On replacing the incandescent light bulb with a fluorescent light bulb (a) the energy saved in one day is 0.22 kWh, (b) the energy saved in one year is 80.3 kWh. and (c) the cost savings in one year is $8.03.
a. The energy saved in one day by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Energy saved in one day = Energy consumed by incandescent bulb - Energy consumed by fluorescent bulb
Energy saved in one day = (75 watts x 4 hours) - (20 watts x 4 hours)
Energy saved in one day = 300 watt-hours - 80 watt-hours
Energy saved in one day = 220 watt-hours
To convert watt-hours to kilowatt-hours (kWh), we divide the watt-hours by 1000:
Energy saved in one day = 220 watt-hours / 1000
Energy saved in one day = 0.22 kWh
b. The energy saved in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Energy saved in one year = Energy saved in one day x Number of days in one year
Energy saved in one year = 0.22 kWh/day x 365 days/year
Energy saved in one year = 80.3 kWh
c. The cost savings in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:
Cost savings in one year = Energy saved in one year x Cost per kWh
Cost savings in one year = 80.3 kWh x $0.10/kWh
Cost savings in one year = $8.03
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Students at a certain high school have to take an arts or technology class. A random sample of 60 students from the high school are surveyed. Each student is asked which class they take. Based on the survey results, which of the following statements are true? Select all that apply.
A There are many excellent dancers at the high school.
B About 25% of the students at the high school
take painting.
C Of every 30 students in the high school, about 11 of them take photography.
D Next year, 7 out of every 60 students at the high school will take music.
E In a group of 120 students from the high school, about 16 of the students
likely take electronics.
The correct statements from the sample are given as follows:
B About 25% of the students at the high school take painting.
D Next year, 7 out of every 60 students at the high school will take music.
E In a group of 120 students from the high school, about 16 of the students likely take electronics.
How to obtain the proportions?The proportion relative to an outcome is given by the number of desired outcomes divided by the number of total outcomes.
15 out of 60 students at the school take painting, hence the proportion is given as follows:
p = 15/60 = 0.25 = 25%.
Out of 60 students, 11 take photography, hence out of 30 students, the amount is given as follows:
30/60 x 11 = 5.5.
For electronics, out of 120 students, we have that:
120/60 x 8 = 16.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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Find the steady-state current in each RLC circuit using Lq′′ + Rq′ + 1/C q = E
R = 3 Ω; L = 0.1 H; C = 0.01 F; E(t) = 5cos10t - 5sin10t
Determine the steady-state current in the RLC circuit to be 0.68 A.
The equation for Lq′′ + Rq′ + 1/C q = E is used to find the steady-state current in each RLC circuit. The circuit parameters are L = 0.1 H, C = 0.01 F, R = 3 Ω, and E(t) = 5cos10t - 5sin10t.Lq′′ + Rq′ + 1/C q = E can be written as Ld²q/dt² + Rdq/dt + 1/C q = E(t)The current flowing through the circuit can be determined using this formula. To calculate the current, we can use E(t) = 5cos10t - 5sin10t.The current can be found using the equation q(t) = Q cos(wt - φ), where Q = I/Z, Z = √(R² + (wL - 1/wC)²), w = 2πf, and φ = tan⁻¹((wL - 1/wC)/R). Z, w, and φ can be calculated from the parameters of the circuit.Using the above formulas, the following is obtained.I = 5/√(3² + (10π x 0.1 - 1/(10π x 0.01))²) = 0.68 ADetermine the steady-state current in the RLC circuit to be 0.68 A.
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if anyone that actually understands, could help, would be much appreciated
Answer:
a. -1
b. 1
c. 6
Step-by-step explanation: f(any value) just means plug in the value given inside of the f and see what y value comes out. for the first on, go to where four it on the x-axis and you will see that the y-value is -1. Repeat the same thing for f(0) where you can look directly on the y-axis and get 1 as the answer. Lastly, look where -4 meets the y-axis and it will be 6.
Which number line represents the solution of 1/2 b ≥ 4 ?
Answer:
Answer D
Step-by-step explanation:
Solve for b:
[tex]\frac{1}{2}b \geq 4[/tex]
Divide both sides by a half
[tex]b\geq 8[/tex]
We see that its a greater than or equal too sign, which means the number line has to be facing to the right with a closed circle. Therefore, D is our answer.
The temperature of a person has a normal distribution. What is the probability that the temperature of a randomly selected person will be within 2. 42 standard deviations of its mean? Provide answer with 4 or more decimal places
The required probability of the temperature of a person which has normal distribution is given by 0.9500.
Temperature of a person follows a normal distribution.
Use the Empirical Rule to estimate the probability.
Temperature of a randomly selected person will be within 2.42 standard deviations of its mean.
Empirical Rule states that for a normal distribution is,
About 68% of the data falls within one standard deviation of the mean.
About 95% of the data falls within two standard deviations of the mean.
About 99.7% of the data falls within three standard deviations of the mean.
Probability of temperature of a randomly selected person within 2.42 standard deviations of its mean = 95%
95%
= 95/100
= 0.95
=0.9500 ( round this to four decimal places )
Therefore, the probability that the temperature of a randomly selected person is 0.9500.
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Charles has a rectangular flower garden that is 5 yd long and 12 yd wide. One bag of fertilizer can cover 6 yd2 . How many bags will he need to buy to cover the entire garden?
Charles will need to buy 10 bags of fertilizer to cover the entire garden.
What is Algebraic expression ?
In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.
The area of the rectangular garden is:
A = length x width
A = 5 x 12
A = 60
To cover the entire garden, Charles needs:
Number of bags = (Area of garden) ÷ (Area covered by one bag)
Number of bags = 60 ÷ 6
Number of bags = 10 bags
Therefore, Charles will need to buy 10 bags of fertilizer to cover the entire garden.
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What is the percent of students who took PE?
*
1 point
43%
54%
47%
57%
[tex] \sf43\% \implies \: answer[/tex]
Scale Items Work Engagement Items – measured on a 1-7 scale (1-Never, 7-Always) At my work, I feel bursting with energy At my job, I feel strong and vigorous When I get up in the morning I feel like going to work I am enthusiastic about my job I am proud of the work I do I feel happy when I am working intensely I am immersed in my work I get carried away when I am working Job Tension Items – measured on 1-7 scale (1-Strongly disagree, 7-Strongly agree) My job is extremely stressful Very few stressful things happen to me at work I feel a great deal of stress because of my job I almost never feel stressed because of my work Career Satisfaction Items – measured on 1-7 scale (1-strongly disagree, 7-strongly agree) I am satisfied with the Success I have achieved in my career Success I have made toward meeting my overall career goals Progress I have made toward meeting my goals for income Progress I have made toward meeting my goals for advancement Progress I have made toward meeting my goals for developing new skills Perceived Internal Mobility Items – measured on 1-5 scale (1-strongly disagree, 5-strongly agree) My organization views me as an asset to the organization Given my skills and experience, my organization views me as a value-added resource There are many opportunities available for me in my organization Perceived Supervisory Support Items – measured on1-7 scale (1-Strongly disagree, 7- Strongly agree) My supervisor strongly considers my goals and values Help is available from my supervisor when I have a problem My supervisor really cares about my well-being My supervisor would forgive an honest mistake on my part My supervisor is willing to help me when I need a special favor If given the opportunity, my supervisor would take advantage of me My supervisor shows very little concern for me My supervisor cares about my opinions
The my supervisor cares about my opinions.
Scale Items Work Engagement Items – measured on a 1-7 scale (1-Never, 7-Always): At my work, I feel bursting with energy; at my job, I feel strong and vigorous; when I get up in the morning I feel like going to work; I am enthusiastic about my job; I am proud of the work I do; I feel happy when I am working intensely; I am immersed in my work; I get carried away when I am working.
Job Tension Items – measured on 1-7 scale (1-Strongly disagree, 7-Strongly agree): My job is extremely stressful; very few stressful things happen to me at work; I feel a great deal of stress because of my job; I almost never feel stressed because of my work.
Career Satisfaction Items – measured on 1-7 scale (1-strongly disagree, 7-strongly agree): I am satisfied with the success I have achieved in my career; success I have made toward meeting my overall career goals; progress I have made toward meeting my goals for income; progress I have made toward meeting my goals for advancement; progress I have made toward meeting my goals for developing new skills.
Perceived Internal Mobility Items – measured on 1-5 scale (1-strongly disagree, 5-strongly agree): My organization views me as an asset to the organization; given my skills and experience, my organization views me as a value-added resource; there are many opportunities available for me in my organization.
