The conditional probability that a randomly selected participant wore leather pants and played an acoustic guitar is 6/25. Therefore, the answer is option D. 6/25.
What is conditional probability?Conditional probability is the probability that an event will occur given that another event has already occurred.
It is denoted by P(A|B), where A and B are events, and the vertical line | indicates "given that" or "conditional on".
The conditional probability of an event A given event B is defined as the probability of both A and B happening divided by the probability of B happening:
P(A|B) = P(A and B) / P(B)
In this case, the event A is playing an acoustic guitar and the event B is wearing leather pants.
We can start by finding the probability of wearing leather pants:
P(B) = (6 + 9) + (3 + 7) = 25
This is because there are a total of 6 contestants wearing leather pants and 19 contestants in total.
Next, we need to find the probability of both wearing leather pants and playing an acoustic guitar:
P(A and B) = 6
This is because there are 6 contestants wearing leather pants and playing an acoustic guitar.
Now we can use the formula to find the conditional probability:
P(A|B) = P(A and B) / P(B) = 6 / 25
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A man went to a post office to buy some stamps. If he bought x, 50 cents stamps and y, 25 cents stamps, the total cost would have been $3.50. If, however, he bought twice as many 50 cents stamps and half as many 25 cents stamps, then the total cost would have been $4.75. Evaluate x and y.
A cone has a base area of 24 square inches and a height of 8 inches. What is the area of a cross-section of the cone
that is parallel to the base and 3 inches from the vertex?
The area of the cross-section of the cone that is parallel to the base and 3 inches from the vertex is
Square inches.
Write the answer in friction
Answer:
Step-by-step explanation:
Cone height h = 8
Cone base r = sqrt( 24/pi) = 2.764
AB = h - 3 = 5
BC = 5 / tan(β) = 1.727
FB = FC - BC = 1.036482449 ( FB is the radius of cross-section circle)
Area of a cross-section is: (FB)2 * pi = 3.375 in2
HELP PLEASE ! 10+ POINTS! Social networking sites make some very accurate suggestions for people that you might know. Explain how trees are used to make these suggestions.
sue sells rings for 6$ each. Her expenses are $2.50 per ring, plus $56 for supplies. How many rings does she need to sell for her revenue to equal her expenses? Show work to support your answer
Sue needs to sell 16 rings to make her revenue equal to her expenses
What is revenue?Revenue is the total income generated by a company or organization from its sales or operations. It is the amount of money that a business earns from selling its products or services, or from other sources such as investments or interest on deposits.
According to question:Let's assume that Sue sells x rings.
The revenue generated by selling x rings = $6x
The total expenses for selling x rings = $2.50x + $56
To find the number of rings that Sue needs to sell for her revenue to equal her expenses, we need to set the revenue equal to the expenses and solve for x.
6x = 2.5x + 56
Subtracting 2.5x from both sides, we get:
6x - 2.5x = 56
Simplifying the left side, we get:
3.5x = 56
Dividing both sides by 3.5, we get:
x = 16
Therefore, Sue needs to sell 16 rings to make her revenue equal to her expenses.
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two fractions that are the same size as 3/10
Answer:
6/20 and 9/30
Step-by-step explanation:
x – 19 ≤ 81, if x = 110
The inequality x - 19 ≤ 81 is not satisfied when x = 110.
What is inequalities?
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
The given inequality is X – 19 ≤ 81, and we are asked to evaluate it when X = 110. To do so, we substitute X with 110 and simplify the expression. In this case, we get 110 - 19 ≤ 81, which simplifies to 91 ≤ 81. Since this statement is false, we conclude that the inequality X – 19 ≤ 81 is not satisfied when X = 110.
we can substitute x = 110 and simplify:x - 19 ≤ 81
110 - 19 ≤ 81
91 ≤ 81
This statement is false, since 91 is not less than or equal to 81.
Therefore, the inequality x - 19 ≤ 81 is not satisfied when x = 110.
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Quadrilateral MATH has coordinates M(-6,-3), A(-1,-3), 7(-2,-1), and H(-4,-1). The image of
quadrilateral MATH after the composition r x-axis °T 7,5 is quadrilateral M "A"T"H". State and
label the coordinates of M"A"T"H".
the coordinates of M"A"T"H" are M"(1,8), A"(6,2), T"(5,4), and H"(3,4).
How to find?
The composition r x-axis ° T(7,5) first reflects the quadrilateral MATH about the x-axis and then translates it 7 units to the right and 5 units up.
To find the image of M(-6,-3) after reflection about the x-axis, we flip the sign of the y-coordinate to get M'(-6,3). Then, we translate M' 7 units to the right and 5 units up to get the coordinates of M":
M" = T(7,5) ∘ M' = (7 + (-6), 5 + 3) = (1, 8)
Similarly, we can find the coordinates of A", T", and H":
A' = (-1, 3) → A" = T(7,5) ∘ R(x-axis) ∘ A' = (7 + (-1), 5 - 3) = (6, 2)
T' = (-2, 1) → T" = T(7,5) ∘ R(x-axis) ∘ T' = (7 + (-2), 5 - 1) = (5, 4)
H' = (-4, 1) → H" = T(7,5) ∘ R(x-axis) ∘ H' = (7 + (-4), 5 - 1) = (3, 4)
Therefore, the coordinates of M"A"T"H" are M"(1,8), A"(6,2), T"(5,4), and H"(3,4).
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answer:
the values of x are 13 and 1.
Step-by-step explanation:
x - 7 = +√36 or x - 7 = -√36
Therefore,
x - 7 = +6 or x - 7 = -6
=> x = 7 + 6 or x = 7 - 6
=> x = 13 or x = 1
Therefore, the values of x are 13 and 1.
Answer: x = 25
Step-by-step explanation:
(x – 7)2 = 36 (Given)
2(x -- 7) = 36 (Associative Property)
2x - 14 = 36 (Distributive Property)
2x - 14 + 14 = 36 + 14 (Addition Property of Equality)
2x = 50 (Simplification)
2x/2 = 50/2 (Division Property of Equality)
x = 25 (Simplification)
w/ solution please
thank uuu
The National Park Service writes materials for students to use while in the parks. In a study of the effectiveness of some of these materials, a random sample of students was selected to take a short quiz about oak trees after using these materials. A random sample of park professionals also took the quiz. Investigators compared classifications (low, medium, and high) of the crown shapes—the general shapes of the leafy parts of the trees—made by students in s 6 through 12 with classifications made by professionals. Data from the study are shown in the table.
ProfessionalsStudentsTotalLow544397Medium483987High7916Total10991200
If the professionals and the students do not differ in the distributions of their responses, which of the following is equal to the expected number of students who classify the crown shapes as medium?
The expected number of students who classify the crown shapes as medium is approximately 38.3.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To find the expected number of students who classify the crown shapes as medium, we need to use the assumption that the distributions of responses from the professionals and the students are the same. We can use the row and column totals to calculate the expected counts.
First, let's calculate the marginal totals for the students:
The total number of students is 91.
The total number of students who classified the crown shapes as low is 43.
The total number of students who classified the crown shapes as medium is 39.
The total number of students who classified the crown shapes as high is 9.
Now let's calculate the expected counts for the students who classified the crown shapes as medium:
The total number of classifications for the medium category is 87 (from the table).
The proportion of classifications in the medium category made by the professionals is 48/109.
The expected number of classifications in the medium category made by the students can be calculated as (proportion from professionals) x (total number of student classifications) = (48/109) x 87 = 38.3 (rounded to one decimal place).
Therefore, the expected number of students who classify the crown shapes as medium is approximately 38.3.
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Mr Lim, Mr Bell and Mrs Walker paid for a meal. Mr Lim paid 1/5 of the amount Mr Bell and Mrs Walker paid together. Mr Bell paid 1/4 of the amount Mr Lim and Mrs Walker paid. A) What fraction of the total cost of the meal did Mrs Walker pay?
As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C)
what is fraction ?A fraction is a number that in mathematics represents a portion of a whole. It consists of a horizontal line between the numerator and denominator of two numbers. The denominator is the total number of equally sized components that make up the whole, whereas the numerator is the number of parts that are being taken into account. As an illustration, the fraction 3/4 denotes three of the four equal pieces. The denominator, 4, indicates that the entire is divided into four equal parts, while the numerator, 3, indicates that three parts are being taken into consideration.
given
Payment to Mr. Lim:
1/5(B + W) = (B + W)/5
Payment to Mr. Bell:
1/4(L + W) = (L + W)/4
These equations can be combined to find the value of W, or the amount Mrs. Walker paid:
(L + W)/4 + W + (B + W)/5 = C
To get rid of the fractions, multiply both sides by 20, which is the least common multiple of 5 and 4. This gives us:
20W + 4(B + W) + 5(L + W) = 20C
By enlarging and condensing, we obtain:
20C = 4B + 4W + 5L + 5W + 20W
9W + 4B + 5L = 20C
Now, we may change the expressions for the payments made to Mr. Lim and Mr. Bell to:
9W plus 4 (1/5 B + W) plus 5 (1/4 L + W) equals 20C.
If we simplify, we get:
9W + 4B + 4W + 4W + 4W + 5L + 5W = 20C.
When we multiply both sides by 20 to once more get rid of the fractions, we get:
400C = 180W + 16B + 16W + 25L + 25W
20C = 4B + 4W + 5L + 5W + 20W
9W + 4B + 5L = 20C
Now, we may change the expressions for the payments made to Mr. Lim
If we simplify, we get:
61W + 16B + 25L = 400C
We may now determine W:
W = (400C - 16B - 25L) / 61
We can divide W by the overall cost C to determine the portion of the cost of the lunch that Mrs. Walker covered:
W/C = (400C - 16B - 25L) / (61C)
W/C = 400/61 - (16B + 25L) / (simplified) (61C)
As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C) .
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1. Nathaniel hikes 15 4/5 kilometres on a
three-day hiking trip.He hikes 3 kilometre
on the first day.Then
Nathaniel hikes the same distance on
the second and third days of his trip.
Determine the distance Nathaniel hikes
on the second and third days.
Nathaniel hikes 6 2/5 kilometers on each of the second and third days of his hiking trip.
Calculating the distance hiked on the second and third daysIf Nathaniel hikes a total of 15 4/5 kilometers on a three-day hiking trip and he hikes 3 kilometers on the first day, then he must hike the remaining distance on the second and third days.
To find out how much Nathaniel hikes on the second and third days, we can start by subtracting the distance he hikes on the first day from the total distance he hikes:
15 4/5 - 3 = 12 4/5 kilometers
Since Nathaniel hikes the same distance on the second and third days, we can divide the remaining distance by 2 to find out how much he hikes on each of those days:
12 4/5 ÷ 2 = 6 2/5 kilometers
Therefore, Nathaniel hikes 6 2/5 kilometers on each of the second and third days of his hiking trip.
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In the triangle, x = 3. Find y.
Responses
A y = 3√
y = 3
B y = 6y = 6
C y = 7y = 7
D y = 32√
y = 3 2
E y = 62√
y = 6 2
Answer:
3√2
Step-by-step explanation:
9 + 9 = 18
square root of 18 is
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Pleas help, Will mark brainliest and if you don't know then don't answer
Answer: 10 pigs and 3 chickens
Step-by-step explanation:
So the farmer has seen 40 legs
Pigs have 4 legs & Chickens have 2
Pigs: 40/4= 10 pigs
Chickens: 40/2= 20 chickens
So with us know which answer is correct we choose 10 pigs
Then if we have 10 pigs we have 3 chickens
13-10= 3 chickens
In conclusion we have the 10 pigs & 3 chickens
Rewrite 300-4 in a different way, using the Commutative Law of Multiplication.
A) 30-40
B) 1200
C) 4.300
D) 3.100-4
Answer:
3x100-4
Step-by-step explanation:
3x100=300
(3x100)-4
300-4
A triangular prism has a volume of 1950 cm?. The height of the triangle is 13 cm, and the height of the prism is 20 cm. What is the perimeter of the triangle (assuming all the sides are equal)?
The perimeter of the triangle is therefore P= 45 cm.
What is a triangular prism?A triangular prism is a prism composed of two triangular bases and three rectangular sides. It is a pentahedron.
What is perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.
We know that the volume of a prism is given by
V = Bh, where B is the area of the base and h is the height of the prism. In this case, we have V = 1950 cm³ and h = 20 cm.
So, we can solve for B:
B = V/h = 1950/20 = 97.5 cm².
The base of the triangular prism is a triangle with height 13 cm, so we have
B = 1/2bh = 1/2(13)(b) = 97.5.
Solving for b, we get b = 2B/h = 2(97.5)/13 = 15 cm.
Since all sides of the triangle are equal, we have b = c = 15 cm.
The perimeter of the triangle is therefore P = 3b = 3c = 3(15) = 45 cm.
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Find the derivative of f(x)=−148x+1−−−−−√7
.
Answer: f(x) is -74(x+1/7)^(-1/2)
Step-by-step explanation:
To find the derivative of f(x), we can use the power rule and the chain rule.
First, let's rewrite f(x) as:
f(x) = -148(x+1/7)^(1/2)
Now, we can apply the power rule:
f'(x) = -148 * (1/2) * (x+1/7)^(-1/2)
Finally, we can use the chain rule:
f'(x) = -148 * (1/2) * (x+1/7)^(-1/2) * 1
f'(x) = -74(x+1/7)^(-1/2)
Therefore, the derivative of f(x) is -74(x+1/7)^(-1/2).
f(x) = x + 1, g(x) = 7x + 8 find (fog)(x)
Answer:
(fog)(x) = 7x + 9.
Step-by-step explanation:
To find (fog)(x), we need to first find the composition of f and g, which is given by f(g(x)).
So, we substitute g(x) into f(x) and simplify:
f(g(x)) = f(7x + 8)
= (7x + 8) + 1 (using the definition of f(x))
= 7x + 9
Therefore, (fog)(x) = 7x + 9.
The count in a bacteria culture was 100 after 15 minutes and 1800 after 40 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?
Correct ___17.65___ bacteria
Find the doubling period.
____?_____ minutes
Find the population after 115 minutes.
____?_____ bacteria
When will the population reach 12000.
___?____ minutes
The population will reach 12000 bacteria after 56.4 minutes and other solutions are listed below
What was the initial size of the culture?We can use the formula for exponential growth, which is given by:
N = N0 * e^(kt)
where N is the final population, N0 is the initial population, k is the growth rate constant, and t is time.
To find the initial size of the culture, we can use the values given at 15 minutes and 40 minutes:
100 = N0 * e^(15k)
1800 = N0 * e^(40k)
Dividing the second equation by the first, we get:
18 = e^(25k)
Taking the natural logarithm of both sides, we get:
k = ln(18)/25
Solving for k, we get:
k = 0.1156
Substituting this value of k into the first equation, we can solve for N0:
100 = N0 * e^(15 * 0.1156)
N0 = 17.65
Therefore, the initial size of the culture was 17.65 bacteria.
The doubling periodTo find the doubling period, we use the fact that the population doubles when t increases by a certain amount, which we'll call T. That is:
N0 * e^(kT) = 2N0
Dividing by N0 and taking the natural logarithm of both sides, we get:
T = ln(2)/k
Solving for T, we get:
T = ln(2)/k ≈ 6.00 minutes
Therefore, the doubling period is approximately 6 minutes.
The population after 115 minutesTo find the population after 115 minutes, we can use the formula with the values of N0, k, and t:
N = N0 * e^(kt) = 17.65 * e^(0.1156 * 115) ≈ 10477448.92
Therefore, the population after 115 minutes is approximately 10477448.92 bacteria.
When the population reaches 12000To find when the population reaches 12000, we set N equal to 12000 and solve for t:
12000 = 17.65 * e^(0.1156t)
Dividing by 17.65 and taking the natural logarithm of both sides, we get:
ln(12000/17.65 ) = 0.1156t
Solving for t, we get:
t ≈ 56.42 minutes
Therefore, the population will reach 12000 bacteria after approximately 56.4 minutes.
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Find the total surface area of this triangular prism. 21 cm 20 cm 29 cm 22 cm
Answer:
ти можеш загуглити в інтернеті, і все
Roger and Rohan are partners of R&R Biscuit Company. Given below is details of items that appeared in their current account for the year ended December 31, 2019:
The net profit before appropriation is (d). $1,889,000.
How to solveTo calculate net profit before appropriation to R&R biscuit company by adding all the appropriation expense to share of profit after appropriation and deducting appropriation income.
In this case, interest on capital, drawings and partner's salary are appropriation expense while interest on drawings is appropriation income.
Now,
Net profit before appropriation
= ($650,000+$200,000+$100,000+$30,000-$20,000) + ($650,000+$150,000+$130,000+$25,000-$26,000)
= $960,000 + $929,000
= $1,889,000
So, the correct answer is (d). $1,889,000.
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1+1 I don’t know I’m in 7 th grade
Answer:
2
Step-by-step explanation:
no explanation needed.
A psychologist has developed a test called “WETHIC” to measure the work ethic in a firm’s
workers. The test scores approximate a Normal distribution with a mean of 70 and a standard
deviation of 20. (note: this step involves manual calculation and does not require any SPSS work).
For each question, your answer should take the form of a complete sentence.
1. Convert a WETHIC score of 79 into a z-score and interpret this z-score.
2. Convert a WETHIC score of 62 into a z-score and interpret this z-score.
3. What proportion of workers will have a WETHIC score that is below 79?
4. What proportion of workers will have a WETHIC score that is below 62?
5. What proportion of workers will have a WETHIC score that is above 79?
6. What portion of workers will have a WETHIC score that is above 62?
The WETHIC score of 79 into a z-score is 0.33.
A WETHIC score of 62 into a z-score is 0.80.
The proportion of workers that will have a WETHIC score that is below 79 is 63%.
The proportion of workers that will have a WETHIC score that is below 62 is 21%.
How to calculate the value1) Z score = (79-74)/15 = 0.33 , it means score is 0.33 standard deviations above the mean
2) Z score = (62-74)/15 = -0.80 , it means score is 0.80 standard deviations below the mean
3) P(X<79)
= P(Z<0.33)
= 0.6293
d) P(X<62)
= P(Z<-0.80)
= 0.2119
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I need help with this math problem. It’s from the course “Apply Math”.
The expected value of the gas grill is 6.50 million dollars if a development cost of $4 million is invested.
What is expected value?The expected value is the sum of all possible outcomes multiplied by their associated probabilities.
The expected value of the gas grill can be calculated as follows:
Expected value = (0.10 × 3) + (0.50 × 6) + (0.40 × 8)
= 0.30 + 3.00 + 3.20
= 6.50 million dollars
Therefore, the expected value of the gas grill is 6.50 million dollar.
This calculation allows investors to decide whether or not to invest in a specific project, as the expected return must be greater than the development cost.
In this case, the expected value of 6.50 million dollars is greater than the development cost of 4 million dollars, making the investment a viable option.
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Answer two questions about point
A
Astart color #9e034e, start text, A, end text, end color #9e034e on the number line below.
A vertical number line labeled 7.5 to 7.6 with tick marks every one hundredth unit. Point A appears slightly above tick mark 7.51.
A vertical number line labeled 7.5 to 7.6 with tick marks every one hundredth unit. Point A appears slightly above tick mark 7.51.
What is
A
Astart color #9e034e, start text, A, end text, end color #9e034e rounded to the nearest hundredth?
What is
A
Astart color #9e034e, start text, A, end text, end color #9e034e rounded to the nearest tenth?
the rounded color remains the original colour:: 9e034e
The color code #9e034e represents a shade of deep pink or magenta. To round this color to the nearest tenth, we need to convert the hexadecimal code to its corresponding RGB values and then round those values.
Converting #9e034e to RGB gives us (158, 3, 78).
Rounding each of these values to the nearest tenth gives us (158, 3, 78), which is the same as the original color. Therefore, the rounded color is still #9e034e.
As for the mention of "A" in the question, it's unclear what context it refers to. If it's related to the color, it might mean that the color is used to represent the letter "A" in a certain context. However,
The question doesn't provide enough information to determine the exact meaning of "A."n summary, the rounded color #9e034e remains the same as the original color, and the mention of "A" in the question is unclear.
Determine all pairs of real numbers a and b so that the following function, f(x),
is differentiable at all real values, x.
f(x) =
x- x^2, if x ≤ 1
x^2 - 5x + 4/ square root ax, if 1
sin(x-4)/x+b, if x > 4
1.Using the Chain Rule, show that the following statements are always true:
(a) If f(x) is an odd function then f'(x) is an even function.
(b) If f(x) is an even function then f’(x) is an odd function.
If f(x) is an odd function then f'(x) is an even function, a=7 and b=5.
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
According to our question-
dy/dx = f'(x) = limΔx→0f(x+Δx)−f(x)Δx lim Δ x → 0
Hence, If f(x) is an odd function then f'(x) is an even function, a=7 and b=5.
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Please help I’ve been absent and am confused on this topic!! Can someone tell me if I got this geometry question right? If not please solve for x, simplify to radical form, and explain how you got your answer.
The value of x= 4.
What is trignometric ratios?This is the boundary or contour length of a 2D geometric shape.
Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.
The same wire can be used to create a square if all sides are the same length.
The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.
As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.
Inches, feet, yards, and miles are other globally recognized units of circumference measurement.
According to our question-
cos(60)= x/8
x=1/2*8
x=4
Hence, The value of x= 4.
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Find the average rate of change of f(x) = x² - 4x + 1 from x=3 to x = 5.
Simplify your answer as much as possible.
To find the average rate of change of the function f(x) = x² - 4x + 1 from x=3 to x = 5, we need to find the difference in f(x) between these two values and divide by the difference in x:
f(5) - f(3) / (5 - 3)
= (5² - 4(5) + 1) - (3² - 4(3) + 1) / 2
= (25 - 20 + 1) - (9 - 12 + 1) / 2
= (6) / 2
= 3
Therefore, the average rate of change of f(x) from x=3 to x=5 is 3.
Step-by-step explanation:
Given a interval x=a to x=b, the average rate of change is equal to
[tex] \frac{f(b) - f(a)}{b - a} [/tex]
where [a,b] is the interval.
Here
a is 3
b is 5 so
[tex] \frac{f(5) - f(3)}{5 - 3} [/tex]
Using the function
[tex]f(5) = 25 - 20 + 1 = 6[/tex]
[tex]f(3) = 9 - 12 + 1 = - 2[/tex]
So
[tex] \frac{6 - ( - 2)}{5 - 3} = 4[/tex]
The average rate of change of f from x=3 to x=5 is 4
Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.
We want to copy the original triangle using only two of its sides and the included angle. To do this, we'll create a new triangle with the same side lengths and angle measures as the original triangle.
To copy a triangle using two of its sides and the included angle, follow these steps:
Using point E as the center, draw a circle with a radius equal to the length of side DE.Using point E as the vertex and side DE as one side of the angle, create an angle that is equal to the measure of angle D.Draw ray EF that extends from point E through the angle you created in step 2.Locate the intersection of ray EF and the circle you drew in step 1, and label the point of intersection F.Complete the triangle DEF by drawing a line segment that connects points D, E, and F.Learn more about vertex :
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Homeowners are installing a pollinator garden in
the corner of their backyard. The garden has the in
dimensions shown.
on
°538 = 33 feet
es
22 feet
104°
A
B
%
Part A
A fence will be installed along the entire edge, c,
of the area. What is the length of fence that will
be installed to the nearest tenth of a foot?
16
24
C
Part B
The homeowners will plant wildflowers to cover
the garden. If one packet of wildflower seeds covers
9 ft², how many packets of seeds will they need to
cover the entire garden?
36
(D) 48
Using sine and cosine rule, the length of fence is 19.84 feet and the number of packets to cover the garden is approximately 48
What is the length of fence c?To find the value of of the length of the fence, we can either use sine rule or cosine rule.
Since we have two sides and an angle, we sine rule first
a/sin A = b / sin B
[tex]\frac{33}{sin 104} = \frac{22}{sin B} \\sin B = 0.6469\\B = 40.31^0[/tex]
Using this, we can find the value of angle C
A + B + C = 180 degrees
Reason: Sum of angles in a triangle is equal to 180 degrees
104 + 40.31 + C = 180
C = 35.69 degrees
We can proceed to use cosine rule to find the length of the fence.
[tex]c^2 = a^2 + b^2 -2(a)(b)cosC\\c^2 = 33^2 + 22^2 - 2(33)(22)cos35.69\\c^2 = 393.71\\c = 19.84 ft[/tex]
Part B
Since one packet will cover 9ft², we need to know the total area of the field to determine the number of packets required.
Using heron's formula;
[tex]s = \frac{a + b + c}{2} \\s = \frac{33 + 22 + 29.84}{2} \\s = 42.42\\[/tex]
The area of the field is
[tex]A = \sqrt{s(s-a)(s-b)(s-c)}\\A = \sqrt{42.42(42.42-33)(42.42-22)(42.42-19.84}\\A = 429.24ft^{2}[/tex]
The number of packets will be
x = 429.24 / 9
x = 47.69≅48 packets
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