The constant of proportionality between the total cost and the number of songs is 0.72.
What is the constant of proportionality?The constant of proportionality is the ratio that supplies the variable cost per unit of each song.
Other names for the constant of proportionality include:
SlopeUnit rateConstant rateConstant ratioRate of changeConstant of variation.Determining the constant of proportionality can help us formulate the total cost equation as y = 0.72x.
Number of Songs Total Cost Unit Cost
13 $9.36 $0.72 ($9.36/13)
17 $12.24 $0.72 ($12.24/17)
19 $13.68 $0.72 ($13.68/19)
Check:
y = 0.72x
y = 0.72(13)
y = $9.36
Thus, the constant of proportionality is 0.72, showing that a downloaded song costs $0.72 each.
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14 subtracted from the product of x and -3 is 25
Answer:
14-3x=25
Step-by-step explanation:
-3x=25+14
-3x=39
-3 -3
x = -13
For what value of x is g(x) = 2
Answer:
x = 2
Step-by-step explanation:
For the function g(x) to have to equal only 2, that would have to be for the input, x, to be 2 itself considering there's no equation given.
Hope this helps!
Which of the following are less than -0.625
Answer: The answer is A
Step-by-step explanation:
-5/8 is literally equal to -0.625 meaning this asnwer is equal not less
-0.5 is Greater than -0.625 because -0.6 is much larger
-8/5 is -1.6 which is Less than -0.625
Find the LCM of 14 and 21. I need the explanation
Answer:
LCM = 42
Step-by-step explanation:
There are many ways to do this.
Listing Multiples:
Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.
Multiples of 14:
14, 28, 42, 56, 70
Multiples of 21:
21, 42, 63, 84
Therefore,
LCM(14, 21) = 42
Prime Factorization:
List all prime factors for each number.
Prime Factorization of 14 is:
2 x 7 => 21 x 71
Prime Factorization of 21 is:
3 x 7 => 31 x 71
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 3, 7
Multiply these factors together to find the LCM.
LCM = 2 x 3 x 7 = 42
In exponential form:
LCM = 21 x 31 x 71 = 42
LCM = 42
Therefore,
LCM(14, 21) = 42
Cake / Ladder:
Divide your numbers by prime numbers as long as both numbers are evenly divisible by that prime.
Cake / Ladder
7 14 21
2 3
When there are no more primes that evenly divide into both numbers you are done.
The LCM is the product of the numbers in the L shape, left column and bottom row.
LCM = 7 x 2 x 3
LCM = 42
Therefore,
LCM(14, 21) = 42
Division Method:
Write your numbers in the top row.
Divide your numbers by prime numbers as long as at least one of your numbers is evenly divisible by a prime number.
Division Table
2 14 21
3 7 21
7 7 7
1 1
Bring down any numbers that are not evenly divisible by the prime number.
When the last row of results is all 1's you are done.
Find the product of the prime numbers in the first column to get the LCM:
LCM = 2 x 3 x 7
LCM = 42
Therefore,
LCM(14, 21) = 42
GCF Method:
LCM(14,21) = (14 × 21) / GCF(14,21)
= (14 × 21) / 7
= 294 / 7
= 42
Therefore,
LCM(14, 21) = 42
Venn Diagram:
Inside circle 14: 2
In between circles: 7
Inside circle 21: 3
Then, use prime factorization.
Find the set of prime factors for each number.
Prime Factorization Set for 14 is:
2, 7
Prime Factorization Set for 21 is:
3, 7
Identify the intersections of prime numbers and put them into the Venn Diagram where their circles intersect. Remove the numbers from the original sets.
14 ∩ 21
7
With the remaining prime numbers in each set, if any, put them into their respective circles, not in intersections.
14
2
21
3
Find the union of the sets in the Venn Diagram. This is the superset of all of the prime numbers in the diagram.
14 ∪ 21
The new superset list is
2, 3, 7
Multiply these factors together to find the LCM.
LCM = 2 x 3 x 7 = 42
LCM = 42
Therefore,
LCM(14, 21) = 42
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Find all intervals on which the function f(x) = (e^(2x^2+5)/-6x is decreasing.
The function f(x) is decreasing on the interval x∈(1/2,∞) and all the real values.
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.
Given function,
f(x)=[tex]e^{2 x^{2} +5}[/tex]/-6x
f'(x)=-1/6x([tex]e^{2 x^{2} +5}[/tex])(4x)+[tex]e^{2 x^{2} +5}[/tex](1/6x²)
=[tex]e^{2 x^{2} +5}[/tex]/6x((1/x)-4x)
f'(x)=0
((1/x)-4x)=0
1-4x²=0
4x²=1
x=±1/4
Given that, f(x) is decreasing function then,
f'(x)<0
((1/x)-4x)<0
(1-4x²)/x<0
1-4x²<0
1<4x²
1/4<4x²
x²>1/4
x>1/2
x∈(1/2,∞)
Hence, f(x) is decreasing on the interval x∈(1/2,∞)
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Given that logb(7)≈1.946, logb(9)≈2.197, and logb(16)≈2.773, find the logarithm of logb(1/63)
b is base b
The logarithmic expression given as logₙ(1/63) has its value to be -4.143
How to determine the logarithmic expression?From the question, the given parameters are
logₙ(7) = 1.946
logₙ(9) = 2.197
logₙ(16) = 2.773
The logarithmic expression to calculate is given as
logₙ(1/63)
Express 1/63 as 1/7 * 1/9
So, we have the following representation
logₙ(1/63) = logₙ(1/7 * 1/9)
Apply the product of logarithm
This gives
logₙ(1/63) = logₙ(1/7) + logₙ(1/9)
Apply the exponent of logarithm
This gives
logₙ(1/63) = -logₙ(7) - logₙ(9)
Substitute logₙ(7) = 1.946 and logₙ(9) = 2.197 in logₙ(1/63) = -logₙ(7) - logₙ(9)
logₙ(1/63) = -1.946 - 2.197
Evaluate
logₙ(1/63) = -4.143
Hence, the value of the logarithmic expression is -4.143
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Given that €1 = £0.75
a) How much is €530 in £?
b) What is the £ to €-exchange rate?
Answer: a.) 397.5 b.) 1.3333
Step-by-step explanation:
1 cent = £0.75
530 x 0.75 = 397.5
530 / 397.5 = 1.3333
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Between which two consecutive integers is [tex]\sqrt{201}[/tex]
Answer:
14 and 15
Step-by-step explanation:
[tex]196<201<225 \\ \\ \sqrt{196}<\sqrt{201}<\sqrt{225} \\ \\ 14<\sqrt{201}<15[/tex]
how should i explain this please help???
Answer:
An arithmetic sequence occurs when the difference between each term and the next is constant. Therefore, only addition or subtraction is possible. Also, the amount (4, in this case) must remain the same when added to each successive term.
Given the following function, the values of p and q are...
f(x)= 3x^2-x-4
A. p=1, q=3
B. p=4, q=3
C. p= -4, q= 3
D. p=3, q=-4
Select the best answer for the question.
19. What is the sum of 1/9 2/3, and 5/18?
O A. 4/15
O B. 12/9
O C. 8/30
O D. 19/18
Answer:
the answer Is D 19/18
1/9 +2/3=1/9+ 6/9 =7/9
7/9 +5/18= 14/18 + 5/18 = 19/18
Write the equation of a line passing through the point (6, 4) that is parallel to the line 2x + 3y = 9.
The equation of line parallel to 2x +3y = 9 and passing through the point (6,4) is 3y + 2x = 24
What is gradient ?Gradient or slope is the ratio of the change in y to the change in x between two points in a line.
Gradient tells how steep a line is. A perfectly vertical or horizontal line has no slope.
2x + 3y = 9
making y the subject,
3y = 9 - 2x
y = 9/3 -2x/3
Comparing the above equation, with equation of a straight line, y = mx + c
m, which is slope = -2/3
The new line will also have a slope of -2/3 because they are parallel.
Equation for new line,
y-[tex]y_{1}[/tex] / x - [tex]x_{1}[/tex] = slope
The new point is (6,4)
y - 4 / x -6 = -2/3
By cross multiplying
3(y-4) = -2(x - 6)
3y - 12 = -2x + 12
3y + 2x = 24
In conclusion, the equation o the new line is 3y + 2x = 24
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factorise fully 8x^2-4x
Answer:
4x(2x−1)
Step-by-step explanation:
[tex] {8x}^{2} - 4x[/tex]
Factor out 4.
[tex]4( {2x}^{2} - x)[/tex]
Consider
[tex] {2x}^{2} - x[/tex]
Factor out x.
x(2x−1)
Rewrite the complete factored expression.
=4x(2x−1)
Comet Lee borrowed $16,000 on a 6%, 90-day note. After 20 days, Comet paid $2,000 on the note. On day 50, Comet paid $4,000 on the note. What are the total interest and ending balance due by the U.S. Rule? Use ordinary interest. (Use 360 days. Do not round the denominator in your calculation and round your final answers to the nearest cent.)
The total amount of interest and the final debt owed under the US Rule is $191.09.
Given that,
Comet Lee took out a $16,000 loan with a 90-day, 6% note. Comet settled the note for $2,000 after 20 days. Comet settled the note for $4,000 on day 50.
We have to find what is the total amount of interest and the final debt owed under the US Rule.
First,
To calculate $2000 per 20 days.
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $1600
r is 6%
t is 20 days is 20/360
So,
i= 1600×0.06×20/360
i= $53.33
Apply partial payment to interest due,
$2000-$53.33= $1946.67
Next,
Subtract remainder of payment from principal is adjusted balance
Adjusted balance =$16000-$1946.67
Adjusted balance =$14053.33
Now, Second,
To calculate $4000 per 50 days.
We know that,
i=p×r×t
So, p is $14053.33
r is 6%
t is 50 days is 30/360
So,
i= 14053.33×0.06×30/360
i= $70.27
Apply partial payment to interest due,
$4000-$70.27= $3929.73
Next,
Subtract remainder of payment from principal is adjusted balance
Adjusted balance =$14053.33-$3929.73
Adjusted balance =$10123.6
Now, for 40 days
i= 10123.6×0.06×40/360
i= $67.49
So, balance is 10123.6+67.49= $10191.09
When max make two makes partial payments,
The total interest is $53.33+$70.27+$67.49= $191.09
Therefore, the total amount of interest and the final debt owed under the US Rule is $191.09.
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2a × ( 3 + b ) = 6a + 2ab is an example of the property
Answer:
It's an example of the distributive property
A bag of fertilizer covers 3000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 170 feet. To cover the lawn bags of fertilizer are required
Answer: The correct answer is 17 bags of fertilizer to cover the lawn
Step-by-step explanation:
1 bag of fertilizer covers 3000 SF of lawn
How many bags are needed for an area of 290 feet x 170 feet
Calculate the Square Feet:
290 x 170 = 49,300 SF
Divide space (SF) by bag coverage (SF):
49,300 / 3,000 = 16.43 bags of fertilizer
Round up answer to 17 bags of fertilizer
what is the product of 3/4 of 4/5
Answer:
0.6
Step-by-step explanation:
3/4 of 4/5 is the same as asking: If you take 3/4 of 4/5, what do you get? Furthermore, 3/4 is 75 percent. Therefore, we are solving 75 percent of 4/5 when we are solving 3/4 of 4/5. To solve the problem, we start by labeling 3/4 of 4/5 like this: N1/D1 of N2/D2
Then we use this fraction of a fraction formula to solve the problem:
(N1 x N2) / (D1 x D2)
When we enter 3/4 of 4/5 into the formula, we get:
(3 x 4) / (4 x 5) = 12/20
Therefore, the answer to 3/4 of 4/5 in its lowest form is:
3/4 of 4/5 = 3/5
The answer above is 3/4 of 4/5 in fraction form. Below we have converted the response to a decimal form for you: 3/4 of 4/5 = 0.6
Hint: If you need to figure out a Fraction of Fraction problem like 3/4 of 4/5 in the future, remember that you get the answer by multiplying the numerator to and the denominator this is the same as multiplying the fractions together.
The sum of m and ten multiplied by 4
Answer:
4(m+10)
Step-by-step explanation:
sum is adding
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Kevin has $97,800 in a savings account that earns 2% interest per year. The interest is not
compounded. How much will he have in total in 4 months?
If f(x) = 3x and g(x)=1/x, what is the domain of (gof)(x)?
For the given functions f(x) = 3x and g(x) = 1/x then domain of
(gof)(x) =1/3x is all the real numbers excluding zero.
As given in the question,
Given functions are as follow:
f(x) = 3x
g(x) = 1/x
Now ,
(gof)(x)
= g(f(x))
Substitute f(x) = 3x in the above function we have,
=g(3x)
Replace the value of x by 3x in the given function g(x) we get,
= 1/ 3x
For x = 0 (gof)(x) =1/3x is undefined.
Domain include all the real numbers except zero.
Therefore, for the given functions f(x) = 3x and g(x) = 1/x then domain of (gof)(x) =1/3x is all the real numbers excluding zero.
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PLEASE HELP ASAP!!! I WILL MARK YOU YOU BRAINLIEST
Which equations are true equations?
Select all correct answers.
39-3-6 6-10 +4
56 +8+3² - 2.2³
=
24
04-50-6²-8
82 5² 4² - 7
=
-
-
Answer:
C and A
Step-by-step explanation:
A medic's bag contains individually wrapped tongue depressors (each costing 4 cents) and Band-Aids (each costing 8 cents). If the materials are worth $12.48 and there are 184 individual packages in total, how many tongue depressors and Band-Aids are there?
The total number of tongue depressors and Band-Aids are 56 and 128 respectively.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given that, a medic's bag contains individually wrapped tongue depressors (each costing 4 cents) and Band-Aids (each costing 8 cents). If the materials are worth $12.48 and there are 184 individual packages in total,
Let the number of wrapped tongue depressors be w and that of Band-Aids be b,
Therefore,
w+b= 184
0.04w+0.08b = 12.48
w+2b = 312
On solving the equation, by elimination method, we get,
b = 128
Therefore, w+128 = 184
w = 56
Hence, the total number of tongue depressors and Band-Aids are 56 and 128 respectively.
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Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
The values of the variables x and y are 2 and -7.
We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation is y = -2x + 5. We are given two sets of ordered pairs. The ordered pairs are (6, y) and (x, 1). These points satisfy the given equation. We need to find the values of the variables x and y. We will substitute the coordinates into the equation.
y = -2x + 5
First, we will put (6, y).
y = -2(6) + 5 = -12 + 5 = -7
Now, we will put (x, 1).
1 = -2x + 5
2x = 4
x = 2
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For which value of x is line n parallel to line m?
Answer:
x is 70°
hopefully this will help u
The following number is shown in expanded form:
1 1
4x1+8 x 100 + 9 × 1000
What is the decimal form of the number?
The decimal form of the number is :
9804.0
What is the decimal number?
Decimals are a form of a number in algebra that has a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal number is, for instance, 34.5.
If the question is,
4x1+8 x 100 + 9 × 1000, then simplify it first
4x1+8 x 100 + 9 × 1000=4+800+9000=9804
So, the decimal form is :
9804.0
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PLEASE HURRY I WANT TO FINISH MY TEST AND I NEED THE ANSWER!!
Determine which integer will make the inequality 2(n + 2) < 5(n − 1) true.
The value to make the inequality true is n > 3
InequalityInequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
We need to solve this problem and determine what value will solve this problem.
2(n + 2) < 5(n - 1)
2n + 4 < 5n - 5
Collect like terms
4 + 5 < 5n - 2n
9 < 3n
3n > 9
n > 3
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Find the value of x.
76
139
90°
X
63°
180°
41
90
The measure of the angle 'x' will be 41°. Then the correct option is c.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The measure of the angles will be 76° and 63°.
By the property Supplementary angle, the equation is given as,
76° + x + 63° = 180°
Simplify the equation, then we have
x + 139° = 180°
x = 180° - 139°
x = 41°
The measure of the angle 'x' will be 41°. Then the correct option is c.
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6. Solve for y. 12y - 10 = 14y
02
0 5
O-5
O-2
Answer:
can you pls clear your questions?
100 POINTS WILL GIVE BRAINLYEST AND EVERYTHING!!!! What is the distance from (−7, −24) to (−7, 8)?
−32 units
−16 units
16 units
32 units
Answer:
D) 32 units==============
Given Two endpoints (- 7, - 24) and (- 7, 8)Find the distance between themSince both points have same x-coordinate, the distance between them is the difference of y-coordinates:
d = 8 - (- 24) = 8 + 24 = 32 unitsCorrect choice is D
Answer:
32 units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Define the two given points:
Let (x₁, y₁) = (-7, -24)Let (x₂, y₂) = (-7, 8)Substitute the two points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(-7-(-7))^2+(8-(-24))^2}[/tex]
[tex]\implies d=\sqrt{(-7+7)^2+(8+24)^2}[/tex]
[tex]\implies d=\sqrt{(0)^2+(32)^2}[/tex]
[tex]\implies d=\sqrt{32^2}[/tex]
[tex]\implies d=32[/tex]
Note: As the two given points have the same x-coordinate, the line segment (between the points) is a vertical line. Therefore, to find the distance between the two given points, simply calculate the difference between the y-coordinates:
[tex]\implies 8 - (-24) = 8+23=32[/tex]
plseas help
There are 7 students in grade 11 and 15 students in grade 12 that are part of the VSS robotics club. A committee consisting of a president, vice president, media rep, and accountant is being chosen.
a. In how many ways could the panel be chosen if the president and vice president must be from different grades?
b. In how many ways could the panel be chosen if it must include at least one grade 11 student and at least one grade 12 student?
The number of ways to form the committees, using the Fundamental Counting Theorem, are given as follows:
a) President and vice from different grades: 79,800.
b) At least one from each: 141,960.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, there are two possible cases for the parameters, as follows:
[tex]n_1 = 7, n_2 = 15, n_3 = 20, n_4 = 19[/tex]: President from grade 11, vice from grade 12, the remaining two roles can be chosen from any student.[tex]n_1 = 15, n_2 = 7, n_3 = 20, n_4 = 19[/tex]: President from grade 12, vice from grade 11, the remaining two roles can be chosen from any student.Hence the number of ways is:
N = 7 x 15 x 20 x 19 + 15 x 7 x 20 x 19 = 79,800.
For item b, the total number of outcomes is obtained as follows:
N = 22 x 21 x 20 x 19 = 175,560.
The number of outcomes with only grade 11 students is:
N = 7 x 6 x 5 x 4 = 840.
The number of outcomes with only grade 12 students is:
N = 15 x 14 x 13 x 12 = 32760.
Hence the number of students with at least one of each is:
N = 175,560 - (840 + 32,760) = 141,960.
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