A music fan has amassed a giant collection of albums and CDs. If the music fan has 2000 CDs, which comprise 61.3% of the total collection, how many total albums and CDs are in the collection
There are approximately 3263 total albums and CDs are in the collection.
Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".
let 'x' be the total albums and CDs in the collection
If the music fan has 2000 CDs, which comprise 61.3% of the total collection, then 61.3% of x is equal to 2000.
2000 albums and CDs = 61.3% of the total albums and CDs in the collection
2000 = 61.3% of x
2000 = 0.613x
Solving for x,
x = 3262.6
the total albums and CDs in the collection ≅ 3263
Therefore, the the total albums and CDs in the collection is approximately 3263.
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What is the equation, in point-slope form, for a line that goes through(8, −4) and has a slope of −5/6?
Responses
Answer:
y + 4 = - [tex]\frac{5}{6}[/tex] (x - 8)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - [tex]\frac{5}{6}[/tex] and (a, b ) = (8, - 4 ), that is a = 8, b = - 4 , then
y - (- 4) = - [tex]\frac{5}{6}[/tex] (x - 8) , that is
y + 4 = - [tex]\frac{5}{6}[/tex] (x - 8)
in one statistics course students reported studying an average of 9.92 hours a week with a standard deviation of 4.54. treating this class as the population, what is the precentile for a student in the class who studes 8 hourse a week
The precentile for a student in the class who studies 8 hours a week is 5.74%.
To find the percentile for a student who studies 8 hours a week, we need to first standardize the student's study time by subtracting the mean study time and dividing it by the standard deviation of study time. This will give us the student's z-score. We can then look up the student's z-score in a standard normal table to find the percentile.
The student's z-score is (8 - 9.92) / 4.54 = -1.67.
Looking up -1.67 in a standard normal table, we find that the percentile is about 5.74%. This means that about 5.74% of the students in the class studied for less than 8 hours per week.
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As per the given standard deviation, the percentile for a student in the class who studies 8 hours a week is 50.80%
The term standard deviation in math is known as a measure which shows how much variation from the mean exists.
Here we have given that in one statistics course students reported studying an average of 9.92 hours a week with a standard deviation of 4.54.
Through this details, we have identified that the value of the following are given that,
=> weekly study time = 10 hours
=> average study time = 9.92 hours
=> standard deviation = 4.54 hours
Then the formula to calculate the Test statistic is written as
=> z = (weekly study time - average study time)/standard deviation
Apply the values on it, then we get
=> z = (10 - 9.92)/4.54
=> z = 0.08/4.54 = 0.02
While we take the value of z table, then we get the Cumulative area of the test statistic is 0.5080.
And the percentile is calculated by multiply the value by 100 as,
=> 0.5080 × 100 = 50.80
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Multiply. then in simplest form.
Assume all variables are non-negative.
√x^5 • √x¹⁰
[tex]\sqrt{x^5}\cdot \sqrt{x^{10}}\implies \sqrt{x^5\cdot x^{10}}\implies \sqrt{x^{5+10}}\implies \sqrt{x^{15}}\implies \sqrt{x^{14+1}} \\\\\\ \sqrt{x^{14}\cdot x^1}\implies \sqrt{x^{7\cdot 2} x}\implies \sqrt{(x^7)^2 x}\implies x^7\sqrt{x}[/tex]
Which of the following is a quantitative variable?
a) the texture of a rug
b) the breed of a dog
c) the numbers of toppings on a pizza
d) the colour of a person’s hair
C is the most accurate one i guess
Round 543,829 to the nearest 100 1,000 10,000
Answer:
540,000
Step-by-step explanation:
A watermelon weighs 4.2 kg and a pumpkin weighs 2 kg 250g Express the total weight of the items in kilograms. (30 points
ty
Answer:
6.45 kg
Step-by-step explanation:
250 g is equal to 0.25 kg, so the pumpkin weighs [tex]2+0.25=2.25[/tex] kg.
Thus, the combined weight is [tex]2.25+4.2=6.45[/tex] kg.
all natural numbers less than 10 but greater than 2
Answer:
The numbers are: 3, 4, 5, 6, 7, 8, 9
Step-by-step explanation:
Natural Numbers are whole number from 0 to infinty. If you were to find all blow 10 but greater than 2 you would have 3, 4, 5, 6, 7, 8, 9
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Indicate how electoral votes would have been allocated if Illinois, Tennessee,
Pennsylvania, and New York had all used the popular-vote percentage method of
proportional allocation instead of the winner-takes-all method. (15 points)
The popular vote, which determines the winner of a presidential election, is simply the total number of voters from all 50 states. The popular vote is deemed to have been won by the candidate with the most votes cast nationally.
What is presidential election?Every four years on the first Tuesday in November, the US holds its presidential election. The candidate must have at least 35 years of age, have been born in the US, and have resided in the US for the previous 14 years in order to be eligible.
Traditionally, candidates announce their intention to run for president one year prior to the election. Since there is no national body that organises elections, local authorities organise them with the aid of tens of thousands of administrators.
On January 20, the United States Capitol in Washington, D.C., will host Inauguration Day. The Vice President is sworn in first, then the President.
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avery is throwing a pizza party. she had 7 pounds of cheese available and she needs 3/5 pound of cheese to make each pizza. what is the maximum number of full pizzas she can make?
The maximum number of full pizzas she can make if Avery had 7 pounds of cheese available, and she needs 3/5 pounds of cheese to make each pizza, is 11.
What is division?When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. For instance, 4 2 = 2. As a multiplication fact, this can be expressed as 2 + 2 = 4.
Given:
Avery had 7 pounds of cheese available, and she needs 3/5 pound of cheese to make each pizza,
Calculate the number of pizzas she can make as shown below,
The number of pizzas = total cheese/cheese required to make one pizza
The number of pizzas = 7 / 3/5
The number of pizzas = 7 × 5 / 3
The number of pizzas = 35 / 3
Thus, the total number of pizzas she can make is 11 and 2 / 3.
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Kylie and Matt are driving out of town, leaving from the same house in
different cars. Matt drives at a rate of 40 miles per hour. Matt drives 50
miles before Kylie begins traveling. Kylie drives at a rate of 50 miles per
hour. . Describe a situation in which Kyle and Matt are traveling but are never the same distance from the starting point at the same time.
Write a system of equations to model the situation. How many solutions does the system have ?
The number of solutions the system have is 2. They will meet in 5 hours.
How to find the solution to the given system of equation?For that , we will try solving it first using the method of substitution in which we express one variable in other variable's form and then you can substitute this value in other equation to get linear equation in one variable.
If there comes a = a situation for any a, then there are infinite solutions.
If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.
Matt drives at a rate of 40 miles per hour. Matt drives 50 miles before Kylie begins traveling.
So the total distance for Matt is given by;
M(t)= 40t+50
Kylie drives at a rate of 50 miles per hour.
When he starts(at position 0), Matt will be already at 50. So Kylie's equation is given by:
K(t)= 50t
To find out how many hours until they meet?
K(t)= M(t)
So, 50t= 40t+50
10t= 50
t=5
Therefore the answer of the equation will be 2.
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How many passes scans will go through a list of 10 elements when we use bubble sort algorithm for sorting?
By using the bubble sort algorithm, a total of 9 passes/scans will be there.
Sorting AlgorithmWhen an array or list of items has to be rearranged, a sorting algorithm is used to compare the elements and sort the elements in the array or list. In each data structure, the new order of the items is determined using the comparison operator.
Bubble Sort AlgorithmThe simplest sorting method is called Bubble Sort, and it involves periodically exchanging nearby components if they are arranged incorrectly. Since the average and worst-case time complexity of this approach is relatively high, it is not appropriate for huge data sets.
According to the question, we have
Total number of elements we are having, i.e., n = 10
The total number of passes = n-1 = 10 - 1 = 9
(Number of passes required by bubble sort of n elements will be n-1)
therefore, the total number of passes/scans will be 9
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Assuming no denominator equals zero, which expression is equivalent to the given expression?.
Assuming no denominator equals zero, b^4/a expression is equivalent to the given expression a^3b^5/ a^4b
Definition of Expression in Math? An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
The expression can be rewritten as ...
a^3b^5/ a^4b
The expression can be rewritten as ...
b^4/a
complete question
Assuming no denominator equals zero, which expression is equivalent to the given expression?.
a^3b^5/ a^4b
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Cos 0 = 4/5 and sin 0 < 0. Identify the quadrant of the terminal side of 0 and
find sin 0
Answer:
sinθ = -3/5, Quadrant IV (Option B)
Step-by-step explanation:
Let's first find the sine
cosθ = adj./hyp.
Pythagorean theorem (in terms of right triangle trig) = (opp)^2 + (adj)^2 = (hyp)^2
Plug in the adjacent and hypotenuse
(opp.)^2 + 16 = 25
solve for the opposite side
opp. = 3
To find the quadrant, recall the sin <0, so the sin has to be negative.
So, your sine value is -3/5.
Sine is negative at Quadrants III and IV, so eliminate C and D.
Since your cosine value is positive, it is at Quadrant IV (Cosine is positive at the first and fourth quadrants.)
Therefore, Option B is correct.
Find a polynomial (lowest degree) with 0, i and -5+7 as its roots (zeros). Answer in expanded form.
Answer:
[tex]P(x)=x^5+10x^4+75x^3+10x^2+74x[/tex]
Step-by-step explanation:
Given information:
Polynomial function with real coefficients.Roots: 0, i and -5+7iFor any complex number [tex]z=a+bi[/tex], the complex conjugate of the number is defined as [tex]z^*=a-bi[/tex].
If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.
Therefore, if P(x) is a polynomial, and i is a root of f(x)=0, then its complex conjugate -i is also a root of P(x)=0.
Similarly, if P(x) is a polynomial, and -5+7i is a root of f(x)=0, then its complex conjugate -5-7i is also a root of P(x)=0.
Therefore, the polynomial in factored form is:
[tex]P(x)=x(x-i)(x-(-i))(x-(-5+7i))(x-(-5-7i))[/tex]
[tex]P(x)=x(x-i)(x+i)(x+5-7i)(x+5+7i)[/tex]
Expand the polynomial:
[tex]P(x)=x(x^2-i^2)(x^2+10x+25-49i^2)[/tex]
[tex]P(x)=x(x^2-(-1))(x^2+10x+25-49(-1))[/tex]
[tex]P(x)=x(x^2+1)(x^2+10x+74)[/tex]
[tex]P(x)=x(x^4+10x^3+75x^2+10x+74)[/tex]
[tex]P(x)=x^5+10x^4+75x^3+10x^2+74x[/tex]
what is equal to -4(3x+2)=4
Answer:
x = -1
Step-by-step explanation:
You want the solution to the equation -4(3x+2) = 4.
SolutionFirst of all, we can divide by -4.
3x +2 = -1
Subtracting 2 gives ...
3x = -3
Finally, dividing by 3, we have the solution:
x = -1
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4. Two identical cars of different colors are driving on the freeway. The
green car is driving 50 mph, and the yellow car is driving 70 mph. Which
has more momentum? Why?
The speed of yellow car has a higher speed. Then the yellow car has more momentum.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The equation of the momentum is written as,
P = mv
Where 'm' is the mass and 'v' be the velocity.
On the motorway, two similar vehicles of various colors may be seen. The yellow automobile is traveling at 70 mph while the green vehicle is moving at 50 mph.
Let the mass of the bodies be the same.
The speed of yellow car has a higher speed. Then the yellow car has more momentum.
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This quarter Joseph has earned grades of 81, 89, 80, 84, 89, and 85 on his math quizzes. Based on these scores, he claims to have an average quiz grade of 89. Explain why this claim might be considered inaccurate
The claim might be considered to be inaccurate because Joseph's actual average quiz grade for math is 85
How to find the average ?When given a set of numbers of variables, the average variable can be found by dividing the sum of the variables by the number of variables in the set.
For Joseph therefore, the average of the quiz grades that he has from his math quizzes would be :
= ( 81 + 89 + 80 + 84 + 89 + 85 ) / 6
= 508 / 6
= 84. 6
= 85
This shows that Joseph's claim of an average of 89 in his math quizzes is therefore inaccurate.
Most likely, what Joseph thought he meant was that the mode of his math quizzes was 89 as the mode refers to the variable that appears the most in a set.
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a light is at the top of a pole that is 50 feet high. a ball is dropped 50 feet high and 30 feet away from the light. how fast is the shadow of the ball moving accross the ground 0.5 seconds latter? assume that the ball falls a distance of 16t^2 feet in t seconds.
The distance between the ball and pole is divided by the time taken to travel that distance to calculate the rate of shadow travel, which is 80 fps.
The shadow of the ball is moving at a rate of 80 feet per second (fps). This can be calculated as follows:
Distance Fallen = 16t^2
Distance Fallen in 0.5 Seconds
= 16(0.5)^2
= 4 feet
Distance Between Ball and Pole
= 50 feet - 4 feet
= 46 feet
Time Taken To Travel Distance
= 0.5 Seconds
Rate of Travel = 46/0.5
= 80 fps
The shadow of the ball is moving at a rate of 80 fps. This is calculated by taking the distance between the ball and pole (50 feet-4 feet=46 feet) and dividing it by the time taken to travel that distance (0.5 seconds). This results in 80 fps.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
5,10,20,...
Answer:
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 2 gives the next term.
Step-by-step explanation:
In 1945, a person made $3.20 for working an 8-hour day. model a division problem to determine how much a person made per hour in 1945. what is the hourly wage?
Answer:
$0.40 per hour
(This is 40cents per hour)
Step-by-step explanation:
The "hourly wage" is a rate, a ratio, a comparing of two numbers. We are comparing dollars and hours. So we have information given in the problem about the $ and hours. Compare these two numbers and then simplify. Because we need the hours, on the bottom, to be 1 hour. "Per hour" means per ONE hour.
dollars/hours
= $3.20/ 8hours
Divide.
= $0.40/1 hour
This is the hourly wage, $0.40 (or 40cents) per hour.
There are 25 sweets in a jar.
9 of the sweets are yellow.
Jamie takes at random a sweet from the jar.
(a) Write down the probability that the sweet is yellow.
The probability that the sweet is yellow will be;
⇒ 9 / 25
What is mean by Probability?The term probability refers to the likelihood of an event occurring.
Given that;
There are 25 sweets in a jar.
And, 9 of the sweets are yellow.
Now,
Since, Jamie takes at random a sweet from the jar.
Hence, The probability that the sweet is yellow = 9/25
= 0.36
Thus, The probability that the sweet is yellow = 0.36
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How many numbers can 12345 form?
The total number that can be formed by the numbers 1,2,3,4,5 (without repeating digits) is 120.
Now, half of the unit's digit will be bigger than the ten's digit and in half of them it will be smaller.
Example: Let's say we have three digits 1,2,3. Total number of numbers without repeating digits = 3*2*1=6
Numbers with the Unit's digit greater than the ten's digit
123, 213, 312
Numbers with Ten's digits greater than the unit's digit
321, 132, 231
So total Number of cases = 120/2 = 60
Thus, the Total Number which can be formed by numbers 1,2,3,4,5 (without repeating digits) = 5*4*3*2*! = 5! = 120.
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As per the combination method, the number for formation from the digits 12345 is 120 without repetition.
The term combination method in math is defined as a way of selecting items from a collection where the order of selection does not matter.
Here we have given the digits as 12345.
Here we have calculated the total Number of Numbers which can be formed by numbers 1,2,3,4,5 without repeating digits is written as
=> 5 x 4 x 3 x 2 x 1
Which is also equal to,
=> 5! = 120.
While we looking into the set we have identified that in half them unit's digit will be bigger than the ten's digit and in half of them it will be smaller.
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Discuss the difference between r and p.r represents the p represents theChoose the correct answers below- critical value for the correlation coefficient. -population correlation coefficient. -sample correlation coefficient.
The difference between r and p. r represents the p represents the
Sample correlation coefficient.
Now, According to the question:
What is sample correlation coefficient?
The sample correlation coefficient (r) is a measure of the closeness of association of the points in a scatter plot to a linear regression line based on those points, as in the example above for accumulated saving over time
The sample correlation coefficient uses the sample covariance between variables and their sample standard deviations. The population correlation coefficient uses the population covariance between variables and their population standard deviations.
Hence, The correct answer is : Sample correlation coefficient.
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If 9 movie tickets cost $18, what is the unit price of the
movie tickets?
Answer:
Step-by-step explanation:
the answer is 162 I now this because I took the quiz and got a 100% just for that answer so I hope this is helpful
Answer:
You can do it by dividing 18 by 9 and you would get 2.
ANSWER: 2
Triangle ABC is being rotated 90° about the
origin. What will A' be if A was located at (7. 2)?
Answer:
A' (2, - 7 )
Step-by-step explanation:
under a rotation about the origin of 90°
a point (x, y ) → (y, - x ) , then
A (7, 2 ) → A' (2, - 7 )
A baseball player strikes out 3 times for every 2 hits he gets. If the player strikes out 15 times, how many hits does he get? If the player gets 46 hits, how many times does he strike out?
its in the sreenshot because i didnt want to type
An equilateral triangle has an apothem length 2. What is the area of the triangle?
12√√3
4√3
4
Area = 12√3
What is an equilateral triangle ?An equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees.
Given,
Length of apothem of equilateral triangle = 2
It is an equilateral triangle made up of six 30°-60°-90° right triangles with the short leg of 2 units.
2 is the altitude of small triangles
tan 30° = altitude/base
1/√3 = 2/base
base = 2√3
Area of the equilateral triangle
= 6 × area of the small triangles
= 6 ×1/2 × altitude × base
= 3 × 2 × 2√3
= 12√3
Hence the area of equilateral triangle becomes = 12√3
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Situations and Sequence Types Assignment
Answer:12+6=3=1.5
Step-by-step explanation: