The average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night
According to the given data,
Sample size n = 101
Sample mean x = 6.5
Standard deviation s = 2.14
Level of confidence C = 96%
Using a 96% confidence level, the value of t* for 100 degrees of freedom is 2.081, as given in the question.
Now, the formula for the confidence interval is:x ± (t* × s/√n)Here, x = 6.5, s = 2.14, n = 101, and t* = 2.081
Substituting the values in the above formula, we get:
Lower limit = x - (t* × s/√n) = 6.5 - (2.081 × 2.14/√101) = 6.28
Upper limit = x + (t* × s/√n) = 6.5 + (2.081 × 2.14/√101) = 6.72
Therefore, the 96% confidence interval for the average number of hours of sleep for working college students is between 6.28 and 6.72 hours of sleep each night.
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Ryan buys some jumpers to sell on a stall. He spends £190 buying 80 jumpers. He sells 50% of the jumpers for £12 each. He then puts the rest of the jumpers on a Buy one get one half price offer. He manages to sell half the remaining jumpers using this offer. How much profit does Ryan make?
Ryan makes a profit of £240. the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
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Use the table you created to play the "Two Spinner
Game" below.
For this game, we say the spinners "match" if they
land on the same color (e.g., both red, or both blue).
How do you win? Once again, that's your choice:
(1) If the spinners MATCH, you win.
(2) If the spinners DO NOT MATCH, you win.
Which game would you be more likely to win?
Therefore, you would be more likely to win the game by choosing option (2) - winning if the spinners do not match.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of mathematics, science, engineering, finance, and other fields to model and analyze uncertain situations. It helps to make predictions, to assess risks and opportunities, and to make informed decisions based on available information. Probability theory provides a foundation for statistical inference, which is used to draw conclusions from data and to test hypotheses about the underlying population.
Here,
In the "Two Spinner Game", there are two possible outcomes for each spin - a match or a non-match. The probability of the spinners matching is the probability of both spinners landing on the same color. Let's say that there are 3 red sections, 3 blue sections, and 2 green sections on each spinner.
The probability of the first spinner landing on red is 3/8, and the probability of the second spinner landing on red is also 3/8. Therefore, the probability of both spinners landing on red (a match) is (3/8) x (3/8) = 9/64.
Similarly, the probability of both spinners landing on blue (another match) is (3/8) x (3/8) = 9/64, and the probability of both spinners landing on green (a match) is (2/8) x (2/8) = 4/64.
The probability of the spinners not matching is the probability of them landing on different colors. There are 3 different pairs of colors that are not a match: red-blue, red-green, and blue-green. The probability of each of these pairs is (3/8) x (3/8) = 9/64.
So, there are 6 possible outcomes, and the probability of winning by a match is 9/64 + 9/64 + 4/64 = 22/64, or about 34.4%. The probability of winning by a non-match is 3 x 9/64 = 27/64, or about 42.2%.
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What is the value of x in the equation 1/4(4 + x) = 4/3
The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.
Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:
1/4(4 + x) = 4/3
4 * 1/4(4 + x) = 4 * 4/3
Simplifying:
4 + x = 16/3
Subtract 4 from both sides of the equation:
4 + x - 4 = 16/3 - 4
Simplifying:
x = 16/3 - 12/3
x = 4/3
A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.
Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.
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Write a quadratic function in standard form to represent the data in the table.
Ordered pairs arranged in a table. From left to right the pairs are: 2, 3, and 4, 1, and 6, 3, and 8, 9, and 10, 19.
y = x2 − x +
What are the zeros of the function? Set the function = 0, factor, and use the zero-product property. Show your steps!
f(x) = x² + 7x – 60
(100 POINTS AND BRAINLIEST)
The zeroes of the function are -12 and 5.
What is meant by Zeros of the function?Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.
According to the question:
To find the zeros of the function
f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.
So we start with the equation:
x² + 7x - 60 = 0
Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:
x² + 7x - 60 = (x + 12)(x - 5) = 0
Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:
x + 12 = 0 or x - 5 = 0
Solving for x, we get:
x = -12 or x = 5
The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.
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Elena and Jada were racing on their bikes. Elena started 15 meters ahead of Jada. Elena biked at a rate of 20 meters per second. Jada biked at a rate of 22 meters per second. Let x represent time in seconds and y represent distance in meters. After how many seconds will Jada pass Elena?
Jada overtakes Elena after 7.5 seconds.
The set of equations that best captures the scenario is =y=15+20x.
Let's establish a coordinate system with Elena's starting point as the origin. Elena's separation from the origin at time x is given by: y=15+20x
y1 = 15 + 20x
Jada's distance from the origin at time x is determined similarly by:
y2 = 22x
Finding the moment x at which Jada overtakes Elena and their distances from the origin are equal is our goal.
y1 = y2
With the formulas for y1 and y2 substituted, we obtain:
15 + 20x = 22x
When we simplify this equation, we obtain:
2x = 15
x = 7.5
Jada therefore overtakes Elena after 7.5 seconds.
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find the length of the cord pt.3
According to the circle theorem, we can find the length of the cord, x = 4 units.
Define circle theorem?Geometrical assertions known as "circle theorems" set forward significant conclusions pertaining to circles. These theorems provide significant information regarding several aspects of a circle.
A circle's chord is a line segment that hits the circle twice on its edge, separating it into two equal pieces. The circle is divided into two equal pieces by the longest chord of the circle, which runs through its centre.
Here in the given circle,
As per the intersecting chords theorem,
AB × CB= BE × BD
⇒ 6 × 6 = 9× x
⇒ x = 36/9=4
Therefore, the length of the chord, x = 4 units.
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Please help quick with this question.
Answer:
b = [tex]\frac{S-2la}{h+l}[/tex]
Step-by-step explanation:
S = bh + lb + 2la ( reversing the equation )
bh + lb + 2la = S ( subtract 2la from both sides )
bh + lb = S - 2la ← factor out b from each term on the left side
b(h + l) = S - 2la ← divide both sides by (h + l)
b = [tex]\frac{S-2la}{h+l}[/tex]
The equation y = 8x represents the
relationship between the amount of
time Shanay takes to weave thread
into fabric and the number of rows.
How long will it take Shanay to weave
72 rows of fabric at this constant rate?
I NEED YOUR HELP ASAP!!
To create a modified box plot for a data set, determine the outliers of the data set and the smallest and largest numbers in the data set that are not outliers. Next, determine the median of the first half of the data set, the median of the entire data set, and the median of the second half of the data set.
What are the values that are needed to create a modified box plot for this data set?
19, 15, 22, 35, 16, 22, 4, 22, 24, 16, 17, 21
Enter your answers in the blanks in order from least to greatest.
Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.
Give a short note on Median?
In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.
The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.
To create a modified box plot, we need the following values:
The smallest number in the data set that is not an outlier: 15
The median of the first half of the data set: 17
The median of the entire data set: 20.5
The median of the second half of the data set: 22
The largest number in the data set that is not an outlier: 35
So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.
An urn contains eight green balls and six red balls. Four balls are randomly selected from the urn in succession, with replacement. That is, after each draw the selected ball is returned. What is the probability that all four balls drawn are red. Round your answer to three decimal places
The probability of drawing four red balls in succession, with replacement, is 0.04 or 4%.
Since we are replacing the ball after each draw, the probability of drawing a red ball remains the same for each draw. The probability of drawing a red ball on any given draw is:
P(Red) = Number of Red Balls / Total Number of Balls
P(Red) = 6 / (8 + 6)
P(Red) = 0.4286
So, the probability of drawing four red balls in a row is the product of the probability of drawing a red ball four times in a row:
P(4 Red Balls) = P(Red) * P(Red) * P(Red) * P(Red)
P(4 Red Balls) = 0.4286 * 0.4286 * 0.4286 * 0.4286
P(4 Red Balls) = 0.04 or 4%
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The average between 3. 15 and x is 40 what is x?
The value of x that makes the average between 3.15 and x equal to 40 is 76.85.
In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:
(3.15 + x) / 2 = 40
To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.