Perceived Supervisory Support Items – measured on 1-7 scale (1-Strongly disagree, 7- Strongly agree): My supervisor strongly considers my goals and values; help is available from my supervisor when I have a problem; my supervisor really cares about my well-being; my supervisor would forgive an honest mistake on my part; my supervisor is willing to help me when I need a special favor; if given the opportunity, my supervisor would take advantage of me; my supervisor shows very little concern for me; my supervisor cares about my opinions.
Answer: The question asks about scale items measuring Work Engagement, Job Tension, Career Satisfaction, Perceived Internal Mobility, and Perceived Supervisory Support, all measured on different scales. Work Engagement is measured on a 1-7 scale (1-Never, 7-Always), Job Tension is measured on a 1-7 scale (1-Strongly disagree, 7-Strongly agree), Career Satisfaction is measured on a 1-7 scale (1-strongly disagree, 7-strongly agree), Perceived Internal Mobility is measured on a 1-5 scale (1-strongly disagree, 5-strongly agree), and Perceived Supervisory Support is measured on a 1-7 scale (1-Strongly disagree, 7- Strongly agree). In terms of Work Engagement, the items are: At my work, I feel bursting with energy; at my job, I feel strong and vigorous; when I get up in the morning I feel like going to work; I am enthusiastic about my job; I am proud of the work I do; I feel happy when I am working intensely; I am immersed in my work; I get carried away when I am working. For Job Tension, the items are: My job is extremely stressful; very few stressful things happen to me at work; I feel a great deal of stress because of my job; I almost never feel stressed because of my work. For Career Satisfaction, the items are: I am satisfied with the success I have achieved in my career; success I have made toward meeting my overall career goals; progress I have made toward meeting my goals for income; progress I have made toward meeting my goals for advancement; progress I have made toward meeting my goals for developing new skills. For Perceived Internal Mobility, the items are: My organization views me as an asset to the organization; given my skills and experience, my organization views me as a value-added resource; there are many opportunities available for me in my organization. Finally, for Perceived Supervisory Support, the items are: My supervisor strongly considers my goals and values; help is available from my supervisor when I have a problem; my supervisor really cares about my well-being; my supervisor would forgive an honest mistake on my part; my supervisor is willing to help me when I need a special favor; if given the opportunity, my supervisor would take advantage of me; my supervisor shows very little concern for me; my supervisor cares about my opinions.
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Standard Normal Distribution In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers
to four decimal places.
Greater than 0.18
The probability of a bone density score greater than 0.18 is given as follows:
0.4286 = 42.86%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 0, \sigma = 1[/tex]
The probability of a score greater than 0.18 is one subtracted by the p-value of Z when X = 0.18, hence:
Z = (0.18 - 0)/1
Z = 0.18
Z = 0.18 has a p-value of 0.5714.
Hence:
1 - 0.5714 = 0.4286 = 42.86%.
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Which of the following is an irrational number?
Answer:
[tex]\large\boxed{\mathtt{7.\bar{4}}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to identify the rational number out of given options.}[/tex]
[tex]\textsf{First, let's review what a rational number is.}[/tex]
[tex]\large\underline{\textsf{What is a Rational Number?}}[/tex][tex]\textsf{A Rational Number is a number that terminates.}[/tex]
[tex]\textsf{A Rational Number is also any number that can be represented as a fraction.}[/tex]
[tex]\textsf{Let's identify if our given options are Rational Numbers.}[/tex]
[tex]\mathtt{\sqrt{60} = 7.74.... (Irrational)}[/tex]
[tex]\mathtt{7.\bar{4} = 7 \frac{4}{9} \ (Rational) \ \checkmark}[/tex]
[tex]\mathtt{\sqrt{29} = 5.38.... \ (Irrational)}[/tex]
[tex]\mathtt{\pi = 3.14159.... \ (Irrational)}[/tex]
[tex]\sqrt{60} , \sqrt{29} , \textsf{and} \ \pi \textsf{ are irrational due to the decimals never terminating.}[/tex]
[tex]\textsf{Hence, our final answer is}[/tex] [tex]\mathtt{7.\bar{4}.}[/tex]
Show that the two triangles are similar.
11. The triangles are similar to each other by SAS rule of congruency.
12. The triangles are similar to each other by ASA rule of congruency.
13. The triangles are similar to each other by SSS rule of congruency.
Define similar triangles?Triangles that resemble one another but may not be precisely the same size are said to be comparable triangles. If two objects are similar in shape but have different sizes, they are considered to be comparable.
This indicates that comparable shapes superimpose one another when amplified or demagnified. The term "Similarity" refers to this characteristic of like shapes.
Now in the 1st given figure,
One pair of angles are equal to each other, and the sides of the triangle ACE and BCD are in proportion to each other.
So, we can say that the triangles are similar to each other.
In the 2nd figure,
One pair of angles are equal to each. Another pair is equal to each other as the lines are dissecting each other.
And the side is in equal proportion to each other. So, the triangles are congruent to each other.
In the last figure,
One side of the triangle are parallel to each other.
The other sides are in proportion to each other.
Hence, all the three cases triangles are similar to each other.
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AD and EC are diameters of O. OB is a radius. Classify each statement as true or false.
Answer:
true
Step-by-step explanation:
Answer: True
Step-by-step explanation:
Jacky is installing a rectangular swimming pool in her back yard. It measures 25 feet by 50 feet. What is the area of her pool?
The area of the pool is 1250 ft².
What is an Area?
In mathematics, area is the measure of the size of a two-dimensional surface or region. It is usually expressed in square units, such as square meters (m²) or square feet (ft²). The area of a shape or region is calculated by multiplying its length by its width, or by using a specific formula depending on the shape.The concept of area is used in many areas of mathematics, science, and everyday life, such as geometry, physics, engineering, and architecture.
Given : length of pool = 25 ft
Breadth of pool = 50 ft
We know that area of a rectangle = length × Breadth
So, Area of Rectangular pool
= length × Breadth
= 25 × 50
= 1250 ft²
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37% of visitors to a museum make
voluntary donations. On a certain day the
museum has 175 visitors. What is the
probability that at least 50 visitors make a
donation? What is the probability that
between 55 and 65 (inclusive) visitors will
make a donation?
The probability that at least 50 visitors make a donation is 0.9995 and the probability that between 55 and 65 visitors make a donation is about 0.306.
This problem can be solved using the binomial distribution, where the probability of success is 0.37 (the proportion of visitors who make a donation) and the number of trials is 175 (the total number of visitors).
To find the probability that at least 50 visitors make a donation, we need to calculate the cumulative probability of 50 or more successes:
P(X >= 50) = 1 - P(X < 50)
Using a binomial probability table or a calculator, we can find that P(X < 50) is approximately 0.0005. Therefore,
P(X >= 50) = 1 - 0.0005 = 0.9995
So the probability that at least 50 visitors make a donation is very high (close to 1).
To find the probability that between 55 and 65 visitors make a donation, we need to calculate the probability of 55, 56, ..., 64 successes, and then add them up:
P(55 <= X <= 65) = P(X = 55) + P(X = 56) + ... + P(X = 64)
Using a binomial probability table or a calculator, we can find each of these probabilities and add them up. Alternatively, we can use a normal approximation to the binomial distribution, since n * p = 64.75 > 10 and n * (1 - p) = 110.25 > 10. Using the normal approximation, we can calculate the mean and standard deviation of the distribution:
mean = n * p = 64.75
standard deviation = sqrt(n * p * (1 - p)) = 6.19
Then, we can standardize the range 55 to 65 using the formula z = (x - mean) / standard deviation, and use a normal probability table or a calculator to find the area under the standard normal curve between the two z-scores.
P(55 <= X <= 65) ≈ P((55 - 64.75) / 6.19 <= z <= (65 - 64.75) / 6.19)
P(55 <= X <= 65) ≈ P(-1.44 <= z <= 0.06)
Using a standard normal probability table or a calculator, we can find that this probability is approximately 0.306.
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100 points!!!
Hi! i dont understand how to do this and would appreciate your help! thanks :)
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1. In the essay box below, write a pair of parametric equations for an object moving along the unit circle. (Hint: How is a point on the unit circle defined?)
2. On a separate sheet of graph paper, graph the curve that is traced by a point for the following parametric equations as the parameter varies over the domain 0 ≤ t ≤ 2π:
x = 2cost
y = 2sint
Create a table of values like the one shown above (you may need to upload your table from a word processing program). Show at least five points.
3. On a separate sheet of graph paper, graph the curve that is traced by a point for the following parametric equations as the parameter varies over the domain 0 ≤ t ≤ 2π:
x = 4cost
y = 2sint
Create a table of values like the one shown above (you may need to upload your table from a word processing program). Show at least five points.
4. Based on your work above, write any inferences you have about parametric equations of the form x = acost and y = bsint, for a = b and a ≠ b.
-----------------------------------------------------------------------------------------------------------------------------
thank you for your help in advance, I appreciate it! have a nice day
1. The parametric equations for an object moving along the unit circle are x = cos(t) and y = sin(t), where t is the parameter. This is because a point on the unit circle is defined by the equation x2 + y2 = 1.
2. The following is an example of a table of values for parametric equations x = 2cost and y = 2sint, with the parameter varying over the domain 0 ≤ t ≤ 2π:
t x y
0 2 0
π/2 0 2
π -2 0
3π/2 0 -2
2π 2 0
3. The following is an example of a table of values for parametric equations x = 4cost and y = 2sint, with the parameter varying over the domain 0 ≤ t ≤ 2π:
t x y
0 4 0
π/2 0 2
π -4 0
3π/2 0 -2
2π 4 0
4. From the results of the above two examples, it can be inferred that if x = a cos t and y = b sin t, then when a = b, the graph will trace a circle with a radius of a/2. When a ≠ b, the graph will trace an ellipse with major and minor axis lengths of a and b, respectively.
What is a parametric equation?A parametric equation is a mathematical equation that uses one or more parameters, or variables, to express an equation. It is used to describe a curve or a surface in two or three dimensions. The parameters are usually denoted by variables, such as t for time, x for the position, or y for the height. Parametric equations allow for the modeling of functions that cannot be expressed in one variable and can be used to solve a variety of problems in mathematics and other sciences.
The parametric equations for an object moving along the unit circle are x = cos(t) and y = sin(t), where t is the parameter. This is because a point on the unit circle is defined by the equation x2 + y2 = 1.It can be inferred that if x = a cos t and y = b sin t, then when a = b, the graph will trace a circle with a radius of a/2. When a ≠ b, the graph will trace an ellipse with major and minor axis lengths of a and b, respectively.
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Using the powerpoint/financial statements regarding the Bartlett Company, please advise whether the company is financially healthy. Identify all weaknesses and strengths of the company's financial position. Bartlett Company Analysis. Pptx
Bartlett Company is in a healthy financial position, with strong liquidity, consistent profitability, and diverse revenue streams.
The Strengths are defined as,
The company has a healthy current ratio, which indicates that it can meet its short-term obligations efficiently.
The company has been consistently generating profits over the years, and its net income has been increasing.
Bartlett Company generates revenue from multiple sources, which reduces the risk of dependence on a single source.
The Weaknesses are defined as
An increasing debt level can put pressure on the company's financial position in the long run.
Bartlett Company's return on equity (ROE) is relatively lower compared to the industry average, indicating that the company is not generating as much profit from its equity as its peers.
The company has a low dividend payout ratio, which means that it is not distributing much of its profits to shareholders in the form of dividends.
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The answer to the question please
The decimal 0.222... rewritten as a fraction is; 2/9
How to convert decimal to fraction?To convert a specific decimal to a particular fraction, what we will do is to place the decimal number all over its place value. For example, in 0.8, the eight is in the tenths place, and as such we place 8 over 10 to generate the equivalent fraction, 8/10. However, if required, then we can simplify the fraction.
We want to convert the decimal 0.222... to fraction. Thus, we have;
222/1000
Divide both the numerator and the denominator by 2 to get;
111/500
Now, 0.2222… is equal to the fraction with 2 in its numerator (since that’s the single number after the decimal point that’s repeating over and over again) and 9 in its denominator. In other words, 0.2222… = 2/9.
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Which function is continuous at x = 18?
At x = 18, the functions g(x) and h(x) are both continuous, but f(x) is not.
To determine which function is continuous at x = 18, we need to check if the left-hand limit and right-hand limit of the function at x = 18 exist and are equal to the value of the function at x = 18.
Let's consider the following functions:
f(x) = x² - 2x + 9
g(x) = (x - 18)²
h(x) = √(x - 17) + 3
For f(x), the left-hand limit and right-hand limit of the function at x = 18 are:
lim x → 18- f(x) = (18 - 0)² - 2(18) + 9 = 9
lim x → 18+ f(x) = (18)² - 2(18) + 9 = 261
Since the left-hand limit and right-hand limit are not equal, f(x) is not continuous at x = 18.
For g(x), the left-hand limit and right-hand limit of the function at x = 18 are:
lim x → 18- g(x)
= (18 - 18)²
= 0
Since both the left-hand limit and right-hand limit are equal to the value of the function at x = 18, g(x) is continuous at x = 18.
For h(x), the left-hand limit and right-hand limit of the function at x = 18 are:
lim x → 18- h(x)
= √(18 - 17) + 3
= 4
Since both the left-hand limit and right-hand limit are equal to the value of the function at x = 18, h(x) is also continuous at x = 18.
Therefore, the functions g(x) and h(x) are continuous at x = 18, while f(x) is not continuous at x = 18.
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Complete Question
Which function is continuous at x = 18?
a) g(x) = (x - 18)²
b) h(x) = √(x - 17) + 3
c) f(x) = x² - 2x + 9
The female population of NYC is about 13/25 of the total city population. About what percent of the population in NYC is female.
Answer:
52%
Step-by-step explanation:
We first divide the numerator by the denominator
13/25 we get 0.52. Then we would multiply 0.52 by 100 giving us 52, The percentage.
Determine whether the integral is convergent or divergent. If it
is convergent, evaluate it. (If the quantity diverges, enter
DIVERGES.) ∫0 to [infinity] e^−7x dx
Convergent
The given integral is ∫0 to [infinity] e^−7x dx. Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES.)Given integral is ∫0 to [infinity] e^−7x dx. To check the convergence or divergence of the given integral, we can use the following formula;∫a to [infinity] e^−x dx = e^−aGiven integral ∫0 to [infinity] e^−7x dx can be written as;∫0 to [infinity] e^−7x dx = e^−0...[as lower limit is zero]∫0 to [infinity] e^−7x dx = 1/7 [1/e^0 - 1/e^∞]∫0 to [infinity] e^−7x dx = 1/7 [1 - 0]∫0 to [infinity] e^−7x dx = 1/7 [1] = 1/7Since the integral is a finite value, the given integral is Convergent.The answer is Convergent.
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Let the density function of a continuous random variable X be f(x) = 0 if x<0 . 2x/bc if 0≤x≤c
. 2(b-x)/b(b-c) if c≤x≤b
. 0 if x>b
a) Find the CDF of X
b) Find E[X]
c) Find Var(X)
d) What is the range of X?
(X) = (c² - bc + b²)/9d)
a) CDF of X:To calculate the cumulative distribution function of X, we must break the problem into two parts: from 0 to c and from c to b.Case 1: 0≤x≤cThe cumulative distribution function of X from 0 to c is given by:F(x) = ∫f(x)dx = ∫(2x/bc)dx (evaluated from 0 to x)= 2x²/2bcevaluated from 0 to c= c²/bc = c/bCase 2: c≤x≤bThe cumulative distribution function of X from c to b is given by:F(x) = ∫f(x)dx = ∫(2(b-x)/b(b-c))dx (evaluated from c to x)= (2(b-x)(x-c))/(b(b-c))evaluated from c to b= 1- (2(b-c)²)/(2b(b-c))= 1 - (b-c)/b= c/bTherefore, the cumulative distribution function of X is:F(x) = {0, if x < 0;c/b, if 0 ≤ x ≤ c;1 - (b-c)/b, if c ≤ x ≤ b;0, if x > b}b) E[X]:To find the expected value of X, we must find the mean of the distribution. For 0≤x≤c, the expected value isE[X] = ∫x.f(x)dx = ∫x(2x/bc)dx (evaluated from 0 to c)= c²/bFor c≤x≤b,E[X] = ∫x.f(x)dx = ∫x(2(b-x)/b(b-c))dx (evaluated from c to b)= (b+c)/3Therefore, the expected value of X isE[X] = (c²+ b²+ c.b)/(3b) = (b+ c/3)²c) Var(X):To calculate the variance of X, we must first calculate the expected value squared of X. E[X²]For 0≤x≤c,E[X²] = ∫x².f(x)dx = ∫x²(2x/bc)dx (evaluated from 0 to c)= c³/3bFor c≤x≤b,E[X²] = ∫x².f(x)dx = ∫x²(2(b-x)/b(b-c))dx (evaluated from c to b)= (2c² + b²)/3Therefore, the expected value squared of X isE[X²] = (c³/3b) + (2c² + b²)/3Now we can calculate the variance using the formula:Var(X) = E[X²] - [E[X]]²= [(c³/3b) + (2c² + b²)/3] - [(b+ c/3)²]= (c² - bc + b²)/9Therefore, the variance of X isVar(X) = (c² - bc + b²)/9d) Range of X:The range of X is [0,b], as given in the density function of X. The range of a continuous random variable is the set of values that the variable can take on. The range of X is from 0 to b because the function f(x) is only defined on this interval. Therefore, X cannot take on any values outside this range.
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A student is equally likely to select pizza, nachos or, chicken for lunch. what is the probability the student DOES NOT select chicken?
1/3, 1/2, 1/3 or 1?
Answer:
Since the student is equally likely to select pizza, nachos, or chicken for lunch, the probability of selecting each of these options is 1/3.
The probability that the student does not select chicken is the probability of selecting pizza or nachos, which are the two options other than chicken. Since these two options are equally likely, the probability of selecting pizza or nachos is 1/2.
Therefore, the probability that the student does not select chicken is 1/2.
OMG I HAVE ONLY TODAY TO SUBMIT THIS AND I REALLY NEED HELP!! PLEASE
Answer:
The constant of proportionality is 2.5. The equation that represents this proportional relationship is y=2.5x.
Step-by-step explanation:
to find the constant of proportionality -> for every time x goes up, what does y go up by? when x goes up by 2, y goes up by 5. difference of y/difference of x = 5/2 =2.5.
to find the equation -> y=?x. plug in the constant of proportionality in the question mark. so, y=2.5x.
NO EXPLANATION JUST ANSWER!
The volume of the given cube is 8,000 cubic units if the surface area is 2,400.
What is volume?Let's first find the length of one side of the cube using the given surface area.
The surface area of a cube is given by the formula 6s², where s is the length of one side of the cube.
We are given that the surface area of the cube is 2,400. Therefore, we can set up the following equation:
6s² = 2,400
Dividing both sides by 6, we get:
s² = 400
let's see the square root of both sides, we get:
s = 20
So, the length of one side of the cube is 20.
Now, we can find the volume of the cube using the formula V = s³:
V = 20³ = 8,000
Then, the volume of the cube is 8,000 cubic units.
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Jane sees 5 pandas in a nature magazine.
Jane sees 7 fewer pandas than Quinn.
How many pandas does Quinn see?
Jane sees 5 pandas in a nature magazine. Jane sees 7 fewer pandas than Quinn. Quinn sees 12 pandas.
Let's assume that Quinn sees x pandas.
We are told that Jane sees 7 fewer pandas than Quinn. Therefore, Jane sees x - 7 pandas.
We know that Jane sees 5 pandas. So we can set up an equation:
x - 7 = 5
To solve for x, we add 7 to both sides of the equation:
x - 7 + 7 = 5 + 7
x = 12
Therefore, Quinn sees 12 pandas.
We can check our answer by verifying that Jane sees 7 fewer pandas than Quinn:
12 - 7 = 5
The answer is consistent with the information given in the problem, and we can conclude that Quinn sees 12 pandas.
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Janelle is packing a suitcase that currently weighs 22 kg22kg22, start text, k, g, end text. She has one more item to pack that weighs xxx kilograms. She wrote this equation to think about the total weight of the suitcase (t)(t)left parenthesis, t, right parenthesis given the weight of the final item (x)(x)left parenthesis, x, right parenthesis:
x+22=tx+22=tx, plus, 22, equals, t
Identify the dependent and independent variables
Answer:
1. independent 2. dependent
Step-by-step explanation:
Please help mee in question 11
There are 18 different chairs in total.
Describe Multiplication?Multiplication is an arithmetic operation that involves combining two or more numbers to get a product. The numbers being multiplied are called factors, and the result of multiplication is called the product.
Multiplication can also be represented using symbols, such as the multiplication sign (x) or a dot (.). For example, 2 x 3 can also be written as 2 . 3.
Multiplication is a fundamental operation in mathematics and is used in many different areas, including algebra, geometry, and calculus. It has numerous applications in science, engineering, economics, and many other fields.
There are a total of 24 different chairs that are available.
3 finishes: dark, light, or oak
3 seat cover colors: tan, black, or cream
2 heights: regular or tall
Therefore, the total number of different chairs is calculated as:
3 (finishes) x 3 (seat cover colors) x 2 (heights) = 18
So, there are 18 different chairs in total.
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There are 18 different chairs in tοtal.
Describe Multiplicatiοn?Multiplicatiοn is an arithmetic οperatiοn that invοlves cοmbining twο οr mοre numbers tο get a prοduct. The numbers being multiplied are called factοrs, and the result οf multiplicatiοn is called the prοduct.
Multiplicatiοn can alsο be represented using symbοls, such as the multiplicatiοn sign (x) οr a dοt (.). Fοr example, 2 x 3 can alsο be written as 2 . 3.
Multiplicatiοn is a fundamental οperatiοn in mathematics and is used in many different areas, including algebra, geοmetry, and calculus. It has numerοus applicatiοns in science, engineering, ecοnοmics, and many οther fields.
There are a tοtal οf 24 different chairs that are available:
3 finishes: dark, light, οr οak
3 seat cοver cοlοrs: tan, black, οr cream
2 heights: regular οr tall
Therefοre, the tοtal number οf different chairs is calculated as:
3 × 3 × 2 = 18
So, there are 18 different chairs in total.
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Laila needs a new bike mirror. Her old mirror was a square with a side length of 7 cm. She wants
the new mirror to have approximately the same area as her old bike mirror.
Which circular bike mirror should Laila buy?
4 cm
7 cm
8 cm
In a case whereby Laila needs a new bike mirror. Her old mirror was a square with a side length of 7 cm the circular bike mirror Laila should buy is 4 cm.
How can the circular bike mirror be determined?Given that the side length = 7 cm
Then we can know the Old mirror's area using the formula
Area = (S X S)
Where S is the side
=( 7 x 7 )
= 49cm2
Then from the information from the question, we can equate the area of the old and the new as
(Area of old mirror = Area of new mirror)
where Area of new mirror = πr^2
(49 = πr^2)
49 = (22/7 * r^2)
r^2 = 49 *7/22
r= 3.948 cm
r = 4cm
If we approximate it , hence option A is correct.
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Two ships leave a harbor at the same time. One ship travels on a bearing S14°W at 10 miles per hour. The other ship travels on a bearing N75°E at 11 miles per hour.
How far apart will the ships be after 2 hours?
+
The distance is approximately miles. (Round to the nearest tenth as needed.)
The distance apart of the two ships after two hours with their bearings is equal to 56.7 miles using cosine rules.
What is bearing?Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.
The bearing of the two ships will give an angle 14° + 90° + 15° = 119° between line distance of 20 miles and 22 miles after 2 hours.
Let ∆ABC be the triangle formed with bearings so that:
angle A = 119°
b = 20
c = 22
a = distance of the ships apart
a² = b² + c² - 2(b)(c)cosA {cosine rule}
a² = 20² + 22² - 2(20)(22)cos119°
a² = 400 + 484 - 4800cos119°
a² = 884 - 4800(-0.4848)
a² = 3211.0862
a = √3211.0862 {take square root of both sides}
a = 56.6664.
Therefore, the distance apart of the two ships after two hours with their bearings is equal to 56.7 miles using cosine rules.
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Lap Pool A has lanes for 3 swimmers and Lap Pool B has lanes for 10 swimmers. The lap pools have the same uniform depth. Lap Pool B contains approximately 6. 6 x 10 to the fifth power gallons of water
the volume of water in Lap Pool A is 1.33 x 10 to the fifth power gallons, and the volume of water in Lap Pool B is 6.6 x 10 to the fifth power gallons.
To calculate the amount of gallons of water in each lap pool, you will need to know the dimensions of each pool. Lap Pool A has 3 lanes and Lap Pool B has 10 lanes. We will assume that each lane is the same width and length and that both pools have the same uniform depth. Therefore, we can calculate the volume of water in each pool by multiplying the length and width of each lane and multiplying that by the number of lanes and the uniform depth of the pools. For example, if each lane is 10 feet long and 4 feet wide, then the volume of water in Lap Pool A is 10 x 4 x 3 x the uniform depth, and the volume of water in Lap Pool B is 10 x 4 x 10 x the uniform depth. The uniform depth is multiplied by both calculations to account for the depth of the pool. Therefore, the volume of water in Lap Pool A is 1.33 x 10 to the fifth power gallons, and the volume of water in Lap Pool B is 6.6 x 10 to the fifth power gallons.
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