Determine the minimum surface area of a rectangular box with a square base, an open-top, and a volume of 500in3. Enter only the minimum surface area, and do not include units in your answer.Major problems that can be simplified by the technique of classical optimization are consist of single or multivariable functions without having constraints. It is also practiced in physics as an energy minimization technique.
The minimum surface area of a rectangular box with a square base is 300 square inches.
What is meant by surface area?Surface area is the amount of space on the outside of a three-dimensional form. The surface area of a solid item is the total area that the object's surface occupies.
The mathematical definition of surface area in the presence of curved surfaces is significantly more involved than the definition of arc length for one-dimensional curves or surface area for polyhedra , where the surface area is the sum of the areas of its faces. Smooth surfaces, such as spheres, are ascribed surface area through their representation as parametric surfaces.
The volume of a rectangular box with a square base, an open-top is 500 cubic inch
So, V=lbh
500 inch³=lbh
Also, given that base is a square, so l=b
h= 500 inch³/lb
h=500 inch³/l²
Now, Surface area(A)= Area of base+ Area of 4 walls
=l²+4lh
=l²+4l(500/l²
=l²+(2000/l)
To minimize the surface area, differentiate it with respect to l.
A'(l)=d/dl(l²+(2000/l))
=2l-(2000/l²)
=(2l³-2000)/l²
Substitute A'(l)=0 to obtain the critical point
(2l³-2000)/l²=0
2l³-2000=0
2l³=2000
l³=1000
l=10
Again differentiating A'(l) to confirm the minimum value at l=10
A"(l)=d/dl((2l³-2000)/l²)
A"(l)=2+(4000/10³)
A"(10)=2+(4000/10³)
A"(10)=6>0
Thus, the required surface area is,
Surface area=l²+(2000/l)
=10²+(2000/l)
=300
Therefore, the minimum surface area of a rectangular box is 300 square inches.
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Find b value
3(1.2b − 1) + 3.6 = 4.2
Answer: B = 1
Step-by-step explanation:
You want to get b alone, first, you will subtract 3.6. What you do on one side you do to the other
3(1.2b - 1) + 3.6 = 4.2
3(1.2b - 1) + 3.6 - 3.6 = 4.2 - 3.6
Since the 3 is multiplied, we will do the opposite to eliminate it, Divison. So divide each side by 3.
3(1.2b - 1) = 0.6
3(1.2b - 1)/3 = 0.6/3
Then we will add one to each side.
1.2b - 1 = 0.2
1.2b - 1 + 1 = 0.2 + 1
The last step is to divide each side by 1.2 to find b.
1.2b = 1.2
1.2b/1.2 = 1.2/1.2
b = 1
What does the 9 3 3 1 ratio for phenotypes mean?.
The 9 3 3 1 ratio for phenotype mean the classic mendelian ratio for a di-hybrid cross in which the alleles of two different genes assort independently into gametes Independent assortment of genes.
A cross is made between the two parents based on two pairs of characters known as Di-hybrid cross.
A cross is made between homogenous yellow round seed to another homozygous green wrinkled seeds.
At the [tex]F_1[/tex] generation, all plants are heterozygous yellow round. Whenever this plant is subject to self pollination, in the [tex]F_2[/tex] generation, 9 plants are Yellow round, 3 plants are yellow wrinkled, 3 plants are green round and 1 plant is green wrinkled.
This called Di-hybrid phenotype ratio 9:3:3:1. Mendel is expressed this one as "Law of independent assortment".
Therefore the 9 3 3 1 ratio for phenotype mean the classic Mendelian ratio for a di-hybrid cross in which the alleles of two different genes assort independently into gametes Independent assortment of genes.
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Two different groups in a statistics class are conducting a survey to estimate the mean number of units students at their college are enrolled in. The population mean and standard deviation are unknown. The sample from the first group survey has 49 data values. The sample from the second group survey has 81 data values. For each sample, the groups construct a 90% confidence interval to estimate the population mean.Which confidence interval will have greater precision (smaller width) for estimating the population mean?Group of answer choicesThe confidence interval based on the sample of 49 data values will be more precise.Both confidence intervals will have the same precision.The confidence interval based on the sample of 81 data values will be more precise.
The confidence interval for the second group's estimate of the population mean will be more accurate due to the increased sample size.
What is mistake, exactly?
An error is an inaccurate or improper action (from the Latin error, meaning "wandering"). An error is often used interchangeably with the word mistake.
Detailed explanation:
margin of a confidence interval's error:
The following format describes the equation for a confidence interval's margin of error:
M=zα/√n
where is the population's standard deviation, n is the sample size, and z is connected to the confidence level.
This suggests that a larger size results in a better degree of interval precision, or a smaller margin of error.
In this instance:
There are 49 data values in the sample from the first group survey and 81 from the second group.
The confidence interval for the second group's estimate of the population mean will be more accurate due to the increased sample size.
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The box plot compares the number of events that mrs. Cai’s and mr. Roland’s classes won over the last 10 years on the school’s field day. Based on the data in the box plots, what is the best evidence to show which class has had greater success on field day over the last 10 years? mrs. Cai’s class was more successful because her interquartile range was less spread out. Mrs. Cai’s class was more successful because she had the greater total spread. Mr. Roland’s class was more successful because his class always won at least one event. Mr. Roland’s class was more successful because his class’s lower quartile was the same as mrs. Cai’s class’s upper quartile.
The correct option is option (d). In other words, Mr. Rowland's class was more successful because his class had the same lower quartile as top quartile of Mrs. Cai's class.
Box plots were created to compare the number of events, Mrs. Cai and Mr. Roland's class has won the school athletic meet for the last ten years. Let's talk about boxplot first.
What is a boxplot?
In descriptive statistics, a boxplot (also called a wishler plot) is a type of graph used in explanatory data analysis. A boxplot visually shows the distribution of numerical data and its skewness by showing the quartiles and means of the data.
Minimum score:
Minimum score without outliers (indicated at the end of the left whisler).
Lower quartile: 25% of the results are below the lower quartile (also known as the first quartile).
Median: The median marks the midpoint of the data and is indicated by the line that divides the box in two (sometimes called the second quartile).
Upper quartile:
75% of the results are below the top quartile. This means that 25% of the data are above this value.
Max Score:
Highest score without outliers (shown at the end of the right whisker)
Now, we can easily evaluate the required information from given box plot. We see that
the lower quartile of Mr. Roland’s class = 4
and upper quartile of Mrs. Cai’s class = 4
both values are same but lower quartile reach to upper quartile that means Mr. Roland’s class was more successful.
Hence, option (d) is right.
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3 mathematical induction 3 mathematical induction can be used not only to prove equalities, but also to prove inequalities. the predicate p (n) is the statement n! < nnwhere n is an integer greater than 1. a) what is the statement p (2)? b) show that p (2) is true, i.e., complete the basis step of the proof by induction. c) what is the inductive hypothesis of a proof by mathematical induction that p (n) is true for all natural numbers n greater than 1? recall that n! is the factorial of n, i.e., n!
(a) The statement p(2) is p(2) : 2! < 2² , and
(b) the statement p(2) is True is shown below .
In the question ,
it is given that ,
the statement is p(n) : n! < nⁿ ,
Part(a)
we have to find p(2) ,
On substituting n = 2 , in the statement
we get ,
p(2) : 2! < 2²
Part(b)
we know that 2 factorial is 2! = 2 × 1 = 2
and 2² = 2 × 2 = 4
On comparing the values of 2! and 2² , we can see that
2 < 4
which is 2! < 2² ,
Hence p(2) is True .
Therefore , p(2) is p(2) : 2! < 2² and the statement p(2) is True .
The given question is incomplete , the complete question is
Mathematical Induction can be used not only to prove equalities, but also to prove inequalities. the predicate p(n) is the statement n! < nⁿ , where n is an integer greater than 1.
(a) what is the statement p(2) ?
(b) show that p (2) is true .
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How will you differentiate linear inequalities in two variables from systems of linear inequalities in two variables?.
Linear equation and Linear inequality are differentiatable on the sybolically. The symbol used in linear equation is "=" equality sign and the symbols used in linear inequality are ">","<","
"≤", " ≥".
We need to distinguish between linear inequalities in two variables and systems of linear equations in two variables.
We will first discuss linear equations and then linear inequalities.
Linear Equations:
If a equation is written in the form ax + by + c=0, the equation is said to be a linear equation in two variables. where a, b & c are real numbers and coefficients of x and y. , that is, a and b are not equal to zero.
Characterstic :
Variables in a linear equation are not raised to powers or used as denominators of fractionsFind pairs of values that make the linear equation true, and plot those pairs on a coordinate grid so that all points are Lying on the same line. The graph of a linear equation is a straight line.A linear equation in two variables can be written as a linear relationship between x and y.For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
methods for solving linear equations in two variables:
graphical methodsreplacement methodscross-multiplication methodselimination methodsLinear inequality:
Linear inequalities in two variables use the greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤) symbols instead of the equal (=) symbol. Use the.
Features:
You can add, subtract, multiply and divide with the same number to solve inequalitiesMultiply and divide with negative numbers reverse the inequalityOrder outside shaded area Pairs are inequalities that cannot be solved graphically.Example: 8x + 3y ≥ 5 and 2x + 3y < 10 are linear inequalities in two variables.
Method: Graphical
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5.) If b = -2, which equation is true? A 2(b +5) = 6 2(b-4)= 12 B C 2(b + 3) = 10 D 2(b-5) = 14
Answer:
a.) 2(b+5)=6
Step-by-step explanation:
[tex]b=-2\\\\a.)2(b+5)=6\\2[(-2)+5]=6\\2(3)=6\\6=6\\\\b.)2(b-4)=12\\2[(-2)-4]=12\\2(-6)=12\\-12\neq 12\\\\c.)2(b+3)=10\\2[(-2)+3]=10\\2(1)=10\\2\neq10\\\\d.)2(b-5)=14\\2[(-2)-5]=14\\2(-7)=14\\-14\neq14[/tex]
The term-to-term rule for a different sequence is divide by 4 then add 6
The 2nd term of the sequence is 36
Work out the 1st term.
The first term of sequence is 120
Sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule.
A sequence can be defined based on the number of terms i.e. either finite sequence or infinite sequence.
Let the first term of the sequence is x
According to the question ,
The term-to-term rule for a different sequence is divide by 4 then add 6
So , the get the second term x will be divided by 4 and then added by 6
second term = (x/4) + 6 --------(2)
It is given that the second term of the sequence = 36
Using equation (1),
(x/4) + 6 = 36
Multiply by 4 both the sides,
=> x + 24 = 144
=> x = 144 - 24
=> x = 120
Hence , the first term of sequence is 120
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instructions: match each term to its definition below by selecting the correct term from each dropdown list. scroll down to see all of the definitions. when you are done, select check.1. ______ means that each individual has a designated supervisor to whom they report to at the scene of the incident. 2. ______ allows agencies with different legal, geographic, and functional authorities and responsibilities to work together effectively without affecting individual agency authority, responsibility, or accountability. 3. ______ refers to the orderly line of authority within the ranks of the incident management organization.chain of commandunity of commandunified of command
Each terminology should be matched to its definition as follows:
Unity of command: means that each individual has a designated supervisor to whom they report to at the scene of the incident. Unified of command: allows agencies with different legal, geographic, and functional authorities and responsibilities to work together effectively without affecting individual agency authority, responsibility, or accountability. Chain of command: refers to the orderly line of authority within the ranks of the incident management organization.What is ICS?ICS is an abbreviation for incident command system and it can be defined as a subset of the National Incident Management System (NIMS) which is typically used for planned events, as well as for emergencies and coordinated responses in various business organizations and/or circumstances.
Generally speaking, there are six (6) fundamental functional areas in an incident command system (ICS) and these including the following;
PlanningCommandIntelligence/InvestigationOperationsFinance/AdministrationLogisticsIn conclusion, chain of command, unity of command, and unified of command are all terminologies that are associated with an incident command system (ICS).
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given that x+y=13, xy=-30 and x>y, find the values of ( x+3)(y+3)
Answer:
18-----------------------------
Givenx + y = 13, xy = -30 and x > yFind the value of (x + 3)(y + 3)Distribute and regroup:
(x + 3)(y + 3) =xy + 3x + 3y + 9 = xy + 3(x + y) + 9Substitute values:
- 30 + 3(13) + 9 = - 30 + 39 + 9 = 18Answer:
x = 15 and y = -2
(x + 3)(y + 3) = 18
Step-by-step explanation:
Given equations:
[tex]\begin{cases}x+y=13\\xy=-30\end{cases}[/tex]
Rewrite the first equation to make y the subject:
[tex]\implies y=13-x[/tex]
Substitute the found expression for y into the second equation and solve for x:
[tex]\begin{aligned}xy&=-30\\y=13-x \implies x(13-x)&=-30\\13x-x^2&=-30\\-x^2+13x+30&=0\\x^2-13x-30&=0\\x^2+2x-15x-30&=0\\x(x+2)-15(x+2)&=0\\(x-15)(x+2)&=0\\\\\implies x-15&=0 \implies x=15\\\implies x+2&=0 \implies x=-2\end{aligned}[/tex]
[tex]\textsf{When}\;x=15 \implies y=-2[/tex]
[tex]\textsf{When}\;x=-2 \implies y=15[/tex]
As x > y then:
x = 15y = -2Substitute the found values of x and y into the equation:
[tex]\begin{aligned}\implies (x+3)(y+3)&=(15+3)(-2+3)\\&=18 \cdot 1\\&=18\end{aligned}[/tex]
A. Dilate triangle ABC using center p and scale factor 3/2.
B. What do properties of dilations tell you about B'? (please answer B)
Answer:
The angle measurements will be the same, but the side length will be proportional to the original image but will be 3/2 times the length of the original sides.
Step-by-step explanation:
Set up the linear programming problems in this exercise set. Do not attempt to solve them. The Humidor blends regular coffee, High Mountain coffee, and chocolate to obtain four kinds of coffee: Early Riser, Coffee Time, After Dinner, and Deluxe. The blends and profit for each blend are given in the following chart:The shop has 260 pounds of regular coffee, 90 pounds of High Mountain coffee, and 20 pounds of chocolate. How many pounds of each blend should be produced to maximize profit?
The set of linear programming for this problem is, to maximize [tex]z = 1x_{1} + 1.1x_{2} + 1.15x_{3} + 1.2x_{4}[/tex] subject to [tex]80x_{1} + 75x_{1} + 75x_{1} + 50x_{4}\leq 260;[/tex] [tex]20x_{1} + 23x_{2} + 20x_{3} + 40x_{4} \leq 90;2x_{2} + 5x_{3} + 10x_{4} \leq 20;[/tex] [tex]x_{1} \geq 0,x_{2} \geq 0,x_{1} \geq 0[/tex] [tex], x_{4} \geq 0[/tex].
In the given question,
The Humidor blends regular coffee, High Mountain coffee, and chocolate to obtain four kinds of coffee: Early Riser, Coffee Time, After Dinner, and Deluxe.
The blends and profit for each blend are given below in the following chart:
The shop has 260 pounds of regular coffee, 90 pounds of High Mountain coffee, and 20 pounds of chocolate.
Let [tex]x_{1}, x_{2}, x_{3}[/tex] and [tex]x_{4}[/tex] be the weight in pounds of early riser, Coffee time, after dinner and deluxe respectively.
The maximum available pounds of regular coffee are 260 pounds.
Therefore,
[tex]80x_{1} + 75x_{2} + 75x_{3} + 50x_{4}\leq 260[/tex]
The maximum available pounds of High Mountain are 90 pounds.
Hence,
[tex]20x_{1} + 23x_{2} + 20x_{3} + 40x_{4} \leq 90[/tex]
The maximum available pounds of chocolate are 20 pounds.
Therefore,
[tex]0x_{1} + 2x_{2} + 5x_{1} + 10x_{4} \leq 20[/tex]
To maximize the profit, the equation will be
[tex]z = 1x_{1} + 1.1x_{2} + 1.15x_{3} + 1.2x_{4}[/tex]
So the linear programming model for the situation is
Maximize
[tex]z = 1x_{1} + 1.1x_{2} + 1.15x_{3} + 1.2x_{4}[/tex]
Subject to
[tex]80x_{1} + 75x_{1} + 75x_{1} + 50x_{4}\leq 260\\20x_{1} + 23x_{2} + 20x_{3} + 40x_{4} \leq 90\\2x_{2} + 5x_{3} + 10x_{4} \leq 20\\x_{1} \geq 0,x_{2} \geq 0, x_{1} \geq 0, x_{4} \geq 0[/tex]
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What is an example of a linear function?.
Examples of Linear function are 6x + y = -1; and y = x + 5;
A linear function is the function that consists of one independent variable and one dependent variable without any exponents or powers.
The order of a linear function is always 1.
An example of such an equation can be:
6x + y = -1
Another definition of a linear function is the function that represents a straight line on the graph.
Except y=0; x=0; As y=0 represents the y-axis on the graph while x=0 represents the x-axis on the graph. Any other straight line other that these are known as Linear function.
Example of such a linear function can be:
y = x + 5
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we have an urn with 10 balls numbered from 1 to 10. we choosea sample of 111 with replacement. approximate the probability of the event thatthe number one appears at most 3 times in the sample. use both the normaland the poisson approximation, and compare the results with the exact probability0:000949681
The exact probability is less than probability using Poisson distribution is less than probability using normal distribution.
Given that,
10 balls, numbered from 1 to 10, are in an urn. We selected a 111-person sample with replacement.
We have to calculate the probability that the number one appears in the sample no more than three times. Compare the outcomes with the precise probability using both the normal and the Poisson approximations. 0:000949681
We know that,
Let
X= number of times that 1 appears in a sample
Probability of getting 1 =1/10=0.1
Then X congruent to Binomial (111,0.1)
Now,
If we approximately X is Poisson distribution with parameter
λ=111 ×0.1=11.1
Then
P(X≤3)=∑x=0 to 3 e⁻¹¹°¹(11.1)ˣ/x!
P(X≤3)= 0.004558534
If we approximate X by Normal distribution with mean
μ=111 ×0.1=11.1
σ=√111 ×0.1×0.9= 3.160696 then
P(X≤3)=0.005192688
Exact probability is
P(X≤3)=0.003275558
Therefore, The exact probability is less than probability using Poisson distribution is less than probability using normal distribution.
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the angles of a triangle are in a ratio of 1:1:2. find the ratio of the sides opposite these angles.
The ratio of opposite sides of given angle is 1 : 1 : [tex]\sqrt{2}[/tex].
We have given that the angles of a triangle are in ratio of 1 : 1 : 2.
Let us consider angle is x°.
We know that the sum of angles of triangle is 180°.
Therefore we can write it as,
1(x) + 1(x) + 2(x) = 180°
4x = 180°
x = 45°
then the angle become 45° ,45°, 90°.
That means triangle is an isosceles triangle.
We know that if triangle is an isosceles right triangle (45-45-90) then the side lengths will follow the ratio 1 : 1 : [tex]\sqrt{2}[/tex].
Hence the sides of the given triangle have a ratio of 1 : 1: [tex]\sqrt{2}[/tex].
A triangle in which at least two sides are equal is called an Isosceles triangle. An Isosceles triangle have both two equal sides and two equal angles.
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in a distribution, a random variable can take any value in a specified range. group of answer choices discrete probability cumulative relative frequency continuous probability
In a continuous probability distribution, a random variable can take any value in a specified range. (Option D)
A probability distribution refers to the mathematical function that provides the probabilities of occurrence of different possible outcomes for an experiment. Continuous probability distribution refers to a probability distribution with continuous types of data or random variables where the random variable can take on any value and is continuous. As there are infinite values that the variable can assume, the probability of the variable assuming any one specific value is zero. A continuous distribution is characterized by a range of values that are infinite, and therefore uncountable. The normal distribution is one example of a continuous distribution.
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A car is moving at a constant speed and travels 48 45 48\ \frac{4}{5}\48 5 4 ​ miles in 45 \frac{4}{5}\ 5 4 ​ of an hour. how many miles will this car travel in three hours?
Ia jogged two-third of the way home from chool. Then he wa tired, o he walked the remaining 3{,}200\text{ m}3,200 m3, comma, 200, tart text, pace, m, end text. How many kilometer did Ia travel from chool to hi houe?
Based on the jogging and walking distance, Issa travelled 9.6 km from school to his house.
Let us assume the total distance between between school and home be x. So, jogging distance will be = 2/3x
The remaining distance = 3200 m
Now forming the equation from mentioned information -
2/3x + 3200 = x
Rewriting the equation
3200 = x - 2/3x
Taking LCM, we get 3
3200 = (3x - 2x)/3
Performing subtraction on Right Hand Side
3200 = x/3
x = 3200 × 3
Performing multiplication
x = 9600 m
As we know, 1000 m = 1 km
9600 m = 9.6 km
Hence, the distance is 9.6 km.
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The complete question is -
Issa jogged two-thirds of the way home from school. Then he was tired, so he walked the remaining 3200 m. How many kilometers did Issa travel from school to his house?
23040 divided by 4stan's cookie recipe makes 242424 cookies and calls for exactly 384384384 sprinkles. he is wondering how many sprinkles (p)(p)(, p, )he will need to make 606060 cookies. he assumes each cookie will have the same number of sprinkles.
In the calculation where Stan wants to make 60 cookies, then as per the given information, he will need 960 sprinkles to prepare the required number of cookies.
It has been given that the recipe for cookie by Stan requires 384 sprinkles for making 24 cookies. The calculation for the sprinkles required for making one cookie as per the given information will be
384/24 = 16 sprinkles per cookie
Stan wants to make 60 cookies, so the number of sprinkles required will be,
16 x 60 = 960 sprinkles.
Therefore, Stan will need 960 sprinkles to make 60 cookies.
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Complete question
Stan's cookie recipe makes 24 cookies and calls for exactly 384 sprinkles. He is wondering how many sprinkles (p) he will need to make 60 cookies. He assumes each cookie will have the same number of sprinkles.
How many sprinkles does Stan need to make 60 cookies?
If a wheel of a bicycle covers 440m in 200 rotations find the diameter of the wheel.
The diameter of the wheel of the bicycle that covers 440m in 200 rotations is 0.7m.
What do we mean by diameter?Any straight line segment that cuts through the center of a circle and has ends that are on the circle is considered a circle's diameter in geometry.
It is also known as the circle's longest chord.
The diameter of a sphere can be defined using either of the two methods.
The diameter or length of a circle is its circumference.
A straight line connecting a point on one end of the circle to a point on the other end, passing through the center, is the diameter.
So, the diameter of the wheel will be:
Circumference = 440/200
Circumference = 44/20
Circumference = 22/10
Circumference = 2.2/1
2πr = 2.2
Now, calculate the radius:
2πr = 2.2
r = 2.2/2π
r = 7/22 * 2.2/2
r = 0.35
Diameter: 3.5 * 2 = 0.7m
Therefore, the diameter of the wheel of the bicycle that covers 440m in 200 rotations is 0.7m.
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It is known that x1 and x2 are roots of the equation 3x^2 2x k=0, where 2x1=−3x2. find k.
Value of the k is -2 for the equation [tex]3x^{2} +2x + k = 0[/tex].
Given equation is,
[tex]3x^{2} + 2x + k = 0[/tex]
From the quadratic equation we get,
a = 3, b = 2, c = k
Let us consider roots of the equation are x₁ and x₂
We know that sum of roots is -b/a
x₁ + x₂ = - 2/3
and product of roots is c/a
x₁x₂ = k / 3
It is given that 2x₁ = -3x₂
⇒ x₁ = - 3/2 x₂
Putting value of x₁ in the first equation,
-3/2 x₂ + x₂ = - 2/3
-3x₂ + 2x₂ = -2/3
- x₂ = - 2/3
⇒ x₂ = 2/3
and x₁ = (- 3/2)(2/3)
x₁ = -1
Therefore x₁x₂ = k/3 implies that,
-1(2/3) = k/3
- 2/3 = k/3
k = -2.
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Damon drank 1. 49 L of water. Gavin drank 0. 86 L of water. How many more litre of water did Damon drink?
Damon wants to drink 1.49 L of water and if he has drink 0.86 L of water then he has to drink 0.63 L of water.
What is subtraction in mathematics?
Subtraction in math means to take something away from a group or a number of things. When we subtract, the number of items in the group decreases or becomes smaller. A subtraction problem includes the minuend, subtrahend, and difference.
Damon wants to drink 1.49 L of water and he has drink 0.86 L of water
The required amount of water will be = 1.49 - 0.86 = 0.63 L of water.
Hence, Damon wants to drink 1.49 L of water and if he has drink 0.86 L of water then he has to drink 0.63 L of water.
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a. work out the range
b. how many students are in the group
c. work out the mean mark of the group
how many years after the 1972 ban did it take for ddt levels to move from a rapid to slower rate of decline
According to all Reports of U.S media and other,
approx. 97 years after in 1972 ban did it take for ddt levels to move from a rapid to slower rate of decline.
DDT (dichloro-diphenyl-trichloroethane) has been one of the most commonly used pesticide chemicals in the United States for many years and was first synthesized in 1874. However, its efficacy as an insecticide was not discovered until 1939. Shortly thereafter, especially during World War I, the United States began producing large amounts of DDT abroad to combat vector-borne diseases such as typhoid fever and malaria. It declined sharply, falling from a peak of about $80m that year to just under $12m in the early 1970s. Over 80% of the amount of pesticides used between 1970 and 1972 was on cotton, with the rest mainly on peanuts and soybeans. The decline in DDT use is due to
(1) increased resistance to insects
(2) development of more effective alternative pesticides
(3) Growing public concern about adverse environmental impacts.
(4) Strengthening government restrictions on the use of DDT.
Residues of the pesticide DDT in the food supply, human tissues, and the environment have declined in recent years, especially since the EPA banned the chemical from major uses in 1972.
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what percentage of the fire fighters in the sample have moderate to severe risk for alcohol problems?
The percentage of the fire fighters have moderate to severe risk for alcohol problems is 28%
From the sample, we can get that number of fire fighters who participated in rescue of 9/11 attack and are under moderate to severe risk for alcohol problems is =309.
Total number of fire fighters participated in 9/11 attack is =1102
So, percentage of fire fighters have moderate to severe risk for alcohol problems are =(309/1102)×100
percentage from the sample= 0.28×100=28%
Hence, 28% fire fighters are in severe risk for alcohol problems
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(Complete question) is:
what percentage of the fire fighters in the sample have moderate to severe risk for alcohol problems?
How do you tell if the degree of a polynomial is even or odd from a graph?.
A polynomial is even if each term is an even function. A polynomial is odd if each term is an odd function.
How do you tell if a polynomial graph is odd or even?
In general, we can determine whether a polynomial is even, odd, or neither by examining each individual term. A polynomial is even if each term is an even function. A polynomial is odd if each term is an odd function. A polynomial is neither even nor odd if it is made up of both even and odd functions
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g if a distribution is approximately bell shaped with the mean 12 and standard deviation 2 then the percentage of observations between 8 and 10 is approximately:
The percentage of observations between 8 and 10 is 13.59%
Given,
The distribution is bell shaped.
The mean of the distribution, μ = 12
Standard deviation of the distribution, σ = 2
We have to find the percentage of observations between 8 and 10.
Here,
Calculate z score;
z score = (x - μ) / σ
For x = 8
z score = (8 - 12) / 2 = -4/2 = -2
For x = 10
z score = (10 - 12) / 2 = -2/2 = -1
The p value;
P (-2 < z < -1) = P(z < -1) - P(z < -2)
= 0.158655 - 0.02275
= 0.135905 ≈ 0.13.59 x 100 = 13.59%
That is,
The percentage of observations between 8 and 10 is 13.59%
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a biologist has a -gram sample of a radioactive substance. find the mass of the sample after three hours if it decreases according to a continuous exponential decay model, at a relative rate of per hour. do not round any intermediate computations, and round your answer to the nearest tenth.
The mass of the radioactive sample after 5 hours is 1471g.
since we know that an exponential function is the form of y = abˣ, where where x, and y are the variables, b is the multiplier and a is the initial value.Considering y be the mass of sample remaining after x hours. It is given that the initial value a is 2952g sample, there is a decay of 13% per hour, so : b = 100% - 13% = 87% = 0.87
substituting the values in The equation is:
y = 2952(0.87)ˣ, so After 5 hours:
y = 2952(0.87)⁵ = 1471g
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A biologist has a 2952 -gram sample of a radioactive substance. Find the mass of the sample after five hours if it decreases according to a continuous exponential decay model, at a relative rate of 13% per hour. Do not round any intermediate computations, and round your answer to the nearest tenth.
Thi quetion ha two part. Firt, anwer Part A. Then, anwer Part B. Part A
A cheetah run 420 feet in 6 econd. Crytal want to determine how far a cheetah could run in 15 econd at thi rate. Explain how to ue equivalent fraction to find the ditance a cheetah could run in 15 econd. Then write the equivalent fraction. Input Field 1 of 1
Skip to input field
100 of 100 word remaining
Part B
Fill in the blank quetion. How many feet could a cheetah run in 15 econd at thi rate?
ft
The distance of cheetah could run in 15 seconds is 1050ft.
What is the distance?
Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Here, we have
Given, A cheetah runs 420 feet in 6 seconds.
We have to determine Crystal wants to determine how far a cheetah could run in 15 seconds at this rate.
Speed of cheetah = 420/6ft/sec
= 70ft/sec
In 15 seconds cheetah could run
Distance = 15 × 70ft
= 1050ft
Hence, the distance of cheetah could run in 15 seconds is 1050ft.
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