Please solve with hand
writing, I don't need program solving.
1. For each function, find an interval [a, b] so that one can apply the bisection method. a) f(x) = (x – 2 – x b) f(x) = cos(x) +1 – x c) f(x) = ln(x) – 5 + x — 2. Solve the following linear
Answers
a) The bisection method can be applied to the function f(x) = \(e^x\) - 2 - x on the interval [0, 1].
b) The bisection method can be applied to the function f(x) = cos(x) + 1 - x on the interval [0, 1].
c) The bisection method can be applied to the function f(x) = ln(x) - 5 + x on the interval [1, 2].
To apply the bisection method for each function, we need to find an interval [a, b] where the function changes sign. Here's how we can determine the intervals step by step for each function:
a) f(x) = \(e^x\) - 2 - x
Step 1: Choose two values, a and b, such that f(a) and f(b) have opposite signs.
Let's try a = 0 and b = 1.
Step 2: Calculate f(a) and f(b).
f(0) = e^0 - 2 - 0 = -1
f(1) = e^1 - 2 - 1 = e - 3
Step 3: Check if f(a) and f(b) have opposite signs.
Since f(0) is negative and f(1) is positive, f(x) changes sign between 0 and 1.
Therefore, the interval [0, 1] can be used for the bisection method with function f(x) = \(e^x\) - 2 - x.
b) f(x) = cos(x) + 1 - x
Step 1: Choose two values, a and b, such that f(a) and f(b) have opposite signs.
Let's try a = 0 and b = 1.
Step 2: Calculate f(a) and f(b).
f(0) = cos(0) + 1 - 0 = 2
f(1) = cos(1) + 1 - 1 = cos(1)
Step 3: Check if f(a) and f(b) have opposite signs.
Since f(0) is positive and f(1) is less than or equal to zero, f(x) changes sign between 0 and 1.
Therefore, the interval [0, 1] can be used for the bisection method with function f(x) = cos(x) + 1 - x.
c) f(x) = ln(x) - 5 + x
Step 1: Choose two values, a and b, such that f(a) and f(b) have opposite signs.
Let's try a = 1 and b = 2.
Step 2: Calculate f(a) and f(b).
f(1) = ln(1) - 5 + 1 = -4
f(2) = ln(2) - 5 + 2 = ln(2) - 3
Step 3: Check if f(a) and f(b) have opposite signs.
Since f(1) is negative and f(2) is positive, f(x) changes sign between 1 and 2.
Therefore, the interval [1, 2] can be used for the bisection method with function f(x) = ln(x) - 5 + x.
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The question is -
1. For each function, find an interval [a, b] so that one can apply the bisection method.
a) f(x) = e^x – 2 – x
b) f(x) = cos(x) + 1 – x
c) f(x) = ln(x) – 5 + x.
Related Questions
rachel and robert run on a circular track. rachel runs counterclockwise and completes a lap every 9090 seconds, and robert runs clockwise and completes a lap every 8080 seconds. both start from the same line at the same time. at some random time between 1010 minutes and 1111 minutes after they begin to run, a photographer standing inside the track takes a picture that shows one-fourth of the track, centered on the starting line. what is the probability that both rachel and robert are in the picture?
Answers
The probability that both Rachel and Robert are in the picture is 3/16.
The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.
Given that
Rachel and Robert both begin at the same point
Rachel completes a lap every 90 seconds.
Robert completes a lap every 80 seconds.
The photographer captures 1/4th of the track, centered on the starting line.
As a result, the photo captures 1/8th of the track on either side of the starting line.
The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.
Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.
Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.
Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).
Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.
i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.
Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}
= {90/8}/60
= 3/16
Therefore the probability that both Rachel and Robert are in the picture is 3/16
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2 intersecting lines are shown. A line with points T, R, W intersects a line with points S, R, V at point R. 4 angles are created. Clockwise, from the top, the angles are blank, (3 x) degrees, blank, (x + 40) degrees.
What is the value of x?
20
35
60
70
Answers
2 intersecting lines are shown. A line with points T, R, and W intersects a line with points S, R, and V at point R. the value of x is mathematically given as
x=20
This is further explained below.
What is the value of x?In most cases, two lines that cross one other are shown. In this example, line TW and line SV meet at point R.
The angles are as follows, starting at the top and moving clockwise:
blank,\(3x \textdegree\),blank,\((x + 40) \textdegree.\)Angels \(3x\textdegree \ and\ (x+40 \textdegree)\) are considered horizontal angles because of the description (opposite when two lines intersect). Vertical angles are equivalent, therefore
x=20
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Which triangle pairs are similar polygons?
Answers
Triangle pairs are similar polygons if they have the same shape but not necessarily the same size. In order for two triangles to be similar, they must satisfy the following conditions:
They must have the same angles. This means that the measures of the angles in one triangle must be the same as the measures of the corresponding angles in the other triangle.
The lengths of the sides must be in the same ratio. This means that if you divide the lengths of the corresponding sides of one triangle by the lengths of the corresponding sides of the other triangle, you must get the same ratio for all pairs of sides.
For example, if triangle ABC is similar to triangle DEF, the ratios of AB/DE, AC/DF, and BC/EF must all be the same.
To determine if two triangles are similar, you can use one of several theorems and postulates, such as the Side-Side-Side (SSS) Similarity Theorem, the Side-Angle-Side (SAS) Similarity Theorem, or the Angle-Angle (AA) Similarity Postulate. These theorems and postulates provide different sets of conditions that must be satisfied in order for two triangles to be similar.
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SECTION A (20 MARKS) QUESTION 1 (a)Identify the relevant population for the below foci, and suggest the appropriate sampling design to investigate the issues, explaining why they are appropriate. Wherever necessary identify the sampling frame as well. 10 marks A public relations research department wants to investigate the initial reactions of heavy soft- drink users to a new all-natural soft drink'. (b) What type of sampling design is cluster sampling? What are the advantages and disadvantages of cluster sampling? Describe a situation where you would consider the use of cluster sampling. 10 marks
Answers
a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is stratified random sampling. The list of all heavy soft-drink users is the sampling frame.
b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.
The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.
a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.
Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.
Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.
b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.
The advantages of cluster sampling are:
Cluster sampling is an efficient method of sampling large populations. It is much cheaper than other types of sampling methods.Cluster sampling is relatively easy to perform compared to other methods of sampling, such as simple random sampling.Cluster sampling can be used when the population is widely dispersed, and it would be difficult to cover the entire population.The disadvantages of cluster sampling are:
Cluster sampling introduces sampling errors that could lead to biased results.Cluster sampling has a lower level of precision and accuracy compared to other types of sampling methods.Cluster sampling increases the standard error of the estimate, making it difficult to achieve the desired level of statistical significance.A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.
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What is the expected value of spinning a 4 equal-segment spinner numbered 1-4? \( 1.5 \) \( 3.5 \) \( 2.5 \) \( 0.5 \)
Answers
The expected value of spinning a 4 equal-segment spinner numbered 1-4 is 2.5.
The expected value of spinning a 4 equal-segment spinner numbered 1-4 can be calculated by taking the average of the possible outcomes, weighted by their respective probabilities.
The spinner is equally likely to land on each of the four numbers, so the probabilities of each outcome are all 1/4.
The expected value is then calculated as follows:
Expected value = (1/4) * 1 + (1/4) * 2 + (1/4) * 3 + (1/4) * 4
= 1/4 + 2/4 + 3/4 + 4/4
= 10/4
= 2.5
Therefore, the expected value of spinning the spinner is 2.5.
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hii please help i’ll give brainliest
Answers
Answer:
3rd one
Step-by-step explanation:
well it would make sense if you said that the longest fish is 12in longer than the shortest because if you took 21in (the longest fish) and subtracted 9 (the shortest fish) you would get 12.
hope that helped please give brainliest.
2). What is the number of permutations for a 6 digit number using the
digits 0 - 9. if numbers cannot be repeated.
Answers
Answer:
Esto quiere decir que la cantidad de números de 3 dígitos se pueden formar con los números 0123456 sin repetir y no comienzan con cero son 180a
Step-by-step explanation:
Espero que te sea útil la respuesta, Saludos!
Type in the percent decrease in the value of the car. $22,000 $18,700
Answers
Answer:
15%
Step-by-step explanation:
1. 18700 ÷ 22000 = 0.85
2. 1 - 0.85 = 0.15
3. move the decimal over 2 spaces 0.15 --> 15.0
4. 15.0 = 15%
Answer: 15%
Just type it in the box.
Please help me find the y-intercept and slope from these two-word problems. ANd tell me if they're proportional and negative or not.
Answers
Answer:
for the 1st one, m=10 and b=2 because from the word problem it says it starts at 10 which would be 10 on the y axis being where the line would pass through and spending 2 a week would be the slope because he is losing 2 per week its a negative slope so y=10x-2.
for the second one m=48 and b=44 its just like the last one but with different numbers but comment if you want me to explain it but the answer is y=48x-44.
Systems requests do not deal with factors involved in improving service.
a. true
b. false
Answers
circuference and area of a circle PLEASE HELP
Answers
Answer:
Area=12.56
Circumference= 12.56
Step-by-step explanation:
Area formula is \(\pi r^{2}\)
Circumference is \(2\pi r\)
Answer:
radius=diameter/2
=4/2=2
circumference of a circle= 2πr
=2*3.14*2
=12.56ft
area of a circle=πr2
=3.14*2*2
=12.56ft
Please help I don't know this
Answers
The length of AC is given as follows:
AC = 25.
How to obtain the length of AC?Applying the secant-tangent theorem, we have that the following equation holds true:
CD² = BC(AC + BC).
Hence the value of x is obtained as follows:
15² = 9(9 + 3x + 1)
15² = 9(10 + 3x)
225 = 90 + 27x
x = (225 - 90)/27
x = 5.
Then the length of AC is of:
AC = 3(5) + 1 + 9
AC = 25.
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If (2^6)x = 1, what is the value of x? Explain your answer.
Answers
Answer:
\(x=\frac{1}{64}\) Exact Form
\(x=0.015625\) Decimal Form
Step-by-step explanation:
\(\frac{(2^6)x}{2^6} =\frac{1}{2^6}\) Divide each term in \((2^6)x=1\) by \(2^6\).
\(x=\frac{1}{2^6}\) Cancel the common factor of \(2^6\).
\(x=\frac{1}{64}\) Raise 2 to the power of 6.
\(x=0.015625\) Decimal Form.
Simplify m^12/(m^8)^3
Answers
Given:
\(\frac{m^{12}}{\mleft(m^8\mright)^3}\)To simplify:
Solving we get,
\(\begin{gathered} \frac{m^{12}}{(m^8)^3}=\frac{m^{12}}{m^{24}^{}} \\ =m^{12-24} \\ =m^{-12} \\ =\frac{1}{m^{12}} \end{gathered}\)Hence, the answer is,
\(\frac{1}{m^{12}}\)Tasha has 10. 4 yards of lace. She uses 2 yards for a project. Then she cuts the remaining lace into 6 equal pieces.
How many yards long is each piece of lace?
Answers
Tasha has 10. 4 yards of lace. She uses 2 yards for a project. Then she cuts the remaining lace into 6 equal pieces.
Each piece of lace will be 1.4 yards long.
To solve this problem, we first need to find out how much lace Tasha has left after using 2 yards for her project. Since she had 10.4 yards of lace and used 2 yards for the project, she will have 8.4 yards left.
Next, we need to divide 8.4 yards by 6, since she is cutting the remaining lace into 6 equal pieces. 8.4 divided by 6 is 1.4, so each piece will be 1.4 yards long.
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I need help asap please
Answers
Answer:
(E) if im wrong don't sew meh
Step-by-step explanation:
24 students in a class took a math test. if 18 students passed the test, what percent passed
- i’m pretty sure 75% passed because 18 / 24 = 75% (“/“ = divide)
Answers
9514 1404 393
Answer:
75%
Step-by-step explanation:
You are correct:
18/24 = 3/4 = (3/4)×100% = 75%
75% of the students passed the test.
Answer:
hope this pic helps you
HELP!!
what is the domain AND range for each problem!
f(x) = 1.5x + 10
g(x) = 25
h(x) = 15 - 3x
Answers
Answer:
1. Domain: \((-\infty, \infty)\), Range: \((-\infty. \infty)\)
2. Domain \((-\infty, \infty)\), Range: 25
3. Domain: \((-\infty, \infty)\), Range: \((-\infty. \infty)\)
Step-by-step explanation:
The domain and range of all non-constant linear functions is \((-\infty, \infty)\).
Jayden wants to lay sod on his front yard and on half of his back yard. His front yard has a length of 50 feet and a width of 70 feet. His back yard has a length of 10 feet and a width of 40 feet. How many square feet of sod does Jayden need to purchase? A. 3,900 square feet B. 3,600 square feet C. 3,700 square feet D. 2,150 square feet
Answers
Answer:
C. 3,700 square feet
Step-by-step explanation:
add the area of both the front and half of the back yard.
Emma has addressed seven invitations to her
birthday party. This is one more than half of the
invitations that she intends to send. How many
invitations does she intend to send?
Answers
Answer:
12
Step-by-step explanation:
This can be solved by working backwards.
7 is one more than half the number of invitations.
Subtract 1. 6 is half the number of invitations.
Double.
12 is the full number of invitations.
Algebra (if you must!):
x = number of invitations
x/2 + 1 = 7
Subtract 1.
x/2 = 6
Multiply by 2.
x = 12
Answer:
12
Step-by-step explanation:
7-1=6
6x2=12
Y=-6x-14
Y=3x-5
Solve by Substitute
Answers
Answer:
x=-1
Step-by-step explanation:
0=-6x-14-3x+5
0=-9x-9
-9x=9
x=-1
what is the margin of error for a 95% confidence interval for the proportion of all employees at this firm who are dissatisfied
Answers
The margin of error for a 90% confidence interval for the proportion of all employees dissatisfied with their jobs, based on a survey of 200 employees where 44% reported dissatisfaction, is 0.068.
We can use the formula for the margin of error for a proportion:
ME = zsqrt((p_hat(1-p_hat))/n)
where z is the z-score associated with the desired level of confidence (90% in this case), p_hat is the sample proportion (0.44), n is the sample size (200), and sqrt is the square root.
From a standard normal distribution table, the z-score for a 90% confidence level is approximately 1.645.
Plugging in the values, we get:
ME = 1.645sqrt((0.44(1-0.44))/200)
ME ≈ 0.068
So the margin of error for a 90% confidence interval is approximately 0.068 or 0.068/1= 0.068 = 0.068 = 6.8% (rounded to 3 decimal places).
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--The given question is incomplete, the complete question is given
"A human resources consulting firm conducted a survey of 200 employees to determine how dissatisfed they were with their jobs. 44% of the employees said they were dissatisfied, what is the margin of error for a 90% confidence interval for the proportion of all employees that are dissatisfied with their jobs? Answer to 3 decimal places"--
Woof Chow Dog Food Company believes that it has a market share of 25 percent. It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food, and 23 people say yes. Based upon this information, what is the value of the test statistic?
Answers
Based upon this information, the value of the test statistic is 0.23.
The term "test statistic" refers to a quantity obtained from the sample and used in statistical hypothesis testing.
The sample proportion, or ratio of the sample size to the number of "yes" responses (23), would be the test statistic in this situation (100). The sample proportion is computed in the following manner:
The test statistic is p = 23/100, or 0.23.
So, 0.23 is the test statistic. The percentage of dog owners that routinely feed their dogs Woof Chow dog food is represented by this sample estimate.
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A statistical test used to help answer the question of whether an observed difference is real or just due to chance error.a. trueb. false
Answers
a. A statistical test used to help answer the question of whether an observed difference is real or just due to chance error- true
The statistical test referred to in the question is known as a hypothesis test. It is used to determine the probability that the observed difference between two groups or variables is not due to chance but rather represents a true difference. The test involves setting up a null hypothesis, which assumes that there is no difference between the groups or variables, and an alternative hypothesis, which assumes that there is a real difference.
The test calculates a p-value, which represents the probability of obtaining the observed difference by chance if the null hypothesis is true.
If the p-value is below a predetermined level of significance (usually 0.05), then the null hypothesis is rejected and the alternative hypothesis is accepted.
This means that the observed difference is considered real and not just due to chance error.
Hence, If the p-value is below a certain level of significance, the null hypothesis is rejected and the alternative hypothesis is accepted, indicating that the observed difference is real.
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In the Green Food System Strategy, the "vision to be achieved by 2050" (numerical targets) is presented. Select the number of the following targets that are correctly described.
-Chemical pesticide use (in terms of weight) will be reduced by 50% by 2050.
-With regard to chemical fertilizers, the use of chemical fertilizers produced in Japan from fossil fuels will be reduced by 30% by 2050.
-Regarding organic agriculture, expand the organic market and increase the ratio of organic farming to arable land to 30% (1 million hectares) by 2050.
-Regarding food loss, reduce household food loss by half from the FY2000 level by 2030.
a. 0 b. 1 c. 2 d. 3 or more
Answers
Option c. 2
Among the given targets, two targets are correctly described:
Regarding chemical pesticide use, the target is to reduce it by 50% by 2050. This aligns with the vision presented in the Green Food System Strategy.
In terms of chemical fertilizers, the target is to reduce the use of chemical fertilizers produced in Japan from fossil fuels by 30% by 2050. This target is also consistent with the strategy's vision.
The remaining two targets are not correctly described:
The target of expanding the organic market and increasing the ratio of organic farming to arable land to 30% (1 million hectares) by 2050 is not mentioned in the given options.
The target of reducing household food loss by half from the FY2000 level by 2030 is also not mentioned in the given options.
Therefore, the correct answer is option c. 2, as two of the targets are accurately described in the provided options.
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construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined. Then show that the critical point at the origin is of the indicated type.
1.dxdt=−x3+xy2,dydt=−2x2y−y3; asymptotically stable
Answers
We can set a = 1 and c = 1/2. With these values, the Lyapunov function V(x, y) = x^2 + (1/2)y^2 satisfies the conditions and shows that the critical point at the origin is asymptotically stable.
To construct a suitable Lyapunov function, let's consider a function of the form V(x, y) = ax^2 + cy^2, where a and c are to be determined. We will choose a and c such that V(x, y) is positive definite and its derivative along the trajectories of the system is negative definite or negative semi-definite.
To show that the critical point at the origin is asymptotically stable, we need to demonstrate that there exists a Lyapunov function V(x, y) with the following properties:
V(x, y) is positive definite, i.e., V(x, y) > 0 for all (x, y) ≠ (0, 0).
V(x, y) is radially unbounded, meaning that as (x, y) approaches infinity, V(x, y) approaches infinity.
The derivative of V(x, y) along the trajectories of the system, dV/dt, is negative definite or negative semi-definite.
To determine the values of a and c, we can calculate the derivative of V(x, y) along the trajectories of the system:
dV/dt = ∂V/∂x * dx/dt + ∂V/∂y * dy/dt
Substituting the given system of differential equations: dV/dt = (2ax - 3ax^3 - cy^2) * (-x^3 + xy^2) + (2cy - 2cy^3 - cy^3) * (-2x^2y - y^3)
To ensure that dV/dt is negative definite or negative semi-definite, we can choose a and c such that the coefficients of x^4, x^2y^2, and y^4 terms in dV/dt are positive or zero. This condition guarantees that the critical point at the origin is asymptotically stable.
By comparing the coefficients, we can set a = 1 and c = 1/2. With these values, the Lyapunov function V(x, y) = x^2 + (1/2)y^2 satisfies the conditions and shows that the critical point at the origin is asymptotically stable.
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Problem: A pole is being held up with a 10 meter rope. The cable is making a 42° of elevation from the ground to
the top of the pole. What is the distance from the base of the pole to the base of the rope ? Round your answer
to the nearest tenth of a meter.
Answers
Answer:
x = 7.4
Step-by-step explanation:
cos(42°) = x/10 or distance from bases / rope length
Using the calculator find the value of cos(42°):
cos(42°) = 0.74 = x/10
Find x using the value of cos(42°):
x/10 = 0.74
x = 7.4
the
net migration is confusing me. i thought of using the formula:
[ (births + immigration) - (deaths + emmigration)] / total
population • 100 but im not sure how to do it with net migration?
do i p
Answers
The value of the rate of growth in Japan is - 0.55.
From the question above, :Birth rate = 7.7 per thousand
Death rate = 9.8 per thousand
Net migration = 0.55 per thousand
The rate of growth can be calculated using the following formula:
r = (birth rate - death rate) + net migration
Where,r = rate of growth
birth rate = number of live births per thousand in a population in a given year
death rate = number of deaths per thousand in a population in a given year
net migration = the difference between the number of people moving into a country (immigrants) and the number of people leaving a country (emigrants) per thousand in a given year
Putting the values in the formula we get,r = (7.7 - 9.8) + 0.55r = - 1.1 + 0.55r = - 0.55.
Therefore, the rate of growth in Japan is - 0.55.
Your question is incomplete but most probably your full question was:
thenet migration is confusing me. i thought of using the formula:[ (births + immigration) - (deaths + emmigration)] / total
population • 100 but im not sure how to do it with net migration.
Japan's birth rate is 7.7 per thousand and its death rate is 9.8 per thousand with a net migration of 0.55 ner thousand. Calculate r for Japan
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The dimensions of a solid block of cheese in the shape of a triangular prism are shownbelow.6.9 cm9.9 cm5.1 cm. Which of the following is the best estimate of the volume of the block of cheese in cubic centimeters
Answers
Answer:
175 cm
Step-by-step explanation:
Is 9,40,41 a right triangle
Answers
Using pythagoras theorem, the values given in the question 9, 40 and 41 represents a right angle triangle
Pythagoras TheoremThis theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle are named the perpendicular, base and hypotenuse. In this case, the hypotenuse is always longest side, as it is opposite to the angle 90°
Mathematically Pythagoras theorem is given as;
x² = y² + z²
x = hypothenusey = legz = legLet's substitute the values into the formula and check if the values are a right angle triangle.
41² = 40² + 9²
1681 = 1600 + 81
1681 = 1681
The values 9, 40, 41 represents a right angle triangle
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