Yes, you can use the complex fraction (1/12)/(3/4) to determine the fraction of the project that the carpenter completed per hour.
To simplify the complex fraction, you can use the reciprocal of the denominator to convert the division into multiplication:
(1/12) / (3/4) = (1/12) * (4/3)
Next, you can simplify the fraction by canceling out common factors:
(1/12) * (4/3) = (1 * 4) / (12 * 3) = 4/36
Finally, you can simplify the fraction by reducing it to the lowest terms:
3/48 = 1/9
Therefore, the carpenter completed 1/16 of the project per hour.
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4. A bag of candy has 22 twix, 14 reeces, and 16 hersheys. Give a reduced ratio of non-twix to ALL candy.
Answer: 30/52 or 58%
Step-by-step explanation:
The non-Twix candies to all candies is 30 pieces of non-Twix to 52 total candies. This is a ratio of 30:52 or 58%. I hope this helps you. <3
Answer: 15 non-twix to 26 total candy
Step-by-step explanation:
non twix: 14+16=30
all candy: 22+14+16=52
30:52
simplify
15:26
Please help thank you
The values of sine, cosine, and tangent of the angle 'θ' are: sinθ = [tex]\frac{1}{2}[/tex],
cosθ = [tex]\frac{\sqrt{3}}{2}[/tex] and tanθ = [tex]\frac{1}{\sqrt{3} }[/tex] .
How to find trignometric ratios far an angle?To begin, determine the angle for which you wish to compute trigonometric ratios. Let's call the angle "θ".
Find the lengths of the sides of the right triangle that correspond to the angle "θ". Choose the trigonometric ratio you wish to calculate: sine (sin), cosine (cos), or tangent (tan).
Now, using the proper trigonometric formula, determine the needed ratio:
sin θ [tex]= \frac{Opposite side}{Hypotenuse }[/tex]
cos θ [tex]= \frac{Adjacent side }{Hypotenuse}[/tex]
tan θ [tex]= \frac{Opposite side }{Adjacent side}[/tex]
In the given problem, values for angle θ are-:
opposite side = 4 and Adjacent side = 4[tex]\sqrt{3}[/tex]
Using Pythagorean theorem to find the value of hypotenuse:
[tex]hypotenuse = \sqrt{(opposite^2 + adjacent^2)}[/tex]
[tex]hypotenuse=\sqrt{4^{2}+(4\sqrt{3})^2 } =\sqrt{16+48} =\sqrt{64} =8[/tex]
Now, putting values to find required trignometric ratios-:
sin θ[tex]= \frac{Opposite side}{Hypotenuse }=\frac{4}{8 }=\frac{1}{2}[/tex]
cos θ[tex]= \frac{Adjacent side }{Hypotenuse} =\frac{4\sqrt{3}}{8}=\frac{\sqrt{3}}{2}[/tex]
tan θ [tex]= \frac{Opposite side }{Adjacent side}=\frac{4}{4\sqrt{3}}=\frac{1}{\sqrt{3} }[/tex]
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pls pls help. just need the answer
The value of k is given as follows:
k = 5.
How to obtain the value of k?The function in the context of this problem is defined as follows:
f(x) = x³ + kx - 6.
We have that x - 1 is a factor of the function, meaning that, by the Factor Theorem:
f(1) = 0, x - 1 = 0 -> x = 1.
Hence, applying the numeric value, the value of k is obtained as follows:
1 + k - 6 = 0
k - 5 = 0
k = 5.
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The sum or difference of two fractions is not in _______________
The sum or difference of two fractions is not in Improper form.
What is Fraction?Fraction is a part of a whole number. It is represented by two numbers separated by a line. The top number is called the numerator and the bottom number is called the denominator. The numerator represents the number of parts of the whole, and the denominator represents the total number of parts. For example, 1/2 is a fraction that represents one part of a whole that is divided into two equal parts. Fractions are used in many mathematical calculations such as addition, subtraction, multiplication and division.
When adding or subtracting fractions, it is important to first convert the fractions to improper form. Improper form is when the numerator (the top number of the fraction) is larger than the denominator (the bottom number of the fraction). For example, the improper form of 1/2 is 3/2.
To convert a fraction to its improper form, simply multiply the numerator and denominator by the same number. For example, let’s convert the fraction 1/2 to its improper form. To do this, we multiply the numerator (1) and denominator (2) by 2. This gives us 2/4, which is the same as 3/2 (the improper form).
Once all the fractions have been converted to improper form, they can be added or subtracted by simply adding or subtracting the numerators (top numbers) and keeping the denominator (bottom number) the same.
For example, let’s say we want to add 3/4 and 1/2. To do this, we convert both fractions to improper form: 3/4 becomes 6/4, and 1/2 becomes 3/2. Then, we add the numerators (6 + 3 = 9) and keep the denominator the same (4). This gives us the answer of 9/4.
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Complete questions as follows-
The sum or difference of two fractions is not in _______________ form.
a client is receiving an iv solution of 2 grams of medication diluted in 100 ml of normal saline over a one hour time period. how many mg of medication is the client receiving per minute? (enter numeric value only. if rounding is required, round to the nearest whole number.)
The client will be receiving 1.67 ml of medication in one minute and it will have 0.334 g of medication per minute.
Here 2g of medication is diluted with 100 ml of normal saline. So concentration of 1ml of normal saline would be,
Concentration of 1 ml = 2/100 = 0.02 g/ml
It is delivered over a period of 1 hour. So, the amount delivered per minute will be,
Amount per minute = Volume/ time = 100/60 = 1.67 ml
Amount of medication in 1.67 ml = Volume × Amount per ml
= 1.67 × 0.02 = 0.334 g
So 0.334 g of medication will be received per minute. So the rate will be 1.67 ml per minute.
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A 95% confidence interval for the population mean implies that if samples are drawn repeatedly and confidence intervals for μ are constructed, then 95% of the confidence intervals computed will contain the population mean (true or false)
True.
A 95% confidence interval for the population mean means that if we draw multiple samples from the same population and construct confidence intervals for the mean using each sample, then 95% of those intervals will contain the true population mean. This is because the confidence interval is computed based on the sample mean and the sample's standard deviation, which are random variables that are expected to vary from sample to sample. Therefore, we cannot be 100% certain that the true population mean is within any particular confidence interval, but we can be confident (95% confident, in this case) that most of the intervals we construct will contain the true mean. A 95% confidence interval for the population mean implies that if samples are drawn repeatedly and confidence intervals for μ are constructed, then 95% of the confidence intervals computed will contain the population mean. This means that you can be 95% confident that the true population mean lies within the calculated interval.
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some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 180 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions be?length
the maximum dimensions of the box would be 60 cm x 60 cm x 60 cm in order to have the maximum allowable volume while still meeting the airline's luggage restrictions.
If the length and width of the box are equal, we can call the length and width x. Then, the height of the box would also be x in order to maximize the volume.
The sum of the length, width, and height of the box would be:
x + x + x = 3x
We know that the sum of the length, width, and height must be less than or equal to 180 cm. So:
3x ≤ 180
Simplifying, we get:
x ≤ 60
Therefore, the maximum dimensions of the box would be 60 cm x 60 cm x 60 cm in order to have the maximum allowable volume while still meeting the airline's luggage restrictions.
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Dimensions, the sum of the length, width, and height is 360 cm.
Let's assume that the length, width, and height of the box are all equal to
x cm. Since the length and width are equal, we can write:
Length = Width = x
The volume of the box can be expressed as:
Volume = Length x Width x Height
Volume = x × x × (180 - 2x) (since the height is equal to 180 - length - width)
To find the dimensions of the box that would give us the maximum volume, we need to differentiate the volume function with respect to x and set it equal to zero:
[tex]dV/dx = 3x^2 - 360x = 0[/tex]
Solving this equation, we get:
x = 0 or x = 120
Since x cannot be zero, the only possible value for x is 120 cm. Therefore, the dimensions of the box should be:
Length = Width = Height = 120 cm
With these dimensions, the sum of the length, width, and height is:
Length + Width + Height = 120 + 120 + 120 = 360 cm
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If you’re are doing a gift exchange, and everyone has to spend at least 10 dollars but less than 20 dollars, what inequality represents the situation?
A. 10 > x > 20
B. 10 ≤ x < 20
C. 10 ≥ x ≥ 20
D. 10 < x < 20
The correct inequality to represent the situation where everyone has to spend at least 10 dollars but less than 20 dollars in a gift exchange is 10 ≤ x < 20. (option b).
The correct inequality to represent the situation is B. 10 ≤ x < 20. This inequality reads "x is greater than or equal to 10, but less than 20". In other words, the amount of money each person spends (represented by x) must be at least 10 dollars, but cannot exceed 20 dollars.
To understand why this is the correct inequality, let's break it down. The symbol ≤ means "less than or equal to", and the symbol < means "less than". So, 10 ≤ x means "x is greater than or equal to 10", and x < 20 means "x is less than 20". Combining these two expressions gives us the inequality 10 ≤ x < 20, which represents the range of values that x can take on in this gift exchange.
Hence the correct option is (b).
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Evaluate the indefinite integral. You must show all of your work to receive credit. ∫(xe^x)/(2(x+1)2)dx
I need some help……..
Answer:
3) vertical
4) neither
Step-by-step explanation:
3) they are formed by two intersecting lines, are opposite of each other and are congruent. therefore, they are vertical angles
4) adjacent angles share a common vertex and common side. since the angles do not share a common side, they are not adjacent to each other. they are also not vertical because they are not congruent and are not formed by two intersecting lines. therefore, they are neither angle type
Ron must spend less than $400 on a rental car. Part A create an inequality that models the amount of money ,x, in dollars Ron can spend on the rental car
Find the slope of a line perpendicular to the line whose equation is
4
�
−
2
�
=
20
4x−2y=20. Fully simplify your answer
the slope of the line perpendicular to 4x - 2y = 20 is -1/2, which can also be expressed as 1/(-2). This means that the line perpendicular to the given line has a slope that is the negative reciprocal of the slope of the given line.
How to solve the question?
To find the slope of a line perpendicular to the given line, we first need to find the slope of the given line. We can do this by putting the equation of the line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Starting with the equation of the line, 4x - 2y = 20, we can isolate y on one side by subtracting 4x from both sides and then dividing by -2. This gives us:
-2y = -4x + 20
y = 2x - 10
Comparing this equation with the slope-intercept form, we can see that the slope of the line is 2.
To find the slope of a line perpendicular to this line, we need to use the fact that the product of the slopes of two perpendicular lines is -1. That is, if the slope of the given line is m, then the slope of a line perpendicular to it is -1/m.
So, the slope of the line perpendicular to 4x - 2y = 20 is:
-1/2
To fully simplify this answer, we can write it as a fraction with a positive numerator by multiplying both the numerator and denominator by -1:
1/(-2)
Therefore, the slope of the line perpendicular to 4x - 2y = 20 is -1/2, which can also be expressed as 1/(-2). This means that the line perpendicular to the given line has a slope that is the negative reciprocal of the slope of the given line.
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I’m rectangle LAGF, OT and GS intersect at point L
The locations of the linear pair angles, the angle expressions, indicates that the value of x is 24, and we get;
m∠FLS = 108°
m∠SLT = 72°
m∠ALG = 18°
What are linear pair angles?Linear pair angles are angles that together form a straight line.
Linear pair angles are supplementary.
The linear pair angles, ∠FLS and ∠FLG, indicates;
(4·x + 12)° + (3·x)° = 180°
7·x + 12 = 180
7·x = 180 - 12 = 168
x = 168/7 = 24
x = 24
Therefore; m∠FLS = (4 × 24 + 12)° = 108°
m∠FLS = 108°∠SLT ≅ ∠FLG, vertical angles theorem, therefore;
m∠SLT = m∠FLG = (3·x)°
x = 24
m∠SLT = m∠FLG = (3 × 24)° = 72°
m∠SLT = 72°
∠ALF = ∠FLG + ∠ALG (Angle addition property)
∠ALF is a right angle, therefore, ∠FLG and ∠ALG are complementary, angles
∠FLG + ∠ALG = 90°
m∠FLG = 72°m∠ALG = 90° - m∠FLG
m∠ALG = 90° - 72° = 18°
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What is the total annual dividend received from
owning 100 shares of stock A, if Company A
issues a $0.20 quarterly dividend to its
shareholders?
total annual dividend = [?]
Round to the nearest hundredth.
Step-by-step explanation:
100 shares * .20 / share * 4 times / year = $80.00 annual
The annual dividend received from owning 100 shares of stock of company A that pays 20 cents per quarter will be $80.
Dividend is a regular payment made by the company to its equity shareholders on pro-rata basis as a percentage of the profit earned by the company. The company pays its subscribers a dividend 20 cents per quarter. So annually, the company will pay four times the amount, i.e., 80 cents (20 x 4).
80 cents will be the dividend paid by the company per share per year. so for a hundred shares of stock, the company will pay the:
Annual Dividend = 0.20 x 4 x 100
Annual Dividend = 0.80 x 100
Annual Dividend = 80
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6) Match the probability of falling BELOW the following z-scores.
1) 1.95
2) -2.7
3) -0.08
4) 0.63
A) .9744
B) .4681
C) .7357
D) .0035
The probability of falling below each z-score is given as follows:
1) 1.95: 0.9744.
2) -2.7: 0.0035.
3) -0.08: 0.4681.
4) 0.63: 0.7357.
How to obtain the probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.Hence the probability of falling below each z-score is given by the p-value of the z-score, found using the z-table.
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3(x + y) = y
If (x, y) is a solution to the equation above and
y = 0, what is the ratio * ?
The answer to this question is x:0
The legs of a right triangle measure 18 cm and 26 cm.
What is the length of the hypotenuse?
Enter your answer, in simplest radical form, in the box.
Answer: The length of the hypotenuse of the right-angled triangle is 31.62 cm.
Step-by-step explanation: Given , that the legs of the right-angled triangle are 18 cm and 26 cm
Lets assume that the two sides of the right-angled triangle :
AC = 18 cm , BC = 26 cm
According to Pythagoras Theorem - In a right- angled triangle , the square of the hypotenuse side is equal to the sum of squares of two sides .
Therefore, according to the diagram AB² = AC² + BC²
⇒ AB² = (18)² + (26)²
⇒ AB² = 324 +676
⇒ AB² = 1000
⇒ AB = √1000
⇒ AB = 31.62 cm
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Mrs. Greenthumb is planning to build a rectangular planter for her garden. She wants the length to be twice as long as the width plus one foot and the total area is 300ft^2
a- What quadratic equation will represent this situation?
b- What are the dimensions of Mrs. Greenthumb's garden?
Using quadratic formula, the dimensions for the rectangular garden is 12 feet by 25 feet
What quadratic equation will represent this situation?a- To represent this situation with a quadratic equation, we can start by letting "x" represent the width of the planter in feet. According to the problem, the length of the planter is twice as long as the width plus one foot. Therefore, the length can be represented by the expression "2x + 1".
The area of a rectangle is given by the formula A = l x w, where A is the area, l is the length, and w is the width. In this case, we know that the total area of the planter is 300ft^2. Therefore, we can write the following quadratic equation to represent the situation:
A = l x w
300 = (2x + 1) * x
300 = 2x^2 + x
2x² + x - 300 = 0
b- To find the dimensions of Mrs. Greenthumb's garden, we can solve the quadratic equation 2x² + x - 300 = 0 for "x". We can use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 2, b = 1, and c = -300. Therefore, we can plug these values into the quadratic formula and simplify to find the solutions:
x = (-1 ± √(1^2 - 4(2)(-300))) / 2(2)
x = (-1 ± √(1 + 2400)) / 4
x = (-1 ± √(2401)) / 4
We can simplify this expression further by noting that sqrt(2401) = 49. Therefore:
x = (-1 ± 49) / 4
The two solutions are:
x = 12 or x = -25/2
Since the width of the planter cannot be negative, we can discard the solution x = -25/2. Therefore, the width of the planter is x = 12 feet.
To find the length, we can use the expression for the length we found earlier: 2x + 1. Plugging in x = 12, we get:
length = 2x + 1 = 2(12) + 1 = 25
Therefore, the dimensions of Mrs. Greenthumb's garden are 12 feet by 25 feet.
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in an integer overflow attack, an attacker changes the value of a variable to something outside the range that the programmer had intended by using an integer overflow.T/F
True. An integer overflow attack occurs when an attacker manipulates a variable in a way that causes it to exceed its maximum value or minimum value, leading to unexpected and potentially harmful behavior.
This can happen if a programmer fails to properly check and validate the input values that are being used in their code, allowing an attacker to inject a value that triggers an overflow.
As a result, the variable may be assigned a value that is outside the intended range, leading to unpredictable behavior and potentially causing the program to crash or execute unintended code. It is important for programmers to take steps to prevent integer overflow attacks, such as validating input values and using data types with sufficient capacity to hold the expected range of values.
This occurs when an arithmetic operation results in a value that is too large to be stored in the allocated memory, causing the value to wrap around and become smaller, or even negative. This can lead to unintended consequences in a program's behavior, which an attacker can exploit to gain unauthorized access or cause other security issues.
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please help!
If r=0.5 m, A = ???
(Use the r key.)
The area of a circle of radius of 0.5 meters is 0.785 square meters.
How to find the area of the circle?Remember that for a circle of radius r, the area is:
A = pi*r²
Where pi = 3.14
Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.
A = 3.14*(0.5m)²
A = 3.14*0.25 m²
A = 0.785 m²
That is the area of the circle.
Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?
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14. An airplane flew 2,800 miles from Los Angeles to New York. The airplane flies at approximately 500
mi/hr. How many hours did it take the plane to reach New York?
Answer:
Speed= 500ml/hr
total distance= 2800 m
total time = d/t
2800/500= 5.6hrs
Step-by-step explanation:
brainliest+100 points
2x + 2y = 4xy is wrong
2x + 2y = 2(x+y) is correct
b.3x+4= 7x wrong
c4x²+5x = 9x² wrong
23x²+3x²+4x = 6x² + 4x = 2x(3x + 2)
3sorry I don't understand this one.....
4-4(3x-5) = -12x + 20
5 120 12 10 4 3 5 26Answer:
120
12 10
4 2 5 2
2 2
your friend is bringing half of a crate of popsicles to the picnic. of you put what is left in the crate evenly into 6 ice buckets, what fraction of the crate will go into each of ice bucket
The fraction of crate that will fit in each ice bucket is therefore determined to be - 1/12.
Describe the fraction in detail:A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, at which numerator and the denominator are divided.
In a simple fraction, both are integers. In a complex fraction, a fraction can be found in either the numerator or the denominator.Proper fractions are those whose numerator is less than their denominator. The fraction is deemed improper when the numerator above the denominator.data provided
proportion of the friend's crate is equal to half.There are six ice buckets in total.The number of ice buckets / proportion of crate in each bucket equals fraction of crate provided by friend.
crate fraction in each bucket equals (1/2) / 6
Each bucket's fraction of the crate is 1 / (2*6).
Each bucket's percentage of the crate is 1/12.
The amount of crate that will fit in each ice bucket is therefore determined to be - 1/12.
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A European derivative instrument on IBM has the following payoff structure at the maturity date in 3 years:
a) ST if ST < 120
b) 120 + 2 * (ST – 120) if 120 < = ST <= 160
c) 200 if 160 <= ST <= 200
d) ST if 200 <= ST where ST is the price at the maturity date.
The spot price is 154 and the volatility is 25%. The risk-free interest rate is 4% and we consider a 6-step binomial tree.
(a) Use Excel to draw this payoff pattern for the following price interval [0 , 300] with a step of 10. (2 marks)
(b) Based on the graph in (a), explain briefly how the premium of this derivative security should compare to IBM spot price. (2 marks)
(c) Price this contract using a 6-step binomial tree and confirm your findings in (b). Show all details and only state if arbitrage opportunity is available or not. (3 marks)
The price of the European derivative instrument on IBM is approximately $212.80.
Based on the graph, we can see that the payoff of the derivative instrument is capped at 200, regardless of the price of IBM at the maturity date.
Therefore, the premium of this derivative security should be lower than the spot price of IBM, as the potential upside is limited.
To price the derivative instrument using a binomial tree, we first need to calculate the up and down factors:
u = e(σ * √Δt) = e(0.25 * √(3/6)) = 1.35914
d = 1/u = 0.73516
where σ is the volatility, Δt is the time step, and u and d are the up and down factors, respectively.
Next, we calculate the risk-neutral probability of an up move:
p = (e(r * Δt) - d) / (u - d) = (e(0.04 * 3/6) - 0.73516) / (1.35914 - 0.73516)
= 0.57348
Expected payoff at node (2, 1) = 200
Expected payoff at node (2, 2) = 44.16
Expected payoff at node (2, 3) = 44.16
Expected payoff at node (3, 1) = 57.76
Expected payoff at node (3, 2) = 57.76
Expected payoff at node (3, 3) = 32.04
Expected payoff at node (4, 1) = 75.68
Expected payoff at node (4, 2) = 44.16
Expected payoff at node (4, 3) = 32.04
Expected payoff at node (5, 1) = 108.36
Expected payoff at node (5, 2) = 57.76
Expected payoff at node (6, 1) = 158.28
Where r is the risk-free interest rate and p is the risk-neutral probability of an up move.
The expected payoff at each node can be calculated using the risk-neutral probabilities and the corresponding payoffs:
At node 5, the expected payoff is:
0.4575 * 0 + 0.5425 * (120 + 2 * (1.25 * 154 – 120)) = 212.80
At node 4, the expected payoff is:
0.4278 * 0 + 0.5722 * (120 + 2 * (1.25 * 136 – 120)) = 199.13
At node 3, the expected payoff is:
0.4008 * 0 + 0.5992 * (120 + 2 * (1.25 * 120 – 120)) = 185.58
At node 2, the expected payoff is:
0.3766 * 0 + 0.6234 * (120 + 2 * (1.25 * 105 – 120)) = 172.98
At node 1, the expected payoff is:
0.3549 * 0 + 0.6451 * (120 + 2 * (1.25 * 92 – 120)) = 161.27
At node 0, the expected payoff is:
0.3354 * 0 + 0.6646 * (1.25 * 80) = 83.07
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A helicopter hovering above a command post shines a spotlight on an object on the ground 250 feet away from the command post as shown in the diagram how far is the object from the helicopter to the nearest foot
The distance of the object from the helicopter is 698 ft.
What is distance?Distance is the length between two points.
To calculate how far the object is above the helicopter, we use the formula below.
Formula:
Sin∅ = O/H..................... Equation 1Where:
∅ = AngleO = OppositeH = Hypotenus = Distance of the object from the HelicopterFrom the question,
Given:
O = 250 ft∅ = 21°Substitute these values into equation 1 and solve for H
H = 250/Sin21°H = 697.61 ftH ≈ 698 ftHence, the distance is 698 ft.
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What is the product (6√5 - 6i) (√3 + √3i) in polar form example : (e - fi) and what quadrant of the complex plane does the product lie?
Answer: Plain: the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.
Step-by-step explanation: To multiply complex numbers in polar form, we multiply their magnitudes and add their angles. We can start by converting the given complex numbers from rectangular form to polar form:
6√5 - 6i = 6(√5 - i) = 12 ∠ -30°
(√3 + √3i) = √3(1 + i) = 2 ∠ 45°
where we have used the fact that ∠θ is the angle between the positive real axis and the line connecting the origin and the complex number a + bi, measured counterclockwise.
Now, we can multiply the two complex numbers in polar form:
(6√5 - 6i)(√3 + √3i) = 12 ∠ -30° * 2 ∠ 45°
= 24 ∠ 15°
Therefore, the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.
To determine the quadrant of the complex plane in which the product lies, we note that the angle 15° is in the first quadrant (between 0° and 90°). Therefore, the product lies in the first quadrant of the complex plane.
4. You want to use ribbon to create a border along the edge of the paper. The length of the paper is 2 times as long as the width. How much ribbon do you need to create the border? O 41/2 feet O 43/5 feet O 41/4 feet 4 4/5 feet
The amount of ribbon you need to create the border is 4 1/4 feet if x = 17/24
How much ribbon do you need to create the border?From the question, we have the following parameters that can be used in our computation:
The length of the paper is 2 times as long as the width
This means that
Length = 2x
Width = x
The perimeter is
Perimeter = 2 * (2x + x)
Perimeter = 6x
Assuming that x = 17/24
So, we have
Perimeter = 6 * 17/24
Evaluate
Perimeter = 17/4
Simplify
Perimeter = 4 1/4
Hence, the amount needed is 4 1/4 feet
Read more about perimeter at
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How do you solve 22+41+31-21 with integers
22 + 41 + 31 - 21 = 73
identify the graph of g(x)=2(x+3)^2
Answer:
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
3
,
0
)
Focus:
(
3
,
1
4
)
Axis of Symmetry:
x
=
3
Directrix:
y
=
−
1
4
x
y
1
4
2
1
3
0
4
1
5
4
Tap to view steps...
the mass of the box on a table is 20kg. a man applied force as below the picture. the static frictional coefficient is 0.6 and the dynamic frictional coefficient is 0.5. (gravitational acceleration =10ms^{-2}
1)what is the minimum force that should be applied to move the box?
2)What is the force that should apply to move in uniform velocity?
Okay, let's solve this problem step-by-step:
1) To move the box initially, the applied force (F) must overcome static friction.
Static frictional force = F_static = μ_static * Weight of box
= 0.6 * 20kg * 10m/s^2
= 12N
So the minimum force to move the box is 12N.
2) Once the box is moving at a uniform velocity, the applied force only needs to overcome dynamic friction.
Dynamic frictional force = F_dynamic = μ_dynamic * Weight of box
= 0.5 * 20kg * 10m/s^2
= 10N
So to keep the box moving at a constant velocity, the applied force should be 10N.
In summary:
Minimum force to move the box (static friction) = 12N
Force to move at constant velocity (dynamic friction) = 10N
Let me know if you have any other questions!