To solve for x, we can start by multiplying both sides of the equation by 2:
3.15 + x = 80
Next, we can subtract 3.15 from both sides of the equation:
x = 76.85
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In a distribution of 387 values with a mean of 72, at least 344 fall within the interval 64-80. Approximately what percentage of values should fall in the interval 56-88? Use Chebyshev’s theorem. Round your k and s values to one decimal place and final answer to two decimal places.
The required percentage of values that should fall in the interval 56-88 is approximately 74.37%.
Chebyshev’s Theorem:Chebyshev's Theorem states that, for any given data set, the proportion (or percentage) of data points that lie within k standard deviations of the mean must be at least (1 - 1/k2), where k is a positive constant greater than 1.Calculation:Given,Mean (μ) = 72N (Total number of values) = 387Interval (x) = 64-80 and 56-88Minimum values (n) = 344Minimum percentage (p) = (344 / 387) x 100 = 88.85%From the given data we have,1. Calculate the variance of the distribution,Variance = σ2 = [(n × s2 ) / (n-1)]σ2 = [(344 × 42) / 386]σ2 = 18.732. Calculate the standard deviation of the distribution,σ = √(18.73)σ = 4.33. Calculate k = (|x - μ|) / σ for the given interval 56-88,Here, x1 = 56, x2 = 88, k1 = |56-72| / 4.33 = 3.7, k2 = |88-72| / 4.33 = 3.7Thus, k = 3.74. Calculate the minimum percentage of values within the interval 56-88 using Chebyshev's Theorem,p = [1 - (1/k2)] x 100p = [1 - (1/3.7)2] x 100p = 74.37% (approximately)Therefore, the required percentage of values that should fall in the interval 56-88 is approximately 74.37%.
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Martina made $60 for 5 hours of work. At the same rate, how many hours would she have to work to make $204 ?
Answer:
WELL 17
Step-by-step explanation:
60 DIVED BY 5 IS 12
SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS
Find an expression that is equivalent to (a - b) ^ 3
An expression equivalent to (a - b)³ is a³ - 3a²b + 3ab² - b³.
What other expressions are the same as 2 5?The fractions 4/10, 6/15, 8/20, etc. are identical to 2/5. In the reduced form, equivalent fractions have the same value. Explanation: When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number.
One way to expand (a - b)³ is to use the binomial formula:
(a - b)³ = C(3,0) * a³ * (-b)^0 + C(3,1) * a² * (-b) + C(3,2) * a * (-b)² + C(3,3) * a * (-b)³
where C(n,k) denotes the number of ways there are to select k objects from a set of n objects, and "n choose k" is the binomial coefficient.
Simplifying the above expression, we get:
(a-b)³ = a³-3a²b+3ab²-b³.
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I NEED HELPP PLEASEEEEEEEE
The slope between the points (-3, 0) and (0, -1) is -1/3.
What is slope?The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.
Let us consider the first two points (-3, 0) and (0, -1).
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
Substituting the values we have:
m = (-1 - 0) / (0 - (-3)) = -1/3
Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.
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a
49⁰
Find the measure of a.
127⁰
72⁰
Answer:
112°
Step-by-step explanation:
Finding the unknown angle in a quadrilateral:
Sum of all angles of a quadrilateral = 360
a + 49 + 72 + 127 = 360
a + 248 = 360
a = 360 - 248
a = 112°
*CORRECT AND FASTEST ANSWER GETS BRAINLIEST!!!*
A greengrocer buys fruit and vegetables from the market and sells them at a 25% mark up. On one particular moring her fruit and vegetables cost her €500. If she sells all of her produce, find:
A) her profit
B) her total income
Answer: Below :)
Step-by-step explanation:
A) To find the profit, we first need to calculate the cost of the produce plus the 25% markup.
The markup is 25% of the cost, which is 0.25 * 500 = €125.
So the total cost of the produce plus markup is €500 + €125 = €625.
Now, if the greengrocer sells all the produce, the total revenue will be 100% plus the 25% markup, which is 125% of the original cost.
125% of €500 is 1.25 * 500 = €625, which is the same as the cost plus markup.
Therefore, the profit is the markup, which is €125.
B) To find the total income, we add the profit to the total cost:
Total income = €500 + €125 = €625
Answer:
A) €125
B) €625
Hi. Please help me convert this non-linear to linear form y=mx+c. The answer is square root of y= 6/p x - 2/q .
