Answer:
Step-by-step explanation:
8 10
How to find p-value from z-score?
The procedure to calculate the p-value from z-score depends on one of two choices: one-tailed (which may be Left-tailed or Right-tailed) or two-tailed tests.
How to find the p-value from the z-score?A z-table, otherwise termed the standard normal table, provides the area under the curve to the left of a z-score.
The technique for using z-tables to find p-values depends on the test being carried out; which may be; one- or two-tailed test.
For one-tailed tests, the directionality is also a factor.
It therefore follows that;
For a Left-tailed z-test: the p-value = Φ(Zscore)
For a Right-tailed z-test: the p-value = 1 - Φ(z-score).
For a Two-tailed z-test: the p-value = 2 * Φ(−|z-score|).
The procedure described above represents how to calculate p-value from z-score.
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The following equations are used to find the p-value from its z-score
Left-tailed test: Φ(z-score)Right-tailed test: 1 - Φ(z-score)Two-tailed test: 2Φ(−|z-score|)How to find p-value from its z-score?From the question, the parameters are given as
p-valuez-scoreAlso, from the question, we understand that:
The p value depends on the z-score for its own value
There are three formulas for calculating the p-value from the z-score, depending on the type of test (i.e. left-tailed test, right-tailed test and two-talied test)
These formulas are:
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There are 30 apples in a box.
The mean weight of these 30
apples is 99 grams.
There are 25 apples in a bag.
The mean weight of the
apples in the box and in the
bag combined is 94 grams.
Work out the mean weight
of the 25 apples in the bag.
Answer: 88 grams
Step-by-step explanation:
The total weight of the 30 apples is [tex](30)(99)=2970[/tex] grams.
The total weight of all the apples in the box and bag is [tex]55(94)=5170[/tex] grams.
So, the weight of the apples in the bag is [tex]5170-2970=2200[/tex] grams.
Thus, the mean weight is [tex]\frac{2200}{25}=88[/tex] grams.
A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 7, s(0) = 5, v(0) = −8 s(t) =
Answer:
[tex]s_(_t_)=\frac{1}{3}t^3+\frac{7}{2}t^2-8t+5[/tex]
Step-by-step explanation:
1.)
[tex]a_t=v'_t\\v_t=\int(a_(_t_)dt\\v_t=\int(2t+7)dt\\v_t=t^2+7t+C\\[/tex]
2.)
[tex]v_0=-8\\-8=(0)^2+7(0)+C\\C=-8\\v_t=t^2+7t-8[/tex]
3.)
[tex]v_t=s'_t\\s_t=\int(v_t)dt\\s_t=\int(t^2+7t-8)dt\\s_t=\frac{1}{3}t^3+\frac{7}{2}t^2-8t+C\\[/tex]
4.)
[tex]s_0=5\\5=\frac{1}{3}(0)^3+\frac{7}{2}(0)^2-8(0)+C\\C=5\\s_t=\frac{1}{3}t^3+\frac{7}{2}t^2-8t+5[/tex]
Petra was preparing for a long trip, and filled her gas tank up with 45
litres of gas the night before she left. She noticed that her odometer read 21 912
km when she left the gas station. During the trip she filled up her tank with 35.45
L on her first stop, then with 30.5 L on her second stop, and finally filled the tank
at the end of her trip with 30 L of gas. The odometer on her car read the last
palindromic number in the twenty-two thousands. What was the average number
of litres per 100 km used by Petra's car during the trip?
The average number of liters per 100 km used by Petra's car during the trip, using proportions, was of:
13.96 liters per 100 km.
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction, which has the meaning of a unit rate, is used along basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.
The total amount of liters used by Petra on her trip was of:
45 + 35.45 + 30.5 + 30 = 140.95 liters.
The last palindromic number in the twenty-two thousands is of:
22922.
Hence the total distance traveled by Petra was of:
22,922 - 21,912 = 1010 km.
The rate of liters per km is of:
140.95/1010 = 0.1396.
Hence the rate of liters per 100 km is:
0.1396 x 100 = 13.96 liters per 100 km.
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The original sale price of Levi's jeans at Sm Department store is Php 1 300.00. On February 14, all jeans will have a 40% discount. How much is the discounted price of that jeans on Valentine's day?
The discounted price of that jeans on Valentine's day is Php 780.
What is the discounted price?From the information, the original sale price of Levi's jeans at Sm Department store is Php 1 300.00 and on February 14, all jeans will have a 40% discount.
The amount of the discount will be:
= Percentage of discount × Sales amount
= 40% × 1300
= 0.4 × 1300
= 520
The discount is Php 520
Discounted Price = 1300 - 520
= Php 780
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Find the value of x and y.
The value of x and y will be x = 16° and y = 20°
What is Angles?
In Euclidean geometry, an angle is the shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. The plane that contains the rays contains the angles created by two beams. The meeting of two planes might also result in an angle. Dihedral angles are what these are.
We can write
(6x + y) = (x + 5y)
[By corresponding angles]
6x + y = x + 5y
6x - x = 5y - y
5x = 4y
x = 4y/5
Now by linear pair
4x + (6x + y) = 180
4x + 6x +y = 180
10x + y = 180
By putting the value of x
10(4y/5) + y = 180
8y + y = 180
9y = 180
y = 180/9
y = 20°
Putting the value of y in x we get
x = 4(20) / 5
x = 4(4)
x = 16°
Hence, value of x = 16° and y = 20°
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Select ALL expressions that are close to a quotient of 1.
(A) 1900 / 21
(B) 210,000 / 190,000
(C) 19 / 210
(D) 2.1 / 1.9
(E) 190 / 210
(F) 190 / 21
Answer:
Step-by-step explanation:
C E F or just E and F
An open box is made from a 40 -cm by 50-cm piece of tin by cutting a square from each corner and folding the edges. The area of the resulting base is 1496cm squared. What is the length of the sides of the squares?
The length of the sides of the squares is 3 cm.
What is a rectangle?A rectangle is a quadrilateral with all four interior angles 90°.
Given that, the dimension of the rectangular tin piece is 40 cm by 50 cm.
Let the length of the sides of the square is x.
Then, the dimensions of the resulting rectangular base are (40 - 2x) by
(50 -2x).
Given that, the area of the resulting base is 1496 square cm.
Therefore, it follows:
(40 - 2x)(50 -2x) = 1496
2000 - 80x -100x + 4x² = 1496
4x² - 180x + 2000 -1496 = 0
4x² - 180x + 504 = 0
x² - 45x + 126 = 0
x² - 42x - 3x + 126 = 0
x(x- 42) - 3(x - 42) = 0
(x - 3)(x - 42) = 0
x-3 =0 or x - 42 = 0
x = 3 or x = 42
Note that the dimension of the rectangular tin piece is 40 cm by 50 cm, therefore, x = 42 cm cannot be the length of the square.
Hence, the length of the sides of the squares is 3 cm.
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Find a polynomial f(x) of degree 4 that has the following zeros.
-3, 4, 0, 8
Leave your answer in factored form.
f(x) = 0
Polynomial of degree 4 in factored form is x(x+3)(x-4)(x-8) = 0
The Standard form of polynomial with degree 4 is ax⁴ + bx³ + cx² + dx + e
Zeros of the polynomial is the points where the polynomial becomes zero.
According to the question,
The zeros of the polynomial are -3 , 4 , 0 , 8
Let equation of polynomial f(x) be
f(x) = ax⁴ + bx³ + cx² + dx + e ------------------(1)
Sum of zeros = -b/a = -3 + 4 + 0 + 8
= 9
Sum of product of two zeros = c/a = (-3× 4 ) +(0 × 4) + (0 × 8) + (8× -3)
= -12 + 0 + 0 -24
= -12 - 24
= -36
Sum of product of sum of three zeros = -d/a = ( -3×4×0) + ( 4×0 ×8 ) + (0×8×-3) + (-3×4×8)
= 0 - 96
= -96
Product of all four zeros = e/a = (-3×4×0×8)
= 0
So, b = -9 , c =-36 , d = 96 and e = 0
Substituting value in equation (1),
Hence , the required polynomial = x⁴ -9x³ -36x²+96x
Factored form ,
x⁴ -9x³ -36x² +96x = 0
=> x(x³ - 9x² - 36x + 96) = 0
=> x(x+3)(x-4)(x-8) = 0
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The following diagram describes the volume of blue and red paint in a mixture.What is the ratio of blue paint to total paint in the mixture? Choose 1 answer:
Answer:
C
Step-by-step explanation:
blue volume = 10
red volume = 6
total = 10 6 = 16
ratio of
blue : total
= 10 : 16 ( divide both parts by 2 )
= 5 : 8
A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $80 million after 4 years, as shown in the graph:
There is a graph of a line with Years on the x axis and Profits in millions on the y axis that passes through 1, negative 100 and 4, 80.
Which equation most closely represents the line depicted in the graph?
a. f(x) = 60x − 160
b. f(x) = −60x + 160
c. f(x) = −80x + 4
d. f(x) = 80x − 4
The equation most closely represents the line depicted in the graph is
f(x) = 60x − 160
What is linear equation?An equation between two variables that gives a straight line when plotted on a graph.
Given a point (4,80) and a slope, m = 60, these can be used to formulate the equation of the graph. Using the point-slope formula:
y - y1 = m(x - x1)
y - 80 = 60(x - 4)
y - 80 = 60x - 240
y = 60x -160
Taking the x and y-intercepts:
At y = 0
0 = 60x - 160
x = 2.7
At x = 0
y = 60(0) - 160
y = -160
Hence, you could state that there is a graph of a line that has a y intercept that is approximately negative $160 million and an x intercept that is approximately 2.7 years.
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What does n1 mean in statistics?
The meaning of the symbol 'n,' represents the total number of individuals or observations in the sample.
What is Statistics?Statistics is the science that studies and develops methods for collecting, analyzing, interpreting, and presenting empirical data. Statistics is the study and manipulation of data, which includes methods for gathering, reviewing,
analyzing, and drawing conclusions from data. Statistics is divided into two categories: descriptive statistics and inferential statistics.
The primary goal of using statistics is to plan the data collected in terms of experimental designs and statistical surveys. Statistics is a mathematical science concerned with numerical data. In short, statistics is an important process that assists in making data-driven decisions.
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Solve the equation √3 Cosecx-2=0
Answer:
60
Step-by-step explanation:
[tex] \sqrt{3} cosecx - 2 = 0[/tex]
[tex] \sqrt{3} cosecx = 2[/tex]
[tex]cosec = \frac{2}{ \sqrt{3} } [/tex]
[tex]sinx = \frac{ \sqrt{3} }{2} [/tex]
[tex]x = sin {?}^{ - 1} ( \frac{ \sqrt{3} }{2} )[/tex]
[tex]x = 60[/tex]
Given: a ║ b and m<6 is 1/8 of m<4, find m<4 and m<6
Answer:
∠ 4 = 160° , ∠ 6 = 20°
Step-by-step explanation:
∠ 4 and ∠ 6 are same side interior angles and sum to 180°
given ∠ 6 = [tex]\frac{1}{8}[/tex] ∠ 4 ( multiply both sides by 8 to clear the fraction )
8 ∠ 6 = ∠ 4
then
∠ 4 + ∠ 6 = 180° , that is
8 ∠ 6 + ∠ 6 = 180°
9 ∠ 6 = 180° ( divide both sides by 9 )
∠ 6 = 20°
∠ 4 = 8 × ∠ 6 = 8 × 20° = 160°
How many minutes will it take to burn 110 calories
At a food festival, 38 of the dishes were from China. Another 12.5% of the dishes were from Japan. What percent of the dishes were from other countries?
If 3/8 fraction of the dishes were from China and another 12.5 percent from Japan, it implies that 50 percent were from other countries.
How is the percentage determined?Firstly, we convert the proper fraction to a percentage by expressing it over 100.
Secondly, the percentages of China and Japanese dishes are added before being subtracted from 100%.
The resulting difference is the percentage of dishes from other countries.
In summary, unit conversion, expressing the fraction as a percentage, and mathematical operations of addition and subtraction are involved.
Dishes from China = 3/8 = 0.375 or 37.5% (3/8 x 100)
Dishes from Japan = 12.5%
Dishes from other countries = 50% (1 - 37.5% - 12.5%)
Thus, the percentage of dishes from other countries is 50%.
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Question Completion:At a food festival, 3/8 of the dishes were from China. Another 12.5% of the dishes were from Japan.
Consider the following scenario: P(E) = 0.4, P(F) = 0.5
a. Find P(E or F) if E and F are disjoint
b. Find P(E or F) if E and F are independent
The probabilities are given as follows:
a. P(E or F) if E and F are disjoint: 0.9 = 90%.
b. P(E or F) if E and F are independent: 0.7 = 70%.
What is a Venn probability?In a Venn probability, two events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Disjoint events are events that cannot happen at the same time, hence P(E and F) = 0, and then the probability is:
P(E or F) = P(E) + P(F) = 0.4 + 0.5 = 0.9 = 90%.
When E and F are independent, we have that:
P(E and F) = P(E)P(F) = 0.4 x 0.5 = 0.2.
Hence the probability in item b is given by:
P(E or F) = P(E) + P(F) - P(E and F) = 0.4 + 0.5 - 0.2 = 0.7 = 70%.
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ? feet.
(Simplify your answer.)
Answer:
The rocket reaches its maximum height at 2.25 second(s) after launch.
The maximum height reached by the object is 88 feet.
Step-by-step explanation:
How long will it take the rocket to reach its maximum height?
h(t)=-16t² + 72t +7 is a quadratic equation in the form at²+bt+c, where a=-16 and b=72 and c=7.
The maximum height would be at the vertex / peak of this equation, and we can find the x-coordinate (aka the value of 't') at this point using the formula [tex]\frac{-b}{2a}[/tex]:
[tex]t=\frac{-b}{2a} =\frac{-72}{2(-16)} =\frac{72}{32} =2.25seconds[/tex]
What is the maximum height?
Since we know how long it takes to reach maximum height, we can sub this value into the equation to find our answer:
h(t)=-16t² + 72t +7
h(2.25)=-16(2.25)² + 72(2.25) +7
=-81+162+7=88feet
Which graph represents a function?
The graph below shows the total cost for lunch, c, when Will and his friends buy a large salad to share and several slices of pizza, p.
A graph titled Lunch Cost. The x-axis shows the number of slices purchased, numbered 1 to 8, and the y-axis shows the cost in dollars, numbered 5 to 40. Blue diamonds appear at points (0, 7.5), (1, 10), (2, 12.5), (3, 15), (4, 17.5), (5, 20), (6, 22.5), (7, 25), (8, 27.5).
For each additional slice of pizza that is purchased, by how much does the total cost of lunch increase?
$1.50
$2.00
$2.50
$3.00
For each additional slice of pizza that is purchased, the total cost of lunch is increase by $2.5
First choose two points
(1, 10) and (2, 12.5)
The cost of one slice of pizza = $10
The cost of two slice of pizza = $12.5
Using these points we have to find the slope of the line
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the graph
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
Slope of the line = (12.5 - 10) / (2-1)
= 2.5/1
= $2.5
Hence, for each additional slice of pizza that is purchased, the total cost of lunch is increase by $2.5
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Identify the range of y = x² - 2x - 3 if the domain is all real numbers.
The range of this quadratic function y = x² - 2x - 3 is all real numbers greater than 2.
What is the domain and range of a function?Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x is defined.
We know a quadratic function y = ax² + bx + c is a graph of a parabola that opens upwards as the coefficient of x² is positive.
Given, y = x² - 2x - 3.
y = x² - 3x + x - 3.
y = x(x - 3) + 1(x - 3).
y = (x - 3)(x + 1).
Now the x-intercepts are at 3 and -1 so the vertex is located at (3 - 1)/2 = 2.
So the range of this function is all real numbers greater than 2 as the parabola opens upwards.
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Vrite an equation in slope-intercept form of the line that passes through (1, −9) and (-3, -9).
Answer:
y = -9
Step-by-step explanation:
The slope-intercept form is y = mx + b
From two points we can easily determine the slope, m = (y2-y1)/(x2-x1)
You would put in the values into the equation.
m = (-9-(-9))/(-3-1) = 0/-4 = 0
Using the slope-intercept form, y = 0(x) + b ⇒ y = b
But we don't know what the y-intercept (b) is yet. Using the point-slope form we can determine b.
Point-slope: (y - y1) = m(x - x1)
(y - (-9)) = 0(x - (-3))
y + 9 = 0
y = -9
So the equation is y = -9.
Find the equation of the tangent line to the graph of the function f(x)=(x^2+6)(x−4) at the point (1,−21) .
im stumped and this is due soon, please help
The equation of the tangent line of the function is y = x + 20
How to find the equation of the tangent linef(x)=(x^2+6)(x−4)
expanding the function gives
f(x)=x^3 - 4x^2 + 6x - 24
At a specific point the slope, m is the derivative
finding the derivative of f(x)
f'(x) = 3x^2 - 8x + 6
The derivative at the point (1, -21) is found by substituting the point to the equation
f'(1) = 3 * 1 - 8 * 1 + 6 = 1
the slope, m = 1
equation of the line of slope = 1 passing through point (1, -21) is calculated using the point slope formula which is
(y - y') = m(x - x')
(y - -21) = 1(x - 1)
y + 21 = x - 1
y = x + 20
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Supergym is a national chain of gyms. Its employees sold 318,860 gym memberships last year. This year, they sold 80% more memberships than that. How many memberships did they sell this year?
Answer: 573,948 memberships
Step-by-step explanation:
1. Multiply the number of memberships the year prior by 80%
318,860 * 0.8 = 255088
If they sold 80% more memberships this year, that means you would add 80% of the previous year's memberships (255088) to the number of memberships sold last year (318860).
2. Add 80% of the previous year's memberships to the number of memberships sold last year
255088 + 318860 = 573948
Triangle CDE is similar to triangle FGH. Find the measure of side HF. Round your
answer to the nearest tenth if necessary.
E
23
D
19
H
G
59
Answer:
HF ≈ 71.4
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{HF}{EC}[/tex] = [tex]\frac{FG}{CD}[/tex] ( substitute values )
[tex]\frac{HF}{23}[/tex] = [tex]\frac{59}{19}[/tex] ( cross- multiply )
19 HF = 1357 ( divide both sides by 19 )
HF ≈ 71.4 ( to the nearest tenth )
PLEASE HELP! 70pts!
Solve for x. SHOW YOUR WORK!
2^(3x+1)=1/4
Answer:
x = -1
Step-by-step explanation:
Question
Find the area of the trapezoid in the figure below. Round your final answer to the nearest tenth.
helpp
The area of the trapezoid is 26 square units
How to get the area of the trapeziumArea of trapezoid
= (sum of parallel lines) /2 * height
Length of the longer parallel line is solved using Pythagoras theorem is applicable to right angle triangle. the formula of the theorem is
hypotenuse² = opposite² + adjacent²
hypotenuse = 5
opposite = 4
adjacent = ?
hypotenuse = 7.2
opposite = 4
adjacent = ?
adjacent = √(hypotenuse² - opposite² )
adjacent 1 = √(5² - 4² ) = 3
adjacent 2 = √(7.2² - 4² ) = 5.987 ≅ 6
length of the longer parallel line
= 3 + 2 + 6
= 11
Area of trapezoid
= (sum of parallel lines) /2 * height
= (2 + 11) /2 * 4
= 6.5 * 4
= 26 square units
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A total of 12 waffles can be made from each batch of waffle mix. Cynthia is making 6 batches for a breakfast board meeting. If the recipe requires 5 cups of milk for each batch, how 12 many cups of milk does she need to make 6 batches of waffle mix?
2 1/2 cups of milk does she need to make 6 batches of waffle mix.
Given:
A total of 12 waffles can be made from each batch of waffle mix.
Cynthia is making 6 batches for a breakfast board meeting. If the recipe requires 5/12 cups of milk for each batch.
Number of cups of milk required = number of batches*milk required for each batch.
= 6 * 5/12
= 30/12
= 15/6
= 5/2
= 2 1/2 cups.
Therefore 2 1/2 cups of milk does she need to make 6 batches of waffle mix.
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The cost C (in dollars) for a company to produce and sell x thousand gadgets is given by C = 1 /30 x^2 − 2x + 2530
(a) What is the company's start-up cost? _____________ $
(b) What is the minimum cost? ______________$
(c) How many gadgets must the company produce and sell in order to incur the least cost? (Be careful with your units!) ______________ gadgets
The company's start-up cost is equal to $1/2530.
The company's minimum cost is equal to $15/37,949.
The number of gadgets that this company must produce and sell in order to incur the least cost is equal to 1/30 gadgets.
How to determine the company's start-up cost?From the information provided, the cost C (in dollars) for a company to produce and sell x thousand gadgets is modeled by the following function:
Function, C = 1/(30x² − 2x + 2530)
Mathematically, the start-up cost for this company is equal to the total cost when no sales of its gadget has been made i.e the level of activity is at zero (x = 0). Therefore, we would substitute the value of x in the function with zero (0):
Start-up cost = 1/(30(0)² − 2(0) + 2530)
Start-up cost = $1/2530.
What is the minimum cost?First of all, we would determine the number of gadgets that this company must produce and sell in order to incur the least cost by differentiating the function for the total cost using the quotient rule:
dC/dx = [(0(30x² − 2x + 2530) - 1(60x - 2))1/(30x² − 2x + 2530)²]
dC/dx = [(0 - 60x + 2)1/(30x² − 2x + 2530)²]
Equating the marginal cost function to zero, we have:
-60x + 2/(30x² − 2x + 2530)² = 0
-60x + 2 = 0
60x = 2
x = 2/60
x = 1/30 gadgets.
Now, we can determine the minimum cost:
Function, C = 1/(30x² − 2x + 2530)
Minimum cost = 1/(30(1/30)² − 2(1/30) + 2530)
Minimum cost = 1/(1/30 - 1/15 + 2530)
Minimum cost = 1/(-1/15 + 2530)
Minimum cost = 1/(37,949/15)
Minimum cost = $15/37,949
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Let sets A and B be defined as follows:
A= {j, k, l, m, q, r}
B is the set of integers greater than -2 and less than 2
(a) Find the cardinalities of A and B.
n(A) =
n(B)=
(b) Select true or false.
(I've attached a picture below to help other)
Step-by-step explanation:
(a)
it just means how many members are in a set.
there is no mystery or strange mathematical approach. we simply need to count them.
when there is an interval given, sure, we can calculate the length. but for a short interval counting is still faster.
n(A) = 6
n(B) = 3 {-1, 0, 1}
the calculation would be 2 - -2 - 1 = 4 - 1 = 3.
the "-1" comes from the fact that the end of the interval is not included.
(b)
z is not in A. as we can see : true
l is in A. as we can see again : yes. true.
-1 is in B. as I listed above : yes, true.
7 is in B. no, definitely not. false.
There are two number cubes (dice) with faces labeled 1, 2, 3, 4, 5 and 6 equally likely. Roll two dice (one at a time) and calculate the sum of the two faces.
a. Display the sample space
b. P(sum of 8) =
c. P(odd sum or sum greater than 9)
d. P(odd sum and sum greater than 9)
Let A = rolling a 3 or a 4 first
Let B = sum of at most 7
Are A and B mutually exclusive? Why or why not?
Are A and B independent? Why or why not?
a. Please find attached the sample space
b. P(sum of 8) = 5/36
c. P(odd sum or sum greater than 9) = 2/3
d. P(odd sum and sum greater than 9) = 1/12
e. P(A) = 1/3
f. P(B) = 1/6
g. P(A and B) = 1/18
h. A and B are not mutually exclusive because both events can occur at the same time.
i. A and B are not independent because the occurrence of A and lead to the occurrence of B.
What are the probabilities?P(sum of 8) = number of sample spaces that sum up to 8 / total number of sample spaces
P(sum of 8) = 5/36
P(odd sum or sum greater than 9) = (sample spaces that have an odd sum / total number of sample spaces) + (sample spaces that have a sum greater than 9 / total number of sample spaces)
P(odd sum or sum greater than 9) =(18 / 36) + (6/36) = 24/36 = 2/3
P(odd sum and sum greater than 9) = (sample spaces that have an odd sum / total number of sample spaces) x (sample spaces that have a sum greater than 9 / total number of sample spaces)
P(odd sum and sum greater than 9) = 18/36 x 6/36 = 1/12
P(A) = (sample spaces that have a 3 first / total number of sample spaces) + (sample spaces that have a 3 first / total number of sample spaces)
P(A) = 6/36 + 6/36 = 1/3
P(B) = (sample spaces that adds up to 7 / total number of sample spaces)
= 6/36 = 1/6
P(A and B) = 1/3 x 1/6 = 1/18
To learn more about probability, please check: brainly.com/question/13234031
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