The contrast coefficients would be as follows:
µll - (µhh + µhl + µlh) / 3: -1, -1, -1, 3µhl - µll: 1, -1, 0, 0µlh - µhl: 0, 1, -1, 0µll - µhh: -1, 0, 0, 1The farmers are interested in whether there is any difference between the low-low combination (it is the cheapest) and the average of the remaining three levels. The hypotheses they want to test are:
H0: µll - (µhh + µhl + µlh) / 3 = 0HA: µll - (µhh + µhl + µlh) / 3 ≠ 0
To test this hypothesis, the following contrast would be used:
µll - (µhh + µhl + µlh) / 3To compare the high- to low-nitrogen content fertilizers, the following contrast would be used:
µhl - µllTo compare the high- to low-phosphorus content fertilizers, the following contrast would be used:
µlh - µhlTo compare the ll combination to the hh combination, the following contrast would be used:
µll - µhhFor each of the contrasts above, the contrast coefficients would be as follows:
µll - (µhh + µhl + µlh) / 3: -1, -1, -1, 3µhl - µll: 1, -1, 0, 0µlh - µhl: 0, 1, -1, 0µll - µhh: -1, 0, 0, 1Learn more about coefficients
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Identify the slope and y-intercept of the following equation:
y = 4x + 1
The slope and y-intercept of the following equation are:
Slope = 4.
y-intercept = 1.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial number.Based on the information provided above, an equation that models the line is represented by this mathematical equation;
y = mx + c
y = 11x + 41
By comparison, we have the following:
mx = 4x
Slope, m = 4.
Initial number or y-intercept, c = 1.
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What is the equation of the line that passes through the point (4,1) and has a slope of 1/2 ?
Answer: 37
Step-by-step explanation: so first you have to realize that i what I’m doing and you not listen to me
[Questions in the image]
Answer:
a) 675
b) 12
c) y = 12x + 675
d) y = 12 (500) + 675 = $6,675
The population of Vatican City is approximately 800 people. The population of China is about 1.75 × 106 times greater. What is the approximate population of China?
A.
1.4 × 106
B.
1.4 × 107
C.
1.4 × 108
D.
1.4 × 109
To find the approximate population of China, we need to multiply the population of Vatican City by 1.75 × 106:
Population of China = Population of Vatican City × 1.75 × 106
Population of China = 800 × 1.75 × 106
Population of China = 1.4 × 109
Therefore, the approximate population of China is 1.4 × 109, which is option D.
Anyone know how to do this
The missing value that completes the frequency table is 100.
How to find the missing value that completes the frequency table?A frequency table is a statistical tool that summarizes data by displaying the frequency (or count) of each category or interval in a data set. It is commonly used in data analysis to organize and understand categorical or numerical data.
The missing value is the frequency for the value range between 28 and 30 (i.e 28 ≤ x ≤30). Looking at the histogram, you will notice that the frequency for the value between 28 and 30 is 100 (Check the attached image).
Therefore, the missing value is 100.
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b. Use ratio language to write two different sentences that compare the amount
of ribbon and the number of bouquets.
The ratio of ribbon to bouquets is 2:5, meaning for every 2 meters of ribbon, 5 bouquets can be made. For every 7 bouquets, 3 meters of ribbon are needed, meaning the ratio is 3:7.
What is ratio?A ratio is a comparison of two numbers or quantities that are related to each other in some way. It is the relationship between the sizes of two or more things, expressed as the quotient of one divided by the other.
Ratios can be used to compare different aspects of a set of data, such as the ratio of boys to girls in a classroom, or the ratio of red cars to blue cars on a street. They are also used in many real-world applications, such as finance, engineering, and science.
Ribbon to bouquets ratio is 2:5, which means that for every 2 units of ribbon, there are 5 bouquets.
With a ribbon to bouquet ratio of 1:3, the number of bouquets is three times the amount of ribbon.
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Question 17 A grain silo has a cylindrical shape. Its radius is 3.5 ft, and its height is 35 ft. Answer the parts below. Make sure that you use the correct units in your answers. X Progress: 0/2 Part 1 of 2 3.5 ft Next Question 35 ft (a) Find the exact volume of the silo. Write your answer in terms of it.
