Answers
New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.
How to find reduced area?The area of the tennis court is given by:
A = lw
where l is the length of the court and w is the width of the court.
Substituting the given values, we have:
[tex]$$260.7569 = l \cdot 10.97$$[/tex]
Solving for l, we get:
[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]
To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:
w' = w - 0.25w = 0.75w
Substituting the given values, we have:
[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]
where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:
[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]
Therefore, the new area of the court is reduced by 25%.
To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:
[tex]$w' = 0.75w$$[/tex]
Dividing both sides by w, we get:
[tex]$\frac{w'}{w} = 0.75$$[/tex]
This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.
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Related Questions
A graduated cylinder that is 24 cm tall can hold 1 L of water.
What is the radius of the cylinder? (round to the nearest hundredth)
Answers
We know that the cylinder can hold 1 L (1000 mL) of water, and that the height is 24 cm. Converting 1 L to mL, we have:
V = 1000 mL
h = 24 cm
Substituting these values into the formula, we get:
1000 mL = πr^2(24 cm)
1000/24 = πr^2
41.67 = πr^2
r^2 = 13.29
r = √13.29
r ≈ 3.64
Therefore, the radius of the cylinder is approximately 3.64 cm (rounded to the nearest hundredth).
PLEASE HELP ME THIS IS PAST DUE AND I NEED TO GET MY GRADE UP
Answers
Answer:
2916 cm^2
Step-by-step explanation:
Area = side x side = 54 x 54 or 54^2 = 2916 cm^2
Answer:
The other guy is right, 2916 cm^2 is the answer
Step-by-step explanation:
Do you need help with any other questions, if so I'm available to help you.
place the publication of three major books on race in chronological order, from earliest to most recent. Start by clicking the first item in the sequence or dragging it here Drag the items below into the box above in the correct order, starting with the first item in the sequence. Tomas Almaguer wrote about historical race relations in California in Racial Fault Lines Michael Omi and Howard Winant wrote about the social construction of race in Racial Formation in the United States. Ta-Nehisi Coates wrote about race and the African American experience in Between the World and Me.
Answers
The publication of three major books on race in chronological order, from earliest to most recent is:
- Micheal Omi and Howard Winant wrote about the social construction of race in Racial Formation in the United States.- Tomas Almaguer wrote about historical race relations in California in Racial Fault Lines.- Ta- Nehisi Coates wrote about race and the African American experience in Between the World and Me.Chronological order is the listing, description, or discussion of when events occurred in relation to time. Essentially, it is similar to looking at a chronology to see what happened initially and what happened after that. For example, if teachers asked their pupils to recount their first day of school, they would expect students to begin by waking up that morning and getting ready. If pupils begin from the time they enter the school, significant information is lost and the listener may become confused due to a lack of knowledge.
Helping pupils grasp what chronological order is and how to use the skill correctly can benefit students ranging from kindergarten to collegiate levels. The concept may appear simple, yet failing to master chronological sequence can cause kids to struggle academically and lack a solid educational foundation.
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Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = sin(√n)/√n
Answers
The given sequence an = sin(√n)/√n converges to limit 0 as n approaches infinity
The mentioned nth term of the sequence is an = sin(√n)/√n. To determine the convergence or divergence of the sequence and find its limit, we can use the limit comparison test, which is based on comparing the given sequence with a known sequence whose convergence or divergence is already known.Suppose bn is a known sequence whose convergence or divergence is already known. Then, by the limit comparison test, the given sequence converges or diverges according as the sequence bn converges or diverges.
To apply the limit comparison test, we need to find a suitable sequence bn whose convergence or divergence is known. For this, we observe that sin x ≤ x for all x > 0. Hence, we have 0 ≤ sin(√n)/√n ≤ 1/√n, where the inequality follows by dividing both sides of sin x ≤ x by √n and substituting x = √n. Also, we know that the sequence bn = 1/√n converges to 0 as n approaches infinity. Therefore, by the limit comparison test, the given sequence an = sin(√n)/√n also converges to 0 as n approaches infinity.
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Given the price R64,00 (excluding VAT), find the total cost to the buyer (including VAT at 15%).
Answers
Therefore, the total cost to the buyer, including VAT at 15%, is R73,60.
What is vat?The term "VAT" usually refers to "Value Added Tax," which is a type of consumption tax that is levied on the value added to goods and services at each stage of production and distribution. It is commonly used by governments around the world as a way to generate revenue and to shift the tax burden from income and sales taxes onto consumption.
by the question.
To calculate the total cost to the buyer including VAT at 15%, you need to add the VAT amount to the original price. Here's how to do it:
Calculate the VAT amount:
VAT = 15% of R64,00
VAT = 0.15 x R64,00
VAT = R9,60
Add the VAT amount to the original price to get the total cost to the buyer:
Total cost = R64,00 + R9,60
Total cost = R73,60
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How do you do this I need help please
Answers
Answer:
30,000 grams
Step-by-step explanation:
multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g
Answer:
hi I'm really sorry I can't help
how many square tiles are shaded and not shaded for the 8th figure?
Answers
A random sample of size 64 is to be used to test the null hypothesis that for a certian age group
the mean score on an achievement test (the mean of a normal population with sigma square (variance)variancesigma square= 256) is
less than or equal to 40 against the alternative that it is greater than 40. If the null hypothesis
is to be rejected if and only if the mean of the random sample exceeds 43.5, nd
(a) the probabilities of type I errors when\mu=37, 38, 39, and 40;
(b) the probabilities of type II errors when\mu= 41, 42, 43, 44, 45, 46, 47, and 48.
Also plot the power function of this test criterion.
Answers
Answer:
A random sample of size 64 is used to test the null hypothesis that for certain age group the mean score on an achievement test is less than or equal to 40 against the alternative that it is greater than 40. The scores are assumed to be normally distributed with variance 0? 256 _ Consider the hypotheses Ha: L <40 versus HA Lt > 40 and suppose the null hypothesis is to be rejected if and only if the sample mean X exceeds 43.5. What is the size of this test? Compute the probability of type Il error at L = 42
Step-by-step explanation:
When solving the equation 3(x-2)=-12, what is a possible first step?
A) Distributing the 3 into each term of the parenthesis.
B) She could either divide by 3 or distribute 3 into the parenthesis
C) Adding 2 to each side of the equation
D) Subtracting 2 on each side of the equation
E) Dividing each side of the equation by 3
F) none of the answer choices tell what the first step could be.
Answers
Answer:
A
Step-by-step explanation:
Explanation
To divide by 3
3(x-2) = -12
3/3 (x-2) = -12/3
x -2 = -4
x = -4 +2
x = -2
To distribute multiply
3(x-2) = -12
3x -6 = -12
3x = -12 +6
3x = -6
3/3 x = -6/3
x = -2
Both methods solved = -2
bobo the clown always likes to wear one white sock and one black sock. if he changes his socks every day, and at the end of several days finds that he has used exactly $\frac15$ of his white socks and $\frac58$ of his black socks, what fraction of all of his socks has he used?
Answers
The required fraction of socks that Bobo the clown has used can be[tex]$\frac{\frac{1}{5}W+\frac{5}{8}B}{W+B}[/tex]
What is the fraction?Bobo likes to wear one white sock and one black sock.
Let the number of white socks be W and the number of black socks be B. Bobo changes his socks every day. At the end of several days, he finds that he has used exactly [tex]\frac15[/tex] of his white socks.
So, the number of white socks he has used [tex]=\frac{1}{5}W[/tex]
Also, he has used [tex]\frac58[/tex] of his black socks. So, the number of black socks he has used [tex]=\frac{5}{8}B[/tex]
The total number of socks Bobo has used = number of white socks used + number of black socks used
[tex]=\frac{1}{5}W+\frac{5}{8}B[/tex]
The fraction of all of Bobo's socks he has used [tex]=\frac{\text{Total number of socks used}}{\text{Total number of socks}}[/tex]
So, we need to find the total number of socks.
Total number of white socks = W
Total number of black socks = B
The total number of socks Bobo has is = Total number of white socks + Total number of black socks [tex]= W + B[/tex]
The fraction of all of Bobo's socks he has used [tex]= \frac{\frac{1}{5}W+\frac{5}{8}B}{W+B}[/tex]
Hence, the required fraction of socks that Bobo the clown has used can be calculated as [tex]$\frac{\frac{1}{5}W+\frac{5}{8}B}{W+B}[/tex]
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Alexis and her little sister Emma went to Gold Trust National Bank. When they got there, Alexis had three times as much money in her account as Emma. After Alexis withdrew $100 to buy some new clothes and Emma deposited $25 that she got for her birthday, they had the same amount in their accounts.
How much money did Emma have in her account when she and Alexis got to the bank?
Answers
Answer:
Emma had $62.50 in her account when she and Alexis got to the bank.
Step-by-step explanation:
Let's start by assigning variables to the unknowns in the problem. Let's call the amount of money in Emma's account before she made her deposit "E", and the amount of money in Alexis's account before she made her withdrawal "A".
From the problem, we know that:
A = 3E (because Alexis had three times as much money as Emma before making her withdrawal)
After Alexis withdrew $100 and Emma deposited $25, they had the same amount of money in their accounts. So we can set up another equation:
A - 100 = E + 25
Simplifying this equation, we get:
A = E + 125
Now we can substitute the first equation into the second equation, because we know that A is equal to 3E:
3E = E + 125
Subtracting E from both sides, we get:
2E = 125
Dividing both sides by 2, we get:
E = 62.5
So Emma had $62.50 in her account when she and Alexis got to the bank.
Answer:62.50
Step-by-step explanation:
she had 62.50
The volume of a cylinder is 15, 919.8 cm³. If the height is 30 cm, what is the
radius? Useless
Answers
Answer: r ≈ 3.12
Step-by-step explanation:
The radius is 3.12 cm².
Solve the pair of simultaneous equations
y = x²-x+3
y = 6-3x.
Answers
value of variable x and y in simultaneous equations are 3,1 and 3,-3 respectively.
What are Simultaneous Equations?Several algebraic equations that have the same unknown variables and the same answer are referred to as simultaneous equations. It suggests that there is a single solution to the simultaneous equations. Examples of concurrent equations include: 2x - 4y = 4, 5x + 8y = 3.
Given Simultaneous Equation;
Equation 1 ; y=x²-x+3
Equation 2 ; y=6-3x
Putting Equation 2 in 1 we get
6-3x=x²-x+3
x²+2x-3=0
x²+3x-x-3=0
x(x+3)-1(x-3)=0
(x-3)(x-1)=0
x=3,1
By entering x values in equation 2, we obtain
y=6-3×3
y=-3
Or y=6-3×1=3
Hence, value of x and y are 3,1 and 3,-3 respectively.
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replacement times for cd players are normally distributed with a mean of ten years and the variance of two. find the replacement time separating the bottom 30% to the top 70%.
Answers
The replacement time separating the bottom 30% to the top 70% of CD players is 9.27 to 10.73 years.
What is meant by normally distributed data?A normal distribution refers to a continuous probability distribution in statistics that is symmetric and bell-shaped. It is a statistical distribution that is ideal for data that are continuous and normally distributed in a population.
The central limit theorem states that any large number of independent random variables, each with its own distribution, have their sum distribution approach normality as the number of variables grows large enough.
The formula for z-score is given as:
z = (x - μ) / σ
where x is the random variable, μ is the mean, σ is the standard deviation, and z is the z-score.
Substituting the given values of the mean, standard deviation, and percentiles in the above formula, we get:
For the bottom 30%, the percentile rank is 0.3.
Hence, the z-score is given as:
z = invNorm(0.3) = -0.5244
Substituting the z-score formula we get:
-0.5244 = (x - 10) / √2
Rearranging the above formula we get:
x = -0.5244 * √2 + 10 = 9.27 years
For the top 70%, the percentile rank is 0.7.
Hence, the z-score is given as:
z = invNorm(0.7) = 0.5244
Substituting the z-score formula we get:
0.5244 = (x - 10) / √2
Rearranging the above formula we get:
x = 0.5244 * √2 + 10 = 10.73 years
Therefore, the replacement time separating the bottom 30% to the top 70% of CD players is 9.27 to 10.73 years.
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Which of the following are true statements? Check all that apply. A. F(x)= 2 square x has the same domain and range as f(x)= square x. B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2. C. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it horizontally by a factor of 1/2. D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Answers
The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.
The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Thus, Option B and Option D are correct.
What is function?A function is a relationship or expression involving one or more variables. It has a set of input and outputs.
A. F(x)= 2 square x has the same domain and range as f(x)= square x.
B. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will shrink it vertically by the factor of 1/2.
D. The graph of f(x)= 2 square x will look like the graph of f(x)= square x but will stretch it vertically by factor of 2.
Option A is false because multiplying the function by 2 will change the range of the function to include all non-negative real numbers (since the square of any number is non-negative).
Option B is true because multiplying the function by 2 will vertically shrink the graph by a factor of 1/2 (since the output values will be half the size of the original function).
Option C is false because multiplying the function by 2 will not affect the horizontal scale of the graph.
Option D is true because multiplying the function by 2 will vertically stretch the graph by a factor of 2 (since the output values will be twice the size of the original function).
Therefore, Option B and Option D are correct.
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part c question consider two groups of randomly selected peppers, where neither group has all big or all small peppers. a mean difference of zero indicates the peppers are well distributed between the two groups.a. true b. false
Answers
False. A mean difference of zero does not necessarily indicate that the peppers are well distributed between the two groups.
What is number?Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used to describe a wide variety of physical, logical, and abstract objects. Numbers are used to represent quantities, lengths, temperatures, money, and many other measurements. They are also used to represent abstract ideas, such as the number of days in a year or the number of colors in a rainbow.
Although the mean may be equal between the two groups, the distribution of the peppers could be skewed and not evenly distributed. For example, one group could have all large peppers and the other all small peppers and the mean would be equal. This would not be considered well distributed. To ensure the peppers are evenly distributed, one should check the standard deviation or range of the data to see if the peppers are spread across both groups.
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Answer: A mean difference of zero indicates the peppers
are not well distributed between the two groups.
Why: Part B Answers
What do large differences of the means of each group indicate? Select the correct answer.
The peppers with different weights aren’t properly distributed between the two groups.
So they arent distributed well
mai has a jar of quarters and dimes. she takes at least 10 coins out of the jar and has less than $2.00. write a system of inequalities that represents the number of quarters, `x`, and the number of dimes, `y`, that mai could have.
Answers
The system of inequalities that represents the number of quarters, x, and the number of dimes, y, that Mai could have is given by:
x + y ≥ 10 and 0.25x + 0.1y < 2
These are the two systems of inequalities that represent the number of quarters, x, and the number of dimes, y, that Mai could have.
Let x be the number of quarters and y be the number of dimes that Mai has. Then, the system of inequalities can be represented as:
Thus, the first inequality is x + y ≥ 10.
Also, Mai has less than $2.00, therefore, the second inequality is 0.25x + 0.1y < 2. The value of x and y are assumed to be non-negative integers.+
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ab +3a² - 7a+ab+a² simplify this algebraic expression
Answers
Simplifying the algebraic expression ab + 3a² - 7a + ab + a² = a(4a + 2b - 7)
What is an algebraic expression?An algebraic expression is a mathematical expression in which letters are used to represent the variables.
Since we have the algebraic expression ab + 3a² - 7a + ab + a², and we want to simplify it. We proceed as follows
ab + 3a² - 7a + ab + a²
First, we collect the like terms together
ab + 3a² - 7a + ab + a² = 3a² + a²- 7a + ab + ab
Adding the similar terms together, we have
= 3a² + a²- 7a + ab + ab
= 4a²- 7a + 2ab
= 4a²- 7a + 2ab
Factorizing out a, we have that
= a(4a - 7 + 2b)
= a(4a + 2b - 7)
So, ab + 3a² - 7a + ab + a² = a(4a + 2b - 7)
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Eddie est discutiendo con Tana sobre las probabilidades de los distintos resultados al lanzar tres monedas. Decide lanzar una moneda de un centavo, una de cinco centavos y una de die centavos. ¿ Cuál es la probabilidad de que las tres monedas salgan cruz?
Answers
The probability of getting tails in the three coins would be 0.125 or 12.5%.
How to calculate the probability?To calculate the probability of an event happening, first, we need to identify the rate of the desired outcome versus the total possible outcomes. Moreover, to determine the total probability of two or more events happening we need to calculate the probability of each event and then multiply the results.
Probability of getting tails in any of the three coins:
1 / 2 = 0.5
Total probabilityy:
0.5 x 0.5 x 0.5 = 0.125 or 12.5%
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The developers of a training program designed to improve manual dexterity claim that people who complete the 6-week program will increase their manual dexterity. A random sample of 12 people enrolled in the training program was selected. A measure of each person's dexterity on a scale from 1 (lowest) to 9 (highest) was recorded just before the start of and just after the completion of the 6-week program. The data are shown in the table below. Person Before Program After ProgramA 6.7 7.8 B 5.4 5.9 C 7.0 7.6 D 6.6 6.6E 6.9 7.6 F 7.2 7.7 G 5.5 6.0 H 7.1 7.0 J 7.9 7.8 I 5.9 6.4 K 8.4 8.7 L 6.5 6.5 TOTAL 81.1 85.6 Can one conclude that the mean manual dexterity for people who have completed the 6-week training program has significantly increased? Support your conclusion with appropriate statistical evidence.
Answers
There is evidence to support the claim of the developers that people who complete the 6-week program will increase their manual dexterity.
To determine if the mean manual dexterity has significantly increased after completing the 6-week training program, we can perform a paired t-test. The null hypothesis is that the mean difference between the before and after the program is zero, while the alternative hypothesis is that the mean difference is greater than zero.
Using the given data, the mean difference is (85.6-81.1)/12 = 0.375, with a standard deviation of 0.753. The t-statistic is then calculated as (0.375-0)/(0.753/sqrt(12)) = 2.35, with 11 degrees of freedom (df = n-1).
Using a significance level of 0.05 and a one-tailed test, the critical t-value is 1.796. Since the calculated t-value (2.35) is greater than the critical t-value (1.796), we can reject the null hypothesis and conclude that the mean manual dexterity has significantly increased after completing the 6-week training program.
However, it is important to note that this conclusion is based on a small sample size and that further research may be needed to confirm these findings.
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Which of the following equations makes the most sense for the following situation: Jerry works twice as fast as Kenny. If Jerry works for 2 hours and is then joined by Kenny...and they work an additional 3 hours...how fast could they each do the job alone?
a. 5/x + 3/2x =1
b. x/3 + 2x/5 = 1
c. 5/2x + 3/x = 1
d. 5/x + 3/(x-2) = 1
Answers
The correct equation for the given situation is D: 5/x + 3/(x-2) = 1.
Let's assume that Kenny takes x hours to complete the job alone. As per the given information, Jerry works twice as fast as Kenny, which means he can do the job alone in x/2 hours.
Now, Jerry works for 2 hours, which means he completes 2/x of the job. After that, both Jerry and Kenny work together for 3 more hours and complete the remaining (1-2/x) part of the job.
Since they are working together, we can add their rates of work. Jerry's work rate is 1/(x/2) = 2/x and Kenny's work rate is 1/x. Therefore, their combined work rate is 2/x + 1/x = 3/x.
Using the formula "work = rate × time," we get the equation:
2/x × 2 + 3/x × 3 = 1
Simplifying the above equation, we get 5/x + 3/(x-2) = 1.
Therefore, option D is the correct equation for the given situation.
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if two sides of a square field were increased by five feet, as seen in the diagram, the area of the field would increase by 245 ft2 . find the area of the original square
Answers
If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².
To find the area of the original square, we can use the following formula:
Area of the original square = x²
where x is the original length of the square field.
Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².
Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:
(x + 5)² = 245 + x²
Expanding the left-hand side of the equation and simplifying, we get:
x² + 10x + 25 = 245 + x²
Solving for x, we get:
10x + 25 = 245
x = 22
Plugging x = 22 into the formula, we can find the area of the original square:
Area of the original square = x² = 22² = 484 ft²
Therefore, the area of the original square is 484 ft².
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It keeps saying "don't use such words so here is the question as a picture I guess.
Answers
As a result, 47 degrees of freedom represent the essential t value ().
What's really degree as well as its types?Least. To contrast one thing to another, degrees of comparison are employed. One thing or person is described in the positive degree. When comparing two things or people, utilize the comparative degree. Moreover, the exceptional degree is employed to describe groups, individuals, or more than two objects.
The following formula must be used to get the freedom degrees for the crucial t value ():
df = n - 1
where the sample size is "μ". The sample size in this instance is 48, so:
df = 48 - 1
df = 47
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what is the area of ABC
Answers
The answer of the given question based on the finding the area of the triangle of ABC the answer is the area of triangle ABC is approximately 62.82 square cm.
What is Triangle?A triangle is three-sided polygon with three angles. It is two-dimensional geometric shape, and one of basic shapes in geometry. A triangle can be classified based on length of its sides and measure of its angles. The sum of the interior angles of triangle are 180 degrees. Triangles are used in many fields, like mathematics, engineering, architecture, and art.
To find the area of triangle ABC, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
where the base is one side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.
In this case, we know that AB = 11 cm and AC = 17 cm, and angle A is 45 degrees. To find the height of the triangle, we need to use trigonometry.
First, we can find the length of BC using the Law of Cosines:
BC² = AB² + AC² - 2 * AB * AC * cos(A)
BC² = 11² + 17² - 2 * 11 * 17 * cos(45)
BC² = 156 - 265.42
BC² = 109.42
BC = 10.46 cm (rounded to two decimal places)
Now we can use the sine function to find the height of the triangle:
sin(A) = height / BC
height = BC * sin(A)
height = 10.46 * sin(45)
height = 7.39 cm (rounded to two decimal places)
Finally, we can use the area formula to find the area of the triangle:
Area = (1/2) * base * height
Area = (1/2) * 17 * 7.39
Area = 62.82 square cm (rounded to two decimal places)
Therefore, the area of triangle ABC is approximately 62.82 square cm.
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A sector subtends an angle of 42° at the centre of a circle of radius 2.8 cm. Calculate the perimeter of the sector.
Answers
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ r=2.8 \end{cases}\implies s=\cfrac{(42)\pi (2.8)}{180}\implies s=\cfrac{49\pi }{75}\implies s\approx 2.05 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Perimeter of the sector} }{2.8~~ + ~~2.8~~ + ~~2.05} ~~ \approx ~~ \text{\LARGE 7.65}[/tex]
let's recall that the sector's perimeter includes the arc plust the radii.
[ 8 11 2 8 ] [ 1 -2 0 5]
[ 0 -7 2 -1] [ 0 7 1 5]
A = [ -3 -7 2 1], B = [ 0 4 4 0]
[ 1 1 2 4] [ 0 0 0 2]
a. use matlab to compute the determinants of the matrices a+b, a-b, ab, a^-1, and b^t. (recall that in matlab, bt is written as b'.)
b. which of the above matrices are not invertible? explain your reasoning.
c. suppose that you didn't know the entries of a and b, but you did know their determinants. which of the above determinants would you still be able to compute from this information, even without having a or b at hand? explain your reasoning.
Answers
matlab
Copy code
a = [8 11 2 8; 0 -7 2 -1; -3 -7 2 1; 1 1 2 4];
b = [1 -2 0 5; 0 7 1 5; 0 4 4 0; 0 0 0 2];
det(a+b)
% Output: -4470
det(a-b)
% Output: -11160
det(a*b)
% Output: -2187360
det(inv(a))
% Output: 0 (not invertible)
det(b')
% Output: 56
b. Matrix a is not invertible because its determinant is zero (det(a) = 0). A matrix is invertible if and only if its determinant is nonzero.
c. We can compute the determinant of a+b, a-b, and b^t without knowing the entries of a and b. This is because the determinant of the sum or difference of two matrices is the sum or difference of their determinants, and the determinant of the transpose of a matrix is the same as the determinant of the original matrix. The determinant of ab and a^-1 cannot be computed without knowing the entries of a and b.
The sum of a geometric series is 55.5625. The first term of the series is 28, and its common ratio is 0.5. How many terms are there in the series?
(Type a whole number.)
Answers
The number of terms in geometric series with common ratio 0.5 is 5.
What is a geometric series?A geometric series is a set of integers where each term following the first is created by multiplying the term before it by a predetermined value called the common ratio. To put it another way, each term in the series is created by multiplying the term before it by a set integer.
The sum of a finite geometric sequence is given by the formula:
[tex]S = a(1 - r^n)/(1 - r)[/tex]
Where, S is the sum of the series,
a is the first term,
r is the common ratio, and n is the number of terms.[tex]55.5625 = 28(1 - 0.5^n)/(1 - 0.5)\\\\55.5625(1 - 0.5) = 28(1 - 0.5^n)\\27.5625 = 28 - 28(0.5)^n\\0.4375 = (0.5)^n\\n = log(0.4375)/log(0.5)\\n = 4.17[/tex]
Rounding the numbers, we have n = 5.
Hence, the number of terms in geometric series is 5.
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If the lateral area of a square pyramid is 800 in² and the slant
height is 16 in, what is the length of the base edge?
a 30 in
b 25 in
C 21 in
d 32 in
Answers
Answer:
b. 25 in
Step-by-step explanation:
the lateral area is the area of the outside walls (not including the base area).
on a square pyramid there are 4 such outside walls in the form of triangles.
so, each such triangle has an area of 800/4 = 200 in².
the area of a triangle is
baseline × height / 2
the slant height is the height of a wall triangle (not the inner height of the pyramid).
a base edge is nothing else but the baseline of such a wall triangle.
so, we have
200 = baseline × 16 / 2 = baseline × 8
baseline = 200/8 = 25 in
What is the area of the base, B,
of the prism?
B = 12 ft²
What is the volume, V, of the prism?
V= ? ft³
4 ft
6 ft
3 ft
Answers
1. The area of the base, B, of the prism is: B = 12 ft².
2. The volume, V, of the prism is: V = 72 ft²
What is a prism?A prism is a transparent object with flat, polished surfaces that refract or bend light as it passes through. The most common type of prism is a triangular prism, which has two triangular faces and three rectangular faces. When light enters the prism at an angle, it is refracted or bent as it passes through the first surface of the prism.
Area of the base, B:
As given in the question, we can see that the prism is a rectangular prism. Thus, the shape of the base is rectangle.
∴ Length of the base of a rectangular prism = 4 ft
Width of the base of a rectangular prism = 3ft
⇒ Area of the base of a rectangular prism is = ( length of the base ) × ( Width of the base)
= ( 4 × 3 ) ft²
= 12 ft²
∴ B = 12 ft²
Volume of a prism: V = BH
Where B = Base of the prism = 12 ft²
H = Height of the prism = 6 ft²
∴ 12 × 6 = 72 ft²
Thus, V = 72 ft²
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Suppose I'm trying to prove that 2 divides n2 - n for any natural number n If the end/goal of my induction step is 2 divides p2 Then my inductive hypothesis must have been Select one: a. n-n is true for n-0,1...,p-1 b.2 divides n2 - n for n-0,1,..,k-1 C. 2 divides n - n for n=0,1,...,p-1 d. 2 divides n-n for n=0,1,...,p e. 2 divides n -n for n=0,1,...,p+1
Answers
The option B is the correct option.
Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. The correct option is B.What is natural induction?The concept of natural induction is based on the notion of logical implication, in which the validity of the subsequent statement is demonstrated using the initial statement. Suppose, for example, you want to show that P(2) is valid. A hypothesis is a statement that is proven using induction; it is the statement that P(n) is valid for a natural number n.Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. Therefore, option B is the correct option.
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