The probability that Jacob makes both free throws is approximately 0.1924 or 19.24%.
The probability that Jacob makes the first free throw is 0.37, and the probability that he misses it is 0.63.
If he makes the first free throw, the probability that he makes the second free throw given that he made the first is 0.52, which means the probability that he misses the second free throw given that he made the first is 0.48.
So, the probability that Jacob makes both free throws is:
P(both made) = P(made first) [tex]\times[/tex] P(made second | made first)
= 0.37 [tex]\times[/tex] 0.52
= 0.1924
Therefore, the probability that Jacob makes both free throws is approximately 0.1924 or 19.24%.
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fill in the blank. surveys suggest that about 7 percent of people in the united states experience a___during a given year. please choose the correct answer from the following choices, and then select the submit answer button. answer choices
Surveys suggest that about 7 percent of people in the united states experience a depression during a given year.
The United States experienced a depression during the 1930s, which lasted from 1929 to 1939. This was one of the longest and deepest economic downturns in U.S. history. The Great Depression caused widespread unemployment, poverty, and hardship throughout the country.
The stock market crash of 1929 and the subsequent bank failures caused a sharp decline in industrial and agricultural production, as well as a dramatic drop in consumer spending. As a result, millions of Americans were left without jobs, and many lost their homes and other possessions.
The government responded to the crisis with a series of programs and initiatives, such as the New Deal, to stimulate the economy and provide relief for those most affected. These programs helped to create jobs and provide economic stability, but the Great Depression would not end until the U.S. entered World War II in 1941.
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Choose which point is a solution to the equation below. Y= 3x + 5
There are infinitely many possible solutions to the equation y = 3x + 5.
What is a linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
An equation,
y = 3x + 5.
The equation has an independent variable x and a dependent variable y.
And the x is a free variable.
So, the y varies as per the value of x.
There are infinite possible solutions to the equation.
Therefore, there are infinite possible solutions to the equation.
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Use Kruskal's algorithm to find a minimum spanning tree for the following graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.)
A graph with 8 vertices and 12 edges is shown.
One edge with weight 12 connects vertex v0 and vertex v1.
One edge with weight 4 connects vertex v0 and vertex v5.
One edge with weight 20 connects vertex v1 and vertex v2.
One edge with weight 5 connects vertex v1 and vertex v3.
One edge with weight 7 connects vertex v1 and vertex v4.
One edge with weight 19 connects vertex v2 and vertex v7.
One edge with weight 2 connects vertex v3 and vertex v4.
One edge with weight 18 connects vertex v3 and vertex v7.
The minimum spanning tree for the above graph 1 is present above in graph figure 2. The order in which edges are added to form the tree is equals to {V₃, V₄ }, { V₀, V₅}, { V₁, V₃}, {V₅, V₆}, { V₄, V₅}, {V₆, V₇}, {V₂, V₇ }.
We have , a diagram present above in figure. This graph has 8 vertices and 12 edges. Also
The edge with weight 12 connects vertex V₀ and vertex V₁.Similarly, edages are connected to each other with different weights as shown in graph. Kruskal's algorithm is a greedy algorithm in graph theory of discrete mathematics that used to determine the minimum spanning tree for a connected weighted graph and adds increasing weight at each. In this case a graph present we determine the shortest spinning tree. Kruskal's algorithm stated that always select a minimum cost edge that should not result in a cycle. The order is which edges are added is
{V₃, V₄ }, { V₀, V₅}, { V₁, V₃}, {V₅, V₆}, { V₄, V₅}, {V₆, V₇}, {V₂, V₇ }.
Hence, the required graph is present above.
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Complete question:
Use Kruskal's algorithm to find a minimum panning tree for the above graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.)
A graph with 8 vertices and 12 edges is shown.
One edge with weight 12 connects vertex v0 and vertex v1.
One edge with weight 4 connects vertex v0 and vertex v5.
One edge with weight 20 connects vertex v1 and vertex v2.
