Two events are mutually exclusive if the probability of their intersection is 0 and they have no sample points in common. Hence, option D is the correct answer.
The two events are called mutually exclusive when they have no sample points in common. Thus, the probability of event A and event B happening is zero. this means that their intersection set is the empty set.
let us take an example-
Let A be a set of odd numbers and B be a set of even numbers.
A = {1,3,5,7,9}
B = {0,2,4,6,8}
A ∩ B = { }
Hence, the two sets - A and B are mutually exclusive of each other.
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a fence must be built to enclose a rectangular area of 20,000square feet. fencing material costs 3 per foot for the twosides facing north and south and 6 per foot for the other twosides. find the cost of the least expensive fence
A fence surrounding the field that is 200 feet long and 100 feet wide will cost $2400 to construct.
What is area?The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
Here,
Area of rectangle=20,000 square feet
Cost of building fence for north and south=$3 per feet
Cost of building fence for east and west=$6 per feet
Let the sides be x and y,
area=x*y
20000=xy
y=20000/x
Perimeter=2l+2b
=2(x+y)
Total cost will be,
=3*2x+6*2y
=6x+12y
C=6x+12*20000/x
C=6x+240000/x
dC/dx=6-240000/x²
dC/dx=0
6=240000/x²
6x²=240000
x²=40000
x=200 feet
y=100 feet
C=6*200+12*100
C=$2400
The cost of building a fence around the field of length 200 feet and width 100 feet is $2400.
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Solve the system of equation.
4x-3y=-9
3x+2y=-11
Answer:
x = 51
y = -82
(51, -82)
Step-by-step explanation:
Look at the attachment
Given f of x is equal to 1 over the quantity x minus 2 end quantity and g of x is equal to the square root of the quantity x plus 2 end quantity comma what is the domain of f (g(x))?
The domain of the given composite f(g(x)) will be (-∞,-√2 - 2)∪(-√2 - 2,√2 - 2)∪(√2 - 2,∞).
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given phrase,
f(x) = 1/(x-2)
g(x) = (x + 2)²
f(g(x)) = 1/((x + 2)² - 2)
The above function will be defines except (x + 2)² - 2 = 0
(x + 2)² = 2
x + 2 = ±√2
x = √2 - 2 and x = -√2 - 2
Thus, the domain will be (-∞,-√2 - 2)∪(-√2 - 2,√2 - 2)∪(√2 - 2,∞).
Hence "The domain of the given composite f(g(x)) will be (-∞,-√2 - 2)∪(-√2 - 2,√2 - 2)∪(√2 - 2,∞)".
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I want to know how to do this problem
Answer:
Step-by-step explanation: k = 25
47 page 28 math monde svp
Answer:
Step-by-step explanation:
Can you explain more please?
a statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. the 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. suppose the distribution of the population of number of pushups that can be done is approximately normal. if we would like to capture the population mean with 95% confidence the margin of error would be .
The true mean number of pushups that can be performed, as determined by the t-distribution, is within a 95% confidence interval of (9, 21).
Since we know the sample standard deviation for this issue, the t-distribution is applied.
Given,
The sample mean, x = 15 .
The sample standard deviation, s = 9 .
The sample size, n = 10 .
As a result, df = 9. Next, we determine the number of degrees of freedom, which is one less than the sample size.
The crucial value for a 95% confidence interval is then determined by looking at the t-table or using a calculator, yielding t = 2.2622.
The margin of error;
M = t × s/n
Then,
M = 2.2622 × 9/√10 = 6
The confidence interval is:
x ± M
Then
x - M = 15 - 6 = 9
x + M = 15 + 6 = 21
Therefore,
The confidence interval is (9, 21).
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edit: I did this, but im curious on what other ppl would find
In 2006, in Canada, 7.4 million out of 31.4 million of canadians said they spoke french.
Between 2006 and 2011, Canada's population went up 6%, and the number of canadians speaking french went up 300 000.
Did the pourcentage of french-speaking canadians go up or down between 2006 and 2011?
The percentage of French-speaking Canadians went down between 2006 and 2011.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In 2006, in Canada, 7.4 million out of 31.4 million of canadians said they spoke french. The percentage will be:
= 7.4/31.4 × 100
= 23.6%
Since Canada's population went up 6%, the bee population will be:
= 31.4 million × (6% × 31.4 million)
= 33,284,000
The number of Canadians speaking french went up 300 000.
