The correct conclusion from the given percentage of students of different categories is option(c): Classical is the preferred music for 52 students.
What is meant by percentage?
A figure or ratio stated as a fraction of 100 is called a percentage. It is frequently indicated by the percent sign, "%."
Given,
Total number of middle school students = 400
Percent of students who prefer rock = 13%
Percent of students who prefer hip hop = 25%
Percent of students who prefer pop = 35%
Percent of students who prefer classical = 13%
Percent of students who prefer jazz = 14%
Now we can find the number of students for each category.
Number of students who prefer rock = 13/100 * 400 = 52
Number of students who prefer hip hop = 0.25 * 400 = 100
Number of students who prefer pop = 0.35 * 400 = 140
Number of students who prefer classical = 0.13 * 400 = 52
Number of students who prefer jazz = 0.14 * 400 = 56
We can now look at different options.
a) This is false as hip-hop is preferred by 100 students.
b) Together Pop and jazz are preferred by 140+56 = 196, which is not more than half (200) of students. So this is false.
c) This is true as classical is preferred by 52 students.
d) Together rock and hip hop are preferred by 52+100 = 152, which is not equal to 172. So this is false.
Therefore the correct conclusion from the given percentage of students of different categories is option(c).
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Answer: c
Step-by-step explanation:
I did the test and it’s right
Solve for x:
-4x + 2(x+4)= -7x- (x + 1)
Answer: x = -3/2
Step-by-step explanation:
-4x + 2(x+4) = -7x - (x+1)
-4x + 2x+8 = -7x -x-1
-2x + 8 = -8x - 1
+2x +2x
8 = -6x - 1
+1 +1
9 = -6x
/-6 /-6
-9/6 = x
-3/2 = x
Please help. Find the output, y When the input, x, is -7.
The output value of y when input value x is -7: -6
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check given expression is a function or not we can check it by a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
A graph of a function,
And input value x = -7
output value y = ?
As it can be seen in the graph,
For input value x = 0
output value of y = -2
Similarly,
for input value x = -7
It can be seen in the graph that
the value of y = -6
Hence, the value of y is -6
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What does a rising sequence do in a piece of music?
A. Increases the dynamic
B. Adds drama and tension
C. Decreases the dynamic
D. Decreases the tempo
How do I simplify this into a radical?
Answer:
Step-by-step explanation:
To simplify the expression X^(12/7) * Y^(35/7) into its simplest form, we need to find the greatest common divisor (GCD) of the exponents 12/7 and 35/7 and divide both exponents by the GCD. Here's the step-by-step process:
Find the GCD of 12/7 and 35/7. To do this, we'll use the Euclidean algorithm method:
a. Divide the larger number, 35, by the smaller number, 12, and get the remainder: 35 ÷ 12 = 2 with a remainder of 11.
b. Divide the smaller number, 12, by the remainder, 11, and get the quotient and remainder: 12 ÷ 11 = 1 with a remainder of 1.
c. The last non-zero remainder, 1, is the GCD of 12/7 and 35/7.
Divide both exponents by the GCD, 1:
a. X^(12/7) becomes X^(12/7 ÷ 1) = X^12.
b. Y^(35/7) becomes Y^(35/7 ÷ 1) = Y^35.
Replace the original exponents in the expression with the simplified exponents: X^12 * Y^35.
So, the expression X^(12/7) * Y^(35/7) is simplified as X^12 * Y^35, which is written as a single radical in its simplest form.
[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ x^{\frac{12}{7}}y^{\frac{35}{7}}\implies \left( x^{12} y^{35} \right)^{\frac{1}{7}}\implies \sqrt[7]{x^{12} y^{35}}\implies \sqrt[7]{x^{7+5} (y^5)^7} \\\\\\ \sqrt[7]{x^7 x^5 (y^5)^7}\implies {\Large \begin{array}{llll} x y^5\sqrt[7]{x^5} \end{array}}[/tex]
You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes.
The system of linear equations representing the given situation is: 2x + y = 10 and 2x + 3y = 22. Solving this system, we find that it takes 6 minutes to jog around the park.
a. Let's use x to represent the number of minutes it takes to jog around the block and y to represent the number of minutes it takes to jog around the park.
From the problem statement, we know that:
2x + y = 10 (jog around the block twice and the park once in 10 minutes)
2x + 3y = 22 (jog around the block twice and the park three times in 22 minutes)
These are the two linear equations that represent the given situation.
b. We can solve this system of equations to find the value of y, which represents the number of minutes it takes to jog around the park.
We can start by eliminating x from the equations. Subtracting the first equation from the second, we get:
(2x + 3y) - (2x + y) = 22 - 10
2y = 12
y = 6
So, it takes 6 minutes to jog around the park.
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Complete question:
You can jog around your block twice and the park once in 10 minutes. you can jog around your block twice and the park 3 times in 22 minutes.
a. write a system of linear equations that represents this situation. let x represent the number of minutes it takes you to jog around your block and y represent the number of minutes it takes you to jog around the park. system of equations:
b. how long does it take you to jog around the park? it takes you minutes to jog around the park.
• describe how to use bundled things to explain regrouping in the subtraction problem 231-67. Make math drawings to aid your explanation.
The information regarding the addition is explained below.
How to explain the additionAdding 29 + 46:
Student 1: May use the traditional column addition method, lining up the digits in the ones, tens, and hundreds place and carrying over if necessary.
Student 2: May use the breaking apart method, where they break apart the numbers into smaller parts (e.g. 20 + 40) and then add the pieces together.
Student 3: May use a number line, counting up from 29 by the increments of 46 until they reach the sum.
Subtracting 54 - 28:
Student 4: May use the traditional column subtraction method, lining up the digits in the ones, tens, and hundreds place and borrowing if necessary.
Using bundled things to explain regrouping in the addition problem 167 + 59:
First, separate the numbers into bundles of ten.
Next, show how you can regroup the ones as ten ones to make a bundle of ten.
Then add the tens and hundreds place to get the answer 226.
Using bundled things to explain regrouping in the subtraction problem 231 - 67:
First, separate the numbers into bundles of ten.
Next, show how you can regroup the tens as ten tens to make a bundle of a hundred.
Then subtract the hundreds place and the tens place to get the answer 164.
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In the diagram, ACDF∼VWYZ
. Find the value of y.
The value of the variable y is 3
How to determine the valueFrom the information given, we have that;
ACDF∼VWYZ
Given that the lengths are;
A= 12CD = 9YW = 6VZ = 3y -1Since the diagrams are equivalent, then,
A/VZ = CD/YW
substitute the values, we have;
12/3y - 1 = 9/6
cross multiply
3y - 1 = 12(6)/9
divide the values
3y - 1 = 8
collect like terms
3y = 9
Make 'y' the subject
y =3
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2/12 Help me answer please
Answer:
Step-by-step explanation:
Let's call the present value of the loan P. The payments of $1,550 in 1 year and $2,400 in 4 years can be expressed as an ordinary annuity with semi-annual payments. We can calculate the present value of this annuity using the formula:
PV = A * (1 - (1 + r)^-n) / r
where
A = $1,550 / 2 = $775 (semi-annual payment)
n = (4 x 2) + 2 = 10 (number of semi-annual periods)
r = 0.045 / 2 = 0.0225 (semi-annual interest rate)
So,
PV = $775 * (1 - (1 + 0.0225)^-10) / 0.0225 = $8,100.40
Thus, the present value of the loan is P = $8,100.40.
Next, we can calculate the present value of the payment of $1,050 in 24 months and the balance in 30 months.
The payment of $1,050 in 24 months can be expressed as a single amount due in 24 months. The present value of this payment can be calculated as:
PV = $1,050 / (1 + 0.0225)^(24/2) = $1,000.54
So, the balance of the loan after this payment would be P - $1,000.54 = $8,099.86.
The balance in 30 months can be expressed as an ordinary annuity due with semi-annual payments. We can calculate the present value of this annuity using the formula:
PV = A * (1 - (1 + r)^-n) / r
where
A = ($8,099.86) / 6 = $1,349.98 (semi-annual payment)
n = 6 (number of semi-annual periods)
r = 0.0225 (semi-annual interest rate)
So,
PV = $1,349.98 * (1 - (1 + 0.0225)^-6) / 0.0225 = $7,999.86
Therefore, the payment required in 30 months for the rescheduled option to settle the loan is $1,349.98 per semi-annual period.
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Find 4 rational numbers between
OR
-1
6
and
5
Four rational numbers between 1/5 and 1/6 are; 41/240, 42/240, 43/240, 44/240
How to Identify Rational Numbers?A rational number is defined as a number that can be expressed as the quotient of fraction p/q of two integers, a numerator p, and a non-zero denominator q.
First, we have to make the denominators the same.
We multiply 1/5 by 48 and 1/6 by 40 to get:
48/240 and 40/240
Thus, the other rational numbers between them are;
41/240, 42/240, 43/240, 44/240
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Complete question is;
Find four rational numbers between 1/5 and 1/6
Help with these questions Pls?
Answer:12
Step-by-step explanation:30-6=24
24 divided by 2 =12
please help!!!!!!!!!
Answer:
yes
Step-by-step explanation:
2*(4+7) = ( 2 * 4 ) + ( 2 * 7 )
Kai is swinging on a trapeze in a circus show. The horizontal distance between Kai and the edge
of the stage, in meters, is modeled by D(t) where t is the time in seconds. The function is
graphed below, along with one segment highlighted.
The sinusoidal expression of the function is D(t) = -cos(3t)
What is sinusoidal expression?A sinusoidal alternating current can be represented by the equation i = I sin ωt, where i is the current at time t and I the maximum current. In a similar way we can write for a sinusoidal alternating voltage v = V sin ωt, where v is the voltage at time t and V the maximum voltage.
here, we have to,
to determine the sinusoidal expression:
When he pushes off, he is 1 m behind the center.
This means that:
Amplitude, a = 1.
But we use, a = -1 because he is behind
The graph has a minimum point at (0,-1) and then intersects its midline at (π/6, 0).
So, the period B is: 2π/B = 4 * π/6 and the vertical shift (d) is 0
Simplify 2π/B = 4 * π/6
2π/B = 2π/3
By comparison, we have:
B = 3
The function is given as:
a cos(Bt) + d
Substitute the calculated values
D(t) = -cos(3t)
Hence, the sinusoidal expression of the function is D(t) = -cos(3t)
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Answer:
period and he completes a swing in ten seconds
Claudia is interested in knowing which figure skater competing in the
Olympic Games is most favored to win a gold medal. To sample the
students in her school, she prepares a list of all of the boys and girls in the
school and randomly chooses a sample from each group so that the size of
each group is proportional to the number of boys and girls in the school.
Which sampling method did Claudia use?
OA) simple random sampling
OB) stratified random sampling
OC) systematic random sampling
OD) simple non-random sampling
OD) Is simple non-randon sampling
Step-by-step explanation:
because Claudia randomly choose a sample from each group.
The velocity v, in meters per second, of a certain type of wave is given by v(h) = 3√h, where h is the depth, in
meters, of the water through which the wave moves. What is the rate of change, in meters per second per meter, of
the velocity of the wave with respect to the depth of the water, when the depth is 2 meters?
Answer:
The rate of change of the velocity of the wave with respect to the depth of the water is 3/2 meters per second per meter when the depth is 2 meters. This can be found by taking the derivative of v(h) with respect to h, which is 3/2√h. When h is 2, the rate of change is 3/2√2, which is equal to 3/2 meters per second per meter.
The number of a country's unemployed workers increased from 3.4 million to 5.5 million last year. If the country's population remained constant at 76 million, how did its unemployment rate change last year? A. It increased by about 27%. B. It decreased by about 27%. C. It increased by about 3%. D. It decreased by about 3%.
The rate at which its unemployment changes is, 54.6 %
What is the rate?Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.
So formula for the rate is,
m = change in one quantity/change in another quantity = Δy/Δx
Given that,
The initial number of unemployed workers was 3.4 million and the final number was 5.5 million.
The change in the number of unemployed workers is:
5.5 million - 3.4 million = 2.1 million
To find the initial number of employed workers, we need to subtract the initial number of unemployed workers from the total population:
76 million - 3.4 million = 72.6 million
Now, we can calculate the initial unemployment rate as:
3.4 million / 72.6 million = 0.0469 or 4.69%
Similarly, the final unemployment rate is:
5.5 million / 76 million = 0.0724 or 7.24%
The change in the unemployment rate is:
(0.0724 - 0.0469) / 0.0469 ≈ 0.546 or 54.6%
Therefore, the unemployment rate increased by about 54.6%, which is closest to answer choice A. It increased by about 27%.
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A one of a kind necklace is worth $3200. The value of the necklace increases by 9% each year. Which explicit and recursive formulas can be used to model the situation.
The fomulas of the sequence are a(n) = 3200(1.09)^n-1 and a(n) = a(n - 1) * 1.09
How to determine the fomulas of the sequencefrom the question, we have the following parameters that can be used in our computation:
First term, a = 3200
Increment, r = 9%
To find the explicit formula, we can use the formula for compound interest:
a(n) = a * (1 + r)^n-1
So, we have
a(n) = 3200(1.09)^n-1
For the recursive formula, we have
a(n) = a(n - 1) * 1.09
This is because the product of the current term and the incremnt rate gives the next term
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melinda is practicing her penalty kicks. She took 40 shots and only missed 8. Based on the data,how many kicks will she make if she takes 60 shots
Answer:
48 kicks
Step-by-step explanation:
If she shoots 40 times and misses 8, we can create a ratio to represent the number of total shots to the number of misses:
40/8 = 60/x X represents the amount she will miss if she takes 60 shots.
We can find the value of x by using cross multiplication:
480 = 40x. We can now isolate x by dividing both sides by 40:
X = 12.
Melinda will miss 12 out of 60 shots.
She will make 48 kicks.
How to show steps upon problem to get answer
The simplified form of the expression xy( x³y⁵ - x⁷ ) is x⁴y⁶ - x⁸y.
What is the simplified form of the expression?Given the expression in the question;
xy( x³y⁵ - x⁷ )
To simplify the expression, apply distributive property.
xy( x³y⁵ - x⁷ )
xy( x³y⁵ ) - xy( x⁷ )
xy( x³y⁵ ) - xy( x⁷ )
Multiply xy and ( x³y⁵ )
x⁴y⁶ - xy( x⁷ )
Multiply xy and ( x⁷ )
x⁴y⁶ - x⁸y
Therefore, the simplified form is x⁴y⁶ - x⁸y.
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angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive
The grades that Angie need to receive in her next test so that her average is 92 is 91.
What is average?The average is defined as the mean value a given data set. The formula to calculate the mean of a given data set is:
Average = Sum of the observations / Total number of observations
Assume the marks that Angie needs in her next test is represented by x.
Given that Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. Therefore, the grades she need to receive in her next test so her average is 92 is:
Average = Sum of the grades of all test / Total Number of test
92 = (88+96+92+93+x)/5
460 = 369+x
460 - 369 = x
x = 91
Hence, she needs 91 grades in her next test.
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The complete question is:
Angie has reviewed grades of 88, 96, 92, and 93 on her last 4 tests. what grade will she need to receive in her next test so that her average of all test is 92?
The width of a rectangle is fixed at 7 cm. Determine (in terms of an inequality) those lengths for which the area will be
less than 175 cm²
The lengths for which the area will be less than 175 cm² are less than 25 cm
How to determine the lengths of the areasFrom the question, we have the following parameters that can be used in our computation:
Width = 7 cm
Area = Less than 175 cm²
The formula of area is represented as
Area = Length * Width
Using the above as a guide, we have the following:
Length * Width < 175
substitute the known values in the above equation, so, we have the following representation
Length * 7 < 175
Divide by 7
Length < 25
Hence, the length is less than 25
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Jesus believes in looking his best when searching for a job. He wants to save $435 for a new suit for his interviews. He currently has $65.00 and he can save $18.00 per week from his work.
How many weeks in total will it take him to save for the suit, assuming he puts the $65.00 into an account on week 1 and starts saving each week thereafter?
Answer:
6.7 weeks.
Step-by-step explanation:
65.00 x 6.7 = 435.50
Answer:
Step-by-step explanation:
He has $65 on the first week. He’s missing $370. If he can save $18 a week. 370/18 = 20.5. But they’re asking for the total weeks it’ll take. So add the first week. 20.5 + 1 = 21.5
not mine but he did he get it right
Use interval notation to write the intervals over which fis (a) increasing, (b) decreasing, and (c) constant.
The intervals of each behavior of the function are given as follows:
a) Increasing: (-∞, -1).
b) Decreasing: (-1, 1).
c) Constant: (1, 3).
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable .
here, we have,
to classify the function as increasing, decreasing or constant:
The function is increasing when the graph moves right and up.
The function is decreasing when the graph moves right and down.
The function is constant when the graph of the function is an horizontal line.
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Help!!
Write an equation to show the total cost, y, for x months.
how can I solve binary operations?
Some way to solve binary operations are listed below
How can binary operations be solvedBy definition, binary operations involve performing arithmetic operations on two operands in a specific way.
An example of a binary expression is a + b
Where a and b are the operands & + is the operator
Some common binary operations and how to solve them are highlited below
Addition (+): To add two binary numbers, start from the right-most bit and work your way left. In binary: 1 + 1 = 10Subtraction (-): To subtract one binary number from another, use the same borrowing method as in decimal subtraction.Other operations are
Multiplication (*), Division (/) and Modulus
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Solve the system by graphing.
a)
y = x
y = 2x+2
By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).
Solving the system of equations:To solve the system of equations, graph the given two lines' first equation. Now determine whether the lines are parallel, intersect, or are the same line.
In the next step, we need to Identify the solution to the system.
If the lines are intersected, the point of intersection is the solution.
If the lines are parallel, the system will have no solution.
If the lines are the same or coincident, then the system will have an infinite number of solutions.
Here we have
y = x ----- (1)
y = 2x+2 ---- (2)
From (1) and (2)
=> y = 2y + 2
=> 2y - y = -2
=> y = - 2
Hence, the solution of the given system of the equation is (-2, -2)
We can check it by graphing the lines as shown figure.
Therefore,
By the given graph we can conclude that the solution of the equation (i.e point of intersection of lines) is (-2, -2).
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Some candles are in the shape of a right circular cylinder. For one such candle, the radius is 9 cm and the height is 26.5 cm. Find the volume of the candle. Round your answer to the nearest whole number. Do not type the units in the space below. (Be sure to use the pi button on your calculator to do the calculation.)
radius = 9 cm
height = 26,5 cm
as we know that
volume of cylinder = πr^2h
= 3,14x9x9x2x26,5
= 13.480 cm cubic
0
A
B
A"
C'
B'
2. What is the relationship among AC, A'C', and A"C"?
B"
Relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides
What is Graph?a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
To widen or enlarge an opening or hollow structure beyond its usual size in simple way changes the the size.
The scale factors is the factor in which each linear measure of the figure is multiplied.
AC is a smaller triangle which is dilated to get A'C' and this A'C' is dilated to get A''C''.
the relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides with a scale factor.
Hence, relationship among AC, A'C', and A"C'' is all the three sides are corresponding sides
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It is estimated that approximately one-half of all aluminum cans will be recycled each year. If a soft drink company produces 350,000 cans one year, how many cans are still in use after 4 years of recycling and re-using, using this function?
N, = 350,000(0.52)
A.87,500
B.25,591
C.175,000
D.21,875
25,591 cans are still in use after 4 years of recycling and re-using. The solution has been obtained by using functions.
What is a function?
A function is a connection between a set of inputs and one output for each input. The usual notation for a function is f(x), where x represents the input. Usually, a function is written as y = f(x).
We are given a function as N = 350,000 [tex](0.52)^{t}[/tex]
t is given to be 4 years.
Substituting this in the function, we get
⇒N = 350,000 [tex](0.52)^{4}[/tex]
⇒N = 350,000 * 0.07311616
⇒N = 25,590.6
⇒N = 25,591
Hence, 25,591 cans are still in use after 4 years of recycling and re-using.
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Full question has been attached below
A company is making T shirts. They know that the probability of a shirt being defective is (.02).
The company makes a profit of $20 for every shirt they sell. However, each defective shirt costs
the company $35 in replacement costs. How much money does the company really make per
Shirt?
The amount of money the company makes per shirt $18.90
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The chances that event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes
= X/n
To calculate the expected profit per shirt, we need to consider the two possible outcomes:
the shirt is defective or not defective.
If the shirt is not defective, the company makes a profit of $20.
If the shirt is defective, the company incurs a cost of $35 and no profit.
The probability of a shirt being defective is 0.02, so the probability of a shirt not being defective is:
= 1 - 0.02
= 0.98.
Therefore, the expected profit per shirt can be calculated as:
Expected profit = (probability of not defective) x (profit per non-defective shirt)
+ (probability of defective) x (cost per defective shirt)
Expected profit = 0.98 x $20 + 0.02 x (-$35)
Expected profit = $19.60 - $0.70
Expected profit = $18.90
So the company really makes $18.90 per shirt, taking into account the cost of defective shirts.
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A road is inclined at an angle of 6 . After driving 4950 feet along this road, find the driver's increase in altitude.
The driver increased altitude is 517 feet.
How to find the side of a right triangle?A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the road is inclined at an angle of 6 degrees. After driving 4950 feet along this road, let's find the altitude as follows:
using trigonometric ratios,
sin 6° = opposite / hypotenuse
Therefore,
sin 6° = a / 4950
cross multiply'
a = 4950 sin 6°
a = 4950 × 0.10452846326
a = 517.415893175
Therefore,
a = 517 feet
Altitude = 517 feet
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