Answer:
Step-by-step explanation:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
In this case, we know that P = $10,000, r = 6.5% = 0.065, and we want to find t when A = $29,500. We also know that the interest is compounded annually, so n = 1.
Substituting these values into the formula, we get:
$29,500 = $10,000(1 + 0.065/1)^(1t)
Dividing both sides by $10,000, we get:
2.95 = (1.065)^t
Taking the natural logarithm of both sides, we get:
ln(2.95) = ln(1.065)^t
Using the property of logarithms that ln(a^b) = b ln(a), we can rewrite the right side as:
ln(2.95) = t ln(1.065)
Dividing both sides by ln(1.065), we get:
t = ln(2.95)/ln(1.065) ≈ 18.2
Therefore, the person must leave the money in the bank for about 18.2 years to reach $29,500. To the nearest tenth of a year, the answer is 18.2 years.
find the following answer
The Venn diagram here shows the cardinality of each set. The cardinality of the n(A∩B∩C) is 6.
Describe Venn Diagram?Venn diagrams can be used to visually represent many different types of information, such as mathematical relationships, logical relationships, and sets of data. They are a useful tool for organizing and visualizing complex information.
A Venn diagram is a graphical representation of the relationships between different sets of objects. It consists of overlapping circles or other shapes that represent each set. The portions of the circles that overlap represent the objects that are in common to the corresponding sets.
Using the principle of inclusion-exclusion, we have:
n(A∩B∩C) = n(An) + n(B∩C) + n(C∩A) - 2n(A∩B) - 2n(B∩C) - 2n(C∩A) + 3n(A∩B∩C)
Substituting the given values, we get:
n(A∩B∩C) = 10 + 9 + 7 - 2(4) - 2(9) - 2(7) + 3(3) = 6
Therefore, n(A∩B∩C) = 6.
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6TH GRADE MATH, WRITE THE EQUATION FOR THIS GRAPH IN THE FORM OF Y=MX+B, TYSM
Answer:
m = 0
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0,2) (1,2)
We see the y stay the same and the x increase by 1, so the slope is
m = 0/1 = 0
So, the slope is 0
Consider g(x) = {a sin x + b, if x 2pi .
A. Find the values of a and b such that g(x) is a differentiable function.
B. Write the equation of the tangent line to g(x) at x = 2pi.
C. Use the tangent line equation from part B to write an approximation for the value of g(6).
Do not simplify
Answer:
A. For g(x) to be differentiable, the derivative of g(x) must exist at every point in its domain. The derivative of a sin x + b is a cos x, which exists for all values of x. Therefore, any values of a and b will make g(x) a differentiable function.
B. To find the equation of the tangent line to g(x) at x = 2π, we need to find the slope of the tangent line, which is the derivative of g(x) evaluated at x = 2π.
g'(x) = a cos x, so g'(2π) = a cos(2π) = a
Therefore, the slope of the tangent line at x = 2π is a. To find the y-intercept of the tangent line, we can plug in x = 2π into g(x) and subtract a times 2π:
y = g(2π) - a(2π)
= (a sin 2π + b) - a(2π)
= b - 2aπ
So the equation of the tangent line is:
y = ax + (b - 2aπ)
C. We can use the tangent line equation to approximate g(6) by plugging in x = 6 and using the equation of the tangent line at x = 2π.
First, we need to find the value of a. Since g'(2π) = a, we can use the derivative of g(x) to find a:
g'(x) = a cos x
g'(2π) = a cos (2π) = a
g'(x) = a = 2
Now, we can plug in a = 2, b = any value, and x = 2π into the tangent line equation:
y = ax + (b - 2aπ)
g(2π) = 2πa + (b - 2aπ)
a sin 6 + b ≈ 12π + (b - 4π)
Since we don't know the value of b, we can't find the exact value of g(6), but we can use the approximation:
g(6) ≈ 12π + (b - 4π)
5. Based on the data in the table below, what is the probability that a driver aged 45 - 54 was involved in an accident? Express your answer as a percentage, rounded to 2 decimal places.
As a result, the probability of a 45-54-year-old motorist becoming involved in an accident is 5.38%, rounded to two decimal places.
What exactly is probability?Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.
To determine the likelihood that a driver aged 45-54 was involved in an accident, divide the number of drivers in that age group who were engaged in an accident by the total number of drivers in that age group:
Probability = Number of 45-54-year-old drivers involved in an accident / Total number of 45-54-year-old drivers
We can observe that 7 drivers aged 45 to 54 were engaged in an accident, with a total of 130 drivers in that age group:
The probability is 7/130 = 0.0538.
To convert this to a percentage, multiply by 100:
Probability = 0.0538 * 100 = 5.38 percent
As a result, the likelihood of a 45-54-year-old motorist becoming involved in an accident is 5.38%, rounded to two decimal places.
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Write an equation of a parabola with x-intercepts at (-2, 0) and (-1,0)
and which passes through the point (-3, 20).
f(x) = -4(x + 7) is the equation for a parabola with x-intercepts at (1/4,0) and (-7,0) and a point of intersection of (0,7). (x - 0.25).
What is an equation?An equation is a mathematical statement containing two algebraic expressions flanked by equal signs (=) on either side.
It shows that the relationship between the left and right printed expressions is equal.
All formulas hav LHS = RHS (left side = right side).
You can solve equations to determine the values of unknown variables that represent unknown quantities.
If a statement does not have an equals sign, it is not an equation. A mathematical statement called an equation contains the symbol "equal to" between two expressions of equal value.
y = f(x) = A(x - a)(x - b)
We have -
a = 1/4
b = -7
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3 and below, then the player will lose 3 times the number that turns up.
The rule of a single-die game states that "If the number that turns up is
However, if the number that turns up is 4 and above, then the player will
gain 4 times the number that turns up." Marvin tosses a 5, then a 2, and
4. Did he win or lose the game? By how many points?
Marvin won the game by 30 points.
How to calculate the won ponits?Marvin tossed three times and got the following numbers: 5, 2, 4.
For the first toss, he tossed a 5, which is 4 or above, so he gains 4 times the number that turns up. Therefore, he gains:
4 x 5 = 20
For the second toss, he tossed a 2, which is below 3, so he loses 3 times the number that turns up. Therefore, he loses:
3 x 2 = 6
For the third toss, he tossed a 4, which is 4 or above, so he gains 4 times the number that turns up. Therefore, he gains:
4 x 4 = 16
To find out whether Marvin won or lost the game, we need to add up his gains and losses.
His total gain is:
20 + 16 = 36
His total loss is:
6
Therefore, his net gain is:
36 - 6 = 30
Marvin won the game by 30 points.
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On a certain weekday, the rate at which vehicles cross a bridge is modeled by the differentiable function R for 0 ≤ t ≤ 12, where R(t) is measured in vehicles per hour and t is the number of hours since 7:00 a.m. (t = 0). Values of R(t) for selected values of t are given in the table above.
The approximate value of R'(5) is -716 vehicles per hour per hour.
To approximate Rʹ(5), we can use the formula for the average rate of change
Rʹ(5) ≈ (R(6) - R(4))/(6-4)
We use the values given in the table to get
R(6) = 3010 vehicles per hour
R(4) = 3442 vehicles per hour
Therefore, Rʹ(5) ≈ (3010 - 3442)/(6-4) = -716 vehicles per hour per hour.
So, the approximate rate of change of the rate at which vehicles cross the bridge at 5:00 a.m. is -716 vehicles per hour per hour. This means that the rate at which vehicles cross the bridge is decreasing at a rate of 716 vehicles per hour every hour around 5:00 a.m.
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The given question is incomplete, the complete question is:
On a certain weekday, the rate at which vehicles cross a bridge is modeled by the differentiable function R for 0 ≤ t ≤ 12, where R(t) is measured in vehicles per hour and t is the number of hours since 7:00 a.m. (t = 0). Values of R(t) for selected values of t are given in the table above. t(hours) 0 2 4 6 8 10 12 R(t) (vehicle per hours ) 2935 3653 3442 3010 3604 1986 2201 . Use the data in the table to approximate Rʹ(5)
Pls help, due tmr and confused..
The nearest whole number, which is 9. So the middle apartment number for house 17 is 9.
What is apartment?An apartment is a self-contained housing unit that occupies only part of a building. Apartments typically consist of one or more bedrooms, a kitchen, a living room, and a bathroom, and usually include amenities such as heating, air conditioning, and appliances. Apartments are usually rented, though some are owned. Living in an apartment can be a great way to save money, as apartments are often more affordable than larger homes.
The rule is to take the house number and divide it by two and round up to the nearest whole number. This will give the middle apartment number. For example, if the house number is 17, divide it by two which equals 8.5, and then round up to the nearest whole number, which is 9. So the middle apartment number for house 17 is 9.
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The graph represents a relation where x represents the independent variable and y represents the dependent variable. a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1 Is the relation a function? Explain. No, because for each input there is not exactly one output. No, because for each output there is not exactly one input. Yes, because for each input there is exactly one output. Yes, because for each output there is exactly one input.
No, the relation is not a function, because for each input there is not exactly one output.
What is graph?A graph is a visual representation of data that shows the relationship between variables or sets of data. It consists of a set of points, called vertices or nodes, which are connected by lines or curves, called edges or arcs. Graphs are commonly used to display numerical information, such as trends, patterns, or relationships, and can be used to analyze and interpret data.
The relation is not a function because for the input x = -1, there are two different output values, y = 3 and y = -2. A function is a relation where each input has exactly one output, but in this case, the input -1 has two different outputs, violating the definition of a function.
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HELP ME ASAP ITS DUE TODAY! YOU WiLL BE MARKED BRAINLIEST IF YOU EXPLAIN AND SOLVE THE QUESTION!
For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal? А. A random sample of 8 taken from a normally distributed population B. A random sample of 50 taken from a normally distributed population C. A random sample of 10 taken from a population dintribution that is skewed to the right D. A random sample of 75 taken from a population distribution that is skewed to the left E. A random sample of 100 taken from a population that is uniform
The conditions in which is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal : (C) A random sample of 10 taken from a population distribution that is skewed to the right.
In statistics, the normal or Gaussian distribution is a continuous probability distribution for real-valued random variables.
The normal distribution is important in statistics and is often used in the natural and social sciences to represent real-valued random variables whose distribution is unknown. Their importance is partly due to the central limit theorem. It states that in some cases the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable - whose distribution converges to a normal distribution as the size of the l sample increases.
Now,
If we look at the options given below, we see that the random samples in options A and B are normally distributed, so their sample means will be approximately normally distributed.
Similarly, option E indicates that the population is uniform, so the sample mean will also be approximately normal.
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Find the poles for the s-domain function F(s) = 80(s+3)/s(s+2)^2 Express your answers in radians per second to three significant figures. Enter your answers in ascending numerical order separated by commas.
The poles of the function F(s) are -2 and 0, both of which are real and negative. Therefore, the poles can be expressed in radians per second as -2.000 and 0.000.
To find the poles of the function F(s), we need to find the values of s that make the denominator equal to zero. So we need to solve the equation:
s(s+2)² = 0
The solutions to this equation are:
s = 0 (double pole)
s = -2 (double pole)
Therefore, the poles of the function F(s) are -2 and 0, both of which are real and negative. So the poles can be expressed in radians per second as:
-2.000
0.000
(Note that the poles are not specified in units of radians per second, but the values are the same whether or not we include the units.)
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determine the amount of mass possessed by the blue mass. show your data and explain your reasoning or show the math
Since I added three 4 kg weights and one 1 kg weight to the left side of the fulcrum, the blue mass is 13 kg and is completely balanced. In light of this, the blue mass's mass is 13 kg.
To keep the beam horizontal for a beam balance, a body with gravitational mass m1 and a standard weight of m2 are placed in the left and right pans, respectively. If a1 = a2, then m1 = m2, and vice versa. Alternatively, the gravitational mass of the body in the left pan is equal to the gravitational mass in the right pan.
For calibrating masses between 13 mg and 4+1 = 5 kg, a beam balance is utilised. Depending on the calibre and sharpness of the knife edge used to make the pivot, a given measurement can be made with a given resolution and accuracy.
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The actual question is :
Determine the amount of mass possessed by the blue mass. Show your data and explainyour reasoning or show the math. The amount of the blue mass is 13 kg since I placed three 4 kg and 1 kg on the left side of the fulcrum and it is completely balance . Therefore the mass possessed by the blue mass is 13 kg .
solve please and thank you it’ll help a lot. 15 points.
Parallelogram (Opposite sides have the same length). Parallelogram (Area is one-half the base times the height). Parallelogram (Opposite sides are parallel). Parallelogram (Angles can be right angles)
What is the assertion of the parallelogram?According to the parallelogram law, the sum of the squares of a parallelogram's four sides is equal to the sum of the squares of its two diagonals. It is essential for the parallelogram to have equal opposite sides in Euclidean geometry.
Are a parallelogram's opposing sides parallel?A parallelogram is a particular sort of polygon. It is a quadrilateral in which the opposite side pairs are parallel to one another. There are six crucial parallelogram characteristics to be aware of: Congruent sides are those when AB = DC.
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Find the missing length indicated
The calculated value of the indicated missing length x in the right triangle is 12
How to determine the value of the indicated missing lengthGiven the right triangle
We can start by calculating the value of x using the following equivalent ratio
x : 9 = 25 - 9 : x
Evaluate the difference
This gives
x : 9 = 16 : x
Next, we express the equivalent ratio as a fraction
So, the ratio becomes
x/9 = 16/x
Cross multiply the equation to calculate x
So, we have the following
x * x = 9 * 16
Evaluate the product
x² = 144
Take the square root of both sides
So, we have the solution to be
y = 12
Hence, the value of x is 12
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A pyrotechnician is running a test for a fireworks display he is providing for an event downtown. He launches a test shell from the top of a tower. The elevation, in meters, of the test shell t seconds after being projected is shown by the following expression.
Look at the picture attached and then choose your answer pls!
Select the best description of the term 29.4 in the expression.
A. the total time the test shell is in the air
B. the initial velocity of the test shell
C. the highest elevation the test shell reaches
D. the initial elevation of the test shell
The best description of that term 29.4 in the expression is the initial velocity of the test shell. That is option B.
Who is a pyrotechnician?A pyrotechnician is defined as the individual that has been trained for safe storage, handling, and functioning of pyrotechnics such as fireworks.
While testing the display of the fireworks, he took note of the following:
The elevation in meters
The time in seconds
The change in velocity should be noted as the velocity of distance covered by a moving object with time.
Therefore, the term 29.4 is the initial velocity of the fireworks he projected.
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Triangle ABC is similar to triangle DEF. What is AC?
Answer:
i think side AC is 14 because if you do subtract BC (18) from EF(12) you get 6, so u add 6 to DF(8) and get 14.
if its confusing ask me questions!!
Answer:
12
Step-by-step explanation:
When triangles are similar, their side ratios are the same. The ratio of EF to BC is 18/12, or 3/2. To find the side AC, we would multiply the corresponding part of DEF by 3/2, the same ratio. The corresponding part of DEF would be DF. DF = 8. 8 times 3/2 is 12. So AC is 12.
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state the third congruence statement that is needed to prove that FGH is congruent to LMN using the ASA congruence therom
Answer:
a
Step-by-step explanation:
Question Id: 467224
1
of a pound. Sylvia's dad bought 8 bags of potatoes at the store for a big family Thanksgiving meal. How many pounds c
A bag of potatoes weighs
potatoes did Sylvia's dad buy?
4x A
X
X
B
2
pounds
4 pounds
C 4 pounds
4 of 10
√x D 3 pounds
Sylvia's dad bought [tex]2\frac{2}{3}[/tex] pounds of potatoes for the thanksgiving meal using division and multiplication.
What is division?One of the four fundamental mathematical processes, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal amount of items. It is a mathematical procedure used for equal distribution and equal grouping. Repetitive subtraction is the procedure of division. It is the multiplying operation's opposite. It is described as the process of creating equitable organizations. When dividing numbers, we break a bigger number down into smaller ones so that the larger number taken will be equal to the multiplication of the smaller numbers.
In this question,
1 bag of potatoes= 1/3 pounds
8 bags of potatoes= 8* 1/3
=8/3
= [tex]2\frac{2}{3}[/tex] pounds
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pls help with this question
Answer:
4/3 or d
Step-by-step explanation:
y 2x 3x y The diagram shows a trapezium. All the lengths are in centimetres. The perimeter of the trapezium is P cm. Find a formula, in terms of x and y, for P. Give your answer in its simplest form.
To find:-
The perimeter of the trapezium.Answer :-
Perimeter: Perimeter is simply the sum of all the side lengths of a figure. Here it is a trapezium so the perimeter would be the sum of all the four sides.
According to the given question , the expressions of the side lengths are , 2x , y , 3x and y .
So the perimeter would be the sum of these four expressions as ,
P = 2x + y + 3x + y
Group like terms ,
P = 2x + 3x + y + y
Add like terms ,
P = 5x + 2y
Also the unit here is centimetres, so the perimeter would be (5x + 2y)cm .
Therefore, the required formula for perimeter is ,
P = (5x + 2y) cm
and we are done!
Answer:
[tex]P=(5x+2y)\; \sf cm[/tex]
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, the perimeter of a trapezium is the sum of its side lengths.
From inspection of the given diagram, the side lengths of the trapezium are:
2x cmy cm3x cmy cmTherefore, the formula for its perimeter, P, in terms of x and y is:
[tex]\implies P=2x+y+3x+y[/tex]
Simplify by collecting like terms:
[tex]\begin{aligned}\implies P&=2x+y+3x+y\\&=2x+3x+y+y\\&=5x+2y\\\end{aligned}[/tex]
Therefore, the formula, in terms of x and y, for P in its simplest form is:
[tex]P=(5x+2y)\; \sf cm[/tex]
123, 185, 143, 137, 192, 185, 129, 143, 154, 165, 143, 138, 187, 176
A bin size ofis most appropriate for the data shown above.
A. 69 B. 2 C. 10 D. 1
The answer of the given question based on statistics to find the most appropriate size of the bin from the data the answer is , the most appropriate bin size for this data set would be A. 69.
What is Statistics?Statistics is the practice of collecting, analyzing, and interpreting the data. It involves use of mathematical tools and techniques to gather insights and knowledge from numerical and categorical information. Statistics is essential in many fields, like business, medicine, social sciences, and engineering, as it enables researchers to draw conclusions from data and make informed decisions based on evidence.
It includes topics like probability, hypothesis testing, regression analysis, and data visualization. The application of statistical methods can help identify patterns, relationships, and trends in data, allowing researchers to make predictions and solve problems.
To determine the appropriate bin size, we need to consider the range of values in the data. The range is the difference between the largest and smallest values, which in this case is 192 - 123 = 69.
To get the bin size, we divide the range by the number of bins. So the bin size would be 69/4 = 17.25. However, since we can't have a fraction of a unit for bin size, we should round up to the nearest whole number. Therefore, the most appropriate bin size for this data set would be A. 69.
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The answer of the given question based on statistics to find the most appropriate size of the bin from the data the answer is , the most appropriate bin size for this data set would be A. 69.
What is Statistics?Statistics is the practice of collecting, analyzing, and interpreting the data. It involves use of mathematical tools and techniques to gather insights and knowledge from numerical and categorical information. Statistics is essential in many fields, like business, medicine, social sciences, and engineering, as it enables researchers to draw conclusions from data and make informed decisions based on evidence.
It includes topics like probability, hypothesis testing, regression analysis, and data visualization. The application of statistical methods can help identify patterns, relationships, and trends in data, allowing researchers to make predictions and solve problems.
To determine the appropriate bin size, we need to consider the range of values in the data. The range is the difference between the largest and smallest values, which in this case is 192 - 123 = 69.
To get the bin size, we divide the range by the number of bins. So the bin size would be 69/4 = 17.25. However, since we can't have a fraction of a unit for bin size, we should round up to the nearest whole number. Therefore, the most appropriate bin size for this data set would be A. 69.
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The complete question is as fpllows:
123, 185, 143, 137, 192, 185, 129, 143, 154, 165, 143, 138, 187, 176
A bin size of is most appropriate for the data shown above.
A. 69
B. 2
C. 10
D. 1
ZOO The graph shows the number of visitors at the 200 during different hours of one day.
a. Find the rate of change in the number of visitors between 10 A.M, and 12.P.M. and describe its meaning in the context of the situation.
b. Find the rate of change in the number of visitors-between 1 P.M. and 2 P.M. and describe its meaning in the context of the situation.
A. the rate of change in the number of visitors between 10 A.M. and 12 P.M. is 200, which means that the number of visitors increased by 200 within those two hours.
What is visitors ?Visitors are people who come to a place for a short period of time. They may come for leisure, business, education, or to visit family or friends. Visiting a place can bring economic, educational, cultural, and social benefits to the host community. It can create jobs, bring in new ideas, and offer opportunities to learn about other cultures. Visitors can also bring new perspectives and experiences, which can lead to more understanding between cultures and help to strengthen relationships.
b. The rate of change in the number of visitors between 1 P.M. and 2 P.M. is 100, which means that the number of visitors increased by 100 within this hour. This indicates that the number of visitors at the zoo is still increasing but at a slower rate.
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Aubrey decides to estimate the volume of a coffee cup by modeling it as a right cylinder. She measures its height as 8.3 cm and its circumference as 14.9 cm. Find the volume of the cup in cubic centimeters
The estimated volume of the coffee cup is approximately 152.8 cubic centimeters.
What is circumference?It is the perimeter of the circle, which can be found by multiplying the diameter of the circle by pi (π), a mathematical constant that is approximately equal to 3.14.
According to question:The volume of a right cylinder is:
V = πr²h
We are given the height of the coffee cup as h = 8.3 cm. To find the radius,
C = 2πr
We are given the circumference of the coffee cup as C = 14.9 cm. Solving for r, we have:
14.9 = 2πr
r = 14.9 / (2π) ≈ 2.372 cm
Now we can substitute these values into the formula for the volume of a cylinder:
V = πr²h
V = π(2.372)²(8.3)
V ≈ 152.8 cubic centimeters
Therefore, the estimated volume of the coffee cup is approximately 152.8 cubic centimeters.
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The tread life (x) of tires follow normal distribution with µ = 60,000 and σ = 6000 miles. The manufacturer guarantees the tread life for the first 52,000 miles.
(i) What proportion of tires last at least 55,000 miles?
(ii) What proportion of the tires will need to be replaced under warranty?
(iii) If you buy 36 tires, what is the probability that the average life of your 36 tires will exceed 61,000?
(iv) The manufacturer is willing to replace only 3% of its tires under a warranty program involving tread life. Find the tread life covered under the warranty.
In linear equation, 48720 is the tread life covered under the warranty.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
1) µ = 60,000 and σ = 6000 miles.
P ( X >= 55000 ) = 1 - P ( X < 55000 )
Standardizing the value
Z = ( X - μ)/σ
Z = ( 55000 - 60000 ) / 6000
Z = -0.83
P((X - μ)/σ > ( 55000 - 60000)/6000
P ( Z > -0.83 )
P ( X >= 55000 ) = 1 - P ( Z < -0.83 )
P ( X >= 55000 ) = 1 - 0.2033
P ( X >= 55000 ) = 0.7967
Part v) What proportion of the tires will need to be replaced under warranty?
X ~ N ( μ = 60000 , σ = 6000 )
P ( X < 52000 )
Standardizing the value
Z = ( X - μ)/σ
Z = ( 52000 - 60000 ) / 6000
Z = -1.33
P((X - μ)/σ > ( 55000 - 60000)/6000
P ( X < 52000 ) = P ( Z < -1.33 )
P ( X < 52000 ) = 0.0918
Part c) If you buy 36 tires, what is the probability that the average life of your 36 tires will exceed 61,000?
X ~ N ( μ = 60000 , σ = 6000 )
P ( X > 61000 ) = 1 - P ( X < 61000 )
Standardizing the value
Z = ( X - μ)/(σ/√n)
Z = (61000 - 60000)/(6000/√36)
Z = 1
P(( X - μ)/(σ/√n) > (61000 - 60000)/(6000/√36)
P ( Z > 1 )
P ( X > 61000 ) = 1 - P ( Z < 1 )
P ( X > 61000 ) = 1 - 0.8413
P ( X > 61000 ) = 0.1587
Part d) The manufacturer is willing to replace only 3% of its tires under a warranty program involving tread life. Find the tread life covered under the warranty.
P ( Z < ? ) = 3% = 0.03
Looking for the probability 0.03 in standard normal table to find the critical value Z
Z = - 1.88
Z = (X - μ)/σ
- 1.88 = ( X - 60000)/6000
X = 48720
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What comes next in pattern
167,118,82,57,41,?
Answer: 32
Step-by-step explanation: got you broski
PLEASE HELP! 15 POINTS!!
Answer:
We can use similar triangles to solve this problem. Let's denote the height of the tree as h. Then, we can set up the following proportion:
h / 120 = 6 / 10
Cross-multiplying and simplifying, we get:
10h = 720
h = 72
Therefore, the height of the tree is 72 feet
Pls help me answer the questions thank you
A. The capacity of most of the trimmer Sara sells is [tex]1\tfrac{1}{5}[/tex]
B. The total gas she needs to fill all trimmers is [tex]$22 \frac{7}{8}[/tex]
What is the use οf expressiοns in mathematics?Expressiοns are used extensively in mathematics, including arithmetic, calculus, and geοmetry. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.
Part A
The capacity of most of the trimmer Sara sells is [tex]1\tfrac{1}{5}[/tex]
Part B
The total gas she needs to fill all trimmers is:
[tex]$\Rightarrow (1 \times 1\frac{1}{2}) + (5 \times 1\frac{5}{8}) + (1 \times 1\frac{7}{8} )+ (3 \times 2\frac{1}{8} ) + (2 \times 2\frac{1}{2} )[/tex]
⇒ [tex]$22 \frac{7}{8}[/tex]
Thus, The total gas she needs to fill all trimmers is [tex]$22 \frac{7}{8}[/tex]
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Determine the following standard normal (z) curve areas. (Round all answers to four decimal places.)
(a) The area under the z curve to the left of 1.73
(b) The area under the z curve to the left of
−0.69
(c) The area under the z curve to the right of 1.3
(d) The area under the z curve to the right of
−2.82
(e) The area under the z curve between −2.22 and 0.52
(f) The area under the z curve between
−1
and 1
(g) The area under the z curve between
−4
and 4
(a) The area under the standard normal curve to the left of 1.73 is 0.9582.
(b) The area under the standard normal curve to the left of -0.69 is 0.2454.
(c) The area under the standard normal curve to the right of 1.3 is 0.0968.
(d) The area under the standard normal curve to the right of -2.82 is 0.9974.
(e) The area under the standard normal curve between -2.22 and 0.52 is 0.6851.
(f) The area under the standard normal curve between -1 and 1 is 0.6826.
(g) The area under the standard normal curve between -4 and 4 is 0.9998.
(a) Using a standard normal table, the area under the standard normal curve to the left of 1.73 is 0.9582.
(b) Similarly, the area under the standard normal curve to the left of -0.69 is 0.2454.
(c) The area to the right of 1.3 is the same as the area to the left of -1.3. Using a standard normal table, this area is 0.0968.
(d) The area to the right of -2.82 is the same as the area to the left of 2.82. Using a standard normal table, this area is 0.9974.
(e) To find the area under the standard normal curve between -2.22 and 0.52, we need to find the area to the left of 0.52 and subtract the area to the left of -2.22. Using a standard normal table, we find that the area to the left of 0.52 is 0.6990 and the area to the left of -2.22 is 0.0139. Therefore, the area between -2.22 and 0.52 is 0.6990 - 0.0139 = 0.6851.
(f) To find the area under the standard normal curve between -1 and 1, we need to find the area to the left of 1 and subtract the area to the left of -1. Using a standard normal table, we find that the area to the left of 1 is 0.8413 and the area to the left of -1 is 0.1587. Therefore, the area between -1 and 1 is 0.8413 - 0.1587 = 0.6826.
(g) The area under the standard normal curve between -4 and 4 is the same as the area to the left of 4 minus the area to the left of -4. Using a standard normal table, we find that the area to the left of 4 is 0.9999 and the area to the left of -4 is 0.0001. Therefore, the area between -4 and 4 is 0.9999 - 0.0001 = 0.9998.
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Graph the image of R(-2,1) after a reflection over the x-axis
The image of R after a reflection over the x-axis is the point S(-2, -1).
To reflect a point over the x-axis, we simply negate its y-coordinate while keeping its x-coordinate the same.
Starting with point R(-2, 1):
The x-coordinate remains the same: -2
The y-coordinate is negated: -1
So the image of R after a reflection over the x-axis is the point S(-2, -1).
To graph the reflection, we can plot the original point R and then draw a dashed line to represent the x-axis. Finally, we can plot the reflected point S on the other side of the x-axis.
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