The histograms display the frequency of temperatures in two different locations in a 30 day period. A histogram titled “Temps in Desert Landing” with When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
Answers
The measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is:
Range, because Flower Town is symmetric
How to Interpret the Histogram?A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.
Now, from the given histograms, we can see that Desert landing is skewed while Flower town is symmetrical entirely.
Thus, The measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is:
Range, because Flower Town is symmetric
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Related Questions
Let u = 2i - 3j, and w=-i-6j. Find ||w - ul.
w-ul = (Type an exact answer, using radicals as needed.)
Answers
The value of ||w - u || = 3 sqrt 2
How to solveGiven:
u = 2i - 3j
w = - i - 6j
w - u = ( - i - 2i ) + ( - 6j - (-3j))
w - u = - 3i - 3j
|| w - u || = sqrt [ - 3^2 + - 3^2 ]
||w - u || = 3 sqrt 2
The concept of a radical in mathematics refers to the symbolic representation (√) of finding the roots of an expression or a number.
The widely known and frequently used kind is the square root (√), which reveals a positive value that, when multiplied by itself at once, generates the radicand.
Other forms may include cube roots (∛) or fourth roots (∜). To simplify radicals, one can factor out those factors within it that result in perfect cubes or squares from their corresponding radicands.
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Based on a poll, 60% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the probability that among three randomly selected Internet users, at least one is more careful about personal information when using a public Wi-Fi hotspot? (Round to three decimal places as needed.)
Answers
The probability that at least one of the three users is more careful is 0.936.
How to find the probability that among three randomly selected Internet users, at least one is more carefulWe need to find the probability that a single randomly selected Internet user is more careful, which is 0.60.
The probability that none of the three users are more careful is (0.40)^3 = 0.064.
Therefore, the probability that at least one of the three users is more careful is 1 - 0.064 = 0.936.
Rounding to three decimal places, the answer is 0.936.
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Which graph represents the following system? Y>x+4 y
Answers
The solution is, Option 4 is correct., the graph represents the following system of inequalities.
Explanation:
We are given two inequality y<-x-4 and y>2x-3.
We need to choose correct graph from given choices.
First we draw the graph of each equation
Equation 1: y<-x-4
We draw the graph using slope intercept form.
Slope=-1 and y-intercept (0,-4)
Test point (0,0). Put (0,0) into equation 1 y<-x-4
We get . This is false statement. Graph will shade away from point (0,0).
Equation 2: y<2x-3
We draw the graph using slope intercept form.
Slope=2 and y-intercept (0,-3)
Take test point (0,0). Put (0,0) into equation 2, y>2x-3
We get . This is true statement. Graph will shade towards the point (0,0).
Please take a look attachment for the graph.
Option 4 is correct.
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complete question:
Which graph represents the following system of inequalities?
y < -x - 4
y > 2x - 3
Solve each inequality given that the function f is increasing over its domain
1.f(2x+3)>f(3x-2), Df=[3,infinity)
2f(x^2-2)
Answers
Answer:
Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:
2x + 3 > 3x - 2
Solving for x, we get:
x < 5
So the solution set is:
Df = [3, infinity) intersect (-infinity, 5) = [3, 5)
Therefore, the inequality is true for all x in the interval [3, 5).
Since f is increasing over its domain, we know that if a > b, then f(a) > f(b). Therefore, we have:
x^2 - 2 < y^2 - 2
Simplifying, we get:
x^2 < y^2
Taking the square root of both sides, we get:
|x| < |y|
So the solution set is:
Df = [3, infinity)
|x| < |y| means that either x < y or -x < y. Therefore, the solution set can be divided into two parts:
Part 1: x^2 - 2 < 0, i.e., x is in the interval (-sqrt(2), sqrt(2)). For this part, we have:
Df intersect (-sqrt(2), sqrt(2)) = empty set
Part 2: x^2 - 2 >= 0, i.e., x is outside the interval (-sqrt(2), sqrt(2)). For this part, we have:
Df intersect (-infinity, -sqrt(2)] union [sqrt(2), infinity) = [3, infinity)
Therefore, the inequality is true for all x in the interval [3, infinity) except for the interval (-sqrt(2), sqrt(2)).
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The standard deviation of a sample taken from population A is 17.6 for a sample of 25. The standard deviation of a sample taken from population B is 21.2 for a sample of 30.
The standard deviation of the sample mean differences is ____. (Round your answer to the nearest hundredth.)
Answers
The standard deviation of the sample mean differences is, 16.98.
Since, We know that;
Standard deviation is defined to be the square root of the population variance of the vector. The sample standard deviation s is defined to the square root of the sample variance of the vector.
Here, The standard deviation of the sample mean differences should be calculated using the standard deviations of the two populations.
In order to see how they differ, we need to first subtract them from each other,
So, we get:
21.2 - 17.6 = 3.6
We then divide this number with the first standard deviation as follows:
⇒ 3.6/21.2 x 100
⇒ 16.98
Therefore, the standard deviation of the sample mean is, 16.98.
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A car costing $34,000 is leased for $473 monthly over 5 years with a $2,420 down payment. The car’s residual value is estimated to be $16,400. If the car is purchased with a $5,000 down payment, the monthly loan payments will be $623 for 60 months. Calculate the costs of leasing this car and buying this car. Is buying or leasing less expensive and by how much less?
Answers
The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.
Buying the car is more expensive than leasing by $13,600 over the 5-year period.
We have,
To calculate the cost of leasing the car, we first need to determine the total amount paid over the lease term:
= (Monthly payment x Number of months) + Down payment
= ($473 x 60) + $2,420
= $28,780
To determine the cost of buying the car, we first need to calculate the total loan amount:
= Cost of car - Down payment + Residual value
= $34,000 - $5,000 + $16,400
= $45,400
Now,
Total loan cost = (Monthly payment x Number of months) + Down payment
Total loan cost = ($623 x 60) + $5,000
Total loan cost = $42,380
So,
The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.
To determine which option is less expensive, we can subtract the cost of leasing from the cost of buying:
Cost of buying - Cost of leasing = $42,380 - $28,780
Cost of buying - Cost of leasing = $13,600
So,
Buying the car is more expensive than leasing by $13,600 over the 5-year period.
Thus,
The cost of leasing the car is $28,780 and the cost of buying the car is $42,380.
Buying the car is more expensive than leasing by $13,600 over the 5-year period.
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At a local college, 82 of the male students are smokers and 328 are non-smokers. Of the female students, 148 are smokers and 252 are non-smokers. A male student and a female student from the college are randomly selected for a survey. What is the probability that both are smokers?
Answers
P(male smoker) = 82 / (82 + 328) = 0.20
Similarly, the probability that a female student is a smoker is:
P(female smoker) = 148 / (148 + 252) = 0.37
To calculate the probability that both are smokers, we need to multiply these probabilities:
P(both smokers) = P(male smoker) x P(female smoker)
P(both smokers) = 0.20 x 0.37
P(both smokers) = 0.074
Therefore, the probability that both a male and a female student selected at random from the college are smokers is 0.074, or approximately 7.4%.
Hi is anyone good at math is so can somone please help me with thisI'm struggling with it!!
Answers
The variables to the parallelogram OPQR are;
1. coordinates of points M is (1, 2.5)
2. The length of PQ is 4
3. The length of QR is 5.4
4. The length of PM is 3.9
5. The length of OM is 2.7
6. The perimeter of the parallelogram OPQR is approximately 18.8
7. if m ∠QMR = 120° m ∠ QMP = 60°
8. If m ∠ QRO = 80° m ∠ROP = 100°
How do we calculate for every listed sides of the of parallelogram OPQR?
To calculate for every listed length of parallelogram OPQR it will be helpful to list all the coordinate for this diagram and they are;
O (0, 0)
p (-2, 5)
R (4, 0)
Q (2, 5)
To find for M, we could just get it from the diagram by looking at the points for x and then y. This is (1, 2.5). You can also calculate it like this
Mx = (Px + Rx)/2 = (-2 + 4)/ 2 = 2/2 = 1
My = (Py + Ry)/2 = ( 5 + 0)/2 = 2.5
To calculate for the length of any side, we say
LPQ = √(Qx -Px)² + (Qy - Py)² = √(2 - -2)² + (5-5)² = √8 = 4
LQR = √(Rx -Qx)² + (Ry - Qy)²
LPM = √(Mx -Px)² + (My - Py)²
LOM = √(Mx -Mx)² + (Oy - My)²
if m∠QMP = 180° - m∠QMR = 180° - 120° = 60°
The question below is as seen in the pictures provided.
The diagonals of parallelogram OPQR intersect at point M.
What are the coordinates of points M?
Find PQ
Find QR
Find PM
Find OM
Find permeter of parallelogram OPQR
if m ∠QMR = 120° what is m ∠ QMP
If m ∠ QRO = 80° what is m ∠ROP
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A restaurant had 160 lunch customers last weekend. Of those, 90 ordered seltzer, 75 ordered a chicken sandwich, and 38 ordered both. There were 45 customers who ordered seltzer and a veggie sandwich. Eleven more people ordered a veggie sandwich than a tuna sandwich. Complete the two-way frequency table for the data.
Answers
The figures that complete the two-way frequency table are attached accordingly.
How is this so?Let represent the table like this:
Chcken Veggie Tuna Total
Seltzer 38 45 A 90
Iced Tea B C D E
Total 75 F G 160
NOte that:
A = 90 - 38 - 45 = 7
B = 75 - 38 = 37
E = 160-90 = 70
C = D + 11
D + 11 + D = 70-37
2D = 33-11
D=22/2
D=11
Thus C = 22
F = 45 + C
F = 45 + 22
F = 22
G = A + D = 18
?thus, the completed two-way frequency table is:
Chcken Veggie Tuna Total
Seltzer 38 45 7 90
Iced Tea B 22 11 70
Total 75 67 18 160
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The Sky Train from the terminal to the rental car and long term parking center is supposed to arrive every 8 minutes. The waiting times for the train are known to follow a uniform distribution.
What is the probability of waiting less than 2 minutes or more than 6 minutes?
Answers
The probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train is 0.5 or 50%.
To calculate the probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train from the terminal to the rental car and long term parking center, we need to find the probability of each event separately and then add them together.
The probability of waiting less than 2 minutes can be calculated as the ratio of the time interval from 0 to 2 minutes (2 minutes) to the total time interval of 8 minutes;
P(waiting less than 2 minutes) = (2 minutes) / (8 minutes) = 0.25
The probability of waiting more than 6 minutes can be calculated as the ratio of the time interval from 6 to 8 minutes (2 minutes) to the total time interval of 8 minutes;
P(waiting more than 6 minutes) = (2 minutes) / (8 minutes) = 0.25
Now, to find the probability of waiting less than 2 minutes or more than 6 minutes, we can add the two probabilities together;
P(waiting less than 2 minutes or more than 6 minutes) = P(waiting less than 2 minutes) + P(waiting more than 6 minutes)
= 0.25 + 0.25
= 0.5
Therefore, the probability of waiting less than 2 minutes or more than 6 minutes will be 0.5 or 50%.
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Solve the system of equation algebraically y =
x ^ 2 + 4x + 3 y = 2x + 6
Answers
y = x ^ 2 + 4x + 3 --- Equation 1
y = 2x + 6 --- Equation 2
We can set the right-hand sides of the two equations equal to each other since they are both equal to y:
x ^ 2 + 4x + 3 = 2x + 6
Subtracting 2x + 6 from both sides, we get:
x ^ 2 + 2x - 3 = 0
We can factor the quadratic equation:
(x + 3)(x - 1) = 0
This gives us two possible solutions:
x + 3 = 0 or x - 1 = 0
Solving for x, we get:
x = -3 or x = 1
Substituting these values back into either Equation 1 or Equation 2, we can solve for y:
When x = -3, y = (-3) ^ 2 + 4(-3) + 3 = 0
When x = 1, y = 2(1) + 6 = 8
Therefore, the solution to the system of equations is (x, y) = (-3, 0) and (1, 8).
For f(x) = x + 4√
x
+
4
, what is the value of the function when x = 8? Round to the nearest hundredth.
Answers
f(8) = 8 + 4√(8+4) = 8 + 4√12 ≈ 12.03
Rounding this to the nearest hundredth gives 12.03.
Find the surface area of a right square pyramid if the area of the base is 169 cm² and the slant height of the pyramid is 13 cm.
Answers
The surface area of a right square pyramid if the area of the base is 169 cm² and the slant height of the pyramid is 13 cm is 507 cm².
Calculating the surface area of square pyramidWe know that the area of the square base is 169 cm², so we can solve for the length of one side.
To find the length, we use the formula for the area of a square:
Area = length x length
169 = length²
Taking the square root of both sides, we get:
length = √169
= 13 cm
Now we can use the formula for the surface area of a square pyramid:
Surface area = area of base + (1/2)perimeter of base x slant height
The perimeter of the base is 4 times the length of one side, so it is:
perimeter of base = 4 x length = 4 x 13 cm = 52 cm
Plugging in the values we have:
Surface area = 169 cm² + (1/2)(52 cm)(13 cm)
Surface area = 169 cm² + 338 cm²
Surface area = 507 cm²
Therefore, the surface area of the right square pyramid is 507 cm².
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answers
The vector-valued function is continuous at t=2,
are
r(t) = 3/ cos t-1(i) + sin t (j)r(t) = e^ t (i) + cos t (j)What is a vector-valued function?A vector-valued function, is described as a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors.
We are required to check if the limit of the function as t approaches 2 exists and is equal to the value of the function at t=2, in order to determine if the vector-valued function is continuous at t=2.
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You invest $1500 in an account at interest rate r, compounded continuously.Find the time required for the amount to double and triple.(Round your answer to two decimal places). r=0.0355
Answers
The time required for the amount to double and triple are 19.53 and 30.95 respectively.
How to find the time required for the amount to double and triple?In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):
[tex]f(t) = P_{0}e^{rt}[/tex]
Where:
f(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.Based on the information provided above, we can reasonably infer and logically deduce that a function for the time required for the amount to double is given by;
[tex]2(1500) = 1500e^{0.0355t}\\\\3000= 1500e^{0.0355t}\\\\2=e^{0.0355t}[/tex]
Taking the natural log (ln) of both sides of the equation, we have:
0.0355t = ln(2)
Time, t = 19.53
Similarly, a function for the time required for the amount to triple is given by;
[tex]3(1500) = 1500e^{0.0355t}\\\\4500= 1500e^{0.0355t}\\\\3=e^{0.0355t}[/tex]
Time, t = 30.95
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You are remodeling a kitchen, including the formal dining room and breakfast nook. It is time to purchase flooring for the space. You need to calculate the area of the entire space and then find the cost of the materials that you would like to purchase to make sure you do not go over your budget of $7,500. See the picture for your blueprint.
Answers
The area of the entire space is 38.57 units².
We have,
From the figure,
Total area.
= Semicircle + Rectangle + Trapezium + Rectangle
Now,
Semicircle:
Radius = 2 units
Rectangle:
Length = 4 units
Width = 3 units
Trapezium:
Parallel sides = 5 units and 3 units
Height = 1 unit
Rectangle:
Length = 2 units
Width = 5 units
Now,
Area of the entire space.
= πr² + 4 x 3 + 1/2 x 1 x (5 + 3) + 2 x 5
= 22/7 x 2 x 2 + 12 + 1/2 x 1 x 8 + 10
= 88/7 + 12 + 4 + 10
= 12.57 + 12 + 4 + 10
= 12.57 + 26
= 38.57 units²
Now,
1 unit = 7 feet
So,
= 38.57 X 7² feet²
= 1889.93 feet²
Thus,
The area of the entire space is 38.57 units².
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Jay’s mean score for four quizzes is 9 . His scores for the first three quizzes are 8,5, and, 9. What is Jay’s score for the last quiz?
Answers
Jay's score for the last quiz is 14.
Let's use the formula for finding the mean:
Mean = (Sum of all scores) / (Number of scores)
We can rearrange this formula to solve for the unknown score:
Unknown score = (Mean x Number of scores) - (Sum of all other scores)
Given that Jay's mean score for four quizzes is 9, we have:
Mean = 9
Number of scores = 4
Jay's scores for the first three quizzes are 8, 5, and 9. The sum of these scores is:
Sum of first three scores = 8 + 5 + 9 = 22
Using the formula above, we can find Jay's score on the fourth quiz:
Unknown score = (Mean x Number of scores) - (Sum of all other scores)
Unknown score = (9 x 4) - 22
Unknown score = 36 - 22
Unknown score = 14
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Suppose loga 2=r, loga 3=s, and loga 5=t Which algebraic expression represents loga 75?
Answers
The algebraic expression represents loga 75 is st²
How to determine the expression?An algebraic expression is an expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.
The statement reads:
loga 2=r,
loga 3=s, and
loga 5=t
Log 75 Log(3*5*5)
That log3*log5*log5
= s*t*t = st²
Therefore the expression is st²
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How do you solve for X???
Answers
Answer:
x= -18
Step-by-step explanation:
-2/3x + -21/4 = 27/4
-8x-63=81
-8x-63+63=81+63
-8x=144
-8x/-8 = 144/-8
x=-18
X
What is the multiplicative inverse of 5/6
Answers
The multiplicative inverse of 5/6 as required to be determined in the given task content is 6/5.
What is multiplicative inverse?It follows from the task content that the multiplicative inverse of the given number; 5/6 is required to be determined.
By definition; it follows that the Multiplicative inverse of an expression refers to its reciprocal. It is the value that, when multiplied by the original, give a product of 1 (the multiplicative identity element).
So,
5/6 × 6/5
= 30/30
= 1
Hence, 6/5 is the multiplicative inverse of 5/6
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A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $1,050,000 if successful and a yearly loss of $350,000 otherwise. The probability of success is 2 If the second mall is selected, it is estimated that the yearly profit will be $700.000 if successful; otherwise, the annual loss will be $210.000. The probability of success at the second mall is
_ Complete parts (a) through (c) below
a. What is the expected profit for the first mall?
Answers
The expected profit for the first mall is $1,750,000
Given data ,
Let the probability be represented as A and B
Now , For Event A:
Probability of success at the first mall (P(A)) = 2 (given)
Profit if successful (P(A) * Profit | Success) = 2 * $1,050,000 = $2,100,000
Loss if unsuccessful (Loss | Failure) = -$350,000
For Event B:
Probability of success at the second mall (P(B)) = unknown (to be calculated)
Profit if successful (P(B) * Profit | Success) = P(B) * $700,000
Loss if unsuccessful (Loss | Failure) = -$210,000
Expected Profit for Event A = P(A) * Profit | Success + (1 - P(A)) * Loss | Failure
Expected Profit for Event A = 2 * $1,050,000 + (1 - 2) * -$350,000
Expected Profit for Event A = $2,100,000 - $350,000
Expected Profit for Event A = $ 1,750,000
Hence , the profit is $ 1,750,000
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On a coordinate plane, point A is (negative 2, 3), point B is (2, 4), and point C is (0, negative 1). The points are connected with lines. Use the graph to find the coordinates of each vertex in triangle ABC. is the coordinate of Point A. is the coordinate of Point B. is the coordinate of Point C.
Answers
Can u mark my answer as the Brainlyest if it work Ty
Need help??? With this question
I don’t think I’m solving it correctly.
Answers
Answer:
116
Step-by-step explanation:
I don't understand please help
Answers
The diameter of the circle is 396 units.
The length of the arc is 0.83π units.
How to find the diameter of the circle?The length of an arc of a circle is given by the formula:
L = θ/360 * πd
where θ is the measure of the angle and is the diameter of the circle
Given: θ = 80° and L = 88π
L = θ/360 * πd
88π = 80/360 * π * d
88 = 80/360 * d
80 * d = 88 * 360
80d = 31680
80d = 31680/80
d = 396 units
PART 2
If θ = 25°, r = 6 (from the image above). Thus, d = 2 * 6 = 12
L = θ/360 * πd
L = 25/360 * π * 12
L = 0.83π units
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The volume of a cone is 35π cubic inches and the height is 4.2 inches. What is the radius of the cone?
Answers
The value of the radius of the cone is, 5 inches
We have to given that;
The volume of a cone is 35π cubic inches.
And, the height is 4.2 inches.
Now, We know that;
Volume of cone is,
V = πr²h/3
Hence, We get;
35π = π × r² × 4.2 / 3
105 = 4.2r²
r² = 105/4.2
r² = 25
r = 5 inches
Thus, The value of the radius of the cone is, 5 inches
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A group consists of seven democrats and eight republicans
Answers
a) The number of ways that four people can be selected from this group of fifteen is: 1365 ways
b) The number of ways that four Republicans can be selected from the eight Republicans is: 70 ways
c) The probability that the selected group will consist of all republicans is: 5.13%
How to solve Permutation and Combination?The selection of people from a given list can be done in the following way: if we want to select r people from a list of n people, then we can do so in:
nCr = n!/(r!(n - r)!)
In the first part of the question, we don't need to decide on specific people from each group, but in the subsequent parts, it becomes an added restriction.
A. This can be done in:
15C4 = 15!/(4!(15 -4!)
= 1365 ways
B. This can be done in:
8C4 = 8!/(4!(8 - 4)!)
= 70 ways
C. The chances that all are republicans is a measure of the ratio of the answer in the first question to the second:
70/1365 = 0.0513 = 5.13%
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Suppose the probability of an event is 0.20. What are the odds in favor of this event?
Answers
Answer:
If the probability of an event is 0.20, the odds in favor of the event can be calculated as follows:
- Divide the probability of the event occurring by the probability of the event not occurring:
0.20 / (1 - 0.20) = 0.20 / 0.80
- Simplify the fraction:
0.20 / 0.80 = 1 / 4
Therefore, the odds in favor of the event are 1 to 4.
Step-by-step explanation:
The odds in favor of an event with a probability of 0.20 is a ratio of 1 to 4.
Explanation:The question is about calculating the odds in favor of an event with a probability of 0.20. The odds in favor of an event is defined as the ratio of the probability that the event will happen to the probability that it will not happen.
In this case, the probability of the event is 0.20, therefore the probability that it will not happen is 1 - 0.20 = 0.80. So, the odds in favor of the event are 0.20 to 0.80 or it can be simplified to 1 to 4.
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From a group of 10 people, you randomly select 2 of them. What is the probability that they are the 2 oldest people in the group?
Answers
The probability that they are the 2 oldest people in the group is 0.011
Understanding probabilityProbability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
The probability of an event A is denoted by P(A)
From the question above, let us calculate the probability.
The probability that the first person selected is the oldest is 1/10.
Then, the probability that the second person selected is the second oldest is 1/9, since there are only 9 people left to choose from.
Therefore, the probability of selecting the two oldest people in the group is:
1/10 * 1/9 = 1/90
So, the probability of selecting the two oldest people in the group is 1/90 or approximately 0.011 or 1.1%.
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Write an equation of a quadratic function that has been reflected in the x-axis, shifted horizontally to the right 2 units and stretched by a factor of 3.
Answers
The equation is writen in the quatradtic form as [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
How to write the equationQuadratic equation is of the form
[tex]f(x) = ax^2 + bx + c[/tex]
the transformations
Reflect it in the x-axis: To reflect a function in the x-axis, we change the sign of the function.
[tex]g(x) = -ax^2 - bx - c[/tex]
Shift it horizontally to the right by 2 units: Our function becomes:
[tex]g(x) = -a(x - 2)^2 - b(x - 2) - c[/tex]
Stretch the function by a factor of 3: To stretch a function vertically, we multiply the function by the stretch factor, k.
[tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
So, the final transformed quadratic function is: [tex]g(x) = -3a(x - 2)^2 - 3b(x - 2) - 3c[/tex]
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Find x round your answer to nearest tenth of a deggre triangle that had 16 20 and x
Answers
In the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.
We have a right triangle with an unknown angle θ (measured in degrees), the opposite side length of 16 units, and a hypotenuse length of 21 units. We're given the formula for calculating the sine of an angle:
sin(θ) = opposite / hypotenuse
By substituting the values we know, we get:
sin(x) = 16 / 21
x = sin⁻¹(16 / 21)
x ≈ 49.6°
Therefore, in the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.
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