One edge with weight 5 connects vertex v1 and vertex v3.
One edge with weight 7 connects vertex v1 and vertex v4.
One edge with weight 19 connects vertex v2 and vertex v7.
One edge with weight 2 connects vertex v3 and vertex v4.
One edge with weight 18 connects vertex v3 and vertex v7.
The five number summary for a set s" data is given below. Min Q1 Median Q3 Max 53 59 63 66 88 What is the interquartile range of thi set of data? Enter just the number as your answ t. For example, if you found that the interquartilerange was 22 you would enter 22 Provide your answer below:
For the given five number summary, the interquartile range is 7.
The five number summary is a set of descriptive statistics that provides a concise summary of a data set. It consists of the following five values:
Minimum: the smallest value in the data setFirst quartile (Q1): the value below which 25% of the data fallsMedian (Q2): the value that separates the data into two equal halves (i.e., 50% of the data falls above the median, and 50% falls below it)Third quartile (Q3): the value below which 75% of the data fallsMaximum: the largest value in the data setIn this problem, the five number summary is: 53 59 63 66 88
Hence,
Q1 = 59
Q3 = 66
Interquartile range = Q3 - Q1
= 66 - 59
= 7
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A waiter can place 20 chairs at 4 tables that are the same size. How many chairs can she place at two
tables?
The total number of chairs that the waiter can place on two tables is 10 chairs.
Given, the total number chairs that the waiter can place on 4 tables is 20 chairs.
So, the number of chairs that the waiter can place on 1 chair = 20/4 chairs = 5 chairs.
Applying the concept of ratio and proportion,
Now, the total number of chairs that can be placed on 2 chairs will be =
= 2 × 5 chairs = 10 chairs
So, the total number of chairs that the waiter can place on 2 tables is 10 chairs.
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Suppose an urn contains 5 blue chips and 3 red chips. Chips are drawn without replacement until either the first red chip is drawn, or until three blue chips are drawn. Let X be the number of blue chips drawn and Y the number of red chips drawn. (a) Find pX,Y , the joint pmf of X and Y . (You might want to make a table.) (b) Find the marginal pmfs pX and pY . (c) Find the conditional pmfs pX|Y (x|0) and pX|Y (x|1).
The joint pmf of X and Y 5/8, the marginal pmfs pX and pY is 3/7 and the conditional pmfs pX|Y (x|0) and pX|Y (x|1) is 5/28 and 41/56.
The probability that the chosen combination has a certain property can be set up by dividing the number of combinations where the property holds by the total number of possible combinations.
The order of the chips chosen does not matter so outcomes can be considered as combinations. We must choose 3 of the 9 chips in the box, where X are chosen from the 3 red chips, and Y are chosen from the 2 white, and the remainder are chosen from the 4 black.
For x∈{0,1,2,3}and y∈{0,1,2}, the probability that x red chips and y white chips are chosen is
To determine the marginal distribution of X, we need not distinguish white chips from black. X chips are chosen from the 3 red chips, and the remainder are chosen from the 5 non-red chips. For x∈{0,1,2,3} the probability that x chips are chosen is,
P(x) = (³ₓ) (₃-ₓ⁶) / (⁹₃)
Similarly, in determining the marginal distribution of Y, we choose Y white chips from among the 3 available, then choose the remaining chips from the 5 non-white chips.
c) To find the conditional distribution,
P(X|Y=0)= 5/28
P(X|Y=1)= 41/56
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find a vector equation of the tangent line to the parametrized curve r(t) = 9t, t , t2 when t = 1. (your instructors prefer angle bracket notation < > for vectors.)
The vector equation of the tangent line is <9t+9, t+2, t^2>.
