cot0 equals 6, lies in quadrant 3 sin20
The exact value of sin 2θ is 12/37
How to find the exact value of sin 2θ?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
We have:
cot θ = 6
Thus, tan θ = 1/6
Using the given information, we can sketch the location of the angle θ in the quadrant (See the attached image).
Thus, we can calculate the value of the hypotenuse using the Pythagoras theorem. That is:
hypotenuse = √((-6)² + (-1)²) = √37
sin θ = -1/√37
cos θ = -6/√37
Using trig. identity:
sin 2θ = 2sinθ·cosθ
sin 2θ = 2 * (-1/√37) * (-6/√37)
sin 2θ = 12/37
Therefore, the exact value of sin 2θ is 12/37
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Complete Question
If cot θ = 6,and θ lies in quadrant 3, find the exact value of sin 2θ
1. Ashenge Private Limited Company is about to start production of new products. Before the start of the new production, it cost the company $200,000 to construct the factory building. Once the construction is over, the cost per unit of production is estimated to be Birr 20. Upon selling, the company will incur a 20% commission expense. Moreover, the price per unit of products is decided to be Birr 50.
Required:
a) Construct the total cost equation in terms of quantity.
b) Determine the break-even quantity and break-even revenue.
The total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
Given that a company is starting a new production, it cost the company $200,000 to construct the factory building.
The cost per unit of production is estimated to be Birr 20.
The company will incur a 20% commission expense.
The price per unit of products is decided to be Birr 50.
We need to find the total cost equation in terms of quantity and determine the break-even quantity.
a) The fixed cost of the company is $200,000, and 40 per unit sell,
Therefore for n units the total cost =
200,000 + 40n
b) BEQ = FC / P−VC
= 200,000 / 50-40
= 20,000
Hence the total cost equation is 200,000 + 40n and the break-even revenue is 20,000.
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Husk takes out a 3200 student loan at 6.7% to help him
Part (a) find the total amount interest that will accrue for loan 1(community college )
Part (b) find the total amount of intrest that will a cure for loan 2 state university
Part (c) find the total amount intrest that accrues until payment begin
(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.
How to solve(a) For loan 1, $3200 at 6.7% for 4 years and 7 months (4 years in college + 3 months deferment), the simple interest = 3200 * 0.067 * (55/12) ≈ $1023.33.
(b) For loan 2, $12,000 at 7.3% for 2 years and 7 months (2 years in college + 3 months deferment), simple interest = 12000 * 0.073 * (31/12) ≈ $2362.33.
(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.
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Solve 8 • w ≤ 72. Graph the solution.
Please help
Answer:
w≤9
Step-by-step explanation:
8w ≤ 72
Divide by 8 on both sides
w ≤ 9
For graph, draw a number line and label a point as 9. Draw a solid line facing to the left and having a closed point at 9. The line should not extend past 9.
The table below shows the number of people in an arena t minutes after an event has ended.
T= minutes after event ended: 4 8 12 16 20 24
F(t)= number of people in area: 15221 10649 7375 4859 3468 2285
-Use the regression capability of your graphing calculator to find an exponential equation matching this data. Round values to three decimal places.
F(T)= ___
-use your equation (with values rounded to three decimal places) to help you answer the following questions.
(Note: do not use the data table to answer these questions) Round your answers to the nearest whole number.
- How many people were in the arena 23 minutes after the event ended?
-How many people were in the arena 60 minutes after the event ended?
How many people were in the arena at the exact moment the event ended?
Approximately 19142 people were in the arena at the exact moment the event ended.
How to solveTo decipher an exponential equation synchronous with the provided data, we will employ the equation of [tex]F(t) = a * b^t.[/tex]
Herein, 'F(t)' stands for the total number of attendees in the stadium at 't' minutes after the stoppage of the event, with 'a' symbolizing the initial value and 'b' being the base.
Exploiting the regression aptitudes of a graphing calculator, the exponential equation that most adequately applies to the listed information is: [tex]F(t) = a * b^t[/tex] with three decimal points specified.
F(t) = 19141.846 * 0.718^t
Using the equation:
[tex]F(23) = 19141.846 * 0.718^2^3 = 2726[/tex]
Answer: Approximately 2726 people were in the arena 23 minutes after the event ended.
How many people were in the arena 60 minutes after the event ended?
[tex]F(60) = 19141.846 * 0.718^6^0 = 123[/tex]
Answer: Around 123 people were in the arena a full hour after the occurrence concluded.
How many people were present precisely when the event wrapped up?
F(0) = 19141.846 * 0.718^0 = 19141.846 * 1 = 19141.846
Answer: Approximately 19142 people were in the arena at the exact moment the event ended.
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If mZRST = 70, mZQST = 2x, and mZQSR = 3x - 10, what is the mZQSR
16
48
32
38
Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.
Explain about the adjacent angles:If two angles share a side and a vertex, they are said to be neighbouring in geometry. In other words, neighbouring angles do not overlap and are placed next to one another immediately.
We may infer from our criteria and the aforementioned instances that any pair of neighbouring angles has a shared vertex and a common side. They really aren't adjacent if one of these elements is absent. By searching for these two characteristics, we can categorise pairs of angles as neighbouring or not adjacent.There are numerous unique connections between angles in pairs. You can recognise other angle connections, such as supplementary and complementary angles, by recognising nearby angles.Given data:
m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10From the figure:
m∠RST = m∠QST + m∠QSR
Put the values
70 = 2x + 3x - 10
5x = 80
x = 16
Thus,
m∠QSR = 3x - 10 = 3(16) - 10
m∠QSR = 38
Thus, the value of x for the given set of adjacent angles is found as: x = 16 and m∠QSR = 38.
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Complete question:
If m∠RST = 70, m∠QST = 2x, and m∠QSR = 3x - 10, what is the m∠QSR?.
The figure is attached:
16
48
32
38
Create a bar graph from the results of the following survey question: "On average, how much time do you spend using your cell phone each week?"
The bar graph from the results of the following survey question titled "Hours spent using your cell phone each week" is found in the attachment.
What is a bar graph?A bar chart, also called a bar graph, is a visual representation of categorical data that uses rectangular bars with heights or lengths that correspond to the measure of the values they represent.
The bars in a bar chart can be plotted either vertically or horizontally.
Vertical bars, horizontal bars, grouped bars, or stacked bars can all be used to make bar graphs.
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The hypotenuse of a certain right triangle is twice the length of the
shorter leg. The shorter leg is 4 cm.
Answer:
Step-by-step explanation:
If the hypotenuse of a right triangle is twice the length of the shorter leg and the shorter leg is 4 cm, then the hypotenuse is 2 * 4 cm = 8 cm.
Using the Pythagorean theorem, we can find the length of the longer leg. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Letting c represent the length of the hypotenuse and a and b represent the lengths of the other two sides, we can write this as c^2 = a^2 + b^2.
Substituting in the known values for c and one of the other sides (let’s say a), we have:
8^2 = 4^2 + b^2 64 = 16 + b^2 b^2 = 48 b = sqrt(48)
So, the length of the longer leg is sqrt(48) cm, or approximately 6.93 cm.
Choose yes or no to tell whether the equation has the given solution 1/4×+3=3=4×+ 1,x=8
Answer:
[tex]\large\boxed{\tt No.}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to determine if the equation has a solution given a value.}[/tex]
[tex]\textsf{Since x is given to us, we can use the \underline{Substitution Property of Equality} to evaluate}[/tex]
[tex]\textsf{the equation.}[/tex]
[tex]\large\underline{\textsf{What is the Substitution Property of Equality?}}[/tex]
[tex]\textsf{The Substitution Property of Equality is a Property that allows us to substitute}[/tex]
[tex]\textsf{a known term, or expression for an unknown variable, or some kind of placeholder.}[/tex]
[tex]\textsf{After Substitution, we can prove that the expressions are still equal with this}[/tex]
[tex]\textsf{property.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\tt \frac{1}{4} x + 3 = " 3 = " 4x+1[/tex]
[tex]\textsf{There's likely a typo in your equation given, hence I will fix it.}[/tex]
[tex]\tt \frac{1}{4} x + 3 = 4x+1[/tex]
[tex]\textsf{Substitute 8 for x in both sides of the equation using our property.}[/tex]
[tex]\underline{\textsf{Use the Substitution Property of Equality;}}[/tex]
[tex]\tt \frac{1}{4} (8) + 3 = 4(8)+1[/tex]
[tex]\underline{\textsf{Follow PEMDAS, multiply first;}}[/tex]
[tex]\tt 2 + 3 = 32+1[/tex]
[tex]\underline{\textsf{Evaluate;}}[/tex]
[tex]\tt 5 \neq 33[/tex]
[tex]\textsf{If the "typo" was the actual equation;}[/tex]
[tex]\tt 5 \neq 3 \neq 33[/tex]
[tex]\large\boxed{\tt No.}[/tex]
A number rounded to the nearest thousand is 47,000 which number could be the number that was rounded
Answer:
Anything greater than or equal to 46,500, and less than or equal to 47,499 could be the answer.
For example, a number, let's say 46,589 falls within that range and may have been the number that was rounded.
Correct answer gets brainliest!!!!
It is a point and point is zero dimensional. Therefore the right options are A and C respectively.
Understanding Point in MathematicsPoint is a basic geometric object that represents a location or a position in space. It is often represented as a dot or a small circle.
Points have no size, shape, or dimension. They are considered to be zero-dimensional objects, and they are often used as a building block for more complex geometric structures.
In addition to representing locations in space, points are also used in other areas of mathematics, such as in coordinate systems and in topology. In geometry, points are used to define lines, planes, and other geometric shapes.
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What is the surface area of this composite solid?
The surface area of the given composite solid is calculated as: 200.24 square units.
How to Find the Surface Area of the Composite Solid?Surface area of the composite solid = surface area of rectangular prism + surface area of cylinder - 2(area of the base of the cylinder)
Surface area of rectangular prism = length * width * height = 10 * 3 * 5
= 150 square units.
Surface area of cylinder = 2πr(h + r)
height (h) = 4
Radius (r) = 2
Plug in the values:
Surface area of cylinder = 2 * 3.14 * 2(4 + 2) = 75.36 square units
Area of the base of the cylinder = πr² = 3.14 * 2²
= 12.56 square units
Thus, we have:
Surface area of the composite solid = 150 + 75.36 - 2(12.56) = 200.24 square units.
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Time (minutes) Jumping Jacks
1 50
2 100
3 150
4 200
Considering the jumping jacks: 50, 100, 150, 200, what is the common difference?
50
Now, think of this table as a set of ordered pairs. This means that the first row can be placed in an ordered pair as (1, 50). The second row can be written as (2, 100). Using this, what is the slope of the line that connects the first two points?
50
What is the slope of the line that connects the 3rd and 4th point?
50
What is the slope of the line that connects the 1st and the 4th point?
150
Is the common difference (aka slope aka rate of change) constant?
Yes
Why is it or is it not constant?
It is constant because it is a linear function.
Answer:
Step-by-step explanation:
The common difference between the number of jumping jacks is 50, as you correctly stated. This means that the number of jumping jacks increases by 50 for each additional minute.
The slope of the line that connects any two points on this table represents the rate of change of the number of jumping jacks with respect to time. Since the common difference is constant, the slope of the line that connects any two points on this table will be the same. In this case, the slope is 50.
The slope of the line that connects the first and fourth points is calculated as (200 - 50) / (4 - 1) = 150 / 3 = 50, not 150.
The common difference (aka slope aka rate of change) is constant because the number of jumping jacks increases by the same amount for each additional minute. This means that the relationship between time and the number of jumping jacks is linear.
1a. Model the periodic motion of the horses using an
equation and a graph.
Horse Equation: Use function notation in degrees. Your
function will graph below
The amount of time it takes the horse to complete a full cycle of motion is known as the period of the motion and can be calculated as follows:
T = 2π/ω.
What is the explanation for the above response?Let's assume that a straightforward harmonic motion can be used to simulate the horse's movements. The simple harmonic motion equation is:
y = A sin(ωt + φ)
where:
The deviation from equilibrium is represented by the number y.
The maximum displacement's amplitude is A.
The angular frequency is equal to two times the frequency ω.
It's time t
The phase angle is φ
The equation can be written as follows, assuming that the horse is moving vertically and that its highest point corresponds to y = 0.
y = A sin(ωt)
where is the angular frequency and A is the motion's amplitude.
On a graph, where the horizontal axis denotes time and the vertical axis denotes displacement, we can draw this function as a sine wave. The
amount of time it takes the horse to complete a full cycle of motion is known as the period of the motion and can be calculated as follows:
T = 2π/ω
We need to know the duration of the horse's motion in order to predict when Ivan will have another chance to make a flawless shot. It's challenging to determine the period precisely in the absence of more details.
You can name the graph of the carousel equation θ = A cos(ωt) as follows:
The time, t, is displayed on the x-axis as seconds.
The angular position from the midline, θ, expressed in degrees, is shown on the y-axis.
The horizontal axis at θ = 0 degrees is the midline.
The largest angle of departure from the midline, or the distance between the wave's crest (highest point) or trough (lowest point), is known as the amplitude, or A.
The interval between two consecutive wave crests or troughs is known as the period, or T, which is the length of time it takes for one full cycle of motion.
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The ratio of children: teenagers: adults in a survey sample are 2: 11:17. a) Which is the largest group represented? b) If there are 180 people surveyed how many are:
The solution is,
there are children = 12, teenagers= 66, adults = 102,
so, adults = 102 is the largest group represented
Here, we have,
given that,
The ratio of children: teenagers: adults in a survey sample are 2: 11:17.
now, we have,
If there are 180 people surveyed
now, let , we have,
children = 2x
teenagers= 11x
adults = 17x
now, we have,
2x + 11x + 17x = 180
or, 30x = 180
or. x = 6
Hence, The solution is,
there are children = 12, teenagers= 66, adults = 102,
so, adults = 102 is the largest group represented.
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Which of the following is not a run-on sentence?
O The average length for a feature film is between 80 and 100 minutes but there are some films that exceed 14 hours in length and one film that was 85
hours long.
O According to data collected throughout film history, the average length for a feature film is between 80 and 100 minutes, although some far exceed the
standard running time.
O There are some movies that clock in at over 14 hours long even though the average movie is around 80 minutes but can run up to 120 minutes.
O With an average film length of 80 to 100 minutes it can be surprising to discover that some movies have been 14 hours long and even 85 hours long.
The option that is not a run-on sentence is this: According to data collected throughout film history, the average length for a feature film is between 80 and 100 minutes, although some far exceed the standard running time.
What is a run-on sentence?A run-on sentence is a sentence that continues without using appropriate punctuation to join independent clauses. In the sentence above, the comma is used in the right place to join the independent clause, so we may not refer to this as a run-on sentence.
The other three options continue on end without appropriate punctuation to break off the independent clauses.
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For the function f(x)=|x-3 | select all the true statements. A. The function is increasing on the interval [3, 5) B. The function is increasing of the Interval (0, 3) C. The vertex is (0, 3) D. The vertex is (3, 0). E. The y-intercept is (0, 3). F. The y-intercept is (3, 0).
Answer:
D and E----------------------
See attached graph to help with answer choices.
Given function:
f(x) = | x - 3 |Answer choices:
A. The function is increasing on the interval [3, 5) - False, correct interval is [3, + ∞)B. The function is increasing on the Interval (0, 3) - False, as shown aboveC. The vertex is (0, 3) - False, the vertex is (3, 0)D. The vertex is (3, 0) - TRUEE. The y-intercept is (0, 3) - TRUEF. The y-intercept is (3, 0) - False, the correct one is given aboveM7|L5
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
Enter ✔
Answer:
Does this shape have at least 1 pair of parallel lines? 40
Has at least 1 pair of parallel lines
Does not have at least 1 pair of parallel
lines
More
Ted made $56 in interest by placing $700 in a savings account with simple interest for 1 year. What was the interest rate?
The interest rate if Ted made $56 in interest for 1 year on a principle of $700 will be 8%.
Given, the interest amount is $56.
The principal amount is $700.
The time period of investment is 1 year.
Now, we have to find the interest rate.
The formula to find the simple interest is,
S.I = PTR/100.
Now, we need to substitute the values in the above formula.
S.I = PTR/100
56 = 700×1×R / 100
56 = 700R/100
5600 = 700R
R = 5600/700
R = 8
Therefore, the interest rate is 8%.
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find the probability that a randomly selected point within the large square falls in the red shaded square 6 6 15 15 p= enter as a decimal rounded to the nearest hundredth
The probability that a randomly selected point within the red-shaded square is 0.16
Finding the probability of a pointFrom the question, we have the following parameters that can be used in our computation:
Red square of 6 by 6White square of length 15The areas of the above shapes are
Red square = 6 * 6 = 36
White square = 15^2 = 225
The probability is then calculated as
P = Red square /White square
So, we have
P = 36/225
Evaluate
P = 0.16
Hence, the calculated value of the probability that the point falls in the red square is 0.16
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The ratio of two numbers is 7 to 3 and the sum of their squares is 232. Find the numbers.
PLEASE HELP I have 30 minutes! What is the end behavior of this equation and how did you get it?
The limit of the function will be:
lim f(x) = ∞ as x → ∞
lim f(x) = 0 as x → -∞
How to explain the functionThe limit of f(x) as x goes towards infinity is infinite while the limit of f(x) approaches 0 when x tends to a negative value. Mathematically speaking,
lim f(x) = ∞ as x → ∞
lim f(x) = 0 as x → -∞
We can comprehend such behavior because the function's base is greater than 1 which explains how its growth accelerates as x increases and diminishes quickly as x declines towards zero.
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Given this unit circle what is the value of x
Answer:
[tex]x=-\dfrac{\sqrt{51}}{10}[/tex]
Step-by-step explanation:
You want the value of x in the third quadrant of a unit circle where y = -7/10.
Pythagorean theoremThe radius of a unit circle is 1, so the Pythagorean theorem tells you the magnitude of the value of x is ...
1² = x² +(7/10)²
x = -√(1 -49/100) = -√(51/100) . . . . . . x < 0 in the third quadrant
x = (-√51)/10
Hey folks help me out for some points :)
Answer:
C
Step-by-step explanation:
Positive numbers represent a positive situation. And negative numbers coincide with a negative situation.
Ex: An increase in temperature corresponds to a positive number, and a decrease in temperature with a negative number.
Is 93 + 7 positive or negative?
Answer:
93 + 7 = 100
Step-by-step explanation:
I would assume positive because 100 is above the x-axis not below it.
Sarah uses a square and two semicircular7 inches regions to design a heart shaped poster find the area of the heart then find the approximate area by using 3.14radius
The poster has an area equal to 192.423 square inches.
How to determine the area of a heart shaped poster
In this problem we must determine the area of a heart shaped poster, that is, the combination of the areas of a square and two semicircles, whose resulting formula is introduced below:
A = D² + (π / 4) · D²
Where:
A - Area of the heart shaped poster, in square inches.D - Side length of the square, in inches.If we know that π = 3.14 and D = 7 in, then the area of the poster is:
A = 7² + (π / 4) · 7²
A = (5π / 4) · 7²
A = 192.423 in²
The area of the poster is equal to 192.423 square inches.
Remark
The image is missing and the statement is not well explained. A correct statement is shown below:
Sarah uses a square with side length of 7 inches and two semicircles with diameter of 7 inches to design a heart shaped poster. Find the area of the heart. Then, find the approximate area by using 3.14.
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HELP ASAP!!!
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The IQR of 10 is the most accurate to use, since the data is skewed.
The range of 10 is the most accurate to use, since the data is skewed.
The IQR of 45 is the most accurate to use to show that they need more money.
The range of 45 is the most accurate to use to show that they have plenty of money.
A measure of variability which the charity should use to accurately represent the data include the following: D. The range of 45 is the most accurate to use to show that they have plenty of money.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 10.
First quartile (Q₁) = 13.75.
Median (Med) = 20.
Third quartile (Q₃) = 26.25.
Maximum (Max) = 55.
For the IQR, we have:
IQR = Third quartile (Q₃) - First quartile (Q₁)
IQR = 26.25 - 13.75
IQR = 12.50
For the range, we have;
Range = maximum - minimum
Range = 55 - 10
Range = 45.
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The coordinates of the midpoints of the four sides of a square are S(-4, 11), Q(2, 5), U(-4, -1), and A(-10, 5).
Determine the perimeter and area of the square.
5
O perimeter is 144 units; area is 48 square units
O perimeter is 48 units; area is 144 square units
O perimeter is 24√/2 units; area is 72 square units
O perimeter is 72 units; area is 24√/2 square units
The perimeter and area of the square are 24√2 units and 12 units² respectively
What is the perimeter and area of the square?
To determine the perimeter and area of the square, we have to find the lengths of the sides.
But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.
SQ = √(x₂ - x₁)² + (y₂ - y₁)²
SQ = √(2 - (-4)² + (5 - 11)²
SQ = 6√2
Let's find for QU
QU = √(-4 - 2)² + (-1 - 5)²
QU = 6√2
Let's find for UA ;
UA = √(-10 - (-4))² - (5 - (-1)²
UA = 6√2
And the distance from AS = 6√2
The perimeter of the square = 4 * (6√2)
Perimeter = 24√2 units
The area of the square is l²
Area of the square = (6√2)²
Area of square = 12 units²
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Construct a truth table for the statement (~ pVq) →q.
Here is the truth table for the statement (~ p V q) → q:
```
p q ~p ~p V q (~p V q) → q
---------------------------------------
T T F T T
T F F F T
F T T T T
F F T F T
```
In the table, `p` and `q` represent the truth values of the propositions `p` and `q`, respectively. The symbol `~` represents negation (i.e., "not"). The symbol `V` represents the logical connective "or" (i.e., "inclusive or"). The symbol `→` represents the conditional connective "implies" (i.e., "if...then").
To fill in the truth table, we first evaluate `~p` and `~p V q` for each combination of truth values for `p` and `q`. Then, we evaluate `(~p V q) → q` for each combination of truth values.
We can see that the statement is always true, regardless of the truth values of `p` and `q`, except for the case where `p` is true and `q` is false.
You’re planning to buy a car and you want to have $25,000 to purchase a car in cash in 5 years. If you’re able to receive 10% interest rate for investing the money, how much money should you invest today in order to have $25,000 in 5 years?
You have to invest $15,506.08
How to solve for the investmentPV = FV / (1 + r)^n
where:
PV = present value (amount of money you need to invest today)
FV = future value (amount of money you want to have in 5 years, which is $25,000)
r = interest rate (10% or 0.1)
n = number of periods (5 years)
Plugging in the values into the formula:
PV = $25,000 / (1 + 0.1)^5
PV = $25,000 / 1.61051
PV = $15,506.08
Therefore, you need to invest approximately $15,506.08 today at a 10% interest rate in order to have $25,000 in 5 years to purchase a car in cash.
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