Answer:
Dimensions of page should be width of 6 inches and height of 9 inches
Step-by-step explanation:
Let x be the width of the printed part in inches
Let y be height of the printed part in inches.
Thus, Area of printed part; A = xy
And area of printed part is given as 24.
Thus, xy = 24
Making y the subject, we have;
y = 24/x
Now, the question says the top and bottom margins are 1.5 inches.
Thus, width of page = x + 1 + 1 = x + 2
And also the margins on each side are both 1m in length, thus the height of page will be:
y + 1.5 + 1.5 = y + 3
So area of page will now be;
A = (x + 2)•(y+3)
From earlier, we got y = 24/x
Thus,plugging this into area of page, we have;
A = (x + 2)•((24/x)+3)
A = 24 + 3x + 48/x + 6
A = 30 + 3x + 48/x
For us to find the minimum dimensions, we have to find the derivative of A and equate to zero
Thus,
dA/dx = 3 - 48/x²
Thus, dA/dx = 0 will be
3 - 48/x² = 0
Multiply through by x²:
3x² - 48 = 0
Thus,
3x² = 48
x² = 48/3
x = √16
x = 4 inches
Plugging this into y = 24/x,we have;
y = 24/4 = 6 inches
We want dimensions of page at x = 4 and y = 6.
From earlier, width of page = x + 2.
Thus,width = 4 + 2 = 6 inches
Height = y + 3 = 6 + 3 = 9 inches
So dimensions of page should be width of 6 inches and height of 9 inches
To minimize paper usage, we need to find the dimensions of the rectangular page. By setting up an equation and solving it, we can find the width and length of the page that result in the least amount of paper used.
Explanation:To minimize the amount of paper used, we need to find the dimensions of the page that will result in the smallest possible area. Let's assume the length of the page is 'L' inches and the width is 'W' inches. We can set up the equation:
Next, we can use the quadratic formula to solve for L:
To find the minimum value of L, we can consider the factors contributing to the uncertainty:
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An urn contains 8 balls identical in every aspect except color. There is 1 red ball, 2 green balls, and 5 blue balls. You draw two balls from the urn, and you do not replace the first ball before drawing the second. Find the probability that the first ball is blue and the second is green.
Answer:
P(blue and green) = P(blue)*P(green) = (5/8)(2/8) = 10/64
The probability that the first ball is blue and the second is green, with no replacement, is approximately 0.179 or 17.9%.
Explanation:The subject of this question pertains to probability, specifically the concept of dependent events in the realm of combinatorics. The problem involves an urn with 8 balls of different colors. The question asks us to find the probability that a blue ball is drawn first and a green ball second, with no replacement.
Firstly, we calculate the individual probabilities. The probability of drawing a blue ball first is 5/8, because there are 5 blue balls out of a total of 8. Since the blue ball isn't replaced, there are now 7 balls left in the urn, and therefore, the probability of drawing a green ball next is 2/7. To find the combined probability, we multiply the individual probabilities: (5/8) * (2/7) = 10/56 = 0.1786 (rounded). So the probability that the first ball is blue and the second is green is approximately 0.179 or 17.9%.
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Emily bought 66 yards of fabric to make curtains How many inches of fabric did Emily buy?
Answer:
2,376
Step-by-step explanation:
Answer:
Step-by-step explanation:
Convert the yards into inches and add a label at the end. You could also find out how many inches are in one yard and times the amount of inches you got from that one yard by 66.
A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder increases and the radius, r, decreases. If the length of the cylinder is increasing by 0.7 cm per second, find the rate at which the radius is changing when the radius is 2 cm and the length is 9 cm.
Answer:
The radius is decreatsing at a rate 0.78 cm per second.
Step-by-step explanation:
We are given the following in the question:
[tex]\dfrac{dl}{dt} = 0.7\text{ cm per second}[/tex]
Instant radius,r = 2 cm
Instant length,l = 9cm
The radius of the cylinder decreases.
Volume of cylinder =
[tex]V =\pi r^2l[/tex]
Since the volume of the cylinder does not changes, we can write:
[tex]\dfrac{dV}{dt}=0[/tex]
Rate of change of volume:
[tex]\dfrac{dV}{dt} = \pi(2r\dfrac{dr}{dt}l + r^2\dfrac{dl}{dt})[/tex]
Puttiung values, we get
[tex]0 = \pi(2(2)\dfrac{dr}{dt}(9) + (2)^2(0.7))\\\\\dfrac{dr}{dt}=-\dfrac{4\times 0.7}{4\times 9} \approx -0.78[/tex]
Thus, the radius is decreatsing at a rate 0.78 cm per second.
Using differentiation, it is found that the radius is increasing at a rate of 0.35 cm/second.
The length of a cylinder is the diameter, which is double the radius, hence:
[tex]l = 2r \rightarrow r = \frac{l}{2}[/tex]
Applying differentiation, the rate of change of the radius is given by:
[tex]\frac{dr}{dt} = \frac{1}{2}\frac{dl}{dt}[/tex]
We are given that the rate of change of the length is [tex]\frac{dl}{dt} = 0.7[/tex], hence:
[tex]\frac{dr}{dt} = \frac{1}{2}\frac{dl}{dt} = \frac{1}{2}(0.7) = 0.35[/tex]
The radius is increasing at a rate of 0.35 cm/second.
A similar problem is given at https://brainly.com/question/9543179
What’s the volume of this triangular prism ?
Answer: 157.5
Step-by-step explanation: To get the volume of an object you must multiply the width x height ÷ it by 2 x length
Therefore 7 x 5 = 35 ÷ 2 = 17.5
17.5 x 9 = 157.5
Answer:
157.5
Step-by-step explanation:
The first step is to find the area of the triangular base. The formula for the area of a triangle is bh/2, or in this case 5×7/2=17.5. Multiplying this by the length of the prism, you get 9×17.5=157.5. Hope this helps!
Which is not a property of countercurrent multiplication?
Answer:
It is opposed by the vasa recta.
Step-by-step explanation:
Question:
Which of these is not a property of the renal counter-current multiplier?
It is opposed by the vasa recta.
It exploits the structure of the nephron loop.
It depends on active ion transport to function.
It creates a hyperosmotic interstitial fluid in the kidney medulla.
Answer:
The correct option is;
It is opposed by the vasa recta
Step-by-step explanation:
Counter current multiplication is the process whereby energy is used to build osmotic pressure gradient in the kidney such that water is reabsorbed from the exit tubular fluids reducing the volume of produced urine by increasing the urine concentration while the vasa recta capillaries slows blood flow rate so as to keep the osmotic pressure gradient constant enabling water to be reabsorbed thus concentrating the urine in line with counter current multiplication.
Two cars leave towns 450 kilometers apart at the same time and travel toward each other. One car's rate is 12 kilometers per hour less than the other's. If they meet in 3 hours, what is the rate of the slower car?
Answer:
The rate of the slower car is 69km/hr
Step-by-step explanation:
Please kindly check the attached files for explanation.
Seo-Yun hosted a party. She had 50 party
favors to give away, and she gave 3 party
favors to each of her guests as they arrived at
the party.
Let g(n) be the number of party favors Seo-
Yun had before the nth guest arrived.
g is a sequence. What kind of sequence is it?
Answer: It’s an arithmetic sequence
g(n)=50-3•(n-1)
Step-by-step explanation:
Answer:
it’s a arithmetic sequence and answer is 50-3(n-1) please give brainliest anyway bye have a good day but I don’t think u are because u probably bored of khan academy anyway bye have a good day! :D
Step-by-step explanation:
What is the median of the data set 87,98,106,82,111,120
Answer:
Median = 102
Step-by-step explanation:
To find the median we will following the steps below;
study the numbers, if they are not arrange from ascending to descending order, you try to do that.
87,98,106,82,111,120
82, 87, 98,106, 111, 120
Pick the middle number, if there is just one number that falls in the middle, that number is your median, but if there two numbers that falls in the middle, you add the two numbers and then divide by 2.
In this case, two numbers falls in the middle, so we will add and divide by 2
That is;
Median = 98 + 106 /2
=204 /2
=102
Median = 102
I believe the answer is A can someone confirm please and thank you, I cant get this answer wrong.
Answer:
A is correct.
Step-by-step explanation:
1 2 3 4 5 6 7 8 9 10 David has $90 to spend on sneakers. The sales tax in his state is 6%. Vincent has $95 to spend on sneakers. The sales tax in his state is 9%. Both boys are interested in a pair of sneakers that costs $86. Who will be able to buy the sneakers?
Vincent will be able to buy the sneakers.
1. David: $90
- David's total cost: $91.16
- David cannot afford the sneakers.
2. Vincent: $95
- Vincent's total cost: $93.74
- Vincent can afford the sneakers.
To determine who will be able to buy the sneakers, let's calculate the total cost including sales tax for each boy:
1. David:
- Sneaker cost: $86
- Sales tax rate: 6%
- Total cost [tex]\(= 86 + 0.06 \times 86\)[/tex]
- Total cost [tex]\(= 86 + 5.16\)[/tex]
- Total cost [tex]\(= 91.16\)[/tex]
2. Vincent:
- Sneaker cost: $86
- Sales tax rate: 9%
- Total cost [tex]\(= 86 + 0.09 \times 86\)[/tex]
- Total cost [tex]\(= 86 + 7.74\)[/tex]
- Total cost [tex]\(= 93.74\)[/tex]
Jamal has a pair of shoes that have a total mass of 960 grams and four identical books that have a total mass of 2 kilograms. Which has the greater mass : one shoe or one book use the drop down Menus to explain
One shoe has a mass of 950 divided _____ = _____ grams . One book has a mass of _____ divided 4 = _____ grams . So one _____ has a greater mass
Answer: One book has a greater mass.
Step-by-step explanation:
Jamal has a pair of shoes with a total mass of 960 grams. This means that each shoe has a mass of:
960 grams ÷ 2= 480 grams per shoe.
Jamal also has four identical books with a total mass of 2 kilograms. Note that 1000 grams make a kilograms. Therefore 2 kilograms will be (2 × 1000 grams) = 2000 grams.
Each book will have a mass of:
2000 ÷ 4 = 500 grams per book.
One shoe has a mass of 960 divided 2 = 480 grams . One book has a mass of 2000 divided 4 = 500 grams . So one book has a greater mass.
A grocery store has a small bag of apples for $5 and a large bag for $8. If you bought 6 bags and spent $45, how many of each size of bags did you buy?
Answer:
1 small bags and 5 large bags
Step-by-step explanation:
In this case we can solve it using a 2x2 system of equations, like this:
let x: number of small bag
let y: number of large bag
So:
5 * x + 8 * y = 45
x + y = 6 => x = 6 - y
Replacing, we are left with that:
5 * ( 6 - y) + 8 * y = 45
30 - 5 * y + 8 * y = 45
- 5 * y + 8 * y = 45 - 30
3 * y = 15
y = 15/3
y = 5
Now to calculate x:
x = 6 - 5
x = 1
this means that 1 small bag and 5 large bags
Answer:
he bought 1 bag of small apple and 5 bags of Large apple
Step-by-step explanation: given that A small bag of apples = $5 and
A large bag = $8.
If you bought 6 bags and spent $45,
Let number of small apple be S
And large Apple be L
L + S = 6 ....... (1) ×8
8L + 5S = 45 .......(2)
Solve equation 1 and 2 simultaneously
8L + 8S = 48
8L + 5S = 45
Eliminate L
3S = 3
S = 1
Substitute S in equation 1
L = 6 - 1 = 5
Therefore, he bought 1 bag of small apple and 5 bags of Large apple
The circumference of a circle is 6π centimeters.What is the radius?
Answer:
37.699cm
Step-by-step explanation:
thank me and rate!!! plz thank you :)
Fill in the blank...
Answer:
Positive
Step-by-step explanation:
If a is positive, the parabola opens up or to the right. If it's negative it does the opposite.
Ramon earns $1,600 each month and pays $53.60 on electricity. To the nearest tenth of a percent, what percent of Ramon's earnings are spent on electricity each month?
Answer:
3.4%
Step-by-step explanation:
Ramons monthly salary is $1600
The electricity is $53.60
So, to find the percentage of his earnings spent on electrcity, we´re going to divide:
[tex]\frac{53.60}{1600} = 0.0335[/tex]
multiply that by 100 to get the percent
0.0335 x 100 = 3.35%
rounded to the nearest tenth would be 3.4%
i hope this helps!
Let X be an exponential random variable with parameter Λ, which is itself a random variable with distribution Exponential(β). Find a formula for the conditional density of Λ given X = x, and identify its type (i.e. its name and parameter(s)).
Answer:
Step-by-step explanation: solution solved below
Final answer:
To find the conditional density of Λ given X = x, calculate the joint density function of X and Λ and apply the formula for conditional density.
Explanation:
The conditional density of Λ given X = x when Λ is a random variable with distribution Exponential(β) can be found as follows:
Calculate the joint density function of X and Λ.
Use the formula for conditional density: f(Λ|X=x) = f(X,Λ) / f(X=x).
Identify the type of the conditional density based on the distribution it follows.
Name three uses for mercury
Answer:
Sample Response:
Mercury is used for making thermometers, barometers, diffusion pumps, and other laboratory instruments. It can also be used to make mercury-vapor lamps, advertising signs, and mercury switches as well as pesticides, dental preparations, batteries, and catalysts.
Mercury is used for making thermometers, barometers and mercury switches
Mercury is used for making thermometers, barometers, diffusion pumps, and other laboratory instruments.
It can also be used to make mercury-vapor lamps, advertising signs, and mercury switches as well as pesticides, dental preparations, batteries, and catalysts.
Therefore, the three uses of mercury are making thermometers, barometers and mercury switches
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What is the volume of wax needed for the candle in the shape of a prism?
Answer:
Step-by-step explanation:
You need answer choices for someone to answer.
Estimate the result by rounding the numbers to the second decimal before performing the operation. Then also round your answer to the second decimal. 8123÷0.211 How do you do it?
Answer:
40615
Step-by-step explanation:
Note, rounding off decimals involves observing if the said decimal is up to the value of 5. If it is, then it can be rounded up, if not, its rounded off.
Since we need to round the numbers to the second decimal before performing the operation, we will have, 8123÷0.2
Note, 8123 has no decimal so we ignore
But 0.211 has a second decimal which is the first 1 so because it's not up to 5, we round it off to 0.
Hence we have 8123 ÷ 0.2= 40615.0
Since our answer has no decimal, we leave it like that.
Answer:
38680.95
Step-by-step explanation:
Solution:-
- We will round the denominator of the fraction " 0.211 " to two decimal places.
0 . 2 1 1
1st 2nd 3rd
3rd digit = 1 < 5 ... "Truncate the 3rd decimal value and on wards"
ans: 0.21
- Now perform the division:
8123 / 0.21 = 38680.95238
- Now again round the resulting answer to 2nd decimal place:
38680. 9 5 2
1st 2nd 3rd
3rd digit = 2 < 5 ... "Truncate the 3rd decimal value and on wards"
- The resulting answer will be after rounding to 2nd decimal place:
Answer: 38680.95
Analyzing an Oblique Prism
The base area of an oblique pentagonal prism is 15 sq. in. The prism measures 3 inches in height and the edges connecting the bases measure 5 inches each. Which statements about the prism are true? Check all that apply.
The volume of the prism is computed using the expression (15)(3).
The volume cannot be determined because the dimensions of the base are unknown.
The edge length can be used in place of the height of an oblique prism if the height is unknown.
The unit on the volume measure of the prism is cubic inches.
The edge length times the height is the area of the base in any prism.
Answer: A and D
I just worked on this!
Answer:
1 and 4... A and D
Step-by-step explanation:
A zoo keeper published the following stem-and-leaf plot showing the number of lizard at each major zoo in the country. How many zoos have exactly 42 lizards
This question is incomplete because it lacks the diagram showing the leaf and stem plots
Find attached to this answer the diagram showing the Stem and leaf plots
Answer:
Only one Zoo has exactly 42 lizards
Step-by-step explanation:
If you check out the attached diagram , you will observe that there is a separation using a vertical line
In the diagram also we have been provided with a key which was explained as :
2|0 = 20 lizards
On the left hand side, we have number ranging from 0 - 6 arranged in a vertical form. On the right hand side we almost have numbers that are arranged in front of each number horizontally
Let me further explain the attached diagram
It is important to note that the numbers arranged vertically on the left are in the units of tens. Hence, using the given key :2l0
0|
1|
2| 0 6 8 8 8
This means , we have 20 lizards in one zoo, 26 lizards in one zoo, 28 lizards in 3 zoos
3| 0 2 6 6 7 8
30 lizards in one zoo, 32 lizards in one zoo, 36 lizards in 2 zoos , 37 lizards in one zoo and 38 lizards in one zoo
4| 1 2 6 6
We have 41 lizards in one zoo, 42 lizards in one zoo, and 46 lizards in two zoos
5l
6|
Based on the explanation given above, we can see that only one Zoo has exactly 42 lizards
Answer:20
Step-by-step explanation:
KHAN
Which mark on the tape measure is closest to 2.23607 inches?
Answer:
5.7 cm or 2 1/4 in
Step-by-step explanation:
Your tape measure is not shown.
On my tape measure, 5.7 cm is the closest mark. On the inch scale, 2 1/4 inches is the next-closest mark.
_____
On a tape measure graduated in 1/32 inch between 2 and 3 inches, you can find the closest mark by rounding to the nearest 32nd:
2.23607 × 32 ≈ 71.55 ≈ 72 --- 32nds of an inch
72/32 = 2 1/4 . . . . the closest mark on an inch ruler graduated in 32nds
__
For a ruler graduated in millimeters, you can find the closest millimeter in the same way. There are 25.4 mm to the inch.
2.23607 in × 25.4 mm/in ≈ 56.80 mm ≈ 57 mm
57 mm = 5.7 cm . . . closest mark on metric scale
__
When we check the error, we find the metric mark is closer than the inch mark.
5.7 cm ≈ 2.24409 in . . . . error of 0.00802 in
2 1/2 in = 2.25000 in . . . error of 0.01393 in
Final answer:
The mark on the tape measure closest to 2.23607 inches is just above 2 3/16 inches, which can be more precisely measured with a tape measure that features millimeter or half-millimeter markings.
Explanation:
The student has asked which mark on the tape measure is closest to 2.23607 inches. To answer this question, we must consider the precision of the measuring device. When using a ruler without millimeter markings, such as the bottom ruler mentioned, the measurement can be understood in tenths of a centimeter. This would make it difficult to conclusively measure and report on the hundredths digit for a length.
Conversely, using a tape measure with millimeter or even half-millimeter markings (akin to the top ruler), the user can measure more precisely. Given that 1 inch equals 2.54 centimeters, 2.23607 inches would be approximately 5.679818 centimeters. This would be between the 2.5 cm and 2.6 cm marks on a metric tape measure or between 2 3/16 inches and 2 1/4 inches on an imperial tape measure; 2.23607 inches is very close to, but slightly above, 2 3/16 inches, so this would be the mark on an imperial tape measure that is closest to 2.23607 inches.
Which equation is the correct translation of the following statement?
Four less than a number is nine.
4 - x = 9
9 - 4 = x
9 - x = 4
x - 4 = 9
Answer: x - 4 = 9 (x will equal 13)
What I did was since 4 is less than 13 we could use 13-4 since 4 is less than 13.
13-4 will get u 9 so that x will equal 13
13-4=9
Answer:
Answer: x - 4 = 9
Step-by-step explanation:
3. Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped
with side lengths of 10 inches, and the hole had side lengths of 4 inches, how much wood was
left after the hole was cut out?
Answer:
it would be 40 inche and there be not that much for the hole to left
Answer:
840 cubic squares
Step-by-step explanation:
A rectangle is enlarged by a factor of 1.5. The width is given as w=2 and the length is given as l =7 in. What would be the perimeter of the new rectangle?
Answer:
Hence Perimeter for new rectangle will be 27 units .
Step-by-step explanation:
Given:
A rectangle with enlarged factor of 1.5
L=7 and W=2
To Find:
Perimeter for new rectangle
Solution:
First calculate the new dimensions for new rectangle ,
Given that original length and width as 7 and 2 respectively and it is increasing by 1.5 times of the original ones
So
New length =1.5 *L
=1.5 *7
=10.5 units
And for width,
New width=1.5 *W
=1.5 *2
=3
Hence New dimensions are 10.5 and 3 units .
So perimeter of new rectangle =2(New length + New breadth)
=2(10.5+3)
=2(13.5)
=27 units
Write the number 6 x 10-5 in standard form.
Answer:
Step-by-step explanation:
[tex]6*10^{-5}= \frac{6}{100000}\\\\=0.00006[/tex]
Estimate the square root to the nearest (a) integer and (b) tenth. Square root of 685
Final answer:
The square root of 685 lies between 26 and 27. To the nearest integer, the estimate is 26, and to the nearest tenth, the estimate is 26.2, given that it is roughly 9/53 of the way from 26 to 27.
Explanation:
To estimate the square root of 685 to the nearest integer and tenth, we have to determine which two perfect squares it lies between. The perfect square closer to 685 without going over is 676 (√676 is 26), and the next perfect square is 729 (√729 is 27). Thus, the square root of 685 lies between 26 and 27.
To estimate to the nearest integer, we would round √685 to 26, as it's closer to 676. For the nearest tenth, we need to see how much 685 exceeds 676. It exceeds by 9, and since 729-676 is 53, 685 is roughly 9/53 of the way from 26 to 27. So, a quick estimation for √685 to the nearest tenth could be 26 + (9/53)*1 which is approximately 26.2. Therefore, the estimated value of the surd √685 to the nearest tenth would be 26.2.
The angular velocity of a fan blade is 4.6 radians per second.
Approximately how many revolutions does the fan blade make in 2.4 minutes?
State your answer, rounded to the nearest tenth of a revolution.
Answer:
In 2.4 minutes the fan made 105.5 revolutions.
Step-by-step explanation:
In order to solve this problem we need to convert the speed from radians to revolutions. To do that we can use a rule of three as shown below:
2pi rad/s -> 1 rev/s
4.6 rad/s -> x rev/s
2pi/4.6 = 1/x
2pix = 4.6
x = 4.6/2pi = 2.3/pi rev/s
Now we need to conver the time at which the blade was spinning from minutes to seconds, to do that we need to multiply by 60.
t = 2.4*60 = 144 s
To calculate the number of revolutions we multiply the angular velocity of the fan by the time it was spinning:
rev = (2.3/pi)*144 = 331.2/pi = 105.5 revolutions
Answer:
105.4 revolutions
Step-by-step explanation:
By converting 2.4 min into seconds, we'll have
2.4 minutes = 60 x 2.4 = 144 seconds.
Now, in 2.4 minutes, the fan rotate 4.6 [rad/s] x 144s = 662.4 radians
As the answer is required in revolution
therefore, 1 radian = 0.159155 revolutions
so 0.159155 x 662.4 = 105.4 revolutions
The fan rotated 105.4 revolutions in 2.4 minutes
Allie is waiting to be tall enough to ride the thunder dragon roller coaster. You have to be at least60 inches to ride. Write this situation as an inequality
Answer:
[tex]x\geq 60[/tex] where x denotes height of Allie
Step-by-step explanation:
An inequality compares two values. One value is less than, greater than, or not equal to another value.
Given: Allie is waiting to be tall enough to ride the thunder dragon roller coaster. You have to be at least 60 inches to ride.
To write: an equality
Solution:
Let the height of Allie be x inches.
As a person has to be at least 60 inches to ride,
the inequality can be [tex]x\geq 60[/tex]
95 students at a college were asked whether they had completed their required English 101 course, and 72 students said "yes". Find the best point estimate for the proportion of students at the college who have completed their required English 101 course. Round to four decimal places.
0.7579 is the best point for the proportion of students at the college who have completed their required English 101 course.
Step-by-step explanation:
"The proportion is written in the fraction form as required number in the numerator and the total number in the denominator."
Here, the 95 students at a college were asked whether they had completed their required English 101 course.
So, the total students = 95
It is given that, 72 students said "yes".
So, the number of completed students = 72
To estimate the best point for the proportion of students who completed their English 101 course :
Now, the numerator is the no.of students who have completed their required English 101 course.
Proportion = 72 / 95
⇒ the best point is calculated as 72 divided by 95
⇒ 0.7579 (round to four decimal places).