To find the tangent line to the curve at t=1, we need to find the derivative of r(t) and evaluate it at t=1.
r(t) = 9t <1> + 1 <2> + t^2 <3>
Taking the derivative of r(t) with respect to t, we get:
r'(t) = 9 <1> + 1 <0> + 2t <3>
Evaluating r'(1), we get:
r'(1) = 9 <1> + 1 <0> + 2(1) <3> = 9 <1> + 2 <3>
So the vector equation of the tangent line at t=1 is:
r(1) + tr'(1) = <9,1,1> + t<9,2,0>
Simplifying, we get:
<9t+9, t+2, t^2>
So the vector equation of the tangent line is <9t+9, t+2, t^2>.
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Find 2×2_matrix which transforms the APQR having vectices P(3,2), Q(5,6) and R (4,-1) into AP'Q'R' having vertices P'(2,3), Q'(6,5) and R'(-1,4).
The transformation rule for triangle PQR into triangle P'Q'R' is given as follows:
(x,y) -> (y,x).
Which is a reflection over the line y = x.
How to obtain the transformation?The vertices of the original triangle are given as follows:
P(3,2), Q(5,6) and R (4,-1).
The vertices of the transformed triangle are given as follows:
P'(2,3), Q'(6,5) and R'(-1,4).
The x-coordinate and the y-coordinate were exchanged, hence the rule is defined as follows:
(x,y) -> (y,x).
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What is the inverse of function ?
f(x) = 64x³-1
O A.
O B.
O c.
O D.
f¹ (2) = 4√x-1
f¹(x) = +¹
4
f¹(z) = Vz+1
64
f¹(x)=√x-4+1
F
The inverse of the function f(x) = 64x³ - 1 is [tex]f^{-1}(x) = (\frac{3\sqrt{(x + 1)}}{4})[/tex].
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, A function f(x) = 64x³ - 1.
Let, y = 64x³ - 1.
64x³ = y + 1.
x³ = (y + 1)/64.
[tex]x = (\frac{(y + 1)}{64})^{\frac{1}{3}[/tex].
[tex]x = (\frac{3\sqrt{(y + 1)}}{4})[/tex].
[tex]y = (\frac{3\sqrt{(x + 1)}}{4})[/tex].
[tex]f^{-1}(x) = (\frac{3\sqrt{(x + 1)}}{4})[/tex].
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Find the coordinates of the point on y sin(x) that is closest to the point (4, given: (pts) work/calculus: 2 (42) 2). (10 pts)
The coordinates of the point on y sin(x) that is closest to the point (4, y) is (3.579, 0.323).
To find the point on the curve y = sin(x) that is closest to the point (4, y), we can use the distance formula between two points. The distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
We want to minimize this distance, so we can minimize the square of the distance:
d^2 = (x2 - x1)^2 + (y2 - y1)^2
Let (x, sin(x)) be a point on the curve y = sin(x). Then the distance squared between this point and (4, y) is:
d^2 = (x - 4)^2 + (sin(x) - y)^2
To minimize this distance, we can take the derivative of d^2 with respect to x, set it equal to zero, and solve for x:
d^2 = (x - 4)^2 + (sin(x) - y)^2
d^2/dx = 2(x - 4) + 2(sin(x) - y)cos(x) = 0
Simplifying this expression, we get:
x - 4 + (sin(x) - y)cos(x) = 0
We can solve this equation numerically using a numerical method such as Newton's method or the bisection method. Once we have found the value of x that minimizes the distance, we can find the corresponding value of y = sin(x) and the closest point on the curve is (x, sin(x)).
Using a numerical method, we can find that the value of x that minimizes the distance is approximately 3.579. Therefore, the closest point on the curve is (3.579, sin(3.579)) which is approximately (3.579, 0.323).
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find the prime factorization of the following number. 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280 and 560write any repeated factors using exponents. 560
Prime Factorization is finding which prime numbers multiply together to make the original number.
Prime factorization of the following numbers is
1 = 1
2 = 2 × 1
4 = 2² × 1
5 = 5 × 1
7 = 7 × 1
8 = 2³ × 1
10 = 2 × 5
14 = 2 × 7
16 = 2⁴
20 = 2² × 5
28 = 2² × 7
35 = 5 × 7
40 = 2² × 5
56 = 2³ × 7
70 = 2 × 5× 7
80 = 2⁴ × 5
112 = 2⁴ × 7
140 = 2² × 5 × 7
280 = 2³ × 5 × 7
560 = 2⁴ × 5 × 7
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If c > 0, s^2+ t^2 = 6, and st = c+5, what is (s+t)^2 in terms of c ?
Answer: We can start by expanding the square on the left-hand side of the equation:
(s + t)^2 = s^2 + 2st + t^2
We know that s^2 + t^2 = 6, so we can substitute that into the equation:
(s + t)^2 = 6 + 2st
We also know that st = c + 5, so we can substitute that into the equation:
(s + t)^2 = 6 + 2(c + 5)
Simplifying the right-hand side:
(s + t)^2 = 6 + 2c + 10
So, in terms of c, (s + t)^2 = 6 + 2c + 10.
Step-by-step explanation:
Connect and Reflect: Evaluate your work by answering these questions: How did this activity help you understand the US involvement in World War I? Did it change what you learned in any way? What would you like to know more about?
The United States forces arrived in Europe in 1917 and helped tip the scales in favor of Britain and France, leading to an Allied victory over Germany and Austria in November 1918. More than four million Americans had served in the armed forces by the time of the armistice, and 116,708 had died.
What led to US involvement in World War I despite maintaining neutrality?When World War I broke out in Europe in 1914, President Woodrow Wilson declared that the United States would remain neutral, and many Americans agreed. However, public opinion on neutrality began to shift after the sinking of the British ocean liner Lusitania by a German U-boat in 1915, which killed nearly 2,000 people, including 128 Americans.
Wilson requested a declaration of war against Germany in response to the Zimmermann telegram, which threatened an alliance between Germany and Mexico against America.
The United States of America officially entered World War I on April 6, 1917. Millions of Americans served overseas and helped the war effort at home over the next year and a half. Their contributions aided in the victory of the war and shaped both America and the world for future generations.
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please help this is due bye 6:00
5+ – 6f–9+8f–8f
The simplified expression for the expression (5 – 6f–9+8f–8f) is (-4 - 6f).
How to apply operation on Expression?The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition and Subtraction (from left to right).
Given:
5 – 6f–9+8f–8f
Solving the Expression
= 5 – 6f–9+8f–8f
= 5 - 9 -6f + 8f - 8f
= -4 + f(-6 +8 -8)
= -4 + f(-6)
= -4 - 6f
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1. Which of the following is not a variable cost?
A. wages paid to labor
B. seeds and fertilizers for paddy farmers
C. rent on land
D. electricity bills
2. The average total cost of producing computers in a factory is RM500 at the current
output level of 100 units per week. If fixed cost equals RM10,000
A. average fixed cost equals RM10,000.
B. total cost equals RM60,000 per week.
C. variable cost equals RM50,000 per week.
D. average variable cost equals RM400.
3. Which of these statements is false?
A. There are no fixed costs in the long run.
B. Total costs are equal to total fixed costs plus total variable costs.
C. In the short run, all inputs are fixed inputs.
D. A fixed cost is a cost that does not change as output changes.
4. Economies of scale occurs if the firm's:
A. long run average cost curve is horizontal.
B. average cost increases as the firm expands its production.
C. long run average cost decreases as the firm increases its output.
D. long run average cost curve is upward-sloping.
5. If total costs are RM200 for one unit of output and RM310 for two units, what is the marginal cost of the
second unit?
A. RM100
B. RM110
C. RM200
D. RM210
6. In the production of refrigerators, the item which represents variable costs is:
A. the tax on the company's property.
B. the salary of the night watchman.
C. the cost of fuel and electric power.
D. The insurance premium for the premises.
7. The average total cost of producing computers in a factory is RM250 at the current
output level of 100 units per week. If fixed costs equal RM5,000
A. average fixed cost equals RM50.
B. total cost equals RM40,000 per week.
C. variable cost equals RM10,000 per week.
D. average variable cost equals RM400.
9. The marginal cost of a good is
A. the addition to total cost of producing one more unit of output.
B. decreasing when average total cost is decreasing.
C. the difference between average total cost and average fixed cost.
D. always equal to average variable cost when the firm is maximizing profit.
Answer:
ur mom jk its
c
Step-by-step explanation:
The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below.
Commute Time (min),x Well-Being Index score,y
5 69.2
15 68.4
30 67.5
35 67.3
60 66.3
84 66.1
105 64.6
(a) Find the least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable.
(b) Interpret the slope and y-intercept, if appropriate.
(c) Predict the well-being index of a person whose commute is 35 minutes.
(d) Suppose Barbara has a 15-minute commute and scores 68.5 on the survey. Is Barbara more "well-off" than the typical individual who has a 15-minute commute?
(a) The least-squares regression line treating the commute time, x, as the explanatory variable and the index score, y, as the response variable is y = 70.22 - 0.075x
(b) The slope and y-intercept, if appropriate is the slope of the regression line, -0.075, indicates that for every additional minute of commute time, the well-being index score decreases by an average of 0.075.
(c) The well-being index of a person whose commute is 35 minutes is the slope of the regression line, -0.075, indicates that for every additional minute of commute time, the well-being index score decreases by an average of 0.075.
(d) Yes, she is. Barbara more "well-off" than the typical individual who has a 15-minute commute.
Regression of Commute Times(a) To find the least-squares regression line, we need to find the slope and y-intercept of the line that minimizes the sum of the squared vertical distances between the actual data points and the predicted values on the line. Using a calculator or software, we get:
Slope: b = -0.075
y-intercept: a = 70.22
Therefore, the least-squares regression line is:
y = 70.22 - 0.075x
(b) The slope of the regression line, -0.075, indicates that for every additional minute of commute time, the well-being index score decreases by an average of 0.075. The y-intercept, 70.22, represents the predicted well-being index score for someone with a commute time of 0 minutes (which is not a meaningful value in this context).
(c) To predict the well-being index of a person with a commute time of 35 minutes, we can substitute x = 35 into the regression equation and solve for y:
y = 70.22 - 0.075(35) = 67.97
Therefore, the predicted well-being index score for someone with a commute time of 35 minutes is 67.97.
(d) To determine whether Barbara is more "well-off" than the typical individual with a 15-minute commute, we can compare her actual well-being index score of 68.5 to the predicted score based on the regression equation:
y = 70.22 - 0.075(15) = 68.47
Barbara's score of 68.5 is slightly higher than the predicted score of 68.47, which suggests that she is somewhat better off than the typical individual with a 15-minute commute. However, we should note that this comparison is based on a single data point and may not be representative of the larger population.
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Which equation shows the same relationship as 1/2=3x1/6
Answer:
1 /2
Step-by-step explanation:
3×1 = 3
So it is 3 /6 = 1/2
3/6 ÷2 = 1/2
if 5/8 of a number is 565 ,what is 5/4 of the number?
The number of 5/4 is 1130
how to find the number x?
writing this as an algebraic expression.
An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. Also, solve questions in Algebraic Expressions Worksheets
[tex]\frac{5}{8}x[/tex] = 565
[tex]\frac{5x}{8}[/tex] = 565
5x = 565 * 8
5x = 4520
x = [tex]\frac{4520}{5}[/tex]
x = 904
so the number is 904
What is 5/4 of 904 ?
[tex]\frac{5}{4}[/tex] * 904
= 1130
so the answer to this question is 1130
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Alexandra is making a set of bowls in her pottery class.
She has 3/4 pound of clay.
She needs 3/2 pounds of clay to make one whole set of bowls.
Use the drop-down menus to complete each of the statements below about the bowls
that Alexandra can make.
The amount of full sets Alexandra can make would be 3.
What is meant by fraction?When there is no common factor between the fraction's numerator (top) and denominator (bottom), the fraction is said to be in its simplest form.
A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction.
A fraction is a piece of a whole number and a means to divide a number into pieces that are each equal. The numerator, also known as the number of equal parts being counted, is expressed as being greater than the denominator, also known as the number of parts in the entire.
Multiply both the numerator and denominator of 5 / 2 by 2.
5/2 × 2/2 = 10/4
The sets of bowls you can make, divide by 3 / 4.
(10/4)/(3/4) = 3 and 1/3.
The amount of full sets Alexandra can make is 3.
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When a new charter school opened in 2000, there were 540 students enrolled. write a formula for the equation n , representing the number of students attending this charter school t years after 2000, assuming that the student population:Increases by 11% per year N(t)=Decreases 23 students per year N(t)=Decreases 8.9% per year. N(t)=Increases 81 students per year . N(t)=Remains constant (does not change). N(t)=Increases 6.4% per year. N(t)=
a) Increased by 44 students per year= N(t) = 240 + 44t
b) Decreased by 32 students per year=N(t) = 240 - 32t
c) Increased by 40 students every 2 years=N(t) = 240 - 32t
d) Decreased by 24 students every 4 years=N(t) = 240 - 32t
e) Remained constant= N(t) = 240
f) Increased by 5 students every semester (twice in a year)=N(t) =240+10t
The original population of students in the year 2000 is 240.
[tex]N_0=240[/tex]
Let the number of years = t
a) If the population increased by 44 students every year, the population, after t years, would have increased by 44t
Therefore,
[tex]N(t)=N_0+44t[/tex]
N(t) = 240 + 44t
b) If the population decreased by 32 students per year, the population, after t years, would have decreased by 32t
Therefore, [tex]N(t)=N_0-32t[/tex]
N(t) = 240 - 32t
c) If the population Increased by 40 students every 2 years and increase is uniform per year, the population will increase by 40/2 = 20 students in 1 year. So in t years, the population would increase by 20 t.
Therefore,
[tex]N(t)=N_0+20t\\\\N(t)=240+20t[/tex]
d) Decreased by 24 students every 4 years
In 1 year, it decreases by 24/4 = 6 students
In t years, it decreases by 6t students
[tex]N(t)=N_0-6t\\\\N(t)=240-6t[/tex]
e) Remained constant
N(t)=N0
N(t)=240.
f) If the population increases by 5 students twice in a year
In 1 year, it increases by 5*2 = 10 students
In t years, it increases by 10t students
[tex]N(t)=N_0+10t\\\\N(t)=240+10t[/tex].
The Complete Question:-
When a new charter school opened in 2000, there were 240 students enrolled. Write a formula for the function N ( t ), representing the number of students attending this charter school t year after 2000, assuming that the student population:
a) Increased by 44 students per year
b) Decreased by 32 students per year
c) Increased by 40 students every 2 years
d) Decreased by 24 students every 4 years
e) Remained constant
f) Increased by 5 students every semester (twice in a year)
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A kite is flying at an angle of elevation of 43o. If the string is 37 m long and is stretched tight, find the height of the kite to the nearest tenth of a meter.
The required height of the kite to the nearest tenth of a meter is 25.2 m.
What is the sine ratio in a triangle?In a right-angled triangle, the ratio of the perpendicular (with respect to an angle) to the hypotenuse gives the sine value of that angle. This relationship is used to solve problems regarding height and distance chapter.
Draw the figure as per the given instructions.
The position of the kite is at A and the string is AC which is 37 m long. The angle of elevation is ∠ACB, which is 43°. The height of the kite is AB.
So, apply the formula of sine ratio (perpendicular/hypotenuse) = sinα, where α be the opposite angle of that perpendicular.
AB/AC = sin∠ACB
AB/37 = sin43°
AB = 37sin43°
≈37×0.68
= 25.16
≈ 25.2
Therefore, the obtained answer is 25.2 m.
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Question 5(Multiple Choice Worth 2 points)
(Linear Functions LC)
Which of the following equations represents a linear function?
Ox= 3
Oy=2x-5
Oy=³x²
O3x-6=4
All the linear functions are,
⇒ x = 3
⇒ y = 2x - 5
⇒ 3x - 6 = 4
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We know that;
Degree of variables in a linear function is always one and the graph shows the straight line.
So, By all options;
All the linear functions are,
⇒ x = 3
⇒ y = 2x - 5
⇒ 3x - 6 = 4
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If a trend line has equation y = 15 + 0.8x, what type of association would you expect the data to have?
A partially-filled water tank contains 300 gallons of water. water is then pumped into the tank at a constant rate. After n minutes, the amount of water, w, in the tank is W = 300 + 9 gallons. After how many minutes will W = 450 gallons?
A. 33 1/3
B. 5
C. 50
D. 16 2/3
Show your work
The amount of time when the water tank will have 450 gallons will be 16²/₃ minutes. The correct option is D.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a partially-filled water tank contains 300 gallons of water. water is then pumped into the tank at a constant rate. After n minutes, the amount of water, w, in the tank is W = 300 + 9n gallons.
The time will be calculated as:-
W = 300 + 9n
450 = 300 + 9n
9n = 150
n = 150 / 9
n = 16²/₃ minutes.
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airlines sometimes overbook flights. suppose that for a plane with 50 seats, 55 passengers have tickets. define the random variable y as the number of ticketed passengers who actually show up for the flight. the probability mass function of y appears in the accompanying table. y 45 46 47 48 49 50 51 52 53 54 55 p(y) 0.05 0.10 0.13 0.14 0.25 0.16 0.06 0.05 0.03 0.02 0.01 (a) what is the probability that the flight will accommodate all ticketed passengers who show up? (b) what is the probability that not all ticketed passengers who show up can be accommodated? (c) if you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? what is this probability if you are the third person on the standby list?
a) Probability that the flight will accommodate all ticketed passengers who show up is 0.16
b) Probability that not all ticketed passengers who show up can be accommodated is 0.67
c) The probability that you will be able to take the flight is 96%
Probability is a powerful tool to understand the likelihood of different outcomes in various situations, including overbooking of flights
In this scenario, the random variable y represents the number of ticketed passengers who actually show up for the flight, out of a total of 55 ticketed passengers for a plane with only 50 seats. The probability mass function of y provides the probabilities for each possible outcome.
(a) The probability that the flight will accommodate all ticketed passengers who show up is the probability of y being equal to 50, which is 0.16.
(b) The probability that not all ticketed passengers who show up can be accommodated is the sum of the probabilities of y being greater than 50, which is
=> 0.05 + 0.10 + 0.13 + 0.14 + 0.25 = 0.67.
(c) If you are the first person on the standby list, the probability of being able to take the flight is the probability of y being less than or equal to 50, which is 0.89. This means that there is an 89% chance that you will get on the plane. If you are the third person on the standby list, the probability is the probability of y being less than or equal to 52 (since two people need to cancel or not show up for you to get on), which is 0.96. This means that there is a 96% chance that you will get on the plane.
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The integers from 1 to n, inclusive, are placed in order and equally spaced on a circle. At the ends of a diameter are the numbers 7 and 23 as shown in the figure. What is the value of n?
The required value of n is the integer "32" as shown in the given figure.
What are integers?integer, positive or negative whole-valued number, or 0. The integers are formed from a collection of counting numbers such as 1, 2, 3,...
Here,
According to the question,
Let the number of integers between 7 and 23, inclusive, be x (note that x is not necessarily equal to n). Then the number of integers between 1 and 7, inclusive, and the number of integers between 23 and n, inclusive, must also be x, because the integers are equally spaced on the circle.
n = 2(x) ....(i)
Since from above definition
x = 23 - 7
x = 16
Substitute the value of x = 16 in equation (i),
n = 2(16)
n = 32
Therefore, the value of n is "32".
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I need help with this question.
The measure of angle C in triangle BCD is 39⁰.
option B.
What is the measure of angle C in ΔBCD?
The measure of angle C in triangle BCD is calculated by applying the following formula as shown below.
Angle D = 92 ⁰ ( vertically opposite angles are equal )
∠CDB = 180 - 92⁰ = 88⁰ ( sum of angles on a straight line )
∠AED = 180 - (35 + 92 ) ( sum of angles in a triangle)
∠AED = 53⁰
In the quadrilateral FBDE,
angle B = 180 - 53 ( opposite angles of a cyclic quadrilateral are supplementary)
angle B = 127
∠CBD = 180 - 127 ( sum of angles on a straight line)
∠CBD = 53⁰
Then, the value of ∠BCD is calculated as;
∠BCD + ∠CBD + ∠CDB = 180 ( sum of angles in a triangle )
∠BCD + 53 + 88 = 180
∠BCD + 141 = 180
∠BCD = 180 - 141
∠BCD = 39⁰
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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 = (5√n) / (5√n + 6)
The sequence with nth term an = (5√n)/(5√n + 6) diverges.
To determine the convergence or divergence of the sequence with the given nth term, we can use the limit comparison test by comparing it with the divergent series 1/n.
We have
lim n→∞ an/(1/n) = lim n→∞ (5√n)/(5√n + 6) * n = 5/5 = 1
Since the limit is a positive finite number, and the series 1/n diverges, the series with the nth term also diverges by the limit comparison test.
Therefore, the sequence with the nth term an = (5√n)/(5√n + 6) diverges.
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Which of the following predicate logic expressions is the correct translation of the definition of the limit of a real-valued function f(x) of a real variable x at a point a in its domain? The limit of f(x) as the variable x approaches a is L if for every real number ε > 0 there exists a real number 8 >0 such that If(x) – LI<ɛ whenever 0 < lx – al
The correct translation of the definition of the limit of a real-valued function f(x) of a real variable x at a point a in its domain in predicate logic expressions.
For all ε > 0, there exists δ > 0 such that for all x, if 0 < |x-a| < δ, then |f(x)-L| < ε.
In symbols, this can be written as:
∀ε > 0, ∃δ > 0 such that ∀x, (0 < |x - a| < δ) → (|f(x) - L| < ε).
Note that "ε" and "δ" are the Greek letters epsilon and delta, respectively, and they are used to represent small positive numbers. This definition says that if we want the limit of f(x) to be L, we can find a positive number δ such that the distance between f(x) and L is less than ε whenever x is within δ units of a (but not equal to a). The limit is said to exist if we can find such a δ for any value of ε.
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If the information in this pictogram was displayed in a pie chart what would the central angle of the Dexter representing moderate conditions be
The central angle of the pie chart representing the moderate conditions is 80°
What is central angle?Central angle is the angle subtended by an arc of a circle at the center of a circle. The radius vectors form the arms of the central angle.
Given that, a pictogram which was displayed in a pie chart, we need to find the central angle of the pie chart,
Sea conditions is shown,
Calm = 3 blue dots
Moderate = 2 and a half dot
Rough = 5 and 3 parts of the dot
Each dot = 4 points
Therefore,
Calm = 3×4 = 12
Moderate = 2×4 + 1/2 × 4 = 10
Rough = 5×4 + 3/4 ×4 = 23
The central angle = 10 / 12+10+23 × 360° = 80°
Hence, the central angle of the pie chart representing the moderate conditions is 80°
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The complete question is:-
If the information in this pictogram was displayed in a pie chart, what would the central angle of the sector representing rough conditions be? Give your answer in degrees Sea conditions
Calm Key
Moderate
Rough