There is a constant of proportionality between the two purchases and each book costs $4.99.
Step-by-step explanation:A correspondence relation between two variables is of direct proportionality when the quotient between the corresponding quantities is always the same. This quotient is called the constant of proportionality.
In other words, when dividing any quantity of one of the magnitudes by the one that corresponds to it in the other, the value it gives is always the same. This value is known as the constant of proportionality.
In this case, the constant of proportionality [tex]k[/tex] will relate the number of books bought [tex]N[/tex] and their cost [tex]C[/tex] in the following way:
[tex]C=k*N[/tex]
So k is the price per book.
For the 12 books:
[tex]k=\frac{59.88}{12}[/tex]
[tex]k=4.99[/tex]
And for the 21 books:
[tex]k=\frac{104.79}{21}[/tex]
[tex]k=4.99[/tex]
The constant [tex]k[/tex] for the two purchases is the same, thus there is a constant of proportionality between the two purchases and each book costs $4.99.
During a sale the regular price of an item is reduced by 20 percent if the sale price is $600 what is the regular price
2. Which situation does have a final value of 0? A. A jet tose lo a height of 1000 feet ubove the ground. It then descended to a height of 100 feet. B. The tempetature at 1:00 p.m. was 10"F. It dropped another 10 over 4 hours. C Pace deposits $10 in his account and then withdrew $10. D. Keith guinod 8 yards during the first quarter of the football game and then lost 8 yards during the second quarter. pls helpp
Find the arc length of the circle with a central angle of 30 degrees and a radius 12. Leave the answer in terms of π.
[tex]\text{Arc length,}\\\\s = r \theta \\\\~~=12\cdot \left(30 \times \dfrac{\pi}{180} \right)\\\\~~=12\cdot \dfrac{\pi}6\\\\~~=2\pi[/tex]
Is the vertex of the graph a maximum or a minimum?
Answer:
maximum
Step-by-step explanation:
Concepts
The vertex of a graph represents the turning point in a parabola.
Example: The graph shown in your question first steadily increases, but then at the point (1,3), it begins to go down. The point (1,3) is called the vertex in this case because it symbolizes the turning point.
Application
We are asked to determine if the vertex of this graph is a maximum or minimum. If the vertex is maximum, it's the highest point on the graph. If it's the minimum, it's the lowest point on the graph. Using your stunning eyes, you can see that the vertex is the highest point on the graph, making the answer maximum.
Why is 10^15/10^4 equal to 10^11
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the expression 10¹⁵/10⁴ equals 10¹¹.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression 10¹⁵/10⁴ can be simplified as,
[tex]\dfrac{10^{15}}{10^4}\\\\= 10^{15} \cdot 10^{-4}\\\\= 10^{15-4}\\\\=10^{11}[/tex]
Hence, the value of the expression 10¹⁵/10⁴ equals 10¹¹.
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If 35 boxes equals to 21 dollars in total, how much does each box cost?
What is the volume of the right triangular prism in cubic meters?
Answer:
8×3×2=48
Step-by-step explanation:
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Answer:
48 cubic meters
Step-by-step explanation:
Drag numbers to the table so it shows a proportional relationship between x and y.
PLEASE HELP
Answer:
See below ~
Step-by-step explanation:
Finding the proportionality constant, k :
y = kxTake the point (0.5, 3)3 = 0.5kk = 6Table :
[tex]\left[\begin{array}{ccc}0.5&3\\1.5&9\\4.5&27\end{array}\right][/tex]
Find the amount of sheet metal needed to form a conical funnel of base radius 30 cm and vertical height 50 cm, allowing for a 0.5 cm overlap at the join
The amount of sheet metal needed to form the conical funnel is 5525 cm²
How to determine the amount of sheet?The given parameters are:
Radius, r = 30 cmVertical height, h = 50 cmOverlap = 0.5 cmStart by calculating the slant height (l) of the cone using:
l = √(r² + h²)
This gives
l = √(30² + 50²)
Evaluate
l = 58.31
The lateral surface area of the conical funnel including the overlap is then calculated as:
A = πrl + Overlap * l
This gives
A = 3.142 * 30 * 58.31 + 0.5 * 58.31
Evaluate
A = 5525.4556
Approximate
A = 5525
Hence. the amount of sheet metal needed is 5525 cm²
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Mr. Jones grades 12 exams
in 2 hours. At that rate,
how many hours would it
take to grade 48 exams?
Answer:
8 hours
Step-by-step explanation:
12/2= 6
He grades 6 exams per hour
48/6= 8
it would take 8 hours to grade 48 exams
Bonus:
it takes him 10 minutes to grade an exam. That doesnt matter for this question but it's good 2 know
Answer:
8 hours
Step-by-step explanation:
To solve this it seems you need to set up a proportion.
12/2=48/x
cross multiply the 2 and 48.
2•48=96.
divide by the remaining number to get x.
96/12=8.
PLS ANSWER FAST TYYYYYSMMM!!!
Answer:
option 3, [tex]972\pi in^{3}[/tex]
Step-by-step explanation:
The formula to find the volume of a sphere is [tex]\frac{4}{3} \pi r^{3}[/tex]
where r os the radius
given: diameter = 18in
radius = diameter / 2
radius = 18 / 2
r = 9in
Plug in radius:
[tex]\frac{4}{3} \pi (9)^{3}\\\\\frac{4\pi (9)^{3}}{3} \\\\Factor (9)^{3}: (3)^{6}\\\\\frac{(3)^{6} * 4\pi }{3} \\\\[/tex]
cancel common factor: 3
[tex]3^{5} * 4\pi \\3^{5} = 243\\243 * 4\pi\\972\pi[/tex]
Let me know if you have any questions !
(I will mark brainliest) Will 3/8 + 2/8 be closer to 1/2 or 1? How do you know?
Answer:
1/2
Step-by-step explanation:
3/8 + 2/8 is 5/8, 1/2 is equal to 4/8, so 5/8 is only 1/8 away from 1/2 while 5/8 is also 3/8 away from 1 or 8/8 therefore, it is closer to 1/2
Complete the sentence.
------- is 4 times as much as 9.
Answer:
36
Step-by-step explanation:
4 x 9 = 36
36 / 4 = 9
Therefore, 36 is 4 times as much as 9.
[tex]{\sf Hello!}[/tex]
The answer is 36
⇢ 4 × 9 = 36
PLEASE SOLVE FOR X AND Y!!!! I WILL MARK BRAINLIEST!!!!
opposite sides and diagonals of a parallelogram are equal
+ diagonals of a parallelogram meet eachother in the middle so:
10x+14=x+77
10x-x=77-14
9x=63
x=63÷9
x= 7
y+8=4y-19
y-4y=-19-8
-3y=-27
y=-27÷-3
y=9
2z+3=37
2z=37-3
2z=34
z=34÷2
z=17
At a local pizza place, the cost of a large cheese pizza is $13.99. Each additional topping is $1.25. The Tigerd family orders a large pizza topped with pepperoni, mushrooms, olives, and sausage. How much did their pizza cost? Show your work.
Answer:
$18.99
Step-by-step explanation:
The total cost is the base cost plus that of the added toppings.
total cost = base cost + (number of toppings) × (topping cost)
total cost = $13.99 + 4 × $1.25 = $18.99
Their pizza costs $18.99.
Explain how you would graph the inequality, "b ≤ 0
Answer:
the inequality, b ≤ 0 has interval Notation of -∞,0
Step-by-step explanation:
the inequality, b ≤ 0 has interval Notation of -∞,0
A cube has a surface area of 486 inches square. Can the length of each side of the cube be 11 inches? Explain
Answer:
The volume of cube whose total surface area is 486 cm² is 729 cm³
Step-by-step explanation:
If the tax on a $25 shirt is 10%, what would the final cost be?
Answer: $27.5
Step-by-step explanation:
10 percent of 25 is 2.5 (which is the tax). We just add that to the cost of the shirt and we get the final cost of $27.5.
What is the value of x?
I need this done fast please
hope this helps :)
............
what does (5x3)+(4x2) equal
Answer:
23
Step-by-step explanation:
5 x 3 = 15
4 x 2 = 8
15 + 8
= 23
An insurance firm wants to estimate the percentage of senior citizens in a small town with approximately 2,534 residents. it asks a group of 85 randomly selected people in the town about their age.
select the statement that is true.
a. the sample is 2,534 people. the population is 85 people.
b. the sample is 85 people. the population is 2,449 people.
c. the sample is 85 people. the population is 2,534 people.
d. none of the answer choices are true.
Using sampling concepts, it is found that the correct statement is given by:
c. the sample is 85 people. the population is 2,534 people.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, a group of 85 people, which is the sample, is taken from the entire population of 2,534 people, hence option c is correct.
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PLEASE HELP WILL GIVE BRAINLEST!
Answer:
5[tex]\pi[/tex]/12 rad
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
75(π/180) = 5π/12 radians
arc length = central angle (2πr)
360
measure of the inscribed angle = 75º
measure of the central angle = 150º
arc length = 150 (2π1000)
360
arc length = (5/12)
If each of the numbers in the following data set were multiplied by 12, what
would be the median of the data set?
28, 58, 20, 14, 18, 71, 36
Answer:
answer: 336!!
Step-by-step explanation:
have a good day!
A new TV costs $675 and the finance rate is 9.5%. If a down payment of $75 is made
and the TV is financed for one year, what is the monthly payment?
Answer:
The monthly payment will be $54.75
Step-by-step explanation:
Hope this helps!
in how many ways can 4 people be seated in a row of 12 chairs
Answer:
11,880.
Step-by-step explanation:
This is given by the number of permutations of 4 from 12
= 12P4
= 12!/(12-4)!
= 12!/8!
= (12*11*10*9*8*7*6*5*4*4*2*1) / (8*7*6*5*4*4*2*1)
= 12^11*10*9
= 11,880.
9+n=-2
how do i find the unknown exponent n?
1. Find the least common multiple of x² + x-12 and x² + 2x - 15
Least Common Multiple = (x-3) (x+5) (x+4)
Step-by-step explanation:
First we solve for x² + x-12
Factorise=> x² + 4x - 3x - 12
Taking common=> x ( x+4 ) - 3 (x+4 )
=> (x-3) (x+4)
Now we will solve for x² + 2x - 15
Factorise=> x² + 5x - 3x - 15
Taking common=> (x-3) (x+5)
we see here (x-3) is common in both the equations so We write it only 1 time as we have to find least common multiple .
Ans. Lest common multiples are = (x-3) (x+5) and (x+4)
I need help asap please
When Digitalis knows that it'll sell many of the processors, it's expected to make money since there's a higher probability that it's not defective.
How to illustrate the probability?Since the processor is sold for $3300 and a profit of $429 is made, the selling price will be:
= $3300 - $429
= $2871
In this case, there's a 13% chance that it's defective and 87% that's it's not defective. Therefore, it's expected to make money since there's a higher probability that it's not defective.
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8x+21=3 need the answer please
Answer:
[tex]x=-\frac{9}{4}[/tex]
Step-by-step explanation:
Step 1: Subtract 21 from both sides
[tex]8x + 21 = 3[/tex]
[tex]8x + 21 - 21 = 3 - 21[/tex]
[tex]8x = -18[/tex]
Step 2: Divide 8 from both sides
[tex]8x = -18[/tex]
[tex]\frac{8x}{8}=-\frac{18}{8}[/tex]
[tex]x=-\frac{9}{4}[/tex]
Answer: [tex]x=-\frac{9}{4}[/tex]
