b) To find the joint density of the minimum and maximum of the U_i's, we can use the following approach:
Let M = min(U_1, U_2, U_3, U_4, U_5) and let X = max(U_1, U_2, U_3, U_4, U_5). Then we have:
P(M > m, X < x) = P(U_1 > m, U_2 > m, U_3 > m, U_4 > m, U_5 > m, U_1 < x, U_2 < x, U_3 < x, U_4 < x, U_5 < x)
Since the U_i's are independent and uniformly distributed on (0,1), we have:
P(U_i > m) = 1 - m, for 0 < m < 1
P(U_i < x) = x, for 0 < x < 1
Substituting these expressions, we get:
P(M > m, X < x) = (1 - m)^5 * x^5
Therefore, the joint density of M and X is:
f(M,X) = d^2/dm dx (1-m)^5 * x^5 = 30(1-m)^4 * x^4, for 0 < m < x < 1.
c) To find P(R > 0.5), we need to find the probability that the distance between the minimum and maximum of the U_i's is greater than 0.5. We can use the following approach:
P(R > 0.5) = 1 - P(R <= 0.5)
Now, R <= 0.5 if and only if the difference between the maximum and minimum of the U_i's is less than or equal to 0.5. Therefore, we have:
P(R <= 0.5) = P(X - M <= 0.5)
To find this probability, we can integrate the joint density of M and X over the region where X - M <= 0.5:
P(R <= 0.5) = ∫∫_{x-m<=0.5} f(M,X) dm dx
The region of integration is the triangle with vertices (0,0), (0.5,0.5), and (1,1). We can split this triangle into two regions: the rectangle with vertices (0,0), (0.5,0), (0.5,0.5), and (0,0.5), and the triangle with vertices (0.5,0.5), (1,0.5), and (1,1). Therefore, we have:
P(R <= 0.5) = ∫_{0}^{0.5} ∫_{0}^{m+0.5} 30(1-m)^4 * x^4 dx dm + ∫_{0.5}^{1} ∫_{x-0.5}^{x} 30(1-m)^4 * x^4 dm dx
Evaluating these integrals, we get:
P(R <= 0.5) ≈ 0.5798
Therefore,
P(R > 0.5) = 1 - P(R <= 0.5) ≈ 0.4202.
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Plot Points & Graph Exponential Function
Whats the y=2^x+1 -8?
The graph of y = 2ˣ +1 -8 is the curve of the exponential function y = 2ˣ shifted downward by 8 units and shifted to the left by 1 unit along the x-axis.
The exponential function y = 2ˣ represents a curve that grows rapidly as x increases.
The graph of y = 2ˣ +1 -8 is the same curve shifted downward by 8 units and shifted to the left by 1 unit along the x-axis.
To plot some points for the graph, choose a few x-values and then calculate the corresponding y-values using the function:
When x = -2, y = 2⁻¹ - 8 = -8.5
When x = -1, y = 2⁰ - 8 = -7
When x = 0, y = 2¹ - 8 = -6
When x = 1, y = 2² - 8 = -4
When x = 2, y = 2³ - 8 = 0
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A circle has a radius of 5 in. Find the length s of the arc intercepted by a central angle of 2.9 radians. Do not round any intermediate computations, and round your answer to the nearest tenth
The length of the arc intercepted by a central angle of 2.9 radians is 14.5 inches. Rounded to the nearest tenth, this is 14.5 inches.
To find the length (s) of the arc intercepted by a central angle of 2.9 radians in a circle with a radius of 5 inches, you can use the following formula:
Arc length (s) = radius × central angle (in radians)
In this case, the radius is 5 inches, and the central angle is 2.9 radians. Plugging these values into the formula, we get:
s = 5 × 2.9
s ≈ 14.5 inches
Therefore, the length of the arc intercepted by a central angle of 2.9 radians in a circle with a radius of 5 inches is approximately 14.5 inches, rounded to the nearest tenth.
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The volume of the right cone below is 5677 units³. Find the value of x.
Answer:
21 units
Step-by-step explanation:
You want the height (x) of a cone with base radius 9 units and volume 567π cubic units.
VolumeThe volume of a cone is given by the formula ...
V = 1/3πr²h
Solving for the height, and using x for the height, we find ...
x = 3V/(πr²) = 3(567π units³)/(π(9 units)²) = 21 units
The height of the cone is 21 units.
