A scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive.
Assume the rate of change is linear and complete the table.
The complete table is
Time (mins) 0 1 2 3 4 5 6 7 8 9 10
Amount of air (ft³) 40 36 32 28 24 20 16 12 8 4 0
What is the Rate of change :
The rate of change refers to the speed at which a quantity is changing with respect to time or some other variable.
It is a measure of how quickly or slowly a quantity is increasing or decreasing, and it is often represented as the slope of a graph or function. To fill the table we need to know the rate of change per minute in the air. Using the rate of change we can fill the table as follows
Here we have
A scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive.
To complete the table, calculate the rate of change of the amount of air in the scuba tank.
We know that the scuba tank started with 40 cubic feet of air and was empty after a 10-minute dive, so we can use this information to find the rate of change:
Rate of change = (final amount - initial amount) / time
Rate of change = (0 - 40) / 10 = -4 ft³/min
The negative sign indicates that the amount of air in the scuba tank is decreasing over time, which makes sense since the diver is using up the air during the dive.
Using this rate of change, we can complete the table as follows:
For 1 min = 40 ft³ - 4 ft³ = 36 ft³
For 2 min = 36 ft³ - 4 ft³ = 32 ft³
For 3 min = 32 ft³ - 4 ft³ = 28 ft³
Similarly, we can fill the table as given below
Therefore
The complete table is
Time (mins) 0 1 2 3 4 5 6 7 8 9 10
Amount of air (ft³) 40 36 32 28 24 20 16 12 8 4 0
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Nora planted 65 seeds. 80% of them sprouted. How many seeds sprouted
Answer:
52
Step-by-step explanation:
80% of 65 is 65 x 0.80
65 x 0.80 = 52
Therefore 52 seeds were planted.
The value 3pi/4 is a solution for the equation 3√2 sec theta +7 = 1.
A. True
B. False
Answer:
False
Step-by-step explanation:
3√2 sec(theta) + 7 = 1
3√2 sec(theta) = -6
sec(theta) = -2/√2
sec(theta) = -√2
theta = arcsec(-√2)
However, the range of secant function is [-∞, -1] U [1, ∞]. Since -√2 is not within this range, we cannot take the arcsecant of -√2. Therefore, there is no real value of theta that satisfies the equation, including 3π/4.
Therefore, the statement "The value 3π/4 is a solution for the equation 3√2 sec(theta) + 7 = 1" is False.
I hope it helps you
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
a) What is the probability that an American chosen at random died as a passenger car occupant last year?
Give your answer as a fraction or decimal. If decimal, make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 1. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
b) What is the probability that you died as a passenger car occupant last year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 2. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
c) What is the probability that you will die as a passenger car occupant next year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 3. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
d) What is the probability that an American chosen at random will die as the result of a tornado next year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
LicenseQuestion 4. Points possible: 2
Unlimited attempts.
The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people.
Cause Deaths
Passenger car occupant 13,100
Motorcycle driver 4,500
Tornado 553
Skydiving 56
e) What is the probability that you will die as the result of a tornado next year?
Make sure your answer is accurate to at least 2 significant figures (values after leading zeros)
a) The probability that an American chosen at random died as a passenger car occupant last year is 0.0042.
b) The probability that you died as a passenger car occupant last year is 0.0042
c) The probability that you will die as a passenger car occupant next year P(C) is 0.0042.
d) The probability that an American chosen at random will die as the result of a tornado next year is 0.0000018
e) The probability that you will die as the result of a tornado next year is 0.0000018
What are the probabilities?The given probabilities are determined as follows:
The probability that an American chosen at random died as a passenger car occupant last year is:
P(A) = 13,100 / 312,000,000
P(A) = 0.0042
b) The probability that you died as a passenger car occupant last year is:
P(B) = 13,100 / 312,000,000
P(B) = 0.0042
c) The probability that you will die as a passenger car occupant next year P(C) would be 0.0042 since the values do not change.
d) The probability that an American chosen at random will die as the result of a tornado next year is:
P(D) = 553 / 312,000,000
P(D) = 0.0000018
e) The probability that you will die as the result of a tornado next year, P(E) = 0.0000018
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if you roll a number cube 20 times. which scenario is least likely?
a) you find the experimental probability of rolling a 1 or 2 to be 0.3.
b) you find the experimental probability of rolling a 3 or 4 to be 0.4.
c) you find the experimental probability of rolling a 5 or 6 to be 0.5.
d) you find the experimental probability of rolling a number divisible by 3 to be 0.35
1. Which number is the greatest? 20 -100 -45 50
Answer:
D) 50
Step-by-step explanation:
-100 <-45 < 20 < 50
Answer:
50
Step-by-step explanation:
any numbers approaching negative (before 0) in an increasing manner are the lowest, whereas numbers approaching positive in a increasing manner are the greatest.
What is the answer to
7 + 60 / (3x5)
Altina Restaurant Flexible Budget for November 2010
A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?
b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?
d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?
e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?
f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?
g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?
Walton's actual check average is $9.52
The actual food cost is lower than the flexible budget by $5020
What is Net Income?Net income, considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.
The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.
Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.
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please answer and explain how to get it.
The value of x is given as follows:
x = 4.2 cm.
How to obtain the value of x?The value of x is obtained applying the proportions in the context of the problem.
The ratio between the volumes is given as follows:
3375/512 = 6.59
The side lengths are measured in units, while the volume is measured in cubic units, hence the proportion to obtain the value of x is given as follows:
8/x = cubic root of 6.59
8/x = 1.9
x = 8/1.9
x = 4.2 cm.
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AB and BC are perpendicular lines
Fine the value of x
Answer:
25 + x + x = 90
2x = 65
x = 32.5°
14. Use the tree diagram below to answer the question.
Small
Blue
White
Medium
Large
Small
Medium
Large
Small
The number of outcomes that contains blue shirts is 3
What is a Tree Diagram?A tree diagram is a graphical representation of a hierarchy or branching structure, often used in fields such as mathematics, computer science, linguistics, and biology. It is called a tree diagram because it looks like a tree, with a single root node that branches out into multiple child nodes.
In mathematics, a tree diagram is used to represent the possible outcomes of a series of events or decisions, with each branch representing a different option or outcome.
The outcome for blue shirts is 3 because there is only small medium and large
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Describe and compare the solution sets of x 1 plus 3 x 2 minus 2 x 3
equals0
and x 1 plus 3 x 2 minus 2 x 3
equalsminus6
.
Question content area bottom
Part 1
Describe the solution set, xequals
left bracket Start 3 By 1 Matrix 1st Row 1st Column x 1 2nd Row 1st Column x 2 3rd Row 1st Column x 3 EndMatrix right bracket,
of x 1 plus 3 x 2 minus 2 x 3
equals
0
in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice.
(Type an integer or fraction for each matrix element.)
To the right of 1.61, 9.24, and 15.09, the area under the X² curve with five degrees of freedom is 0.078, 0.0001, and 0, respectively.
Describe area?A surface's area can be measured in two dimensions by multiplying its length by its breadth. It is employed to determine the size of a room or a plot of land. The size of a shape, like a circle or a square, can also be determined using area. Area is frequently expressed in square metres or square feet.
Here in the question,
(a)1.61
The following formula can be used to determine the area under the 1.61-degree curve with five degrees of freedom to the right:
Area = 1 - Φ(x; df)
Where df stands for the degrees of freedom and (x; df) is the cumulative distribution function of the chi-square distribution.
For df = 5, Φ(1.61; 5) = 0.922.
As a result, 1 - 0.922 = 0.078 represents the area under the 1.61-degree curve with 5 degrees of freedom to the right.
(b) 9.24
For df = 5, Φ(9.24; 5) = 0.9999.
As a result, 1 - 0.9999 = 0.0001 is the value of the area under the X² curve with 5 degrees of freedom to the right of 9.24.
(c) 15.09
For df = 5, Φ(15.09; 5) = 1.
As a result, 1 - 1 = 0 represents the area under the 15.09-based X² curve with 5 degrees of freedom to the right.
The area under the X² curve with five degrees of freedom to the right of 1.61, 9.24, and 15.09, respectively, is 0.078, 0.0001, and 0.
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1. The solution set can be written as:
{x = [t, s, (3/2)t + (3/2)s] : t, s ∈ R}
2. The solution set can be written as:
{x = [t, s, (3/2)t + (3/2)s - 3] : t, s ∈ R}
What is 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. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
To find the solution set in parametric vector form for the equation x₁ + 3x₂ - 2x₃ = 0, we can write:
x₁ = t (arbitrarily setting x1 = t)
x₂ = s
x₃ = (3/2)t + (3/2)s
where t and s are arbitrary parameters.
Therefore, the solution set can be written as:
{x = [t, s, (3/2)t + (3/2)s] : t, s ∈ R}
This is a set of infinitely many vectors that lie on a plane in three-dimensional space.
Part 2
For the equation x₁ + 3x₂ - 2x₃ = -6, we can rewrite it as x₁ + 3x₂ - 2x₃ = 0 - 6, which is of the same form as the equation in Part 1, but with a constant on the right-hand side.
Using the same method as in Part 1, we can find the solution set as:
x₁ = t
x₂ = s
x₃ = (3/2)t + (3/2)s - 3
where t and s are arbitrary parameters.
Therefore, the solution set can be written as:
{x = [t, s, (3/2)t + (3/2)s - 3] : t, s ∈ R}
This is also a set of infinitely many vectors that lie on a different plane in three-dimensional space.
Comparing the two solution sets, we can see that they are both sets of infinitely many vectors and have a similar form (parametric vector form). However, they lie on different planes in three-dimensional space, and the second set is shifted downward by 3 units along the third axis.
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if 3+1=34
2+2=44
2+3=65
5+3=158
7+2=?
Answer:
7 + 2 = 149 here.
7 × 2 = 14, and 7 + 2 = 9.
Im doing my math homework and i need helpp
the power tells you how many times the base is multiplied.
1) 3^4 = 3 x 3 x 3 x 3
= 81
If r = 6 units and h = 8 units, what is the volume of the cylinder shown above? Use 3.14 for
Answer:
the volume of the cylinder is 904.32 m³
Step-by-step explanation:
Every month, Ms. Hughes pays her car loan through automatic payments (withdrawals) from her savings account. She pays the same amount on her car each month. At the end of the year, her savings account balance changed by -$2,940 from payments made on her car loan.
What is the change in Ms. Hughes’s savings account balance each month due to her car payment? Show your work and/or explain your reasoning.
What is the total change in Ms. Hughes’s savings account balance after making six monthly payments on her car loan? Show your work and/or explain your reasoning.
After making six monthly payments on her car loan, Ms. Hughes's savings account balance will decrease by $1,470.
To find the change in Ms. Hughes's savings account balance each month due to her car payment, we can divide the total change in balance for the year ($-2,940) by the number of months in a year (12):
Change in savings account balance each month = $2,940 / 12 = -$245
So, Ms. Hughes's savings account balance decreases by $245 each month due to her car payment.
To find the total change in Ms. Hughes's savings account balance after making six monthly payments on her car loan, we can multiply the change in savings account balance each month by the number of months (6):
Total change in savings account balance after six monthly payments = -$245 * 6 = -$1,470
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A recipe for cookies makes 3 dozen cookies and uses
3
2 1/4 cups of flour and 3/4
cups of sugar. Sam needs to
make 5 dozen cookies. How many cups of flour and
sugar will Sam need for the recipe?
The number of cups of flour and sugar that Sam needs for the recipe will be 3.75 cups and 1.25 cups, respectively.
Given that:
A recipe for cookies makes 3 dozen cookies and uses 2 1/4 cups of flour and 3/4 cups of sugar.
The utilization of two or more additional numbers that compares is known as the ratio.
The expression that represents the 'n' dozen of cookies is given as,
⇒ n (2¹/₄) / 3 + n(3/4) / 3
⇒ n (2.25) / 3 + n(0.75) / 3
Put n = 5, then we have
⇒ 5 (2.25) / 3 + 5(0.75) / 3
⇒ 11.25/3 + 3.75/3
⇒ 3.75 + 1.25
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21 is 28% of what number? Enter your answer in the box. HELPPP ME PLEASE!!! (40 POINTS)
Answer:
To find out what number 21 is 28% of, we can use the proportion:
21 / x = 28 / 100
where x is the unknown number we are trying to find.
We can solve for x by cross-multiplying and simplifying:
21 * 100 = 28 * x
2100 = 28x
x = 2100 / 28
x = 75
Therefore, 21 is 28% of 75.
Answer:
21 is 28 percent of 75
Step-by-step explanation:
Show that sin^2x+cos^2x=1 by using the unit circle.Hint:start with the equation of the circle and finish labeled the circle
Proof that cos²(x) + sin²(x) = 1 using the unit circle shows that this equation represents a circle with radius 1
How to prove the unit of a circle?The equation of the unit circle is given by:
x² + y² = 1
where x and y are the coordinates of any point on the circle. Let us assume that the point P on the circle makes an angle of x with the positive x-axis. Then, the coordinates of P are given by:
x = cos(x)
y = sin(x)
Substituting these values in the equation of the circlet:
cos²(x) + sin²(x) = 1
Therefore, we have shown that sin²(x) + cos²(x) = 1 using the unit circle.
Graphically, this equation represents a circle with radius 1 centered at the origin, and any point (cos(x), sin(x)) on the circle will satisfy this equation.
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Which is the costant and coefficient of 5x + 12
Answer:
12 = constant
5x = coefficient
Step-by-step explanation:
12 is a constant because it can not be changed.
5 is a coefficient because it can changed by the variable (x)
Which of the following criteria is required to ensure
communication competence?
A. The message achieves the intended effect
B. The message is grammatically correct
C. the message is free from too much emotion
D. the message is well received
Subject: Professional Communication
the criteria is required to ensure communication competence is The message achieves the intended effect. Option A
What is communication competence?Communicative competence is simply described as the ability to achieve communicative goals in an appropriate and socially way.
It is well organized and goal-oriented, this means that it involves the ability to evenly select and apply skills that are appropriate and are also effective in a given context.
The different components of communication competence are;
Grammatical competencesociolinguistic competencediscourse competencestrategic competence.Hence, the message should always be effective for the context.
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!!!!!!PLEASE HELP MEEE!!!!!
Choose the ordered pair that is a solution for this equation.
4x + 2y = 8
The ordered pair (1, 2) is a solution for the equation 4x + 2y = 8.
Choosing the ordered pair that is a solution for this equation.To find an ordered pair that is a solution for the equation 4x + 2y = 8, we need to find a pair of values for x and y that satisfies the equation when we substitute them into the equation.
One way to do this is to choose a value for x and then solve for y, or vice versa.
For example, we can choose x = 1 and then solve for y:
4x + 2y = 8
4(1) + 2y = 8
4 + 2y = 8
2y = 4
y = 2
So, when x = 1 and y = 2, the equation is satisfied:
4(1) + 2(2) = 8
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The graph of a function f is shown below. findf(-1)
please be detailed
The function f of the line is f(x) = 2x - 2 and f(-1) = -4.
What is a slope of a line?The slope of a line determines the steepness of the line and is calculated by dividing the vertical change (rise) between any two points on the line by the horizontal change (run) between those same two points. The formula for slope is (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) represent any two points on the line. The slope can be positive, negative, zero or undefined, depending on the direction and steepness of the line. If the line moves up from left to right, it has a positive slope, while a line that moves down from left to right has a negative slope.
From the graph we can take two points on the line (1,0) and (0,-2). Now we can find the equation of the line passing through these points, for that we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is one of the points on the line.
First, we can find the slope:
m = (y₂ - y₁) / (x₂ - x₁) = (-2 - 0) / (0 - 1) = -2/-1 = 2
Next, we can choose either point and substitute the values into the point-slope equation:
y - y₁ = m(x - x₁)
Using point (1,0):
y - 0 = 2(x - 1)
Simplifying:
y = 2x - 2
Therefore, the equation of the line passing through points (1,0) and (0,-2) is y = 2x - 2. That is f(x) = 2x - 2.
f(-1) = 2 × -1 - 2 = -2 -2 = -4.
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Use the given zero to find the remaining zeros of the polynomial function.
P(x) = 2x3 − 5x2 + 6x − 2; 1 + i
Using the given zero . The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.
What is the polynomial function?If 1 + i is a zero of the polynomial function P(x), then its conjugate, 1 - i, must also be a zero of the polynomial, since complex zeros of polynomial functions with real coefficients always come in conjugate pairs.
To find the remaining zero, we can use polynomial division or synthetic division to divide P(x) by (x - 1 - i)(x - 1 + i), which is the quadratic factor corresponding to the two known zeros:
2x^2 - 3x + 2
P(x) = --------------
(x - 1 - i)(x - 1 + i)
Now we need to solve for the roots of the quadratic factor 2x^2 - 3x + 2. We can use the quadratic formula:
x = [3 ± sqrt(9 - 4*2*2)] / (2*2)
= [3 ± sqrt(1)] / 4
= 1/2 or 2
Therefore, the remaining zeros of P(x) are 1/2 and 2. The three zeros of the polynomial function are 1 + i, 1 - i, 1/2, and 2.
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help me pls I’ll give brainliest
The equation is expanding Pascal's triangle and the Binomial theorem
(x + 0.5)³ = x³/8 + 3x²/4 + 3x/2 + 1/8
(s + 4t)⁶ = s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶
(3a - 3b)⁴ = 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴
(3m - 2n)⁵ = 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵
(a-4)⁵ = a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024
What is the binomial theorem formula?The binomial theorem formula for any positive integer n.
(x + y)n = nC0 xn + nC1 xn-1 by+ nC2 xn-2 y2 + … + nCn-1 x yn-1 + nCn x.
11) Using the Binomial Theorem, we have:
(x + 0.5)³ = C(3,0) x³(0.5)⁰ + C(3,1) x²(0.5)¹ + C(3,2) x¹(0.5)² + C(3,3) x⁰(0.5)³
= x³/2³ + 3x²/2² + 3x/2 + 1/2³
= x³/8 + 3x²/4 + 3x/2 + 1/8
12) Using Pascal's Triangle, we have:
(s + 4t)⁶ = C(6,0) s⁶(4t)⁰ + C(6,1) s⁵(4t)¹ + C(6,2) s⁴(4t)² + C(6,3) s³(4t)³ + C(6,4) s²(4t)⁴ + C(6,5) s(4t)⁵ + C(6,6) (4t)⁶
= s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶
13) Using Pascal's Triangle, we have:
(3a - 3b)⁴ = C(4,0) (3a)⁴(-3b)⁰ + C(4,1) (3a)³(-3b)¹ + C(4,2) (3a)²(-3b)² + C(4,3) (3a)(-3b)³ + C(4,4) (-3b)⁴
= 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴
14)Using Pascal's Triangle, we have:
(3m - 2n)⁵ = C(5,0) (3m)⁵(-2n)⁰ + C(5,1) (3m)⁴(-2n)¹ + C(5,2) (3m)³(-2n)² + C(5,3) (3m)²(-2n)³ + C(5,4) (3m)(-2n)⁴ + C(5,5) (-2n)⁵
= 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵
15) Using Pascal's Triangle, we have:
(a-4)⁵ = C(5,0) a⁵(-4)⁰ + C(5,1) a⁴(-4)¹ + C(5,2) a³(-4)² + C(5,3) a²(-4)³ + C(5,4) a(-4)⁴ + C(5,5) (-4)⁵
= a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024
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The equation is expanding Pascal's triangle and the Binomial theorem ,
[tex](x + 0.5)^3= x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]
[tex](s + 4t)^6 = s^6+ 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4+ 6s(4t)^5 + 4t^6[/tex]
[tex](3a - 3b)^4 = 81a^4 - 324a^3b + 486a^2b^2- 324ab^3 + 81b^4[/tex]
[tex](3m - 2n)^5 = 243m^5 - 810m^4n + 1080m^3n^2- 720m^2n^3 + 240mn^4- 32n^5[/tex]
[tex](a-4)^5= a^5 - 20a^4 + 160a^3 - 640a^2+ 1280a - 1024[/tex]
What is the binomial theorem formula?
