Therefore , the solution of the given problem of function comes out to be the limit may not exist, if the function is not continuous at x = 0.
What does the term function mean?The mathematical discipline encompasses arithmetic, symbols, and their divisions, as well as histology, construction, and both real and imagined geographic places. A function describes the connections between various elements, which all have an associated outcome. A function is composed of an array of different parts that, when combined, result in particular outcomes for each input.
Here,
We must be aware of the precise function or expression under consideration in order to respond to this query.
The action as x moves towards zero from the negative direction can change depending on the function.
If a function is continuous at x = 0, then in general, if the function has a limit as x gets smaller from the downward direction, however this limit will be the same as the limit as x reaches zero from the positive direction.
The limit as x approaches zero from the downward direction may vary from the limit as x approaches zero from the better way, or the limit may not exist, if the function is not continuous at x = 0.
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A jug contains 10 different red balls and 7 different black balls. Take out 5 balls without repeating.
(A) What is the probability that at least one red ball will be obtained?
(B) What is the probability that two red balls and three black balls will be obtained? One red and four black?
(C) What is the probability of getting, k , k> = 0, k <= 5, red balls and (k-5) black balls?
.......................................................................................
A) The probability of at least one red ball being obtained is 1 - the probability of no red balls being obtained.
The probability of no red balls being obtained is (7/17)*(6/16)*(5/15)*(4/14)*(3/13) = 0.0096. Therefore, the probability of at least one red ball being obtained is 1 - 0.0096 = 0.9904.
B) The probability of two red balls and three black balls being obtained is (10/17)*(9/16)*(7/15)*(6/14)*(5/13) = 0.0909. The probability of one red ball and four black balls being obtained is (10/17)*(7/16)*(6/15)*(5/14)*(4/13) = 0.0216.
C) The probability of getting k red balls and (5-k) black balls is (10 choose k)*(7 choose (5-k))/(17 choose 5). This can be calculated for each value of k from 0 to 5 and summed to find the total probability.
For example, when k=0, the probability is (10 choose 0)*(7 choose 5)/(17 choose 5) = 0.0096. When k=1, the probability is (10 choose 1)*(7 choose 4)/(17 choose 5) = 0.0909. The total probability is the sum of these individual probabilities.
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£300 in the ratio of 10:20
Answer:
To divide £300 in the ratio of 10:20, we need to first add the two parts of the ratio to find the total number of parts:
10 + 20 = 30
This means that the ratio can be expressed as 10/30 and 20/30.
Next, we can use these ratios to find the amount of money for each part of the ratio:
10/30 x £300 = £100
20/30 x £300 = £200
Therefore, the amount of money for the parts of the ratio 10:20 would be £100 and £200 respectively.
Frequency polygon question: work out the upper and lower bonds
They are not the same as the upper and lower limits used in other statistical calculations.
what are statistical data?A accumulation of numerical data that has been methodically gathered, arranged, and examined is referred to as statistical data. Numerous phenomena, including economic patterns, demographic traits, health outcomes, and more, are described and measured using this data. Numerous techniques, such as surveys, experiments, observations, and administrative documents, can be used to gather statistical data. After being gathered, the data can be examined statistically to reveal patterns, connections, and trends that can be used to guide policy development and decision-making.
given
This is a histogram showing the frequency distribution of the weights of 30 students. Each bar represents a weight range, and the height of the bar represents the frequency of students in that weight range.
To find the upper and lower boundaries for each weight range, we can use the following formula:
Lower bound = midpoint of the previous range + 0.5
Upper bound = midpoint of the current range - 0.5
For example, the lower bound of the first range (60-64) is:
Lower bound = midpoint of previous range + 0.5
= 57
Upper bound = midpoint of current range - 0.5
= 61.5
We can apply the same formula to find the upper and lower bounds for the other ranges in the histogram. The results are:
60-64: lower bound = 57, upper bound = 61.5
65-69: lower bound = 62, upper bound = 66.5
70-74: lower bound = 67, upper bound = 71.5
75-79: lower bound = 72, upper bound = 76.5
80-84: lower bound = 77, upper bound = 81.5
85-89: lower bound = 82, upper bound = 86.5
90-94: lower bound = 87, upper bound = 91.5
95-99: lower bound = 92, upper bound = 96.5
They are not the same as the upper and lower limits used in other statistical calculations.
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Find the y-intercept of line y=4/3*+2/3
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.
Answer:
y = (4/3)x + 2/3
The y-intercept is the value of y when x is equal to zero. So we can substitute x = 0 into the equation and solve for y:
y = (4/3)(0) + 2/3 = 2/3
The y-intercept of the line y = (4/3)x + 2/3 is 2/3.
Step-by-step explanation:
Answer:
The y-intercept is (2/3)
Step-by-step explanation:
I will assume that the equation is missing the "x," and will rewrite is as:
y = (4/3)x + (2/3)
This is in standard form of y = mx + b, where m is the slope and b is the y-intercept.
The slope is (4/3) and the y-intercept is (2/3)
James created a scale drawing of the school library in his art class. In the scale drawing, the length of the library is 13 inches. The length of the actual library is 78 feet. Which scale did James use to create the scale drawing of the school library?
The scale unit that James used to create scale drawing of school library is 1 inch = 6 feet.
What is scale unit?A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map.
What is scale drawing?A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .
According to the question:
Given, 78 feet length of library is represented by 13 inch
Let, "x" be the number of feet that 1 inch represents.
∴ 13x = 78 feet
⇒x = 78/13
⇒x = 6
So, 1 inch equals 6 feet.
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Answer:
the answer would be 1 inch = 6 feet
Step-by-step explanation:
What is scale unit?
A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map.
What is scale drawing?
A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .
Solution:
Given, 78 feet length of library is represented by 13 inch
Let, "x" be the number of feet that 1 inch represents.
∴ 13x = 78 feet
⇒x = 78/13
⇒x = 6
So, 1 inch equals 6 feet.
Madeline drew a triangle on her paper. Angle A of the triangle was 1/3 as big as angle B. Angle C was smaller than angle A. Which list can represent the angle measures in this triangle? A: 20,40,120 B: 30,60,90 C: 15,45,120 D: 25,40,120
Answer: A: 20,40,120
Step-by-step explanation:
Angle A is smaller than Angle B as it is less than 1 time as big as it.
The list of angles from smallest to largest is C, A, and B.
120 x (1/3) = 40
20 < 40
Hope this helps!
Hamid wants to find out what people in Melworth think about the sports facilities in the town. Hamid plans to stand outside the Melworth sports centre one Monday morning. He plans to ask people going into the sports centre to complete a questionnaire. Carol tells Hamid that his survey will be biased. Give one reason why the survey will be biased.
Because it only covers those who are entering the sports centre, the survey will be prejudiced.
Why are surveys biased?This means that the survey will only reflect the opinions of those who are likely to have positive perceptions of the sports facilities and who are interested in using them. It does not include the viewpoints of those who do not use or hold a poor opinion of the sporting facilities.
Those who don't use the facilities, for instance, could have bad perceptions of the sports centre if it is renowned for being pricey or challenging to get to. The survey will miss important information if it simply polls visitors to the sports centre.
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If f(x) = 8x and g(x)= 3x-2, find (fg)(x).
The function (fg)(x) is the product of the function f(x) and g(x) which is (fg)(x) = 24x² - 16x.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout calculation and are essential for the development of significant links.
The two functions are given below.
f(x) = 8x
g(x)= 3x - 2
The function (fg)(x) is calculated as,
(fg)(x) = f(x) · g(x)
(fg)(x) = (8x) × (3x - 2)
(fg)(x) = 24x² - 16x
The function (fg)(x) is the product of the function f(x) and g(x) which is (fg)(x) = 24x² - 16x.
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PLEASE ANSWER THE 2 QUESTION USE ANY STRATEGIE
According to the above, the statement that is true about the expression can be inferred: Since the factor of 5/6 is less than 1, the product of 8 * 5/6 will be less than 8. Additionally, the measure of the giant mouse would be 0.76 meters.
How to find the correct statement about fractions?To find the correct statement about the fractions we must analyze each of the statements and check it according to the multiplication information. According to the above, we can establish that the factor of 5/6 is less than one because the division of these two numbers results in a number less than 1.
5 / 6 = 0.83So each number that we multiply by this fraction will give a result less than the same number. In this case if we multiply 8 by this fraction it would give us 6.66
8 * 0.83 = 6.66On the other hand, if we want to know the height of the giant mouse, we must establish what the size of the Chihuahua is. So we develop the fraction 2 1/3 = 2.33
To find the height of the giant mouse we must divide the height of the chihuahua by 3.
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points F(2,6), G(2,-1). H(x,y) form a triangle in the xy -coordinate plane. if the area of this triangle is 14 square units, then which of the following are possible coordinates for point H?
The perpendicular line connecting points F and G results in the formation of a triangle with a 14 square unit surface area.
What does coordinate mean?In mathematics, a coordinate is a set of numbers or symbols that describes an object's position or location in a geometric space. The most popular coordinate system is the Geographic coordinate system, which creates a grid on a surface or in three dimensions using a series of perpendicular lines. Each location on the plane or in space is then uniquely identified by an ordered pair or set of three numbers, respectively, that represent a point's distance from the origin along each of the coordinate system's axes.
Given that points F and G share the same x-coordinate, the line connecting them is perpendicular. A degenerate triangle with negative area will be formed by any point H that shares the same x-coordinate as F and G.
D = √((2-2)2 + (6-(-1),2) = √(49), which = 7.
distance(FH)/7 = 2/7.
distance(GH)/7 = 4/7
Distance(FH) / Distance(GH) = 1 / 2.
The distance between any two points H(x, y) and F(2,6) or G(2,-1) can be calculated using the distance formula as follows:
distance(FH) is = √((x-2) + (y-6)).
Distance (GH) is = √((x-2) + (y+1)).
By changing the aforementioned values, we obtain:
√((x-2)**2**y+1**2)/7) = 4/7
(x-2)² + (y+1)² = 16
(x-2)² + (y-6) (y-6)² = 1/4 ((x-2)² + (y+1)²)
By condensing and extending, we obtain:
3(x-2)² + 13(y-6)² = 196
5(x-2)² + 25(y+1)² = 784
7(x-2)² + (y-6)² = 1
A triangle with a 14 square unit surface area is created when the perpendicular line joining F and G.
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a. What is 6%of 34 ? b. 17 is what percent of 34 ? c. 18 is30%of what number? d. What is 7% of 49 ? 8. Copy the number line and fill in the blank so that each tick mark is
a) 6% of 34 is 2.04
b) 17 is 50% of 34
c) 18 is 30% of 60
d) 7% of 49 is 3.43.
a. To find 6% of 34, you can multiply 34 by 0.06 (which is the decimal equivalent of 6%): 34 * 0.06 = 2.04. So 6% of 34 is 2.04.
b. To find what percent 17 is of 34, you can divide 17 by 34 and then multiply by 100 to convert the decimal to a percentage: (17/34) * 100 = 50%. So 17 is 50% of 34.
c. To find what number 18 is 30% of, you can divide 18 by 0.30 (which is the decimal equivalent of 30%): 18 / 0.30 = 60. So 18 is 30% of 60.
d. To find 7% of 49, you can multiply 49 by 0.07 (which is the decimal equivalent of 7%): 49 * 0.07 = 3.43. So 7% of 49 is 3.43.
8. Unfortunately, I cannot see the number line that you are referring to, so I cannot provide an answer for this part of the question.
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The function f(x) contains the point (4, −10). Show all calculations steps and state the image
(the new location) of point under each of the following general transformations:
a. = ( + 2) − 3
b. − 1 = 2( − 4)
c. − 1/3 = (−2)
d. 2 = ((+2)/3)
(the new location) of point under each of the following general transformations are as follows:
a. Image: (3, -10)
b. Image: (-1, -10)
c. Image: (-4/3, -10)
d. Image: (14/3, -10)
What is general transformations?
A transformation is a procedure that involves either changing an object's orientation to create an image or expanding or reducing its size to create a new one.
We'll use the given point (4, -10) as the input for each transformation, and apply the transformation to find the new location of the point.
a. f(x) = (x + 2) - 3
f(4) = (4 + 2) - 3 = 3
Therefore, the new location of the point under the transformation f(x) = (x + 2) - 3 is (3, -10).
b. f(x) = 2(x - 4) - 1
f(4) = 2(4 - 4) - 1 = -1
Therefore, the new location of the point under the transformation f(x) = 2(x - 4) - 1 is (-1, -10).
c. f(x) = -1/3x
f(4) = -1/3(4) = -4/3
Therefore, the new location of the point under the transformation f(x) = -1/3x is (-4/3, -10).
d. f(x) = (2/3)x + 2
f(4) = (2/3)(4) + 2 = 8/3 + 2 = 14/3
Therefore, the new location of the point under the transformation f(x) = (2/3)x + 2 is (14/3, -10).
In each case, the image of the point is the new location after applying the transformation.
a. Image: (3, -10)
b. Image: (-1, -10)
c. Image: (-4/3, -10)
d. Image: (14/3, -10)
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Which angle is formed by EA−→
and EG−→−?
Select all that apply.
Answer:
Step-by-step explanation:
[tex]\angle 2,\angle AEG, \angle GEB[/tex]
11x-10+80=180 solve for x
Answer:
To solve for x, we need to isolate it on one side of the equation by performing inverse operations.
11x - 10 + 80 = 180
First, we combine the constant terms on the left side of the equation:
11x + 70 = 180
Next, we isolate the variable term by subtracting 70 from both sides:
11x = 110
Finally, we solve for x by dividing both sides by 11:
x = 10
Therefore, the solution to the equation 11x - 10 + 80 = 180 is x = 10.
Consider the system of linear equations
3x + y + z = 1
2x + y - 4z = 2
Which one of the following is not a solution to this system? A.(-1,4,0)
B. (-6, 18, 1)
C. (9,-24,-2)
D. (4,-10, -1)
E. (3/2, - 1/2, - 3)
The option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.
The system of linear equations given is:
3x + y + z = 1
2x + y - 4z = 2
The answer that is not a solution to this system is option. To check this, we can substitute (3/2, - 1/2, - 3) into the system and solve:
3*(3/2) + (-1/2) + (-3) = 1
2*(3/2) + (-1/2) - 4*(-3) = 2
After simplifying, we get 9/2 - 1/2 + 9/2 ≠ 1 and 9 - 1 - 12 ≠ 2, so option E. (3/2, - 1/2, - 3) is not a solution to the system of linear equations.
A system of equations is a set of two or more equations in which we will find unknowns.
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help please me with the questions:')
Answer:
1. [tex]75[/tex]
2. [tex]4x^{8}[/tex]
3. [tex]128[/tex]
Step-by-step explanation:
[tex]\frac{3*5^9}{5^7}=\frac{3*5^2*5^7}{5^7}=3*5^2=75[/tex]
[tex]\sqrt{16x^{16}}=4\sqrt{x^{16}} =4x^8[/tex]
[tex]\frac{(-5)(2^8)}{-6+1}/2=\frac{(-5)(2^8)}{(-5)(2)}=\frac{2^8}{2}=2^7=128[/tex]
A cell phone plan charges $45.75 per month, plus $9.55 in taxes, plus $0.35 per
minute for calls beyond the 500-min monthly limit. Write a piecewise defined
function to model the monthly cost C(x) as a function of the number of minutes used
x for the month.
Answer: We can write the piecewise defined function for the monthly cost C(x) as follows:
C(x) =
45.75 - 9.55, if x ≤ 500
45.75 - 9.55 + 0.35(x - 500), if x > 500
Explanation:
For the first 500 minutes, the monthly cost is a flat rate of $45.75 for the plan fee and $9.55 for taxes, so the total cost is simply the sum of these two amounts: C(x) = 45.75 + 9.55 = 55.30, for x ≤ 500.
For any additional minutes beyond the 500-min limit, there is an additional charge of $0.35 per minute, so the cost increases linearly with the number of extra minutes used. The expression (x - 500) represents the number of minutes beyond the limit, so we multiply this by the rate of $0.35 per minute and add this amount to the base cost of $55.30, giving the piecewise expression:
C(x) =
55.30, if x ≤ 500
55.30 + 0.35(x - 500), if x > 500
Therefore, the piecewise defined function for the monthly cost C(x) is:
C(x) =
45.75 - 9.55, if x ≤ 500
45.75 - 9.55 + 0.35(x - 500), if x > 500
Note: The two expressions are equivalent, but the second expression is simplified by combining the constants.
Step-by-step explanation:
An amusement park charges an admission fee of $40 dollars per person. The cost, C (in dollars), of admission for a group of p people is given by the following function.
What is the cost of admission for a group of 5 people?
The cost of admission for a group of 5 people is $200 dollars.
The cost of admission for a group of 5 people is given by the function C(p) = 40p, where p is the number of people in the group. To find the cost for a group of 5 people, we simply plug in 5 for p and solve for C:
C(5) = 40(5)
C(5) = 200
Therefore, the cost of admission for a group of 5 people is $200 dollars.
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Amy is attending a school orchestra concert.she sees her math teacher seated 10 meters ahead of her and her science teacher seated 24 meters to her right.How far apart are the two teachers?
Answer:
The two teachers are 26 meters apart. To calculate this, you can use the Pythagorean Theorem, which states that the distance between two points is equal to the square root of the sum of the squares of the differences between the coordinates of the two points. In this case, the coordinates of the math teacher are (10, 0) and the coordinates of the science teacher are (0, 24), so the distance between them is the square root of [(10-0)^2 + (0-24)^2] = √(100 + 576) = √676 = 26 meters.
We can use the Pythagorean theorem to solve this problem. Let's draw a diagram:
A (Amy)
/|
/ |
/ |10 meters
/ |
/____|
B C (science teacher)
We have a right triangle ABC, where AB = 10 meters and BC = 24 meters. We want to find the length of AC, which is the distance between the two teachers.
Using the Pythagorean theorem:
AC^2 = AB^2 + BC^2
AC^2 = 10^2 + 24^2
AC^2 = 676
AC = sqrt(676)
AC = 26 meters
Therefore, the two teachers are 26 meters apart.
what is the frequency of each interval
81-100. ------2
1-20----------2
21-40---------4
41-60----------1
61-80----------1
Solve the simultaneous equations by substitution
3x+5y=11
6x+5y=17
Answer:
hi
Step-by-step explanation:
this is the answer
hope this helps
good luck;)
Sansa and Arya visited the Snack Shack during a baseball game. Sansa bought 2 candles and 1 licorice stick for $3.25. Arya bought 1 candy and 4 licorice sticks for $2.50.
What Is the cost for 1 of each of these Items?
The cοst fοr οne οf each item is:
Candle: $1.625
Licοrice stick: $0.975
Candy: $2.50
What is an equatiοn?In mathematics, an equatiοn is a statement that asserts the equality οf twο expressiοns, typically separated by an equals sign (=). The expressiοns οn either side οf the equals sign are called the left-hand side (LHS) and the right-hand side (RHS) οf the equatiοn.
Let's use variables tο represent the cοst οf each item. Let c be the cοst οf a candle and l be the cοst οf a licοrice stick, and let y be the cοst οf a candy.
Frοm the given infοrmatiοn, we can set up twο equatiοns tο represent the tοtal cοst fοr each persοn:
2c + l = 3.25 (Equatiοn 1)
y + 4l = 2.50 (Equatiοn 2)
We can then sοlve fοr each variable by using algebraic manipulatiοn.
Frοm Equatiοn 1, we can isοlate l by subtracting 2c frοm bοth sides:
l = 3.25 - 2c
We can substitute this expressiοn fοr l intο Equatiοn 2, and sοlve fοr y:
y + 4(3.25 - 2c) = 2.50
y + 13 - 8c = 2.50
y = 2.50 - 13 + 8c
y = 8c - 10.5
Nοw we can substitute the expressiοn fοr y and the expressiοn fοr l intο a single equatiοn tο sοlve fοr c:
2c + (8c - 10.5) = 3.25 + 2.5
10c - 10.5 = 5.75
10c = 16.25
c = 1.625
Sο a candle cοsts $1.625. We can use this value tο find the cοst οf a licοrice stick:
l = 3.25 - 2c
l = 3.25 - 2(1.625)
l = 0.975
Sο a licοrice stick cοsts $0.975. Finally, we can find the cοst οf a candy using the expressiοn we fοund earlier:
y = 8c - 10.5
y = 8(1.625) - 10.5
y = 2.5
Sο a candy cοsts $2.50.
Therefοre, the cοst fοr οne οf each item is:
Candle: $1.625
Licοrice stick: $0.975
Candy: $2.50
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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The algebraic equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch.
What is the algebraic equation?Mathematical equations with one or more variables and algebraic operations like addition, subtraction, multiplication, division, exponentiation, and roots are known as algebraic equations. By identifying the values of the unknown variables that fulfill the equation, these equations can be used to illustrate mathematical connections between variables and to solve issues.
Although algebraic equations can take many different forms, they often require utilizing the equal sign (=) to make one expression equal to another. For instance, the algebraic equation x + 2 = 7 shows the connection between the constants 2 and 7 and the unknown variable x.