HELP!!!!
Please help!!!
The lengths of three metal rods, A, B and C, are such that length of A : length of B = 3 : 2 and
length of A : length of C = 2 : 5
The difference in length between the longest rod and the shortest rod is 55 cm. Find the total length of the three rod in metres.
The lengths of rods A, B and C are respectively;
30 cm, 10 cm and 75 cm
How to solve ratio problems?We are given that;
Ratio of length of Rod A to length of Rod B is; 3:2
Ratio of length of Rod A to length of rod C is 2:5
Thus;
2/3 Length of Rod A = the length of Rod B
5/2 Length of Rod A = the length of Rod C
If length of Rod A = x, then we can say that;
5x/2 is length of Rod C
⅔x is the lenggh of Rod B
Difference between longest and shortest is 55. Thus;
(5/2)x - (2/3)x = 55
Multiply through by 6 to get;
15x - 4x = 330
11x = 330
x = 330/11
x = 30 cm
Length of Rod B = (2/3) * 30
= 10 cm
Length of Rod C = (5/2) * 30
= 75 cm
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An amount of 22,000 is borrowed for 5 years at 3.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back? Use the calculator provided and round your answer to the nearest dollar.
The requried, if the loan is paid in full at the end of the 5-year period, the borrower would have to pay back $26,130 (rounded to the nearest dollar).
The formula for the future value of an investment with compound interest is:
[tex]FV = PV * (1 + r)^n[/tex]
Where PV is the present value (the amount borrowed), r is the annual interest rate (as a decimal), and n is the number of compounding periods. In this case, since the interest is compounded annually for 5 years, n = 5.
Substitute in the values given, we get:
[tex]FV = 22,000 * (1 + 0.035)^5[/tex]
FV = 22,000 * 1.19416
FV = 26,129.09 = 26,130
Therefore, if the loan is paid in full at the end of the 5-year period, the borrower would have to pay back $26,130 (rounded to the nearest dollar).
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The table below gives the Uk population in
percentage according to a census.
England-83%
Wales-5%
Scotland-9%
N Ireland-3%
(a) Represent this information by a pie
chart.
b) Find the population of England if the
total population of the UK is 60 m.
The information as shown in a pie chart is found in the attachment.
The population of England is 49.8 million.
What is the population of England?The population of England is calculated as a percentage of the total population of the United Kingdom.
The data table given shows that England has 83% of the UK population and the total population of the UK is 60 million.
Hence, the population of England is calculated as follows:
The population of England = 83% of 60 million
The population of England = (83/100) x 60,000,000
The population of England = 49,800,000
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the standard deviation of the sampling distribution is called the standard error of the median. true false
The standard deviation of the sampling distribution is called the standard error of the mean, not the median. The standard error of the median is a different measure that is used to estimate the variability of the median of a sample.
When we take a sample from a population, the values of the sample statistics, such as the mean, median, standard deviation, etc., will vary from sample to sample. The distribution of the sample statistics is called the sampling distribution.
The standard deviation of the sampling distribution of the mean is called the standard error of the mean. It is a measure of the variability of the sample means from sample to sample.
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customers experiencing technical difficulty with their internet cable service may call an 800 number for technical support. it takes the technician between 30 seconds and 13 minutes to resolve the problem. the distribution of this support time follows the uniform distribution. a. what are the values for a and b in minutes? (do not round your intermediate calculations. round your answers to 1 decimal place.)
To find the values for a and b in minutes, we need to use the information given about the uniform distribution. We know that the technician takes between 30 seconds and 13 minutes to resolve the problem.
Given that the support time follows a uniform distribution and takes between 30 seconds and 13 minutes to resolve the problem, we can find the values of a and b as follows:
Step 1: Convert the time range to minutes
30 seconds = 0.5 minutes
13 minutes = 13 minutes
Step 2: Identify the values for a and b
In a uniform distribution, 'a' is the minimum value and 'b' is the maximum value.
So, a = 0.5 minutes and b = 13 minutes
The values for a and b in minutes are:
a = 0.5 minutes
b = 13.0 minutes
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for a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what is the expected winnings per ticket? question options:
The expected winning and the value of that prize, which gives an expected winning is c. $3.13 per ticket.
The expected winnings per ticket in the raffle can be calculated by adding the products of the probability of the expected value of winning each prize. The predicted wins per ticket may be computed as the total of each prize's value multiplied by its probability of winning, i.e.
Expected winnings per ticket
= (1/800) × $400 + (4/800) × $200 + (12/800) × $125 + (30/800) × $60 + (753/800) × $0
If we condense the equation, we obtain:
Calculating the total wins anticipated per ticket
= $0.50 + $1.00 + $1.88 + $0.75 + $0
Expected winnings per ticket = $3.13
Therefore, if you buy a ticket, the expected winnings per ticket are $3.13.
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Complete question:
For a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what are the expected winnings per ticket? question options:
a) $5.36
b) $5.63
c) $5.33
d) $5.66
A computer company wants to determine the proportion of defective computer chips from a day’s production. A quality control specialist takes a random sample of 100 chips from the day’s production and determines that there are 12 defective chips. Assuming all conditions are met, he constructs a 95% confidence interval for the true proportion of defective chips from a day’s production. What are the calculations for this interval?
12 plus-or-minus 1.65 StartRoot StartFraction 12 (1 minus 12) Over 100 EndFraction EndRoot
12 plus-or-minus 1.96 StartRoot StartFraction 12 (1 minus 12) Over 100 EndFraction EndRoot
0.12 plus-or-minus 1.65 StartRoot StartFraction 0.12 (1 minus 0.12) Over 100 EndFraction EndRoot
0.12 plus-or-minus 1.96 StartRoot StartFraction 0.12 (1 minus 0.12) Over 100 EndFraction EndRoot
answer d
you put $300 per month in an investment plan that pays an APR of 3.5% how much money will you have after 18 years? Compare this amount to the total deposits made over the time period.
To solve this problem, we can use the formula for the future value of an annuity:
FV = PMT * ((1 + r)^n - 1) / r
where:
PMT = the monthly payment ($300)
r = the monthly interest rate (APR / 12 = 0.035 / 12 = 0.002917)
n = the number of months (18 years x 12 months/year = 216 months)
Plugging in the values, we get:
FV = 300 * ((1 + 0.002917)^216 - 1) / 0.002917
FV ≈ $77,300.31
Therefore, after 18 years of making monthly deposits of $300 into an investment plan with an APR of 3.5%, you will have approximately $77,300.31.
To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:
Total deposits = PMT * n
Total deposits = $300 * 216
Total deposits = $64,800
We can see that the total deposits made over the 18-year period were $64,800, which is less than the final value of the investment of approximately $77,300. This is because of the effect of compound interest, where the interest earned on the investment is reinvested and earns additional interest over time, resulting in a higher final value.
your favorite cereal has a little prize in each box. there are 5 such prizes. each box is equally likely to contain any one of the prizes. so far, you have been able to collect 2 of the prizes. what is the probability that you will get the third different prize in the next box you buy?
The probability of getting a different prize in the next box you buy is: P(A) = 3 / 5 = 0.6 or 60%.
The probability of getting a different prize in the next box you buy depends on the number of prizes left and the total number of prizes.
Since there are 5 prizes in total and you have already collected 2, there are 3 remaining prizes. The probability of getting a different prize in the next box you buy is 3 out of 5, or 60%. This is because each box is equally likely to contain any one of the prizes, and you have already collected 2 out of the 5 prizes.
To calculate the probability, you can use the formula: P(A) = number of favorable outcomes / total number of possible outcomes In this case, the number of favorable outcomes is 3 (the number of remaining prizes) and the total number of possible outcomes is 5 (the total number of prizes). Therefore, the probability of getting a different prize in the next box you buy is: P(A) = 3 / 5 = 0.6 or 60%
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The functions and are defined as follows.
Find and .
Simplify your answers as much as possible.
Answer: f(2) = -7 , g(3) = -29
Step-by-step explanation: this problem can be solved via substitution
-2(2) - 3 = -4 - 3 = -7
-3(3)^2 - 2 = -3(9) - 2 = -27 - 2 = -29
A manufacturer must test that his bolts are 4.00cm
long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 49
randomly selected bolts off the assembly line, he calculates the sample mean to be 3.87cm
. He knows that the population standard deviation is 0.44cm
. Assuming a level of significance of 0.02
, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
The value of the test statistic for the test of the manufacturer to test his bolts is -0.296.
