Answer:
3
Step-by-step explanation:
21 is 7 times the number three. You can get this answer by dividing 21 by 7 (answer is 3). You can check your work by multiplying 7 x 3 (you would get 21)
What is the volume of this hemisphere?
Therefore , the solution of the given problem of volume comes out to be a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.
What is volume, exactly?The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are these marks for cubic measurements. To compute an object's measurements, you must, however, comprehend its volume. Converting an object's weight into mass units including grams and kilograms is a common procedure.
Here,
The formula: can be used to determine the capacity of a hemisphere with a radius of 2 inches.
=> V = (2/3) * π * r³
where "π" is a mathematical constant that is roughly equivalent to 3.14159 and "r" is the hemisphere's radius.
When we substitute the radius's value, we obtain:
=> V = (2/3) * π * 2³
=> (2/3) * π* 8
=> V = 16.755 cubic inches. (approx)
Therefore, a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.
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Find an equation for the line that passes through the points (4,2) and (-6,4) .
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{4}}} \implies \cfrac{ 2 }{ -10 } \implies - \cfrac{ 1 }{ 5 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{ 1 }{ 5 }}(x-\stackrel{x_1}{4}) \\\\\\ y-2=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}\implies y=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}+2\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 5 }x+\cfrac{14}{5} \end{array}}[/tex]
Answer this please!
4. The equation h = -16t² + 20t + 19 gives the height h, in feet, of a ball as a function of time t, in seconds,
after it is kicked. What is the maximum height the ball reaches?
Answer:
The maximum height occurs at the vertex of the parabolic equation, which is given by the formula:
t = -b/2a
where a = -16 and b = 20. Substituting these values, we get:
t = -20 / (2 * -16) = 0.625 seconds
To find the maximum height, we can substitute this value of t back into the original equation:
h = -16(0.625)^2 + 20(0.625) + 19
h = -6.25 + 12.5 + 19
h = 25.25 feet
Therefore, the maximum height the ball reaches is 25.25 feet.
Answer:
h=16(t+5/8)^2+51/4
h=25.25
Q14: In the store, Lean Statks up eight cans each weighing 1 1/3 kg. What is the total weight of the cans
Answer:
10 2/3 kg
8 X 1 1/3 kg = 10 2/3 kg
What is 6 equations that are equivalent to 6m=48?
Answer:
3m=24
m=8
12m=96
24m=192
48m=384
96m=768
The homework scores for some students in a health class are shown.
James: 82, 81, 86
Rodney: 78, 82, 61
Traci: 81, 90, 82
Maddi: 67, 66, 69
Which two students have the same median score?
Group of answer choices
James and Rodney
James and Traci
Traci and Maddi
Rodney and Maddi
Answer:
To find out which two students have the same median score, we need to find the median score for each student and compare them.
For James, the median score is 82 (the middle score when the scores are arranged in order).
For Rodney, the median score is 78 (the middle score when the scores are arranged in order).
For Traci, the median score is 82 (the middle score when the scores are arranged in order).
For Maddi, the median score is 67 (the middle score when the scores are arranged in order).
Therefore, the two students who have the same median score are James and Traci, as they both have a median score of 82.
A group of collage students are going to a lake house for the weekend and plan on renting small cars(s) and large(l) cars to make the trip. Each car can hold 5 people and each large car 8 people. A total of 15 cars were rented which can hold 90 people altogether. Determine the number of large car and rental cars.
Answer:
10 small, 5 large
Step-by-step explanation:
if they were all small cars, 5x15 would be 75. there need to be 15 more spots, and each large can hold an extra 3. 15/3 is 5. so there are 10s and 5l
students would need to rent 5 small cars and 8 large cars
For what values of c does the quadratic equation x^2-2x+c=0 have
1)no real roots
2)two roots of same sign
3)one root equal to zero and one neg root
4)two roots of opposite sign
The quadratic equation has no real roots for c > 1, two roots of the same sign for c ≥ 1, one root equal to zero & one negative root for 0 < c < 1, and two roots of opposite signs, c < 1.
What is a quadratic equation?
A quadratic equation is a polynomial equation of degree 2, which means that the highest exponent of the variable in the equation is 2. It has the general form:
[tex]ax^2 + bx + c = 0[/tex]
The quadratic equation [tex]x^2 - 2x + c = 0[/tex] has roots given by the quadratic formula:
x = (-b ±[tex]\sqrt{b^2 - 4ac}[/tex]) / (2a)
where a = 1, b = -2, and c is the unknown constant.
