Step-by-step explanation:
These points are in (X, Y) form. What you want to do is plug in the X coordinates into the equation and see if it equals the Y coordinate.
Equation: Y = X + 4
Point A: (-1, 3)
(-1) + 4 = 3
Point B: (2, 6)
(2) + 4 = 6
Point C: (-2, -2)
(-2) + 4 = 2
Point D: (2, 4)
(2) + 4 = 6
Only point A and point B equal their Y coordinate, making A and B the only correct answers.
Classify the following triangle. Check all that apply.
• A. Equilateral
• B. Obtuse
• C. Isosceles
• D. Scalene
• E. Acute
• F. Right
Answer:
I don't have a way to explain, but it is an Equilateral and Isosceles :)
Hope it helps!
Δ′ABC ∼Δ′A'B'C and AC=20cm A'C'=15cm B'C'=12cm and A'B'=9cm find the length of the other sides of ΔABC
The length of the other sides of ΔABC are AB =12 cm and BC = 16 cm.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
Given that, ΔABC ∼ΔA'B'C' and AC=20 cm A'C'=15 cm B'C'=12 cm and A'B'=9 cm.
Here, AB/A'B' = BC/B'C' = AC/A'C'
AB/9 = BC/12 = 20/15
AB/9 = BC/12 = 4/3
Now, AB/9 = 4/3
AB =12 cm
BC/12 = 4/3
BC = 16 cm
Therefore, the length of AB =12 cm and BC = 16 cm.
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Caride Pls this is needed very urgently
1.) Common ailments of senior citizens are arthritis, arteriosclerosis and loss of hearing. A survey of 200 senior citizens found that 70 had arthritis, 60 had arteriosclerosis, 80 had loss of hearing, 35 had arthritis and arteriosclerosis, 33 had arthritis and loss of hearing, 31 had arteriosclerosis and loss of hearing and 15 had all three.
How many of the senior citizens in the survey had; (1). none of these ailments, (f), arthritis but neither of the other two ailments, (iii), exactly one of these ailments, (iv). arteriosclerosis and loss of hearing but not arthritis, (v). arteriosclerosis or loss of hearing but not arthritis, (vi). exactly two of these ailments?
Answer:
i) 84
ii) 7
iii) 47
iv) 16
v) 56
vi) 54
Step-by-step explanation:
The easiest way to understand this problem visually is to create a Venn diagram (See attached diagrams below to help you)
First, note that the total amount of people with each condition beside the relevant circle. Then, since 15 have all 3, write 15 in the center.
We're told 35 had arthritis and arteriosclerosis, and 15 had all 3, so the amount with arthritis and arteriosclerosis only is 25-25=20. So we write 20 in the crosssection between arthritis and arteriosclerosis that doesn't include loss of hearing.
We're told 33 had arthritis and loss of hearing, and 15 had all 3, so the amount with arthritis and loss of hearing but not arteriosclerosis is 33-15=18. So we write 18 in the crosssection between arthritis and loss of hearing that doesn't include arteriosclerosis.
We're told 31 had arteriosclerosis and loss of hearing, and 15 had all 3, so the amount with arteriosclerosis and loss of hearing only is 31-15=16. So we write 16 in the crosssection between arteriosclerosis and loss of hearing that doesn't include arthritis.
(see diagram A to see how this should look)
70 people have arthritis and (18+25+20=63) have arthritis and another condition, so the amount with only arthritis is 70-63=7
60 people have arteriosclerosis and (20+15+16=51) have arteriosclerosis and another condition, so the amount with only arteriosclerosis is 60-51=9
80 people have loss of hearing and (18+15+16=49) have loss of hearing and another condition, so the amount with only loss of hearing is 80-49=31
Marking in these figures completes the diagram (See diagram B to see how it should look)
i)
The total amount of people represented within the diagram (ie, the ones with conditions) is 7+20+9+18+15+16+31=116. If 200 were surveyed, this means the amount without these conditions is 200-116=84
ii)
Above, we found the amount with arthritis only was 7
iii)
7 have only arthrits, 9 have only arteriosclerosis, and 31 have only loss of hearing , so the amount with only one ailment is 7+9+31=47
iv)
Above, we found that 16 had arteriosclerosis and loss of hearing but not arthritis
v)
The amount with arteriosclerosis or loss of hearing but not arthritis is equal to the amount with arteriosclerosis only plus the amount with loss of hearing plus the amount with both arteriosclerosis and loss of hearing: 9+31+16=56
vi)
Above, we found the amount with arthritis and arteriosclerosis only is 20, the amount with arthritis and loss of hearing but not arteriosclerosis is 18, and the amount with amount with arteriosclerosis and loss of hearing only is 16. So the total amount with exactly two conditions is 20+18+16=54
Diego’s history teacher writes a test for the class with 30 problems. The test is worth 50 points and has two types of problems: multiple choice worth 1 point each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning
By using a system of equations of two variables the number of short answer problems is 10.
Total number of problems in the Test = 30
Maximum points of test = 50
Point of multiple choice = 1
Point of short answer problems = 3
Let the number of multiple choice questions is x and the number of short answer problems is y
So, x + y = 30 - (1)
and 1.x + 3.y = 50 ⇒ x + 3y = 50 -(2)
Equation (2) - Equation (1)
x + 3y - (x + y) = 50 - 30
2y = 20
y = 10
Put y = 10 in equation (1)
x = 30 - 10 = 20
Hence, the number of multiple-choice questions = 20 and the number of short answer problems = 10.
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Which equations are true for the values of x, y, and z? Select three options.
2 lines intersect to form 4 angles. Clockwise, from top, the angles are: 65 degrees, x, y, z.
Answer:
Step-by-step explanation:
Based on the information provided, the following three equations are true for the values of x, y, and z:
x + y + z = 360 degrees (Since the sum of the angles in a quadrilateral must equal 360 degrees)
x = 65 degrees (As given, the first angle is 65 degrees)
y + z = 295 degrees (From equation 1, 360 - 65 = 295)
So, the values of x, y, and z can be calculated as 65 degrees, 115 degrees, and 180 degrees respectively.
1. If you roll a single die and get 4 fives in a row, what is the probability that you'll get a five on the
next roll?
2. What is the probability that you'll get 5 fives in a row when rolling a single die?
3. A roulette wheel has 38 numbers. If the "lucky" number 7 comes up twice in a row, what is the
probability it will come up on the very next roll?
4. What is the probability of getting three 7's in a row on a roulette wheel?
5. If I type randint(1,10) on my calculator, I get a random integer between 1 and 10 (inclusive). If I
do this 6 times, what is the probability that all 6 outcomes will be a 1?
6. If I roll a pair of dice, what is the probability of getting a pair of sixes?
7. If I roll a pair of dice, what is the probability of getting any pair?
1. 1/6 is the probability of rolling a five on the next roll.
2. The probability of getting 5 fives in a row when rolling a single die is 1/7776 .
3. 1/38 is he probability of 7 coming up on the very next spin is
4. 1/54782 is the probability of getting three 7's in a row on a roulette wheel.
5. (1/10)⁶ is the probability of getting a 1 on all six trials.
6. 1/36 is the probability of getting a pair of sixes when rolling a pair of dice is
7. The probability of getting any pair is 1/6
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
1. The probability of rolling a five on a single roll of a fair die is 1/6, since there are six equally likely outcomes: rolling a 1, 2, 3, 4, 5, or 6.
the probability of rolling a five on the next roll is still 1/6, regardless of whether the previous rolls resulted in four fives in a row or not.
2. The probability of getting a five on a single roll of a fair die is 1/6, as there are six equally likely outcomes.
the probability of getting 5 fives in a row when rolling a single die is:
(1/6) × (1/6) × (1/6) × (1/6) × (1/6) = 1/7776
3. The probability of any particular number coming up on a single spin of an American roulette wheel with 38 numbers is 1/38, since there are 38 equally likely outcomes.
As these are independent , the probability of 7 coming up on the very next spin is still 1/38.
4. The probability of getting three 7's in a row on a roulette wheel is:
(1/38) × (1/38) × (1/38) = 1/54,872
5. The probability of generating a 1 on a single trial is 1/10.
The probability of getting a 1 on a single trial by itself six times
(1/10) × (1/10) × (1/10) × (1/10) × (1/10) × (1/10) = (1/10)⁶
The probability of getting a 1 on all six trials is (1/10)⁶
6.
The probability of getting a pair of sixes when rolling a pair of dice is:
1/36
7.
The probability of getting any pair when rolling a pair of dice is:
Number of ways to get a pair / Total number of possible outcomes
= 6 / 36
= 1 / 6
So the probability of getting any pair is 1/6
Hence,
1. The probability of rolling a five on the next roll is 1/6.
2. 1/7776 is the probability of getting 5 fives in a row when rolling a single die.
3. The probability of 7 coming up on the very next spin is 1/38.
4. The probability of getting three 7's in a row on a roulette wheel is 1/54782
5. The probability of getting a 1 on all six trials is (1/10)⁶
6. The probability of getting a pair of sixes when rolling a pair of dice is:
1/36
7. the probability of getting any pair is 1/6
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Select the correct choices to complete the sentence.
In the figure, line m is parallel to line n. Classify the relationship between ∠2 and ∠7 as alternate interior, alternate exterior, or corresponding.
The solution is Option B.
The angles ∠2 and ∠7 are alternate exterior angles
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the parallel lines be represented as m and n
Now , the transversal line is t
The angles formed on line m is ∠1 , ∠2 , ∠3 and ∠4
And , the angles formed on line n is ∠5 , ∠6 , ∠7 and ∠8
Now , the angles ∠2 and ∠7 are situated outside or exterior and is represented by alternate exterior angles
So , pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Hence , the angles are alternate exterior angles
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What is the area of this compound figure?
Answer:
Step-by-step explanation:
Use division to find which of the following fractions are equivalent to
6
24
? Select all that apply.
Answer: C and D are the correct ones
Step-by-step explanation:
HII NEED HELP PLEASE
Answer:
x=4
Step-by-step explanation:
since triangles LMJ and KLJ are = by hyp. and one side
<=> 4x+6=3x+10
<=> 4x-3x=10-6
<=> x=4
What is the probability of tossing a coin and it landing on head 8 times in a row
Answer:
The probability of tossing a fair coin and it landing on heads 8 times in a row is (1/2)^8 = 1/256. This means that there is a 1 in 256 chance that a fair coin will land on heads 8 times in a row. The probability of an event can be calculated by taking the number of favorable outcomes and dividing it by the number of possible outcomes. In this case, there is only one favorable outcome (tossing a heads 8 times in a row) and two possible outcomes for each toss (heads or tails), so the probability is 1/2^8 = 1/256.
Step-by-step explanation:
Answer:
it should be 0.04percent.
how many sides does a regular polygon have if each interior angle measures 140
A regular polygon with interior angles that measure 140 degrees has 9 sides. All interior angles are congruent, meaning they have the same degree measure.
To find the number of sides in a regular polygon with a given interior angle measure, we can use the formula:
n = 360 / (180 - x)
where n is the number of sides and x is the measure of each interior angle in degrees.
This formula is derived from the fact that the sum of the interior angles in a polygon with n sides is given by the formula (n-2) * 180. In a regular polygon, each interior angle measures (Sum of interior angles / n). If we substitute the formula for the sum of interior angles into the formula for the measure of each interior angle, we get:
x = (n-2) * 180 / n
Solving for n:
n = 360 / (180 - x)
So, when we plug in the given interior angle measure of 140 degrees, we get:
n = 360 / (180 - 140)
n = 360 / 40
n = 9
Therefore, a regular polygon with interior angles that measure 140 degrees has 9 sides.
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How many sides does a regular polygon have if each interior angle measures 140?
Here are 2 points in the plane.
B
Explain how to construct a line segment that is half the length
of segment AB .
O Construct a new point and create an angle bisector.
Create two circles centered at each point to the other and make a line through their intersections to
cut it in half.
O
Link them with a segment, make a new point on it and make a circle centered at A and B to the new
point.
To construct a line segment that is half the length of segment AB, follow the steps below.
What is the intersection points of the circle?
The intersections of two circles determine a line known as the radical line. If three circles mutually intersect in a single point, their point of intersection is the intersection of their pairwise radical lines, known as the radical center.
Draw a straight line passing through points A and B.
Bisect the line segment AB at point C.
Draw a circle centered at point C with a radius equal to AC or BC.
The intersection points of the circle and the line passing through A and B will be points D and E.
The line segment DE will be half the length of segment AB.
Therefore, To construct a line segment that is half the length of segment AB, follow the steps above.
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b. how many such strings are if 2 of the ones are to be next to each other and the third is not next to the other two? (for example, 0011000100.
The total number of strings that satisfy the given conditions is 24.
Let us count the number of strings where the two ones that are next to each other are in the first two positions, and the third one is in the fifth position. There are two choices for the value of the fourth digit (0 or 1), and two choices for the value of the last digit (0 or 1). Therefore, there are 2 \cdot 2 = 4 strings with this property: 110010, 110100, 111010, and 111100.
We can obtain the same number of strings by considering the case where the two ones that are next to each other are in the last two positions, and the third one is in the fifth position.
Now, let us count the number of strings where the two ones that are next to each other are in the first two positions, and the third one is in the sixth position. There are two choices for the value of the third digit (0 or 1), and two choices for the value of each of the other digits (digits 4 and 5 must be different from each other and from digit 3). Therefore, there are 2 \cdot 2 \cdot 2 = 8 strings with this property: 1100010, 1101010, 1110010, 1111010, 1000110, 1001110, 1010110, and 1011110.
Again, we can obtain the same number of strings by considering the case where the two ones that are next to each other are in the last two positions, and the third one is in the sixth position.
Thus, the total number of strings that satisfy the given conditions is 4+4+8+8=24.
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Question 7(Multiple Choice Worth 2 points) (09.06 LC) How many hectometers are in 580 millimeters? O 0.0058 hectometers O 0.058 hectometers O 58,000 hectometers O 580,000 hectometers
Answer:
0.058 hectometers
Step-by-step explanation:
There are 0.058 hectometers in 580 millimeters.
To convert millimeters to hectometers, you need to divide the number of millimeters by 100,000. So, 580 millimeters divided by 100,000 equals 0.0058 hectometers, or 0.058 hectometers when rounded to two decimal places.
On a cold day the temperature at Thabana was 6 degres it dropped by 7 degres during the night how many degres will the night temperature be?
Answer:
Step-by-step explanation: The temperature at Thabana dropped by 7 degrees, so we can calculate the night temperature by subtracting 7 from the original temperature of 6 degrees:
Step 1: Subtract 7 from 6:
6 - 7 = -1
Step 2: The night temperature will be -1 degrees.
Mackenzie's company reimburses her $0. 75 per mile that she drives for business. If she goes on a business trip and drives a total of 982 miles, how much will her reimbursement be?
Mackenzie's reimbursement for a business trip would be $736.50 per mile when she drives of a total of 982 miles with $0. 75 per mile.
Mackenzie's reimbursement for driving 982 miles for business can be calculated by multiplying the number of miles driven by the reimbursement rate per mile.
Mackenzie's company reimburses her $0. 75 per mile which is rate per mile.
Reimbursement = miles driven x rate per mile
Filling the value in above equation.
So,
Reimbursement = 982 miles x $0.75/mile
Reimbursement = $736.50
Therefore, Mackenzie's reimbursement for driving 982 miles with the rate of $0. 75 per mile for business would be $736.50.
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A rectangular piece of Bluestone measures 18" on the two long sides and 12" on
the two short sides. To determine the perimeter (or length around the outside), you
add the lengths of the four sides. What is the perimeter of the plate?
The perimeter of the plate is 60"
How to determine the perimeter of the plate?From the question, we have the following parameters that can be used in our computation:
Length = 18"
Width = 12"
The perimeter of the rectangle piece can be calculated as
Perimeter = 2 * (Length + Width)
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (18 + 12)
Evaluate
Perimeter = 60
Hence, the perimeyer is 60"
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Solve the following system of equations
using the elimination method.
3x + 2y = 5
2x + 4y = 2
Answer:
x=2 , y= (-1/2)
Step-by-step explanation:
3x + 2y = 5
2x + 4y = 2
Consider Equation 1:- (3x+2y=5)
Multiply both sides by 2
2(3x + 2y) = 5*2
6x + 4y = 10
Subtract both equations-
6x + 4y =10
-2x + 4y =2
=> 4x =8
x = 2
Substitute the value of x in equation 1
3*2 + 2y = 5
6 + 2y = 5
2y = 5-6
2y = (-1)
y = (-1/2)
Hope is helps ;)
The area of a rectangular window is 4234 cm².
If the length of the window is 73 cm, what is its width?
Answer:
58
Step-by-step explanation:
4234 = 73x divide by 73 on both sides and x=58
Which graphs represent functions?
Graph A
Graph B
Graph C
Answer:
Graphs B and D
I can't see all the options since the image is cropped but it does look like the first option
Step-by-step explanation:
A function, y = f(x0 can have one and only one value for a specific value of x
Graphically we can determine whether a graph represents a function or not by drawing a vertical line through a value of x and finding out if it intersects the graph at more than one point
Graph A: Not a function
If we draw a vertical line at say x = 0, it intersects the graph at two points y = 2 and y = -2. Therefore it is not a function
We need to see only one violation of this rule to conclude it is not a function
Graph B: Function
This is a function. There are 5 points plotted for 5 values of x (x = -5, -4, -1, 1 and 2) and at none of these values of x does a vertical line cross two points
Graph C Not a function
At x = 1, the vertical line will cross at 2 points (1, 5) and (1, -3). Essentially there are 2 y values, 5 and -3 for a single x value of 1
So not a function
Graph D Function
At no value of x does a vertical line pass through more than one point. Hence it is a function
Samantha drove 468 miles from Omaha, Nebraska to Chicago, Illinois. She drove 251 miles during the first day. Set up an equation (where D represents the distance traveled during the second day) that could be used to find the distance Samantha traveled during the second day. Then, SOLVE the equation.
Samantha drove 217 miles during the second day.
How set up and solve an equation?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Let D be the distance Samantha traveled during the second day. Then the total distance she drove is 468 miles. The equation will be:
D + 251 = 468
Solving for D:
D = 468 - 251
D = 217
Therefore, Samantha drove 217 miles during the second day.
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jim's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs jim per pound, and type b coffee costs per pound. this month's blend used three times as many pounds of type b coffee as type a, for a total cost of . how many pounds of type a coffee were used?
Type A: 5.45 per pound, Type B: 4.35 per pound. This month's mixture: We know that an is 5.45 per pound, so we divide total cost 401.65 by 5.45 to get a result of 73.69 LB of Type A. 2B + A = 410.35 2(4.35) = 8.70 A + 8.70 = 410.35 A = 401.65.
Total cost is a term used in economics to describe the least expensive way to produce a specific amount of a good (TC). Fixed costs, which are unaffected by the quantity of a good produced and include inputs like buildings and machinery, possibly including sunk costs, and variable costs, which change with the quantity of a good produced and include inputs like labor and raw materials, make up the total economic cost of production. Economics considers the total potential cost of each manufacturing item as one of the total cost's fixed or variable costs.
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12. Angle of a right-angled isosceles triangle is:
a. 1 : 2 : 3
b. 1 : 1 : 2
c. 1 : 3 : 4
d. 2 : 2 : 3
Aaron made a picture frame with the dimensions shown in the figure. What is the area of the picture frame? A bigger outer rectangle has sides of 12 cm and 10 cm, and an inner rectangle has sides of 8 cm and 6 cm. A. 120 square centimeters B. 88 square centimeters C. 72 square centimeters D. 64 square centimeters
The area of the picture frame 72 cm². Therefore, option C is the correct answer.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Given that, a bigger outer rectangle has sides of 12 cm and 10 cm.
So, the area of a outer rectangle = 12×10
= 120 cm²
An inner rectangle has sides of 8 cm and 6 cm
The area of a inner rectangle = 8×6
= 48 cm²
The area of the picture frame = 120-48
= 72 cm²
Therefore, option C is the correct answer.
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Answer: C | 72 square centimeters
Step-by-step explanation:
The answer is C. 72 square centimeters. The area of the picture frame can be found by subtracting the area of the inner rectangle from the area of the outer rectangle. The area of the outer rectangle is 120 square centimeters (12 x 10). The area of the inner rectangle is 48 square centimeters (8 x 6). Therefore, the area of the picture frame is 120 - 48 = 72 square centimeters.
a bagel store sells 6 different types of bagels. in how many ways can you buy 20 bagels with at least one bagel of each kind?
The number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.
To calculate the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels, we can use the concept of stars and bars.
First, we need to ensure that we have at least one of each type of bagel. So, we take one bagel of each type, which leaves us with 14 bagels to buy.
Now, we can use stars and bars to distribute the remaining 14 bagels among the 6 types of bagels. We represent the 14 bagels as stars and the 5 possible locations between the types of bagels as bars.
Using this method, we need to distribute 14 stars among 5 bars, which can be done in
(14+5-1) choose (5-1) = 18 choose 4 = 3060 ways.
Therefore, the number of ways to buy 20 bagels with at least one bagel of each kind from a bagel store that sells 6 different types of bagels is 3060.
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1000, 200, 40, .... Find the 50th term:
PLEASE GIVE BRAINLIEST
thank you and have a good day :)
Answer:
5.6294995342131E-32
Step-by-step explanation:
the common ratio is 1/5, therefore with the equation an = a x r
n-1
we can figure out the answer to this by plugging in the common ratio for r,
and n as the number in the sequence that we want to obtain.
a is simply the first number (1000)
the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.
False. The probability of the union of two events occurring can be greater than the probability of the intersection of two events occurring.
The probability of the union of two events A and B, written as P(A union B), is the sum of the individual probabilities of the two events minus the probability of their intersection.
P(A union B) = P(A) + P(B) - P(A intersection B)
If the two events are not mutually exclusive, meaning that they have a non-empty intersection, then P(A union B) will be greater than P(A intersection B).
In other words, the union of two events gives you the combined probability of both events happening, while the intersection gives you the probability of both events happening simultaneously, which is always smaller or equal to the probability of either event happening.
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The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring? TRUE/ FALSE.
PLEASE HELP! O is the centre of a sphere and has coordinates (2, -3,5). If AB is a diameter of the sphere
and A has coordinates (5, 1, 1), find the coordinates of B. Give your answer as an ordered
triple (x, y, z).
Answer:
(-2, -6, -6)
Step-by-step explanation:
The center of the sphere, O, and point A, are located on the same diameter of the sphere, AB. Thus, the line segment joining these two points is the radius of the sphere. Therefore, the length of the line segment, OA = OB = r, where r is the radius of the sphere.
We can find the length of the line segment, OA, using the distance formula:
√((5 - 2)^2 + (1 + 3)^2 + (1 - 5)^2) = √(3^2 + 4^2 + (-4)^2) = √49 = 7
Since OA = OB = 7, the coordinates of B can be found by subtracting the radius, 7, from the x, y, and z-coordinates of point A:
B = (5 - 7, 1 - 7, 1 - 7) = (-2, -6, -6)Therefore, the coordinates of B are (-2, -6, -6).
Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week.
The common region to both the graphs represents the solution set of the given inequalities.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is that you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week.
Assume that you worked {x} hours Mowing lawns and {y} hours babysitting.
We can write the inequalities as -
x + y ≤ 15
3x + 5y ≥ 60
Refer to the graph attached. The common region to both the graphs represents the solution set.
Therefore, the common region to both the graphs represents the solution set of the given inequalities.
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