The binomial theorem formula for any positive integer n.
[tex](x + y)^n = nC_0 x^n + nC_1x^{n-1} y+ nC_2 x^{n-2} y_2 + … + nC_{n-1} x y^{n-1} + nC_n x.[/tex]
11) Using the Binomial Theorem, we have:
[tex](x + 0.5)^3 = C(3,0) x^3(0.5)^0 + C(3,1) x^2(0.5)^1 + C(3,2) x^1(0.5)^2 + C(3,3) x^0(0.5)^3[/tex]
=[tex]x^3/2^3 + 3x^2/2^2 + 3x/2 + 1/2^3[/tex]
= [tex]x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]
12) Using Pascal's Triangle, we have:
[tex](s + 4t)^6 = C(6,0) s^6(4t)^0+ C(6,1) s^5(4t)^1+ C(6,2) s^4(4t)^2 + C(6,3) s^3(4t)^3 + C(6,4) s^2(4t)^4+ C(6,5) s(4t)^5 + C(6,6) (4t)^6[/tex]
= [tex]s^6 + 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4 + 6s(4t)^5 + 4t^6[/tex]
13) Using Pascal's Triangle, we have:
[tex](3a - 3b)^4 = C(4,0) (3a)^4(-3b)^0 + C(4,1) (3a)^3(-3b)^1 + C(4,2) (3a)^2(-3b)^2 + C(4,3) (3a)(-3b)^3 + C(4,4) (-3b)^4[/tex]
= [tex]81a^4 - 324a^3b + 486a^2b^2 - 324ab^3 + 81b^4[/tex]
14)Using Pascal's Triangle, we have:
[tex](3m - 2n)^5= C(5,0) (3m)^5(-2n)^0 + C(5,1) (3m)^4(-2n)^1 + C(5,2) (3m)^3(-2n)^2+ C(5,3) (3m)^2(-2n)^3 + C(5,4) (3m)(-2n)^4 + C(5,5) (-2n)^5[/tex]
= [tex]243m^5- 810m^4n + 1080m^3n^2 - 720m^2n^3 + 240mn^4 - 32n^5[/tex]
15) Using Pascal's Triangle, we have:
[tex](a-4)^5= C(5,0) a^5(-4)^0+ C(5,1) a^4(-4)^1 + C(5,2) a^3(-4)^2 + C(5,3) a^2(-4)^3 +C(5,4) a(-4)^4 + C(5,5) (-4)^5[/tex]
= [tex]a^5 - 20a^4 + 160a^3 - 640a^2 + 1280a - 1024[/tex]
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A deli wraps its cylindrical containers of hot food items with plastic wrap. The containers have a diameter of 5.5 inches and a height of 3 inches. What is the minimum amount of plastic wrap needed to completely wrap 8 containers? Round your answer to the nearest tenth and approximate using π = 3.14.
Answer:
B
Step-by-step explanation:
a twenty sided fair die is rolled, with the numbers 1 through 20 on its faces. what is the probability that you will roll a number that is NOT between 4 and 12?
The probability of rolling a number that is NOT between 4 and 12 is approximately 0.55 or 55%.
What is probability?Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this occurs, we state that there is a possibility that the event will occur.
