In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
aX1 + bX2 ≤ c
where a, b, and c are constants.
The first constraint, 1.5X1 + 2.5X2 ≤ 80, is already in standard form.
The second constraint, 2X1 + 1.5X2 ≤ 70, can be rewritten in standard form as follows:
-2X1 - 1.5X2 ≤ -70
You can now write the problem in the following standard form:
Maximize Z = 5X1 + 4X2
Subject to:
1.5X1 + 2.5X2 ≤ 80
-2X1 - 1.5X2 ≤ -70
X1, X2 ≥ 0
In this case, the optimal solution occurs at X1 = 40 and X2 = 0, which gives a maximum value of Z = 200.
This means that if you produce 40 units of X1 and 0 units of X2, you will achieve the highest possible value of Z.
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The subtotal for Abdiel's takeout order is $21.50. What will Abdiel's total be if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount? (2 points)
$22.15
$27.95
$23.22
$23.65
Answer: To calculate the total, we need to first calculate the discount and then the tip.
First, calculate the discount: $21.50 x 10% = $2.15
Then, subtract the discount from the subtotal: $21.50 - $2.15 = $19.35
Next, calculate the tip: $19.35 x 20% = $3.87
Finally, add the tip to the subtotal after the discount to find the total: $19.35 + $3.87 = $23.22
Therefore, Abdiel's total would be $23.22 if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount.
Step-by-step explanation:
$540 is invested in an account earning 9.1% interest (APR), compounded
continuously. Write a function showing the value of the account after t years, where
the annual growth rate can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage of
growth per year (APY), to the nearest hundredth of a percent.
Answer: The formula for continuously compounded interest is given by:
A = P * e^(rt)
Where:
A = the final account balance
P = the initial investment (principal)
r = the annual growth rate as a decimal
t = the number of years the investment is held
In this case, P = 540, r = 0.091 and t = t years.
So, the function showing the value of the account after t years is:
A = 540 * e^(0.091t)
To find the percentage of growth per year (APY), we can use the formula:
APY = (e^r - 1) * 100
Substituting r = 0.091, we find:
APY = (e^0.091 - 1) * 100 = 9.56%
So, the APY is approximately 9.56%, to the nearest hundredth of a percent.
Step-by-step explanation:
Here is my question please show all of your work and answer as well
A shipment of 12 X-Ray machines includes 4 that are defective. In how many ways can a hospital purchase 5 of these machines and receive at least 2 of the defective machines
Answer:
Step-by-step explanation:
The number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is calculated as follows:
The number of ways the hospital can receive exactly 2 defective machines is C(4,2) = 6, where C(n, k) is the number of combinations of n things taken k at a time.
The number of ways the hospital can receive exactly 3 defective machines is C(4,3) = 4.
The number of ways the hospital can receive exactly 4 defective machines is C(4,4) = 1.
So, the total number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is 6 + 4 + 1 = 11.
find the number of sides of a regular prism which has 10 faces and 12 vertices
I NEED THE ANSWER THE QUESTION QUICK
Answer:
A regular prism with 10 faces and 12 vertices has 6 sides. This is because the number of faces and vertices are related by the equation F+2 = E+2V, where F is the number of faces, E is the number of edges, and V is the number of vertices. In this case, 10+2 = 12+2V, so V = 6 and the number of sides of the prism is also 6
Step-by-step explanation:
1. A regular prism has 10 faces and 12 vertices.
2. The number of faces and vertices is related by the equation F+2 = E+2V.
3. Where F is the number of faces, E is the number of edges, and V is the number of vertices.
4. In this case, 10+2 = 12+2V, so V = 6.
5. Therefore, the number of sides of the prism is also 6.
Using the table, what is the average daily balance of the credit card for the January 1 - January 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00. Day 1112131 Activity − Purchase Purchase Purchase Adjustment −+200+250+400 Closing Balance 800100012501650
The average daily balance of the credit card for the January 1 - January 31 billing period is $1283.87.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
The average daily balance can be determined by dividing the total daily balances for January by the number of days in January.
The average daily balance = Total balance / Total number of days in January.
Total balance = (800 x 1 days) + (1000 x10 days) + (1250 x 10 days) + (1650 x 10 days)
Total balance = 800 + 10,000 + 12,500 + 16,500 = 39800
The average daily balance = 39800/31 = $1283.87
Therefore, the average daily balance of the credit card for the January 1 - January 31 billing period is $1283.87.
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Scott deposits $300 into an account that pays a simple interest at a rate of 4% per year. How much interest will he be paid in the first 6 years?
Answer:
$72
Step-by-step explanation:
300
4% per year
so 12$ per year,
6 years = 12*6 = 72
Question 9 of 12
In the straightedge and compass construction of the congruent angle below,
which of the following reasons can you use to prove that LABC = LFDE?
D
B
E
C
A. Draw a line through points A and Cand another line through points
Fand E. Then AABC AFDE by SSS, and ZABC LFDE by
CPCTC.
B. Draw a line through points A and Cand another line through points
F and E. Then AABC AFDE by SSA, and LABC = LFDE by
CPCTC.
C. Draw a line through points A and C and another line through points
Fand E. Then AABC AFDE by AAS, and LABC LFDE by
CPCTC.
D. Draw a line through points A and Cand another line through points
F and E. Then AABC AFDE by ASA, and LABC LFDE by
CPCTC.
The correct option that can be used to prove that ∠ABC = ∠FDE is option (A). It is done using rules of congruency.
What is meant by congruency?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
For the construction of the congruent angle, the compass measurement used is the same for both figures.
Now we draw a line through points A and C and another line through points F and E.
We can then say that
AB = FD
BC = DE
CA = EF
These are the sides of the triangles ΔABC and ΔFDE
As all sides are equal, we can say that
ΔABC ≅ ΔFDE by SSS congruency rule.
Now CPCTC rule says that "corresponding parts of congruent triangles are congruent". This means that the corresponding angles and sides of two or more triangles must also be identical in order for them to be considered congruent.
So ∠ABC ≅ ∠FDE by CPCTC as they are corresponding angles.
Therefore the correct congruency rules that can be used to prove that
∠ABC = ∠FDE is option (A).
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PLEASE HELP DUE IN FEW MINUTES ASAP THANK YOU
Answer:
[tex]\frac{(s + 15.4)(8.1)}{2}[/tex] = 81
8.1s + 124.74 = 162
8.1s = 37.26
s = 4.6
Find the derivative of the following function. S = t^23 ln|t| Which rule of differentiation will be most helpful in beginning this problem? A. The chain rule B. The product rule C. The sum or difference rule D. The constant rule E. The power rule The expression in |t| appears as a subexpression of the given function. What is the derivative of this expression? d/dt (ln|t|) = t/|t|^2 Find the derivative of the given function ds/dt =
The derivative of the given function is 23t^22 ln |t| + t^22
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
The product rule will be most helpful in beginning this problem.
S = t^23 ln|t|
Differentiate with respect to t
D(s) = ds/dt = D( t^23 ln|t| )
Apply the rule :
D(uv) = u'v+uv'
u' =du/dt , v'=dv/dt
D(s) = 23t^22 ln |t| + t^23 (1/t)
D(s) = 23t^22 ln |t| + t^22
The derivative of the given function is 23t^22 ln |t| + t^22
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The derivative of the given function is 23t²² ln |t| + t²².
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
The product rule will be most helpful in beginning this problem.
S = t²³ ln |t|
Differentiate with respect to t
D(s) = ds/dt = D( t²³ln|t| )
Apply the rule :
D(uv) = u'v+uv'
u' =du/dt , v'=dv/dt
D(s) = 23t²² ln |t| + t²³ (1/t)
D(s) = 23t²² ln |t| + t²²
The derivative of the given function is 23t²² ln |t| + t²²
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A city has cone-shaped buildings for storing salt and sand for icy roads. Each
building has a radius of 50 feet and a height of 30 feet. Find the volume of the
building. Use 3.14 for 7.
OA. 19,625 ft³
OB. 78,500 ft3
O C. 4710 ft³
OD. 235,500 ft3
(a) The perimeter of a rectangular field is 350 m.
If the width of the field is 79 m, what is its length?
Answer: 96 m.
Step-by-step explanation: Let's call the length of the rectangular field "L".
We know the perimeter of the field is equal to the sum of all its sides, so:
350 = 2L + 2 * 79
Expanding the right side, we have:
350 = 2L + 158
Subtracting 158 from both sides:
192 = 2L
Dividing both sides by 2:
L = 96 m
So the length of the rectangular field is 96 m.
Zak has 18 tennis balls. This i
Matt has 9 more tennis balls
How many tennis balls does
Answer:
The cost of 3 tennis balls and 2 golf balls is $7. The cost of 6 tennis balls and 3 golf balls is$12. Find the cost of 1 tennis ball and 1 golf ball.
Step-by-step explanation:
the mitchell family took a roadtrip from detroit to toronto. their route was 750 kilometers long and required 54 liters of gas. what was the family's fuel efficiency in miles per gallon?
Family's fuel efficiency is 32.67 miles per gallon.
What is unit conversion?
Unit conversion is the conversion between different units and measurements of the same quantity done by the division or multiplication.
Mitchell family's fuel efficiency in km/l =[tex]\frac{750}{54}[/tex]
=13.89 km/l
The fuel efficiency in miles per gallon = 13.89*2.35
= 32.67 m/g
(1 kilometer per liter = 2.35 miles per gallon)
Hence, mitchell family's fuel efficiency is 32.67 miles per gallon.
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A:
1. ∠ABC≅∠AED (Given)
2. Isosc. △ABE, base BE (Given)
3. AB ≅ AE (Def. of Isosc. △)
4. BE ≅ BE (Reflex. Prop. of ≅)
5. △BDE≅△BCE (SAS Steps 3, 1, 4)
6. BC ≅ ED (CPCTC)
B:
1.∠ABC≅∠AED (Given)
2. Isosc. △ABE, base BE (Given)
3. AB ≅ BE (Def. of Isosc. △)
4. BE ≅ AC (Sym. Prop. of ≅)
5. △BDE≅△BCE (SAS Steps 3, 1, 4)
6. BC ≅ DE (CPCTC)
C:
1.∠ABC≅∠AED (Given)
2. Isosc. △ABE, base BE (Given)
3. AB ≅ BE (Def. of Isosc. △)
4. ∠B≅∠E (Sym. Prop. of ≅)
5. △ABC≅△AED (ASA Steps 1, 3, 4)
6. BC ≅ DE (CPCTC)
D:
1.∠ABC≅∠AED (Given)
2. Isosc. △ABE, base BE (Given)
3. AB ≅ AE (Def. of Isosc. △)
4. ∠A≅∠A (Reflex. Prop. of ≅)
5. △ABC≅△AED (ASA Steps 1, 3, 4)
6. BC ≅ ED (CPCTC)
In isosceles triangle ΔABE, the correct option is option D. which proves that BC ≅ ED.
What is the isosceles triangle?
An isosceles triangle is a triangle having any two sides equal in length. The third side is called the base of the isosceles triangle. In an isosceles triangle, the angles opposite to equal sides are equal in measure.
1.∠ABC ≅ ∠AED (Given)
2. Isosc. △ABE, base BE (Given)
3. AB ≅ BE (Def. of Isosc. △)
4. ∠A ≅ ∠A (Reflex. Prop. of ≅)
5. △ABC ≅ △AED (ASA Steps 1, 3, 4)
6. BC ≅ ED (CPCTC)
option 1 is wrong in that the step 3. AB is not congurent with BE,
option 3 is wrong in that step 5. △ABC≅△AED should be prove by BD ≅ CE, ∠A BE ≅ ∠AEB, BE ≅ BE
hence, in isosceles triangle ΔABE, the correct option is option D. which proves that BC ≅ ED.
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Find the length of the third side. If necessary, round to the nearest tenth. 9 12
The required length of the third side of the right-angle triangle is 15 units.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as the hypotenuse, are perpendicular and the base is Pythagorean triplets.
Here,
For the right triangle lenght of the two legs to be 9 and 12 units, a measure of the third side is to be determined.
So, Applying the Pythagoras theorem,
h² = p² + b²
h = √9² + 12²
h = √225
h = 15
Thus, the required length of the third side of the right-angle triangle is 15 units.
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Describe as precisely thoroughly as possible why critical values of a function f(x) occur either where f′(x) = 0 or where f′(x) is undefined.
Well, most books define critical values of a function as x-values where f'(x)=0 or f'(x) is undefined, so they occur there because that's the definition of what a critical value is.
But the reason we define it that way is that when you're looking for local extrema (local mins and/or local maxs), these must occur when f'(x)=0 or f'(x) is undefined.
If f has a local extremum at a point x=c, then f'(c)=0 or f'(c) is undefined.
Which is the best estimate of the difference between 5 5/6 and 3 1/4
The best estimate of the difference between the two numbers is 31/12 or 2 7/12.
What are mixed fractions?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.
to transform a mixed fraction into an incorrect fraction.
By denominator, divide the numerator.
Take the quotient as a whole number and use the remaining amount as the proper fraction's numerator while maintaining the original denominator.
Covert the mixed fraction into improper fractions:
5 5/6 = 35/6
3 1/4 = 13/4
The difference between the two numbers is:
35/6 - 13/4
Take the LCM.
70/13 - 39/12
(70 - 39) / 12
31/12 = 2 7/12
Hence, the best estimate of the difference between the two numbers is 31/12 or 2 7/12.
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Please solve this for me, no other information was given with this question
The percentages of the weights are given as follows:
a) Over 15.5 pounds: 2.07%.
b) Under 11.9 pounds: 75.8%.
c) Between 11.9 pounds and 15.9 pounds: 22.13%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters for this problem are given as follows:
[tex]\mu = 10, \sigma = 2.7[/tex]
The proportion over 15.5 pounds is one subtracted by the p-value of Z when X = 15.5, hence:
Z = (15.5 - 10)/2.7
Z = 2.04
Z = 2.04 has a p-value of 0.9793.
1 - 0.9793 = 0.0207.
The proportion under 11.9 pounds is the p-value of Z when X = 11.9, hence:
Z = (11.9 - 10)/2.7
Z = 0.7
Z = 0.7 has a p-value of 0.7580.
The proportion between is the subtraction of the p-values, hence:
0.9793 - 0.7580 = 0.2213 = 22.13%.
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Determine the range, mean, variance, and standard deviation of the sample data set.
12,17,23,15,15,18,19,17,14,15
Statistics is a discipline, principally within applied mathematics, concerned with the systematic study of the collection, presentation, analysis, and interpretation of data.
The measures used in statistics are mean, range, standard deviation, variance etc.
The range can be calculated by finding the difference between the lowest and highest observation i.e. 23 - 12 = 11.
Variance is a measure of dispersion of data points from the mean. In the above given data, the variance is 9.389.
Standard deviation is the square root of the variance, hence, is 3.06.
Mean = sum of data divided by no of observations (10).
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Kai bought his younger sister, Loni, a sticker book and 12 stickers. Each week he gives his sister two new stickers. Let w represent the number of weeks that Loni collects stickers, and let s represent the total number of stickers she has collected. a. Determine the independent and dependent variables. The number of weeks, w, is the ? variable. The total number of stickers, s, is the ? variable.
Answer:
w = independent variables = dependent variable======================================================
Reason:
The number of weeks can be any number from the set {0,1,2,3,...} so we say that this value is independent. It does not depend on the number of stickers.
But the number of stickers does depend on the number of weeks. As w changes, so does the value of 's'.
The equation would be: s = 2w+12
Plug in w = 0 to find that s = 12. This is the starting amount of stickers.Plug in w = 1 to find s = 14. This is the number of stickers after 1 week.Plug in w = 2 to find s = 16. This is the number of stickers after 2 weeks.And so on. Each time 'w' goes up by 1, 's' goes up by 2.
approximatly 31,500 citizens of a country died in automobile accidents in 2015, express this toll in deaths per day. round to the nearest whole number. There are approximatly how many deaths due to automobile accidents
Using simple division we know that 86 people or citizens dies each day in 2015.
What is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction.
Division in mathematics is the process of dividing an amount into equal parts.
For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.
So, we know that:
31,500 people died in 2015.
We also know that 2015 had 365 days.
Then, people died easily day would be:
= 31,500/365
= 86.30
Rounding off: 86 people
Therefore, using simple division we know that 86 people or citizens dies each day in 2015.
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the statistical methods of analysis of variance assume that the populations are normally distributed.A. TrueB. False
The statement of statistics "the statistical methods of analysis of variance assume that the populations are normally distributed" is true. So the correct answer is (a)True.
What is statistics?Statistics is a branch of applied mathematics that involves collecting, describing, analyzing, and drawing conclusions from quantitative data. It gives us information to figure out how things work. Statistics are used to conduct research, evaluate results, develop critical thinking, and make informed decisions. Statistics can be used to examine nearly any area of research to find out when and why things happen, and whether their recurrence is predictable.
Who uses statistics?Statistics are used in many different applications and professions. Statistics are generated each time data is collected and analyzed. This ranges from government agencies to academic research to investment analysis.
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Find fo g, go f, and g o g.
f(x) = 2x, g(x) = x²
(a)
fog
2x4
(b) gof
16x4
(c) gog
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The required values of the given composite functions follow as:
(a) fog(x) = 4x², (b) gof(x) = 2x², and (c) gog(x) = x⁴.
What are composite functions?Composite functions are mathematical functions that are formed by taking the output of one function and using it as the input for another function.
(a) To find fog(x), we need to evaluate g(f(x)).
Since function f(x) = 2x, we have:
g(f(x)) = g(2x) = (2x)² = 4x²
Therefore, fog(x) = 4x².
(b) To find gof(x), we need to evaluate f(g(x)).
Since g(x) = x², we have:
f(g(x)) = f(x²) = 2(x²) = 2x²
Therefore, gof(x) = 2x².
(c) To find gog(x), we need to evaluate g(g(x)).
Since function g(x) = x², we have:
g(g(x)) = g(x²) = (x²)² = x⁴
Therefore, gog(x) = x⁴.
Thus, the required values of the given composite functions follow as:
(a) fog(x) = 4x², (b) gof(x) = 2x², and (c) gog(x) = x⁴.
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10. Solve for x.
(7x + 3)º
(2x + 6)°
Answer:
The answers are x=-37 and x=3
Step-by-step explanation:
The solution set for the equation (7x+3)(2x-6)=0 is {−37,3}. To solve for x, one can use the distributive property to expand the equation and then solve for x. For example, 7x² - 3x - 12x - 18 = 0 can be rearranged to 7x² - 15x - 18 = 0 and then solved using the quadratic formula.
In the state of Indiana, 322000 people lacked basic math skills. If this is 5.6% of the population of Indiana residents aged 5 years and older, estimate the population of Indiana residents aged 5 years and older.
Express your answer rounded to the nearest hundredth of a million.
The number of people in Indiana residents is given by the equation
A = 5,750,000 or 5.75 million
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of people in Indiana residents aged 5 years and older be A
Now , the equation will be
Substituting the values in the equation , we get
The percentage of population residents aged 5 years and older = 5.6 %
The number of residents aged 5 years and older = 322,000
So , the total population A is calculated as
( 5.6 % ) of A = 322,000
On simplifying the equation , we get
( 5.6 / 100 ) A = 322,000
Divide by 6.6 on both sides of the equation , we get
A / 100 = 57,500
Multiply by 100 on both sides of the equation , we get
A = 5,750,000
A = 5.75 million
Hence , the population of Indiana is A = 5,750,000 or 5.75 million
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Consider an urn containing four balls, numbered 110, 101, 011 and 000, from which one ball is drawn at random. For k = 1, 2, 3 let Ak be the event of drawing a ball with 1 in the kth position. Show your work in answering the following:a) Are A1, A2, and A3 pairwise independent?b) Are A1, A2, and A3 mutually independent?
a)The events A1, A2, and A3 are pairwise independent.
b) The events are not mutually independent.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Observe the given numbers:
Out of 4 numbers, 2 have 1 at first position
so outcomes in event A1 is
A1 ={ 110, 101}
Similarly, possible outcomes in A2 is
A2 ={110, 011}
A3 = {101,111}
The probabilities of events are
P(A1) = 2/4 = 0.5
P(A2) = 2/4 = 0.5
P(A3) = 2/4 = 0.5
Also,
(A1 and A2) = {110}
(A1 and A3) = {101}
(A2 and A3) = {011}
The probabilities are
P(A1 and A2) = 1 /4 = 0.25
P(A1 and A3) = 1 /4 = 0.25
P(A2 and A3) = 1 /4 = 0.25
a)
From above we have
P(A1 and A2) = P(A1)P(A2) = 0.25
P(A1 and A3) = P(A1)P(A3) = 0.25
P(A2 and A3) = P(A2)P(A3) = 0.25
So events A1, A2, and A3 are pairwise independent.
b)
Since P(A1 and A2), P(A1 and A3) and P(A2 and A3) are not equal to zero so events are not mutually independent.
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a)The events A1, A2, and A3 are pairwise independent.
b) The events are not mutually independent.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Observe the given numbers:
Out of 4 numbers, 2 have 1 at first position
so outcomes in event A1 is
A1 ={ 110, 101}
Similarly, possible outcomes in A2 is
A2 ={110, 011}
A3 = {101,111}
The probabilities of events are
P(A1) = 2/4 = 0.5
P(A2) = 2/4 = 0.5
P(A3) = 2/4 = 0.5
Also,
(A1 and A2) = {110}
(A1 and A3) = {101}
(A2 and A3) = {011}
The probabilities are
P(A1 and A2) = 1 /4 = 0.25
P(A1 and A3) = 1 /4 = 0.25
P(A2 and A3) = 1 /4 = 0.25
a)
From above we have
P(A1 and A2) = P(A1)P(A2) = 0.25
P(A1 and A3) = P(A1)P(A3) = 0.25
P(A2 and A3) = P(A2)P(A3) = 0.25
So events A1, A2, and A3 are pairwise independent.
b)
Since P(A1 and A2), P(A1 and A3) and P(A2 and A3) are not equal to zero so events are not mutually independent.
To learn more about the probability from the given link
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1 1/2 times x = 2 3/4
the pair of linear equations is graphed below
solve for pie
please please i neeed help
Answer:
h=V/πr2
Step-by-step explanation:
Rewrite the equation as π r 2 h = V . π r 2 h = V
Divide each term in π r 2 h = V by π r 2 and simplify.
Jo has a 15 GB monthly cell phone plan. Jo has used 4 GB in the first 20 days of the month. At that rate, how many GB will Jo use after a month of 30 days?
Answer:
6 GB
Step-by-step explanation:
First find the rate per day. You can do that by dividing 4GB by 20 days.
4/20 = 1/5 = 0.2GB per day
Then, just multiply 30 days by the rate of 0.2GB/day.
30 x 0.2 = 6