The treatments of this experiment are the four different concentrations of the fungus mixtures that are given. The four concentrations are 0 ml/l, 1.25 ml/l, 2.5 ml/l, and 3.75 ml/l.
The experimental units are the 20 individual containers, each containing an equal number of the insects.
The response variable of the experiment is the number of insects that are still alive in each container one week after spraying.
The researchers will measure the number of insects that are still alive in each container after one week and this will be used to determine the effectiveness of the fungus mixture.
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The equation, 687.5 = 550(1 0.05t), represents the amount of money earned on a simple interest savings account. what does the value 550 represent?
The value 550 represents the initial deposit into the savings account.The equation 687.5 = 550(1 + 0.05t) is an equation in the form of A = P(1 + rt), which represents simple interest.
The equation 687.5 = 550(1 + 0.05t) is an equation in the form of A = P(1 + rt), which represents simple interest. The equation states that the amount A (687.5) is equal to the product of the initial deposit P (550) and the sum of one and the interest rate (0.05) multiplied by the time t (t is unknown). Thus, the value of 550 represents the initial deposit into the savings account.
The value 550 represents the initial deposit into the savings account.
The equation 687.5 = 550(1 + 0.05t) is an equation in the form of A = P(1 + rt), which represents simple interest.
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when isa travels to the usa for a holiday he leaves the uk at 1.00 pm local time and lands at 5.00 pm local time. on the return journey he leaves at 8.00 pm local time and lands at 10.00 am local time the next day. find the length of the flight in hours and the time difference between the uk and the part of the usa that isa visited
Isa took 4 hour when isa go from UK to USA and took 14 hour when she returns and time difference will be 10 hours
What is a definition distance?
the extent or amount of space between two things, points, lines, etc. the state or fact of being apart in space, as of one thing from another; remoteness
when isa travels to the usa for a holiday he leaves the uk at 1.00 pm local time and lands at 5.00 pm local time.
so isa took 4 hour
on the return journey he leaves at 8.00 pm local time and lands at 10.00 am local time the next day
isa tool 14 hour
find the length of the flight in hours and the time difference between the uk and the part of the usa that isa visited
length of flight is 18 hour
time difference will be 14-4 = 10 hour
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A club is holding a raffle. ten thousand tickets have been sold for $2 each. there will be a 1st prize of $3000, 3 second prizes of $1000 each, 5 third prizes of $500 each, and 20 consolation prizes of $100 each. find the expected winnings of a single ticket
A single ticket's estimated earnings are around -$0.9442, which indicates that a consumer may expect to lose approximately $0.9442 for each ticket purchased.
To find the expected winnings of a single ticket, we need to calculate the weighted average of the winnings based on the probabilities of winning each prize.
The probabilities of winning each prize are as follows:
1st prize: 1 winner out of 10,000 tickets sold (probability = 1/10,000 = 0.0001)
2nd prize: 3 winners out of 10,000 tickets sold (probability = 3/10,000 = 0.0003)
3rd prize: 5 winners out of 10,000 tickets sold (probability = 5/10,000 = 0.0005)
Consolation prize: 20 winners out of 10,000 tickets sold (probability = 20/10,000 = 0.0020)
No prize: (1 - (probability of winning any prize)) = 1 - (0.0001 + 0.0003 + 0.0005 + 0.0020) = 0.9971
Now, let's calculate the expected winnings:
Expected winnings = (Probability of 1st prize × $3000) + (Probability of 2nd prize × $1000) + (Probability of 3rd prize × $500) + (Probability of consolation prize × $100) + (Probability of no prize × -$2)
Expected winnings = (0.0001 × $3000) + (0.0003 × $1000) + (0.0005 × $500) + (0.0020 × $100) + (0.9971 × -$2)
Expected winnings ≈ -$-0.9442
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The complete question:
A club is holding a raffle. Ten thousand tickets have been sold for $2 each. There will be a 1st prize of $3000, 3 second prizes of $1000 each, 5 third prizes of $500 each and 20 consolation prizes of $100 each. Find the expected winnings of a single ticket.