The range between 4 and 12 inclusive contains 9 numbers (4, 5, 6, 7, 8, 9, 10, 11, and 12) out of 20.
To find the probability of rolling a number that is NOT between 4 and 12, we need to find the probability of rolling one of the 11 numbers that are outside of this range.
The probability of rolling any one of these 11 numbers is 11/20, since there are 11 favorable outcomes out of 20 possible outcomes.
Therefore, the probability of rolling a number that is NOT between 4 and 12 is:
P = 11/20 ≈ 0.55
So, the probability of rolling a number that is NOT between 4 and 12 is approximately 0.55 or 55%.
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A group of marketing researchers for a popular cell phone manufacturer collected the following information about young adults (aged 18–25): 1% use a cell phone that is 3 years or older, 2% use a cell phone that is 2–3 years old, 20% use a cell phone that is 1–2 years old, and 77% use a cell phone that is less than 1 year old. Suppose a young adult was selected at random. Let X equal the age of a randomly selected person’s cell phone. Which of the following is the probability distribution for the age of that person’s cell phone?
according to the question 77% population use a cell phone that is less than 1 year old.
What is probability?Probability theory, a subfield of mathematics, quantifies the likelihood that an event is going to happen or that a statement is true. The probability for an event is a number between 0 and 1, where 0 roughly denotes how probable the event is to occur and 1 denotes certainty. A probability is a numerical representation of the likelihood that a certain event will occur. In addition to numbers from 0 to 1, probability values can also be stated as percentages between 0% and 100%. the fraction of an entire set of equally likely possibilities that result in a certain occurrence out of all possible outcomes, expressed as a ratio.
given,
The probability distribution for the age of a randomly selected young adult's cell phone can be represented using a probability mass function (PMF) as follows:
P(X = 3) = 0.01 (1% use a cell phone that is 3 years or older)
P(2 ≤ X ≤ 3) = 0.02 (2% use a cell phone that is 2-3 years old)
P(1 ≤ X ≤ 2) = 0.20 (20% use a cell phone that is 1-2 years old)
P(X < 1) = 0.77 (77% use a cell phone that is less than 1 year old)
Note that the values of the PMF correspond to the probabilities of the different age categories for the cell phones of young adults. The PMF satisfies the two main properties of a probability distribution: 1) the probabilities are non-negative, and 2) the sum of the probabilities is equal to 1.
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Five cards are dealt from a standard deck. What is the probability that at least four of them are hearts?
Step-by-step explanation:
To calculate the probability of getting at least four hearts when dealing five cards from a standard deck, we can use the concept of combinations and probability.
There are a total of 52 cards in a standard deck, and 13 of them are hearts (assuming no jokers). So the probability of drawing a heart on the first card is 13/52, or 1/4.
Now, there are two possible scenarios that would result in at least four hearts:
Four hearts and one non-heart: This can happen in C(13,4) * C(39,1) ways, where C(n, k) is the number of combinations of n items taken k at a time. The first part C(13,4) represents choosing 4 hearts out of 13, and the second part C(39,1) represents choosing 1 non-heart out of the remaining 39 cards. The total number of ways to choose 5 cards from 52 is C(52,5).
Five hearts: This can happen in C(13,5) ways, where C(13,5) represents choosing all 5 hearts out of 13.
So, the total number of favorable outcomes is C(13,4) * C(39,1) + C(13,5), and the total number of possible outcomes is C(52,5). Therefore, the probability of getting at least four hearts is:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
Plugging in the values and simplifying, we get:
P(at least 4 hearts) = (C(13,4) * C(39,1) + C(13,5)) / C(52,5)
= (715 * 39 + 1287) / 2,598,960
= 27,885 / 2,598,960
≈ 0.0107566
So, the probability of getting at least four hearts when dealing five cards from a standard deck is approximately 0.0107566 or about 1.08%.
Is (-1, -3) a solution to this system of equations?
16x - 7y = 5
x = -1
yes
no
Answer:
Yes, it is
Step-by-step explanation: