu.
Scroll down to "1-PropZTest" or "2-PropZTest" and press enter, depending on the type of test you want to perform.
Enter the sample statistics and the population parameters, if known. The calculator will use these values to calculate the test statistic and p-value.
Press enter to get the result. The calculator will give you the test statistic and the p-value, which you can use to make inferences about the population.
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PLease help 1 and 2 Pythagorean Theorem and if you can explain please
Answer:
Step-by-step explanation:
The Pythagorean theorem has the formula a squared(leg) + b squared(leg) = c squared(longest leg). This means [tex]12^{2} +16^{2} =20^{2} -- > 144+256=400[/tex] which is true meaning number 1 is a right triangle. [tex]10^{2} +49.5^{2} = 50.5^{2} -- > 100+2450.25=2550.25[/tex] is true meaning number 2 is also a right triangle because the sum of the shortest legs squared are equal to the longest leg (hypotenuse) squared.
Enter the value of c when the expression 21. 2x + c is equivalent of to 5. 3(4x - 2. 6).
The value of c is 21.8.
We can solve for c by simplifying the expression on the right side of the equation and equating it to the expression on the left side.
Starting with the right side, we distribute the 3 across the parentheses:
5 * 3 * (4x - 2.6) = 60x - 13
Now, we can set this equal to the expression on the left and solve for c:
21.2x + c = 60x - 13
c = 60x - 13 - 21.2x
c = 38.8x - 13
However, we are asked to find the value of c, not in terms of x. Since we were not given a specific value for x, we cannot solve for c exactly. Therefore, we can only express the value of c in terms of x, which is c = 38.8x - 13.
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an airplane is 58 m long. a scale model of the plane is 40.6 cm long.
determine the scale factor used to create the model as a decimal rounded
to the nearest thousandth
If a scale model of the plane is 40.6 cm long, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.
To determine the scale factor used to create the model, we need to divide the length of the actual airplane by the length of the model airplane:
58 m / 40.6 cm
To perform this calculation, we need to convert the units so that they match. We can convert 58 m to cm by multiplying by 100:
58 m = 58 × 100 cm = 5800 cm
Now we can divide:
5800 cm / 40.6 cm = 142.857...
Rounding to the nearest thousandth, we get:
142.857... ≈ 142.857
Therefore, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.
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a) Factorise x²-2x-3
Answer:
Solution: (x-3)(x+1)
Step-by-step explanation:
1) Using Mid term break:
x²-2x-3
x²+x-3x-3
2) Take Common Factors from the two pairs
(x²+x) + (-3x-3)
x(x+1) -3(x+1)
3) Rewrite in Factored Form:
(x-3)(x+1)
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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During the period 2000-2016, the average costs B (in dollars) for a new boat and the average costs H (in dollars) for a hovercraft can be modeled
by the following functions:
B = 30 +140 and H=-1012 +350 + 400
where t is the number of years since 2000
(a) How can the difference of the costs of a hovercraft and the costs of a boat be expressed? (4 points)
(b) About how much was the difference in the year 2010? (2 points)
The difference between the costs of a hovercraft and a boat in the year 2010 was approximately $1,558.
(a) The difference in costs between a hovercraft and a boat can be expressed as follows:
Cost difference = Hovercraft cost - Boat cost
Cost difference = (-1012 + 350t + 400) - (30 + 140t)
Cost difference = -1012 + 350t + 400 - 30 - 140t
Cost difference = 220t - 642
Therefore, the difference in costs between a hovercraft and a boat can be expressed as 220t - 642.
(b) To find the difference in the year 2010, we need to substitute t = 10 in the expression we derived in part (a):
Cost difference = 220t - 642
Cost difference = 220(10) - 642
Cost difference = 2200 - 642
Cost difference = 1558
Therefore, the difference between the costs of a hovercraft and a boat in the year 2010 was approximately $1,558.
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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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why zero is neither positive or negative probe with scientific ?
Answer: As the Integers being positive or negative depends on the 0 As it is reference present on the centre of the number line
Numbers on the left side are negative while that on right side being positive
Step-by-step explanation:
Please help me ill give out brainest
which expression is equivalent to 1/5x(5y+60)
a. 1/5(2xy+3xy+40x)
b. xy+60x
c. y+12x
d. 25xy+300y
e. 13xy
f. x(y+12)
Answer:
The correct answer is ** x(y+12) or f.
We can simplify the expression 1/5x(5y+60) by multiplying the factors in the parentheses and then dividing by 5. This gives us:
```
1/5x(5y+60) = 1/5 * 5xy + 1/5 * 60x = x(y+12)
```
this 3 questions please????????
Consider the following function
f(x) = x^2/x^2 -9
Find the criticat number of renter your antwers as a comma-separated list) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)
Critical numbers: 0, -3, 3
Increasing intervals: (-∞, -3), (3, ∞)
Decreasing intervals: (-3, 0), (0, 3)
Let's analyze the given function and find the critical numbers, as well as the intervals where it is increasing or decreasing.
Function: f(x) = x^2 / (x^2 - 9)
1. Find the critical numbers:
To find the critical numbers, we need to compute the first derivative of the function and set it equal to zero or identify where it's undefined.
f'(x) = (2x(x^2 - 9) - x^2(2x)) / (x^2 - 9)^2 = (2x^3 - 18x - 2x^3) / (x^2 - 9)^2 = -18x / (x^2 - 9)^2
Setting f'(x) equal to zero:
-18x = 0
x = 0
Now, let's check where f'(x) is undefined:
x^2 - 9 = 0
x = ±3
Thus, the critical numbers are 0, -3, and 3.
2. Find the open intervals where the function is increasing or decreasing:
To determine the intervals, we will examine the sign of f'(x) in the intervals determined by the critical numbers: (-∞, -3), (-3, 0), (0, 3), (3, ∞).
Interval (-∞, -3): Choose x = -4, then f'(-4) > 0. So, f(x) is increasing on this interval.
Interval (-3, 0): Choose x = -1, then f'(-1) < 0. So, f(x) is decreasing on this interval.
Interval (0, 3): Choose x = 1, then f'(1) < 0. So, f(x) is decreasing on this interval.
Interval (3, ∞): Choose x = 4, then f'(4) > 0. So, f(x) is increasing on this interval.
Your answer:
Critical numbers: 0, -3, 3
Increasing intervals: (-∞, -3), (3, ∞)
Decreasing intervals: (-3, 0), (0, 3)
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Christy went jogging on saturday. the table shows how far she had jogged after various times.
distance (miles) 10
15
20
time (hours)
2
3
4.
christy subtracted to find her jogging rate for each time period and said that her rate
increased each hour, from 8 to 12 to 16 miles per hour. is christy correct? explain why or
why not.
She is incorrect when she said that her rate increased each hour from 8 to 12 to 16 miles per hour. Her jogging rate was actually a steady 5 miles per hour.
You asked if Christy is correct when she said that her rate increased each hour, from 8 to 12 to 16 miles per hour. Let's analyze the data given in the table and see if she's right.
The table shows the distance Christy jogged and the corresponding time:
- 10 miles in 2 hours
- 15 miles in 3 hours
- 20 miles in 4 hours
To find her jogging rate for each time period, we need to divide the distance by the time.
1. For the first 2 hours:
Jogging rate = distance / time = 10 miles / 2 hours = 5 miles per hour
2. For the first 3 hours:
Jogging rate = distance / time = 15 miles / 3 hours = 5 miles per hour
3. For the first 4 hours:
Jogging rate = distance / time = 20 miles / 4 hours = 5 miles per hour
Christy's jogging rate remained constant at 5 miles per hour throughout her run. Therefore, she is incorrect when she said that her rate increased each hour from 8 to 12 to 16 miles per hour. Her jogging rate was actually a steady 5 miles per hour.
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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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For a random sample of 75 kindergartners, mothers' incomes are plotted on the x-axis and fathers' incomes are plotted on the y-axis. The resulting scatter plot produces a linear association described by the equation y=1. 23x+5. 3. Which conclusion can be made about this sample?
The intercept of 5.3 suggests that even if a mother had no income, the expected minimum fathers' income would be $5.30.
In mathematical terms, the equation y=1.23x+5.3 is in slope-intercept form, where y represents the fathers' incomes and x represents the mothers' incomes. The slope of the line, 1.23, represents the change in fathers' incomes for every one unit increase in mothers' incomes. The y-intercept of the line, 5.3, represents the minimum fathers' income when the mothers' income is zero.
With this equation, we can make several conclusions about this sample. Firstly, the positive slope suggests a positive correlation between the incomes of mothers and fathers. As the mothers' incomes increase, the fathers' incomes also tend to increase.
Secondly, the slope value of 1.23 suggests that fathers' incomes increase by $1.23 for every $1 increase in mothers' incomes.
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5.
Sarah deposited $800 in an account that earns
2% interest compounded annually. Claire deposited
$800 in an account that earns 2% simple interest.
How much will each girl have in their account at the
end of 8 years if they do not make any deposits or
withdrawals?
Answer:
Sarah will have $937.28 and Claire will have $928.
Step-by-step explanation:
All my work is provided in the screenshots that are attached to my answer! Drop questions in the comments and I'll try to respond if I remember/see them lol.
Have a great day!
The carbon monoxide wel wat is predicted to be 0.02.2+1 arts permitin), where is the population in thousands In was the population of the oty i predicted to be ) - 12 those perle Therefore, it was the one will be D) - 02/12 - 02.10 Find that which in de will be increasing in 2 years.
I apologize, but I am having trouble understanding your question. Can you please provide more context and clarity? Specifically, what do you mean by "carbon monoxide wel wat" and "arts permitin"? Additionally, what city or population are you referring to? Once I have a better understanding of your question, I will do my best to provide a helpful response.
Hi! It seems like the question is asking about the prediction of carbon monoxide levels in relation to population growth. Unfortunately, the text is a bit unclear, so I'll try my best to answer based on the provided information.
The given equation for carbon monoxide levels (CO) is: CO = 0.02(2 + P), where P is the population in thousands. To find the predicted increase in CO levels after 2 years, you would need to know the population growth rate or the population for those years. Please provide more information or clarify the question, and I'll be happy to help further
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The ceiling of Stacy's living room is a square that is 25 ft long on each side. Stacy knows the diagonal of the ceiling from corner to corner must be longer than 25 ft, but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry
The length of the diagonal of Stacy's ceiling using the Pythagorean Theorem and trigonometry is 35.36 ft.
(a) Using the Pythagorean Theorem:
Since the ceiling is a square, we can treat it as two right triangles. Let's call the length of the diagonal 'd'. Now, we can apply the Pythagorean Theorem (a² + b² = c²) to one of the right triangles:
a² + b² = d²
25² + 25² = d²
625 + 625 = d²
1250 = d²
Now, take the square root of both sides:
√1250 = d
d ≈ 35.36 ft
(b) Using trigonometry:
In one of the right triangles, the angle between the two sides of the square (25 ft each) is 45 degrees. We can use the tangent function (tan) to relate the angle to the side lengths:
tan(45) = opposite side / adjacent side
tan(45) = 25 / 25
Since tan(45) = 1, we have 1 = 1, which confirms the angle is 45 degrees. Now, we can use the sine or cosine function to find the diagonal:
sin(45) = opposite side / hypotenuse
sin(45) = 25 / d
OR
cos(45) = adjacent side / hypotenuse
cos(45) = 25 / d
Both functions give us the same result since the angles are 45 degrees. Solving for 'd':
d = 25 / sin(45)
d ≈ 35.36 ft
So, the length of the diagonal of Stacy's ceiling is approximately 35.36 ft using both methods.
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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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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?
(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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You invest $2500 in an account to save for college. account 1 pays 6%annual interest compounded quarterly. account 2 pays 4% annual interest compounded continuously. which account should you choose to obtain the greater amount in 10 years?
account 1
or
account 2
You should choose Account 1 to obtain the greater amount in 10 years. Account 1 will have a higher balance after 10 years.
Account 1 pays 6% annual interest compounded quarterly, which means the interest is calculated and added to the principal four times a year. You can use the formula A = P(1 + r/n)^(nt) to calculate the future value, where A is the final amount, P is the principal ($2500), r is the annual interest rate (0.06), n is the number of times compounded per year (4), and t is the number of years (10).
Account 2 pays 4% annual interest compounded continuously. You can use the formula A = Pe^(rt) to calculate the future value, where A is the final amount, P is the principal ($2500), e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (0.04), and t is the number of years (10).
When you compare the final amounts for both accounts, Account 1 will have a higher balance after 10 years.
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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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help!!
this is due by today, if anyone could help i would really appreciate help
the question is: what is the area of the shaded portion?
How many numbers from 2 through 100 can be expressed as p², where p is a prime number?
F. 4
G. 5
H. 7
J. 8
K. 9
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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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:
A population of insects increases at a rate of 280 +64 +0.9t^2 insects per day Find the Insect population after 5 days, assuming that there are consects att Round your arwer to the ne
Since we need to round our answer to the nearest whole number, the insect population after 5 days will be approximately 367 insects.
Given the rate at which the insect population increases, we can determine the population after 5 days using the given formula: 280 + 64 + 0.9t^2 insects per day.
First, we need to substitute t with the number of days, which is 5:
280 + 64 + 0.9(5)^2
Now, calculate the value of the equation:
280 + 64 + 0.9(25) = 280 + 64 + 22.5 = 366.5
OR,
The population of insects after 5 days can be found by plugging in t = 5 into the given equation:
Population = 280 + 64 + 0.9(5)^2
Population = 280 + 64 + 22.5
Population = 366.5
Rounding to the nearest insect, the population after 5 days is 367 insects.
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Points E, F, G and H lie on the circle and EG = EH.
HF and EG intersect at K.
ET is a tangent to the circle at E.
Angle FET = 47° and angle FEG = 25°.
Find the value of x.
Using the inscribed angle theorem, the value of x in the circle shown is calculated as: m<x = 36°.
How to Apply the Inscribed Angle Theorem?According to the inscribed angle theorem an inscribed angle has an angle measure that is always half of the measure of the arc it intercepts.
Measure of arc EFG = 2(25 + 47) [inscribed angle theorem]
Measure of arc EFG = 144°
Measure of angle EHG = 1/2(m(EFG)) [inscribed angle theorem]
Substitute:
Measure of angle EHG = 1/2(144) = 72°
m<EHG = m<EGH = 72° [this is because triangle EHG is an isosceles triangle since sides EG = EH].
Therefore, we have:
m<x = 180 - 2(72)
m<x = 36°
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Dan's small business earned about $85,000 this year. Based on data from similar businesses, Dan expects his annual earnings to increase by 12% each year. Write an exponential equation in the form y=a(b)x that can model Dan's annual earnings, y, in x years. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = _____ To the nearest hundred dollars, how much is Dan's small business predicted to earn in 5 years?
The equation would be written as: y = $85,000(1 + 0.12/1)^5
Then the predicted earning would be y = $132,559
How to solve for the earningy=a(b)x
where y = income
a = $85,000
b = (1 + r = percent increase)
then x = time period = 5 years
When we put in the values we would have y = $85,000(1 + 0.12/1) ^5
The exponential function of the form y = a(b)^x is: y = $85,000(1 + 0.12/1) ^5
When we solve the above, we would have the income = y = $132,559
Therefore the predicted earnings that Dans small business would have in a period of five years is equal to $132,559
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Many artists incorporate geometry shapes into their art. an artist wants to make a sculpture shaped like a cone with a height of 4.2 inches and a radius of 2.5 inches.the artist needs to know the volume of the sculpture to purchase the correct amount of materials
part a. which equation shows the art is used to calculate the volume of a cone with the given measurements
part b. what is the volume,in cubic inches,of the cone? use 3.14 for pie and round your answer to the nearest tenth
The volume of the cone is approximately 26.1 cubic inches.
What is the equation used to calculate the volume of a cone with a radius of 2.5 inches and a height of 4.2 inches?The formula used to calculate the volume of a cone is:
V = (1/3) × π ×[tex]r^2[/tex] × h
where V is the volume of the cone, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant that is approximately equal to 3.14.
Part b. Plugging in the given values, we get:
V = (1/3) × 3.14 ×[tex]2.5^2[/tex]× 4.2
V = (1/3) × 3.14 × 6.25 × 4.2
V = 26.125 cubic inches (rounded to the nearest tenth)
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