Answer:
428.75π ft³
Step-by-step explanation:
You want the exact volume of a cylinder 35 ft high with a radius of 3.5 ft.
VolumeThe volume is given by the formula ...
V = πr²h
V = π(3.5 ft)²(35 ft) = 428.75π ft³ . . . . . use the given values
The exact volume of the cylinder is 428.75π ft³.
Pls help
write an exponetial fuction given an intial value of 50 and a growlth of 1. 2
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=\textit{elapsed time} \end{cases} \\\\\\ A = 50(1 + 0.2)^{t} \implies \boxed{A =50(1.2)^t}[/tex]
An 800 investment that earns 3% annual interest compound yearly for 4 years
The final amount earned on the investment after 4 years is $900.40.
An investment of $800 is made at an annual interest rate of 3% compounded yearly for 4 years. To calculate the final amount earned on the investment after 4 years, we can use the formula for compound interest:
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
where:
A = the final amount
P = the principal investment, which is $800 in this case
r = the annual interest rate, which is 3% or 0.03 as a decimal
n = the number of times the interest is compounded per year, which is once per year in this case
t = the number of years, which is 4 in this case
Plugging in the values, we get:
A = 800(1 + 0.03/1)¹ˣ⁴
A = 800(1.03)⁴
A = 800(1.1255)
A = $900.40
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traffic accidents at a particular intersection in campustown follow a poisson distribution with an average rate of 1.4 per week. (a) find the exact calculation using the poisson distribution for the probability that there would be exactly 70 accidents at this intersection in one year (i.e., 52 weeks). (b) find an approximation using the normal distribution for the probability that there would be exactly 70 accidents at this intersection in one year (i.e., 52 weeks).
The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.
What is Prοbability ?Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.
(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:
P(X = k) =( [tex]e^{(-λ)[/tex] * [tex]λ^k[/tex]) / k!
where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).
To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.
So, we have:
P(X = 70) = ([tex]e^{(-72.8)[/tex]* [tex]72.8^(70)[/tex]) / 70!
Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:
P(X = 70) ≈ 0.00382
Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.
(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:
mean = λ = 1.4
variance = λ = 1.4
Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:
[tex]Z = (X - mean) / \sqrt{(variance)[/tex]
Fοr X = 70, we have:
Z = (70 - 1.4) / [tex]\sqrt{(1.4)[/tex] ≈ 57.09
We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.
Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.
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The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:
P(X = 70) = (e^(-λ) * λ^x) / x!
where λ = average rate of accidents per week = 1.4
and x = number of accidents in 52 weeks = 70
Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23
(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.
To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:
z = (x - μ) / σ
where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37
Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:
P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)
≈ P(Z ≤ -0.44)
≈ 0.3300
Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.
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estimate the area of the circle to the nearest unit.
Answer:
Step-by-step explanation: We know that ,
Area of circle =πr² and
r = radius of circle.
Now,
Diameter of circle =56 cm [given]
So, radius of circle=D/2=56/2
Radius of circle=28
Now,
Area of circle=πr²
Area of circle=22/7 ×(28)² [π=22/7]
Area of circle=22×4×28
Area of circle=2464cm²
Hence, Area of circle is 2464cm²
I hope it's help you.
Answer:
48 cm²
Step-by-step explanation:
Area of circle formula: A = πr²
= π (d/2)²
= 3.14 * (4)²
= 50.24
The area of the circle is closest to Option D, 48 cm²
18. (5) two conducting plates have charge /- 0.0000470 mc and each has area 0.138 m2. what is the strength of the electric field between the plates? m = milli
The magnitude of the electric field between the plates is 3.86 × [tex]10^7[/tex]N/C. The sign indicates the direction of the electric field, which depends on the sign of the charge on the plates.
The strength of the electric field between the plates can be calculated using the formula:
E = σ/ε0
where σ is the surface charge density, ε0 is the permittivity of free space, and E is the electric field strength.
The surface charge density is given by:
σ = Q/A
where Q is the charge on each plate and A is the area of each plate.
Substituting the given values, we get:
σ = ±0.0000470 C / 0.138 [tex]m^2[/tex] = ±0.000341 C/[tex]m^2[/tex]
The permittivity of free space is:
ε0 = 8.85 × [tex]10^{-12[/tex] F/m
Substituting the values, we get:
E = σ/ε0 = ±0.000341 C/[tex]m^2[/tex] / 8.85 × [tex]10^{-12[/tex] F/m = ±3.86 × [tex]10^7[/tex] N/C
The magnitude of the electric field between the plates is 3.86 × [tex]10^7[/tex]N/C. The sign indicates the direction of the electric field, which depends on the sign of the charge on the plates.
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Figure A is a scale image of Figure B, as shown.
The scale that maps Figure A onto Figure B is
Enter the value of x.
The value of x is equal to 21 units when scale is 1:7 and a given side on figure A is 3 units.
We know that Figure A is a scaled image of Figure B, with a scale of 1:7. This means that every length in Figure A is one-seventh the length of the corresponding length in Figure B. For example, if a side in Figure B is 14 units long, the corresponding side in Figure A would be 2 units long (14 divided by 7).
In question a side on figure A is 3 units:
Side on Figure B = 7 * Side on Figure A
x = 7 * 3
x = 21 units
Therefore, x is equal to 21 units when scale is 1:7 and a given side on figure A is 3 units.
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The complete question is :
Figure A is a scale image of Figure B, as shown.
The scale that maps Figure A onto Figure B is 1:7
Enter the value of x.
9. The Star Point Ranger Station and the Twin Pines Ranger Station are 30 miles apart along a straight, mountain road. Each station gets word of a cabin fire in a remote area known as Ben's Hideout. A straight path from Star Point to the fire makes an angle of 34° with the road, while a straight path from Twin Pines makes an angle of 14° with the road. Find the distance, d, of the fire from the road. 34° Star Point Ben's Hideout D d 30 mi 14° Twin Pines 10. In problem 9 we had two expressions that were both equal to d. Use both of your expressions and the value you found for d in problem 7 to check your answers. Explain why they were not exactly equal. Does it matter if this application were real life? Why or why not?
The distance of the fire from the road is d ≈ 6.15 miles + 2.94 miles ≈ 9.09 miles.
The two expressions for d give slightly different values. This is due to the fact that we rounded the values of x and y in our calculations.
How to Solve the Problem using Trigonometry?In problem 9, we can use trigonometry to find the distance, d, of the fire from the road. Let x be the distance from Star Point Ranger Station to the fire, and let y be the distance from Twin Pines Ranger Station to the fire. Then, we have:
tan(34°) = d/x
tan(14°) = d/y
Multiplying both sides of each equation by the respective denominator and simplifying, we get:
d = x tan(34°)
d = y tan(14°)
Since the two expressions for d are both equal, we can set them equal to each other and solve for x and y:
x tan(34°) = y tan(14°)
x = (y tan(14°))/tan(34°)
Substituting the value we found for y in problem 7, which was y = 6.15 miles, we get:
x = (6.15 miles) * tan(14°) / tan(34°) ≈ 2.94 miles
Therefore, the distance of the fire from the road is d ≈ 6.15 miles + 2.94 miles ≈ 9.09 miles.
Now, let's check our answers using both expressions for d:
d = x tan(34°) ≈ 2.94 miles * tan(34°) ≈ 2.94 miles * 0.704 = 2.07 miles
d = y tan(14°) ≈ 6.15 miles * tan(14°) ≈ 6.15 miles * 0.249 = 1.53 miles
As we can see, the two expressions for d give slightly different values. This is due to the fact that we rounded the values of x and y in our calculations. If we use the exact values, we would get slightly different values for d, but they would still be very close.
In real life, it is important to be as accurate as possible when dealing with emergencies such as fires. However, in this case, the difference between the two values of d is relatively small, so it may not have a significant impact on the response to the fire. Nevertheless, it is important to use the most accurate values possible to ensure the safety of those involved.