Given that,
A manufacturer must test that his bolts are 4.00 cm long when they come off the assembly line.
So population mean, μ = 4 cm
Sample size, n = 49
Sample mean, x = 3.87 cm
Population standard deviation, σ = 0.44 cm
Level of significance, α = 0.02
Test statistic, z = (x - μ) / σ
Substituting,3
z = (3.87 - 4) / 0.44 = -0.296.
Hence the value of the test statistic for the test of the manufacturer to test his bolts is -0.296.
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Viet, Quinn, and Lucy are going to play Bingo, using a standard game set. They make some predictions before the game begins. The table shows how the numbers match with the letters B, I, N, G, and O.Suppose the game changed to have 90 numbers, instead of 75 numbers, matched with the letters B, I, N, G, and O. How would Viet's, Quinn's, and Lucy's probability models change? Explain.
The probability model of Viet, Quinn, and Lucy will change to 18/90 instead of 15/75.
Given that,
Viet, Quinn, and Lucy are going to play Bingo, using a standard game set.
They make some predictions before the game begins.
The given table shows how the numbers match with the letters B, I, N, G, and O.
Total numbers = 75
Numbers which each letter has = 15
Probability of having each number = 15/75
Now if the game changed to 90 numbers, each letter will be having 90/5 = 18 numbers.
So probability changed to 18/90.
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hii plsssss answer questionnnnnnn :)
Answer:
75π
Step-by-step explanation:
Length of an arc formula:
Arc Length = 2πr(θ/360)Where:
r = radiusθ = central angleHere we are given the following:
Radius(r) = 90mCentral Angle(θ) = 150°By plugging these values into the formula we acquire(Note that the answer must be in terms of π, meaning that we do not simplify it and leave it in the final answer):
Arc Length = 2π(90)(150/360)Arc Length = 2π(90)(5/12)Arc Length = 2π(37.5)Arc Length = 75πThe length of the arc is 75πm
USE STRUCTURE Complete the table to show the effect that the transformation has on the table of the parent function f(x)=x2
.
g(x)
is a reflection of f(x)
across the x-axis.
x f(x) g(x)
-2 4
-1 1
0 0
1 1
2 4
Answer:
x f(x) g(x)
-2 4 -4
-1 1 - 1
0 0 0
1 1 -1
2 4 -4
Step-by-step explanation:
When a point is reflected across the x-axis the reflected point will have the same x value as the pre-image point
Therefore if point(x, y) is reflected across the x-axis the reflected point will be (x, -y)
When f(x) = x² is reflected across the x-axis, the reflected function becomes
f'(x) = -f(x) = -x²
Using this information we can complete the table as follows:
x f(x) g(x)
-2 4 -4
-1 1 - 1
0 0 0
1 1 -1
2 4 -4
-1/6 divided by -7/4 times 0.5
Answer:
[tex]\frac{1}{21}[/tex]
Step-by-step explanation:
To start, let's divide [tex]-\frac{1}{6}[/tex] by [tex]-\frac{7}{4}[/tex]. To do this, we're going to have to flip around the second number and multiply it by the first one (this is how to divide fractions).
[tex]-\frac{1}{6}[/tex] × [tex]-\frac{4}{7} = \frac{4}{42} =\frac{2}{21}[/tex]
Now, it's time for us to multiply that result by 0.5. As you may already know, 0.5 is equivalent to [tex]\frac{1}{2}[/tex], so let's use that value instead.
[tex]\frac{2}{21}[/tex] × [tex]\frac{1}{2} = \frac{2}{42} = \frac{1}{21}[/tex]
So, our final answer is [tex]\frac{1}{21}[/tex]. Let me know if you need more help!
Answer:0.00298
Step-by-step explan
The volume of a cylinder is 225T cm³ and its height is 9 cm.
What is the length of the cylinder's radius?
o 7 cm
o 10 cm
o 5 cm
9 cm
Answer:
The answer for radius is 5cm
Step-by-step explanation:
Volume of Cylinder =pir²h
225pi=pir²×9
225=9r²
divide both sides by 9
9r²/9=225/9
r²=25
√r²=√25
r=5cm
I need this quick i only have 2 minutes
Answer:
[tex]2 \frac{1}{3} + 1 \frac{3}{4} [/tex]
[tex]2 \frac{4}{12} + 1 \frac{9}{12} = 3\frac{13}{12} = 4 \frac{1}{12} [/tex]
The correct answer is A.
if 5 students chosebasketball, 2 students chose tennis, 3 students chose baseball, 7 students chose soccer, and 8 students chose football, what percentage of the students selected football over tennis or baseball.
Answer: 12%
Step-by-step explanation:
2/25 is .08
3/24 is .12
Together that’s .20 so 20%
8/25 is 32
So 32-20=12%
What is the awnseress
Answer:
<
Step-by-step explanation:
because 42.18 is smaller than 42.7
The rectangle below has an area of x^(2)-6x-7x 2-6x-7x, squared, minus, 6, x, minus, 7 square meters and a width of x-7x-7x, minus, 7 meters.
The length of rectangle is,
⇒ (x + 1)
We have o given that;
The rectangle has an area of x² - 6x - 7
And, a width of x - 7
Now, Let the length of rectangle = y
Hence, We get;
y = (x² - 6x - 7) / (x - 7)
y = (x + 1) (x - 7) / (x - 7)
y = (x + 1)
Thus, The length of rectangle is,
⇒ (x + 1)
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The two data sets below list the number of movies watched per month by a movie-loving family, and the medical expenses per month for a family. Use conditional formatting as follows. Note that the data have been generated by live random formulas. This highlights the effect of conditional formatting: The formatting should change as the spreadsheet recalculates (by pressing the F9 key). 5 6 7 1. In column B, use a Highlight Cells Rules option to change the font color to RED (from the "Standard Colors" section of the color palette) if the number of movies is greater than 15. 8 2. In column E, use a Highlight Cell Rules/Equal To option to change the number format for all zero values to currency with no decimals. (It should be the same currency format type as currently used in column E, except with no decimals.) 9 10 11 ExcelNow! Movies 17 14 15 12 13 14 15 16 17 Jan 18 Feb 19 Mar 20 Apr 21 May 22 Jun 23 Jul 24 Aug 25 Sep 26 Oct 27 Nov 28 Dec 29 19 19 18 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Medical $609.50 $0.00 $282.59 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $503.82 $0.00 $0.00 10 7 5 8 14 7 30 31 32 33 34 35 36 37
This will highlight the cells as described, emphasizing the effect of conditional formatting. When you press the F9 key, the spreadsheet will recalculate, and the formatting will change accordingly.
To apply the conditional formatting as described:
1. In column B, highlight cells with the number of movies greater than 15 in red.
-Select the data range in column B where the number of movies is listed.
-Go to the Home tab, click on Conditional Formatting, and choose "Highlight Cells Rules."
- Select "Greater Than" and enter 15 in the input box.
- Choose "Custom Format," go to the "Font" tab, and select red from the "Standard Colors" section.
Click OK to apply the formatting.
2. In column E, change the number format for all zero values to a currency with no decimals:
- Select the data range in column E where the medical expenses are listed.
-Go to the Home tab, click on Conditional Formatting, and choose "Highlight Cells Rules."
-Select "Equal To" and enter 0 in the input box.
- Choose "Custom Format," go to the "Number" tab, select "Currency" from the "Category" list, and set the "Decimal Places" to 0.
Click OK to apply the formatting.
This will highlight the cells as described, emphasizing the effect of conditional formatting. When you press the F9 key, the spreadsheet will recalculate, and the formatting will change accordingly.
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The members of a particular group are getting to know one another and attempting to reach an understanding of how each of them should act within the group. This stage of group development is known as ________.
a. forming
b. norming
c. storming
d. adjourning
This stage of group development is known as forming.
The group development process is a series of stages that a group goes through as they form, develop, and eventually come to an end. The first stage of this process is known as forming. During this stage, group members are getting to know each other and trying to establish common goals and a shared understanding of how the group will operate. They may be polite and reserved, as they are still trying to feel out the dynamics of the group.
Once the group has established its purpose and members have a sense of what is expected of them, they move into the norming stage. During this stage, group members begin to work together more closely and develop norms for behavior and communication. They may start to form stronger relationships with each other and trust begins to build.
The third stage of group development is storming. During this stage, conflicts may arise as group members struggle for power and influence. There may be disagreements about how the group should function or how tasks should be completed. However, if the group is able to work through these conflicts, they will move on to the next stage of development.
The final stage of group development is adjourning. During this stage, the group comes to an end. This may be due to the completion of a task or project, or it may be due to other reasons, such as members leaving the group or the group disbanding. During this stage, members may reflect on their accomplishments and evaluate the group's overall success.
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the p-value of a significance test is: question 4 options: the probability, assuming the null hypothesis is true, that the sample would produce a result at least as extreme (meaning, as far away from expected) as was actually observed. the probability that the null hypothesis is true. the probability that the null hypothesis is false. the probability, assuming the null hypothesis is false, that the sample would produce a result at least as extreme (meaning, as far away from expected) as was actually observed.
The correct answer to your question is: the p-value of a significance test is the probability, assuming the null hypothesis is true, that the sample would produce a result at least as extreme (meaning, as far away from expected) as was actually observed.
This means that the p-value represents the strength of evidence against the null hypothesis, with lower values indicating stronger evidence against the null hypothesis. It is important to note that the p-value does not tell us the probability that the null hypothesis is true or false, but rather the likelihood of observing a result as extreme as the one observed in the sample data, assuming the null hypothesis is true.
The p-value of a significance test is: the probability, assuming the null hypothesis is true, that the sample would produce a result at least as extreme (meaning, as far away from expected) as was actually observed.
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A botanist wishes to estimate the typical number of seeds for a certain fruit. She samples 70 specimens and counts the number of seeds in each. Use her sample results (mean = 18.7, standard deviation = 6.2) to find the 90% confidence interval for the number of seeds for the species. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. 90% C.I. = )
The 90% confidence interval for the number of seeds in the fruit is (17.480, 19.920). To find the 90% confidence interval for the number of seeds in the fruit, we will follow these steps:
1. Identify the sample size (n), sample mean (x), and sample standard deviation (s): n = 70, x= 18.7, s = 6.2.
2. Since we want a 90% confidence interval, we will use a z-score of 1.645 (from a standard normal distribution table or calculator).
3. Calculate the standard error (SE) using the formula: SE = s/√n = 6.2/√70 = 0.741.
4. Calculate the margin of error (ME) using the formula: ME = z * SE = 1.645 * 0.741 =1.220.
5. Determine the confidence interval by adding and subtracting the margin of error from the sample mean: (x - ME, x+ ME) = (18.7 - 1.220, 18.7 + 1.220) = (17.480, 19.920).
Therefore, the 90% confidence interval for the number of seeds in the fruit is (17.480, 19.920).
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How many solutions does this system of equations have? 3x+2y=6 -4x+5y=15
In ΔDEF, d = 5.2 inches, e = 6.8 inches and ∠F=166°. Find the length of f, to the nearest 10th of an inch.
The length of side f is 8.38 in the triangle DEF.
In a triangle, the sum of the angles is always 180 degrees.
∠D + ∠E + ∠F = 180 degrees
∠D + ∠E + 166 degrees = 180 degrees
∠D + ∠E = 14 degrees
Now, we can use the Law of Cosines to find the length of side f:
f² = d² + e² - 2de cos(∠F)
f² = (5.2 inches)² + (6.8 inches)² - 2(5.2 inches)(6.8 inches) cos(166 degrees)
f² = 70.29 inches²
Taking the square root of both sides, we get:
f = 8.38 inches
Therefore, the length of side f is 8.38 in the triangle DEF.
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The base of a triangle is fixed at 2. 218 mm. Determine the number of significant figures of the area of the triangle with a height of 1. 86 mm
The area of this triangle has 5 significant figures. With the following formula, we can determine a triangle's area:
Area equals (1/2) x base x height.
When we enter the values we have:
(1/2) x 2.218 mm x 1.86 mm is the area.
= 2.0586 mm2 in size
With a fixed base of 2.218 mm and a height of 1.86 mm, the area of the triangle is 2.06 mm2 (rounded to the nearest hundredth).
The number of important figures in the obtained area will next be determined. Every digit is important in decimal numbers greater than or equal to 1, so we may infer that there are five significant figures in this case:
2,0,6,7, and 4 due to the fact that the number 2.06274 is greater than 1
Therefore, the area of this triangle has 5 significant figures.
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