According to the empirical law of statistics, 99.7% of the males are between 54.5" and 81.5" tall.
What is empirical rule?The 68-95-99.7 rule, also known as the empirical rule, indicates where most of the values in a normal distribution are distributed: The majority of values—about 68%—fall within the range of the mean. The average value is within two standard deviations for about 95% of the data. Almost all values, 99.7% of them, fall within a 3 standard deviation range.
Here,
mean=68 inch
standard deviation=4.5 inch
The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.
68−4.5=63.5
68+4.5=72.5
The range of numbers is 63.5 to 72.5
The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.
68−2⋅4.5=59
68+2⋅4.5=77
The range of numbers is 59 to 77
Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.
68−3⋅4.5=54.5
68+3⋅4.5=81.5
The range of numbers is 54.5 to 81.5
99.7% of the boys are between 54. 5 and 81. 5 inches tall using the empirical rule of statistics.
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Olivia has has read 40 pages of a 70 page book, 60 pages of an 85 page book, and 43 pages. What is the percentage f pages that Olivia has not read?
Answer:
Below
Step-by-step explanation:
Total pages read = 40 + 60 +43 = 143 pages read
Total pages of all of the books = 70 + 85 + x
percentage READ = (143) / ( 70 + 85 + x) * 100% = ???
percentage NOT read = 100 - ???
(since 'x' was not given in the question post)
Read pages:
40+60+43=143
All pages:
70+85+43=198
198-143=55
55/198=0,2778
0,2778×100%=27.78%
What is the average rate of change of the function f(x)=2(3)xfrom x = 2 to x = 4?.
The average rate of change of the function f(x)=2(3)x from x = 2 to x = 4 = 72
How do functions work?The term "function" refers to the relationship between a collection of inputs and outputs with one each. Simply described, a function is an association of inputs where each input is coupled with exactly one output. Every function has an associated domain, codomain, or range. The most common way to represent a function is as f(x), where x represents the input.
To calculate the average rate of change, use the slope formula:
y2−y1/x2−x1=m
f(4)−f(2)/4−2=m
Finding the values of f(4) and f(2) will help us to simplify this.
f(4)=2(3)4=2(81)=162
f(2)=2(3)2=2(9)=18
m=162−18/2
m=144/2
m=72
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Danni placed $5700 in a savings account which compounds interest continuously at a rate of 2. 1%. How much will she have in the account after 4 years? round your answer to the nearest whole number. Do not include a $ in your answer.
Using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
Compound interest works by periodically adding collected interest to your main, which is the sum you first deposited into the savings account so that interest can then be earned on both.
In essence, your interest begins to generate interest of its own.
Compound interest formula: [tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]
Now, calculate the amount Danni will have after 4 years:
[tex]A=P\left(1+\frac{r}{100}\right)^{n t}[/tex]
A = 5700(1+0.021)⁴
A = 5700(1.0210⁴
A = $6,194.09
Therefore, using the compound interest method, we can calculate that Danni will have $6,194.09 in her account after 4 years.
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Answer:
A=6199.48
Step-by-step explanation:
Use the formula for calculating compound interest A=P0ert where A is the unknown, P0=5700, r=0.021, and t=4. Substitute the values into the formula and simplify.
A=5700e0.021⋅4
A=5700e0.084
A=5700(1.0876...)
A=6199.48
The amount in the account after four years is A≈6199, to the nearest dollar.
New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.
a) Create a probability model for this game.
b) Find the expected value and standard deviation of your prospective winnings.
c) You play this game five times. Find the expected value and standard deviation of your average winnings.
d) 100 people play this game. What's the probability the person running the game makes a profit?
a) Probability model
P(40) = 1/6
P(0) = 5/36
P(-10) = 25/36
b) E(X) = -5/18
standard deviation = 18.331
c) standard deviation = 91.65
d) Probability = 0.560
From the question, we have
a) X = -10, 0 or 40 for your winnings (or losses). The corresponding probabilities are:
P(40) = 1/6
P(0) = (5/6)(1/6) = 5/36
P(-10) = 1 - 1/6 - 5/36 = 25/36
b) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18
E(X^2) = (100)(25/36) + 1600(1/6) = 3025 / 9
Var(X) = E(X^2) - [E(X)]^2 = 3025 / 9 - (-5/18)^2 = 108875 / 324
standard deviation = sqrt [Var X] = 119043 / 6494 =18.331
c) E(X) = (-10)(25/36) + 0(5/36) + 40(1/6) = -5/18
5 * E(X) = - 25/18
standard deviation = 5 * 18.331 = 91.65
d) Probability :
P(X < 0) = P{ z < [0 - (-5/18)] / [(119043 / 6494) / sqrt 100] } = P(z < 0.1515) = 0.560
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
Complete question:
From the Data at Hand to the World at Large 4. New game You pay $10 and roll a die. If you get a 6, you win $50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What's the probability the person running the game makes a profit?
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Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap. Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? (round off your answer to four decimal digits)
The time taken for Bob take to run one lap of the track is 69 seconds
Akira is running around a circular track. Akira runs counterclockwise.
It takes him 95 seconds to run one complete lap
Bob starts running at the same time as Akira
Bob and Akira pass each other for the first time after 26 seconds
It takes him 95 seconds to run one complete lap
In 26 seconds he covers 26/95 laps
In this time Bob must have covered 69/95 laps
An inverse relationship
c/95 = 69/95
c = (69/95) x 95
c = 69
Therefore, time taken for Bob take to run one lap of the track is 69 seconds.
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At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident. a) What is the probability that you will have to deal with no more than 4 incidents of identity theft in the next year (52 weeks)? b) When you have had 12 more incidents of identity theft, your company will send a detective to investigate. What are the expected value and variance of the time (in weeks) until a detective is sent to investigate? c) Use normal approximation to find the probability that the detective will be sent within 2 years.
Answer: At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident.
Step-by-step explanation:
A double recipe of cookies calls for 5 cups of flour.
Which of the following proportions could be used to find the amount of flour for a triple recipe?
3/2 = 5/f
5/2= f/3
2/3 = f/5
2/5 = f/3
Answer:
You could divide 5 in half and then add that to the five to find the amount of flour to use in a triple recipe. Hope this helps.
Step-by-step explanation:
Clingman Dome, in the Great Smoky Mountains, is the highest point in Tennessee.
Clingman Dome is 6,643 feet above sea level. Use the information to answer questions 4-5.
a) Considering the scale factor, the height that she should build the model is of: 22.1 inches.
b) Essence has enough information to build the accurate scale model, as she needs only the scale and either the actual or the drawn model.
What are scales?An scale is defined as the relation between the actual length of a segment and the length of drawn segment, as follows:
Scale = Actual length/drawn length
The scale for this problem is given as follows:
Scale factor = 300 ft/1 in.
Which means that each inch on the drawing represents an actual height of 300 ft.
The height of the Clingman Dome is given as follows:
6,643 feet.
Considering the scale factor of 300 ft/1 in, the height of the drawing is obtained as follows:
6643/300 = 22.1 inches.
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Given AB, find C which is 1/3 of the distance from A to B. A(1,2) B(-5,8)
Answer: (2,0)
Step-by-step explanation:
Find the distance from line L to point P for each of the following: Line L contains points (-5,3) and (4,-6). Point P(2,4)
Answer and explanation in one:
(4+9)/(-2-1) = 13/-3 = -13/3
y=-13x/3 + b
4=26/3 + b
b = 4-26/3 = (12-26)/3 = -14/3
y=-13x/3 -14/3 is the line through the two given points
find the line perpendicular and through (14,-6)
y=3x/13 + b, plug in the point to find b
-6 = 3(14)/13 + b
b = -6 -42/13 = -78/13 - 42/13 = -120/3
y= 3x/13 - 120/13
find the intersection point of the two lines, set them equal
3x/13 -120/13 = -13x/3 - 14/3
multiply by 39
9x - 360 = -169x - 182
178x = 360-182 = 178
x = 1
y= -27/3=-9
the point is (1,-9)
calculate the distance from (1,-9) to (14,-6)
d^2 = 9+169 = 178
d = sqr178 = about 13.34
An initial population of 20 fish is introduced into a lake. This fish population grows according to a continuous exponential growth model. There are 52 fish in the
lake after 7 years.
