Answer:
1. 192 books.
2. 96 books.
3. 24 books.
Step-by-step explanation:
1. Let's find the volume of each book and the volume of the box, this way:
Volume of a book = 4 * 6 * 1 = 24 inches ³
Volume of the box = 24 * 24 * 8 = 4,608 inches ³
2. If Hardy fills the box completely, what is the greatest number of books that fit into the box?
Greatest number of books = Volume of the box/Volume of a book
Greatest number of books = 4,608/24
Greatest number of books = 192
3. If Hardy fills the box completely with the least number of layers, there will be (blank) books on the bottom layer.
The height of the box is 8 inches, so it can only can hold 2 or 8 layers of books, since the books are 4 * 6 * 1 inches.
Greatest number of layers = Height of the box/Width of a book
Greatest number of layers = 8/1 = 8
Minimum number of layers = Height of the box/Height of a book
Minimum number of layers = 8/4 = 2
Upon saying that, we have:
Number of books per layer = Greatest number of books/Minimum number of layers
Number of books per layer = 192/2 = 96
4. To fill the box completely, Hardy places 8 layers of books in the box. There are (blank) books in each layer.
Number of books per layer = Greatest number of books/Number of layers
Number of books per layer = 192/8
Number of books per layer = 24
Find the distance between the given points. (2,4) (6,-2)
Answer:
y=-1/2x+7
Step-by-step explanation:
Derrick has 72 inches of ribbon to make bows. He uses all of his ribbon to make 9 bows of equal length l . How many inches of ribbon does each bow use? Write an equation to model the situation. Then solve the problem.
To find out how much ribbon is used for each bow, we set up and solve the equation 72 = 9l. Our solution is that each bow uses 8 inches of ribbon.
Explanation:This is a problem about division in real-life situations or practical arithmetic. Given that Derrick has 72 inches of ribbon and he wants to make 9 bows of equal length from the ribbon. A suitable equation to model this situation is: 72 = 9l .
To solve this equation for l (which represents the length of ribbon used for each bow), you would divide both sides of the equation by 9. This results in l = 72 ÷ 9. Performing the division calculation gives you that l = 8. Hence, each bow uses 8 inches of ribbon.
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5 3/4 - 3 1/2. What is the answer?
Answer:
2 and 25/100
Step-by-step explanation:
Form a union for the following sets.
K= {2, 3, 5, 8}
L = {3, 5, 7}
00)
O (3,5}
O [2, 3, 5, 7, 8]
O (2,7,8)
Answer:
The Correct option is third one { 2, 3 , 5 , 7 , 8 }.
Therefore,
KUL = { 2, 3 , 5 , 7 , 8 }
Step-by-step explanation:
Set:
A set in mathematics is a collection of well defined and distinct objects, also consist of a collection of elements.
Examples given here is
K = { 2, 3 , 5 , 8 }
K is a set consist of number two, three, five, and eight.
Similarly,
L = { 3 , 5 , 7 }
L is a set consist of number three, five, and seven.
Union:
The union of a collection of sets is the set of all elements in the collection.
It is denoted as ' ∪ '
Therefore,
(K∪L) = { 2, 3 , 5 , 7 , 8 }
It is the collection of set K and L both together.
Therefore,
KUL = { 2, 3 , 5 , 7 , 8 }
Which equation has a constant of proportionality of 3.5?
Answer:
Question not clear, but likely y = 3.5x if this is one of the answer options
Step-by-step explanation:
The question is not clear as you haven't posted the answer options,
however if any are y = 3.5x, then this would be the answer.
find the area of the trapezoid 21m by 7m by 21m
Answer:
its 294 hope this helps
Step-by-step explanation:
I need help with this
Answer:
with what
Step-by-step explanation:
find the measure of ∠6
Answer:
75 degrees would be it
How do you calculate y-intercept
Answer:
In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y intercept of the line.
Step-by-step explanation:
i) from the general equation of line we know that any line can be represented in the form y = mx + c , where m is a constant and is called the slope of the line and c is also a constant and is the y-intercept.
ii) In the equation y = mx + c if we substitute the value of x as zero we will get a point on the y axis given by y =(m × 0) + c ⇒ y = c. Therefore the point of the line on the y axis is (0, c) and so c is also called the y intercept of the line.
iii) If for example we have the line 3y = 6x + 12 then we first get this equation of the line to match the general form of the equation of the line, that is y = mx + c. Therefore dividing both the left and the right sides of the given equation of the line by 3 we get y = 2x + 4 which matches with the general form of the equation for line and we see that the slope of the given line is m = 2 and the y intercept is given by c = 4.
Select a real-world problem for the equation 18w = 108. Then solve the problem. A If total rainfall for last month was 108 inches and it rains 18 inches this month, how many inches of rainfall were there total? B If after 108 days someone has made 18 new friends, how many friends did she make per day? C A lab technician earns 18 dollars per hour, if he worked for 108 hours, how much did he earn? D If one full glass holds 18 ounces of water, how many full glasses will hold 108 ounces?
The problem is multiplying w by 18 to get a total of 108.
The answer would be :
D If one full glass holds 18 ounces of water, how many full glasses will hold 108 ounces?
To solve for the number of cups divide both sides of the equation by 18:
18w = 108
W= 108 / 18
W = 6
It would take 6 18 ounce glasses to equal 108 total ounces.
Suppose Tommy walks from his home at (0, 0) to the mall at (0, 8), and then walks to a movie theater at (6, 8). After leaving the theater Tommy walks to the store at (6, 0) before returning home. If each grid square represents one block, how many blocks does he walk?
Answer:
He walks 28 blocks.
Step-by-step explanation:
0,0 to 0,8 is 8 blocks
0,8 to 6,8 is 6 blocks
6,8 to 6,0 is 8 blocks
returning home (6,0 to 0,0) is 6 blocks
8+6+8+6=28 blocks
Question :
Jessica rode 9 miles farther than Roger rode. Let r represent the number of miles Roger rode . Write am expression for the number of miles jessica rode
Answer:
9+r
Step-by-step explanation:
jessica rode 9 more miles so u would add it to the number of miles roger rode
The expression for the number of miles Jessica rode, given that Roger rode r miles, is r + 9.
Explanation:The question asks us to write an expression for the number of miles Jessica rode, given that she rode 9 miles farther than Roger.
If we let r represent the number of miles Roger rode, then the expression for the number of miles Jessica rode would be r + 9.
This is because Jessica's distance is Roger's distance plus the additional 9 miles.
Which of these is a ratio table?
Pls help
Answer:the one at the very bottom
Step-by-step explanation:Because 1-2 is right so then 2-blank would have to be 4 which is the very bottom one.
The correct answer would be option (D) which is a ratio table.
What is a Ratio Table?A ratio table is a table that shows the recurring relationship between two values. A set of data points can be used to observe the constant relationship. A set of data with a constant relationship between two values is a comparison of miles traveled to hours traveled. A special type of ratio is the comparison of two different quantities. A rate compares quantities measured in different units.
As per option (D), we have
A B
1 2
2 4
3 6
The ratio of A and B is :
A:B = 1/2 = 1:2
A:B = 2/4 = 1/2 = 1:2
A:B = 3/6 = 1/2 = 1:2
Hence, we can conclude that this is a ratio table.
The correct answer would be option (D)
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A model rocket was built using a scale factor of 1:15 if the height of the actual rocket is 9.9m, what is the height of the millimeters
Answer:
660 mm
Step-by-step explanation:
we know that
The scale factor is [tex]\frac{1}{15}[/tex]
That means
1 unit in the model represent 15 units in the actual
or
1 m in the model represent 15 m in the actual
To find out the height of the model rocket, divide the height of the actual rocket by 15
so
[tex]9.9\ m=\frac{9.9}{15}= 0.66\ m[/tex]
Convert m to mm
Remember that
[tex]1\ m=1,000\ mm[/tex]
To convert meters to millimeters, multiply by 1,000
so
[tex]0.66\ m=0.66(1,000)=660\ mm[/tex]
Final answer:
To find the height of a model rocket built to a 1:15 scale with the actual rocket height at 9.9 meters, multiply 9.9 by the scale factor (1/15) and convert the result to millimeters, yielding 660 millimeters for the model's height.
Explanation:
The student asked how to find the height of a model rocket that was built using a scale factor, given the height of the actual rocket. To solve this problem, we use the scale factor to determine the model's dimensions. For example, if a model rocket was built using a scale factor of 1:15 and the actual rocket is 9.9 meters tall, we would calculate the model's height in millimeters by multiplying the actual height by the scale factor and converting meters to millimeters (1000 millimeters = 1 meter).
Here's the calculation:
Model Height in meters = Actual Height in meters * Scale Factor = 9.9m * (1/15)Model Height in millimeters = Model Height in meters * 1000 = (9.9m * (1/15)) * 1000By performing the multiplication, we find that the model's height would be 660 millimeters.
how do i learn how to do divison without using a peice of paper, i wanna do it in my head, can i get some help?
Answer:I did lattice math over the summer in between 4th and 5th grade when I was bored and wanted to enjoy the sun and now I can do division in my head
Step-by-step explanation: go learn how to do lattice and then do it over and over again. Give yourself a prize time you do like 5 or something and do double digits to challenge yourself
Answer:
Abri do what i showed you on paper but in your head do the circles divide them into groups in your head ( also we are sister i am 13 she is younger i'm in 7th grade she is in 6th )
Step-by-step explanation:
.
Paul has $35000 to invest. His intent is to earn 11% interest on his investment. He can invest part of his money at 8%
interest and part at 14% interest. How much does Paul need to invest in each option to make get a total 11% return on
his $35000?
Investing for 8% return: $
9
Investing for 14% return: $
B
Answer:
$17,500 at 8%$17,500 at 14%Step-by-step explanation:
The fraction that needs to be invested at the higher rate is ...
(11% - 8%)/(14% -8%) = 3%/6% = 1/2
Half the money should be invested at each of the rates:
$17,500 for 8% return
$17,500 for 14% return.
_____
If you let x represent the amount at the higher rate, then the total return is ...
14%x + 8%(35000 -x) = 11%(35000)
(14% -8%)x = (11% -8%)(35000) . . . . subtract 8%·35000
x = (11% -8%)/(14% -8%)×35000 . . . . divide by the coefficient of x
Note that this formula is exactly the one we started with, above.
A dvd is marked down 15% the regular price is $12 what is the sale price?
15% off means the dvd is selling for 85% of the original price ( 100% - 15%=85%)
Multiply the original price by 85%
12 x 0.85 = 10.20
The price is $10.20
What is the answer to 6(4)
Subtract: 5 - 3 1/3 what is the answer
Answer:
5/3
Step-by-step explanation:
3 1/3=10/3
5-10/3
15/3-10/3
5/3
Find the sum:261+345+502
Answer:
1108
Step-by-step explanation:
1
261
345
502
------
1108
:)
A multiple choice exam has 100 questions, each with 5 choices. If a student randomly guesses the answer to a question on the exam, what is the probability that he will get that answer correct?
Final answer:
The probability of a student guessing the correct answer on one multiple choice question with five possible choices is 20%. For specific targets, such as guessing more than 75% correctly, the binomial probability formula would be used.
Explanation:
If a student is taking a multiple choice exam with 100 questions and each question has 5 choices, the probability of guessing correctly on any single question is simply 1 in 5, as there is only one correct answer out of five possibilities. To calculate the probability of an event such as this, where each event is independent and there's an equal chance of each outcome, we use the formula for the probability of a single event, which is P(Event) = Number of successful outcomes / Total number of possible outcomes.
Therefore, the probability of the student guessing the correct answer on one question is P(Correct) = 1/5 or 20%.
If we are dealing with a question about guessing more than a certain percentage correctly, such as more than 75%, we would use the binomial probability formula, which is a bit more complex and depends on the specific question being asked.
What is the justification for step 2 in the solution process? 12 − x = 7x + 32 Step 1: -x = 7x + 20 Step 2: -8x = 20 A. the addition property of equality B. the division property of equality C. the subtraction property of equality D. the multiplication property of equality
Answer:
C. the subtraction property of equality
Step-by-step explanation:
Answer:
C. the subtraction property of equality
Step-by-step explanation:
which equations are true please help?
Answer:
All the equation are true .
Step-by-step explanation:
Because In each equation you find that after working it out you will remain with x each side
What number is equivalent to the expanded form (2 x 100) + (3 x 1) + (4 x 1/10) + (3 x 1/1,000
The equivalent number to the given expanded form is 203.403
Step-by-step explanation:
To find the equivalent number of the expanded form, Use BODMAS rule.
B - bracket
O - of
D - division
M - multiplication
A - addition
S - subtraction
In the given equation, look for the BODMAS order to solve the expanded form:
step 1: solve the numbers inside the bracket.
(2*100)+(3*1)+(4*1/10)+(3*1/1000) = 200 + 3 + 4/10 + 3/1000
step 2: In the order of BODMAS, division comes before addition. So, Division has to be given priority and then addition should be performed.
200 + 3 + 0.4 + 0.003 = 203.403
If Nora's house has an assessed value of $76,320 and a real estate tax rate of $2.98 per $100,
what will she pay in real estate tax?
A.$3,567.34
B.$2,274.34
C.$2,008.94
D.$1,345.26
Option B:
$2,274.34
Step-by-step explanation:
Given Nora's house has an assessed value = $76,320
Real estate tax rate = $2.98 per $100
[tex]=\frac{2.98}{100}[/tex]
= $0.0298
Tax for assessed value $76,320 = $76,320 × $0.0298
= $2274.336
= $2274.34
Hence, tax for Nora's house is $2274.34.
What is the value of x and y of the parallelogram?
Answer:
X=15
Y=45
Step-by-step explanation:
Keelahs clothing store buys coats for $50 and then sells them for $80 what is the percent increase on the price of the coat?
Answer:
X= 60% increase
Step-by-step explanation:
Original: 50
New: 80
1. 80-50/50 = X/100
2. 30 * 2/ 50* 2 = X/100
3. X= 60% increase
Y=-2x on a graph line
Answer: Its gonna be a line going down to the right
Step-by-step explanation:
Which of the following represents Exponential Growth? Choose all that apply.
Group of answer choices
y=(5/4)^x
y=4^-x
y=5^x
y=(4/5)^x
Answer:
[tex]y=(\frac{5}{4})^x[/tex]
[tex]y=5^x[/tex]
Step-by-step explanation:
we know that
In a exponential function of the form
[tex]y=a(b^x)[/tex]
where
a is the initial value
b is the base
If the value of b >1 ----> then is a exponential growth
If the value of b <1 ----> then is a exponential decay
Verify each case
case a) we have
[tex]y=(\frac{5}{4})^x[/tex]
[tex]b=\frac{5}{4}[/tex]
b> 1
therefore
The function represent exponential growth
case b) we have
[tex]y=(4)^{-x}[/tex]
[tex]b=\frac{1}{4}[/tex]
b< 1
therefore
The function represent exponential decay
case c) we have
[tex]y=5^x[/tex]
[tex]b=5[/tex]
b> 1
therefore
The function represent exponential growth
case d) we have
[tex]y=(\frac{4}{5})^x[/tex]
[tex]b=\frac{4}{5}[/tex]
b< 1
therefore
The function represent exponential decay
The functions y=(5/4)^x and y=5^x represent exponential growth since the value of the function increases as the exponent (x) increases. This pattern follows the characteristic of exponential growth, where larger values lead to faster rates of increase.
Explanation:Exponential growth occurs in mathematics when a quantity increases by a fixed percentage or fraction over equal intervals of time. This can be represented by a mathematical function where the variable is an exponent. Looking at the provided options, let's determine which ones represent exponential growth:
y=(5/4)^x: This function represents exponential growth because as x increases, the value of the function also increases proportionally.y=4^-x: This function does not represent exponential growth; instead, it represents exponential decay, as the value of the function decreases as x increases.y=5^x: This is a classic example of exponential growth, with the base 5 being raised to the power of x. As x increases, the function's value grows exponentially.y=(4/5)^x: Similar to the second function, this represents exponential decay, not growth, as the function's value diminishes as x increases.Therefore, the functions that represent exponential growth are y=(5/4)^x and y=5^x.
5. Use multiplicatonto show
that 1/4 is
equivalent to 3/12
Answer:
1 Simplify 3/12 to 1/4
1/4 =1/4
2 Since both sides equal, there are infinitely many solutions.
Infinitely Many Solutions