TOPIC 1 ANGLES AND TRIANGLES
SKILLS PRACTICE continued
PROBLEM SET 2: Classifying Angles
> Identify each pair of angles as complementary, supplementary, or vertical angles.
Answers
Each pair of angles has been identified as adjacent, complementary, supplementary, or vertical angles as shown in the image attached below.
What is a complementary angle?In Mathematics and Geometry, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°);
55 + 35 = 90°
What are adjacent angles?In Mathematics and Geometry, adjacent angles can be defined as two (2) angles that share a common vertex and a common side. This ultimately implies that, both angles 1 and 2, 5 and 6, 9 and 10 are pair of adjacent angles.
In conclusion, the linear pair theorem is sometimes referred to as linear pair postulate (supplementary angle) and it states that the measure of two angles would add up to 180° provided that they both form a linear pair.
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Related Questions
The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = Sqrt 2 + t , y = 1 + 1 /2 t, where x and y are measured in centimeters. The temperature function satisfies Tx(2, 9) = 7 and
Ty (2, 9) = 1. How fast is the temperature rising on the bug's path after 2 seconds? (Round your answer to two decimal places.)
Answers
The temperature is rising at a rate of 7.5 degrees Celsius per second along the bug's path after 2 seconds.
What is differentiation?A derivative of a function with regard to an independent variable is defined as differentiation. In calculus, differentiation can be used to calculate the function per unit change in the independent variable.
We can use the chain rule of differentiation to find how fast the temperature is changing on the bug's path. Let T denote the temperature function, and let x and y be functions of time t given by x = sqrt(2) + t and y = 1 + t/2. Then the temperature function on the bug's path is given by T(x(t), y(t)), and we want to find dT/dt at t = 2.
Using the chain rule, we have:
dT/dt = dT/dx * dx/dt + dT/dy * dy/dt
We are given Tx(2, 9) = 7 and Ty(2, 9) = 1, so we can evaluate the partial derivatives at (x, y) = (2, 9):
dT/dx(2, 9) = 7
dT/dy(2, 9) = 1
To find dx/dt and dy/dt, we can take the derivatives of x and y with respect to t:
dx/dt = 1
dy/dt = 1/2
Now we can plug in the values:
dT/dt = 7 * 1 + 1 * 1/2
dT/dt = 7.5
Therefore, the temperature is rising at a rate of 7.5 degrees Celsius per second along the bug's path after 2 seconds.
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Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 193 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x=167.90 cm, y=81.47 kg, r=0.303, P-value=0.002, and y=−107+1.13x. Find the best predicted value of y (weight) given an adult male who is 153 cm tall. Use a 0.01 significance level.
Answers
Answer:
At a 0.01 significance level, we reject the null hypothesis and conclude that the predicted weight of 65.89 kg is significantly different from the actual weight, which could be anywhere between 53.45 kg and 78.32 kg.
Step-by-step explanation:
Given the linear regression equation:
y = -107 + 1.13x
where x is the height in cm and y is the weight in kg.
To find the predicted value of y for a person with a height of 153 cm, we substitute x = 153 into the regression equation:
y = -107 + 1.13(153)
y = -107 + 172.89
y = 65.89
Therefore, the best predicted weight for an adult male who is 153 cm tall is 65.89 kg.
To check if this predicted value is statistically significant at a 0.01 significance level, we can perform a hypothesis test.
Null Hypothesis: The predicted weight for a person with a height of 153 cm is not significantly different from the actual weight.
Alternative Hypothesis: The predicted weight for a person with a height of 153 cm is significantly different from the actual weight.
We can use a t-test to test this hypothesis, with the test statistic:
t = (y_predicted - y_actual) / (s / sqrt(n))
where y_predicted is the predicted weight, y_actual is the actual weight, s is the standard error of the estimate, and n is the sample size.
The standard error of the estimate can be calculated using:
s = sqrt((1 - r^2) * Sy^2)
where Sy is the sample standard deviation of the y variable.
From the given information, we have:
Sy = 22.77 kg
r = 0.303
Therefore,
s = sqrt((1 - 0.303^2) * 22.77^2) = 20.19 kg
The sample size is n = 100.
Substituting these values into the t-test formula, we get:
t = (65.89 - y_actual) / (20.19 / sqrt(100))
t = (65.89 - y_actual) / 2.019
We want to test at a 0.01 significance level, which corresponds to a two-tailed test with a critical value of t = ±2.576 (from a t-distribution with 98 degrees of freedom, since n-2=98).
If the absolute value of t is greater than 2.576, we reject the null hypothesis and conclude that the predicted weight is significantly different from the actual weight.
Substituting t = 2.576 and t = -2.576 into the t-test formula, we get:
2.576 = (65.89 - y_actual) / 2.019
y_actual = 53.45 kg
-2.576 = (65.89 - y_actual) / 2.019
y_actual = 78.32 kg
Therefore, at a 0.01 significance level, we reject the null hypothesis and conclude that the predicted weight of 65.89 kg is significantly different from the actual weight, which could be anywhere between 53.45 kg and 78.32 kg.
Strategic decisions occur:
infrequently and involve long-term decisions
infrequently and involve immediate decisions
frequently and involve long-term decisions
frequently and involve immediate decisions
Answers
Strategic decisions occur infrequently and involve long-term decisions.
Decision making is the process of taking decisions from two or more alternatives.
Strategic decision making is one of the important decision making process in an organization. This is one of the best ways to achieve the goals and objectives of an organization.
This is a long term process of decision making since it focus on long term goals.
So this does not occur frequently.
Hence the correct option is (A) infrequently and involve long-term decisions.
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Can someone help me with this problem?
Answers
In the given diagram, the measure of angle BAC, m ∠BAC, is 66°
Circle Geometry: Calculating the measure of angleFrom the question, we are to calculate the measure of the unknown angle
In the given diagram, we have a circle
We are to calculate the measure of angle BAC, m ∠BAC
From one circle theorems, we have that
The angle subtended by an arc at the center of a circle is twice the angle subtended at the circumference
Thus,
From the give circle, we can write that
132° = 2 × m ∠BAC
Divide both sides by 2
132° / 2 = m ∠BAC
66° = m ∠BAC
Therefore,
m ∠BAC = 66°
Hence,
Measure of the angle is 66°
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For the function f shown in the graph below, what is the local minimum? Question
Each answer choice below represents a relation by a set of ordered pairs. In which of the answer choices is the relation a function?
Select all correct answers.
Select all that apply:
{(4,9),(0,−2),(0,2),(5,4)}
{(5,−5),(5,−4),(7,−2),(3,8)}
{(4,3),(8,0),(5,2),(−5,0)}
{(6,9),(9,−4),(6,1),(−5,11)}
{(4,12),(2,6),(−5,6),(3,−2)}
Answers
To determine whether a relation is a function, we need to check whether each input (x-value) in the relation is associated with exactly one output (y-value). One way to do this is to check if there are any repeated x-values with different y-values.
Out of the given answer choices:
{(4,9),(0,−2),(0,2),(5,4)} is not a function since there are two different y-values associated with the x-value 0.
{(5,−5),(5,−4),(7,−2),(3,8)} is not a function since there are two different y-values associated with the x-value 5.
{(4,3),(8,0),(5,2),(−5,0)} is a function since there are no repeated x-values.
{(6,9),(9,−4),(6,1),(−5,11)} is not a function since there are two different y-values associated with the x-value 6.
{(4,12),(2,6),(−5,6),(3,−2)} is a function since there are no repeated x-values.
Therefore, the answer choices that represent a function are:
{(4,3),(8,0),(5,2),(−5,0)}
and
{(4,12),(2,6),(−5,6),(3,−2)}
So the correct options are:
{(4,3),(8,0),(5,2),(−5,0)}
and
{(4,12),(2,6),(−5,6),(3,−2)}
To determine whether a relation is a function, we need to check whether each input (x-value) in the relation is associated with exactly one output (y-value). One way to do this is to check if there are any repeated x-values with different y-values.
Out of the given answer choices:
{(4,9),(0,−2),(0,2),(5,4)} is not a function since there are two different y-values associated with the x-value 0.
{(5,−5),(5,−4),(7,−2),(3,8)} is not a function since there are two different y-values associated with the x-value 5.
{(4,3),(8,0),(5,2),(−5,0)} is a function since there are no repeated x-values.
{(6,9),(9,−4),(6,1),(−5,11)} is not a function since there are two different y-values associated with the x-value 6.
{(4,12),(2,6),(−5,6),(3,−2)} is a function since there are no repeated x-values.
Therefore, the answer choices that represent a function are:
{(4,3),(8,0),(5,2),(−5,0)}
and
{(4,12),(2,6),(−5,6),(3,−2)}
So the correct options are:
{(4,3),(8,0),(5,2),(−5,0)}
and
{(4,12),(2,6),(−5,6),(3,−2)}
A fair die with sides labeled 1 through 6 is rolled two times. The values of the two
rolls are added together. The sum is recorded as the outcome of a single trial of a
random experiment. Compute the probability that the sum is greater than 10.
Answers
A fair die is rolled twice, then the probability that the sum is greater than 10 is 1/12.
Finding the total number of possible outcomes when the dice is rolled twice:
A total of 6*6 = 36 outcomes are possible as there are 6 outcomes for the first roll and 6 outcomes for the second.
Making a list of all results that add up to greater than 10:
5 + 6 = 11
6 + 5 = 11
6 + 6 = 12
There are only three favorable outcomes.
So, the probability of getting a number greater than 10 =
[tex]\frac{no\ of\ favorable\ outcomes}{total\ number\ of\ possible\ outcomes}[/tex]
P(sum > 10) = 3/36 = 1/12
Therefore, there is a 1/12 probability that the sum of the two dice is greater than 10.
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A particular sound wave can be graphed using the function y=-1 sin 5x. Find the period of the function.
Answers
We refer to a function as periodic if it repeats across time with a fixed interval.
It is written as f(x) = f(x + p), where p denotes the function's period and is a real number.
Period is defined as the elapsed time between the two instances of the wave.
Here, we have,
A function's period is the amount of time between repetitions of the function. A trigonometric function's period is defined as the length of one complete cycle.
A periodic function is one whose values repeat at regular intervals. For instance, periodic functions include the trigonometric functions, which repeat every 2 pi radians.
Waves, oscillations, and other periodic events are all described by periodic functions in science. A period is the amount of time that separates two waves, whereas a periodic function is a function that repeats its values at regular intervals.
Each set of numbers that are separated by a comma in a number when expressed in standard form is known as a period. It has four periods, making it 5,913,603,800. The place value chart displays each period using a distinct color.
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Expressed in simplest a + bi form, (7-3i) + (x - 2i)² - (4i + 2x²) is
Answers
Therefore, the expression (7-3i) + (x - 2i)² - (4i + 2x²) in the simplest a + bi form is: -2x² - 1 - (4x + 7i)
What are the different forms of linear equation?Linear Equation General Form Example
Slope intercept form y = mx + b y + 2x = 3
Point–slope form y – y1 = m(x – x1 ) y – 3 = 6(x – 2)
General Form Ax + By + C = 0 2x + 3y – 6 = 0
Intercept form x/a + y/b = 1 x/2 + y/3 = 1
As a Function f(x) instead of y f(x) = x + C f(x) = x + 3
The Identity Function f(x) = x f(x) = 3x
Constant Functions f(x) = C f(x) = 6
Let's start by expanding the square term (x - 2i)² using the formula for (a + b)²:
(x - 2i)² = x² - 4xi + 4i²
Note that i² = -1, so we can simplify this expression to:
(x - 2i)² = x² - 4xi - 4
Substituting this expression and the given values into the original expression, we get:
(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)
Grouping the real and imaginary terms, we get:
(7 - 4 - 2x²) + (-3i - 4i - 4x) + (x²)
Simplifying the real part, we get:
-2x² - 1
Simplifying the imaginary part, we get:
-7i - 4x
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On Friday, three friends shared how much they read during the week.
• Barbara read the first 100 pages from a 320-page in the last 4 days
• Judy read the first 54 pages from a 260-page book in the last 3 days.
• Nancy read the first 160 pages from a 480-page book in the last 5 days
Part B
If the three friends continue to read everyday at their rates, who will finish reading
their book first? Second? Third? (Show all work)
Answers
Barbara:
Barbara read 100 pages in 4 days, so she reads 100 / 4 = 25 pages per day.
Barbara's book has 320 pages, so it will take her 320 / 25 = 12.8 days to finish the book.
Judy:
Judy read 54 pages in 3 days, so she reads 54 / 3 = 18 pages per day.
Judy's book has 260 pages, so it will take her 260 / 18 = 14.44 days to finish the book.
Nancy:
Nancy read 160 pages in 5 days, so she reads 160 / 5 = 32 pages per day.
Nancy's book has 480 pages, so it will take her 480 / 32 = 15 days to finish the book.
Therefore, Barbara will finish reading her book first, Judy will finish second, and Nancy will finish last.
10. A flagpole is supported by two identical wires. What is the distance (X) between the two wires?
Answers
Using the Pythagoras theorem, we can find the value of x to be = 10ft.
Option B is correct.
Define Pythagoras theorem?The right-angled triangle's three sides are related in line with the Pythagoras theorem, also referred to as the Pythagorean theorem. The hypotenuse of a triangle's other two sides add up to a square, according to the Pythagorean theorem, which states that.
Here in the question,
We have 2 right-angled triangles.
So, base of the large triangle, x
= √ (13² - 12²) + √ (13² - 12²)
= √ 5² + √ 5²
= 5 + 5
= 10ft.
Therefore, the length of the side, x = 10ft.
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What integer is the square root of 115 closest to?
Answers
Answer:
10
Step-by-step explanation:
How many solutions can be found for the equation 3y + 5 − 2y = 1
Answers
We can solve the equation to find it's number of solutions, but we already know it only has 1 solution because it is a linear equation (y is raised to the first power).
[tex]3y + 5 - 2y = 11[/tex]
[tex]y + 5 = 11[/tex]
[tex]y = 6[/tex]
This confirms that there is only 1 solution.
Question 3
A cuboid has volume of 168 cm³.
The area of the base of the cuboid is 24 cm² and its width is 4 cm
Work out the surface area of the cuboid.
Answers
The calculated value of the surface area of the cuboid is 188cm²
Working out the surface area of the cuboidFrom the question, we have the following parameters that can be used in our computation:
A cuboid has volume of 168 cm³.The area of the base of the cuboid is 24 cm² Its width is 4 cmThis means that
Height = 168/24 = 7
Length = 24/4 = 6
The surface area of the cuboid is then calculated as
Area = 2 * (lw + wh + lh)
Substitute the known values in the above equation, so, we have the following representation
Area = 2 * (4 * 6 + 4 * 7 + 7 * 6)
Evaluate
Area = 188
Hence, the area is 188cm²
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The preimage below does a translation of 3 units up, 2 units left, then a reflection across the x-axis. The image coordinates after this transformation are L'(-2,-1), K'(0,-2), and J'(2,0). Explain or show your work for how the transformation on JKL was completed to get the coordinates of L', K', and J'.
Answers
The final image points are: L'(-2,-1), K'(0,-2), J'(2,-3)
How to explain the transformationIt should be noted that to innitiate the first transformation, we must translate three units in a positive y-direction and two units to the left along the x-axis. This is accomplished via adding three to the respective points' measurements on the y-axis and immediately subtracting two from the x-coordinates. Consequently, the consecutive coordinates of J, K, and L become:
J(3,3), K(5,2), L(3,1)
Subsequently, the second alteration requires that we reflect across the x-axis; this can simply be achieved by inverting the y-values of each given point. In conclusion, the modified coordinates of J', K', and L' are now:
J'(3,-3), K'(5,-2), L'(3,-1)
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A standard deck of 52 cards has 4 suits: clubs, spades, hearts, and diamonds. Each suit has number cards 2 through 10, a jack, a queen, a king, and an ace. The jack, queen, and king are considered "face cards".
What is the probability of drawing one card from a standard deck of cards and choosing a "face card"????
A. 1/3
B. 3/52
C. 1/4
D. 3/13
Answers
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and I only need #3
Answers
Answer:
The graph will be translated down 2 units.
The new horizontal asymptote is y=2 because the graph now crosses over the y axis at 2. This is at the point (0,2).
Teresa bought 6 CDs that were each the same price. Including sales tax, she paid a total of 84.60 . Each CD had a tax of 0.80 . What was the price of each CD before tax?
Answers
Answer:0.70
Step-by-step explanation:
Solve the percent word problem below:
Answers
Explanation
The percentage can be found by dividing the value by the total value and then multiplying the result by 100. The formula used to calculate the
percentage is: (value/total value)×100%.
CAN SOMEONE HELP WITH THIS QUESTION?
Answers
Answer:
X2 = 1.697916 X3 = 1.431
Step-by-step explanation:
use Newton's formula of the method of approximating of zeros of a function : x_n+1. = x_n - f(x_n)/f'(x_n)
Find the size of the following angles
Answers
Step-by-step explanation:
Q1. By linear pair, I know that 72* + unknown angle = 180*
therefore unknown angle = 180-72 = 108*
Now because this is a pentagon, the total of all interior angles of a polygon equals 540*
so 108* + 100* + 110* + 45* (Half of 90 , written as a semi-square) + Y* = 540
Y* = 540 - 363 = 177*
Q2. 360 - (80+70+110) = q
q = 360 - 220 = 140*
Q3. 160+160+ S* = 360*
360* - 320* = S*
S* = 40*
Hope it helps
The distance between Eilat and Jerusalem is 292 kilometers. Give this distance in miles. Round the answer to the nearest tenth.
Answers
This distance in miles is 181.3 miles.
It's worth noting that the conversion factor of 1 kilometer equals 0.621371 miles is an exact value defined by international agreement, so there is no rounding involved in the conversion itself. The rounding occurs only when expressing the result in a specific number of decimal places. It's also worth noting that conversions between units of measurement are important in many fields, including science, engineering, and international trade.
To convert kilometers to miles, we can use the conversion factor of 1 kilometer equals 0.621371 miles. Therefore, to find the distance between Eilat and Jerusalem in miles, we can multiply the given distance of 292 kilometers by 0.621371:
292 km × 0.621371 = 181.344052 miles
Rounding this result to the nearest tenth gives:
181.3 miles
Therefore, the distance between Eilat and Jerusalem is approximately 181.3 miles.
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The cost in dollars to produce x shovels in a factory is given by the function C(x)=33x+430. The number of shovels that can be produced in h hours is given by the function N(h)=30h
7. Find the rule for C(N(h)).
8. Find the cost when h=12 hours
Answers
Okay, to find the maximum number of shovels that can be produced with $10,000, we need to do the following:
1) Set the cost function C(N(h)) = 10,000. So: 990h + 430 = 10,000
2) Subtract 430 from both sides: 990h = 9,570
3) Divide both sides by 990: h = 9.75 (round to 10 hours)
4) Substitute 10 hours into the function for number of shovels:
N(10) = 30(10) = 300 shovels
Therefore, the maximum number of shovels that can be produced with $10,000 is 300 shovels.
Let me know if you have any other questions!
Please answer both questions
Step 1 step 2 step 3 and step 4 nicely please and I need this by today
Answers
The volume of the figure is equal 30 cubic feet.
The new volume of the figure is equal 60 cubic feet.
If Molly sells all of the dog beds, she would earn $6.25.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;
Volume of figure = 5 × 3 × 2
Volume of figure = 30 cubic feet.
When the height is doubled, we have;
Volume of figure = 5 × 3 × 2(2)
Volume of figure = 60 cubic feet.
For the cost of fabric used, we have:
Cost of fabric used = 2.5 × $4.50
Cost of fabric used = $11.25
Profit = selling price - cost
Profit = $17.50 - $11.25
Profit = $6.25.
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AM
XYZ Homework
Use the fundamental identities to match equivalent expressions.
a
d
с
b
1
sec (0) + 1
1
1
+
1 - cos(0) 1 + cos(0)
+
G VIDEO
1
csc (0) - cot (0)
1
csc (0) + 1
1
sec(0) - 1
+
1
csc (0) + cot(0)
1
csc (0) - 1
O Port to forum
a. 2 csc (0)cot (0)
b. 2 sec (0)tan (0)
c. 2 cot (0)
d. 2 csc² (0)
Answers
Using the fundamental identities, the equivalent expressions are hereby matched as follows:
a. 2 csc (θ) cot (θ) = 2 sin²(θ) / (sin(θ) + cos(θ))
b. 2 sec (θ) tan (θ) = (2 sec²(θ)) - 2 sec(θ)
c. 2 cot (θ) = 2 / sin(θ) - csc(θ)
d. 2 csc² (θ) = 2 / (csc(θ) - 1)(csc(θ) + 1)
How did we arrive at these expressions?Using the fundamental identities, rewrite each expression as follows:
a. 2 csc (θ) cot (θ) = 2 / sin(θ) * cos(θ) = 2 cos(θ) / sin(θ) = 2 / sin(θ) - 2 / sin(θ) + 2 cos(θ) / sin(θ) = 2 / sin(θ) - 2 / (1 + cot(θ)) = (2 - 2 sin(θ)) / (sin(θ) + cos(θ)) = (2 sin²(θ)) / (sin(θ) + cos(θ))
b. 2 sec (θ) tan (θ) = 2 / cos(θ) * sin(θ) / cos(θ) = 2 sin(θ) / cos²(θ) = 2 / cos²(θ) - 2 / cos(θ) = (2 sec²(θ)) - 2 sec(θ)
c. 2 cot (θ) = 2 cos(θ) / sin(θ) = 2 / sin(θ) - 2 / sin²(θ) = 2 / sin(θ) - csc(θ)
d. 2 csc² (θ) = 2 / sin²(θ) = 2 / (1 - cos²(θ)) = 2 / (1 - cos(θ))(1 + cos(θ)) = 2 / (csc(θ) - cot(θ))(csc(θ) + cot(θ)) = 2 / (csc(θ) - 1)(csc(θ) + 1)
Therefore, the matches are:
a. 2 csc (θ) cot (θ) = 2 sin²(θ) / (sin(θ) + cos(θ))
b. 2 sec (θ) tan (θ) = (2 sec²(θ)) - 2 sec(θ)
c. 2 cot (θ) = 2 / sin(θ) - csc(θ)
d. 2 csc² (θ) = 2 / (csc(θ) - 1)(csc(θ) + 1)
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NEED HELP PLEASE NOW
Answers
Answer:
im pretty sure its the first one that you chose :)
Step-by-step explanation:
The probability of winning a profit of twice your wager is 1/6, the probability of winning a profit equal to your wager is 1/3, and all other probabilities of winning are zero. What is your expected value for this game? Assume the wager is $1.
Answers
The expected value for the game is 2/3.
What is expected value?The average value we would anticipate to find if we repeated an experiment several times is the anticipated value of a random variable. It is calculated by averaging the outcomes of multiplying each potential result of the random variable by the associated probability. In other words, it's the weighted average of all potential possibilities, with the weights being the likelihoods that each outcome would actually happen. In several disciplines, including finance, economics, and engineering, predictions and judgements are made using the expected value, a fundamental idea in probability theory.
Let us suppose the profit = X.
Thus,
Probability of winning twice our wager = 1/6 thus, the expected value is:
(2)(1/6) = 1/3
No, for profit equal to wager we have:
(1)(1/3) = 1/3
The total expected value is:
E(X) = (1/3) + (1/3) + 0 = 2/3
Hence, the expected value for the game is 2/3.
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John invested in a savings bond for 4 years and was paid simple interest at an annual rate of 4%. The total interest that he earned was $48. How much did he invest?
Answers
the principal or invested amount is $41.38
The computation of the invest amount is given below:
As we know that
Principal = Amount ÷ (1 + rate × time)
= $48 ÷ (1 + 0.04 × 4)
= $48 ÷ 1.16
= $41.38
Hence, the principal or invested amount is $41.38
Basically we have applied the above formula so that the same would be calculated
URGENT!! I WILL GIVE
BRAINLIEST!!!!! AND ALSO 100 POINTS!!!!!
Answers
Answer: All of the slopes are the same.
Which function includes the minimum or maximum value of f as a number that appears as it is shown?
a) f(x)=(x+2)^{2}−16
b) f(x)=(x−2)(x+6)
c) f(x)=x^{2}+4x−12
d) f(x)=x^{2}+6x−2x−12
Answers
To find the minimum or maximum value, we can complete the square by adding and subtracting (4/2)^2 = 4 to the function to get:
f(x) = (x^2 + 4x + 4) - 4 - 12
f(x) = (x + 2)^2 - 16
Since (x + 2)^2 is always non-negative, the minimum value of f(x) is -16, which occurs when (x + 2)^2 = 0, or x = -2
The x-coordinate of the vertex is given by: x = -b/2a
The y-coordinate of the vertex is simply the value of the function at x = -b/2a.
So, in order for the function to include the minimum or maximum value of f as a number that appears as it is shown, we need to rewrite each of the given functions in vertex form.
a) f(x) = (x+2)^2 - 16
Vertex form: f(x) = a(x-h)^2 + k
f(x) = (x-(-2))^2 - 16
f(x) = (x+2)^2 - 16
The vertex occurs at (-2, -16), and the minimum value of the function is -16.
b) f(x) = (x-2)(x+6)
To find the vertex form, we need to expand the expression:
f(x) = x^2 + 4x - 12
Vertex form: f(x) = a(x-h)^2 + k
Completing the square: f(x) = (x+2)^2 - 16
The vertex occurs at (-2, -16), and the minimum value of the function is -16.
c) f(x) = x^2 + 4x - 12
Vertex form: f(x) = a(x-h)^2 + k
Completing the square: f(x) = (x+2)^2 - 16
The vertex occurs at (-2, -16), and the minimum value of the function is -16.
d) f(x) = x^2 + 6x - 2x - 12
Simplifying: f(x) = x^2 + 4x - 12
Vertex form: f(x) = a(x-h)^2 + k
Completing the square: f(x) = (x+2)^2 - 16
The vertex occurs at (-2, -16), and the minimum value of the function is -16.
Therefore, all the functions have the same minimum value of f as a number that appears as it is shown, which is -16.
1.2 A Telkom account holder notices that her phone bills for three consecutive months were
significantly different. In May, her account was one and a half times more than her account in June.
Her account in July was R 50 more than her account in June. In total, she spent R 575 in cellular-
phone accounts in the three months. What was her account for each month?
Answers
The balance on the account of the Telkom account holder, every month was :
May - R 225June - R 150July R 200How to find the account balance ?We know that May was one and half times June :
M = 1. 5 x J
July was R 50 more than June :
L = J + 50
Total spent was R 575 :
M + J + L = R 575
Then we can solve by substitution:
( 1. 5 J ) + J + ( J + 50 ) = 575
3. 5 J + 50 = 575
3. 5 J = 525
J = 525 / 3. 5 = R 150
L would be:
= 150 + 50
= R 200
M would be:
= 1. 5 x 150
= R 225
The balances for the Telkom account holder is therefore May - R 225, June - R 150, and July R 200.
Find out more on account balance at https://brainly.com/question/29601825
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