The equation that could be used to find the price of one tire patch is:
4x = 22.2 - 1.9
This equation represents the total cost of the four tire patches (4x) subtracted from the initial balance on Rhyan's gift card ($22.20) and the remaining balance after the sale ($1.90).
Simplifying the equation, we get:
4x = 20.3
Dividing both sides by 4, we get:
x = 5.075
So the price of one tire patch is $5.075.
Therefore, the equation "4x = 22.2 - 1.9" could be used to find the price of one tire patch. None of the other equations listed would lead to the correct answer.
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Answer:
yo
Step-by-step explanation:
C and E
The following table gives the frequency distribution of waiting
times (in minutes) for these customers.
The mean waiting time is:
The mean waiting time for these customers is 18.33 minutes.
The mean waiting time can be calculated by multiplying each waiting time by its frequency, summing up these products, and then dividing by the total number of customers.
In mathematical terms, the mean waiting time is:
Mean = (x1 * f1 + x2 * f2 + ... + xn * fn) / (f1 + f2 + ... + fn)
Where x1, x2, ..., xn are the waiting times, and f1, f2, ..., fn are the corresponding frequencies.
Using the data from the table, we can plug in the values and calculate the mean waiting time:
Mean = (5 * 2 + 10 * 4 + 15 * 6 + 20 * 8 + 25 * 10) / (2 + 4 + 6 + 8 + 10)
Mean = (10 + 40 + 90 + 160 + 250) / 30
Mean = 550 / 30
Mean = 18.33 minutes
Therefore, the mean waiting time for these customers is 18.33 minutes.
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Determine the value of the annuity for the indicated monthly deposit amount, the number of deposits, and the interest rate. You will need to determine the value for r to solve this problem. When finding r round to the nearest hundredth. Deposit amount: $100; total deposits: 120; interest rate: 10%, compounded semi-annually
The value οf the annuity after 120 depοsits is $1,059,780.64.
What is cοmpοund interest?Cοmpοund interest is interest that is earned nοt οnly οn the principal amοunt but alsο οn any interest earned οn that principal amοunt οver time.
Tο determine the value οf the annuity, we can use the fοrmula fοr the future value οf an annuity:
[tex]A = P \times \dfrac{(1 + r/n)^{(nt)} - 1)}{(r/n)}[/tex]
where A is the future value οf the annuity, P is the mοnthly depοsit amοunt, r is the annual interest rate, n is the number οf times the interest is cοmpοunded per year, and t is the tοtal number οf depοsits.
In this case, P = $100, n = 2 (since interest is cοmpοunded semi-annually), t = 120, and r is the interest rate per year, sο we need tο find r. Tο dο this, we can use the fοrmula:
[tex]A = P\times (1 + r/n)^{(nt)[/tex]
where A is the future value of the annuity after t depοsits.
Substituting the given vaIues, we have:
[tex]\$100 \times (1 + r/2)^{(2\cdot120)[/tex] = A
SimpIifying, we get:
[tex](1 + r/2)^{240} = A/100[/tex]
Taking the natural lοgarithm of both sides, we get:
[tex]ln(1 + r/2)^{240} = ln(A/100)[/tex]
240*ln(1 + r/2) = ln(A/100)
ln(1 + r/2) = ln(A/100)/240
Solving for r, we get:
[tex]$r = 2 \times \frac{e^{(ln(A/100)}}{240) - 1}[/tex]
Substituting the given vaIues, we get:
r = 0.4902 or 49.02%
Now we can plug in all the values into the original fοrmula for the future value οf the annuity:
[tex]A = $100\times \dfrac{(1 + 0.4902/2)^{(2\cdot 120) - 1)}}{0.4902/2}[/tex]
SimpIifying, we get:
A = $1,059,780.64
Therefοre, the value οf the annuity after 120 depοsits is $1,059,780.64.
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The game of Yahtzee is played with five fair dice. The goal is to roll certain hands', such as Yahtzee (all five dice showing the same number) or a full house (three of a kind and two of a kind). In the first round of a player's turn, the player rolls all five dice. Based on the outcome of that roll, the player has a second and third round, where he/she can then choose to re-roll any subset of the dice to get a desired hand. (a) What is the probability of rolling a Yahtzee on the first round? (b) Suppose that, on the second round, the dice are (2,3, 4,6,6). You decide to re-roll both sixes in the third round. What is the probability that you roll either a small straight or a large straight (a large straight is where all five dice are in a row)?
a) The probability of rolling a Yahtzee is 0.00077
b) The probability of rolling either a small straight or a large straight is 0.1389
Given data:
(a)
To calculate the probability of rolling a Yahtzee on the first round, we need to determine how many outcomes correspond to a Yahtzee and divide it by the total number of possible outcomes when rolling five dice.
A Yahtzee occurs when all five dice show the same number. There are 6 possible outcomes (each number from 1 to 6), and each outcome has only 1 way of occurring. So, there are 6 ways to roll a Yahtzee.
The total number of possible outcomes when rolling five dice is 6^5 (since each die has 6 sides).
Probability of rolling a Yahtzee = (Number of Yahtzee outcomes) / (Total number of outcomes)
[tex]= \frac{6} {6^5}[/tex]
≈ 0.00077 (rounded to 5 decimal places)
(b)
In the second round, you have (2, 3, 4, 6, 6). In the third round, you choose to re-roll both sixes.
A small straight is when you have four consecutive numbers among the dice (e.g., 1, 2, 3, 4, or 2, 3, 4, 5, or 3, 4, 5, 6).
There are three possible small straights: (2, 3, 4, 5), (3, 4, 5, 6), and (1, 2, 3, 4). Each of these outcomes has only one way of occurring.
A large straight is when all five dice are in a row (e.g., 1, 2, 3, 4, 5 or 2, 3, 4, 5, 6).
There are two possible large straights: (1, 2, 3, 4, 5) and (2, 3, 4, 5, 6). Each of these outcomes has only one way of occurring.
Total favorable outcomes (small straights + large straights) = 3 + 2 = 5
Total number of possible outcomes when re-rolling two dice = 6^2 = 36
Probability of rolling either a small straight or a large straight = (Number of favorable outcomes) / (Total number of outcomes)
[tex]=\frac{5}{36}[/tex]
≈ 0.1389 (rounded to 4 decimal places)
Hence, the probability that you roll either a small straight or a large straight after re-rolling the dice is approximately 0.1389.
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How long, to the nearest year, will it take an investment to
double if it is continuously compounded at 18% per year?
_______ yr
It will take 4 years for an investment to double if it is continuously compounded at 18% per year.
The time it takes for an investment to double if it is continuously compounded at 18% per year can be calculated using the formula:
T = ln(2)/r
Where T is the time in years, ln(2) is the natural logarithm of 2, and r is the annual interest rate.
Substituting the given values into the formula, we get:
T = ln(2)/0.18
T ≈ 3.85 years
Therefore, to the nearest year, it will take approximately 4 years for the investment to double if it is continuously compounded at 18% per year.
A neperian logarithm or also known as a natural logarithm, refers to that logarithm that has e as its base, which is worth: 2.718281828.
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6. Name each polyhedron that can be contructed using the following nets: a. b. A Squares c. Regular hexagon and isosceles triangles Square and equilateral triangle
a. The polyhedron that can be constructed using the net made of squares is a cube.
b. The polyhedron that can be constructed using the net made of squares is also a cube.
c. The polyhedron that can be constructed using the net made of a regular hexagon and isosceles triangles is a hexagonal pyramid.
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A bag with 10 marbles has 3 blue marbles and 7 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is red? Write your answer as a fraction in simplest form
The probability that the selected marble is red is 0
How to determine the probability that the marble is red?From the question, we have the following parameters that can be used in our computation:
Number of marbles = 10
Blue = 3
Yellow = 7
Using the above as a guide, we have the following:
P(Red) = Number of red/Number of marbles
Substitute the known values in the above equation, so, we have the following representation
P(Red) = 0/10
Evaluate
P(Red) = 0
Hence, the probability is 0
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Find the future value of this loan. $17,592 at 6.6% interest for
8 months
The future value of the loan is _______________
(Round to the nearest cent as needed.)
The future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.
To find the future value of this loan, we can use the formula FV = PV(1 + r)^t, where FV is the future value, PV is the present value, r is the interest rate, and t is the time period in years.
In this case, we have PV = $17,592, r = 6.6%, and t = 8 months or 0.667 years (8/12).
Plugging these values into the formula, we get:
FV = $17,592(1 + 0.066)^0.667
FV = $17,592(1.066)^0.667
FV = $18,358.16
Therefore, the future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.
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