[tex]2^{10}\cdot 2^{15}\implies 2^{10+15}\implies 2^{25}\implies 2^{5\cdot 5}\implies (2^5)^5\implies {\Large \begin{array}{llll} 32^5 \end{array}}[/tex]
What can you say about the series an in each of the following cases? (a) lim. 72 = 5 absolutely convergent conditionally convergent divergent cannot be determined (b) lim 0:2 = 0.5 absolutely convergent conditionally convergent divergent cannot be determined na absolutely convergent conditionally convergent divergent cannot be determined
The Test of convergence of series, helps us to check the given series are absolutely convergent
divergent, conditionally convergent.
Using the convergence test we get,
a) The lim. 72 = 5 is divergent. The correct option is option( C).
b) lim 0:2 = 0.5 is absolutely convergent. The correct option is option ( A).
Firstly , we discuss how to check absolutely convergent , divergent or conditionally convergent.
Steps to Determine :
Step 1: Take the absolute value of the series. Then determine whether the series converges.
If it converges, then we say the series converges absolutely.
If it does not converge, then we say it does not converge absolutely and we follow to Step 2
Step 2: Use the Alternating Series Test to determine whether the original series converges or diverges.
If it converges, then we say the series converges conditionally.
If the Alternating Series Test fails, we attempt another test.
Absolute Convergence Test :
If ∑∞ |an| converges, then ∑∞ aₙ converges
n = 1 n =1
We say that ∑∞ aₙ converges absolutely
n=1
if this case is true. If a series does not converge absolutely but converges by another test, we say that the series converges conditionally.
The Alternating Series Test: An alternating series, ∑∞( −1)⁽ⁿ⁻¹⁾aₙ , converges if the following 3
n=1
conditions are satisfied:
Check that lim an =0n→∞
Check that aₙ >0 , for all n.Check that aₙ ≥ aₙ₊₁, for all n. (This determines whether an is non- increasing.)Geometric Series Test: a series of the form
∑∞ ar⁽ⁿ⁻¹⁾ , the series converges if |r|< 1 and
n=1
diverges if |r | ≥1 nᵗʰ Term Test/Divergence Test
∑∞ aₙ , diverges if lim aₙ
n=1 n→ ∞
does not exist or does not equal zero.
p-series Test : The series ∑∞ (1/nₚ) converges if
n=1
p>1 and diverges if p ≤1.
we have given that
a) ∑∞ |aₙ₊₁/aₙ| = 5 >1
n = 1
Ratio Test: If 0 < aₙ and limn→∞(aₙ₊₁/aₙ) < 1, then an converges.If the limit is greater than 1, then
the series diverges. And if the limit is equal to 1, then the test gives no information.
so, it is divergent
b) ∑∞ |aₙ₊₁ /aₙ| = 0.5 <1
n = 1
: If 0 < an and limn→∞(aₙ₊₁/aₙ) < 1, then series converges. So, it is absolutely convergent .
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A beach ball has a radius of 12 in. how much air will the beach ball hold?
Volume of beach ball or the amount of air will the beach ball hold is 2304π in³.
Formula
Volume of Sphere is 4/3πr³
The volume, V, of a sphere with radius r is 4/3πr³
By employing a technique that roughly represents the surface area of a sphere using square pyramids, it is possible to obtain the formula for the volume of a sphere using the formula for its surface area, which is 4πr^2.
Where r is the radius of the sphere .
As given
12 inches is the radius of a beach ball.
r = 12 in
Substitute the r in above volume equation,
V =4/3πr³
V=4/3π(12)³
V= 2304π in³
Therefore, the amount of air will the beach ball hold is 2304π in³.
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The International Monetary Fund i trying to raie $1,600 billion in 12 year for new fund to lend to developing countrie. At 4% interet compounded quarterly, how much mut it invet today to reach $1,600 billion in 12 year? (Ue the Table provided. )
They must invest $269.54 billion quarterly at 4% compound interest.
How can it determine how much it needs to invest now to reach $1,600 billion in twelve years?
We use the compound interest formula to figure out how much the International Monetary Fund needs to raise over the next 12 years in order to lend to developing nations at 4% interest compounded quarterly.
Interest that is calculated based on the initial principal as well as all of the interest that has accumulated over previous periods is referred to as compound interest. The power of compound interest is the process of producing "interest on interest. "Any frequency schedule, from continuous to daily to annual, can be used to compound interest.
What is the formula for compound interest?
Given that A = amount raised = $1600 billion, r = compound interest rate = 4% quarterly = 4% 1/4 year = 4% 4 = 16% = 0.16 per year, and n = number of years = 12, we have P = A/(1 + r)n. Substituting the values of the variables into the equation, we have P = $1600 billion/(1 + 0.16)12 P = $1600 billion/(1.16)12 P = $1600 billion/5.93
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please help this assignment is killing me
Consider the quadratic equation, x2 + 6x + 10 = 0.
From the list below, determine which expression correctly represents the solution set of the quadratic equation above.
Type yes next to each correct representation. Type no next to each incorrect representation. You must type an answer in every text box.
{ }
{-4, -2}
x1 = -4, x2 = -2
("If you can't see the image, it is a circle with a slash through it.")
no solution
Answer:
No solution
Step-by-step explanation:
We can easily tell that there are no solutions by using the discriminant rule.
The discriminant rule comes directly from the discriminant of the quadratic equation and is b^2-4ac
It can tell us three things about the solution:
When the discriminant is less than 0, there is no solution.
When the discriminant equals 0, there is one distinct solution.
When the discriminant is greater than 0, there are two distinct solutions
In the problem a = 1, b = 6, c = 10.
Plugging in what we have gives us 6^2*4(1)(10) = -4.
-4<0 so there are no real solutions.
How do you write 1,000,000 in words?.
The given number 1,000,000 can be written in words as
Ten Lakhs only.
Given, a number 1,000,000
we have to write the given number in words.
now to write any number in words, we have to know the place value of the digits of the given number
As, the place value of the digit 1 is tenth lakh and remaining digits in the number are all zeros.
So, the number 1,000,000 can be written in words as
Ten Lakhs only.
Hence, the given number 1,000,000 can be written in words as
Ten Lakhs only.
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Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter λ = .01386(as suggested in the article "Competition and Dispersal from Multiple Nests," Ecology, 1997: 873–883).
a. What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m?
b. What is the probability that distance exceeds the mean distance by more than 2 standard deviations?
c. What is the value of the median distance?
The solutions and probabilities are,
(a)
P(X < 100) = 0.748
P(X < 200) = 0.936
P(100 < X < 200) = 0.188
(b) P(X > M+2σ) = 0.0498
(c) Median = 50.01 m
Given data,
Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter,
λ = 0.01386
[tex]F(x) = 1 - e^-^λ^x[/tex]
(a)
The probability that the distance is at most 100 m is,
[tex]F(100) = 1 - e^-^0^.^0^1^3^8^*^1^0^0[/tex] = 0.748
The probability that the distance is at most 200 m is,
[tex]F(200) = 1 - e^-^0^.^0^1^3^8^*^2^0^0[/tex] = 0.936
The probability that the distance is between 100 and 200 m is,
F(200) - F(100) = 0.936 - 0.748 = 0.188
(b)
The probability that distance exceeds the mean distance by more than 2 standard deviations
Mean, μ = 1/λ = 1/0.01386 = 72.1501
Standard deviation, σ = 1/λ = 72.1501
Value more than 2 SD from mean = µ + 2*σ
= 72.1501 + 2*72.1501 = 216.4503
Probability of greater than 216.4503,
P(X > 216.4503) = e^(-0.0139 * 216.4503)
= 0.0498
(c)
The value of the median distance is,
Median = ln(2) / λ
= ln(2) / 0.0138 = 50.01
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I don’t understand my math test. please help!! :)
Answer:
4 ) {2,3}
5) {0,1,2,3,4,5}
6) { }
A line that includes the points (–7,10) and (r,6) has an undefined slope. What is the value of r?
Answer:
-7
Step-by-step explanation:
This one is tricky if you aren't sure what undefined means. It means that the slope points straight up and downwards. So, it must have the same "x" coordinate at every single point on the line.
To see what that looks like mathematically, just use your slope equation. Since the bottom evaluates to 0, it is undefined.
if each human lung contains about 300 million alveoli with a summed total surface area for gas exchange of 40 square meters, what is the approximate surface area of a single alveolus?
For a single alveolus requires the surface area of 0.133 square meters for gas exchange.
In this question, we have been given each human lung contains about 300 million alveoli with a summed total surface area for gas exchange of 40 square meters.
we need to find the approximate surface area of a single alveolus.
By unitary method the required surface area would be,
A = 40/300
A = 10/75
A = 0.133 square meters
Therefore, the approximate surface area of a single alveolus = 0.133 square meters
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Suppose we are making a 95% confidence interval for the population mean from a sample of size 15. What number of degrees of freedom should we use?.
We require a degree of freedom of 14 to create a 95% confidence interval for the population mean from a sample size of 15.
Given that,
Assume that a sample size of 15 will be used to calculate a 95% confidence interval for the population mean.
We have to find how many degrees of freedom should we utilize.
We know that,
The answer to the problem is
A 95% confidence interval is being created.
The sample size is 15 (<30). Therefore, in order to account for the decreased sample size and use the sample SD, we must adapt and use a t-value rather than a Z score.
As a reflection of sample size, it should be noted that the t-value is dependent on the degrees of freedom (df). df = n-1 is the formula used to calculate a confidence interval using the t-distribution.
Therefore, we require a degree of freedom of 14 to create a 95% confidence interval for the population mean from a sample size of 15.
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i really need help please <33
Tonya's homework assignment has four problems a, b, c, d. Her teacher instructed her to simplify each expression and then find out its value. The value of a is 3/28, the value of b is 1/2, the value of c is 15/56 and the value of d is 1/15.
Each problem has two fractions. They are given below and should be simplified.
a) 2/7 × 3/8 = 1/7 × 3/4 = 3/28
b) 2/3 × 3/4 = 1/1 × 1/2 = 1/2
c) 3/7 × 5/8 = 15/56
d) 3/10 × 2/9 = 1/5 × 1/3 = 1/15
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The length l of a rectangle is decreasing at the rate of 2 cm/sec while the width w is increasing at the rate of 2 cm/sec. When l = 12 cm and w = 5 cm, find the rates of change of (a) the area, (b) the perimeter, and (c) the lengths of the diagonals of the rectangle. Which of these quantities are decreasing, and which are increasing?
Using Area and perimeter formulae of rectangle,
a) the rate of change of Area is 14 cm²/sec
b) the rate of change of perimeter is zero.
c) length of diagonal is 13 cm
We have given that
length (l) is decreasing at the rate of 2 cm/min
and the width (w) is increasing at the rate of
2cm/min,
⇒ dl/dt = −2 cm/min and dw/dt = 2cm/sse
Thus the perimeter (P) of a rectangle is,
P=2(l+w) ---(1)
differentiating above equation with respect to time (t) we get,
dp/dt = 2(dl/dt + dw/dt )
=> dp/dt = 2( -2 + 2 ) = 0
=> P = constant
Hence, there is no change in perimeter of rectangle.
(b)Now, it is given that length (l) is decreasing at the rate of 2 cm/min
and the width (w) is increasing at the rate of 2 cm/min,
Thus the area (A) of a rectangle is, A= l× w
=> dA/dt = l ×dw/dt + w×dl/dt (used differentaion
we have l = 12 cm and w = 5 cm
=> dA/dt = 12 (2) + 5(-2)
=> dA/dt = 24 - 10 = 14
Hence, the area is increasing at the rate of
14 cm²/min.
c) length of diagonal = √(12)² + (5)² = √144+25
=> length of diagonal = √169 = 13 cm
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Nov 22, 9:11:24 AM
An online furniture store sells chairs for $100 each and tables for $350 each. Every
day, the store can ship at most 18 pieces of furniture and must sell no less than
$3200 worth of chairs and tables. If a represents the number of tables sold and y
represents the number of chairs sold, write and solve a system of inequalities
graphically and determine one possible solution.
After solving system of inequalities one possible solution is number of chairs y = 12 and number of tables a = 6.
Given:
An online furniture store sells chairs for $100 each and tables for $350 each. Every day, the store can ship at most 18 pieces of furniture and must sell no less than $3200 worth of chairs and tables.
Using a and y as variables, we get
100y + 350a ≥ 3200
Simplified,
50(2y + 7a) ≥ 3200
2y + 7a ≥ 3200/50
2y + 7a ≥ 64
y + a = 18
a = 18 - y
on solving two equations
2y + 7a = 64
2y + 7(18-y) = 64
2y + 126 - 7y = 64
-5y = 64 - 126
-5y = -62
5y = 62
y ≈ 12 chairs
a = 18 - 12
a = 6 tables.
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Find three consecutive even integers such that the sum of the smallest number and twice.
Let x, x+2 & x+4 be the 3 integers.
x+2(x+2)=(x+4)+20
x+2x+4=x+4+20
3x+4=x+24
3x-x=24-4
2x=20
x=20/2
x=10 answer for the smallest integer.
10+2=12 for the middle integer.
10+4=14 answer for the largest integer.
Proof:
10+2*12=14+20
10+24=34
34=34
Therefore, the three consecutive integers are 10, 12, and 14.
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The right question is:
Find three consecutive even integers such that the sum of the smallest number and twice the middle number is 20 more than the largest number.
How do you find the slope and y intercept of a system of equations?.
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 6x + 2, is 6.
This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we may still solve for the intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to obtain the y-intercept. The key message is (0, y).
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For this linear regression model, r2= 0.90. What does this mean?
A) The maximum long jump was around 90 inches.
B) Each year the winning long jump distance increased by 90%.
C) 90% of the variation in long jump distances is explained by the regression line.
D) The data ends around 1990
C) 90% of the variation in long jump distances is explained by the regression line.
(The number r2 gives the proportion of the variation in the long jump explained by the change in years.)
The given linear regression model means that 90% of the variation in long jump distances is explained by the regression line. (Option C)
Linear regression refers to a basic and commonly used form of predictive analysis. It is used to determine the relationship between two quantitative variables. It is used to determine the strength of the relationship between two variables and the value of the dependent variable at a certain value of the independent variable. Regression models describe the relationship between variables by fitting a line to the observed data. Linear regression models use a straight line, while logistic and nonlinear regression models use a curved line. The regression model illustrates how a dependent variable changes as the independent variable(s) change. The given linear regression model r2= 0.90, where r2 gives the proportion of the variation in the long jump explained by the change in years, the model means that 90% of the variation in long jump distances is explained by the regression line.
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The rate of acceleration due to gravity i 9. 8 meter / econd2, How fat i that in mile per econd2?
According to the conversion factor where 1 meter is equal to 0.000621371 miles, we find out that the rate of acceleration due to gravity upon conversion is equal to [tex]0.0060894358 miles/second^{2}[/tex].
It is given to us that -
The rate of acceleration due to gravity is [tex]9.8 meter/second^{2}[/tex]
We have to find out the rate of acceleration in [tex]miles/second^{2}[/tex]
We know the conversion factor between meter and miles is -
[tex]1 meter = 0.000621371 miles[/tex]
So, the given rate of acceleration due to gravity can be written as -
[tex]9.8 meter/second^{2}\\= 9.8 * 0.000621371 miles/second^{2}\\= 0.0060894358 miles/second^{2}[/tex]
Thus, using the conversion factor from meter to miles, we find out that the rate of acceleration due to gravity is equal to [tex]0.0060894358 miles/second^{2}[/tex].
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How many triangle exist with 12 feet 15 feet and 18 feet side length?.
A scalene triangle exists with the side lengths 12,15 and 18 feet.
The three sides of the triangle are 12 feet , 15 feet and 18 feet.
Now we know from the properties of triangle that if the sum of the smaller sides is greater than the largest side , then it is a triangle.
Here we can see that the triangle is formed by the given sides.
Now, 12 +15 = 27 > 18 hence the triangle is possible.
Since all the sides are of different lengths the triangle is scalene.
Scalene refers to any triangle with three unequal sides. Because there are three different sides, there must also be three different sizes of angles. This triangle is one of the three varieties that can be distinguished by the traits of its sides.
A scalene triangle is a triangle with variable lengths for each of its three sides and three angles. The different measures have no impact on the total interior angle of the scalene triangle.
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X + 3 + 7 (X-5) Step by step
Answer: 8x - 32
Step-by-step explanation: x + 3 + 7(x - 5)
x + 3 - 35
which gives you 8x - 32
let x be the number of tails in three flips of a fair coin. let y be the outcome of a roll of a fair six-sided die. assume x and y are independent. give the joint probability mass function of x, y . be precise about the values for which the joint probability mass function is defined.
The joint probability mass function of x,y is 0.1458 if x is number of tails in three flips of coins and y is the outcome of six-faced die.
We know very well that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.
Here, coin is tossed three times means that 2³=8 different possible outcomes possible.
The total combination of tail appearing in 3 times flipping are {TTT,TTH,THT,HTT,HTH,HHT,THH}
So, total 7 combinations are possible for a tail appearing on flipping coin three times.
So, probability of tail appearing in three flips=7/8
Therefore, value of x=7/8
Now, we know that a dice has six faces and for each face there is equal probability to come at the top face and that probability value is 1/6
So, joint probability of mass function of x,y = (probability of tail appearing in three flips × probability of outcomes of a six-sided dice)
=>P(x,y)=(7/8)×(1/6)
=>P(x,y) = 7/48
=>P(x,y)=0.1458
Hence, value of joint probability is 0.1458.
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use the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points
An equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4) is 3x + y - 5 = 0.
In the given question, using the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4).
The distance between any two points can be determine using the distance formula which is given by √[x(2)-x(1)]^2+[y(2)-y(1)]^2.
Let point P(x, y) be equal distance from points A(3, 6) and B(- 3, 4).
Since they are equidistant, PA = PB
Hence by applying the distance formula for PA = PB, we get
√(x - 3)^2 + (y - 6)^2 = √(x - (- 3))^2 + (y - 4)^2
√(x - 3)^2 + (y - 6)^2 = √(x + 3)^2 + (y - 4)^2
Taking square on both side, we get
(x - 3)^2 + (y - 6)^2 = (x + 3)^2 + (y - 4)^2
Using the formula (a-b)^2=a^2-2ab+b^2
x^2+ 9 - 6x + y^2 + 36 - 12y = x^2 + 9 + 6x + y^2 + 16 - 8y
Now solving
6x + 6x + 12y - 8y = 36 - 16
12x + 4y = 20
3x + y = 5
3x + y - 5 = 0
Thus, the relation between x and y is given by 3x + y - 5 = 0
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The right question is:
Use the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4).
what is the name of the variable that is used to predict another variable? multiple choice response explanatory coefficient of determination standard error of the estimate
The name of the variable that is used to predict another variable is the explanatory variable.
The correct answer option is: b
What are response and explanatory variables?
The variable that researchers are attempting to explain or predict is known as the response variable. Because it is dependent on another variable, it is also known as the dependent variable.
The variable that is used to explain or predict the response variable is referred to as the explanatory variable.
What is the coefficient of determination and standard error of the estimate?
The coefficient of determination is a measurement used to explain how much variability in one factor can be explained by its relationship to another related factor.
The standard error of the estimate is an estimate of the accuracy of any predictions. It is denoted as SEE. The regression line decreases the sum of prediction deviations squared It is also referred to as the sum of squares error.
Dependent and independent variables are variables in mathematical modeling, statistical modeling, and experimental sciences, according to the question. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they depend, by some law or rule, on the values of other variables.
The name of the variable that is used to predict another variable is the explanatory variable.
The correct answer option is: b
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What is the y-intercept of 5x 2y 28 0?.
14 is the value of y-intercept .
What in mathematics is a y-intercept?
A point on the y-axis at which the slope of a line passes is referred to as an intercept in mathematics. It is a place on the y-axis where a straight line or a curve crosses. This is shown by writing the equation for a line as y = mx+c, where m denotes the slope and c the y-intercept.The standard form of line intercept
y = mx + c
5x - 2y = -28
- 2y = - 5x -28
y = 5/2x + 14
lets compare with equation
m = 5/2
c = 14
Thus, the y-intercept is y= 14
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The complete question is -
What is the y-intercept of 5x - 2y = -28?
if three workers can make three widgets in three minutes, how many workers will it take to make 18 widgets in six minutes?
Answer:
It will take nine workers
Step-by-step explanation:
rate = [tex]\frac{widgets}{workersx time}[/tex]
[tex]\frac{3}{(3)(3)}[/tex] = [tex]\frac{1}{3}[/tex]
rate x time x workers = jobs
[tex]\frac{1}{3}[/tex] (6)(w) = 18
2w = 18 Divide both sides by 2
w = 9.
It will take 9 workers.
pls help me don't want to get it wrong because then I will have to redo that ALEKS topic
The absolute value depicted in the number line is
|x| ≥ 5How to compare the written equation to the plotted equationThe number line shows a solid circle since it is not hollow circle or dot the inequality must either be
greater than or equal to less than or equal toSolving the absolute value
= |x| ≥ 5
x ≥ ±5
x ≥ 5
and
x ≤ 5
The number line shows greater that 5 and less than -5 which is shown in the equation
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five cards are drawn at random and without replacement from an ordinary deck of cards. let x1 and x2 denote, respectively, the number of spades and the number of hearts that appear in the five cards. (a) determine the joint pmf of x1 and x2. (b) find the two marginal pmfs. (c) what is the conditional pmf of x2, given x1
There are (525) possible combinations of 5 cards, and each combination has an equal chance of being drawn.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is .According to our question-
It is simpler to derive this from first principles than to add up the x2 (which will work but is harder).
There are (525) possible combinations of 5 cards, and each combination has an equal chance of being drawn.
The number of combinations that contain x1 spades is what we are looking for.
There are (13x1) ways to select the spade, followed by (395x1) ways to select the other card.
Hence, There are (525) possible combinations of 5 cards, and each combination has an equal chance of being drawn.
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11xsquared=7x+2x
i need the workings done too
Answer: x=2 or x=7/11
explanation:
11x^2=7x+2x
11x^2-7x-2x=0
x(11x-7)-2(11x-7)=0
(x-2)(11x-7)=0
x=2 or x=7/11
Find the equation of a line that pae through the point (-2,-3) and ha a gradient of -3. Leave your anwer in the form y = m x c
The equation of line is y = -3x - 9
To solve this problem we will use slope intercept form in straight lines.
The slope-intercept form is one of the ways to represent a straight line.
To form the slope-intercept form of a line we need the slope of the line and it,s y intercept.
y = Mx + c
Where,
M = Slope of the line
c = y-intercept of the line
(x,y) are the points that satisfy the line or we can say lie on a line.
now, moving to the problem we have,
M = -3
x = -2
y = -3
Equation of line is y = -3x + c
There is one unknown term here which is c.
So to find it we will put (-2,-3) in the line.
-3 = (-3)(-2) + c
c = -9
Hence the equation of a line is y = -3x -9
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Here i the probailty cale of each event abc and d write down the letter of the event that i impoible
Using the Probability Scale,
a) Letter D shows event is impossible.
b) Letter C show likely event
c) Probability that the selected bead is red or purple is 3/4.
Probability is an estimate or calculation of the likelihood or likelihood that something will happen. For example, the likelihood of an event occurring can be "certain," "impossible," or "probable."
In mathematics, probability is usually written as a fraction or decimal number between 0 and 1.
Probability Scale :
Impossible events have a probability of 0 and specific events have a probability of 1. This means that the probability cannot exceed 1. This can be expressed on a probability scale.
Now , we conclude from above discussion,
a) The letter D shows that the event that is impossible.
b) The letter C shows that the event is likely.
c) we have, total number of beads in bag = 12
blue beads in bag = 2
red beads in bag = 1
purple beads in a bag = 3
red Julia beads in a bag = 6
one randomly bead is selected from a bag .
Probability that the selected bead is purple (p)
= 3/12 = 1/4
Probability that the selected bead is red (p') = 1/12
Probability that the selected bead is red or purple (P) = p + p' = 1/4 + 1/12 = 3/4
Hence, the required probability is 3/4 and letter D , for probability of event is zero .
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Complete question:
Here is a probability scale It shows the probability of each of the events A, B, C and D.
a) Write down the letter of the event that is impossib/e.
b) Write down the letter of the event that is like/y.
A bag contains 12 beads
2 of the beads are blue 1 of the beads is green. 3of the beads are purple.The rest of the beads are red Julia takes a bead from the bag at random
c) Show that the probability that this bead is purple or red is 3/4.
What is an example of a system of inequalities?.
Answer: y ≥ 2x – 2, y ≥ -(1/2) x – 3. This system of inequalities has three equations that are all connected by an “equal to” symbol.
The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an arrowhead. It is an example of an inequality. This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3.
Step-by-step explanation:
