The gcd of 630 and 147 can be expressed as 21 = (-3) x 630 + 13 x 147.
Here are the solutions for each pair of numbers:
(a) To find the gcd of 56 and 42, we can use the Euclidean algorithm:
56 = 42 x 1 + 14
42 = 14 x 3 + 0
So the gcd of 56 and 42 is 14. To express 14 as a linear combination of 56 and 42, we can use the extended Euclidean algorithm:
14 = 56 - 42 x 1
= (-1) x 56 + 1 x 42
So the gcd of 56 and 42 can be expressed as 14 = (-1) x 56 + 1 x 42.
(b) To find the gcd of 81 and 60, we can again use the Euclidean algorithm:
81 = 60 x 1 + 21
60 = 21 x 2 + 18
21 = 18 x 1 + 3
18 = 3 x 6 + 0
So the gcd of 81 and 60 is 3. To express 3 as a linear combination of 81 and 60, we can use the extended Euclidean algorithm:
3 = 21 - 18 x 1
= 21 - (60 - 21 x 2) x 1
= (-1) x 60 + 3 x 21
= (-1) x 60 + 3 x (81 - 60 x 1)
So the gcd of 81 and 60 can be expressed as 3 = (-1) x 60 + 3 x 81.
(c) To find the gcd of 259 and 77, we can use the Euclidean algorithm:
259 = 77 x 3 + 28
77 = 28 x 2 + 21
28 = 21 x 1 + 7
21 = 7 x 3 + 0
So the gcd of 259 and 77 is 7. To express 7 as a linear combination of 259 and 77, we can use the extended Euclidean algorithm:
7 = 28 - 21 x 1
= 28 - (77 - 28 x 2) x 1
= 3 x 28 - 77 x 1
= 3 x (259 - 77 x 3) - 77 x 1
So the gcd of 259 and 77 can be expressed as 7 = 3 x 259 - 10 x 77.
(d) To find the gcd of 72 and 42, we can use the Euclidean algorithm:
72 = 42 x 1 + 30
42 = 30 x 1 + 12
30 = 12 x 2 + 6
12 = 6 x 2 + 0
So the gcd of 72 and 42 is 6. To express 6 as a linear combination of 72 and 42, we can use the extended Euclidean algorithm:
6 = 42 - 30 x 1
= 42 - (72 - 42 x 1) x 1
= (-1) x 72 + 2 x 42
So the gcd of 72 and 42 can be expressed as 6 = (-1) x 72 + 2 x 42.
(e) To find the gcd of 80 and 61, we can use the Euclidean algorithm:
80 = 61 x 1 + 19
61 = 19 x 3 + 4
19 = 4 x 4 + 3
4 = 3 x 1 + 1
3 = 1 x 3 + 0
So the gcd of 80 and 61 is 1. To express 1 as a linear combination of 80 and 61, we can use the extended Euclidean algorithm:
1 = 19 - 4 x 3
= 19 - (61 - 19 x 3) x 3
= 10 x 19 - 3 x 61
= 10 x (80 - 61 x 1) - 3 x 61
So the gcd of 80 and 61 can be expressed as 1 = 10 x 80 - 13 x 61.
(f) To find the gcd of 630 and 147, we can use the Euclidean algorithm:
630 = 147 x 4 + 42
147 = 42 x 3 + 21
42 = 21 x 2 + 0
So the gcd of 630 and 147 is 21. To express 21 as a linear combination of 630 and 147, we can use the extended Euclidean algorithm:
21 = 147 - 42 x 3
= 147 - (630 - 147 x 4) x 3
= (-3) x 630 + 13 x 147
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tres veces la diferencia de 15 y 13
The Beta [a, b] density has the form: f(x) = {[(a+b)/([(a) r()) } Xa-1 (1 - X)B-1 + - where a and ß are constants and 0 SX S1. You can check Blitzstein's book to get more details for this distribution (p. 380, or table C on p. 605).
The Beta distribution is a continuous probability distribution with support on the interval [0,1], and is often used to model random variables that have limited range, such as probabilities or proportions.
The Beta [a, b] density has the form f(x) = {[(a+b)/([(a) r()) } Xa-1 (1 - X)B-1 +, where a and b are constants and 0 <= x <= 1. This density function describes the probability of observing a value x from a Beta [a, b] distribution.
The parameters a and b are often referred to as shape parameters, and they control the shape of the distribution. Specifically, the larger the values of a and b, the more peaked the distribution will be, while smaller values of a and b will lead to flatter distributions.
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Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) provides a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.
Formulate null and alternative hypotheses to test the analyst's claim.
Null hypothesis: The percentage of stocks traded on the NYSE that went up on January 31, 2006, is not 30%.
Alternative hypothesis: The percentage of stocks traded on the NYSE that went up on January 31, 2006, is 30%.
To test the financial analyst's claim that 30% of the stocks traded on the NYSE went up on the same day, we can formulate the null and alternative hypotheses using the information about the DJIA stock market performance. Here are the hypotheses:
Null Hypothesis (H0): The proportion of stocks that increased in price on the NYSE is 30% (p = 0.30).
Alternative Hypothesis (H1): The proportion of stocks that increased in price on the NYSE is not 30% (p ≠ 0.30).
These hypotheses will help determine whether the analyst's claim about the overall stock market performance is accurate or not.
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0.2w – 5 = 13
Solve pleaseeee I'm struggling
Answer:
90
Step-by-step explanation:
true or false? when performing regression analysis, different samples will all yield the same sample regression line.
False. When performing regression analysis, different samples will not necessarily yield the same sample regression line.
This is because the sample regression line is based on the specific data points in the sample, and different samples may have different data points that can lead to different regression lines. However, if the samples are representative of the same population and the relationship between the variables is consistent, the regression lines may be similar. The term "content loaded" does not apply to this question.
False. When performing regression analysis, different samples will not all yield the same sample regression line. The regression line depends on the specific data points in the sample, so if you have different samples, it's likely that their regression lines will be different as well.
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Jean invested $380 in stocks. Over the next 5 years the value of her investment grew as shown in the accompanying table. Find the equation that best models the data
An equation that best models the data is [tex]y = 380(1.04)^x[/tex]
How to write and determine an exponential function?In Mathematics and Geometry, an exponential function is typically represented by the following mathematical equation:
[tex]f(x) = a(b)^x[/tex]
Where:
x represent time.a represent the base value, vertical intercept, or y-intercept.b is the growth rate, common ratio, and rate of change.Based on the table, we would calculate the value of a and b as follows;
[tex]f(x) = a(b)^x[/tex]
380 = a(b)⁰
a = 380
Next, we would determine value of b as follows;
395 = 380(b)¹
395 = 380b
b = 395/380
b = 1.04
Therefore, the required exponential function is given by;
[tex]f(x) = y = 380(1.04)^x[/tex]
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
a circle has radius 6 units. for each arc length, find the area of a sector of this circle which defines that arc length. 4 units 5 units 10 units l units
The areas of the sectors for arc lengths of 4, 5, 10, and l units are approximately 3.14, 3.93, 9.42, and 0.84l units², respectively.
To find the area of a sector of a circle, we need to use the formula:
Area of sector = (angle of sector/360) x πr²
where r is the radius of the circle.
For each given arc length, we need to find the angle of the sector first. The formula for finding the angle of a sector is:
angle of sector = (arc length / radius) x 180/π
Using this formula, we get:
For 4 units arc length:
angle of sector = (4/6) x 180/π ≈ 38.2 degrees
Area of sector = (38.2/360) x π x 6² ≈ 3.14 units²
For 5 units arc length:
angle of sector = (5/6) x 180/π ≈ 47.7 degrees
Area of sector = (47.7/360) x π x 6² ≈ 3.93 units²
For 10 units arc length:
angle of sector = (10/6) x 180/π ≈ 95.5 degrees
Area of sector = (95.5/360) x π x 6² ≈ 9.42 units²
For l units arc length:
angle of sector = (l/6) x 180/π ≈ (30l/π) degrees
Area of sector = [(30l/π)/360] x π x 6² ≈ 0.84l units²
So, the areas of the sectors for arc lengths of 4, 5, 10, and l units are approximately 3.14, 3.93, 9.42, and 0.84l units², respectively.
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Based on the scatter plot below, which is a better prediction for x when y = 9?
101
8
9
N
0
2
Submit
6
●
9
8
X
10
According to the scatter plot below, when x = 5, the value of y is 1.
We know that,
A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.
A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables).
With a particular confidence interval, a scatter plot might imply several types of relationships between variables.
Weight and height, for example, would be on the y-axis, whereas height would be on the x-axis. Positive (increasing), negative (falling), or null correlations exist (uncorrelated).
Here,
Based on the scatter plot below, when x=5 then value of y is 1.
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the margin of error of a confidence interval is the error from biased sampling methods. group of answer choices true false
The statement "the margin of error of a confidence interval is the error from biased sampling methods" is false. The margin of error of a confidence interval is not the error from biased sampling methods.
The margin of error represents the range within which the true population parameter (such as the mean or proportion) is likely to be found with a certain level of confidence. It is not directly related to biased sampling methods, which refer to systematic errors in the sampling process that may lead to inaccurate or unrepresentative results.
The margin of error of a confidence interval is the measure of how much the sample statistic is likely to differ from the population parameter, given a certain level of confidence. It is affected by sample size, variability, and the chosen level of confidence, but not biased sampling methods.
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For a study that has one independent variable with three levels and 4000 participants per level, what is the recommended maximum number of analyses (comparisons or contrasts) to plan? (hint: This is the same as the number of independent research questions that can be asked)
a. One, because this is the number of independent variables.
b. Two, because this is one less than the number of groups.
c. 11999, because this is one less than the number of participants.
d. Any number...as long as the analysis is pre-registered there is nothing to worry about.
For a study that has one independent variable with three levels and 4000 participants per level, the recommended maximum number of analyses (comparisons or contrasts) to plan b. Two, because this is one less than the number of groups.
The recommended maximum number of analyses (comparisons or contrasts) to plan for a study that has one independent variable with three levels and 4000 participants per level is b. Two, because this is one less than the number of groups. Each level of the independent variable will need to be compared to the other two levels, resulting in two independent research questions. It is important to limit the number of analyses to avoid increasing the chance of making a Type I error.
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Which statement about f(x) = 12x² - 36x + 27 is true?
A The zeros are t
because f(x) = 3(2x - 3)(2x + 3).
The zeros are
because f(x) = 3(2x - 3)(2x + 3).
The only zero is
because f(x) = 3(2x - 3)².
The only zero is because f(x) = 3(2x - 3)².
Answer: the last one
Step-by-step explanation:
factor the quadratic expression, the greatest common factor is 3, 3(4x^2-12x+9) is a perfect trinomial square. There is only one root 3/2 but it is a double
A certain test preparation course is designed to help students improve their scores on the GRE exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 7 students' scores on the exam after completing the course:
24,6,21,8,16,10,18
Using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal
Step 1:Calculate the sample mean for the given sample data. Round your answer to one decimal place.
Step 2:Calculate the sample standard deviation for the given sample data. Round your answer to one decimal place.
Step 3:Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Step 4:Construct the 80% confidence interval. Round your answer to one decimal place (Lower endpoint, Upper endpoint)
Step 1: The sample mean is (24+6+21+8+16+10+18)/7 = 15.7 (rounded to one decimal place)
Step 2: The sample standard deviation is calculated using the formula:
s = sqrt[(Σ(x - mean of x)^2) / (n - 1)]
where Σ is the sum of the squared deviations from the mean, mean of x is the sample mean, and n is the sample size.
Using the given data, we get:
s = sqrt[((24-15.7)^2 + (6-15.7)^2 + (21-15.7)^2 + (8-15.7)^2 + (16-15.7)^2 + (10-15.7)^2 + (18-15.7)^2) / (7-1)]
s = 6.679 (rounded to one decimal place)
Step 3: To find the critical value, we use a t-distribution with n-1 degrees of freedom and a confidence level of 80%. From a t-distribution table or using a calculator, we find the critical value to be 1.397 (rounded to three decimal places).
Step 4: Using the formula for the confidence interval:
CI = mean of x ± t*(s / sqrt(n))
where mean of x is the sample mean, t is the critical value, s is the sample standard deviation, and n is the sample size.
Plugging in the values, we get:
CI = 15.7 ± 1.397*(6.679 / sqrt(7))
CI = (9.47, 21.93)
So the 80% confidence interval for the average net change in a student's score after completing the course is (9.47, 21.93).
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Pls i need this !!!!
Answer:
$80
Step-by-step explanation:
please mark brainliest answer
Find the area of the triangle pictured.