Thank you so much.
Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:
Square both sides of the equation to eliminate the square root:
√y = (6/p)x - (2/q)
√y^2 = (6/p)x - (2/q)^2
Simplifying the right-hand side, we get:
y = (36/p^2)x - (4/q) + 4/q^2
Rearrange the equation to the form y = mx + c:
y = (36/p^2)x + (4/q^2 - 4/q)
So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).
Step-by-step explanation:
Let A, B, and C be subsets of some universal set U. (a) Draw two general Venn diagrams for the sets A, B, and C. On one, shade the region that represents A - (B nC), and on the other, shade the region that represents (A -B) U (A C). Based on the Venn diagrams, make a conjecture about the relationship between the sets A-(BnC) and (A -B)U (A -C). (b) Use the choose-an-element method to prove the conjecture from Exer- cise (5a). (c) Use the algebra of sets to prove the conjecture from Exercise (5a).
In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.
To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].
This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).
To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).
We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).
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B=6,c=7.5 what is A in Pythagorean therom
Answer: 4.5
Step-by-step explanation:
A^2 +B^2 =C^2
A^2 + 6^2 =7.5^2
A^2 + 36= 56.25
A^2= 20.25
A= square root of 20.25
A= 4.5
The number of employees for a certain company has been decreasing each year by 5%. If the company cumently has 860 employees and this rate continues, find the number of employees in 10 years
The number of employees in 10 years will be approximately
(Round to the nearest whole number as needed)
Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.
What is exponential decay equation?The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.
Exponential decay equation is one of the two exponential functions. The other is the exponential growth equation.
The annual decrease in the number of employees = 5%
The current number of employees in the company = 860
The expected time = 10 years.
The exponential decay equation is as follows, y = 860 x 0.95^10.
y = 860 x 0.95^10 = 515
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Luke bought 4 kilograms of apples and 0.29 kilograms of oranges. How much fruit did he buy
in all?
He bought 4.29 Kilos of fruit.
4+0.29=4.29
Luke bought 4.29 kilograms of fruit in all
Step-by-step explanation:
Simple addition will be used to find the total fruit Luke bought.
Given
Amount of apples he bought = 4 kilograms
Amount of oranges he bought = 0.29 kilograms
so the total fruit will be:
[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]
[tex]=4+0.29[/tex]
[tex]=4.29[/tex]
So,
Luke bought 4.29 kilograms of fruit in all
Keywords: Measurement, addition
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Im a trapezoid measuring 8cm, 10cm, 16 cm and 10cm on its sides. What is my Perimeter? 1-5 po lhat
Answer:
See Below.
Step-by-step explanation:
To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.
In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.
Perimeter = 8 cm + 10 cm + 16 cm + 10 cm
Perimeter = 44 cm
Therefore, the perimeter of the trapezoid is 44 cm.
A certain population is strongly skewed to the left. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be closer to normal.
II. The sampling model of the sample means will be closer to normal.
III. The variability of the sample means will be greater.
A. I and II only
B. I only
C. III only
D. II and III only
E. II only
A. I and II only true if we use a large sample rather than a small one
sampling model
Define sampling modelA sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.
When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.
Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.
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Use substitution to solve -4x + y = 3, 5x - 2y = -9
Using the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)
We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:
-4x + y = 3 (Equation 1)
5x - 2y = -9 (Equation 2)
Solving Equation 1 for y, we get:
y = 4x + 3
Now, we substitute this expression for y into Equation 2 and solve for x:
5x - 2(4x + 3) = -9
5x - 8x - 6 = -9
-3x = -3
x = 1
We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:
-4(1) + y = 3
y = 7
Therefore, the solution to the system of equations is (x, y) = (1, 7)
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48 identical looking bags of lettuce were delivered to Circle J grocers. Unfortunately, 12 of these bags of lettuce are contaminated with listeria. Joe, from Joes Cafe randomly selects 4 bags of the lettuce for his cafe. Let X equal the number of the selected packets which are contaminated with listeria. a. How many possible ways are there to select the 4 out of 48 packets (order does not matter) without replacement? b. What is the probability thatX=0
c. What is the probability thatX=4? d. What is the probability thatx>2? e. What is the expected value ofX? f. What is the standard deviation ofX? g. What is the probability that X is smaller than its expected value?
h. What is the probability thatX=5?
Probability that X = 5:Since, Joe selects only 4 bags of lettuce. X can't be 5.P(X=5) = 0Hence, the probability that X = 0 is 0.3164 and the probability that X = 5 is 0.
The given problem can be solved using the concept of binomial distribution.
In the given question, there are 48 bags of lettuce out of which 12 bags are contaminated with listeria.
Joe selects 4 bags of lettuce. X is the random variable which represents the number of contaminated bags of lettuce selected by Joe. X can take values from 0 to 4. (as Joe selects only 4 bags).
Part A)Number of ways to select 4 bags of lettuce out of 48:This can be solved using the concept of combinations. The formula to calculate the number of combinations is[tex]:nCr = n! / r!(n-r)![/tex]Here, n = 48 and r = 4.
Number of ways = 48C4 = 194,580
Part B)Probability that X = 0:This can be calculated using the formula for the binomial distribution :
[tex]P(X = r) = nCr * p^r * q^(n-r)[/tex]
Here, p = probability of selecting contaminated bag = 12/48 = 0.25q = probability of selecting non-contaminated bag = 1-0.25 = 0.75Also, n = 4 and r = [tex]0P(X=0) = 4C0 * 0.25^0 * 0.75^4= 0.3164[/tex]
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Suppose f is a continuous function defined on a rectangle R=[a,b]X[c,d]. What is the geometric interpretation of the double integral over R of f(X,y) if f(X,y)>0
If f(x,y) > 0 and is a continuous function defined over a rectangle R=[a,b]x[c,d], then the double integral over R of f(x,y) can be interpreted as the volume of a solid that lies in the first octant and under the graph of the function f(x,y) over the region R.
The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0, where f is a continuous function defined on a rectangle R = [a,b] × [c,d] is given as follows:
The double integral of f(x,y) over R, if f(x,y) > 0, gives the volume under the graph of the function f(x,y) over the region R in the first octant.
Consider a point P (x, y, z) on the graph of f(x, y) that is over the region R, and let us say that z = f(x,y). If f(x,y) > 0, then P is in the first octant (i.e. all its coordinates are positive).
As a result, the volume of the solid that lies under the graph of f(x,y) over the region R in the first octant can be found by integrating the function f(x,y) over the rectangle R in the xy-plane, which yields the double integral.
The following formula represents the double integral over R of f(x,y) if f(x,y) > 0:
∬Rf(x,y)dydx
The geometric interpretation of the double integral over R of f(x,y) if f(x,y) > 0 is given by the volume of the solid that lies under the graph of the function f(x,y) over the region R in the first octant.
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using the net below find the area of the triangular prism
6 cm
3 cm
4 cm
6 cm
5 cm
2 cm
Answer:153
Step-by-step explanation:
In a regular pentagon PQRST. PR intersects QS
at O. Calculate angle ROS.
Answer: 72°
Step-by-step explanation:
To find the interior angle of this shape, use the formula 180(n-2)/n, where n is the amount of sides. Plugging 5 in for the interior angle of a pentagon, you get 180(3)/5, or 108°.
Using the statement that PR intersects QS, we can see that triangle QOR is isosceles (to get this, look at triangle PQR, and note that because it has 2 equal side lengths, and its last length is not equivalent to the other 2 sides, it is isosceles). Solving for angle PRQ, we know one angle is 108°, and the other two are equal. The total angle in a triangle is 180°, so (180°-108°)/2 = 36° (angles QPR and PRQ).
Since the angle of R = 108°, we can find angle PRS as 108° - 36°, or 72°. Since triangles PQR and QRS are similar (share the same angles and side lengths), we can see that angle RQS and RSQ are both 36°.
Since ORS is a triangle, its angle total is 180°. Since we know the angles ORS and OSR (respectively) already as 72° and 36°, we can subtract these angles to find angle ROS. 180°-72°-36° = 72°