I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $96 for the project. What are the dimensions of the vegetable patch with the largest area i can enclose?.
The dimensions of the vegetable patch with the largest area we can enclose are
length = 12 feet and breadth = 6 feet.
Given, a rectangular vegetable patch.
The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot.
We have a budget of $96 for the project.
Let the length of the rectangle be, l
and breadth of the rectangle be, b
according to the ques,
4l + 8b = 96
l + 2b = 24
l = 24 - 2b
Now, area of the rectangle be,
Area = length×breadth
Area = l×b
A = (24 - 2b)b
A = 24b - 2b²
On differentiating both sides, we get
A' = 24 - 4b
b = 6
l = 24 - 12 = 12
So, the dimensions of the vegetable patch with the largest area we can enclose are
length = 12 feet and breadth = 6 feet.
Hence, The dimensions of the vegetable patch with the largest area we can enclose are
length = 12 feet and breadth = 6 feet.
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A pizza shop needs 5 ounces of cheese and 3 ounces of sauce to make one pizza. after 4 hours of being open one evening, the pizza shop has used 192 ounces combined of sauce and cheese. how many pizzas were made so far that evening?
The total number of pizzas were made in 4 hour in pizza shop is 24.
Describe the term unitary method?The unitary approach involves calculating the value of an individual unit, from which we can calculate the values of the necessary number of units. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a separate unit.For the stated question-
For one pizza-
Ounce of cheese required = 5.
Ounces of sauce required = 3.
Total requirement = 8 ounces.
After 4 hours,
Total ounces combined of sauce and cheese used = 192.
Thus,
Number of pizza = 192 / 8
Number of pizza = 24
Thus, the total number of pizzas were made in 4 hour in pizza shop is 24.
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Graph the equation.
y = x
Answer:
Slope: 1
__________
y-intercept: (0,0)
Step-by-step explanation:
The equation of a line is 2y = 8x + 10
find the SLOPE of a line that is
a) parallel to the line
b) perpendicular to the line
c) neither parallel or perpendicular
Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2075x.
What is an expression that represents the total amount that Zoe paid?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information, Zoe goes to a restaurant and the subtotal on the bill was x dollars. A tax of 5% is applied to the bill and Zoe decides to leave a tip of 15% on the entire bill.
The expression will be:
= x + (5% × x) + (15% × 1.05x)
= x + 0.05x + 0.1575x
= 1.2075x
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3) A class of 168 students went on a field
trip. They took 6 vehicles, some vans and
some buses. Find the number of vans and
the number of buses they took if each van
holds 6 students and each bus hold 50
students.
Answer:
They took 3 vans and 3 buses.
Step-by-step explanation:
Given:
The number of students in the class = 168The number of vans and buses = 6The number of students each van can hold = 6The number of students each bus can hold = 5To find:
The number of vans and the number of buses they took.
Explanation:
Let the number of vans = v
Let the number of buses = b
The total number of vans and buses is 6:
[tex]v+b=6[/tex]
⇒[tex]v=6-b....[/tex]Equation(1)
Each van holds 6 students and each bus hold 50 students.
The number of students on the trip is 168.
[tex]6v+50b=168[/tex]....Equation(2)
Substitute equation (1) into equation (2):
[tex]6v+50b=168[/tex]
[tex]6(6-b)+50b=168[/tex]
Then solve the equation for b:
[tex]36-6b+50b=168[/tex]
[tex]44b=168-36[/tex]
[tex]44b=132[/tex]
[tex]\frac{44b}{44}=\frac{132}{44}[/tex]
[tex]b=3[/tex]
Then, solve for v:
[tex]v=6-b=6-3=3[/tex]
Answer:
They took 3 vans and 3 buses.
PLS HELP ASAP!!!! 50 PTS
Answer: x=4
Step-by-step explanation:
6x + 10 = 5x + 14
x + 10 = 14
x = 4
Francisco is building a window seat below a bay window in the shape of an isosceles trapezoid. His blueprint for the window seat is shown below.
What is the area of the window seat?
Answer:
56
Step-by-step explanation:
Which set of ordered pairs (x, y) could represent a linear function
A = \{(1, - 2), (3, 1), (5, 4), (8, 7)\}
B = \{(- 6, 6), (- 3, 3), (0, 0), (3, - 4)\}
C = \{(- 2, 8), (- 1, 6), (0, 4), (2, 1)\}
D = \{(- 8, 6), (- 4, 3), (0, 0), (4, - 3)\}
{(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Linear function is a function whose graph is a straight line
Slope of a line tells us how steep the line is . Slope of a line is same at all the points.
For option A:
m=1+2/3-1=3/2
m=3/2
m=7-4/8-5=3/3=1
Slopes are not same
For option B:
m=3-6/-3+6=-3/3=-1
m=0-3/0+3=-1
m=-4/3
Slopes are not same
For option C:
m=6-8/-1+2=-2
m=4-6/1=-2
m=-3/2
Slopes are not same
For option D:
m=3-6/-4+8=-3/4
m=-3/4
m=-3/4
Slopes are same at every point, so this set of ordered pairs could represent a linear function
Hence, {(- 8, 6), (- 4, 3), (0, 0), (4, - 3)}set of ordered pairs (x, y) could represent a linear function
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Terry has a goal of making $300 in commission for the week. If her commission is based on 18% of sales how much does she need to sell to make her goal? I need an answer ASAP pls
The amount of sales Terry must make is $1667
How to determine the amount in sales?From the question, we have the following parameters that can be used in our computation:
Commission = 18% of sales
Commission = $300
These parameters mean that
Commission = 18% of sales
Substitute the known values in the above equation, so, we have the following representation
18% of sales = 300
Divide both sides by 18%
Sales = 1667
Hence, the amount is $1667
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can someone please help me?
The value of x in the given function, f(x) = 3/2x - 4 when f(x) = 5, is x = 6
Determining the value of x in a functionFrom the question, we are to determine the value of x in the given function for the given value of f(x).
The given function is
f(x) = 3/2x - 4
and
f(x) = 5
Now, to determine the value of x, put f(x) = 5 in the given function
f(x) = 3/2x - 4
5 = 3/2x - 4
Add 4 to both sides of the equation
5 + 4 = 3/2x - 4 + 4
9 = 3/2x
Multiply both sides by 2
2 × 9 = 2 × 3/2x
18 = 3x
Divide both sides by 3
18/3 = 3x/3
6 = x
Therefore,
x = 6
Hence, the value of x is 6
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State whether the following statement is true and explain why or why not: A trinomial is always a higher degree than a monomial. Give an example proving your answer is correct.
Grading: 2 points: Correct Answer; 2 points: Explanation; 1 point: Example
The given statement that a trinomial is always a higher degree than a monomial is false because greater number of terms does not means higher degree.
A monomial is an algebraic expression with only one term. Or we can say that the representation of a single concept is a monomial.
An example of an unary expression is: 12
A trinomial is an algebraic expression containing three terms. An example of a ternary is: x + y + 7
A trinomial is always of higher degree than a monomial is false statement .
A counterexample can be used to explain why this is wrong. Suppose we have a monomial, 8⁵ and then a trinomial x² + 2x + 3 . This is just a random example. This monomial has a higher degree because 5 is greater than 2. So basically it doesn't matter what the monomial is, if the degree is higher it is just a term than the maximum degree of the trinomial. Just because this has three terms does not mean that the highest degree term is greater than his one term in the monomial.
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The average waiting time at a drive-in window of a local bank is 10. 3 minutes, with a standard deviation of 2. 7 minutes. Assume the variable is normally distributed. If a customer arrives at the bank, find the probability that the customer will have to wait between 4 and 9 minutes.
29.78% of customers will most likely probability be waiting between 4 and 9 minutes.
Explain the term z-score of the normal distribution?An observation's Z score indicates however many standard deviations it deviates from the mean. The standard normal distribution's mean is zero. Positive Z scores are those above the mean, while negative Z scores are those below the mean.The formula for the z score is-
z = (x - μ)/σ
In which,
μ = mean of 10. 3 minutes
σ = standard deviation of 2. 7 minutes.
z score for the x = 4 minutes.
z = (4 - 10.3)/2.7
z = -2.33
z score for the x = 9 minutes.
z = (9 - 10.3)/2.7
z = -0.48
Thus,
Probability that the customer will have to wait between 4 and 9 minutes.
P(4 < x < 9) = P(-0.48 < z < -2.33)
Use z score table-
P(4 < x < 9) = 0.3085 - 0.0107
P(4 < x < 9) = 0.2978
P(4 < x < 9) = 29.78%
Thus, 29.78% of customers will most likely be waiting between 4 and 9 minutes.
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the difference of vidya's age and 15 is 66 use the variable v to represent vidya's age
Answer:
[tex]\huge\boxed{\sf v = 81}[/tex]
Step-by-step explanation:
Let Vidya's age be v.
Given condition:v - 15 = 66
Add 15 to both sides
v = 66 + 15
v = 81[tex]\rule[225]{225}{2}[/tex]
two poles are connected by a wire that is also connected to the ground. the first pole is 30 ft tall and the second pole is 15 ft tall. there is a distance of 45 ft between the two poles. where should the wire be anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed?
At 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.
What is the quadratic equation?
Any equation in algebra that can be written in standard form as where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation. In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.
Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 45 ft, the distance from the anchor point to the right pole is 45 - x
The wire length from the top of the left pole to the anchor point is
[tex]L^{2} _l = 30^{2} + x^{2}[/tex]
= x² + 900
Similarly for the 2nd part of the wire
[tex]L^{2} _r = 15^{2} + (45-x)^{2}[/tex]
= 256 + 2025 - 45x + x²
= x² + 2281 - 45x
We want to minimize the length of the wires, or [tex]L_l + L_r[/tex]
√x² + 900 + √ x² + 2281 - 45x
we can take the first derivative of this and set it to 0
[tex]\frac{x}{\sqrt{ x^2 + 900} } + \frac{45 - x}{\sqrt{x^2 + 2281 - 45x} } = 0[/tex]
x = 30
Hence, at 30 ft the wire is anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed.
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Four small candies cost $.96 how much do six candies cost
Six candies would cost $1.44.
Answer:
$1.44
Step-by-step explanation:
We need to figure out how much one piece of candy costs. So you do .96/4, which is going to equal 0.24.
1 piece of candy = $0.24
So we do 0.24*6= 1.44
I hope this helps!!!
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Given the equation |x+10|=15
, x= 5 is one solution. What is the other solution?
Answer:
x = - 25
Step-by-step explanation:
the absolute value function always gives a positive value , however , the expression inside the bars can be positive or negative, that is
| - a | = | a | =a
given
| x + 10 | = 15 , then
x + 10 = 15 ( subtract 10 from both sides )
x = 5
OR
-(x + 10) = 15
- x - 10 = 15 ( add 10 to both sides )
- x = 25 ( multiply both sides by - 1 )
x = - 25
solutions are x = 5 , x = - 25
Answer: -25
Step-by-step explanation:
Find the indicated side of the
right triangle.
30°
X
60°
3
Answer:
6
Explanation:
x = 3 /cos(60) = 6
a tower that is 106 feet tall casts a shadow 135 feet long. find the angle of elevation of the sun to the nearest degree.
The angle of elevation of the sun is [tex]tan^{-1}[/tex](106/ 135).
The angle of elevation:
The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.
Here we have to find the angle of elevation of the sun.
Data given:
length of the tower = 106 feet
shadow form by the tower = 135 feet
The formula for the angle of elevation = height/base
tanФ = height/base
= 106/ 135
Ф = [tex]tan^{-1}[/tex](106/135)
Therefore the angle of elevation is [tex]tan^{-1}[/tex]( 106/ 135).
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