The statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is false.
What is meant by probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
The given statement is:
"the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring."
This is a false statement.
The probability of the union of two events is the probability of individual events without considering the probability of the intersection of the events.
When the events do not have an intersection, then the probability of a union of events is greater than the probability of an intersection of events.
The chance of both occurrences occurring together is given by the union of two events, but the probability of both events occurring simultaneously is given by the intersection of two events, which is smaller than probability of union of events.
Therefore the statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is false.
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AB and BC form a right angle at point B. If A = (-3-1) and B = (4,4) what is the equation of Bc
Answer: The equation of a line in the form y = mx + b can be found using the slope-intercept form, where m is the slope of the line and b is the y-intercept. To find the equation of BC, we need to find the slope of the line and one point on the line.
The slope of the line can be found using the two points A and B. The slope of the line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively. Plugging in the values, we get:
m = (4 - (-1)) / (4 - (-3)) = 5 / 7
So the slope of the line BC is 5/7.
One point on the line BC is B = (4, 4), so we can use this point and the slope to find the y-intercept:
b = y - mx
where y and x are the y and x coordinates of point B, respectively. Plugging in the values, we get:
b = 4 - (5/7) * 4 = 4 - 20/7 = -16/7
So the equation of line BC in the slope-intercept form is:
y = (5/7)x - 16/7
Step-by-step explanation:
Which three capital cities sit on or nearly on the equator?
Answer: Demographic republic of Congo, Uganda and Gabon
Mackenzie has 8 markers. Ty has three times as many. If they combine their markers, how
many do they have?
Show your work
Answer:
32 markers
Step-by-step explanation:
Ty has 8 x 3 = 24 markers.
Together, they have 8 + 24 = 32 markers.
medbiz develops and sells medical imaging devices. they are developing a computer program that reads heart images and detects heart muscle damage. early studies show the machine has a 90% success rate. the programs is shown 100 images of hearts with muscle damage. what distribution should be used to calculate the probability that the first heart it detects with muscle damage is the 8th image? group of answer choices
To calculate the probability that the first heart it detects with muscle damage is the 8th image geometric distribution should be used.
According to the question medbiz develops and sells medical imaging devices. they are developing a computer program that reads heart images and detects heart muscle damage.
Machine has success rate of 90%
Number of images of hearts with muscle damage = 100
To calculate the probability that the first heart it detects with muscle damage is the 8th image, geometric distribution should be used because
Geometric distribution is a type of discrete probability distribution that represents the probability of the number of successive failures before a success is obtained in a Bernoulli trial. A Bernoulli trial is an experiment that can have only two possible outcomes, ie., success or failure
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The question is incomplete, the following question is complete:
MedBiz develops and sells medical imaging devices. They are developing a computer program that reads heart images and detects heart muscle damage. Early studies show the machine has a 90% success rate. The programs is shown 100 images of hearts with muscle damage. What distribution should be used to calculate the probability that the first heart it detects with muscle damage is the 8th image?
binomial distribution
geometric distribution
hypergeometric distribution
none of the other choices
f(x) = 3x + 5
g(x) = 4x² - 2
h(x)=x²-3x+1
Find f(x) - g(x) — h(x).
The expression for f(x) - g(x) - h(x) is 6x - 5x² + 6.
Option C is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 3x + 5
g(x) = 4x² - 2
h(x) = x² - 3x + 1
Now,
f(x) - g(x) - h(x)
= 3x + 5 - (4x² - 2) - (x² - 3x + 1)
= 3x + 5 - 4x² + 2 - x² + 3x - 1
= 6x - 5x² + 6
Thus,
6x - 5x² + 6 is the expression.
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Select all the measures of variability that can be used to compare two data sets.
A. Mean
B. Interquartile Range
C. Median
D. Mode
E. Range
Range, interquartile range, standard deviation, and variance are four measures of variability that can be used to compare two data sets.
Variability is most generally measured proving the following descriptive data:area:
Difference between highest and lowest values.
Range is the straightforward allowance to calculate variability. To asset the area, follow these steps:
Sort all the values in the dataset from lowest to highest.
