Answer:
d. empirical discrete distribution
Step-by-step explanation:
Empirical refers to what you observe, in this case the relative frequency
Discrete probability distributions is what you are trying to develop.
a, b and c are different forms an empirical discrete distribution can take. You could say that a,b and c are "types" of the "empirical discrete distribution"
The use of the relative frequency method leads to an empirical discrete distribution, which reflects observed frequencies in a sample and is distinct from theoretical models like the binomial distribution.
The use of the relative frequency method to develop discrete probability distributions leads to what is known as an empirical discrete distribution. This method involves determining probabilities based on the frequency of observed outcomes in a sample. In contrast, other discrete distributions such as the binomial distribution, hypergeometric distribution, and Poisson distribution are based on mathematical models with specific properties and assumptions beyond empirical observation.
An empirical discrete distribution captures the observed frequencies of outcomes in a sample and uses these frequencies as probabilities. It does not assume a specific theoretical distribution model, unlike the uniform distribution which assumes each outcome is equally likely, or the binomial distribution which is based on a fixed number of independent trials with a constant probability of success.
To convert a quantity from km/h to m/s, you must a. multiply by 3600 and divide by 1000 b. multiply by 1000 and divide by 60 c. multiply by 60 and divide by 1000 d. multiply by 1000 and divide by 3600e. none of these is correct
Answer:
The correct answer is D
Multiply by 1000 and divide by 3600
Step-by-step explanation:
We know that in 1 km we have 1000 m and in 1 h we have 60 minutes and each minute have 60 seconds, then we multiply 60*60 to know how many seconds are in an hour and we have that 1 h have 3600 s. Using a conversion factor we have:
[tex]\frac{km}{h}(\frac{1000 m}{1km})(\frac{1h}{3600s})[/tex]
With this we can see that to convert a quantity from kn/h to m/s we must multiply by 1000 and divide by 36000
To convert from kilometers per hour to meters per second, you should multiply by 1000 (to convert kilometers to meters) and then divide by 3600 (to convert hours to seconds). An example with a speed of 50 km/h would result in approximately 13.9 m/s after conversion.
Explanation:To convert a quantity from kilometers per hour (km/h) to meters per second (m/s), the correct approach is (a) multiply by 1000 and then divide by 3600. This is because 1 km is equal to 1000 meters, and 1 hour is equal to 3600 seconds. Therefore, to change the unit from km/h to m/s, you need to perform these conversion operations.
Let's consider an example. If you have a speed of 50 km/h and want to convert it into m/s, here's the step-by-step process:
Multiply 50 (km/h) by 1000 to convert kilometers into meters. You'll get 50000 m/h.Next, divide 50000 m/h by 3600 to convert hours into seconds. The result is approximately 13.9 m/s.Learn more about Unit Conversion here:https://brainly.com/question/19420601
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Write an example of a number with a first non-zero digit six place values away from the decimal point. Then, write this number in scientific notation.
Answer:
The answer to your question is: 7.00 x 10⁶
Step-by-step explanation:
- Write a number with a non-zero digit 7
- Six place values away from the decimal point 7 000 000.00
-Write this number in scientific notation 7.00 x 10⁶
An example of a number with its first non-zero digit six places away from the decimal is 0.000001, which is written in scientific notation as 1 × 10^-6 by moving the decimal six places to the right.
An example of a number with its first non-zero digit six place values away from the decimal point is 0.000001. To write this number in scientific notation, we follow the standard convention: moving the decimal point such that there is only one non-zero digit to the left of the decimal point and counting the number of places the decimal point has moved to determine the power of 10.
In this case, we move the decimal point six places to the right, which gives us 1 × 10^-6. This means that 0.000001 in scientific notation is expressed as 1 × 10^-6 .
IF A SUBSCRIPTION IS $499 PLUS 8% TAX FOR 30 DAYS, BUT IS BEING PRORATED FOR 7 DAYS, PLUS THERE IS A $10 OFF COUPON, WHAT'S THE FINAL COST?
Answer:
Your final answer is $528.92
Step-by-step explanation:
[tex]499 + 8\% = 538.92[/tex]
[tex]538.92 - 10 = 528.92[/tex]
Answer:
$519.6048
Step-by-step explanation:
Cost of subscription is $499 + 8% tax for 30 days
Cost of subscription for 30 days = $499
Cost of subscription for 1 days = [tex]\frac{499}{30}[/tex]
So, Cost for (30-7 = 23)days = [tex]\frac{499}{30} \times 23 [/tex]
= [tex]382.56[/tex]
Cost of subscription for 23 days = [tex]382.56[/tex]
Sale tax = 8 %
Sales Tax = [tex]30.6048[/tex]
Cost of subscription = $499+$30.6048 = $529.6048
There is an off of $10
So, Final cost = $529.6048-$10= $519.6048
Hence The final cost is $519.6048
Which of the following is equivalent to
Answer:
Step-by-step explanation:
To solve this, we need to remember that when you multiplicate two roots you can multiply the numbers inside the two roots and put them inside just one root.
So in this case we have ∛5ab² ·∛25ab
We are going to multiply the numbers inside the roots and we get
∛5ab²·25ab = ∛75a²b³
But 75 = 5³ so we have
∛75a²b³ = ∛5³a²b³
Since we have powers of 3 inside the root, we can take them outside the root with the exponent divided by 3.
∛5³a²b³ = 5b∛a²
Thus, the correct answer is a) 5b∛a²
A cyclist rides his bike at a speed of 18 miles per hours.what is this speed in kilometers per hour? How many kilometers will the cyclist travel in 2 hours ?
Answer:
about 29 km/h57.94 kmStep-by-step explanation:
The conversion factor cancels units of miles and leaves units of km.
[tex]\dfrac{18\,mi}{h}\cdot\dfrac{1.609344\,km}{1\,mi}=\dfrac{28.968192\,km}{h}[/tex]
The speed rounds to 29 km/h.
Multiplying the distance per hour by the number of hours, we find the distance to be ...
(28.968192 km/h)×(2 h) = 57.936384 km ≈ 57.94 km
Sydney Blackwell manages an office building with leases of $60,000 per year. Her management agreement is for 7 years, with fees as follows: 7% the first year; 5% the second and third years; and 3 % the remaining years. What will be Sydney's total management fee?
Answer:
total management fee is $16200
Step-by-step explanation:
given data
leases = $60000 per year
time = 7 year
fees 1st year = 7%
fees 2nd and 3rd year = 5%
fees remaining year = 3%
to find out
total management fee
solution
we find here commission for each here
for 1st year = 7% of $60000 = $4200 ............1
for 2nd and 3rd year = 5% of $60000 = $3000 ............2
for remaining year = 3% of $60000 = $1800 ................3
and that is 4 year so fees = 1800 × 4 = $7200 ................4
now add all these to get total
total fees = 4200 + 3000 + 1800 + 7200
total fees = 16200
so total management fee is $16200
Sydney Blackwell's total management fee for a 7-year period, with varying annual rates applied to a $60,000 lease, amounts to $17,400.
Explanation:Calculating Sydney's Total Management Fee
To calculate Sydney Blackwell's total management fee for managing an office building, we need to apply the corresponding percentage rates to the annual lease amount over the span of the management agreement. The lease amount is $60,000 per year, and the management agreement spans 7 years with varying fees each year.
Here's the breakdown of fees per year and total fee calculation:
First year: 7% of $60,000 = $4,200Second and third years: 5% of $60,000 = $3,000 per year, for a total of $6,000 over two yearsRemaining four years: 3% of $60,000 = $1,800 per year, for a total of $7,200 over four yearsAdding up the fees from all years:
$4,200 + $6,000 + $7,200 = $17,400
Therefore, the total management fee Sydney will receive over the 7-year period is $17,400.
What are significant figures?
A. They are a close approximation of the actual value of what is being measured
B. They are all known digits in a measurement
C. The limit of a measurement
D. The gauge of the accuracy of a measurement
The best option is A: They are a close approximation of the actual value of what is being measured.
Significant figures, also known as significant digits, are a set of rules used to determine the precision or accuracy of a measured or calculated value. They indicate the reliability of the digits in a number and help communicate the level of certainty associated with a measurement or calculation.
The correct definition of significant figures is:
A. They are a close approximation of the actual value of what is being measured.
Significant figures represent the digits in a number that contribute to its precision. They include all the known digits in a measurement, as well as one estimated digit. The estimated digit is the least certain or the first uncertain digit in the measurement. The number of significant figures reflects the level of confidence in the measurement and helps convey the precision of the value.
Option B ("They are all known digits in a measurement") is incorrect because significant figures include both known digits and one estimated digit.
Option C ("The limit of a measurement") is incorrect because significant figures do not define a limit but rather represent the precision of the measurement.
Option D ("The gauge of the accuracy of a measurement") is partially correct, as significant figures can provide an indication of the accuracy, but they primarily convey the precision or reliability of the measurement rather than the overall accuracy.
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a) 31 c) 30
b) 28 d) 61
Answer:
A) 31
Step-by-step explanation:
The difference of low-end values for successive classes is 31. This is the class width.
3. The population of Columbus, Ohio, in 2014 was about 823,000. The population of the United States was about 319 million in 2014. (a) Write each population in scientific notation. (b) About how many times larger was the population of the United States than the population of Columbus, Ohio? Show your work. Answer:
Answer:
The answer to your question is:
a)
8.23 x 10 ⁵
3.19 x 10⁸
b)
387.6 ≈ 388 times
Step-by-step explanation:
Columbus, Ohio population = 823, 000
United states population = 319 million
a)
823 000 = 8.23 x 10 ⁵ move the decimal point 5 places to the left
319 000 000 = 3.19 x 10⁸ move the decimal point 8 places to the left
b)
To find the answer, just divide the USA population by the Columbus, Ohio population
3.19 x 10⁸ / 8.23 x 10 ⁵ = 387.6 ≈ 388 times
Final answer:
a) The population of Columbus, Ohio in scientific notation is 8.23 × 10⁵ and that of the United States is 3.19 × 10⁸. and b) the US population is 388 times larger as compared to Columbus.
Explanation:
a)The population of Columbus, Ohio, in 2014 was about 823,000. This can be written in scientific notation as 8.23 × 10⁵.
The population of the United States in 2014 was about 319 million. In scientific notation, this is 3.19 × 10⁸.
b) To determine how many times larger the population of the United States was than the population of Columbus, Ohio, we divide the population of the United States by that of Columbus:
3.19 × 10⁸ / 8.23 × 10⁵ = 387.605 approx 388 times larger
Therefore, the population of the United States was about 388 times larger than the population of Columbus, Ohio in 2014.
The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of pi and then round to 2 decimal places.
Answer: 12.56 inches
Step-by-step explanation: First, when know the following:
A clock is a circle, so the total movement, from 12 to 12 is 360° or 2π.
It is also know that a circle circunference (The total size of the circle on a straight line) is 2π * Radius
The minute hand does a circle on its travel, that circle radius is equal to 6 inches.
The movement from 12 to 4 is a third (4/12 = 1/3). Knowing this:
120° = (1/3) * 360° = (1/3) * 2π = (2/3) * π
So the travel from 12 to 4 is (2/3)π
To know the distance on inches, we multiply the distance on radians per the radius.
Total distance = 6 * (2/3)π
Total distance = 4π inches
Total distance = 12.56 inches
Final Answer:
The tip of the minute hand moves approximately 12.57 inches from 12 o'clock to 4 o'clock.
Explanation:
To solve this problem, we will consider the movement of the minute hand as an arc on a circle. The distance that the tip of the minute hand moves is the length of the arc that it traces as it moves from 12 o'clock to 4 o'clock. Here's how we'll calculate it:
Step 1: Determine the angle of movement in degrees.
The clock is divided into 12 hours, so each hour represents an angle of 360 degrees / 12 = 30 degrees. Since the minute hand moves from 12 o'clock to 4 o'clock, it covers 4 hours. Thus, the angle covered is 4 hours * 30 degrees/hour = 120 degrees.
Step 2: Convert the angle from degrees to radians.
To find the arc length, it is convenient to work with radians rather than degrees. The conversion from degrees to radians is performed using the factor π radians = 180 degrees.
[tex]\( \text{Angle in radians} = \text{Angle in degrees} \times \frac{\pi}{180} \)[/tex]
So, for our angle:
[tex]\( \text{Angle in radians} = 120 \times \frac{\pi}{180} \\\\\( \text{Angle in radians} = \frac{2}{3} \pi \)[/tex]
Step 3: Use the arc length formula.
The arc length (s) on a circle can be calculated using the formula s = r * θ, where r is the radius (length) of the circle (in this case, the length of the minute hand), and θ is the angle in radians.
[tex]\( s = r * \theta \\\\\( s = 6 \text{ inches} * \frac{2}{3} \pi \\\\\( s = 4 \pi \text{ inches} \)[/tex]
So, the distance the tip of the minute hand moves is [tex]\( 4 \pi \)[/tex] inches.
Step 4: Calculate the numerical value of the arc length.
To find the numerical value, we will approximate [tex]\( \pi \)[/tex] to 3.14159.
[tex]\( s \approx 4 * 3.14159 \\\\\( s \approx 12.56636 \text{ inches} \)[/tex]
Step 5: Round the numerical value to two decimal places.
[tex]\( s \approx 12.57 \text{ inches} \)[/tex]
Therefore, the tip of the minute hand moves approximately 12.57 inches from 12 o'clock to 4 o'clock.
Sherita's club is selling grapefruit to raise money. For every box they sell, they get $1.35 profit. They have sold 84 boxes already. How many more
boxes must they sell to raise $270?
A. 135 boxes
116 boxes
B.
c.
157 boxes
OD. 114 boxes
Answer: 156.7
Step-by-step explanation:
1.35x84= 113.4
270-113.4=156.60
Answer:
B
Step-by-step explanation:
1.35 x 84 = $113.40
270 - 113.40 = $156. 60
156.60 / 1.35 = 116 boxes
Gerry is looking to buy a new car and finds one she likes for $1,000. The dealership is currently offering 15% off. How much money will Gerry save if she buys the car? Select one: A. $15 B. $985 C. $850 D. $150
D 1000 X .15 = 150.
.15 = 15%
Answer:
D) $150.
Step-by-step explanation:
Gerry is looking to buy a new car and finds one she likes for $1000. It means 100% corresponds to $1000.
There is 15% off. It means, she can save 15% of the total value of the car. We need to calcualte the amount of money that she can save taking the 15% off (O)
O = $1000 * (15%)
O = $1000*(15/100)
O = $1000*(0.15)
O = $150.
100% corrsponds to $1000, and 15% corresponds to $150.If she takes 15% off, we can conclude that she can save $150.
Finally, the answer is D) $150.
true or false Linear? y = –5x
True. It is linear because it forms a straight line.
Answer:
TrueStep-by-step explanation:
It is a straight line, which is always linear.
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Which of the following are exact numbers?
~The mass of a paperclip~The surface area of a dime~The number of inches in a mile~The number of ounces in a pound~The number of microseconds in a week~The number of pages in this worksheet (1)
Answer:
Explanation with the help of discrete variables and continuous variables.
Step-by-step explanation:
We have to tell that which of the following can be an exact number.
This can be done with the approach of discrete and continuous variables.
Discrete variables are the variables that are countable and cannot be expressed in decimal form. They are point estimated.
Continuous variable are the variable that are estimated with the help of an interval. Their values can be expressed with the help of a decimal expansion. They are not countable.
a) Mass of a paper clip, Surface are of dime, Inches in a mile, Ounces in pound, microseconds in a week
Since all mass, area, weight(ounces), time, length(inches) are continuous variable, they can be estimated with the help of an interval. Thus, they can have exact number but not always.
b) Number of pages in a worksheet
Since this is a discrete quantity and it is countable. Thus, it will always have a point estimation and are exact numbers always.
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The length of a rectangle is 4 inches longer than its width. The area of the rectangle is 12 square inches. What are the length and width?
Which equation models this problem?
w – (4 + w) = 12
w + (4 + w) = 12
w(4 + w) = 12
4 • w = 12
Answer:
w(4 + w) = 12 is the correct answer.
Step-by-step explanation:
You have to think that area is lenght x widht, so the first and second options musn't be correct. (you have + and -)
The last one, it isn't correct because, you have width but don't have lenght.
Length is not 4.
show that when the measure of an angle is added to three times the angle's complement, the result is equal to the sum of the anle's complment and the angle's supplement.
Answer with Step-by-step explanation:
Let x be the angle
We have to show that when the measure of an angle is added to three times the angle's complement , the result is equal to the sum of the angle;s complement and the angle' s supplement.
Angle's complement =90-x
(by definition of complementary angles)
Therefore, the angle's supplement=180-x ( By definition of supplement angles )
According to question
[tex]x+3(90-x)=270-2x[/tex]
[tex]90-x+180-x=270-2x[/tex]
Hence, when the measure of an angle is added to three times the angle's complement , the result is equal to the sum of the angle's supplement.
Hence, proved
find the area and circumference.
Answer:
area ≈ 176.7 cm²circumference ≈ 47.1 cmStep-by-step explanation:
The radius is half the diameter, so is ...
r = d/2 = 15 cm/2 = 7.5 cm
The area formula is ...
A = πr²
Filling in the radius, we have ...
A = π·(7.5 cm)² = 56.25π cm² ≈ 176.7 cm² . . . area
__
The circumference formula is ...
C = πd
Filling in the diameter, we have ...
C = π·(15 cm) = 15π cm ≈ 47.1 cm . . . circumference
3. Jim is cutting up apples he is planning to serve 1/3 to each 8 people, how many apples does jim need to serve?
Answer:
3
Hope this helps! .. Do you need an explaination?
Answer:
3
Step-by-step explanation:
because I said
Owens Industries is trying to increase its profile in the community. As part of this effort, Owens sponsors a Little League baseball team. The cost of sponsorship is $850. How should Owens record this transaction in order to maintain a balanced accounting equation (A = L + SE)?
The Owens Industries should credit $850 to their Assets, denoted by A and debit the sum of $850 to the Stockholder's Equity, denoted by SE.
Step-by-step explanation:In the question,
As the Owens industries is trying to increase its profile.
Cost of sponsorship = $850
To maintain the profile he can, by using the transaction accounting balance equation,
A = L + SE
The Owens Industries should credit $850 to their Assets, denoted by A and debit the sum of $850 to the Stockholder's Equity, denoted by SE.
That is,
$850 = L + $850
L = 0
This is how the accounting equation can be balanced.
Simplify the radical expression.
[tex]\mathbb{ANSWER:}[/tex]
Refer to the attachment for the answer.
Which of the following rational functions is graphed below?
Answer:
A
Step-by-step explanation:
from the graph you can tell that there is a vertical asymp. at -3.
In the anwers A is the only one with vertical asymp. at -3.
Answer:
A f(x)=[tex]\frac{x}{x+3}[/tex]
Step-by-step explanation:
To answer this question, to identify which rational function relates to that graph we must at first look for Rational Function in this form:
[tex]P(x)=\frac{Q(x)}{R(x)}[/tex]
Where P(x)= Polynomial Quotient, Q(x)=Quotient, R(x)=Remainder. Q(x) and R(x) are Polynomial Functions.
So exclude B, then C, for they do not fit as Polynomial Functions.
Then rather than setting the graph, the second step would be looking for the vertical asymptote, given by the equation on the denominator. We must detach it from the original function then solve it.
x+3=0 ∴ x=-3
A student is conducting a research project that involves using a survey. The survey asks subjects about their political affiliation and their favorite politicians. No identifiable information will be collected. This study would be categorized as which type of review?
Answer:
This study will be identified as : exempt review
Step-by-step explanation:
A student is conducting a research project that involves using a survey. The survey asks subjects about their political affiliation and their favorite politicians.
No identifiable information will be collected.
This study will be identified as : exempt review
To qualify for a review at the exempt level, the research should be less than the minimal risk defined.
City A is due north of City B. Find the distance between City A (37 degrees 2 prime north latitude) and City B (19 degrees 44 prime north latitude). Assume that the radius of Earth is 3960 miles.
Answer:
1196 mi
Step-by-step explanation:
The latitude difference is 17°18', so is about 0.301942 radians. Then the arc length is ...
s = r·θ = (3960 mi)(0.301942) ≈ 1196 mi
The distance between City A and City B, given their latitudes and the radius of the Earth, is found using the arc length formula (length = radius x angle in radians) to be approximately 2011 miles.
Explanation:The subject of this question is Geography and it entails finding the distance between two cities located at different latitudes on Earth. The difference between the two latitudes is used to find the distance. Since the Earth is a sphere, we can use the formula for the length of an arc to find the distance between these two cities. To do so, subtract the latitude of City B (19 degrees 44 prime) from the latitude of City A (37 degrees 2 prime) to get the difference in degrees which is equal to 17 degrees 18 prime. Convert this to decimal form by dividing the prime by 60 (17 + 18/60 = approx. 17.3 degrees).
Then use the formula for the length of an arc: length = radius x angle (in radians). The radius of the Earth is given as 3960 miles and the angle in radians is obtained by multiplying the angle in degrees by π/180. Therefore, the distance is 3960 miles x 17.3 x π/180 = approximately 2011 miles. As such, City A and City B are estimated to be about 2011 miles apart.
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Please help!!!step by step
Answer:
slope = -1/3, y-intercept (0, -3), x-intercept (-9 , 0)
Step-by-step explanation:
3 - x = 3(y + 4)
3 - x = 3y + 12
3y = 3 - x - 12
3y = -x -9
y = -1/3 x - 3
slope = -1/3
when x = 0 (y-intercept)
y = -1/3 × 0 - 3
y = -3
y-intercept (0, -3)
when y = 0 (x-intercept)
0 = -1/3 x - 3
1/3 x = -3
x = -9
x-intercept (-9 , 0)
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Suppose the schools pay $2.00 per bottle for the juice and sell it to community members for $2.50 per bottle. What percent markup are they charging?
- the answer is 25% markup
just exlpain how to get the answer
Answer:
The answer to your question is 25%
Step-by-step explanation:
Data
Initial price = $2.00
Final price = $2.50
First we subtract the final price to the inicial price
increment = 2.50 - 2.00
= $0.50 It's the amount that the school increases to the community members
Now we use a rule of three to find the percent
$2.00 ---------------------- 100%
$0.50 --------------------- x
x = 0.50 x 100/2 = 50/2 = 25%
A softball team is ordering pizza to eat after their tournament. They plan to order cheese pizzas that cost $6 each and four-topping pizzas that cost $10 each. They order c cheese pizzas and f four-topping pizzas. Which expression represents the total cost of all of the pizzas they order?
The equation would be [tex]6c + 10f[/tex].
The expression which represents the total cost of all of the pizzas they order is 6c + 10f.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now it is given that,
Cost of cheese pizza = $6
Cost of four-topping pizzas = $10
Number of cheese pizza order = c
Number of four-topping pizzas order = f
Hence,
Total cost cheese pizza = Cost of cheese pizza*Number of cheese pizza order
⇒Total cost cheese pizza = 6*c = 6c
Similarly,
Total cost of four-topping pizzas = Cost of four-topping pizzas*Number of four-topping pizzas order
⇒Total cost of four-topping pizzas = 10*f = 10f
Hence, total cost of all of the pizzas they order
= Total cost cheese pizza + Total cost of four-topping pizzas
⇒ total cost of all of the pizzas they order = 6c + 10f
Hence,The expression which represents the total cost of all of the pizzas they order is 6c + 10f.
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NEED A QUICK ANSWER.
solve for x.
Enter your answer in the box.
x =
°
brainliest will be given to whoever answers correctly.
90 + x + 107 + 144 + 138 = 540
479 + x = 540
x = 540 - 479
x = 61
Answer:
x=61°
Step-by-step explanation:
There are 5 sides in a polygon.
Sum of interior angles = (n-2) times 180
[tex](5-2) \cdot 180=540[/tex]
The sum of interior angles in a polygon is 540 degree
Now add all the interior angles and set it to 540
Right angle is 90 degree
[tex]90+x+138+144+107= 540[/tex]
[tex]479+x= 540[/tex]
Subtract 479 from both sides
[tex]x=61[/tex]
The register that holds bit values (flags) that describe comparison operation results, control conditional BRANCH execution, or indicate actual or potential error conditions ____.
Answer:
program status word
Step-by-step explanation:
The acronym for PSW is Program Status Word. The Program Status Word or the PSW consists of status bits which shows the present Central Processing Unit state.
The PSW or Program Status Word is IBM System/360 architecture which means it is an independent model architecture for S/360 series of computers developed by IBM.
The status register contains all the information about the processor.
Thus the answer is program status word.
The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ. What would the value of σ have to be to ensure that 95% of all readings are within 0.6° of μ?
Answer: 0.3061.
Step-by-step explanation:
Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean [tex]\mu[/tex], the actual temperature of the medium, and standard deviation [tex]\sigma[/tex].
Let X be the random variable that represents the reading of the thermometer.
Confidence level : [tex]=95\%[/tex]
We know that the z-value for 95% confidence interval is 1.96.
Then, we have
[tex]-1.96<\dfrac{X-\mu}{\sigma}<1.96[/tex] [tex]z=\dfrac{X-\mu}{\sigma}[/tex]
[tex]\Rightarrow\ -1.96\sigma<X-\mu<1.96\sigma[/tex]
But all readings are within 0.6° of [tex]\mu[/tex].
So, [tex]1.96\sigma=0.6[/tex]
[tex]\Rightarrow\ \sigma=\dfrac{0.6}{1.96}=0.30612244898\approx0.3061[/tex]
Hence, the required standard deviation will be
The confidence level is 95% in normal distribution then The value of standard deviation is 0.3061.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
Given
The temperature reading from a thermocouple placed in a constant temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ.
Let x be the random variable that represents the reading of the thermometer.
The confidence level is 95%. Then the z-value for 95% confidence level interval is 1.96.
Then we have
[tex]-\ \ 1.96 \ < \dfrac{x- \mu}{\sigma} < 1.96\\-1.96 \sigma < x- \mu \ < 1.96 \sigma[/tex]
But all the readings are within 0.6° of μ. Then
[tex]1.96 \sigma = 0.6\\[/tex]
On solving
[tex]\sigma = \dfrac{0.6}{1.96}\\\\\sigma = 0.306122 \approx 3061[/tex]
Thus, the standard deviation is 0.3061.
More about the normal distribution link is given below.
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You are standing 41 meters from the base of a building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82°. If the total height of the building is another 124 meters above the 86th floor, what is the approximate height of the building? (Round your answers to one decimal place.)
Answer:
408.6 meters.
Step-by-step explanation:
Let x be the height from the base of the building to the 86th floor,
∵ the total height of the building is another 124 meters above the 86th floor,
So, the total height of the building = ( x + 124 ) meters,
Now, the angle of elevation from the point on the ground to 86th floor = 82°,
Also, the distance from the point to the base of the building = 41 meters,
Thus, by trigonometric ratio,
[tex]tan 82^{\circ}=\frac{x}{41}[/tex]
[tex]\implies x = 41\times tan 82^{\circ}=284.614788895\approx 284.6\text{ meters}[/tex]
Hence, the height of the building = ( 284.6 + 124 ) = 408.6 meters.
The height of the building in consideration is given approximately as 408.61 meters
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
Consider the figure attached for the given situation as described in the problem.
The person watching the building's 86th floor is at A.
The 86th floor is at C, the base of the building is at B.
The total height of the building is at D.
Using the tangent ratio to find the height of the building, we get:
[tex]\tan(82^\circ) = \dfrac{x}{41} \\\\x = \tan(82^\circ) \times 41\\x \approx 284.61 \: \rm meters[/tex] (from calculator).
Thus, the height of the building is length of AD
= |AD| = x + 124 ≈ 284.61 + 124 = 408.61 meters
Thus, the height of the building in consideration is given approximately as 408.61 meters
Learn more about tangent ratio here:
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