The length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.
Now, According to the question:
The area of a rectangular page can be calculated using the area of a rectangle which is just the product of the length and the width of the page.
A = lw
Here, l represents the length of the page and w represents the width of the page.
Determine the dimensions of a page given that the printed area is [tex]30in^2[/tex]
and the page has margins on each side, each having a width of 1in.
We will first set up an equation using the details that we know. We know that the printed area is [tex]30in^2[/tex] We can let x be the length of the printed area and y be the width of the printed area. Assuming that the printed area is rectangular, the area is
[tex]A_p=xy[/tex]
30 = xy
[tex]y = \frac{30}{x}[/tex]
Now, we want to minimize the amount of paper used. The length of the entire page would be x + 2 since we have to consider the 1-in margins at the top and the bottom. Similarly, the width would be y+ 2 since we have to consider the margins at the sides. The area of the page is as follows.
A = (x+2)(y + 2)
We can substitute the value of y in terms of x.
A(x) = (x + 2)([tex]\frac{30}{x} +2[/tex])
A(x) = x ([tex]\frac{30}{x}[/tex]) + 2x + 2[tex](\frac{30}{x} )[/tex] + 4
A(x) = 30 + 2x + [tex]\frac{60}{x}[/tex] + 4
A(x) = 34 + 2x + [tex]\frac{60}{x}[/tex]
We want to minimize this area, so we will apply differentiation to this function. By finding its derivative and equating it to zero, we can find the value/s of x that will minimize the area.
A'(x) = [tex]2-\frac{60}{x^2}[/tex]
0 = [tex]2-\frac{60}{x^2}[/tex]
[tex]2 =\frac{60}{x^2}[/tex]
[tex]2x^2=60\\\\x^{2} =\frac{60}{2}\\ \\x^{2} =30\\\\x =[/tex]±[tex]\sqrt{30}[/tex]
Since we are dealing with dimensions, we can only choose the positive value, x =√30. Now, to determine if this would really minimize the area of the page, we can substitute it into the second derivative of the function. If the result is positive, the value of x would give the minimum area.
A"(x) = [tex]\frac{120}{x^3}[/tex]
[tex]A"(\sqrt{30} )=\frac{120}{(\sqrt{30})^3 }[/tex]
[tex]A"(\sqrt{30} )=0.73[/tex]
We can now use the value of x to find the dimensions of the page. Take note that the dimensions of the page are x + 2 and y + 2
x + 2 = √30 + 2
y + 2 = [tex]\frac{30}{x}[/tex] + 2
y +2 = [tex]\frac{30}{\sqrt{30} }[/tex] + 2
y + 2 = [tex]\sqrt{30}+2[/tex]
Therefore, the length of the page is √30+2in and the width of the page is √30+2in. The approximate dimensions of the page are 7.48 in × 7.48 in.
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Gina is going to buy 100 stickers
Gina should buy from Stickers4u.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Gina is going to buy 100 stickers.
If she buys from the shop - Stickers4u,
then the cost is,
= 100/25 x 2.15
= 4 x 2.15
= 8.6.
And if she buys from the World stationary,
then the cost is,
= (100 - 50)/10 x 1.65
= 5 x 1.65
= 8.25
Therefore, she should buy from Stickers4u.
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given the definitions
u= 1 2 3 4 5 6 7
a= 1 2 4 5
b= 1 3 5 7
how many elements are in A' u B?
help it is for a grade tomorrow
Answer:
Step-by-step explanation:
customers: 6
minutes: 40
Every day, Patrick's orange juice stand uses 3/4 of a bag of oranges. How many days will 1 1/2 bags of oranges last?
Answer:
2 days
Step-by-step explanation:
We want to divide 1 1/2 by 3/4
1 1/2 ÷ 3/4
Change the mixed number into an improper fraction.
3/2 ÷ 3/4
Copy dot flip
3/2 * 4/3
Rewrite
3/3 * 4/2
1 * 2
2
It will last 2 days
Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + [1/(32√2)] + [1/(243√3)] + [1/(1024√4)] + [1/(3125√5)] + ….
p = _____
A. converges B. diverges
The answer is B. diverges.
Theorem 9.11 states that if the sequence of positive terms (an) satisfies the condition 1/an^p converges, then the p-series ∑an converges if p > 1 and diverges if p ≤ 1. In this case, the positive terms of the sequence are given by [1/(n^(3/2))]. So, [1/an^p] = [1/(n^(3/2))^p] = [1/n^(3p/2)].
For the series to converge, we need [1/an^p] to converge, or [1/n^(3p/2)] to converge.
If 3p/2 > 1, then [1/n^(3p/2)] converges and the series converges.
If 3p/2 ≤ 1, then [1/n^(3p/2)] diverges and the series diverges.
So, to determine the value of p, we need to find the value of p such that 3p/2 = 1. Solving for p, we find that p = 2/3.
Since 2/3 ≤ 1, the series diverges. Therefore, the answer is B. diverges.
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how to solve that and what is the answer
The equation that represents the cost of the skirt will be 3/4(18 + s) = 31.50. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Let 's' be the cost of the skirt. Then the equation is given as,
3/4(18 + s) = 31.50
The equation that represents the cost of the skirt will be 3/4(18 + s) = 31.50. Then the correct option is D.
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Evaluate the limit.
3. A dilation is represented in the following table. Determine the scale factor for the dilation.
Express your answer in function notation (x,y) → (kx,ky).
Pre-Image
Image
I
(2,4)
(1, 2)
(1, 0)
(0.5, 0)
(-4,-1)
(-2,-0.5)
The scale factor of the dilation, expressed in function notation, (x, y) → (k·x, k·y), is (x, y) → (0.5·x, 0.5·y)
What is a dilation transformation?A dilation transformation is a transformation in which the dimensions of the image are obtained by multiplying the dimensions of the pre-image by a value, known as a scale factor of the dilation.
The possible table, based on the similarities of the coordinate points can be presented as follows;
Pre-Image [tex]{}[/tex] Image
(2, 4) [tex]{}[/tex] (1, 2)
(1, 0) [tex]{}[/tex] (0.5, 0)
(-4, -1) [tex]{}[/tex] (-2, -0.5
The specified formula for the image, following the dilation of the point (x, y) by a scale factor of k is; (x, y) → (k·x, k·y)
Therefore, we get;
k = k·x/x = k·y/y
The comparison of the points in the table with the points (x, y), and (k·x, k·y), indicates that we get;
When (x, y) = (2, 4) and (k·x, k·y) = (1, 2)
Therefore;
k = k·x/x = k·y/y = 1/2 = 2/4 = 0.5
The scale factor of the dilation , k = 0.5, therefore;
(x, y) → (0.5·x, 0.5·y)
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if monique wanted to run 7/8 mile and she went to the school track which was one quater of a mile long how lany laps would she have to run
Which of the following questions could I use to find the answer check all that apply.
A. L x 1/4=7/8. YES OR NO
B. 7/8 x 1/4 = L. YES OR NO
C. 7/8 X 4=L. YES Or NO
D. L/ 7/8 = 1/4. YES OR NO
hURRY
if Monique wanted to run 7/8 mile and she went to the school track which was one quarter of a mile long. The number of lap Monique will complete is
C. 7/8 X 4 = L. What is a lap in race?One complete lap around a track or across a pool, from one end to the other: The track has 400 meters or approximately 25 mile per lap.
A lap is end to end of a track and in the problem a lap is 1/4 mile and Monique wants to complete 7/8 miles'. the comparison is as follows
assuming the number of laps is L
1 lap = 1/4 mile
L laps = 7/8 miles
cross multiplying
1 * 7/8 = L * 1/4
multiplying by 4 for each side
1 * 7/8 * 4 = L * 1/4 * 4
1 * 7/8 * 4 = L * 1
7/8 * 4 = L
hence option C is correct
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If m
∠
∠
BAC is 48
∘
∘
, what is the measure of
∠
∠
GAE?
Answer:
132
Step-by-step explanation:
180 - 48 = 132 These angles are supplemental. They add to 180
Answer:
<GAE = 48
Step-by-step explanation:
<BAC = 48
<BAC = <GAE
You roll two six-sided dice numbered from one through six. What is the probability that the maximum of the two dice is greater than or equal to six? Report your answer to three decimal places.
The probability that the maximum of the two dice is greater than or equal to six is 0.722.
What is probability?
Probability is a way of calculating how likely something is to happen. Probability can range from 0 to 1, with 0 indicating an impossibility and 1 indicating a certainty.
We are given that two six-sided dice numbered from one through six are rolled.
The sample space of the event is
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Probability that the maximum of the two dice is greater than or equal to six is
26 out of 36 i.e. 26/36
This is equal to 0.722.
Hence, the probability that the maximum of the two dice is greater than or equal to six is 0.722.
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please help me will give u extra points :)
•
From the graph, the compound inequality represented is x < -2 and x > 5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Inequalities shows the non equal comparison of two or more numbers and variables. Compound inequality is an inequality that is composed of more than one inequality.
From the graph, the inequality is not a solid circle, so it is either > or < sign.
From the graph, the inequality shown is x < -2 and x > 5
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my’s Annual Expenditures
Rent $ 8,580.00
Utilities $ 3,480.00
Internet & Phone $ 1,896.00
Entertainment $ 2,232.00
Student Loan Payment $ 4,116.00
Home & Auto Insurance $ 1,164.00
Food $ 6,000.00
Car Payment & Gas $ 2,820.00
Travel $ 1,200.00
Savings $ 1,200.00
Personal Expenses $ 1,847.00
Pet Expenses $ 965.00
Business Expenses $ 4,800.00
Q1. Amy’s day job is as a secretary at a law firm. After taxes and health insurance, she nets $1550 bi- weekly. How much does Amy net in a year from her day job?
Q2. Based on her net income and annual expenditures summary, by how much did Amy over or under spend this year?
Part a: Amy's net amount in a year from her day job is found as $40411.
Part b: Amy under spend this year by amount $8331.
Define the term annual expenditure?Just before annual contribution margin, all expense items in the profit and loss statement, including operating costs including finance charges, are referred to as annual expenditure.Part a:
The calculation is done bi- weekly.
Total days = 2*7 = 14.
Net amount = $1550.
Net amount for the year = (1550/ 14)*365
Net amount for the year = $40411
Thus, Amy's net in a year from her day job is found as $40411.
Part b:
Total amount spend : Sum of all expenditures.
Total amount spend : $32,080
Difference = $40,411 - $32,080
Difference = $8331
Thus, based on her net income as well as annual expenditures summary,
Amy under spend this year by amount $8331.
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Find the value of M and N
Answer: n=110, m=110
Step-by-step explanation: I think m=110 because of vertical angles. m might also equal 70.
What is the volume of the cube shown?
WILL GIVE BRAINLEST
Answer:
11.390625 in^3
Step-by-step explanation:
2.25^3 = 11.390625 in^3
Given the following diagram what can you conclude?
Answer:
YXZ=AXZ
because if you see the letters they form triangle
Express each of the following as the sum Of a whole number and a fraction 9/7
Answer:
1 + 2/7
Step-by-step explanation:
9/7 =
(7+2) / 7 =
7/7 + 2/7 = ==> use distribution
1 + 2/7 ==> 7/7 = 1, so simplify the expression
Kim has to prepare for a 16 miles race for 2/6 of the race Kim decides to walk preserve her energy she than sprints for 3/7 of the remaining time after she walked what is half of the race left
The half-distance left is 40/7 or 5.714 miles
How to find the distance?Given that:
The total race is 16 miles long.
Kim walked for 2/6 of the race, which is (2/6) * 16 = 16/3 miles.
After walking 16/3 miles, there are 16 - 16/3 = 32/3 miles left in the race.
Kim then sprints for 3/7 of the remaining distance, which is (3/7) * 32/3 = 32/7 miles.
Half of the race is left after she finished sprinting and walking, which is
16 - 32/7 = 80/7 miles
Divide this by 2:
80/7 ÷2
= 40/7 miles are left.
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Point P is on line segment O Q . Given O Q = 11 OQ=11 and O P = 9 , OP=9, determine the length P Q ‾ . PQ
Answer: PQ is 9 units.
Step-by-step explanation:
The length of PQ can be found using the proportion of OQ and OP.
(PQ / OQ) = (OP / OQ)
PQ = (OP / OQ) * OQ
Substituting in the given values:
PQ = (9 / 11) * 11
PQ = 9
Therefore, the length of PQ is 9 units.
Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.
[1 h 4
3 6 8]
The value of h can be any value other than 2.
Value of h for Consistent SystemThe augmented matrix of a consistent linear system must have a unique solution, which means the determinant of the coefficient matrix must be non-zero.
For the given matrix, the coefficient matrix is:[1 h
3 6]
The determinant of this matrix is (1 * 6) - (3 * h) = 6 - 3h.
For the determinant to be non-zero and the system to be consistent, 6 - 3h must not be equal to zero, so h cannot be equal to 2.
Therefore, the value of h can be any value other than 2.
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Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
x-7=-2
Traveling 120km total, 1st 59km are 90km P/h. Remaining km are 50km P/h. How long does the trip take total?
The total trip took a total of 1.87 hours.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here: Total distance=120 km and 59 km at 90 km/hr and the remaining distance at 50 km/hr
Remaining distance= 120-59
=61 km
Thus for the first 59 km the time it took was
Time= Distance/ Speed
= 59/90
=0.65 hr
Similarly time taken for the second part of the journey is = 61/50
=1.22
Hence, total time taken for the trip is 1.22+0.65=1.87 hr.
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A jar contains 7 poker chips: 4 blue, 2 red and 1 white. You randomly select two chips from the jar. What is the probability that your selection includes two different colored chips? Report your answer to three decimal places.
The probability of selecting two different coloured chips is the fraction 14/49.
What is probability?Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.
total possible outcome = 7
blue chips = 4
red chips = 2
white chips = 1
probability of selecting blue chips = 4/7
probability of selecting red chips = 2/7
probability of selecting white chips = 1/7
probability of selecting two coloured chips at random = 4/7 × 2/7 + 4/7 × 1/7 + 2/7 × 1/7
probability of selecting two coloured chips at random = 8/49 + 4/49 + 2/49
probability of selecting two coloured chips at random = 14/49
Therefore, the probability of selecting two different coloured chips is the fraction 14/49
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In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothing and carry‑on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not normally distributed, especially when the population includes both men and women, but they are not very non‑Normal. A commuter plane carries 22 passengers. What is the approximate probability P that the total weight of the passengers exceeds 4500 pounds? Use the four‑step process to guide your work. Give your answer as a percentage precise to two decimal places. P=___?
The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Total of 22 is more than 4500 is equivalent to average of 22 is more than [tex]$\frac{4500}{22}[/tex]=204.545
[tex]$$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$[/tex]
= 1 - 0.8997
= 0.1003
= 10.03%
Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.
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someone help !!
geometry: find the value of x
Answer:
x = 18
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 , then
sum = 180° × 3 = 540°
sum the 5 interior angles and equate to 540
3x + 23 + 95 + 7x - 4 + 90 + 9x - 6 = 540
19x + 198 = 540 ( subtract 198 from both sides )
19x = 342 ( divide both sides by 19 )
x = 18
two letters without replacement from the three letters a b and c how many ways can this be done if the order of choice is taken into consideration how many ways can this be done if the order of the choices is not taken into consideration
Answer:
If order is considered = 6
If order is not considered = 3
Step-by-step explanation:
If order is to be taken in consideration then the following values can be taken:
a, b
a, c
b, a
b, c
c, a
c, b
Total = 6 ways
If order is not taken in consideration then the following values can be taken:
a, b
a, c
b, c
Total = 3 ways
Please help me with this question.
The solution to the system of equations in this problem is given as follows:
X = [28571
14286].
How to solve the system of equations?The system is defined by the following equation:
X = DX + E.
The matrices D and E are known, while X = [A; B] is the output matrix. Applying the multiplication of matrices, the system of equations is defined as follows:
0.2A + 0.3B = 10000.0.5A + 0.4B = 20000.Inserting this system into a calculator, the solution is given as follows:
A = 28571.B = 14286.Hence the matrix X is given as follows:
X = [28571
14286].
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A 9 footbpiece of twine costs $8.64. What is the price per inch?
Answer: 0.08 dollars
Step-by-step explanation:
8.64 divided by 9 = 0.96
0.96 divided by 12 = 0.08
show that if xt x is not invertible, then at least one column of x is a linear combination of the others. this implies that there is only one way in which problem with invertibility of xt x may arise'
If the matrix xt x is not invertible, then its determinant is equal to 0. A determinant of 0 implies that the matrix is singular, meaning that its columns are linearly dependent.
This means that one of the columns of x can be expressed as a linear combination of the other columns, which implies that there is only one way in which the invertibility problem may arise: when the columns of the matrix x are linearly dependent.
If the determinant of xt x is equal to 0, then at least one column of x can be expressed as a linear combination of the others. For example, if column c can be expressed as a linear combination of columns a and b, then we can write:
c = k1a + k2b
where k1 and k2 are constants. This means that the information in column c is already represented in columns a and b, and so it is redundant.
This is the only way in which the invertibility problem of xt x may arise. If the columns of the matrix are linearly independent, then the determinant of xt x will be non-zero, and the matrix will be invertible.
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Your question is incomplete, but most probably, the full question was:
Proof that [tex]X^{T} X[/tex] is not invertiblethen at least one column of x is a linear combination of the others. This implies that there is only one way in which a problem with the invertibility of xt x may arise
i need help solving rhis problem please show your work
The length of the GH is 4, when H is the midpoint of GI.
What is midpoint of a line?An area of a line that connects two distinct locations is referred to as a line segment. It is the least path between two places that can be determined to have a length.
A line segment's midpoint is the point on the segment when it is divided into two similar segments. The point on a line segment that is equally spaced from the two terminating points is known as the midpoint of the segment.
Given that H is the midpoint of GI.
Then we can say that,
GI / 2 = GH
Substitute the equations of the length of GH and GI as given:
(9x - 19) / 2 = 3x - 5
9x - 19 = 2(3x - 5)
9x - 19 = 6x - 10
9x - 6x = -10 + 19
3x = 9
x = 3
Substitute the value of x in the equation of the length of the segment GH thus:
GH = 3x - 5
GH = (3)(3) - 5
GH = 4
Hence, the length of the GH is 4, when H is the midpoint of GI.
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