Answer:
15.75cm^2
Step-by-step explanation:
9 × 3.5 × 1/2 = 15.75cm^2
I hope the answer is correct
Can someone help me asap? It’s due today. I will give brainliest if it’s all correct.
Please do part a, b, and c
Answer:
A: Chicken: 75 / Steak: 125 / Fish: 50
B: The wedding planner's claim is valid.
C: The wedding planner's claim is valid because if we follow the sample and use the ratio, the total amount of guests who might choose chicken and steak is about 200 people.
Apologies if this answer isn't thorough enough, I tried to do it as quickly as possible. Best of luck!
A marketing research firm wishes to study the relationship between wine consumption and whether a person likes to watch professional tennis on television. One hundred randomly selected people are asked whether they drink wine and whether they watch tennis. The following results are obtained:
Based on the results obtained, the firm can analyze the data and determine if there is a significant correlation between the two variables. This information can be used to develop marketing strategies for wine and tennis-related products and services.
A marketing research firm is conducting a study to understand the relationship between wine consumption and an interest in watching professional tennis on television. They randomly select 100 people and gather data on their wine-drinking habits and whether they watch tennis or not.
To analyze the data, the marketing research firm can create a cross-tabulation, also known as a contingency table, with two rows representing the categories of wine consumption (wine drinkers and non-wine drinkers) and two columns representing the categories of watching tennis (tennis watchers and non-tennis watchers).
From the data collected, the firm can calculate the percentages of people in each category (e.g., percentage of wine drinkers who watch tennis, percentage of non-wine drinkers who watch tennis, etc.) to determine if there is a relationship between wine consumption and an interest in watching professional tennis on television.
The marketing research firm can then use statistical tests, such as the chi-square test, to assess if the observed relationship between wine consumption and tennis watching is statistically significant or if it could have occurred by chance.
In conclusion, the marketing research firm is using a systematic approach to study the relationship between wine consumption and an interest in watching professional tennis on television. This research can provide valuable insights for businesses in the wine and sports industries to better target their marketing efforts.
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In the first question, we determined the equilibrium point for the supply and demand functions given below to be (1600, 80). Given this, find the producer surplus at that point. Round your answer to the nearest cent if necessary and do not include the dollar sign. 3200 p = D()- p = S(x) 25 V
The producer surplus at the equilibrium point (1600, 80) is $64,000.
In order to calculate the producer surplus, we first need to find the equilibrium price and quantity, which you have already determined as (1600, 80). Now, let's find the supply function, S(x), and the price at which quantity supplied is zero.
You've provided the supply function as "p = S(x) 25 V", but it seems to have some typos. Assuming the correct supply function is p = 25x, let's proceed.
Set the supply function, p = 25x, equal to 0:
0 = 25x
x = 0
Now we have the points (0, 0) and (1600, 80) to calculate the producer surplus. Producer surplus is represented by the area of a triangle. The base of the triangle is the equilibrium quantity (1600), and the height is the equilibrium price (80).
Use the formula for the area of a triangle: Area = (1/2) * base * height
Producer Surplus = (1/2) * 1600 * 80
Producer Surplus = 0.5 * 128000
Producer Surplus = 64,000
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at burnt mesa pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. wood from several excavations gave a mean of (year) 1244 with a standard deviation of 44 years. the distribution of dates was more or less mound-shaped and symmetric about the mean. use the empirical rule to estimate the following. (a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found between ___ and ___ a.d.
(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found between ___ and ___ a.d.
(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found between ___ and ___ a.d.
(a) Using the empirical rule, we know that about 68% of the data falls within one standard deviation of the mean. Since the standard deviation is 44 years, we can calculate the range of years by adding and subtracting 44 from the mean of 1244. So, the range of years centered about the mean in which about 68% of the data will be found is between 1200 and 1288 A.D.
(b) About 95% of the data falls within two standard deviations of the mean. So, we can calculate the range of years by adding and subtracting twice the standard deviation (2 x 44 = 88) from the mean of 1244. The range of years centered about the mean in which about 95% of the data will be found is between 1156 and 1332 A.D.
(c) Almost all of the data falls within three standard deviations of the mean. So, we can calculate the range of years by adding and subtracting three times the standard deviation (3 x 44 = 132) from the mean of 1244. The range of years centered about the mean in which almost all of the data will be found is between 1112 and 1376 A.D.
Hi! I'd be happy to help you with this question. We'll use the empirical rule, which states that for a mound-shaped and symmetric distribution:
(a) About 68% of the data will fall within 1 standard deviation from the mean. In this case, the mean is 1244 and the standard deviation is 44 years. So, the range will be between (1244 - 44) and (1244 + 44), or 1200 and 1288 A.D.
(b) About 95% of the data will fall within 2 standard deviations from the mean. The range will be between (1244 - 2 * 44) and (1244 + 2 * 44), or 1156 and 1332 A.D.
(c) Almost all the data (approximately 99.7%) will fall within 3 standard deviations from the mean. The range will be between (1244 - 3 * 44) and (1244 + 3 * 44), or 1112 and 1376 A.D.
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what will the the measures of the interior be?
The sum of the measures all the interior angles of a polygon having 14 sides is 2160°.
How to calculate the sumThe formula we use for this is
Sum of interior angles of a polygon
= ( n-2)*180
Where “n” is the number of sides of the polygon.
Here n=14
So, sum = (14–2)*180 = 2160 degrees
Therefore, the sum of the measures all the interior angles of a polygon having 14 sides is 2160°.
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What will be the sum of the measures all the interior angles of a polygon having 14 sides?
Please help me solve this problem! I need help. where to start?
Answer:
150
Step-by-step explanation:
An equilateral triangle has 3 congruent angles.
Each angle of an equilateral triangle measures 60°.
A square has 4 right angles.
Each angle of a square measures 90°.
The measures of the 2 angles of equilateral triangle and one right angle of the square have a total measure of
60° + 60° + 90° = 210°
A full circle has a degree measure of 360°.
x° = 360° - 210°
x = 150
Determine the number of terms required to approximate the sum of the series with an error of less than 0.001.
∑
[infinity]
n=4
(−1)n+1
n4
You need approximately 5 terms (starting from n=4) to achieve an error less than 0.001. To determine the number of terms required to approximate the sum of the series with an error of less than 0.001.
We can use the alternating series error bound formula:
Error ≤ |Rn| ≤ an+1
Where Rn is the remainder or error in the nth partial sum, and an+1 is the absolute value of the (n+1)th term in the series.
In this case, the alternating series is:
∑
[infinity]
n=4
(−1)n+1
n4
To find the absolute value of the (n+1)th term, we can plug in n+1 for n:
|an+1| = |(−1)n+2/(n+1)4|
Since we want the error to be less than 0.001, we can set up the inequality:
|an+1| ≤ 0.001
Plugging in the formula for |an+1| and solving for n, we get:
|(−1)n+2/(n+1)4| ≤ 0.001
(n+1)4 ≥ 1000
Taking the fourth root of both sides, we get:
n+1 ≥ 5.623
n ≥ 4.623
Therefore, we need at least 5 terms to approximate the sum of the series with an error of less than 0.001.
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A spinner with four sections is spun 30 times. (R=7 Y=8 B=6 G=9) Based on these results, what is the experimental probability that the next time the spinner is spun, it lands on yellow?
Answer is - 4/15
The experimental probability it lands on yellow is 4/5
What is the experimental probability it lands on yellow?From the question, we have the following parameters that can be used in our computation:
Number of times = 30
Results: (R=7 Y=8 B=6 G=9)
The experimental probability it lands on yellow is
P(Yellow) = Y/Total
So, we have
P(Yellow) = 8/30
Simplify
P(Yellow) = 4/15
Hence, the probability is 4/15
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April is filling six identical cones for her piñata. Each cone has a radius of 1.5 inches and height of 9 inches.
What is the total volume of the cones?
True or False??
1. If Z is a random variable from a standard normal distribution and if P(Z
2. If z is a random variable with a standard normal distribution and if a is a positive number and if P(z > a) = 0.15, then P(-a < z < a) = 0.7?
1. True or False? If Z is a random variable from a standard normal distribution and if P(Z
It seems like the question is incomplete. Please provide the complete question to get an accurate answer.
2. True or False? If z is a random variable with a standard normal distribution and if a is a positive number and if P(z > a) = 0.15, then P(-a < z < a) = 0.7?
Answer: True
Explanation: Since z follows a standard normal distribution, it is symmetric around the mean (which is 0). So, P(z > a) = P(z < -a) = 0.15. To find the probability between -a and a, we can use the property P(-a < z < a) = 1 - P(z > a) - P(z < -a) = 1 - 0.15 - 0.15 = 0.7.
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Find the median 0. 6, 0. 9, 1. 7, 1. 1, 2. 5, 0. 6
The median of the set of numbers after arranging them in order from least to greatest {0.6, 0.9, 1.7, 1.1, 2.5, 0.6} is 1.
To find the median of a set of numbers, we need to first arrange them in order from least to greatest.
The set of numbers given is 0.6, 0.9, 1.1, 1.7, 2.5, and 0.6.
Arranging them in order, we get 0.6, 0.6, 0.9, 1.1, 1.7, 2.5.
Since there are six numbers in this set, the median is the middle number when they are arranged in order. In this case, the middle numbers are 0.9 and 1.1. To find the median, we take the average of these two numbers:
Median = (0.9 + 1.1)/2 = 1.
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Step-by-step explanation:
0.6,0.6,0.9,1.1,1.7,2.5
The median is 0.9+1.1 / 2
2 /2 = 1
the median of the distribution is 1
At the beginning of a population study, a city had 350,000 people. Each year since, the population has grown by 4.4%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t .
Answer: The exponential function that models the population growth of the city over time is:
y = 350,000 * (1 + 0.044)^t
where t is the number of years since the start of the study, y is the city's population, and 0.044 is the annual growth rate expressed as a decimal.
The function is an example of exponential growth, where the population is increasing at a constant rate over time.
Step-by-step explanation:
the price of a ball should not be more than $2. which inequality can be used to represent this problem?
In summary, the inequality x ≤ 2 represents the problem "the price of a ball should not be more than $2" and means that the value of x (the price of the ball) must be less than or equal to 2.
An inequality is a mathematical expression that compares two values and indicates whether they are equal or not, or whether one is greater than or less than the other. In this case, we want to represent the problem "the price of a ball should not be more than $2" using an inequality.
Let x be the price of the ball. The expression "the price of a ball should not be more than $2" means that the price of the ball, represented by x, must be less than or equal to $2. We can write this inequality as:
x ≤ 2
The symbol "≤" means "less than or equal to," and it indicates that the value of x should be less than or equal to 2. For example, if the price of the ball is $1.50, then x is less than 2, and the inequality x ≤ 2 is true. However, if the price of the ball is $3, then x is greater than 2, and the inequality x ≤ 2 is false.
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I need help with this question
In the given right triangle, using SOH CAH TOA, the value of x is 9
Trigonometry: Calculating the value of xFrom the question, we are to determine the value of x in the given diagram.
The diagram, shows a right triangle with a hypotenuse of 18 and included angle of 30°. x is opposite side.
To determine the value of x, we will use SOH CAH TOA
Where
sin (angle) = Opposite / Hypotenuse
cos (angle) = Adjacent / Hypotenuse
tan (angle) = Opposite / Adjacent
Thus,
We can write that
sin (30°) = x / 18
1/2 = x / 18
Cross multiply
2 × x = 1 × 18
2x = 18
Divide both sides by 2
2x / 2 = 18 / 2
x = 9
Hence, the value of x is 9
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units and the center of the circle is (1, 0). Then the correct options are A, B, and E.
Given that:
Equation of circle, x² + y² - 2x - 8 = 0
Convert the equation into a standard form, then we have
x² + y² - 2x = 8
x² - 2x + 1 + y² = 9
(x - 1)² + y² = 3²
The radius of the circle is 3 units and the center of the circle is (1, 0). Then the correct options are A, B, and E.
More about the equation of the circle link is given below.
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The complete question is given below.
Xion baked 9 brownies for his friends. He wants to share them equally among his 4 friends so that everyone gets the same amount. If he wants to use all the brownies, how many brownies will each child get?
Answer:
(Excluding Xion) Each person will get 2 1/4 brownies
Step-by-step explanation:
9 brownies distributed equally to 4 friends. If each person gets two brownies, there is one left over. Divide 1 by 4 and you get 1/4. 1/4 in decimal form is 0.25. 2+0.25=2.25
Or you could just use a calculator to divide 9 by 4 and it would come up with 2.25