1) To have no real roots, the discriminant [tex]b^2 - 4ac[/tex] must be negative. So, we need:
[tex]b^2 - 4ac[/tex] < 0
[tex](-2)^2 - 4(1)(c)[/tex] < 0
4 - 4c < 0
4 < 4c
1 < c
Therefore, the quadratic equation has no real roots for c > 1.
2) To have two roots of the same sign, the discriminant [tex]b^2 - 4ac[/tex] must be negative or zero.
[tex]b^2 - 4ac[/tex] = [tex](-2)^2 - 4(1)(c)[/tex] = 4 - 4c
For two roots of the same sign, the discriminant must be negative or zero, so
4 - 4c ≤ 0
Simplifying the inequality, we get:
c ≥ 1
Therefore, for the quadratic equation, [tex]x^2 - 2x + c = 0[/tex] to have two roots of the same sign, c must be greater than or equal to 1.
3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:
x = 0 or x < 0
Setting x = 0 in the quadratic equation, we get:
c = 0
So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:
[tex](-2)^2 - 4(1)(c)[/tex] > 0
4 - 4c > 0
1 > c
Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.
4) To have two roots of opposite signs, the discriminant [tex]b^2 - 4ac[/tex] must be positive.
So we need:
[tex]b^2 - 4ac[/tex] > 0
[tex](-2)^2 - 4(1)(c)[/tex] > 0
4 - 4c > 0
Simplifying the inequality, we get:
c < 1
Therefore, for the quadratic equation to have two roots of opposite signs, c must be less than 1.
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For c > 1, the quadratic equation has no real roots; for c ≥1, it has two roots of the same sign; for c<1, it has one root that is equal to zero and one root that is negative; and for 0 <c <1, it has two roots of the opposite signs.
Describe the quadratic equation?The largest exponent of the variable in a quadratic equation, which is a polynomial equation of degree 2, is 2. The formula is: ax² + bx + c.
The quadratic equation x² - 2x + c has roots given by the quadratic formula:
x = (-b ±√[b²-4ac]) / (2a)
where a = 1, b = -2, and c is the unknown constant.
1) To have no real roots, the discriminant b² - 4ac must be negative.
So, we need:
b² - 4ac < 0
(-2) ² - 4(1) < 0
4- 4c < 0
1 < c
Therefore, the quadratic equation has no real roots for c > 1.
2) To have two roots of the same sign, the discriminant b² - 4ac must be negative or zero.
b² - 4ac = (-2) ² - 4(1)c = 4 - 4c
For two roots of the same sign, the discriminant must be negative or zero, so
4 - 4c ≤ 0
Simplifying the inequality, we get:
c ≥ 1
Therefore, for the quadratic equation, x² - 2x + c to have two roots of the same sign, c must be greater than or equal to 1.
3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:
x = 0 or x < 0
Setting x = 0 in the quadratic equation, we get:
c = 0
So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:
(-2) ² - 4(1)c > 0
4 - 4c > 0
1 > c
Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.
4) To have two roots of opposite signs, the discriminant b² - 4ac must be positive.
So, we need:
b² - 4ac > 0
(-2) ² - 4(1)c > 0
4 - 4c > 0
Simplifying the inequality, we get:
c < 1
Hence, c must be lower than 1 in order for the quadratic equation to have two roots with opposing signs.
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A grocery store sells a bag of 3 oranges for $2.43. What is the unit cost?
Answer:
$0.81
Step-by-step explanation:
We know
A grocery store sells a bag of 3 oranges for $2.43.
What is the unit cost?
We take
2.43 / 3 = $0.81
So, the answer is $0.81
7 1/2 divied by 3/4 what is it?
Answer:
7/9
Step-by-step explanation:
Find the reciprocal of the divisor
Reciprocal of 3/4 : 4/3
Now multiply it with the dividend..
so, 7/12 ÷ 3/4 = 7/12 × 4/3
=7/12×4/3 = 28/36
And after reducing the fraction, the answer is 7/9
At the base level is the gross income per month of your family. (use $5,000 as an example) 10 percent of the gross income is used for family activities such as eating out, entertainment, ... etc. Your monthly allowance is 10 percent of the family activity money. You give 10 percent of your monthly allowance to support a charity organization in your community. From the energy pyramid, how much money do you give to charity each month?
How much in one year?
give to charity each month?
Based on the given information, you would be giving $5 per month or $60 per year to charity.
How do we calculate the money we give to charity each month?Starting with a monthly gross income of $5,000, we can calculate the amount set aside for family activities as 10% of the gross income, which is:
= $5,000 x 0.10
= $500
Now, we will calculate the monthly allowance as 10% of the family activity money, which is:
= $500 x 0.10
= $50
Since you give 10% of your monthly allowance to support a charity organization, you will be giving:
= $50 x 0.10
= $5 per month
Now, in order to calculate how much you would give to charity in one year, we simply multiply the monthly amount by 12 which gives us:
= $5 x 12
= $60 per year
Therefore, the amount we would be giving to the charity is $5 per month or $60 per year.
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classifying parallelograms
After addressing the issue at hand, we can state that Hence, x = 5.5 and rectangle m El H = 180.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. Alternately, it might be regarded as a hexagon with a fundamental rule or one with equal angles. Another option for the parallelogram is a straight angle. Four vertices in a square have equal lengths. Four 90° angle vertices and equal parallel sides make up a quadrilateral with a rectangular cross section. Because of this, it is occasionally referred to as a "equirectangular rectangle". A rectangle is occasionally referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
El = 3x + 5, EG = 5x + 16, and m IF G = 270 are all known values. We also understand that a rectangle's diagonals are of equal length. Hence, we can write:
El = HG
EG = IF
From the knowledge provided above, we can formulate two equations in terms of x:
3x + 5 = HG
5x + 16 = IF
90 m HG F and 90 m EFG
Since we know that GH is a straight line because m GHE = 0, m El G must be 180 degrees.
Now that the formulas for HG and IF are equivalent to one another, we may find x:
3x + 5 = 5x + 16
2x = 11\sx = 5.5
Hence, x = 5.5 and m El H = 180.
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Aaron wraps present in a store. In one hour, he wraps 8 games and one console. How much wrapping paper does Aaron use? How much wrapping paper does Aaron use? Use exercises 1-3 to answer the question.
The wrapping paper used by Aaron is 9 and 2/3 feet of paper
Finding the amount of wrapping paper used:To solve this problem, use the given information about how much wrapping paper is needed for each game and gaming console, and then multiplied by the number of games and consoles that Aaron wraps in one hour. For simple calculation convert mixed fractions into an improper fraction and solve the problem.
Here we have
Aaron wraps present in a store. In one hour, he wraps 8 games and one console.
From the given figure,
Each game takes 2/3 foot of wrapping paper
Each gaming console takes 4 1/3 feet of wrapping paper
From the data
Aaron wraps 8 games in 1 hour
The wrap is used for 8 games = 8 × [ 2/3 foot ] = 16/3 foot
He wraps one console.
The wrap used for 1 console = 4 1/3
Here 4 1/3 = 13/3 [ Converting mixed fraction to improper fraction ]
Hence,
Total amount of wrap used = 16/3 + 13/3
= [ 16 + 13]/3 = 29/3 = 9 2/3
Therefore,
The wrapping paper used by Aaron is 9 and 2/3 feet of paper
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Nakia is an architect designing a house with a peaked roof. She is trying to decide what the limitations are on her design. If AB is 8 feet and triangle ABC will be isosceles, describe the possible lengths for AC.
The possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).
How did we get the value?If triangle ABC is isosceles, then AC must be equal to BC. Let's call the length of AC "x".
Using the Pythagorean theorem, we can find the length of the diagonal line segment BD (which is also the height of the peaked roof):
BD^2 = AB^2 - (AC/2)^2
BD^2 = 8^2 - (x/2)^2
BD^2 = 64 - x^2/4
To ensure that the roof is peaked, we need BD to be less than x (otherwise, the roof would be flat). So we can set up an inequality:
BD < x
√(64 - x^2/4) < x
64 - x^2/4 < x^2
256 - x^2 < 4x^2
5x^2 > 256
x^2 > 51.2
x > √(51.2)
Therefore, the possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).
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The table below shows the cost of downloading songs from a website. Number of Songs Number of Songs Total Cost Total Cost 6 6 $ 1.80 $1.80 12 12 $ 3.60 $3.60 20 20 $ 6 $6 What is the constant of proportionality between the total cost and the number of songs?
Answer:
Step-by-step explanation:
To find the constant of proportionality, we can use the formula for a proportional relationship: y = kx, where y is the total cost, x is the number of songs, and k is the constant of proportionality.
Using the table, we can find two pairs of values for y and x:
When x = 6, y = $1.80
When x = 12, y = $3.60
We can set up a proportion:
y1 / x1 = y2 / x2
$1.80 / 6 = $3.60 / 12
Simplifying, we get:
$0.30 = $0.30
This tells us that the constant of proportionality is $0.30.
We can check this by using another pair of values:
When x = 20, y = $6
Using the formula y = kx, we get:
$6 = ($0.30)(20)
Simplifying, we get:
$6 = $6
This checks out, so we can be confident that the constant of proportionality is $0.30.
An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the Pearson correlation coefficient r for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
Number of TV commercials, x 4
8
12
16
18
Car sales, y (in hundreds) 2
5
9
8
9
The linear regression line is:Y = 0.51X - 14.05
What is number?Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics, and is used in nearly every branch of the discipline. In everyday life, the notion of number is used to count objects, keep track of scores, measure amounts, and label objects.
City TV Commercials Car Sales
A 60 20
B 50 15
C 70 25
D 45 17
E 55 19
Calculating the linear regression line:
m = Slope = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
= (5(1475) - (325)(95)) / (5(5850) - (325)2)
= (7375 - 30875) / (29250 - 105625)
= -38500 / -75375
= 0.51
b = Intercept = (ΣY - m(ΣX)) / N
= (95 - 0.51(325)) / 5
= (95 - 165.25) / 5
= -70.25 / 5
= -14.05
Therefore, the linear regression line is:
Y = 0.51X - 14.05.
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If A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9 find the value of X
Therefore, the value of x is -4 if A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.
Here,
Since A = B, we know that AB = B². So, we can rewrite the equation AB = 3x - 5 as B² = 3x - 5.
Similarly, we can rewrite BC = 5x - 6 as B² = 5x - 6, and AC = 2x - 9 as A² - B² = (2x - 9) - (B^2).
Since we know that A = B, we can substitute B for A in the last equation to get:
B² - B² = (2x - 9) - (B²)
Simplifying this equation, we get:
0 = 2x - 9 - B²
Now we can substitute the equation B² = 3x - 5 into the above equation to get:
0 = 2x - 9 - (3x - 5)
Simplifying this equation, we get:
0 = -x - 4
Solving for x, we get:
x = -4
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Three men took part in a business. They put in N2 000, N4 000 and N1 500 as capital. The profit made was divided among them in the same proportion as the amounts put in. If the profit was N300, how much did each man get?
Answer:
The total amount of capital invested is:
N2,000 + N4,000 + N1,500 = N7,500
The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:
N2,000 / N7,500 * N300 = N80
The second man gets:
N4,000 / N7,500 * N300 = N160
The third man gets:
N1,500 / N7,500 * N300 = N60
Therefore, each man gets N80, N160, and N60, respectively.
Step-by-step explanation:
Answer:
N80, N160, and N60
Step-by-step explanation:
The total amount of capital invested is:
N2,000 + N4,000 + N1,500 = N7,500
The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:
N2,000 / N7,500 * N300 = N80
The second man gets:
N4,000 / N7,500 * N300 = N160
The third man gets:
N1,500 / N7,500 * N300 = N60
Therefore, each man gets N80, N160, and N60, respectively.
Consider the equation 5 + x = n . What must be true about any value of x if n is a negative number? Explain your answer. Include an example with numbers to support your explanation. Enter your answer, your explanation, and your example in the space provided.
Answer:
x < 5 because any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be less than 5.
The average yearly salary of a lawyer is $25 thousand less than twice that of an architect. Combined, an architect and a lawyer earn $209 thousand. Find the average yearly salary of an architect and a lawyer
Answer:
Step-by-step explanation:
Let's call the average yearly salary of an architect "A" and the average yearly salary of a lawyer "L".
From the first sentence, we know that:
L = 2A - 25
From the second sentence, we know that:
A + L = 209
We can substitute the first equation into the second equation:
A + (2A - 25) = 209
Simplifying:
3A - 25 = 209
Adding 25 to both sides:
3A = 234
Dividing both sides by 3:
A = 78
Now we can use the first equation to find L:
L = 2A - 25 = 2(78) - 25 = 131
Therefore, the average yearly salary of an architect is $78,000 and the average yearly salary of a lawyer is $131,000.
The Hanwell Company acquired a 30% equity interest in The Northfield Company for CU400,000 on 1 January 20X6. In the year to 31 December 20X6 Northfield earned profits of CU80,000 and paid no dividend. In the year to 31 December 20X7 Northfield incurred losses of CU32,000 and paid a dividend of CU10,000. In Hanwell's consolidated statement of financial position at 31 December 20X7, what should be the carrying amount of its interest in Northfield, according to IAS 28 Investments in associates?
-6..
6-
550
4
CN
4.
6
Ty
IS
6
X
Is this an odd function
The given function does not satisfy the condition for an odd function (f(-x) = -f(x)), we can conclude that -6.66 is not an odd function
Hi there! An odd function is a mathematical function that satisfies the condition f(-x) = -f(x) for all values of x in its domain. In simpler terms, an odd function exhibits symmetry with respect to the origin in a coordinate plane.
Now, let's analyze the given function: -6.66. This function represents a constant function since it has no variables (e.g., x or y). Constant functions have a graph that appears as a horizontal line on the coordinate plane.
For constant functions, f(-x) will always equal f(x) because the function's value doesn't change regardless of the input.
In this specific case, the function value is -6.66,
so f(-x) = f(x) = -6.66 for all x.
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In a triangle if y equals 940 inches Y equals 100 degrees W equals 38 degrees what length is w
Answer: W = 357.2
Step-by-step explanation:
x/38 * 940/100
100x * 35,720
x=357.2
prime and composite numbers hard questions reasoning questions
1-Is the sum of two prime numbers always a prime number?
Solution:
No. Here is an example.
3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.
2-Is the product of two prime numbers also a prime number?
Solution:
Never because it will have 1 and itself as factors and also the two numbers involved in the product.
Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.
3-Which is the largest 3 digit prime number?
Solution:
Start with the largest three digit number 999.
4- Which is the smallest 2 digit prime number?
Solution
Start with the smallest 2 digit number 10.
10 is not a prime number
Answer: 11 is a prime number
The identity (x + y)² is equal to x² +y².
True
False
Answer:
False
Step-by-step explanation:
[tex](x+y)^{2} = x^{2} +2xy +y^{2}[/tex]
This means that they are not equal. For this reason, the statement is false.
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The given quadratic equation is f(x) = x³ - 3x² + 2x-1. The two solutions to the equation are x = (3x + √(9x² + 4))/2x² and x = (3x - √(9x² + 4))/2x².
What is quadratic equation?A quadratic equation is written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
To solve this equation, we will use the quadratic formula.
The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the solutions are given by
x = [-b ± √(b² - 4ac)]/2a.
In this equation, a = x², b = -3x, and c = -1. Plugging these values into the formula, we get x = [3x ± √(9x² - 4(x²)(-1))]/2(x²). Simplifying this, we get
x = [3x ± √(9x² + 4)]/2x².
Now, we must solve for the two solutions. The first solution is x = (3x + √(9x² + 4))/2x². The second solution is
x = (3x - √(9x² + 4))/2x².
Therefore, the two solutions to the given equation are
x = (3x + √(9x² + 4))/2x² and
x = (3x - √(9x² + 4))/2x².
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What is the equation in slope-intercept form of the line that passes through the points (0,4) and (2,0)?
Answer:
C: y=2x-4
Step-by-step explanation:
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Let W be the event that a randomly chosen person drinks sixty-four ounces of water per day. Let V be the event that a randomly chosen person has varicose veins. Place the correct event in each response box below to show:
Given that the person drinks sixty-four ounces of water per day, the probability that a randomly chosen person has varicose veins.
For the given situation the probability event can be denoted mathematically as P(V|W).
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The event we are interested in is "a randomly chosen person has varicose veins" (V), given that "the person drinks sixty-four ounces of water per day" (W).
So, we can write this as -
P(V|W)
which is the conditional probability of event V given event W.
Therefore, the event can be denoted as P(V|W).
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Solve the system
y=9x
x+y=1
Answer: (1/10, 9/10)
Step-by-step explanation: