In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.
Central Limit Theorem:
The sampling distribution of the sample percentage for a proportion p in a sample of size n will be roughly normal with a mean (μ = p) and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n} }[/tex].
In a given year, 3% of books checked out from the library are downloaded.
That means p = 0.03
and n = 75
By the Central Limit Theorem
Mean = μ = p = 0.03
Standard deviation = [tex]s = \sqrt{\frac{p(1-p)}{n} }[/tex]
[tex]s = \sqrt{\frac{(0.03)(0.97)}{75} }[/tex]
[tex]s=0.0197[/tex]
Hence,
In terms of the percentage of downloaded books, the sampling distribution's mean is 0.03 and its standard deviation is 0.0197.
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1. Find the measure of y.
110°
z
yº
100°
87°
Answer:
97.8263768112
Step-by-step explanation:
Geometric Mean is denoted as 'x'
x = √(110×87)
x = √9570
∴ x = 97.8263768112
Define Geometric MeanThe Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values. For instance, the geometric mean for a given pair of numbers, say 3 and 1, is equivalent to (3 + 1) = 3 = 1.732.In other terms, the geometric mean is the product of n numbers divided by the nth root. The geometric mean differs from the arithmetic mean, as is noted. As a result of the fact that in arithmetic mean, the data values are added before being divided by the total number of values. However, when calculating the geometric mean, we multiply the provided data values before taking the root of the entire number of data values using the radical index. Take the square root, for instance, if there are two data points, the cube root if there are three, the fourth root if there are four, and so on.To learn more about Geometric Mean refer https://brainly.com/question/28347817
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These marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two yellow marbles if the first one is placed back before the second draw. Write your answer as a ratio. Reduce to simplest terms
The probability of drawing two yellow marbles if the first one is placed back before the second draw is 1/25.
Explain the term probability with replacement?For queries where the results are repeated in the sample space, probability with replacement is utilized. This indicates that the item is replaced with in sample space after being picked, keeping the sample space's total number of items constant.The formula for the probability;
probability = favourable outcome/total outcome
The bag contains the marbles as;
yellow marbles: 2pink marble: 3blue marble: 5Total marble: 10Thus, probability of drawing 1st yellow marble.
probability(1st yellow) = 2/10 = 1/5
As the ball is placed again in the bag.
probability(2nd yellow) = 2/10 = 1/5
So, probability of drawing two yellow marble = 1/5 x 1/5 = 1/25.
Thus, the probability of drawing two yellow marbles if the first one is placed back before the second draw is 1/25.
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Given that there are 4 different trails to the top of a mountain.
We need to determine in how many different ways a person can hike up and down the mountain if:
a. He must take the same train both ways
b. He can, but need not, take the same train both ways
c. He does not want to take the same trail both ways.
For case (a), the person can hike up and down the mountain in 4 different ways. For case (b), the person can hike up and down the mountain in 15 different ways. For case (c), the person can hike up and down the mountain in 12 different ways.
In case (a), the person must take the same trail both ways, so there are only 4 different options available, one for each of the 4 trails.
In case (b), the person can take the same trail both ways if they choose, but they are not required to do so. This means that they have 4 different options for the trail they take on the way up, and then 4 different options for the trail they take on the way down. This results in a total of 4 x 4 = 16 different possibilities.
However, one of these possibilities is the case where the person takes the same trail both ways, which has already been counted in case (a), so we need to subtract this possibility to avoid double counting. This results in a total of 16 - 1 = 15 different possibilities.
In case (c), the person does not want to take the same trail both ways, so they have 4 different options for the trail they take on the way up, and then 3 different options for the trail they take on the way down (since they cannot take the same trail they took on the way up). This results in a total of 4 x 3 = 12 different possibilities.
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ayden deposits $2000 into a savings account with an annual interest rate of 3%. If he makes no further deposits or withdrawals, which graph shows the growth of his account balance?
$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.
How to resolve our equation?Ayden deposits $2000 into a savings account with an annual interest rate of 3%.
To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest.
A = $2,060.00
I = A - P = $60.00
A is equal to P(1 + rt).
First, convert R percent to r a decimal; for example, R/100 is 3%/100, or 0.03 per year.
A = 2000(1 + (0.03 × 1)) = 2060 \sA = $2,060.00
$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.
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Lisa paid $46.58 for 16.7 gallons of gasoline. What was the cost per gallon, rounded to the nearest hundredth?
What is the sum of x + y for the system of equations
below?
y=-3x-1
y = -2/3x + 6
O-24
-3
O-11
O5
The sum of x and y is 5.
What is an equation?An equation is a statement of two expressions connected by equal sign.
Given that, the system of equations, y=-3x-1 and y = -2/3x + 6
Simplifying the equations,
-3x-1 = -2x/3+6
Multiplying the both sides by -3
9x +3 = 2x-18
7x = -21
x = -3
Put x = -3 in any one of the equations,
y = -3(-3)-1
y = 9-1
y = 8
Hence, the sum is 5
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I need an answer to this asap!! Lotos of points!!!
A- The red triangle is the image of the blue triangle. What kind of transformation occurred? How do you know?
Determine the scale factor of the transformation.
^Question 1
Answer: Ask three before me!
Step-by-step explanation: Ask three before me!
Find two consecutive positive integers such that the square of the first decreased by 21 equals 6 times the second
The given two consecutive positive integers are 9 and 10.
What is an integer?It is a whole number that can be positive, negative, or zero.
Let consider x and x+1 as two consecutive positive integers.
Given that,
[tex]x^{2} -21=6(x+1)[/tex]
[tex]x^{2} -6x-27=0[/tex]
It can be written in fractional form like,
(x-9)(x+3)=0
so the values of x are 9 and -3.
Here, only positive integers are considered.
Hence 9 and 10 are the two consecutive positive integers.
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Find the volume of the pyramid.
Answer:
180 ft^3
Step-by-step explanation:
volume of the pyramid = (1/3)(area of base) (height)
v= 1/3×(10×12÷2)×(9)
= 180 ft^3
Answer:
answer on the picture.....
The triangle below is equilateral. Find the length of side x to the nearest
tenth.
Answer:
1.7
to the nearest tenth
Step-by-step explanation:
Since the triangle is equilateral, all three sides are the same which is x
The vertical line of length [tex]\sqrt{7}[/tex] bisects the base so each of the two right triangles that is formed has lengths x, x/2 and [tex]\sqrt{7}[/tex]
Using the Pythagorean theorem,
c² = a² + b²
where c is the hypotenuse which has a length x and a and b are the two shorter sides which are x/2 and √7 in this case
Substituting for c, a and b we get
x²= (√7)² + (x/2)²
==> x² = 7 + x²/4
==> x² - x²/4 = 7
==> 3x²/4 = 7
==> x² = 7 x 4/3 = 28/3
x = √(28/3) = 1.732 or 1.7 to the nearest tenth
The average height of the five players on the basketball team was 77 inches. One of the players was 71 inches tall. Another was 74 inches tall, and two were each 78 inches tall. How tall was the tallest player on the team?
How to solve this question
Answer:
The tallest player on the team was 78 inches tall
Step-by-step explanation:
solve the system if x = 2y + 3 and 4x - 5y = 9
The solution of the system of equations:
x = 2y+ 3
4x - 5y = 9
Is x = 1, y = -1.
How to solve the system of equations?Here we have the following system of equations:
x = 2y+ 3
4x - 5y = 9
To solve it, we can notice that the variable x is already isolated on the first equation, then we can take it and replace it on the other equation, then we will get:
4*(2y + 3) - 5y = 9
Now we can solve that equation for y:
4*(2y + 3) - 5y = 9
8y + 12 - 5y = 9
8y - 5y = 9 - 12
3y = -3
y = -3/3
y = -1
And the value of x is:
x = 2y + 3
x = 2*(-1) + 3
x = -2 + 3 = 1
So the solution is x = 1 and y = -1.
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what are the three strategy of cube roots
i need explanation pls
Answer:
look at the explanation below
Step-by-step explanation:
The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:
Step 1: Start with the prime factorization of the given number.
Step 2: Then, divide the factors obtained into groups containing the same factors.
Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number not a perfect cube and we cannot find the cube root of that number
i hope this helps
luka is making lemonade to sell at a school fundraiser. his recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. he uses 3 cups of lemon juice. how many cups of water does he need?
Luka will require 24 cups of water to make lemonades as calculated from the data given.
The quantity of sugar which he use is twice the amount of lemon which he us ,
= 2 x 3 = 6
and ,
as we know the amount of water is 4 times as much as lemon juice
Therefore, amount of water
= 4 * 6
= 24
A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.
A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.
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What is v equal to?
v-(-12)>23
Answer:
V>11
Step-by-step explanation:
a memory researcher is testing an experimental behavioral treatment to see if it helps or hurts the memory of alzheimer's syndrome patients. after 3 months of treatment, she tests the patient's memories using a standardized test, and the data is presented below. the population mean for this test is 50. did the treatment affect the patients' memories? use .01 as the level of significance. 43 56 78 76 58 54 44 38 44 71 83 90 the appropriate alternative hypothesis will be .
H1: The treatment affected the patients' memories.The alternative hypothesis, H1, states that the treatment affected the patients' memories.
To test this hypothesis, the researcher needs to compare the test scores to the population mean of 50. The researcher will use a one-tailed t-test with a .01 level of significance. If the calculated t-value is greater than the critical value, then the null hypothesis will be rejected and the alternative hypothesis will be accepted.
To conduct the t-test, the researcher will need to calculate the mean of the patient's test scores, the standard deviation, and the t-value. The mean is calculated by taking the sum of the test scores and dividing by the number of test scores. The standard deviation is calculated by taking the square root of the sum of the squared deviations from the mean divided by the number of test scores minus one. The t-value is calculated by taking the difference between the mean of the patient's test scores and the population mean, divided by the standard deviation of the patient's test scores, multiplied by the square root of the number of test scores. If the calculated t-value is greater than the critical value, then the null hypothesis can be rejected and the alternative hypothesis can be accepted, indicating that the treatment did affect the patient's memories.
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There are 2 1/4 cups of orange juice in a container. The container holds 3 servings for a toddler, what is the serving size of vitamin C for a toddler
Hello,
I hope you and your family are doing well!
To find the serving size of vitamin C for a toddler, we need to know how much vitamin C is in each serving of orange juice. If we assume that each serving of orange juice contains a certain amount of vitamin C, then we can use the following equation to find the serving size:
serving size = (total amount of vitamin C in container) / (number of servings)
Since there are 2 1/4 cups of orange juice in the container, and the container holds 3 servings, the serving size is:
serving size = (2 1/4 cups) / (3 servings) = 3/4 cup per serving
So the serving size of vitamin C for a toddler is 3/4 cup.
Please rate this answer 5 stars and brainliest if you find it helpful.
Happy Holidays!
the amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 110 minutes and a standard deviation of 11 minutes. what is the probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes?
The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes is 0.0474 or 0.033.
Given,
In a normal random variable
Mean , [tex]\mu[/tex] = 110 minutes
Standard deviation , [tex]\sigma[/tex] = 11 minutes
then
The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes will be
a)
To find the Probability that a randomly selected product will be assembled in less than 91.630 minutes, first calculate the z-score at 91.360 minutes
[tex]z-score = \frac{x-\mu}{\sigma}\\\\z-score=\frac{91.63-110}{11}\\\\z-score=\frac{-18.37}{11}=-1.67\\[/tex]
from z-score table , [tex]p(x < -1.67)=0.04746[/tex]
b)
To find the Probability that a randomly selected product will be assembled in more than 130.35 minutes, first calculate the z-score at 130.35 minutes.
[tex]z-score = \frac{130.35-110}{11}\\\\z-score=\frac{20.35}{11}=1.85[/tex]
From z-score table,
[tex]p(x > 1.85)\\\\=1-p(x < 1.85)\\\\=1-0.967\\\\=0.033[/tex]
Thus, the probability for product assembled in more than 130.35 minutes is 0.033
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Please help me thanks :)
After doing the equation the area of ΔABC is 15√7.
The Heron area formula is what?
Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in terms of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: Area is equal to the square root of (a + b + c)/2, where s is half the perimeter.
Given that:
Let AB = 6x , BC = 5x , AC = 4x
then 6x+5x+4x = 30
15x = 30
x = 2
so AB = 12
BC = 10
AC = 8
Area = √s(s - a)(s - b)(s - c)
s = a+b+c/2
s = 12+10+8/2
s = 30/2
s = 15
Area = √15(15- 12)(15 - 10)(15 - 8)
Area = √15(3)(5)(7)
Area = √1575 = 15√7
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cross-tabulation can only be used for two variables; each variable must have well-defined labels. true false
The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false
The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that that present the results of the entire group of respondents
The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "
The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables
The cross tabulation can be used for two or more variables
Therefore, the the given statement is false
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I NEED HELP!!!! Use the graph of the polynomial equation y=x^4-10x² + 16 to describe its concavity. How many points of inflection does this curve have?
Answer:
Concave Up: (-∞, [tex]-\sqrt{\frac{5}{3}}[/tex]), ([tex]\sqrt{\frac{5}{3}}[/tex], ∞)
Concave Down: ([tex]-\sqrt{\frac{5}{3}[/tex],[tex]\sqrt{\frac{5}{3}[/tex])
Points of Inflection: (-1.2910, 2.1111), (1.2910, 2.1111)
Step-by-step explanation:
To find the concavity of a function, we need to take the second derivative.
y' = 4x^3 - 20x
y'' = 12x^2 - 20
Finding the points of inflection involves setting the second derivative equal to 0. Add 20 over, divide by 12, and take the square root. The positive and negative square roots of 5/3 are the potential points of inflection.
Setting up a number line can help to determine concavity. Let's plug in -2 into the second derivative. From this, we have found that from negative infinity to the negative square root of 5/3, the graph is concave up, as f''(-2) > 0. f''(0) < 0, so from the negative square root of 5/3 to the positive square root of 5/3, the graph is concave down. f''(2) is also > 0, and therefore from the positive square root of 5/3 to infinity, the graph is concave up.
Since the graph shifted direction at both potential points of inflection, they are both actually points of inflection. To find the y-values for each point of inflection, plug the x-value back into the original polynomial equation.
2. Divide. Write the answer in simplest
form.
6 2/3 divided by 4 1/5
Answer:
100/63
Step-by-step explanation:
6 2/3 ÷4 1/5
20/3÷21/5
20/3×5/21
1 37/63 or 100/63 or 1.587301587
so the answer is one (whole number) thirty seven over sixty three
I need some with this I would really appreciate if you could be able to help me with this.
I don't see the picture. Can you send it in the message.
1-36) what is the sum of 2 + (1/5 + 1/5² + 1/5³ +...,.. +... 1/(5 to power n) ..)
help how
Answer:
[tex]\displaystyle \frac{9}{4}[/tex]
Step-by-step explanation:
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} )[/tex]
The second term of this sum is an Infinite Geometric Progression
To find the sum of an Infinite Geometric Progression,
- Find the first term ( 1/5 ) of the progression and call it a
- Find the common ratio, (divide any term by it's predecessor. i.e [tex]\displaystyle \frac{\frac{1}{5^2} }{\frac{1}{5} } = \frac{5}{5^2} = \frac{1}{5}[/tex]) and call it r
Finding the sum of given Geometric Progression:
Sum of Infinite GP: [tex]\displaystyle \frac{a}{1-r}[/tex]
Plugging our values in this equation, we get:
Sum of Geometric Progression = [tex]\displaystyle \frac{\frac{1}{5} }{1 - \frac{1}{5} } = \frac{\frac{1}{5} }{\frac{5 - 1}{5} } = \frac{1}{4}[/tex]
Adding to find the actual answer:
[tex]\displaystyle (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = 2 + \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{9}{4}[/tex]
The sum of the digits of a certain two digit number is 13. Twice the tens digit exceeds the unit digit by 2. What is the number?
Answer:
Step-by-step explanation:
6.5
ow many ways can you get exactly six heads and exactly six tails if after six tosses you have had three tails and three heads?
The number of possible combinations available as calculated from the given data is 259200.
Coin just has a head and a tail.
The potential configuration is (6! * 6!)/2.
Divide by two because each coin has two faces.
The potential configuration is (6! * 6!)/2.
The potential configuration is (( 720 x 720)/2
The potential configuration is 259200.
259200 different combinations are available.
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data.
Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.
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A water tank holds 675 gallons but is leaking at a rate of 4 gallons per week. A second water tank holds 900 gallons but is leaking at a rate of 7 gallons per week. After how many weeks will the amount of water in the two tanks be the same?
Answer:
It will take approximately 20.454545454545455 weeks for the amount of water in the two tanks to be the same.
Step-by-step explanation:
To find the number of weeks it will take for the amount of water in the two tanks to be the same, we can set up the following equation:
675 - 4w = 900 - 7w
Then, we can solve for w by adding 4w to both sides and then adding 7w to both sides:
11w = 225
w = 225 / 11
thus, It will take approximately 20.454545454545455 weeks for the amount of water in the two tanks to be the same.
Solve for e.
2e + 3 + 7 = 2
e = [?]
Seraphina is driving two hours to visit her family. For the first hour, she traveled at a speed of 62 miles per hour. Then, in the second hour, she traveled at a speed of 74 miles per hour. What is the percentage increase of Seraphina's speed? If necessary, round to the nearest tenth of a percent.
A. 19.4%
B. 80.6%
C. 83.8%
D. 16.2%
The percentage increase of Seraphina's speed will be A. 19.4%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Given that Seraphina is driving two hours to visit her family. For the first hour, she traveled at a speed of 62 miles per hour. Then, in the second hour, she traveled at a speed of 74 miles per hour.
The percentage increase of Seraphina's speed will be:
= Increase in speed / Initial speed × 100
= (74 - 62) / 62 × 100
= 12 / 62 × 100
= 19.4%
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I'm a little confused on this one.
Answer: m = -1 , b = -8
Step-by-step explanation:
y=mx+c
m = gradient of the line / slope of the line
c = y intercept
-x=-1x so the gradient is -1
-8 = y intercept