Subtract the lowest value from the highest value. Interquartile range:
area of the middle half of the distribution
standard deviation:
mean distance from mean
Standard deviation is a useful measure of the variance of a normal distribution.
A normal distribution distributes data symmetrically without skew. Most of the values are clustered around the central region, with values tapering away from the center. Standard deviation indicates how far the data are, on average, from the center of the distribution.
deviation:
mean squared distance from mean
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Belle has a collection of trading cards. The table shows how many of each type of card she has. A card will be randomly drawn from her collection and replaced 60 times
Type: Number:
Baseball 13
Football. 8
Basketball. 5
Soccer. 9
What is a reasonable prediction for the number of times a basketball or soccer card will be drawn?
Which expression would NOT be equivalent to 4(10+5)?
Answer:
Not Possible
Step-by-step explanation:
No answer choices are shown however, we can solve for some that are equivalent so we know which ones are not.
Here are some that are equivalent:
20(2+1)
2(20+10)
40+20
60
Which properties justify the steps taken to solve the system {2a+7b=0 3a-5b=31
Drag the awnsers into the boxes to match each step ASAP
The properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division, Simplify, etc.,
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
'The properties that justify the steps taken to solve the system 2a + 7b = 0, 3a - 5b = 31 are:
2a + 7b = 0, 3a - 5b = 31
10a + 35b = 0, 21a - 35b = 217 <-------> Multiplication property of equality.
31a = 217 <-------> Substraction property of equality.
a = 7 <-------> Division property of equality.
2(7) + 7b = 0, <-------> Substitution property of equality.
14 + 7b = 0, <-------> Simplify
7b = -14, <-------> Simplify
b = -14/7, <-------> Division property of equality.
b = -2
Therefore, the properties justify the steps are taken to solve the system 2a+7b=0 3a-5b=31 as Multiplication, Substraction, Division, Simplify, etc.,
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The perimeter of a rectangle is 30 inches. The width of the rectangle is two-thirds of its
length, as shown.
What are the length and the width of the rectangle? Check your solution.
Answer:
The length is [tex]9[/tex] inches and the width is [tex]30[/tex] inches.
Step-by-step explanation:
The perimeter of the rectangle is [tex]2x + \frac{4x}{3} = 30[/tex]. We multiply [tex]3[/tex] by both sides which will give us [tex]6x + 4x = 90[/tex]. Adding, we have [tex]10x = 90[/tex]. Dividing [tex]10[/tex] by both sides will give us [tex]x = 9[/tex]. The length of the rectangle is [tex]9[/tex], and the width is [tex]\frac23 \cdot 9 = 6.[/tex] Checking our answer, we have [tex]6 + 6 + 9 + 9 = 30.[/tex] Therefore, the length of the rectangle is [tex]\boxed{9 \text{ inches}}[/tex] and the width of the rectangle is [tex]\boxed{30 \text{ inches}}[/tex].
Hope that helps!
Label each figure correctly. Area is understood to be square feet and perimeter is understood to be feet. (PLEASE HELP)
The area and perimeters of the shapes are: (1) Area = 702 ft², perimeter = 96 ft (2): Area = 20 in² Perimeter = 21 in
How to find the area and perimeters?Perimeter is the distance round the object while the area is the floor space the object occupies
1) Area = (l*w) + (L*W)
Area = (6*9) + (24*27)
Area = 54 + 648
Area = 702 ft²
ii) perimeter = 24+27+30+9+6= 96 ft
2) Area = (l*w) + (L*W)
Area = (2*3) +( 7*2)
Area = 6+14 = 20 in²
ii) perimeter =2+7+2+2+3+2+3 = 21 in
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Five packets of marshmallows cost £4. 80. How much will eight packets cost?
Five packets of marshmallows cost £4. 80. Then, eight packets of marshmallows cost £7.68.
The problem states that five packets of marshmallows cost £4.80. We need to find out how much eight packets of marshmallows will cost.
To solve the problem, we can use the concept of proportionality. If we assume that the cost of marshmallows is directly proportional to the number of packets, then we can set up a proportion between the cost of five packets and the cost of eight packets.
The proportion can be written as follows:
5 packets / £4.80 = 8 packets / x
where x is the cost of eight packets.
To solve for x, we can cross-multiply the proportion and simplify:
5 packets x = £4.80 x 8 packets
5x = £38.40
x = £38.40 / 5
x = £7.68
Therefore, eight packets of marshmallows will cost £7.68.
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What is the slope of the line that passes
through the points (10, 3) and (7,0)?
Write your answer in simplest form.
Answer:
0.75
Step-by-step explanation:
The slope-intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
the angle of depression from the top of a cliff to a nearby town is 23 degrees. if the top of the cliff is 360 feet above the town, how far is the town from the base of the cliff? do not round until you reach your answer, and then round your answer to the nearest tenth of a foot.
The length of town from the base of the cliff is 848.25 feet
Concept of height and distance
You can use trigonometry formulas to find height and distance from anything. If you know the distance from the Qutub Minar to your current location and the angle at which you can see the top of the Minar, you can find the altitude of the Qutub Minar. Use trigonometry to find the elevation. This is because the ground, minaret elevation, and contour lines all combine to form a 90 degree right triangle between the minaret and the ground.
The distance is usually the "base" of the right triangle formed by the minar's elevation and line of sight. The length of the horizontal plane also forms the base of a triangle parallel to the ground at a given height, so we know the distance. The line of sight forms the "hypotenuse" of a right triangle. Lines perpendicular to the ground form the "height" of the triangle.
To calculate elevation or depression you can use the following formulas:
sinθ = hypotenuse /height.
cosθ = hypotenuse /base,
tanθ = base /height
where θ is the elevation or depression angle.
and in this question the angle of depression is 23 degree and height is 360 feet and we have to calculate the base
tan 23 degree = 360/base
base = 360/tan 23
=360/0.4244
= 848.25 feet.
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For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the total cost, C, after h hours of babysitting. How much money will she make if she baby-sits 5 hours?
The equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.
What is an equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
Let us suppose the number of hours = x.
The cost of additional hour is $5.
The cost of x hours is 5x.
Given that, Nicole charges a flat fee of $3, plus $5 per hour.
C = 3 + 5x
If she baby sits for 5 hours, that is x = 5, then:
C = 3 + 5(5)
C = 3 + 25
C = $28
Hence, the equation of the total cost is C = 3 + 5x and the amount earned after 5 hours is $28.
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Find the number that makes the ratio equivalent to 1:2.
The equivalent to the ratio 1:2 is 2 : 4
How to determine the equivalent ratioFrom the question, we have the following parameters that can be used in our computation:
Ratio = 1 : 2
To determine the equivalent expression, we multiply each proportion of the ratio by the same number (say 2)
Using the above as a guide, we have the following:
Ratio = 2 * 1 : 2 * 2
Evaluate
Ratio = 2 : 4
Hence, the ratio is 2 : 4
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imagine math - item 92070
I'm sorry, but I'm not sure what you mean by "Imagine math - item 92070." Can you please provide more context or clarification so I can assist you better?
suppose 4 math majors and 6 computer science majors randomly take seats in the front row of a classroom. a. what's the probability the math majors are seated together? b. what's the probability the math majors are seated together and the computer science majors are seated together?
The probability the math majors are seated together is 0.028 and all seated togeather with their group is 0.0047.
Probability is the probability that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics.
Probability determines the likelihood of an event occurring.
P(A) = f / N. Odds and probabilities are related, but odds depend on probabilities. Before we can determine the probability that an event will occur, we first need the probability.
total number of teacher is 10
so number of ways total 10 teacher seat = 10!/(6!*4!)
= 210
and
the number of ways the math majors are seated together
= 6
probability = 6/210 = 0.028
the number of ways the math majors are seated together and the computer science majors are seated together
= 1
probability = 1/210
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3. The width of a rectangle is 8 inches less than the length, x, of the rectangle. The sum of the length
and width is more than 60 inches. Which of the following represent the possible values of the length
of the rectangle?
A x > 34
B
x <34
C
X> 24
D
x > 26
8-X < 60
The possible values of the length of the rectangle is x > 34, the correct option is A.
How to find the area and the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Area of the rectangle = [tex]L \times W \: \rm unit^2[/tex]
Perimeter of the rectangle = [tex]2(L + W) \: \rm unit[/tex]
The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Given that width is 8 inches less than the length x
Sum of length and width more than 60
Now, the length is x
Width is x-8
x-8+x>60
2x>60
x>30
Therefore, the length of rectangle will be x > 34
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If P is the centroid, and GP=2.2, find the indicated
lengths.
A
PC =
GC =
ttt
B
++
H
type your answer...
type your answer...
C
The length of PC and GC is 4.4 and 6.6 respectively.
What is centroid of a triangle?
A centroid of a triangle is defined as a equidistant from all the point present on the triangle. It is always lies on the interior of the triangle. The centroid divided the median in the ratio 2:1
Given ABC is the triangle.
In which G, H, J are the midpoints on AB, BC, AC sides respectively.
Then, AH, CG, BJ are the medians and they are intersect at the point P.
P is the centroid of the triangle.
Given, GP =2.2 we have to find the PC and GC.
We know that the centroid divided the median in 2:1 ratios.
i.e., AP:PH = CP:PG = BP:PJ = 2:1
We know , GP = 2.2, then, [tex]\frac{CP}{PG} = \frac{2}{1}[/tex]
⇒CP= 2(2.2)= 4.4then, GC = GP+PC= 2.2 + 4.4= 6.6.
Hence, the length of PC and GC is 4.4 and 6.6 respectively.
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There are 21 pieces of $2 notes and $10 notes in an envelope. If the total value of all the notes is less than
$110, find the minimum number of $2 notes in the envelope.
Answer:
Let the number of $2 notes be x, while that of $10 notes be y.
Set two equations
x + y = 21 y = 21 - x ------- 1
2x + 10y < 110 ------ 2
Sub 1 into 2
2x + 10(21-x) < 110
2x + 210 - 10x < 110
-8x < -100
x > 12.5
Minimum number of $2 notes in the envelope = 13
Each week, Desiree earns $925 and pays $149 in payroll tax. How long does it take Desiree to earn at least $3000 after taxes?
Each week, Desiree earns $925 and pays $149 in payroll tax it will take Desiree at least 4 weeks to earn at least $3000 after taxes.
What is Gross earning ?
Gross earnings refer to the total amount of money that an individual earns before any deductions are taken out. These earnings can include regular salary or wages, as well as any bonuses, tips, or commissions that are earned. Gross earnings are usually reported on a paycheck or pay stub, and may be subject to various taxes and other deductions.
Desiree's net earnings after payroll tax can be calculated by subtracting the tax amount from her gross earnings:
Net Earnings = Gross Earnings - Payroll Tax
Net Earnings = $925 - $149
Net Earnings = $776
To earn at least $3000 after taxes, Desiree needs to earn a total of:
Total Earnings = $3000 + Payroll Tax
Total Earnings = $3000 + $149
Total Earnings = $3149
We can now set up an equation to solve for the number of weeks, x, it will take for Desiree to earn at least $3149:
Net Earnings per week * Number of Weeks = Total Earnings
$776 * x = $3149
Solving for x:
x = $3149 / $776
x = 4.05
Therefore, it will take Desiree approximately 4.05 weeks to earn at least $3000 after payroll tax. Since you can't earn partial weeks, we can round up to 5 weeks to ensure that Desiree has earned at least $3000.
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What is 2x times 2x in algebra
Answer: 4x2
Step-by-step explanation:
Answer:
[tex]4x^2[/tex]
Step-by-step explanation:
[tex](2x)(2x)=(2*2)(x*x)=4x^2[/tex]
The temperature in Wintergreen Resort in Virginia fell from 15.8
degrees Celsius to - 2.7 degrees Celsius. What is the difference
between the two temperatures?
The term "difference" os the result of subtracting one number from another.
So in other terms you want to know what would be the result of subtracting -4.6 from 13.5 :
13.5 - -4.6 = Difference between the two temperatures
Two minus signs turn into a positive sign so :
13.5 - -4.6 =
13.5 + 4.6 =
18.1 = Difference between the two temperatures
Your answer is : The difference between the two temperatures is 18.1
Solve for x.
-x+8=259
X =
Answer:x=251
Step-by-step explanation:
Step 1: Subtract 8 from both sides of the equation.
Explanation: Subtracting 8 from both sides of the equation keeps the equality balanced.
Step 2: x = 251
Explanation: Subtracting 8 from both sides of the equation gives us
x = 259 - 8 = 251.
Answer:
Step-by-step explanation:
x = -251
Hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2. If the surface area of hexagonal prism B is 172 cm^2, find the surface area of hexagonal prism A, the preimage.
Hexagonal prism A has a surface area of 43 cm2.
What is the surface area equation?A three-dimensional shape's surface area is the total area on its surface. A cuboid's surface area is calculated by adding the areas of each of its six rectangular sides. The cuboid's length, width, and height may all be identified, and the formula SA=2lw+2lh+2hw can be used to determine its surface area (SA).
The surface area of a hexagonal prism is given by the formula:
SA = 2B + PH
where B is the base's surface area, P is its perimeter, and H is the prism's height.
Since prism B is a dilation of prism A with a scale factor of 2, its surface area is four times the surface area of prism A. So we can write:
SA_B = 4×SA_A
where SA_B is the surface area of prism B and SA_A is the surface area of prism A
We are given that SA_B = 172 cm², so we can substitute this value into the equation above to find SA_A:
172 = 4×SA_A
SA_A = 43 cm²
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what value of k makes -4 > k + 15 true
Answer:
-19 > k
Step-by-step explanation:
-4 > k + 15
Subtract 15 from each side.
-4-15 > k + 15-15
-19 > k
Any value less than -19 would make this statement true
Answer:
- 19 > k
Step-by-step explanation:
- 4 > k + 15
Subtract 15 from both sides.
- 4 - 15 > k
- 19 > k
Find the slope of the line graphed below.
Answer:
the slope is -6/-5
A large rectangular movie screen in an IMAX theater has an area of 11,224 square feet. Find the dimensions of the screen if it is 30 feet longer than it is wide
With an area of 11,224 square feet and the dimensions of the screen if it is 30 feet longer than it is wide, the width of the screen is 91.5 feet, and the length of the screen is 121.5 feet.
Let's call the width of the screen "w". Then, the length of the screen would be "w + 30". The area of the screen is 11,224 square feet, so we can set up an equation:
w * (w + 30) = 11,224
Expanding the right side of the equation, we get:
w^2 + 30w - 11,224 = 0
We can use the quadratic formula to solve for w:
w = (-b ± √(b^2 - 4ac)) / 2a
Where a = 1, b = 30, and c = -11,224.
Plugging in the values, we get:
w = (-30 ± √(30^2 - 4 * 1 * -11,224)) / 2 * 1
= (-30 ± √(900 + 44,896)) / 2
= (-30 ± √(45,796)) / 2
= (-30 ± 213) / 2
Taking the positive solution, we get:
w = (183 / 2) = 91.5 feet
So the width of the screen is 91.5 feet, and the length of the screen is 91.5 + 30 = 121.5 feet.
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The length of a cell phone is 1.41.4 inches and the width is 2.82.8 inches. The company making the cell phone wants to make a new version whose length will be 1.611.61 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:
Since the side lengths are proportional, the ratio of the width to length in the old phone will be equal to the ratio of the width to length in the new phone. That is:
(width of old phone) / (length of old phone) = (width of new phone) / (length of new phone)
We know the length of the old phone is 1.41.4 inches, and the width is 2.82.8 inches, so we can use that information to solve for the width of the new phone:
(2.82.8 inches) / (1.41.4 inches) = (width of new phone) / (1.611.61 inches)
Cross multiplying, we get:
(width of new phone) = (2.82.8 inches) * (1.611.61 inches) / (1.41.4 inches)
Using a calculator, we can find that the width of the new phone is approximately 3.23.2 inches.
