Translate: Knowing that sen alpha = 0. 6 and that a is an acute angle, calculates the rest of trigonometric ratios
Rest of the trigonometric ratios for the acute angle alpha are cos(alpha) = 0.8 and tan(alpha) = 0.75.
If we know that sin(alpha) = 0.6, we can use the Pythagorean identity to find cos(alpha) and tan(alpha). Here's how:
Since sin(alpha) = opposite/hypotenuse, we can represent sin(alpha) as the ratio of the length of the side opposite the acute angle alpha to the length of the hypotenuse of the right triangle. Let's assume that the length of the opposite side is a and the length of the hypotenuse is h. Then we have:
sin(alpha) = a/h = 0.6
Solving for a, we get:
a = 0.6h
Using the Pythagorean theorem:
[tex]a^2 + b^2 = h^2[/tex]
Since a and h are related by a = 0.6h, put 0.6h for a to get:
[tex](0.6h)^2 + b^2 = h^2[/tex]
Simplifying:
[tex]0.36h^2 + b^2 = h^2[/tex]
[tex]b^2 = h^2 - 0.36h^2 = 0.64h^2[/tex]
[tex]b = \sqrt{0.64h^2} = 0.8h[/tex]
So now we know that b = 0.8h and a = 0.6h. Using these values, we can find cos(alpha) and tan(alpha) as follows:
[tex]cos(alpha) = adjacent/hypotenuse = b/h = 0.8h/h = 0.8tan(alpha) = opposite/adjacent = a/b = 0.6h/0.8h = 0.75[/tex]
Therefore, the rest of the trigonometric ratios for the acute angle alpha are cos(alpha) = 0.8 and tan(alpha) = 0.75.
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An article suggests the uniform distribution on the interval (6.5, 21) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) What are the mean and variance of depth? (Round your variance to two decimal places.) mean variance (b) What is the cdf of depth? F(x) = {0 x < 6.5 6.5 lessthanorequalto x < 21 1 21 lessthanorequalto x (c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.) What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.) (d) What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.) What is the probability that the observed depth is within 2 standard deviations of the mean value?
Answer : a ) Variance = (21 - 6.5)^2/12 = 13.7708, b) 1, 21 <= x, c) Probability = 0.5862, D) Probability = 0.8552
The uniform distribution on the interval (6.5, 21) can be represented as U(6.5, 21).
(a) The mean and variance of a uniform distribution can be calculated using the following formulas:
Mean = (a + b)/2
Variance = (b - a)^2/12
where a and b are the lower and upper bounds of the distribution, respectively.
For the given distribution, a = 6.5 and b = 21.
Therefore, the mean and variance of depth are:
Mean = (6.5 + 21)/2 = 13.75
Variance = (21 - 6.5)^2/12 = 13.7708
(b) The cdf of a uniform distribution can be calculated using the following formula:
F(x) = (x - a)/(b - a)
For the given distribution, F(x) = (x - 6.5)/(21 - 6.5) for 6.5 <= x < 21.
Therefore, the cdf of depth is:
F(x) = {
0, x < 6.5
(x - 6.5)/14.5, 6.5 <= x < 21
1, 21 <= x
(c) The probability that observed depth is at most 10 can be calculated using the cdf:
P(X <= 10) = F(10) = (10 - 6.5)/14.5 = 0.2414
The probability that observed depth is between 10 and 15 can be calculated using the cdf:
P(10 <= X <= 15) = F(15) - F(10) = (15 - 6.5)/14.5 - (10 - 6.5)/14.5 = 0.5862
(d) The standard deviation of a uniform distribution can be calculated using the following formula:
Standard deviation = sqrt(Variance)
For the given distribution, the standard deviation is:
Standard deviation = sqrt(13.7708) = 3.7118
The probability that the observed depth is within 1 standard deviation of the mean value can be calculated using the cdf:
P(13.75 - 3.7118 <= X <= 13.75 + 3.7118) = F(13.75 + 3.7118) - F(13.75 - 3.7118) = (13.75 + 3.7118 - 6.5)/14.5 - (13.75 - 3.7118 - 6.5)/14.5 = 0.5118
The probability that the observed depth is within 2 standard deviations of the mean value can be calculated using the cdf:
P(13.75 - 2*3.7118 <= X <= 13.75 + 2*3.7118) = F(13.75 + 2*3.7118) - F(13.75 - 2*3.7118) = (13.75 + 2*3.7118 - 6.5)/14.5 - (13.75 - 2*3.7118 - 6.5)/14.5 = 0.8552
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quadratic function in vertex form y=x^2+4x+6
Answer:
y = (x + 2)² + 2
Step-by-step explanation:
a quadratic function in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
y = x² + 4x + 6
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² to x² + 4x
y = x² + 2(2)x + 4 - 4 + 6
= (x + 2)² + 2 ← in vertex form
What is the best way to design a study to determine how much traffic there is during the morning rush
hour along a city street?
A. Send a survey to the local businesses surrounding the street, asking them how many times they
drive and how many times they take transit to work each year.
OB. Survey local car dealerships to see how many cars are sold in the area over the past year.
X
O C. Make video recordings of the street during rush hour every day for year and count the numbers
of vehicles that pass a certain point.
OD. Count the number of cars that pass a particular point during rush hour over 3 days, and then
take the average
The best way to design a study to measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year and count the number of vehicles that pass a certain point, then calculate the average using the given formula.
The best way to accurately measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year. After recording the video, count the number of vehicles that pass a specific point in the video. Then, calculate the average number of vehicles that pass the point each day during one year by using the following formula: Average = (Number of vehicles per day1 + Number of vehicles per day2 + ... + Number of vehicles per dayn) / n, where n is the number of days the video recording was made. This method is the most reliable way to measure the amount of traffic during the morning rush hour since it provides an average based on the data collected over a full year.
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use substitution to solve the system x-3y=10, x+5y=-22
Answer:
x = -2
y = -4
Step-by-step explanation:
Given equations:x - 3y = 10 --------------(1)
x + 5y = -22 -----------(2)
Taking Eq. (1)
x - 3y = 10
Add 3y to both sidesx = 10 + 3y ------------(3)
Put Eq. (3) in Eq. (1)10 + 3y + 5y = -22
Subtract 10 from both sides8y = -22 - 10
8y = -32
Divide 8 to both sidesy = -32/8
y = -4Put y = -4 in Eq. (3)x = 10 + 3(-4)
x = 10 - 12
x = -2[tex]\rule[225]{225}{2}[/tex]
Answer:
[tex]\bf x=-2[/tex][tex]\bf y=-4[/tex]Step-by-step explanation:
To solve the given system, let's begin by solving for x in x- 3y=10:-
[tex]\tt x-3y=10[/tex]
Add 3y to both sides:-
[tex]\tt x-3y+3y=10+3y[/tex]
[tex]\tt x=10+3y[/tex]
Substitute x= 10+3y into x+5y=-22:-
[tex]\tt 10+3y+5y=-22[/tex]
Simplify:-
[tex]\tt 10+8y=-22[/tex]
Now, solve for y in 10+8y=-22:-
[tex]\tt 10+8y=-22[/tex]
Subtract 10 from both sides:-
[tex]\tt \tt 10+8y-10=-22-10[/tex]
[tex]\tt 8y=-32[/tex]
Divide both sides by -8:-
[tex]\boxed{\bf y=-4}[/tex]
Now, substitute y=-4 into x=10+3y:-
[tex]\tt x=10+3y[/tex]
[tex]\tt x=10+3\times-4[/tex]
Simplify:-
[tex]\boxed{\bf x=-2}[/tex]
Therefore, x=-2 and y=-4
_________________________
Hope this helps! :)
whats 2 + 2n is it 4n or 4 or something diffrent?
Answer:
it depends
Step-by-step explanation:
it depends on the value of n
for instance if n was = to 7 then
2+2n = 2+2(7) = 2+14 = 16
Answer: 2+2n
Step-by-step explanation:
The expression 2 + 2n can be simplified as follows:
2 + 2n = 2(1 + n)
So the expression 2 + 2n is equivalent to 2 times the quantity 1 plus n, or simply 2(1 + n). It cannot be simplified any further unless there is additional information or context provided.
Find the greatest common factor of 270 and 360. (Give the answer in the numerical form in the top box and in exponential form by filling in the boxes for exponents.)
*please can I get the numbers that go in the boxes*
Answer:
the GCF of 270 & 360 is 90
exponent form: 3³x 2 x 5 = 270 & 3²x 2³x 5 = 360
Step-by-step explanation:
3 x 3 x 3 x 2 x 5 = 270
3 x 3 x 2 x 2 x 2 x 5 = 360
Shuffle: Charles has seven songs on a playlist. Each song is by a different artist. The artists are Celine Dion, Phil Collins, Elton John, Mariah Carey, Joey Meintyre, Kavana, and Adam Rickilt. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Adam Rickitt and the second song is by Phil Collins? Write vour answer as a fraction or a decimal, rounded to four decimal places.
0.0002
The required probability can be calculated as follows:Explanation:There are 7 different songs from 7 different artists, thus there are 7! ways of shuffling these songs. In other words, there are 7! = 5040 different playlists in which these songs can be shuffled.We need to calculate the probability of Adam Rickitt's song being played first and Phil Collins' song being played second. This can be done in two steps.Step 1: We place Adam Rickitt's song at the beginning of the playlist. There is only one way to do this. After Adam Rickitt's song has been placed, we are left with 6 remaining songs that can be shuffled. Thus, there are 6! = 720 different playlists.Step 2: We place Phil Collins' song as the second song on the playlist. There is only one way to do this as well.Therefore, the probability that Adam Rickitt's song is played first and Phil Collins' song is played second is given by the product of the probabilities of the two steps as follows:P = 1/5040 × 1 = 1/5040 = 0.000198 rounded to 4 decimal places. Thus, the probability is approximately 0.0002. Therefore, the probability that the first song is by Adam Rickitt and the second song is by Phil Collins is 0.0002.
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The ratio of boys and girls in a class is 3:5. There are 32 students in the class.
How many students are girls?
Using ratios, we can find that the number of girls in the class are 20.
What are ratios?If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalises two ratios.
For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls) There are 3 out of 4 girls and 1 out of 4 guys.
Now in the question, total students in class = 32.
The ratio between the boys and girls is 3:5.
So, total parts from the ratio = 3+5=8
Now 5/8 students in the class are girls.
= 5/8 × 32
= 5 × 4
= 20.
Therefore, the number of girls in the class are 20.
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find the area of the shaded region of the given circle
diameter = 14cm
[tex]radius \: = \frac{d}{2} = \frac{14}{2} \\ = 7cm[/tex]
Area of circle ( A1 ) = [tex]\pi {r}^{2} [/tex]
[tex] = \frac{22}{7} \times 7 \times 7 \\ [/tex]
[tex] = 154 {cm}^{2} [/tex]
Area of Square ( A2 ) = l²
= ( 14 )²
= 196cm²
Area of shaded region = A2 - A1
= 196 - 154
= 42cm²
....Thank you !! :)
I need help solving this problem
By speed fοrmula, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.
What is speed?Speed is defined as the distance travelled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn.
Mathematically, speed is calculated as fοllοws:
speed = distance/time
Where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.
We can use the fοrmula:
time = distance/speed
where distance is the distance frοm the star tο Earth, and speed is the speed οf light.
Putting the values, we get:
time = (3.9 x 10¹⁴ km) / (3.0 x 10⁵km/s)
Simplifying, we can divide the distances and divide the pοwers οf ten:
time = 1.3 x 10⁹ s
Therefοre, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.
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After spending 60 percent of his money , Joseph has a re 600. How much did he have in the beginning?
After spending 60% of his money Joseph has rs. 600., He has 1500 in the beginning.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Let the total amount be x
He spent 60% of his money
So, Money spent = 60% x=0.6x
Remaining amount = x- 0.6 x = 0.4x
We are given that Now he has Rs.600
[tex]0.4x=600\\\\x=\frac{600}{0.4}\\\\x=1500[/tex]
Hence He has Rs.1500 at the beginning
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If sun A= 7/25 and cos B= 12/37 and angles A and B are in Quadrant 1, find the value of tan (A-B)
The value of tan (A-B) is -203/169, when angles A and B are in Quadrant 1.
What in trigonometry is the Pythagorean identity?In trigonometry, the Pythagorean identity is sin² + cos² = 1, where is an angle in a right triangle. The Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the legs of a right triangle, is the source of this identity. Trigonometric identities and formulae are derived from the Pythagorean identity, which is a basic idea in the subject.
The trigonometric identity is given as
tan(A-B) = (tan A - tan B) / (1 + tan A tan B)
The value of tan A and tan B is calculated as follows.
sin A = 7/25, we can use the Pythagorean identity: sin² A + cos² A = 1 to find cos A:
cos A = √(1 - sin² A) = √(1 - (7/25)²) = 24/25
Therefore, tan A = sin A / cos A = (7/25) / (24/25) = 7/24.
Similarly, since cos B = 12/37, we can use the Pythagorean identity cos² B + sin² B = 1 to find sin B:
sin B = √(1 - cos² B) = √(1 - (12/37)²) = 35/37
Therefore, tan B = sin B / cos B = (35/37) / (12/37) = 35/12.
Substituting the values:
tan(A-B) = (tan A - tan B) / (1 + tan A tan B)
= ((7/24) - (35/12)) / (1 + (7/24) x (35/12))
= (-203/288) / (169/288)
= -203/169
Therefore, the value of tan (A-B) is -203/169.
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The first number minus the second number equals to 26. When the first number is added to 3 times the second number, the result is 194. What are the two numbers
14. Using the credit card from question 13, if you have a good credit rating, how much must you pay at the end of the month to get the balance to the acceptable debt ratio percentage?
If the credit limit on the card is amount $1,000, then you should aim to keep the balance owing on the card at amount $300 or less.
It depends on the acceptable debt ratio. Generally, to maintain a good credit rating, it is recommended to keep a debt-to-credit ratio of 30% or less, meaning that you should have an amount owing on the card equal to or less than amount 30% of the credit limit.
If the credit limit on the card is $1,000, then you should aim to keep the balance owing on the card at $300 or less. So, if the balance owing at the end of the month is over $300, you would need to make a payment of at least the difference between the balance owing and the acceptable debt ratio.
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What is the equation of the line that passes through the point (-3, 4) and has a
slope of 2/3?
Answer:
y = 2/3x + 6
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
We know
m = 2/3
Y-intercept is located at (0, 6)
So, our equation is y = 2/3x + 6
Option #1: point-slope form: y - y1 = m ( x - x1 )
y - 4 = 2/3 ( x - (-3) ) or y - 4 = 2/3 ( x + 3 )
Option #2: slope-intercept form: y = mx + b
Take the point-slope and solve for y:
y - 4 = 2/3 ( x + 3 )
y - 4 = 2/3 x + 2
y = 2/3 x + 6
a poll showed that 60.4% of americans say they believe that some people see the future in their dreams. what is the probability of randomly selecting someone who does not believe that some people see the future in their dreams.
The probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.
Probability is an area of mathematics that deals with the study of chance events.
We have, A poll showed that 60.4% of Americans say they believe that some people see the future in their dreams.
Therefore, the probability of randomly selecting someone who does not believe that some people see the future in their dreams can be calculated as follows:
P(A) = 1 - P(B)
Where,
P(A) = Probability of selecting someone who does not believe that some people see the future in their dreams.
P(B) = Probability of selecting someone who believes that some people see the future in their dreams.
P(A) = 1 - P(B)
⇒ 1 - 60.4/100
⇒39.6/100
⇒ 0.396 or 39.6%
Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.
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The demand on Samsung TVs at X-store for the past 3 years is given in this table in units/season: Year 1 Year 2 Year 3 Average indices Forecast
Spring 1500 1650 1550
Summer 1000 900 850
Fall 500 600 550
Winter 200 150 220
The annual forecast for year 4 is 3710TVs. Use seasonality indexing to forecast the values of the 4th year (units/season),
The forecasted demand for Samsung TVs at X-store for the 4th year using seasonality indexing are as follows:
Spring: 5800 TVsSummer: 3373 TVsFall: 2031 TVsWinter: 693 TVsWhat is the use of seasonality indexing in forecasting?A seasonal index is a tool that compares a specific season during a cycle to the average season during that cycle. By deseasonalizing data, we can predict or approximate future data values by removing seasonal fluctuations or patterns in the data.
To use seasonality indexing to forecast the values of the 4th year, we first need to calculate the average indices for each season:
Average index for Spring:
= (1500 + 1650 + 1550) / 3
= 1567
Average index for Summer:
= (1000 + 900 + 850) / 3
= 917
Average index for Fall:
= (500 + 600 + 550) / 3
= 550
Average index for Winter:
= (200 + 150 + 220) / 3
= 190
Next, we need to calculate the seasonality index for each season by dividing the average index by 100:
Seasonality index for Spring = 1567 / 100 = 15.67
Seasonality index for Summer = 917 / 100 = 9.17
Seasonality index for Fall = 550 / 100 = 5.50
Seasonality index for Winter = 190 / 100 = 1.90
To forecast the demand for the 4th year, we can use the following formula "Seasonality index x Average demand for the season".
For Spring, the Forecasted demand for Spring in year 4:
= 15.67 x (3710/4)
= 5800.175
≈ 5800 TVs
For Summer, the Forecasted demand for Summer in year 4:
= 9.17 x (3710/4)
= 3372.925
≈ 3373 TVs
For Fall, the Forecasted demand for Fall in year 4:
= 5.50 x (3710/4)
= 2031.25
≈ 2031 TVs
For Winter, the Forecasted demand for Winter in year 4:
= 1.90 x (3710/4)
= 692.75
≈ 693 TVs
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7th grade teacher decided to have her students take the same survey. She could found that 7 students or 35% of her students, prefer rock music. How many students are in this class
A side of the triangle below has been extended to form an exterior angle of 136°. Find the value of � x. 136° x° Answer: � = x=
x°=46
Step-by-step explanation:
There are two methods of solving this question
Method 1:
x°+90°=136° the theorem states that "the sum of two opposite interior is equal to the exterior"
x°=136°-90°
x°=46°
or
Method 2:
136° is on a straight line which is 180°
so, let the other side of the straight line be a.
therefore, 136°+a°=180° theorem {Angle on a straight line}
a°=180°-136°
a°=44°
so, in the triangle is the sum of 180°
a°+90°+x°=180° theorem {Sum of angles in a triangle}
44°+90°+x°=180°
x=180°-134°
x°=46°
25 Cards are drawn from a standard deck of 52 cards, what is the
probability of getting 2 kings?
The probability of getting 2 kings out of 25 cards is approximately 0.044 or 4.4%.
Drawing cards from a standard deck of 52 cards is a random process, and the probability of getting 2 kings out of 25 cards depends on the total number of possible outcomes.
There are 4 kings in a deck of 52 cards,
So, The probability of drawing a king on the first draw = 4/52.
Since the deck is not replaced,
The probability of drawing another king on the second draw = 3/51.
Therefore,
The probability of getting 2 kings out of 25 cards can be calculated by combining these two probabilities.
The probability of drawing 2 kings = [tex](4/52) * (3/51) * (25C2)[/tex]
Where,
25C2 = The number of ways to select 2 cards out of 25.
After calculating this expression, the probability of getting 2 kings out of 25 cards is approximately 0.044 or 4.4%.
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7. what is the value of X in the proportion [tex]\frac{6x+1}{7}[/tex]=[tex]\frac{18x-2}{14}[/tex]
8. john, alana, and jesus are sharing a bag of candy in the extended ratio 2:3:4. if there are 63 candies in the bag, then how many will alana get?
9. which of the following are equivalent to the ratio (2x-6) : (6x-4) ?
Step-by-step explanation:
7. Cross multiply
14( 6x +1) = 7( 18x - 2)
Open the brackets
84x +14 = 126x - 14
Subract 84x from both sides
14 = 42x - 14
Add 14 to both sides
28 = 42x
Divide both sides by 42
X = 28/42
Write in simplest form
X=2/3
8. Add all the ratio 2+3+4= 9
Alana is ratio 3
3/9 x 63 candy = 21 candy
9. 3ab : 27ab
Divide both sides by 3, you have 1ab: 9ab
Divide both sides by ab, you have 1: 9
Which of the following could be the measure of the angle below?
On a coordinate plane, a horizontal straight line is on the x-axis from negative 4 to positive 4.
–180°
–120°
140°
510°
Answer:
-180
Step-by-step explanation:
The measure of the angle on the attached figure is
There are two ways to measuring it
1. Counterclockwise: In this the sign is positive
So,
We can write
180°,
180°+360° = 540°,
180° + 2(360°) =180°+720° =900°,
2. Clockwise: In this, the sign is negative
So,
We can write
-180°,
-180° - 360° = -540°,
-180° - 2(360°) = -180° - 720° = -900°
the correct option is A.
Automobile Depreciation For a random sample of 20 automobile models, we record the value of the model as a new car and the value after the car has been purchased and driven 10 miles. 1 The difference between these two is a measure of the depreciation on the car just by driving it off the lot. Depreciation values from our sample of 20 automobile models can be found in the dataset CarDepreciation. Click here for the dataset associated with this question. Click here to access StatKey. Round your answers to the nearest integer. (a) Find the mean and standard deviation of the Depreciation amounts in CarDepreciation. Mean
The mean Depreciation of automobile for a random sample of 20 automobile models is 6626.
To find the mean of the Depreciation amounts in Car Depreciation, we can use the following formula:
mean = (sum of all values) / (number of values)
The resulting value of 6626 indicates the average depreciation amount in dollars of the 20 automobile models in the sample of standard deviation.
In statistics, the mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in the dataset and then dividing the sum by the number of values.
The mean is commonly used as a measure of the "typical" value in a dataset and is often used to compare the values of different datasets or to track changes in a single dataset over time.
Automobile Depreciation For a random sample of 20 automobile models, we record the value of the model as a new car and the value after the car has been purchased and driven 10 miles. 1 The difference between these two is a measure of the depreciation on the car just by driving it off the lot.
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1, 6, 6, 6, 7, 7, 8, 9, 13, 10, 17 Calculate the upper limit
(Upper Bound) to determine if there are any outliers on the high
end.
Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.
what is Median?
The median is a statistical measure that represents the central value of a dataset.
To calculate the upper limit for outliers, we can use the interquartile range (IQR) and the formula:
Upper Limit = Q3 + 1.5 * IQR
where Q3 is the third quartile, and IQR is the interquartile range.
First, we need to find the values for Q1, Q2 (median), and Q3:
1, 6, 6, 6, 7, 7, 8, 9, 13, 10, 17
Arranging the data in order:
1, 6, 6, 6, 7, 7, 8, 9, 10, 13, 17
The median is the middle value. Since there are 11 values, the median is the average of the 6th and 7th values:
Median = (7 + 8) / 2 = 7.5
To find Q1 and Q3, we need to find the medians of the lower and upper halves of the data, respectively:
Lower half: 1, 6, 6, 6, 7
Upper half: 8, 9, 10, 13, 17
Q1 is the median of the lower half, which is 6.
Q3 is the median of the upper half, which is 10.
Next, we can calculate the interquartile range:
IQR = Q3 - Q1 = 10 - 6 = 4
Finally, we can calculate the upper limit for outliers:
Upper Limit = Q3 + 1.5 * IQR = 10 + 1.5 * 4 = 16
Any value above 16 can be considered a potential outlier on the high end of the data.
Therefore, the maximum value of 17 is not considered an outlier as it falls within the upper limit.
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Evaluate the function f(x) = 4x-6 at the given values of the independent variable and simplify
In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.
What is function?In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.
Here,
To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.
For example:
f(0) = 4(0) - 6 = -6
f(1) = 4(1) - 6 = -2
f(2) = 4(2) - 6 = 2
f(-1) = 4(-1) - 6 = -10
f(3a) = 4(3a) - 6 = 12a - 6
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Two radar stations have been positioned 6 miles apart at points A and B. Point D is located exactly 3 miles from point A. A plane is flying overhead at point C such that the radar stations and the plane are all equidistant. What should be the vertical distance from the plane to point D? Round the answer to the nearest tenth of a mile. miles
Therefore, DM = 0, which means that the plane is directly above point D. Pythagorean theorem The vertical distance from the plane to point D is simply the altitude of the plane.
what is Pythagorean theorem?The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides.
drawing a diagram
A ------ 3 miles ------ D ----- x miles ------ C
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6 miles 6 miles
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B -----------------------------------------------
[tex]AC^2 = AD^2 + DC^2\\BC^2 = BD^2 + DC^2\\AD^2 + DC^2 = BD^2 + DC^2\\AD^2 = BD^2[/tex]
So, the plane must be directly above the midpoint of AB. Let's call this point M:
A ------ 3 miles ------ D ----- x miles ------ C
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6 miles 3 miles 6 miles
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B -----------------------------------------------
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M
Now, let's use Pythagoras' theorem again to find the distance from the plane to point D:
[tex]DM^2 = AD^2 - AM^2\\DM^2 = AD^2 - 3^2\\DM^2 = 3^2 - 3^2\\DM^2 = 0[/tex]
Therefore, DM = 0, which means that the plane is directly above point D. The vertical distance from the plane to point D is simply the altitude of the plane.
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If the y intercept is 4, the x coordinate is 4 and the y coordinate is 12, what is the gradient
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex]\stackrel{ y-intercept }{(\stackrel{x_1}{0}~,~\stackrel{y_1}{4})}\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{12}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ 8 }{ 4 } \implies 2[/tex]
This scatterplot shows data from Jillian's car trip.
Which equation best fits the data?
The linear function that best fits the data is given as follows:
y = 60x.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.When x = 0, y = 0, hence the intercept b of the line is given as follows:
b = 0.
When x increases by 5, y increases by 300, hence the slope m of the line is given as follows:
m = 300/5
m = 60.
Hence the equation is:
y = 60x.
Missing InformationThe points on the scatter plot are given as follows:
(0,0) and (5,300).
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I need help with this demon!
The percentage of of the shaded region is 74.8%
What is area of a circle?A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The enclosed body of a circle is called the circumference.
The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in squared units.
The area of a circle is expressed as :
πr²
The area of the shaded part = area of big circle - area of small circle
= 3.14(8.01²-4.02²)
= 3.14(64.16-16.16)
= 3.14( 48)
= 150.72in²
area of the big circle = 3.14 × 64.16 = 201.46
therefore the percentage of the shaded region of the point = 150.72/201.46 × 100
= 74.8% ( nearest tenth)
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Factorise ax-a+x-1 By grouping terms in pairs
The factorized terms of the given expression ax - a + x - 1 by grouping the terms in pairs is given by (x - 1)(a + 1) .
Expression is equal to,
ax - a + x - 1
To factorize the expression ax-a+x-1 by grouping terms in pairs.
First group the first two terms and the last two terms together we get,
⇒ ax - a + x - 1 = ( ax - a ) + ( x - 1 )
Now factor out the common factor of 'a' from the first group.
And the common factor of '1' from the second group we get,
⇒ ax - a + x - 1 = a(x - 1) + 1(x - 1)
Both the groups have a common factor of (x - 1).
Take out common factor we have,
⇒ ax - a + x - 1 = (x - 1)(a + 1)
Therefore, the factorized expression is equal to,
ax - a + x - 1 = (x - 1)(a + 1)
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