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THANK YALL I MADE A 60
Answer:
Glad we helped
Step-by-step explanation:
Rodrigo practiced playing the guitar 15
1
3
hours over the past 3 weeks. He practiced for 5
1
4
hours during the first week and 4
2
3
hours during the second week.
How much time did Rodrigo spend practicing during the third week? Use the numbers and symbols to select the equation that represents the problem. Then solve the equation. Symbols may be used more than once or not at all.
15
1
3
5
1
4
4
2
3
x = +
a) The time that Rodrigo spent practicing during the third week is 5.42 hours.
b) The equation that represents the problem is 15¹/₃ = 5¹/₄ + 4²/₃ + x.
What is an equation?An equation is a mathematical statement showing that two or more mathematical or algebraic expressions are equal or equivalent.
Equations are represented using the equal symbol (=), unlike algebraic expressions that contain variables, constants, numbers, and values.
The time spent during the first week = 5¹/₄ hours
The time spent during the second week = 4²/₃ hours
The total time spent during the three weeks period = 15¹/₃ hours
Let the time spent during the third week = x
15¹/₃ = 5¹/₄ + 4²/₃ + x
x = 15¹/₃ - (5¹/₄ + 4²/₃)
x = 5.41663
Thus, solving the equation, Rodrigo spent 5.42 hours practicing the guitar during the third week.
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y = - 10/9 + x/7 linear or nonlinear?
Answer:
linear
Step-by-step explanation:
yw
Solve for x. Type your answer as a number
From the figure, the value of x is given as 17 units
How to find the value of x?In mathematics, a ratio shows how many times one number contains another.
The ratio of the sides of the figure is as follows
3x-7/x+5 = 2/1
cross and multiply to have 3x - 7 = 2(x+5)
opening the brackets to have
3x -7 = 2x +10
collecting like terms to have
3x-2x = 10+7
x = 17 units
In conclusion, the value of x is 17 units
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then what is the value of
M-N?
The value of M - N is [tex]8x^2[/tex] + 11x - 9 by subtracting the value of N from the value of M.
To find the value of M - N, we first need to subtract the second polynomial N from the first polynomial M.
M - N = ([tex]5x^2[/tex] + 7x - 4) - ([tex]-3x^2[/tex] - 4x + 5)
To subtract the polynomials, we need to add the opposite of the second polynomial (i.e., add the negative of N) to the first polynomial M:
M - N = [tex]5x^2[/tex] + 7x - 4 + [tex]3x^2[/tex] + 4x - 5
Now we can combine like terms:
M - N = ([tex]5x^2 + 3x^2[/tex]) + (7x + 4x) + (-4 - 5)
M - N = [tex]8x^2[/tex] + 11x - 9
Therefore, the value of M - N is [tex]8x^2[/tex] + 11x - 9.
In summary, we found the value of M - N by subtracting the polynomial N from the polynomial M and then combining like terms. The resulting polynomial is [tex]8x^2[/tex] + 11x - 9.
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How do you do this step by step please thank uu
Answer: 2sw or 2ab
Step-by-step explanation:
Need to find the value of c but confused which trig function to use etc. thanks a bunch!
Therefore, the value of x in each triangle is approximately 5.4 and 11.1, respectively.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions such as sine, cosine, and tangent, which are used to relate the angles of a triangle to the lengths of its sides. Trigonometry has a wide range of applications in fields such as physics, engineering, navigation, surveying, and astronomy. For example, trigonometry is used in navigation to calculate the angles between a ship and a lighthouse, or between two ships, in order to determine their relative positions. In engineering, trigonometry is used to calculate the forces acting on structures such as bridges and buildings, and to design and build machines that rely on the principles of motion and energy.
Here,
For the first triangle, we have:
Using the sine ratio,
sin(36) = x / 9
Solving for x, we get:
x = 9 sin(36)
≈ 5.4
Rounding to the nearest tenth, we get:
x ≈ 5.4
For the second triangle, we have:
Using the tangent ratio,
tan(27) = x / 21
Solving for x, we get:
x = 21 tan(27)
≈ 11.1
Rounding to the nearest tenth, we get:
x ≈ 11.1
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If all three dimensiona of
a pyramid increase by a factor of two, by what factor does the volume of pyramid increase
Answer:
8.
Step-by-step explanation:
That would be by a factor of 2^3 = 8.
during the 2020 census, jerome was given a geographical area that he was in charge of surveying. on one particular street with 10 homes, he was instructed to interview the residents at 3 of the homes. how could jerome choose a simple random sample of these houses to interview? he plans to visit the homes at 10:00 am. if someone is not home, what should he do?
To choose a simple random sample assign different numbers to the house and visit by choosing randomly.
To choose a simple random sample of the 3 homes to survey,
Jerome could assign each home a number from 1 to 10,
And then use a random number generator or a table of random numbers to select three numbers.
He would then visit the homes corresponding to those numbers for the survey.
For example,
if he assigned the following numbers to each home,
1, 2, 3, 4, 5, 6, 7, 8, 9 ,10
He could use a random number generator or table of random numbers to select three numbers, such as 2, 5, and 9.
He would then visit the homes at 2, 5, 9 for the survey.
If someone is not home when Jerome visits,
He should make a note of it and try to arrange a time to come back and conduct the survey.
If it is not possible to arrange another time,
He should make a note that the household was not surveyed and move on to the next household in the sample.
It is important to keep track of which households were surveyed and which were not.
And to try to minimize any biases that may arise from nonresponse.
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What is the area of the rhombus shown?
Answer:
Step-by-step explanation:
[tex]168yd^{2}[/tex]
Answer:
168 yd²
Step-by-step explanation:
4 × 7 yd × 12 yd / 2 = 168 yd²
if 30% of r is 33, what is 70% of R
Answer:
77
Step-by-step explanation:
We Know
30% of r = 33
Find 1% by taking
33 / 30 = 1.1
What is 70% of R?
We take
1.1 x 70 = 77
So, 70% of R is 77
The question requires to first find the value of R by solving the equation (0.30*R = 33). Then, calculate 70% of R by multiplying the found R value with 0.70.
Explanation:The question tells us that 30% of R equals 33. To find the value of R, we can set up an equation where 0.30 (which is 30% in decimal form) times R equals 33. Dividing both sides of the equation by 0.30 will give us the value for R. Once we have found R, we can then find 70% of R by multiplying R by 0.70 (70% in decimal form).
Step-by-step:Set up an equation: 0.30*R = 33Solve for R: R = 33 ÷ 0.30 Calculate 70% of R: 0.70 * R Learn more about Percentage Calculations here:https://brainly.com/question/329987
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how does a snak moove with no legs
Answer: it slithers
Step-by-step explanation:
To further explain it They move by dragging their body throughout in the form of loops. Hence, snakes have a crawling or slithering type of movement
Answer:
Overlapping belly scales provide friction with the ground that gives snakes a preferred direction of motion, like the motion of wheels or ice skates.
Step-by-step explanation:
Hope this helps! =D
Mark me brinaliest!=D
Create multiple A line with a slope of 4 and y-intercept -6. a. representations of each line described below. b. A line with a slope of that passes through the point (5,7). 2 C. Any line parallel to the line in part (b). d. A line perpendicular to the line in part (b), passing through the origin.
After following all the listed steps, you can determine that it will be a graph with lines going through the y-int of -6.
calculate the probability that at most 13% of the residents in the sample received a jury summons in the previous 12 months.
The probability that at most 13 of the residers in the sample entered a jury process in the once 12 months is 0.000158.
What's Normal Distribution?A normal distribution, also known as a Gaussian distribution or bell wind, is a probability distribution that's symmetric and bell- shaped. It's characterized by its mean( μ) and standard divagation( σ).
Given
Sample size( n) = 500
Probability of an individual entering a jury process( p) = 15 = 0.15
We want to calculate the probability that at most 13 of the residers in the sample entered a jury process.
Let X be the arbitrary variable representing the number of residers who entered a jury process in the sample.
Using the binomial accretive distribution function( CDF), we can calculate the probability as follows
P( X ≤ 13 of n) = Σ( k = 0 to k = 0.13 n)( n C k)
Here, n = 500
p = 0.15
k = int(0.13 n)
So, binom.cdf( int(0.13 500), 500,0.15) ≈0.000158
Thus, The likelihood that 13% of the sample's residents received a jury summons in the previous year is 0.000158.
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The question attached here is seems to be incomplete, the complete question is
What proportion of US Residents receive a jury summons each year? A polling organization plans to survey a random sample of 500 US Residents to find out. Let be the proportion of residents in the sample who received a jury summons in the previous 12 months. According to the National Center for State Courts, 15 \% of US residents receive a jury summons each year. Suppose that this claim is true.
5. Calculate the probability that at most 13% of the residents in the sample received a jury summons in the past 12 months.
A cone with a diameter of 8 centimeters has volume 143.6 cubic centimeters. Find the height of the cone
By answering the presented question, we may conclude that height of the cone is approximately 2.9 centimeters.
what is a cone?A cone is a three-dimensional geometric shape having a flat base and a smooth tapering apex, also known as a vertex. A cone is formed on a plane with no vertices by joining a sequence of line segments, half-lines, or lines that are common to all points on the base. A cone is a three-dimensional structure with a smooth transition from a flat, usually circular, base to the vertex or apex, which acts as the axis to the centre of the base. A cone is a three-dimensional geometric form having an upwardly flattened curving surface.
volume of a cone:
[tex]V = 1/3 * \pi * r^2 * h\\r = 4 cm\\V = 143.6 cm^3\\143.6 = 1/3 * \pi * 4^2 * h\\143.6 = 16/3 * \pi * h\\h = 143.6 / (16/3 * \pi)\\h = 2.9 cm\\[/tex]
height of the cone is approximately 2.9 centimeters.
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Shaggy,Velma, and Fred are camping in the woods.They each have their own tent and the tents are set up in a triangle.Shaggy and Velma are 20 meters apaart.The angle formed at Shaggy is 30 degrees and the angle formed at fred is 105 degrees.How far apart are Velma and Fred?
By using the cosines law we can say that, Velma and Fred are approximately 17.39 meters apart.
What is law of cosine?
The Law of Cosines is a formula used in trigonometry to relate the sides and angles of a triangle. It states that for any triangle with sides a, b, and c and angles A, B, and C opposite those sides, the following equation holds:
[tex]$c^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]
where c is the side opposite angle C.
We can solve this problem using the law of cosines. Let's call the distance between Velma and Fred "[tex]$d$[/tex]". Then, we have:
[tex]$c^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]
where [tex]$c$[/tex] is the distance between Velma and Fred (which we want to find), [tex]$a$[/tex] is the distance between Shaggy and Velma (which is 20 meters), [tex]$b$[/tex] is the distance between Shaggy and Fred, and [tex]$C$[/tex] is the angle formed at Shaggy (which is 30 degrees).
We can rearrange this equation to solve for [tex]$d$[/tex]:
[tex]$d^2 = a^2 + b^2 - 2ab \cos(C)$[/tex]
[tex]$d^2 = 20^2 + b^2 - 2(20)(b) \cos(30)$[/tex]
[tex]$d^2 = 400 + b^2 - 20b \sqrt{3}$[/tex]
We also know that the angle formed at Fred is 105 degrees, which means that the angle formed at Velma is 45 degrees (since the angles in a triangle sum to 180 degrees). This means that we can use the law of sines to find the value of [tex]$b$[/tex]:
[tex]$\dfrac{b}{\sin(B)} = \dfrac{a}{\sin(A)}$[/tex]
[tex]$\dfrac{b}{\sin(105)} = \dfrac{20}{\sin(45)}$[/tex]
[tex]$b = 20 \dfrac{\sin(105)}{\sin(45)}$[/tex]
[tex]$b \approx 27.68$[/tex]
Now we can substitute this value of [tex]$b$[/tex] into the equation we derived earlier to find [tex]$d$[/tex]:
[tex]$d^2 = 400 + (27.68)^2 - 20(27.68)\sqrt{3}$[/tex]
[tex]$d \approx 17.39$[/tex]
Therefore, Velma and Fred are approximately 17.39 meters apart.
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