The first term of the given sequence is 6, and the recursion formula for the remaining terms is 6, 6.333, 6.444, 6.481, 6.4938, 6.4988, 6.5007, 6.5018, 6.5024, 6.5026.
We are given a recursive formula: [tex]a_{n+1} = an + (1/3^n)[/tex] with [tex]a_{1} = 6.[/tex]
Using this formula, we can calculate the first few terms of the sequence as follows:
[tex]a_{1}= 6[/tex]
[tex]a_{2} = a_{1} + (1/3^1) = 6 + 1/3 = 6.333[/tex]
[tex]a_{3} = a_{2} + (1/3^2) = 6.333 + 1/9 = 6.444[/tex]
[tex]a_{4} = a_{3} + (1/3^3) = 6.444 + 1/27 = 6.481[/tex]
[tex]a_{5} = a_{4} + (1/3^4) = 6.481 + 1/81 = 6.4938[/tex]
[tex]a_{6} = a_{5} + (1/3^5) = 6.4938 + 1/243 = 6.4988[/tex]
[tex]a_{7} = a_{6} + (1/3^6) = 6.4988 + 1/729 = 6.5007[/tex]
[tex]a_{8} = a_{7} + (1/3^7) = 6.5007 + 1/2187 = 6.5018[/tex]
[tex]a_{9} = a_{8} + (1/3^8) = 6.5018 + 1/6561 = 6.5024[/tex]
[tex]a_{10} = a_{9} + (1/3^9) = 6.5024 + 1/19683 = 6.5026[/tex]
Therefore, the first 10 terms of the sequence are: 6, 6.333, 6.444, 6.481, 6.4938, 6.4988, 6.5007, 6.5018, 6.5024, 6.5026.
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A landowner wishes to use 3 miles of fencing to enclose an isosceles triangular region of as large an area as possible. What should be the lengths of the sides of the triangle? Let x be the length of the base of the triangle. Write the area as a function of x. [First write the length of the equal-length sides in terms of the base, x, then write the height of the triangle in terms of the base.] V3 A(x) = 4 x Length of base = 1 miles Length of the other two (equal-length) sides = 2 x miles each
The area of the triangle, A(x), can be expressed as A(x) = (x * sqrt(3x^2/4))/2 and the height of the triangle, h, can be expressed as h = sqrt(3x^2/4) in terms of the base.
The landowner wishes to use 3 miles of fencing to enclose an isosceles triangular region of as large an area as possible. Let x be the length of the base of the triangle.The length of the base of the triangle is x miles, while the length of the other two equal-length sides are 2x miles each. Thus, the total length of the three sides of the triangle is 3x miles, which equals 3 miles of fencing as required.
To find the area of the triangle, we must first calculate the height of the triangle. Using the Pythagorean Theorem, we can calculate the height of the triangle in terms of the base. The formula is h^2 = (2x)^2 - (x/2)^2. Thus, the height of the triangle, h, can be expressed as h = sqrt(3x^2/4).The area of the triangle is equal to the base multiplied by the height and divided by two. Thus, the area of the triangle, A(x), can be expressed as A(x) = (x * sqrt(3x^2/4))/2.
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What is the domain and range of the function f (x) = a superscript x? a. domain = negative real numbers, range = negative real numbers c. domain = positive real numbers, range = positive real numbers b. domain = all real numbers, range = all real numbers d. domain = real numbers, range = positive real numbers
The domain and range of the function f(x) =a^x, then option (c) Domain = positive real numbers, range = positive real numbers.
The function f(x) = a^x is an exponential function with a base of a, where a is a positive real number. The domain of the function is all real numbers, because we can raise a positive number to any real power.
However, since a is positive, a^x will always be positive, which means that the range of the function is also positive real numbers. Therefore, the correct option is c. Domain = positive real numbers, range = positive real numbers.
Therefore, the correct option is (c) Domain = positive real numbers, range = positive real numbers.
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Given the following data, find the weight that represents the 28th percentile.
Weights of Newborn
Babies
6.1 9.1 9.5 6.0 8.6
6.2 9.1 6.1 8.0 5.7
6.5 6.4 5.8 9.3 6.2
Therefore, 6.1 pounds are the weight that corresponds to the 28th percentile.
what is percentile ?In statistics, a percentile is a metric that shows the value below which a specific percentage of observations in a group fell. It is frequently used to evaluate an individual's or a group's performance in relation to a specific metric against a broader population. A dataset's 75th percentile, for instance, is the number below which 75% of the observations fall and above which the remaining 25% of observations fall.
given
These procedures must be taken in order to determine the weight that corresponds to the 28th percentile:
5.7, 5.8, 6.0, 6.1, 6.2, 6.4, 8.0, 8.6, 9.1, 9.1, 9.3, 9.5 are the weights to order in ascending sequence.
Determine the 28th percentile's rank:
28th percentage = 28/100 x 13 = 3.64 (rounded up to 4)
Identify the 6.1-pound weight at the fourth level.
Therefore, 6.1 pounds are the weight that corresponds to the 28th percentile.
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Is the relation a function, and what is the range.
last one is the answer
Step-by-step explanation:
not a function because every input has more than 1 output
h(x)= -x + 5, solve for x when h(x) = 3
According to the given information, the solution to H(x) = 3 is x = 2.
What is equation?
In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS and RHS are separated by an equals sign (=), indicating that they have the same value. The general form of an equation is: LHS = RHS
To solve for x when H(x) = 3, we substitute 3 for H(x) in the equation and solve for x:
H(x) = -x + 5
3 = -x + 5
Subtracting 5 from both sides, we get:
-2 = -x
Multiplying both sides by -1, we get:
2 = x
Therefore, the solution to H(x) = 3 is x = 2.
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[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{h(x) = -x + 5}\\\\\mathtt{3 = -x + 5}\\\\\mathtt{-x + 5 = 3}\\\\\textsf{SUBTRACT 5 to BOTH SIDES}\\\\\mathtt{-x + 5 - 5 = 3 - 5}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{-x = 3 - 5}\\\\\mathtt{-x = -2}\\\\\mathtt{-1x = -2}\\\\\textsf{DIVIDE }\mathsf{-1}\textsf{ to BOTH SIDES}\\\\\mathtt{\dfrac{-1x}{-1} = \dfrac{-2}{-1}}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{x = \dfrac{-2}{-1}}\\\\\mathtt{x = 2}[/tex]
[tex]\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{x = 2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
I need help somebody please
Answer: 54 square in
Step-by-step explanation:
I don't know if this is the same person but I answered this same question just now please check my profile or comment if you want the explanation
What is the answer I keep getting 32
Answer:
2 9/14
Step-by-step explanation:
A beverage company delivers three type of drinks which are Milk(M), Carbonateddrinks(C ) and Juice (J) to four stores ( A, B, C, D) for a period of two month. The number of pets of each type of beverage delivered to four stores in first monthis
represented in Matrix K and second month is Matrix L
8 4 3
2 2 2
1 3 1
3 1 3
M C J
A
B
K
C
D
1 3 1
2 7 2
8 3 4
9 2 6
MCJ
A
B
L
CD
i. Calculate the total number of pets delivered over the period of 2 months to eachstore. Suppose, the price charged for pet of each type of drink is given by the matrix. 225
195
212
M
C
J
ii. Calculate the cost of each store ( A, B, C, D) on the beverages in two months
The cost of each store in two months is: Store A is 4281, Store B is 5485, Store C is 3153, and Store D is 6413.
To calculate the total number of pets delivered over the period of 2 months to each store, we need to add the corresponding elements of matrix K and matrix L. The result will be a new matrix representing the total number of pets delivered to each store.
So, we have: Matrix K:
| 8 4 3 |
| 2 1 3 |
| 1 3 2 |
| 7 2 6 |
Matrix L:
| 1 3 2 |
| 8 4 9 |
| 2 6 3 |
| 4 9 2 |
Total pets delivered to each store:
| 9 7 5 |
| 10 5 12 |
| 3 9 5 |
| 11 11 8 |
To calculate the cost of each store in two months, we need to multiply the total number of pets delivered to each store by the price of each type of drink, as given by the matrix:
| 225 195 212 |
So, the cost of each store in two months is:
Store A: (9 × 225) + (7 × 195) + (5 × 212) = 4281
Store B: (10 × 225) + (5 × 195) + (12 × 212) = 5485
Store C: (3 × 225) + (9 × 195) + (5 × 212) = 3153
Store D: (11 × 225) + (11 × 195) + (8 × 212) = 6413
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Snyder’s Moving company has two segments of customer: Small Business (SB) and Residential. 10% of Snyder’s 2,200 clients fall into both categories, using Snyder’s as their mover of choice for both their business and personal needs. The remaining clients are split evenly between segments. A client who falls into one category will use Snyder’s once every 3 years. Clients who fall into both categories use Snyder’s twice every 3 years. SB moves cost 15% more to the clients than Residential moves due to additional insurance costs for Snyder’s. The average profit Snyder’s makes per move, regardless of which type, is $260. Snyder recently launched a marketing campaign to all SB-only clients to encourage them to use Snyder’s for residential moves. 10% of recipients decided to do so. Assuming the campaign cost $500 to execute, how profitable was it?
The marketing campaign by Snyder's Moving company was profitable, generating an additional profit of $31,288 after subtracting the cost of the campaign. The total revenue generated after the campaign was $403,588.
To determine the profitability of the marketing campaign, we need to calculate the additional profit generated by the clients who were convinced to use Snyder's for residential moves.
Let's start by calculating the number of clients in each segment
Clients who fall into both categories, 0.1 x 2,200 = 220
Clients in each segment, (2,200 - 220) / 2 = 990
Now let's calculate the revenue generated by each segment
Revenue from clients in each segment: 990 clients x $260 profit per move = $257,400
Revenue from clients who fall into both categories: 220 clients x 2 moves x $260 profit per move = $114,400
Total revenue generated: $371,800
Now let's calculate the revenue generated after the marketing campaign
10% of 990 SB-only clients decided to use Snyder's for residential moves
0.1 x 990 = 99 clients
Additional revenue generated from these clients: 99 clients x $260 profit per move x 1.15 (15% higher price for SB moves) = $31,788
Total revenue generated after the marketing campaign, $403,588
Finally, let's subtract the cost of the marketing campaign
Profit generated after the marketing campaign: $403,588 - $500 = $403,088
Therefore, the marketing campaign was profitable, generating an additional profit of $31,288.
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A+9 as a verbal expression
Answer:
"9 more than A" is a verbal expression.
Compute the directional derivative of the following function at the given point Pin the direction of the given vector. Be sure to use a unit vector for the direction vector.f(x,y)=ln(5+3x2+2y2); P(2,−1); ⟨1,1⟩
The directional derivative of the function at the given point P in the direction of the given vector is:
(8/21)√(2).
Directional derivativeThe directional derivative of a function in the direction of a unit vector is the rate at which the function changes in that direction.
To compute the directional derivative of f(x, y) = ln(5 + 3x^2 + 2y^2) at the point P(2, -1) in the direction of the vector ⟨1, 1⟩, we need to:
Compute the gradient of f(x, y) at P(2, -1).Normalize the direction vector ⟨1, 1⟩ to obtain a unit vector.Compute the dot product of the gradient of f at P with the unit direction vector.The gradient of f(x, y) is given by:1) ∇f(x, y) = (6x / (5 + 3x^2 + 2y^2), 4y / (5 + 3x^2 + 2y^2))
Therefore, the gradient of f at P(2, -1) is:
∇f(2, -1) = (24/21, -4/21)
2) To obtain a unit vector in the direction of ⟨1, 1⟩, we need to divide it by its length:
||⟨1, 1⟩|| = √(1^2 + 1^2) = sqrt(2)
Therefore, a unit vector in the direction of ⟨1, 1⟩ is given by:
u = ⟨1, 1⟩ / √2) = ⟨√(2)/2, √(2)/2⟩
3) The directional derivative of f at P in the direction of u is given by:
D_uf(2, -1) = ∇f(2, -1) · u
where "·" denotes the dot product. Substituting the values for ∇f(2, -1) and u, we get:
D_uf(2, -1) = (24/21, -4/21) · (√(2)/2, √(2)/2)
= (24/21)(√(2)/2) + (-4/21)(√(2)/2)
= (8/21)√(2)
Therefore, the directional derivative of f(x, y) at P(2, -1) in the direction of ⟨1, 1⟩ is (8/21)√(2).
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1 Find the value of x.
i’m like struggling
Answer: 23 degrees
Step-by-step explanation:
Assuming that 117 is the entire angle we can find that:
94+x = 117
Subtract 94 from both sides:
x = 117-94
x = 23 degrees
A coffee maker is on sale for 45$. If the sales tax is 7%, how much will the buyer spend altogether?
Answer: 38 I think if it's not right I'm sorry I'm bad at math that's like the only thing I suck at
Step-by-step explanation:
find the number equivalant to the ratio 25:6
Answer:
A ratio of 25 to 6 can be written as 25 to 6, 25:6, or 25/6. Furthermore, 25 and 6 can be the quantity or measurement of anything, such as students, fruit, weights, heights, speed and so on. A ratio of 25 to 6 simply means that for every 25 of something, there are 6 of something else, with a total of 31
Step-by-step explanation:
done hope u like it !!
ABC ~ PQR. If AB : PQ = 4:5,
find A(ABC): A(PQR).
Area (ABC) is measured as Area (PQR), which equals 16:25.
To locate,
Area (ABC) is measured as: (PQR).
Solution,
This mathematical issue can easily resolved by utilising the procedure outlined below:
According to the "Area of Similar Triangles Theorem" in mathematics,
When two triangles are similar, their area ratios are proportional to the square of the ratio of the respective sides.
{Statement-1}
In light of the query and assertion 1, we can state,
Area (ABC) is measured as: (PQR)
= (AB: PQ), (BC: QR), and (AC: PR)
= (4:5)2 = (4/5)2
= 16/25 = 16:25
As a result, Area (ABC): Area (PQR) is measured at 16:25.
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HELPPP
12 divided by five +32 x 2.2
Answer:
To evaluate this expression, you need to follow the order of operations, which is:
Do any calculations inside parentheses first. (There are no parentheses in this expression.)
Exponents or radicals (There are no exponents or radicals in this expression.)
Multiplication or division, from left to right. (Perform 32 x 2.2, which equals 70.4.)
Addition or subtraction, from left to right. (Perform 12 divided by five, which equals 2.4, then add that to 70.4.)
Therefore, the answer is:
12 ÷ 5 + 32 x 2.2 = 2.4 + 70.4 = 72.8
A rectangle has a perimeter of 48 feet. Which dimensions could the rectangle have? Choose two. A) 6 feet x 8 feet B) 12 feet x 12 feet C) 16 feet x 8 feet D) 12 feet x 4 feet
Note: I am bad at math
Answer:
Let the length of the rectangle be l and the width be w. Then, according to the problem statement, we have:
Perimeter of rectangle = 2(l + w) = 48 feet
Dividing both sides by 2, we get:
l + w = 24 feet
Now we can check the options:
A) 6 feet x 8 feet: l + w = 6 + 8 = 14 feet, which is not equal to 24 feet. Therefore, this option is not correct.
B) 12 feet x 12 feet: l + w = 12 + 12 = 24 feet, which is equal to the given perimeter. Therefore, this option is correct.
C) 16 feet x 8 feet: l + w = 16 + 8 = 24 feet, which is equal to the given perimeter. Therefore, this option is correct.
D) 12 feet x 4 feet: l + w = 12 + 4 = 16 feet, which is not equal to 24 feet. Therefore, this option is not correct.
So, the correct options are B) 12 feet x 12 feet and C) 16 feet x 8 feet.
the pictograph below shows the approximate gross revenues in the united states from four walt disney animated movies. find the ratio of the gross revenue of the hunchback of notre dame to the gross revenue of beauty and the beast. a. 1
b. 2/3
c. 3
d. 2
e. 3/2
Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order.
y dA, D is bounded by y = x − 6; x = y2
D
The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.
The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.
Given, the double integral ∫∫yA and the region y = x-6 and x = y²
y = x-6
x = y²
y² = y +6
y² - y - 6 = 0
y² - 3y +2y - 6 = 0
(y-3) (y+2) = 0
y = 3 and y = -2
[tex]\int\int\limits_\triangle {y} \, dA\\ \\[/tex]
= [tex]\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}[/tex]
The value for the double integral is 125/12.
Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.
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A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 162 pounds requires 216 milligrams of medicine. What is the weight of a patient who requires 220 milligrams of medicine?
A patient weighing 220 pounds needs 293 milligrams of medicine.
We have given that,
patient weighing 162
pounds requires 216 milligrams of medicine
We have to calculate the amount of medicine required by a patient weighing 220 pounds
Consider the value of amount of medicine is x.
Set up a proportion.
pounds / milligrams of medicine
What is the proportion we get?
[tex]162/216=220/x[/tex]
So,
[tex]162/216=220/x[/tex]
[tex]162x=216\times220[/tex]
[tex]162x=47,520[/tex]
[tex]x=47,520/162[/tex]
[tex]x=293[/tex]
A patient weighing 220 pounds needs 293 milligrams of medicine.
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HELP!!
Write a quadratic equation in standard form that has solutions of -3 and -4.
Answer:
If a quadratic equation has solutions of -3 and -4, then it can be written in factored form as:
(x + 3)(x + 4) = 0
To convert this to standard form, we can multiply out the factors:
x^2 + 7x + 12 = 0
Therefore, the quadratic equation in standard form that has solutions of -3 and -4 is:
x^2 + 7x + 12 = 0
Divide negative 6 and 2 over 5 ÷ negative 4 and 3 over 7. Negative 224 over 155 224 over 155 negative 519 over 35 519 over 35
By dividing we get: -6/2 ÷ 5 = -6/10 = -3/5, -4/3 ÷ 7 = -4/21, -224 ÷ 155 = -1.445, 224 ÷ 155 = 1.448, -519/35 = -14.83, 519/35 = 14.83.
.
To divide fractions, we need to remember the rule: "invert and multiply." This means that we take the reciprocal of the second fraction and then multiply it by the first fraction. For example, to divide -6/5 by 2/5, we invert 2/5 to get 5/2 and then multiply it by -6/5 to get -6/5 x 5/2 = -15/2. Similarly, to divide 224/155 by -1, we invert -1 to get -1/1 and then multiply it by 224/155 to get -224/155. To divide 519/35 by itself, we simply get 1 as the answer.
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Complete question:
Divide:
1. negative 6 and 2 over 5
2. negative 4 and 3 over 7
3. negative 224 over 155
4. 224 over 155
5. negative 519 over 35
6. 519 over 35
Help me with this it's to hard for me
Answer:
Part B: Calculate the range and interquartile range (IQR) for each group and interpret what they tell us about the data.
For Group A:
Range = 5 - 1 = 4
Q1 = 2
Q3 = 4
IQR = Q3 - Q1 = 2
For Group B:
Range = 5 - 2 = 3
Q1 = 2
Q3 = 4
IQR = Q3 - Q1 = 2
The range for Group A is larger than the range for Group B, indicating that there is more variability in the growth of the plants in Group A. However, both groups have the same IQR, indicating that the middle 50% of the data in each group is similar. This suggests that while there may be some variability in the growth of the plants, the overall distribution of growth is similar between the two fertilizers.
The radius of a circle is 8 meters. What is the circle's circumference?
Use 3.14 for л.
Answer:
circumference=50.24
Step-by-step explanation:
c=2x3.14xr
c=2x3.14x(8)
c=50.24
The cost price of 20 articles is the same as sellling price of 16 articles find the gain percent
If the cost price of 20 articles is the same as selling price of 16 articles, then the gain percentage is 25%
To find the gain percent, we first need to calculate the profit earned on the sale of the 16 articles.
Let the cost price of each article be "C" and the selling price of each article be "S".
Given that the cost price of 20 articles is the same as the selling price of 16 articles, we can write:
20C = 16S
We can simplify this equation to:
S = (20/16)C = (5/4)C
Now, let's calculate the profit earned on the sale of 16 articles:
Profit = Total Selling Price - Total Cost Price
Profit = 16S - 20C
Profit = 16(5/4)C - 20C
Profit = 5C/2
The profit earned is 5C/2. The profit percent can be calculated as:
Profit Percent = (Profit / Cost Price) x 100
Profit Percent = (5C/2) / (20C) x 100
Profit Percent = 25%
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a car is traveling at a 3 of 57 miles per hour. What is the car's speed in miles per minute? how many miles will the car travel in 20 minute? (do not round your answer)
The speed of car is found as : 1 of 1140 miles per minutes.
The total number of miles the car will travel in 20 minutes is: 1 / 50 miles.
Explain about the unit conversions?The same attribute is expressed using a unit conversion, but in a diverse unit of measurement.
For e.g., time can be highlighted in minutes rather than hours, and distance can be verbalized in kilometers, feet, or another comparable measurement unit instead of miles.
Speed of car = 3 of 57 miles per hour.
Speed of car = 3 mi / 57 hr
We know, 1 hour = 60 minutes;
So,
Speed of car = 3 mi / 57*60 min
Speed of car = 1 mi / 57*20 min
Speed of car = 1 mi / 1140 min
Thus, the speed of car is found as : 1 of 1140 miles per minutes.
In 20 minute:
Number of miles = 1 mi / 1140 min * 20 min
Number of miles = 20 / 1140 min
Number of miles = 1 / 50 miles
Thus, the total number of miles the car will travel in 20 minutes is: 1 / 50 miles.
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in how many ways can a class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer and a secretary g
The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040
A class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary in the following way:Step-by-step explanation:The number of ways that a class of 40 students can choose a committee consisting of a president, vice president, treasurer, and a secretary can be found by using the permutation formula.If we assume that the positions of the committee members are different, the number of ways can be calculated as follows:The number of ways of selecting the president from 40 students is 40.The number of ways of selecting the vice president from the remaining 39 students is 39.The number of ways of selecting the treasurer from the remaining 38 students is 38.The number of ways of selecting the secretary from the remaining 37 students is 37.The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040Thus, secretary.
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suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.38 . using the empirical rule, what percentage of the students have grade point averages that are between 1.42 and 3.7 ?
Using the empirical rule, the percentage of the students have grade point averages that are between 1.42 and 3.7 is 99.7%
How do we use the empirical rule?The empirical rule states that for a bell-shaped distribution, the percentage of data that lie within a specified number of standard deviations from the mean is as follows: 68% of the data lie within 1 standard deviation of the mean. 95% of the data lie within 2 standard deviations of the mean
99.7% of the data lie within 3 standard deviations of the mean. Mean = 2.56Standard Deviation = 0.38We want to know what percentage of students have a grade point average between 1.42 and 3.7. To do this, we need to convert 1.42 and 3.7 into standard deviations away from the mean.
Using the z-score formula:(1.42-2.56)/0.38 = -2.99 and(3.7-2.56)/0.38 = 3.00This tells us that a grade point average of 1.42 is about 2.99 standard deviations below the mean, and a grade point average of 3.7 is about 3 standard deviations above the mean.
Using the empirical rule, we know that 99.7% of the data lies within 3 standard deviations of the mean. So the percentage of students that have a grade point average between 1.42 and 3.7 is approximately 99.7%.Thus, the correct answer is 99.7%.
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1. Find the given derivative by finding the first few derivatives and observing the pattern that occurs. (d115/dx115(sin(x)). 2. For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable. Enter your answers as a comma- separated list.) f(x) = x + 2 sin(x).
The values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
1. The given derivative can be found by finding the first few derivatives and observing the pattern that occurs as shown below;Differentiating sin x with respect to x gives the derivative cos x. Continuing this process, the pattern that emerges is that sin x changes sign for every odd derivative, and stays the same for every even derivative. Therefore the 115th derivative of sin x can be expressed as follows;(d115/dx115)(sin x) = sin x, for n = 58 (where n is an even number)2. To find the values of x such that the graph of f has a horizontal tangent, we differentiate f with respect to x, and then solve for x such that the derivative equals zero. We have;f(x) = x + 2sin xDifferentiating f(x) with respect to x gives;f'(x) = 1 + 2cos xFor a horizontal tangent, f'(x) = 0, thus;1 + 2cos x = 02cos x = -1cos x = -1/2The solutions of the equation cos x = -1/2 are;x = 2π/3 + 2πn or x = 4π/3 + 2πnwhere n is an integer. Therefore the values of x such that the graph of f has a horizontal tangent are;x = 2π/3 + 2πn, 4π/3 + 2πn, where n is an integer.
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suppose that 78% of all dialysis patients will survive for at least 5 years. in a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?
The probability that the 78% of all the dialysis patients survive for at least five years will exceed 80%, rounded to 5 decimal places is 0.3192.
What is the probability?The proportion of dialysis patients surviving for at least 5 years = 78% = 0.78
Assuming that a simple random sample of 100 dialysis patients is selected, the sample size is n = 100.
Let p be the proportion of dialysis patients in the sample surviving for at least 5 years.
Then, the sample mean is given by:
μp = E(p) = p = 0.78
So, the mean proportion of dialysis patients surviving for at least 5 years is equal to 0.78.
The standard error of the sample proportion is given by:
σp=√p(1−p)/n
σp=√0.78(1−0.78)/100
σp=0.04278
The required probability is to find P(p > 0.80):
P(p > 0.80) = P(Z > (0.80 - 0.78)/0.04278)
P(p > 0.80) = P(Z > 0.467) = 1 - P(Z < 0.467) = 1 - 0.6808 = 0.3192 (rounded to 5 decimal places)
Therefore, the probability that the proportion surviving for at least five years will exceed 80% in a simple random sample of 100 new dialysis patients is 0.3192.
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