The percentage will be:
= 7,700,000/33,284,000 × 100
= 23%
Therefore, the percentage reduced.
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Based on your answer to part b, should kevin increase or decrease his prices toward the end of the season to avoid having unsold produce?
Kevin should decrease his prices toward the end of the season to avoid having unsold produce.
What is price?
The price of a product is the amount that customers are willing to spend. While also taking into account supply costs, seasonal discounts, competitor prices, and retail markup, marketers must connect the price to the product's actual and perceived value.
Consider the following,
Price per Pound (dollars) Quantity Sold (pounds)
1.00 ⇔ 5,700
2.00 ⇔ 4,100
3.00 ⇔ 2,300
Kevin has seen that demand increases when prices decrease.
Hence, Kevin should decrease his prices toward the end of the season to avoid having unsold produce.
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Complete question:
Kevin owns a fruit stand alongside a busy road. For several years, he has kept track of the number of apples that people purchase at different prices. He decides to graph the number of apples sold and the various prices at which he sold them. The graph shows his record of the number of apples sold at different prices.
Fill in the table with the number of apples Kevin sold at each price. Use the graph to estimate approximate quantities of apples.
What is the relationship between the price of apples and the demand for apples among Kevin’s customers?
Based on your answer to part B, should Kevin increase or decrease his prices toward the end of the season to avoid having unsold produce?
Answer: Kevin has seen that demand increases when prices decrease, so he should decrease his prices toward the end of the season to avoid having unsold produce.
Step-by-step explanation: PLATO answer :)
Lucas, Mason, Logan, and Jayden have 5 grapefruits. They want to share them equally. How much grapefruit will each person get?
-7x + 4y = 24
4x - 4y = 0
solve by substitution - please add explanation and work
Answer:
(-8, -8)
Step-by-step explanation:
You need to solve one of the equation for x or y. I am going to solve the bottom equation for x
4x -4y = 0 Add 4y to both sides
4x = 4y Divide both sides by 4
x = y Substitute y in for x in the first equation
-7x + 4y = 24
-7y + 4y = 24 Combine like terms
-3y = 24 Divide both sides by -3
y = -8
Since x = y
x = -8
Check:
-7y + 4y = 24
-7(-8) + 4(-8) = 24
56 - 32 = 24
4x - 4y = 0
4(-8) - 4(-8) = 0
-32 + 32 = 0
0 = 0
whats the answer for shrinking -12(5/6x-5)+2x
Answer: 12x-60
Step-by-step explanation:
-12 x 5/6 = 10
-12 x 5 = -60
10x-60+2x
12x-60
(1 point) 5 dice of different colors are rolled, and the number coming up on each die is recorded. how many different outcomes are possible?
The number of total different outcomes are, 7,776.
What is rolling dice?
Every face of a cube known as a dice has a unique number.
By throwing a dice into the air, players can advance in any game by getting a certain number. Typically, this dice or dice has numbers from 1 to 6 written on each face or side of the cube-like shape.
Given:
Discrete 5 dice of different colors are rolled, and the number coming up on each dice is recorded.
Since all the dice are of different colors.
So any combination of the numbers on the dice is unique.
Dice has numbers 1 to 6.
So, for each dice there are 6 possibilities.
Since number coming on a dice is independent to the number coming on the another dice.
So, total different outcomes are = 6 x 6 x 6 x 6 x 6 = 6^5 = 7776.
Hence, the number of total different outcomes are, 7,776.
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suppose that the cash flow, in dollars , for a pharmacy are normally distributed with an unknown mean and standard deviation. the cash flow of 40 randomly sampled pharmacies are used to estimate the mean of the population. what t-score should be used to find the 80% confidence interval for the population mean?
The t-score should be used to find the 80% confidence interval for the population mean is $1.304
the interval of confidence: This indicates the degree of confidence and ambiguity in a sampling process. It provides us with a range of outcomes, indicating that we would be reasonably certain that our genuine value or variable falls inside the range.
The sample size was 40 pharmacies (n=40). To calculate the degrees of freedom, use the formula: df=n-1=40-1=39.
The scenario specifies an 80% confidence level. So,α=1−CL=1−0.8=0.2 However, we wish to utilize the value for 2, which would be 0.22=0.1. We ought to locate the row for 39 freedom degrees and the column for t0.1 using the table. So the t-score for determining the 80% confidence interval is 1.304. We may alternatively use a calculator and enter 1-α2=0.9 as well as the degrees of freedom into invT, and then enter invT. (0.9,39).
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What kind of triangle has angles 60°, 60°, and 60°?
Answer:
equilateral triangle
Step-by-step explanation:
all of the sides to a equilateral triangle equal to 60 degrees.
The table shows information about the
masses of some dogs.
a) Work out the minimum number of dogs
that could have a mass of more than 26 kg
b) Work out the maximum number of dogs
that could have a mass of more than 26 kg
Mass, x (kg)
0≤x≤10
10≤x≤20
20≤x≤30
30≤x≤40
Frequency
4
8
11
5
a) The minimum number of dogs that could have a mass of more than 26 kg is of: 5.
b) The maximum number of dogs that could have a mass of more than 26 kg is of: 16.
What is shown by the frequency table?The frequency table shows the number of times that each value, or values in each range, appears in the data-set.
11 weights are between 20 and 30, hence:
The minimum number of dogs that could have a mass of more than 26 kg is of 5, when all the dogs in the interval 20 ≤ x < 30 have weights that are less than 26 kg, hence only the dogs on the interval 30 ≤ x < 40 will have a mass of more than 26 kg.The maximum number of dogs that could have a mass of more than 26 kg is of 16, when when all the dogs in the interval 20 ≤ x < 30 have weights that are more than 26 kg, along with all the dogs on the interval 30 ≤ x < 40.More can be learned about frequency tables at https://brainly.com/question/16148316
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Simplify the expression.
2.4-5.4n3n+6
...
2.4-5.4n-3n+6=
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Answer:
8.4-16.2n²
Step-by-step explanation:
2.4-5.4n3n+6
= 2.4-16.2n²+6
= 8.4-16.2n²
a cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 132 inches. find the dimensions of the package of maximum volume that can be sent. (the cross section is circular.)
The required dimensions of the package for maximum volume are radius = 14, height = 44 inches.
Explain cylindrical shape.A cylinder is round and has a top and base looking like a circle. The top and base are level and consistently a similar size. I figure the most effective way to portray the state of a chamber is to consider a container of soup
According to question:We have,
combined length and girth is 132 inches.
So, Girth = 2πr
If length of cylinder is h,
2πr + h = 132
h = 132- 2πr
the dimensions at which the max volume can be sent
Volume of cylinder; V = πr²h
put 132 - 2πr for h to get
V = πr²(132 - 2πr)
V =132πr² - 2π²r³
Differentiating with respect to r ,
dV/dr = 264πr - 6π²r²
For max volume will be when dV/dr = 0
Then,
264πr - 6π²r² = 0
adding 6π²r² to both sides
264πr = 6π²r²
264/6 = (π²r²)/πr
44 = πr
r =44/π = 14 inches
Radius = 14 inches
Put 44/π for r in h = 132 - 2πr to get;
h = 132 - 2π(44/π)
h = 132 -88
h = 44 inches
Thus, required height is 44 inches.
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A statistic summarizing the strength of association between two metric variables is called the ________.
A) product moment correlation
B) covariance correlation
C) inverse correlation
D) bivariate correlation
E) F-statistic
A statistic summarizing the strength of association between two metric variables is called the product moment correlation.
The Pearson product-moment correlation coefficient also known as Pearson’s correlation is a measure of the linear relationship between two variables/measures/questions, in other words, the Pearson product-moment correlation coefficient is a measure of the direction and strength of association that exists between two metric variables measured on at least an interval scale.
A product-moment correlation attempts to draw a line of best fit through the data of two variables, and the Pearson correlation coefficient illustrates how far away all these data points are from the best fit line. Product-moment correlation quantifies the strength as well as the direction of correlation.
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Work with a partner. Supercooling is the process of lowering the temperature
of a liquid or a gas below its freezing point without it becoming a solid. Water
can be supercooled to 86°F below its normal freezing point (32°F) and still
not freeze.
a. Let x represent the temperature of water. Which inequality represents the
temperature at which water can be a liquid or a gas? Explain your reasoning.
Even when water is supercooled to 86 degrees Fahrenheit below its normal freezing point (32 degrees Fahrenheit), it will not freeze. Therefore, x-32≥-86
Define supercooling.The process of lowering a liquid or gas's temperature below its melting point without causing it to solidify is known as supercooling, sometimes known as undercooling. It accomplishes this in the absence of a seed crystal or nucleus around which a crystal structure can form.
Let temperature be x
The temperature at which water turns into a liquid or a gas is represented by inequality is x-32≥-86
The reason is that as water will not freeze even when supercooled to 86°F below its typical freezing point (32°F).
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at the homecoming game, cheerleaders will throw 100 bundled t-shirts into the crowd. the t-shirt sizes consist of 20 small, 30 medium, and the remainder either large or extra large. suppose you catch a t-shirt. what is the probability that you will catch a t-shirt that is not a size medium?
The probability that you will catch a t-shirt that is not of medium size would be 0.7
What is the probability?
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
Small=S=20, M=medium=30,
L = Either large or extra large=50
P(T-shirt that is not a medium)= 1 - P(T-shirt is medium)
= 1 - 30/100
= 1 - 0.3
= 0.7
Hence, the probability that you will catch a t-shirt that is not of medium size would be 0.7
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The length of the rectangle is 5 cm less than twice it’s width.the area of the rectangle is 42 cm^2. What is the width of the rectangle
Answer: Could be 7.
Step-by-step explanation:
the scores on a standardized test have an average of 1200 with a standard deviation of 60. a sample of 50 scores is selected. what is the probability that the sample mean will be greater than 1205? round your answer to three decimal places.
the scores on a standardized test have an average of 1200 with a standard deviation of 60 and 99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
On Subtracting 1 from your sample size, we get
100 – 1 = 99.
On Subtracting confidence level from 1, and then divide by two.
(1 – .997) / 2 = 0.0015
Now, df = 99 and α = 0.0015
from the table at df = 99 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(100) = 2.8
Now, 2.262 × 2.8 = 6.33
So, the confidence interval be,
(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)
Hence, 99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
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A lottery offers one $900 prize, one $600 prize, three $400 prizes, and four $100 prizes. One thousand tickets are sold at $5 each. Find the expectation if a person buys five tickets. Assume that the player’s ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.
The expectation if a person buys five tickets is $____.
The Expected value for 4 tickets = $ 7.6
Given - A lottery offers one $900 prize, one $600 Prize, three $400 prizes, and four $100 prizes. One thousand tickets are sold at $5 each.
To find - Find the expectation if a person buys four tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.
Proof -
Given that,
A lottery offers
one $ 900 prize
one $ 600 prize
three $ 400 prizes
Four $ 100 prizes
And
One thousand tickets are sold at $ 5 each
Now,
If the person bought 1000 tickets then the prize he gets is
= 900 + 600 + 3×400 + 4×100
= 900 + 600 + 1200 + 400
= $3100
And
The cost of 1000 tickets = 5×1000 = $ 5000
Now,
Price 1 ticket = $ 3.1
⇒Expectation of 1 ticket = 5 - $ 3.1 = $ 1.9 (Here $5 is price of 1 ticket)
⇒Expected value for 4 tickets = $ 4× -1.9 = $ 7.6
⇒Expected value for 4 tickets = $ 7.6
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The star Sirius is more than 4 light years farther from Earth than the star
Proxima Centauri. Write an inequality that represents the distances of Sirius
and Proxima Centauri from Earth.
Answer:
dS > dC + 4 LY
Drag each expression to the correct location in the equation. not all expressions will be used. determine the two rational expressions whose difference completes this equation.
The two found rational expressions with the difference that completes the equation is (x + 2)/(x² - 36) and 1/(x² + 6x).
Explain the term rational expressions?The ratio of 2 polynomials is a rational expression. F can be expressed in the form p/q, where q and p are polynomials, if f is a rational expression.Consider the two rational expressions.
(x + 2)/(x² - 36) ...eq 1
and 1/(x² + 6x) ....eq 2
Subtract the second from the first.
= [(x + 2)/(x² - 36)] - [1/(x² + 6)]
Factorise the denominator of the first equation-
= [(x + 2)/(x + 6)(x - 6)] - [1/(x(x + 6)]
Taking the LCM
= [x(x + 2) - (x - 6)]/[x(x + 6)(x - 6)]
Further simplifying,
= [x² + x + 6]/[x(x-6)(x + 6)]
Thus, the two found rational expressions with the difference that completes the equation is (x + 2)/(x² - 36) and 1/(x² + 6x).
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The complete question is-
Drag each expression to the correct location in the equation. Not all expressions will be used.
Determine the two rational expressions whose difference completes this equation.
x² + x + 6
x(x-6)(x + 6)
The area of the Okhotsk Sea is 1.583 × 10^6 km^2. The area of the Indian Ocean is 7.3556 × 10^7 km^2. Find the total area. Write the final answer in scientific notation with the correct number of significant digits.
8.9386 × 10^13 km2
8.939 × 10^13 km2
7.5139 × 10^7 km2
7.514 × 10^7 km2
The total area will be;
⇒ 7.514 × 10⁷ km²
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The area of the Okhotsk Sea is 1.583 × 10⁶ km².
And, The area of the Indian Ocean is 7.3556 × 10⁷ km².
Now,
Since, The area of the Okhotsk Sea is 1.583 × 10⁶ km².
And, The area of the Indian Ocean is 7.3556 × 10⁷ km².
Hence, The total area = 1.583 × 10⁶ + 7.3556 × 10⁷
= 1.583 × 10⁶ + 73.556 × 10⁶
= 75.14 × 10⁶
= 7.514 × 10⁷ km²
Thus, The total area will be;
⇒ 7.514 × 10⁷ km²
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If f(x) varies directly with x and f(x)= 150 when x=45, find the value of f(x) when
x=11. Round you final answer to the nearest whole number. Work must be shown for
this problem or no credit will be earned.
As x and f(x) vary directly when x = 11 , f(x) = 110/3.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, x and f(x) varies directly, let f(x) be y.
∴ y = kx.
150 = 45k.
k = 150/45.
k = 30/9.
K = 10/3.
Now, when x = 11.
y = (10/3)×11.
y = 110/3.
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a recent survey reported that small businesses spend 24 hours a week marketing their business. a local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 24 hours a week on marketing. the chamber conducts a survey of 58 small businesses within their state and finds that the average amount of time spent on marketing is 22.7 hours a week. assuming that the population standard deviation is 6.1 hours, is there sufficient evidence to support the chamber of commerce’s claim at the 0.02 level of significance?
chamber of commerce’s claim at the 0.02 level of significance, z = -1.75
What is z test?
If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.
a recent survey reported that small businesses spend 24 hours a week marketing their business.
these businesses are spending less than 24 hours a week on marketing. the chamber conducts a survey of 58 small businesses within their state and finds that the average amount of time spent on marketing is 22.7 hours a week.
assuming that the population standard deviation is 6.1 hours.
Given n = 93, u =24, x' = 23, α=5.5
z = x'- u / α(/√n) = (23-24/5.5/√5) = -1.75
Hence, chamber of commerce’s claim at the 0.02 level of significance, z = -1.75
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help on photo Mathematics
Answer:
B. 48
Step-by-step explanation:
plug in the value of h into the expression and simplify from there
A plant is already 55 centimeters tall, and it will grow one centimeter every month. The plant's height, (in centimeters), after months is given by the following.H=55+m What is the plant's height after 34 months? PLEASE HELP
The plant's height after 34 months will be 89cm if the plant is already 55 centimeters tall.
What is meant by height?Height is defined in mathematics as the vertical distance from the object's top to its base. It is occasionally referred to as 'altitude.' The term height in geometry refers to the measurement of an object along the y-axis in coordinate geometry.
Height and elevation all refer to the vertical distance between the top and bottom of something or between a base and anything above it. Height refers to something measured vertically, whether it be high or low.
Given, the relation between the height and the months is:
H(m)=55+m
Now, we have to find the height of the plant after 34 months.
So, we substitute m=34 in the expression to obtain height,
H(m)=55+m
H(34)=55+34
H(34)=89cm
Hence the height will be 89cm
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