x -2 98 498 998 2998
p .9971 .0020 .0005 .0003 .0001
f(x)=-2³√x-1-2
please solve ASAP
Answer:1.233
Step-by-step explanation:
here are two plants (A and B) in an industry. To reduce pollution, the government has imposed environmental standards forcing each plant to cut emissions by 60%. At the emissions standard, the marginal social benefit of pollution for Plant A is $500 and the marginal social benefit of pollution for Plant B is $125. The same level of pollution can be achieved at a lower cost by
To achieve the same level of pollution at a lower cost, the government could adjust the environmental standards for each plant based on their respective marginal social benefits of pollution.
The government's environmental standards require Plant A and Plant B to reduce their emissions by 60%. The marginal social benefit of pollution for Plant A is $500 and the marginal social benefit of pollution for Plant B is $125. This means that the benefit of reducing one unit of pollution for Plant A is $500, while for Plant B is $125.
This information suggests that Plant A has a higher marginal social benefit of pollution than Plant B. Since the government's standards require both plants to reduce emissions by the same percentage, Plant A will have to reduce a greater amount of pollution than Plant B to reach the same level of emissions. This means that the cost of reducing pollution for Plant A will be higher than the cost of reducing pollution for Plant B.
To achieve the same level of pollution at a lower cost, the government could adjust the environmental standards for each plant based on their respective marginal social benefits of pollution. For example, if Plant A has a marginal social benefit of $500 and Plant B has a marginal social benefit of $125, the government could require Plant A to reduce its emissions by 50% and Plant B to reduce its emissions by 70%. This would achieve the same level of pollution while minimizing the cost of reducing pollution for both plants.
Thus, To achieve the same level of pollution at a lower cost, the government could adjust the environmental standards for each plant based on their respective marginal social benefits of pollution.
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If A and B are mutually exclusive, then P(A\capB) = 0.
A and B are independent if and only if P(A\capB) = P(A)P(B)
If A and B are two events with P(A) = 0.4, P(B) = 0.2, and P(A B) = 0.5. Find the following:
(a) P(A \cap B) (b) P(A?\cap B) (c) P(A?\cup B?) (d) P(A|B)
If A and B are independent events with P(A) = 0.4 and P(B) = 0.2. Find the
following:
(a) P(A \cap B) (b) P(A?\cap B) (c) P(A? \cup B?) (d) P(A|B)
If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.2. Find the following:
(a) P(A\cap B) (b) P(A?\cap B) (c) P(A? \cup B?) (d) P(A|B)
Roll a die once. The event of getting a "2" and the event of getting a "5" are (a) independent;
(b) mutually exclusive;
(c) Neither
Roll a die twice. The event of getting a "2" on the first roll and the event of getting a "5" on the second roll are
(a) independent;
(b) mutually exclusive;
(c) Neither
(A) P(AB) = P(A B) = 0.5 denotes that there is a 0.5 chance that occurrences A and B will occur simultaneously. We cannot tell whether this relationship holds true for these specific events because the provided information does not specify whether A and B are independent or mutually exclusive.
(b) P(A'B) = P(A') + P(B') - P(A'B') = 0.6 denotes that there is a 0.6 chance that events A and B will occur together.
(c) The chance that either the complement of event A or the complement of event B will occur is 0.5. P(A'B') = 1 - P(AB) = 1 - 0.5 = 0.5.
(d) P(A|B) = P(AB) / P(B) = 0.5 / 0.2 = 2.5 denotes that there is a 2.5 percent chance that event A will occur provided that event B has already occurred.
If P(A) = 0.4 and P(B) = 0.2, respectively, then A and B are independent events.
(a) P(AB) is the probability that both occurrences A and B will occur at the same time. It is calculated as P(A) * P(B) = 0.4 * 0.2 = 0.08. The likelihood that A will occur is independent of the likelihood that B will occur since the two events are unrelated.
(b) P(A'B) = P(A') * P(B) = (1-0.4) * 0.2 = 0.12 is the likelihood that events A and B will occur in complement.
(c) The probability that either the complement of event A or the complement of event B will occur, or both, is given by P(A'B') = 1 - P(A'B) = 1 - 0.08 = 0.92.
(d) P(A|B) = P(AB) / P(B) = 0.08 / 0.2 = 0.4, which represents the likelihood that event A will occur in the absence of event B.
if P(A) = 0.4 and P(B) = 0.2, respectively, and A and B are events that cannot coexist.
(a) P(AB) = 0 (by definition of mutual exclusion), indicating that there is no chance that events A and B will occur simultaneously.
(b) The probability that event A's complement, event B, will occur is P(A'B) = P(B) = 0.2.
(c) The probability that either the complement of event A or the complement of event B will occur, or both, is P(A'B') = P(A') + P(B') = 0.6.
(d) Since P(AB) = 0, the probability of event A occurring provided that event B has already occurred is undefined. P(A|B) = P(AB) / P(B) = 0 / 0.2 = undefined.
Roll a die once. The event of getting a "2" and the event of getting a "5" are mutually exclusive.
Roll a die twice. The event of getting a "2" on the first roll and the event of getting a "5" on the second roll are independent events.
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twenty-six people, numbered consecutively 1 through 26, are seated equally spaced around a circular table. which numbered person is seated directly across from person number 9?
On solving the provided question, we can say that permutation will = 1/2(26) = 13 ways
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.
here,
by permutation,
1 through 26
permutation will = 1/2(26) = 13 ways
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What’s the missing value on the table? Will gift brainliest PLS.
Answer:
B) 23
Step-by-step explanation:
We need to find the pattern of the table. As seen on the other parts of the table, the pattern is 2x + 3. Here, x is the input. So, we substitute 10 for x, giving us:
2 * 10 + 3 = 20 + 3 = 23
So, the missing value in the table is B) 23.
Hope this helped!
Answer:
B. 23
Step-by-step explanation:
Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation. What is YT? using point T as the center of dilation.3units6units12units15units
The value of TY using point T as the center of dilation = 12.
What is a line segment?A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
Here, we have
Given: Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation.
X'Y' and XY are parallels, which means X'Y' = means XY, there is a similarity between the two triangles, we can find YT by using the theorem of Thales,
TY' / TY =TX' / TX =X'Y' /XY,
TY' / TY = TX' / TX = 9/ TY =6/ 2+6=6/8
9/ TY = 6/8
TY= 12
Hence, the value of TY = 12.
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trish goes to a bar with six friends to celebrate her 25th birthday. they're ready to party. each of her friends order her a 1.5 oz. shot (37% abv), and she takes all of them within half an hour. she weighs about 155 pounds. what is her bac level? should she drive?
She should not drive due to her BAC level of 0.117 percentage , which is above the legal limit in most states.
1. Calculate total amount of alcohol consumed:
1.5 oz. x 6 shots
= 9 oz.
2. Calculate amount of alcohol in grams:
9 oz. x 28.35 g/oz.
= 254.15 g
3. Calculate BAC:
(254.15 g/10,000 mL) x (155 lbs x 0.45359 kg/lbs) x (1g/1000mg) x (1.2 g/dL)
= 0.117% BAC
The amount of alcohol consumed by Trish was 9 oz. of 37% abv (alcohol by volume) liquor, which is equivalent to 254.15 g of pure alcohol. To calculate her BAC, we need to convert her weight to kilograms and then multiply the amount of alcohol consumed by her weight, taking into account that there is 1.2 g of alcohol per deciliter of blood. After doing the calculations, we can see that Trish's BAC level is 0.117%, which is above the legal limit for driving in most states, so she should not drive.
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Part B: Starting from the origin, explain how to plot the following three points accurately: (2, −2) (−2, 1.5) (−1, fraction 2 over 4) HELP PLEASEEEE
1. (2,-2). From the origin, go 2 units to the right and two units down
2) (-2,1.5) From the origin, go 2 units to the left and 1.5 units up
3) (-1,[tex]\frac{2}{4}[/tex]) From the origin, go 1 unit to the left and half a unit up
This is a parallelogram. y = ___
The value of y in the parallelogram is 120^o.
Properties of a parallelogram.A parallelogram is a plane figure which has opposite sides to be equal. Some of its properties are:
i. Opposite sides are equal in length
ii. It has two diagonals
iii. Sum of adjacent angles is 180^o
The value of y in the diagram can be determined as;
m<ADC + m<DCB = 180^o (sum of adjacent angles is 180^o)
(x + 8) + 3x = 180
4x = 180 - 8
= 172
x = 172/ 4
= 43
x = 43^o
So that;
m<ADC = x + 8
= 43 + 8
= 51^o
Therefore,
m<ADC + m<DAB = 180^o
51^o + (y + 9) = 180^o
y + 60 = 180
y = 180 - 60
= 120
y = 120^o
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What is a 1:2 ratio example?
A 1:2 ratio example could be 1 cup of flour and 2 cups of sugar. A ratio is a comparison of two or more numbers that shows the relationship between them. A 1:2 ratio means that for every 1 unit, there are 2 units.
A ratio is a comparison between two or more numbers. A 1:2 ratio means that for every 1 unit, there are 2 units. As an example, if you have 1 cup of flour and 2 cups of sugar, the ratio is 1:2 – 1 cup of flour and 2 cups of sugar.
A ratio is a comparison of two or more numbers that shows the relationship between them. A 1:2 ratio means that for every 1 unit, there are 2 units. For example, If you have 1 cup of flour and 2 cups of sugar, the ratio is 1:2. This means that for every 1 cup of flour, there are 2 cups of sugar. Ratios can be used to compare different items, such as ingredients in a recipe, to make sure that the proportions are correct. Ratios are an important tool when measuring and comparing different values.
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MARKING BRAINLIEST! please help asap
Answer: I think its -5
Step-by-step explanation:
Senor Pena found some change on the floor while cleaning a classroom. He found a total of 6 coins that consisted of quarters and nickels. If the total change was $1.30, how many of each coin did he find?
Answer:
There are 5 quarters and 1 nickel
Step-by-step explanation:
Let Q and N be the numbers of Quarters and Nickels that Senor Pena found, respectively.
The value of each coin is $0.25 for quarters and $0.05 for each nickel
The total of $1.30 would be the result of:
1) Quarters: $0.25*Q, and
2) Nickels: $0.05*N
So we can write: $0.25*Q + $0.05*N = $1.30
We also know he found 6 coins, so:
Q + N = 6
We have two equations and two unknowns. We can use substitution to find the answer.
Rearrange the second equation to isolate one of the two variables. lets isolate Q:
Q = 6-N
We can use this definition of Q in the first equation by substitution:
$0.25*Q + $0.05*N = $1.30
$0.25*(6-N) + $0.05*N = $1.30
Leaving off the $ signs for clarity:
0.25(6-N) + 0.05N = 1.30
1.5 - 0.25N + 0.05N = 1.30
-0.2N = -0.20
N = 1
There is 1 nickel
Since Q = 6-N, Q = 5
There are 5 quarters and 1 nickel
CHECK
Do 5 quarters and 1 nickel add to $1.30?
5*($0.25) + 1*($0.05) = $1.30?
$1.25 + $0.05 = $1.30 YES
Round 50276 to the nearest hundred
Answer:
50276 rounded to the nearest hundred is 50300.
Rounding to the nearest hundred means finding the number that is closest to the original number, but ends in two zeroes. In this case 50300 is the nearest number ending in two zeroes to 50276.
Answer:50300
Step-by-step explanation:
In 50276, the number 2 is in the hundreds place. If the number in the tens place if equal or bigger to 0 round up to get 50300.
Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.) Radius r Central Angle θ 16 inches 240°Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.)Radius r Central Angle θ
16 inches 240°
The length of the arc intercepted by the central angle of 240 degrees on a circle with a radius of 16 inches would be 67 inches (rounded to two decimal places)
To find the length of an arc on a circle intercepted by a central angle, we can use the formula: arc length = (θ / 360) * (2 * π * r)
where θ is the measure of the central angle in degrees, π is approximately 3.14, and r is the radius of the circle.
In this case, we are given a circle with a radius 16 inches and a central angle of 240 degrees. Plugging these values into the formula, we get:
arc length = (240 / 360) * (2 * 3.14 * 16) = (2/3) * 100.48 = 67 inches
So the length of the arc intercepted by the central angle of 240 degrees on a circle with a radius of 16 inches would be 67 inches (rounded to two decimal places)
Therefore, the length of the arc would be 67 inches.
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What is a system of three equations that has infinitely many solutions?
The system of three equations x + y + z = 0, x + 2y + 3z = 0, and 4x + 5y + 6z = 0 has infinitely many solutions because the equations are dependent.
1. x + y + z = 0
2. x + 2y + 3z = 0
3. 4x + 5y + 6z = 0
These three equations form a system of equations that has infinitely many solutions because the coefficients of the variables satisfy the conditions for the equations to be dependent. This means that the equations are not independent, and therefore the system of three equations has infinitely many solutions.
The system of three equations x + y + z = 0, x + 2y + 3z = 0, and 4x + 5y + 6z = 0 has infinitely many solutions because the equations are dependent.
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Suppose the slope of a line is positive. Describe what happens to the graph of the line as you move from left to right.
As you move the graph of the line from left to right, the output value of the function increases.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the linear function.b is the intercept, representing the initial value of the linear function.The slope determines if the function is increasing or decreasing over it's domain, as follows:
Positive slope: increasing function.Negative slope: decreasing function.A positive slope means that the function increases when it moves from left to right, that is, when x increases.
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Find an equation of the plane tangent to the following surface at the given point. 7xy +yz +4xz - 48 = 0; (2,2,2) The equation of the tangent plane at (2,2,2) is ... = 0.Find an equation of the plane tangent to the following surface at the given point. yze^xz + 7 = 0; (0, - 7,1) An equation of the tangent plane at (0, - 7,1) is ... = 0. Find an equation of the plane tangent to the following surface at the given point. z = 4 - 4x^2 - 2y^2; (2,3,-30) z = ...?Find an equation for the plane that is tangent to the surfacez = In (x^2 + y^3) at the point P(0,1,0). The equation of the plane is ... = 0
Therefore , the solution of the given problem of equation comes out to be x−3y−4z=0.
The equation is what?When the equals symbol (=) is used to signify equality, a mathematical equation appears to be a formula that connects two statements. In algebra, a factual assertion called an equation shows that several mathematical variables are equal. An equal sign separates the amounts doc d + 6 and 12 in the formula obd + 6 = 12, for instance. The relationship between the syllables to each side of each letter can be expression mathematically. Frequently, the symbol and the message are identical.
Here,
First, we rewrite the surface equation as
f(x, y, z) = x² - y²+2z²
y²+22=0
Thus, our role is as follows:
f(x, y, z) = x² - y²+2z²
We employ the Del, or gradients operator, to determine the normal at any given location in vector space:
Vf(x, Y, Z) = x - y + z
When partially differentiating, keep in mind that we only differentiate with respect to the variable in issue and regard the other factors as constants.
Consequently, (x)(2)+(y)(6)+(z)(2)=(1)(2)+(3)(6)+(2) (-8)
2x−6y−8z=2−18+16
2x−6y−8z=0
x−3y−4z=0
Therefore , the solution of the given problem of equation comes out to be x−3y−4z=0.
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eduardo had 4.5 cups of flour in a jar. he opened a bag of flour, poured in enough to fill the 12-cup jar completely, and still had some left over in the bag. let x represent how much flour was in the bag to start. which inequality describes the problem?
The amount of flour in the bag (x) plus the amount of flour in the jar (4.5 cups) must be greater than or equal to 12 cups.
x + 4.5 ≥ 12
Solve for x:
x ≥ 7.5
The problem states that Eduardo had 4.5 cups of flour in a jar, and then opened a bag of flour and poured it in until the jar was full. The question is how much flour was in the bag to start? To solve this problem, we can use an inequality. Let x represent the amount of flour in the bag to start. The equation we can use is x + 4.5 ≥ 12, which states that the amount of flour in the bag (x) plus the amount of flour in the jar (4.5 cups) must be greater than or equal to 12 cups. To solve for x, we can subtract 4.5 from both sides of the equation, which yields x ≥ 7.5. This means that the bag of flour must have contained at least 7.5 cups of flour for Eduardo to have enough to fill the jar.
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Answer: 7.5 4.5>12
Step-by-step explanation:
I already had this one and got it right
if you buy a concert ticket in advance the cost is $120. if you wait until the day of the concert, they cost $150. what is the percent change in the price,
Answer:
Step-by-step explanation:
Add 25% of 120 to 120
and you get 150 so boom there it is
Answer : 25% difference
Find m∠S in rhombus RSTU
Answer:
In a rhombus, opposite angles are equal, therefore:
m∠S = m∠U = a + 62 degrees
And
m∠R = 2a - 80 degrees
The opposite angles of a rhombus are supplementary, meaning they add up to 180 degrees. So,
m∠S + m∠R = 180 degrees
Therefore,
a + 62 + 2a - 80 = 180
Solving for a, we get:
a = 59
So,
m∠S = a + 62 = 59 + 62 = 121 degrees
partial quotients, 5,166÷.42?
4,200
5,000
840
420
This is the answer hope you understand it
Find the measures of the angles of a triangle with one angle measuring 130 and the other two measuring x.
Answer:
x = 25 degrees
Step-by-step explanation:
The sum of the angles of a triangle is always 180 degrees. Therefore, in a triangle with one angle measuring 130 degrees, the measures of the other two angles must add up to 180-130 = 50 degrees.
So, if the measures of the other two angles are x, the equation would be:
x + x = 50
This means that the measure of each angle is 50/2 = 25 degrees.
Therefore, in a triangle with one angle measuring 130 degrees, the measures of the other two angles are both 25 degrees.
Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australla. Whille booking her
family's plane tickets, she notices on the itinerary that the airline is offering a sixteen hour straight flight from Los
Angeles to Melbourne on a Boeing 747-8 Intercontinental Jet. In an effort to learn more about the capabilities of the Jet,
Sheleah does a little research and stumbles upon the following graph and facts about the Jet's fuel consumption.
Boeing 747-8 Intercontinental Jet
Jet Fuel Available (gallons)
70,000
60,000
50,000
40,000
30,000
20,000
10,000
63,500
2
55,562.5
3
4
47,625
39,687.5
31,750
23,812.5
9
7
8
10
Flight Time (hours)
11
12
15,875
13
14
7,937.5
15
17
The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the Jet to
travel 14,430 kilometers before needing to refuel.
Create a linear model that represents the amount of fuel on the plane, In gallons, as a function of the flight time, In hours.
Show all of your work.
PLEASE HELP I NEED TO FINISH BY TONIGHT
The linear model that represents the amount of fuel on the plane is F(h) = 63,500 - 7937.50h
What is the linear function ?A linear function is a function that has a single variable raised to the power of 1. A linear function increases or decreases by a constant value . As the flight time increases , the amount of fuel declines . Thus, the linear function would be a decreasing function .
The form of the linear function is:
Total fuel left = capacity of the plane - (fuel consumed peer hour x number of hours )
Total fuel left = 63,500 - [(63500 - 55562.5) x h]
F(h) = 63,500 - 7937.50h
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A piece of a cow’s leg bone with a volume of 10 cm3 has a mass of 18 g. What is the density of the bone please answer
what is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curce y
The given curve is a second order, so it is a parabola. The area of the largest rectangle is 32 square units.
What is a curve?
A curve is a mathematical object that is similar to a line but does not have to be straight. A curve can be thought of intuitively as the trace left by a moving point.
Given curve is y = 12 - x².
The vertex of the parabola is on the y-axis. Thus y-axis is a symmetric line of the parabola.
Thus the x-coordinate of the vertices that are lying on the x-axis is the same but the opposite sign.
Thus the y-coordinate of the vertices that are lying on the x-axis is the same.
Thus the x-coordinate of the vertices that are lying on the curve is the same but the opposite sign.
Thus the y-coordinate of the vertices that are lying on the curve is the same.
The y - coordinate of the vertices that are lying on the curve is in form 12 - x².
Assume that the coordinate of the rectangle are A(a,0), B(-a,0), C(-a, 12 - a²), and D(a,12-a²).
The length of the rectangle is 2a.
The width of the rectangle is 12-a².
The area of the rectangle is A = 2a(12-a²).
A = 24a - 2a³
Differentiate with respect to a:
dA/da = 24 -6a² ....(i)
Equate dA/da with zero to find the critical point:
24 -6a² =0
6a² =24
a² = 4
a = ±2
Putting a=2 in A = 24a - 2a³:
A = 24×2 - 2×2³
A = 32
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The given curve is a second order, so it is a parabola. The area of the largest rectangle is 32 square units.
What is a curve?A curve is a mathematical object that is similar to a line but does not have to be straight. A curve can be thought of intuitively as the trace left by a moving point.
Given curve is y = 12 - x²
The vertex of the parabola is on the y-axis. Thus y-axis is a symmetric line of the parabola.
Thus the x-coordinate of the vertices that are lying on the x-axis is the same but the opposite sign.
Thus the y-coordinate of the vertices that are lying on the x-axis is the same.
Thus the x-coordinate of the vertices that are lying on the curve is the same but the opposite sign.
Thus the y-coordinate of the vertices that are lying on the curve is the same.
The y - coordinate of the vertices that are lying on the curve is in form 12 - x².
Assume that the coordinate of the rectangle are A(a,0), B(-a,0), C(-a, 12 - a²), and D(a,12-a²).
The length of the rectangle is 2a.
The width of the rectangle is 12-a².
The area of the rectangle is A = 2a(12-a²).
A = 24a - 2a³
Differentiate with respect to a:
dA/da = 24 -6a² ....(i)
Equate dA/da with zero to find the critical point:
24 -6a² =0
6a² =24
a² = 4
a = ±2
Putting a=2 in A = 24a - 2a³:
A = 24×2 - 2×2³
A = 32
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Complete question is: find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12−x
2
how to graph 2x + y > -1
Answer:
Step-by-step explanation:
“What if you have negative exponents in the denominator? How do you change it into positive exponents?”
The negative exponents in the denominator change it into positive exponents are 1/(2⁻³) = 8, 1/(2x⁻³) = (1/2)x³ and 4/(2(3⁻³)) = (4/2)×3³ = 54
How do you change negative exponents in the denominator into positive exponents?
If you have a fraction with a negative exponent in the denominator, you can change it into a positive exponent by reversing the fraction and taking the reciprocal.
For example, if you have the fraction 1/(x⁻²) you can change it to x² by flipping the fraction and taking reciprocal: 1/(x⁻²) = 1/(1/x²) = x²
Note that when you have a negative exponent in the denominator, it means that the variable is in the denominator and the reciprocal can be taken to move the variable to the numerator, as shown above.
Thus, we can solve the given questions as follow:
1/(2⁻³) = 2³ = 8
1/(2x⁻³) = (1/2)x³
4/(2(3⁻³)) = (4/2)×3³ = (2)×3³ = 2 × 27 = 54
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