By using the Lagrange multipliers, the two points on the cone that is closest to (14, 8, 0) are:
(7, 4, √65) and (7, 4, -√65)
We want to minimize the distance between the point (14, 8, 0) and the points on the cone z^2 = x^2 + y^2. The distance squared between two points (x_1, y_1, z_1) and (x_2, y_2, z_2) is given by:
d^2 = (x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2
In our case, we want to minimize the distance squared between (14, 8, 0) and a point (x, y, z) on the cone z^2 = x^2 + y^2:
d^2 = (x - 14)^2 + (y - 8)^2 + z^2
Subject to the constraint z^2 = x^2 + y^2. We can use Lagrange multipliers to solve this constrained optimization problem. Let L be the Lagrangian:
L = (x - 14)^2 + (y - 8)^2 + z^2 - λ(z^2 - x^2 - y^2)
Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them to zero, we get:
2(x - 14) - 2λx = 0.....(1)
2(y - 8) - 2λy = 0.....(2)
2z - 2λz = 0.....(3)
z^2 - x^2 - y^2 = 0.....(4)
Simplifying the third equation, we get z(1 - λ) = 0. Since we want to find points where z is not zero, we must have λ = 1. Then, from the first two equations, we get x = 7 and y = 4. Substituting these values into the fourth equation, we get:
z^2 = x^2 + y^2 = 65
So the two points on the cone that is closest to (14, 8, 0) by using Lagrange multipliers are:
(7, 4, √65) and (7, 4, -√65)
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What is the measure of ∠D? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠D= ° A right triangle B C D. Angle C is marked as a right angle. Side B C is labeled as 25 feet. Side C D is labeled as 45 feet.
Therefore, the measure of ∠D is approximately 60.96 degrees.
What is measure?A measure is a function that assigns a number to each set in a given space, typically with the goal of describing the size or extent of the set. For example, the Lebesgue measure is a way of assigning a "volume" to sets in n-dimensional Euclidean space.
by the question.
To find the measure of ∠D in a right triangle with sides of 25 feet and 45 feet, we can use the inverse tangent function:
[tex]tan(∠D) = opposite/adjacent = CD/BC = 45/25[/tex]
Taking the inverse tangent of both sides, we get:
[tex]∠D = tan⁻¹(45/25) = 60.95 degrees[/tex]
Rounding this to the nearest hundredth, we get:
[tex]angleD = 60.95 degrees =60.96 degree.[/tex]
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Will give brainiest
Write the equation of the circle using the center and any one of the given points A, B, or C
Answer:
To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:
r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5
Now we can substitute the center and radius into the standard form equation:
(x - 4)^2 + (y + 2)^2 = 5^2
Simplifying and expanding the right-hand side, we get:
(x - 4)^2 + (y + 2)^2 = 25Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.
In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class does not play an instrument?
This probability that a randomly selected student from the classroom doesn't really play an item is , which equals or .
What are the basics of probability?Probability is the possibility of something occurring to occur, to clarify. We may talk about the possibility with one result, or the likelihood of several outcomes, when we don't understand how an occurrence will turn out. Biostatistics seems to be the study of things with a probability distribution.
Is the ace a playing card?The number one is known as the ace and is denoted by the letter A in the majority of Western card games. The ace scores highest, surpassing even the king, in games predicated on the supremacy of one level over the other, such as the majority of trick-taking games.
The total of a number of masculine and female pupils involved in sports [tex]$\mathrm{20}+10=30$[/tex] represents the total amount of pupils that don't play an instrument.
The sum of the four numbers in the table, [tex]$12+20+18+10$[/tex] , corresponds to the total amount of pupils in the class, or 60 .
So, [tex]$30/60=1/2\ \mathrm{Or}\ 0.5$[/tex] or is the likelihood that a randomly selected student from of the class doesn't really play an instrument.
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Complete question:
In 2010, the population of Belvedere was estimated to be 39,366 people with an annual rate of increase of approximately 2.8%.
Select the explicit expression that represents the population in the next 6 years.
OA. 39,366(1.0028)5
OB. 39,366(1.28)5
OC. 39,366(0.028)
OD. 39,366(1.028)
Based on exponential growth function, the explicit expression that represents the population of Belvedere, which was estimated to be 39,366 in 2020 with an annual increase of 2.8%, in the next 6 years is D. 39,366(1.028)^6.
What is an exponential growth function?An exponential growth function is one of the two exponential function, including exponential decay function.
The exponential growth function is given as y = a(1 + r)^t, where:
y is the new valuea is the current valuer is the constant ratioand t is the time in years.Population of Belvedere in 2010 = 39,366
Annual rate of increase = 2.8%
The time, t = 6 years
Exponential function expression: 39,366(1.028)^6
Thus, the population of the city in the next 6 years can be represented by the expression in Option D.
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A building supply has two locations in town. The office receives orders from two of its best customers, each requiring 3/4-inch drywall board to be delivered. Customer A needs at least one hundred sheets delivered and Customer B needs at least one hundred-forty sheets delivered.
Deliveries can be sent from either of the supply companies' warehouses. The warehouse on the north side of town has one hundred-sixty sheets in stock; the south-side warehouse has ninety sheets in stock. Delivery costs per sheet are as follows: $1.50/board from the northern warehouse to Customer A,$1.20/board from the northern warehouse to Customer B, $0.80/board from the southern warehouse to Customer A, and $1.10/board from the southern warehouse to Customer
В.
1. Find the shipping arrangement which minimizes costs.
2. What will be the minimum cost?
3. Will there be any product left in either warehouse after fulfilling the orders?
The shipping arrangement which minimizes costs will be 1.5x + 1.2y + 0.8z + 1.1(240 - x - y - z) subject to
x + z + s1 = 160
y + (240 - x - z) + s2 = 90
x - 100 + s3 = 0
y - 140 + s4 = 0
The minimum cost is $372.00.
There will be product left in either warehouse after fulfilling the orders.
How to explain the informationLet x be the number of sheets delivered from the north-side warehouse to Customer A,
Let y be the number of sheets delivered from the north-side warehouse to Customer B and z be the number of sheets delivered from the south-side warehouse to Customer A.
Then the objective function to be minimized is:
1.5x + 1.2y + 0.8z + 1.1(240 - x - y - z).
There will be 60 sheets of drywall board left in the north-side warehouse and 70 sheets left in the south-side warehouse after fulfilling the orders.
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what is the answer to this problem. solve x
if the radius of a circle is increasing and the magnitude of a central angle is held constant, how is the length of the intercepted arc changing? explain your reasoning.
Answer:
When the radius of a circle is increasing while the magnitude of a central angle is held constant, the length of the intercepted arc is also increasing.
To see why this is the case, let's consider the formula for the length of an arc, which is given by:
s = rθ
where s is the length of the intercepted arc, r is the radius of the circle, and θ is the central angle in radians.
If the radius is increasing but the magnitude of θ is held constant, then the length of the intercepted arc will increase as well. This is because s is directly proportional to r; as r increases, s will also increase.
To see this more concretely, imagine drawing a circle on a piece of paper with a certain radius and then drawing a central angle that intercepts a certain arc length. If we then increase the radius of the circle while keeping the central angle the same, the arc length will increase proportionally to the increase in radius. This is because the same central angle will now subtend a larger arc on the circle, since the circle is larger.
Therefore, when the radius of a circle is increasing while the magnitude of a central angle is held constant, the length of the intercepted arc is increasing as well.
Step-by-step explanation:
Question 70 Approximately 38 percent of people living in on Whave the blood type o positive. A random sample of 100 people from region veled people in the samed the Contra Hypothesis test to vestigate whether the percent of people in thegion with positive blood is different from that of tegen wWwth of the following is the property for the H-0.35 He0.35 с Hep -0.35 D Hp 0.35 H: 0.38
Answer: The null hypothesis (H0) is the statement that there is no significant difference between the proportion of people in the region with the O positive blood type (p) and the population proportion (p0) of 0.38.
The null hypothesis is usually denoted as:
H0: p = p0
In this case, p0 is given as 0.38, so the correct answer is:
H0: p = 0.38
Step-by-step explanation:
use a random sampling distribution of means to determine the probability for different ranges of values of a mean (x-bar). please use the following information to answer questions 1-5. imagine that after graduation, you need to find an apartment to rent. the city in which you intend to live reports that the average rental payment (house or apartment) is $1225.15, with a standard deviation of $777.50. it also reported that the average cost of an apartment rental, rather than a house rental, was $1068.86. for the following questions, treat the average rental payment and standard deviation (house or apartment) as parameters (the population), and treat the average apartment rental cost as a statistic (the sample mean or x-bar) based on a sample of 100. use this information for questions 1-5. 1. what is the mean of the random sampling distribution of means? 2) What is the standard error of the random sampling distribution of means? 3) What is the z statistic for the average cost of an apartment rental? 4) What is the probability of finding an apartment rental with a average cost of $1068.86 or less?
1) The mean of the random sampling distribution of means is the same as the sample mean ($1068.86).
2) The standard error of the random sampling distribution of means is calculated by taking the population standard deviation ($777.50) divided by the square root of the sample size (100), which yields $7.78.
3) The z statistic for the average cost of an apartment rental is calculated by subtracting the population mean ($1225.15) from the sample mean ($1068.86) and dividing the difference by the standard error ($7.78), yielding -37.37.
4) The probability of finding an apartment rental with an average cost of $1068.86 or less is determined by looking up the z statistic in a z table and finding the corresponding probability, which is 0.000.
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What are the roots of the equation 4x^2+16x+25=0 in simplest a+bi form
Answer:
The roots are
[tex]x=-2+\dfrac{3}{2} \ i \ \ or \ \ x=-2-\dfrac{3}{2} \ i[/tex]
Step-by-step explanation:
4x² + 16x + 25 = 0
Using the quadratic formula
That's
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
From the question
a = 4 , b = 16 , c = 25
Substitute the values into the above formula and solve
We have
[tex]x=\dfrac{-16\pm\sqrt{16^2-4(4)(25)} }{2(4)}[/tex]
[tex]x=\dfrac{-16\pm\sqrt{256-400} }{8}[/tex]
[tex]x=\dfrac{-16\pm\sqrt{-144} }{8}[/tex]
[tex]x=\dfrac{-16\pm12 \ i}{8}[/tex]
Separate the real and imaginary parts
That's
[tex]x=\dfrac{-16}{8}\pm\dfrac{12}{8} \ i[/tex]
[tex]x=-2\pm\dfrac{3}{2} \ i[/tex]
We have the final answer as
[tex]x=-2+\dfrac{3}{2} \ i \ \ or \ \ x=-2-\dfrac{3}{2} \ i[/tex]
Hope this helps you
j by 9 and then multiply the quotient by 2
The sequence of the questions is [tex]J/9[/tex] when you multiply [tex]J[/tex] by [tex]9[/tex] and the quotient by [tex]2[/tex].
What in arithmetic is a quotient?In this example, the number being divided (15) is known as the result, and the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.
Is quotient the same as answer?The result of dividing two integers is known as the quotient. Six divided into two results in the number three. Latin's "how many times" is the meaning of the word "quotient." It makes perfect sense: by dividing two numbers, you can determine "how many time" the two digits enters the first.
[tex]2 * (J/9)[/tex]
This means you first divide [tex]J[/tex] by [tex]9[/tex] to get the quotient, and then multiply the quotient by [tex]2[/tex]. So the order of operations is:
[tex]J/9[/tex]
Multiply the quotient by [tex]2[/tex]
For example, if [tex]J = 45[/tex], then:
[tex]J/9 = 45/9 = 5[/tex]
[tex]2 * (J/9) = 2 * 5 = 10[/tex]
So the result of multiplying [tex]J[/tex] by [tex]9[/tex] and then multiplying the quotient by [tex]2[/tex], when [tex]J = 45[/tex], is [tex]10[/tex].
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DO THE MATH: Gracie is a manager at Prescribe Pharmaceutical. An employee turned in the timesheet below. Given that Prescribe Pharmaceutical uses the 7-Minute Rule daily for calculating employee hours worked, how many hours did this employee work for the week?
A. 25 hours and 0 minutes
B. 26 hours and 0 minutes
C. 25 hours and 48 minutes
D. 25 hours and 45 minutes
It took 25 hours and 48 minutes employee worked for the week. Thus, option B is correct.
What is a timesheet?A timesheet is a data table which an emplοyer can use tο track the time a particular emplοyee has wοrked during a certain periοd. Businesses use timesheets tο recοrd time spent οn tasks, prοjects, οr clients. There are different methοds that have been used tο recοrd timesheets, such as paper, spreadsheet sοftware, and οnline time-tracking sοftware. Paper-based timesheets have nοw given way tο the digital fοrmats.
1st Day = 12 + 4 pm - 8:45 am
= 16 - 8:45
= 7:15 hours
2nd day = 12 + 5 pm - 9:14 am
= 17 - 9:14
= 7:46 hours
3rd day = 12 + 4:02 pm - 8:30 am
= 16:02 - 8:30
= 7:32 hours
4th day = 12 + 5:00 pm - 9:08am
= 17:00 - 8:30
= 8:30 hours
5th day = 12 + 3:30 pm - 8:07 am
= 15:30 - 8:07
= 7:23 hours
Adding all the hours of work = 7:15 hours + 7:46 hours +7:32 hours + 8:30 hours + 7:23 hours = 25 hours and 48 minutes
Thus, It took 25 hours and 48 minutes employee worked for the week. Thus, option B is correct.
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sunitha is 24 years older than her daughter kavita. 6 years ago, sunitha was thrice as old as kavitha. find their present ages.
Como le hago ayuda aaaa
When the area is constant, the proportionality constant, 48, reflects the sum of the base and height.
What does the proportionality constant mean?When two quantities grow and shrink at the same rate, they are directly proportional. The proportionality constant k is defined as k=y/x when y and x are two numbers that are directly proportional to one another.
Using the formula for the area of a rectangle, we can determine the missing data in the table:
Area = base x height
The missing values can be located as follows using the values listed in the table:
Base (b) Height (h) Area
24 2 48
3 8 24
8 3 24
4 6 24
We can apply the inverse variation formula to find the constant of proportionality:
y = k/x
This equation can be changed in order to account for k:
k = xy
Using any pair of values from the table, we can find k as follows:
k = xy = 24(2) = 48
Hence, 48 is the proportionality constant. It is possible to verify that this value applies to all of the value pairs in the table:
For the first pair (b=24, h=2), we have xy = 24 x 2 = 48, which is the constant of proportionality.
For the second pair (b=3, h=8), we have xy = 3 x 8 = 24, which is the area.
For the third pair (b=8, h=3), we have xy = 8 x 3 = 24, which is the area.
For the fourth pair (b=4, h=6), we have xy = 4 x 6 = 24, which is the area.
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Question:
The following table shows some values for the base and height of a rectangle whose area is constant. Write down the missing data.
Base (b)
Height (h)
24
2
3
8
4
4
What is the area of the rectangle?
What kind of variation do you see in this table?
What is the constant of proportionality?
How did you determine the constant of proportionality?
67777+776567.55555=?
Answer: 844344.55555
the cylinder has a volume of 45 cubic inches and a height of 5 inches what is the raduis of the cylinder
The radius of the cylinder is 3 inches.
What is the volume of a cylinder?
A cylinder is a three-dimensional solid with two parallel circular bases and a curved lateral surface connecting the two bases. The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex], where r is the radius of the base, h is the height of the cylinder, and π is a constant value approximately equal to 3.14.
Calculating the value of radius :
We are given that the cylinder has a volume of 45 cubic inches and a height of 5 inches. Using the formula for the volume of a cylinder, we get:
[tex]V = \pi r^2h[/tex]
Substituting the given values, we get:
[tex]45 = \pi r^2(5)[/tex]
Simplifying the equation, we get:
[tex]9 = r^2[/tex]
Taking the square root of both sides, we get:
[tex]r = \pm 3[/tex]
Since the radius cannot be negative, we take the positive value of r, which is:
r = 3 inches
Therefore, the radius of the cylinder is 3 inches.
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what is the probability of choosing a red card or a king from a deck of 52 cards? for this event, choosing a red card or choosing a king, where choosing a red card and choosing a king may occur jointly, which rule applies?
The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection
How do we calculate the probability?The probability of choosing a red card or a king from a deck of 52 cards is 8/52 or 2/13. To calculate this, we first need to determine the number of cards that are either red or a king. There are 26 red cards in a deck of 52 cards, so the probability of choosing a red card is 26/52 or 1/2. There are four kings in a deck of 52 cards, so the probability of choosing a king is 4/52 or 1/13.
However, we need to be careful to avoid counting the red kings (two of which exist in a deck of 52 cards) twice. To account for this, we subtract the probability of choosing a red king from the sum of the probabilities of choosing a red card and a king. The probability of choosing a red king is 2/52 or 1/26, so the probability of choosing a red card or a king is:
P(red card or king) = P(red card) + P(king) - P(red king)
P(red card or king) = 26/52 + 4/52 - 2/52
P(red card or king) = 28/52
P(red card or king) = 2/13
The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection (i.e., the probability that they occur jointly).
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Eva is packing for a camping trip. There are 3 sleeping bags and 2 pillows to choose from. For the tent, Eva has 6 options. In how many different ways can Eva pick a set of camping gear that includes one of each item?
Eva has 36 different combinations of camping gear to choose from.
What are combinations?Combinations are arrangements of a given set of objects, without regard to their order. Combinations are used in mathematics to describe the possible arrangements of a given set of objects.
In this case, there are 3 sleeping bags, 2 pillows, and 6 tents. In order to determine the total number of combinations, Eva would need to multiply 3x2x6 which equals 36.
If she decides to pick a sleeping bag first, then she can pick any of the 3 available sleeping bags. She would then need to pick one of the 2 pillows and one of the 6 tents. If the order in which she selects her gear does not matter, then she can use the same method to determine the number of combinations available.
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The number of ways in which Eva can pick a set of camping gear that includes one of each item is 55.
What is combination?Combination involves selecting items from a set of items without regard to the order in which they are selected. It is typically expressed using the notation C(n,r) which stands for the number of combinations of n items taken r at a time, where n is the total number of items and r is the number of items taken at a time.
This is an example of a combination problem, as Eva is looking to select a set of items from multiple categories, rather than a permutation problem, which would be selecting a set of items where the order matters.
In this case,
n= 6 (the number of tents)+ 3 (the number of sleeping bags)+ 2 (the number of pillows)= 11.
We want to choose 1 of each item, so r is 3.
Plugging 11 and 3 into the formula, we get
11C3 = 11! / (3! * 8!)
= 11 * 10 * 9 / (3 * 2 * 1)
= 11 * 5
= 55
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Find the equation of a line that passes through the points (1,3) and (2,2). Leave your answer in the form
y
=
m
x
+
c
The equation of the line that passes through the points (1,3) and (2,2) is y = -x + 4.
To find the equation of the line, we can use the slope-intercept form of a linear equation, y = mx + c, where m is the slope and c is the y-intercept.
First, we need to find the slope of the line. The slope is given by:
m = (y2 - y1)/(x2 - x1)where (x1, y1) and (x2, y2) are the coordinates of the two given points. Plugging in the values, we get:
m = (2 - 3)/(2 - 1) = -1Next, we can use one of the given points and the slope to find the y-intercept. Using the point (1,3), we get:
3 = (-1)(1) + cSimplifying this equation gives us:
c = 4
Therefore, the equation of the line in slope-intercept form is:
y = -x + 4.
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(8,-4) and (-1-2) to the nearest tenth
6 : water pours into a fish tank at a rate of 0.3 cubic meters per minute. how fast is the water level rising if the base of the fish tank is a 2 meter by 3 meter rectangle?
Water pours into a fish tank at a rate of 0.3 cubic meters per minute, the water level is rising at a rate of 1/60 m/min
How to calculate the water level?Given
The base of the fish tank is a 2-meter by 3-meter rectangle.The area of the base of the fish tank = length x breadth= 2 m x 3 m = 6 m².Let, h is the height of the water level in the fish tank after t minutes. Then, the volume of the water in the fish tank after t minutes is given by [tex]V = Area of the base * height V = 6 * h m^3[/tex]The rate at which water pours into the fish tank is 0.3 cubic meters per minute.
Therefore, the rate of change of volume of the water in the fish tank after t minutes is [tex]dV/dt = 0.3 m^3/min[/tex]. As per the chain rule of differentiation,[tex]dV/dt = dV/dh *dh/dt[/tex] We have[tex]V = 6h^3m^3 \Rightarrow dV/dh = 18h^2\Rightarrow dV/dt = 18h^2 * dh/dt[/tex] Given that,[tex]dV/dt = 0.3 m^3/min[/tex]. Therefore,[tex]0.3 = 18h^2 * dh/dt \Rightarrow dh/dt = 0.3/18= 1/60 m/min[/tex] Hence, the water level is rising at a rate of 1/60 m/min.
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Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. Let x= the number of free throws faith makes out of 20 shots. Calculate and interpret the standard deviation of x
If at practice, each player shoots 20 free throws, the standard deviation of x is 0.975.
To calculate the standard deviation of x, we need to first determine the variance. The variance is the average of the squared differences of each observation from the mean.
In this case, Faith is a 95% free throw shooter, so she is expected to make 19 out of 20 shots on average. The probability of making a free throw is 0.95, and the probability of missing a free throw is 0.05. Therefore, the mean of x is:
mean(x) = 20 * 0.95 = 19
To calculate the variance, we need to find the expected value of (x - mean(x))^2. Since Faith's free throw shooting is independent, we can use the binomial distribution to find the probability of making x shots out of 20.
The formula for the variance of a binomial distribution is np(1-p), where n is the number of trials and p is the probability of success. Therefore, the variance of x is:
var(x) = 20 * 0.95 * 0.05 = 0.95
Finally, the standard deviation is the square root of the variance:
sd(x) = √(var(x)) = √(0.95) = 0.975
This means that on average, Faith is expected to make 19 out of 20 free throws, but there is a standard deviation of 0.975, which indicates the degree of variability or spread around the mean. In other words, we can expect Faith to make between 18 and 20 free throws in most cases, but there is a small chance that she may make fewer or more than that.
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-. If f(x) = x² + 3x-2, find f(x) when x = -2
Answer:
-4
Step-by-step explanation:
substitute -2 into the formula and solve
[tex]f(x)=(-2)^2+3(-2)-2\\f(x)=4+(-6)-2\\\boxed{f(x)=-4}[/tex]
Suppose P is a predicate over integers, and you would like to prove that for all integers n, P(n) is true. Which of the following are valid proof approaches? Select all correct choices. Select one or more: O a. Show P(1) and that Vk E Z P(k) + P(k + 1) O b. Show P(0), P(1),P(-1) and that Vk E Z P(k) → P(k + 1) c. Show P(0) and that WK EN P(k) → (P(k + 1) ^ P(k – 1)) O d. Show P(0), P(1), P(-1) and that Vk E Z P(k) → P(k – 1) O e. Show P(0), P(1),P(-1) and that Vk e Z+ P(k) → P(k + 1) and Vk e Z+ P(-k) → P(-(k + 1)) O f. Show P(O), P(1) and that Vk e Z+ P(k) → P(-k)
The valid proof approaches are: b. Show P(0), P(1),P(-1) and that Vk E Z P(k) → P(k + 1) and e. Show P(0), P(1),P(-1) and that Vk e Z+ P(k) → P(k + 1) and Vk e Z+ P(-k) → P(-(k + 1))
Approach a is invalid because it only shows that P holds for some integers, but not for all integers.
Approach c is invalid because it only shows that P holds for non-negative integers, but not necessarily for negative integers.
Approach d is invalid because it only shows that P holds for non-negative integers and negative even integers, but not necessarily for negative odd integers.
Approach f is invalid because it only shows that P(0) and P(1) imply P(-k) for all positive integers k, but not necessarily for all integers.
Approach b is a valid proof approach because it establishes a base case for P(0), and then shows that P holds for P(1) and P(-1), and that if P holds for an arbitrary integer k, then it also holds for k+1.
Approach e is also a valid proof approach because it establishes a base case for P(0), and then shows that P holds for P(1), P(-1), and that if P holds for a positive integer k, then it also holds for k+1, and if it holds for a negative integer -k, then it also holds for -(k+1).
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7. Select all expressions which give the measure of angle A.
(A.) arccos (28/53)
(B.) arccos (45/53)
(C.) arcsin (28/53)
(D.) arcsin (45/53)
(E.) arctan (28/45)
(F.) arctan (45/28)
We cannot use arccos (28/53) and arcsin (28/53) because they correspond to angle B, not angle A. Similarly, arctan (28/45) and arctan (45/28) do not give the measure of angle A.
What accomplishes arccos function?The cosine function has an opposite known as the arccos function. It provides the angle whose cosine is the specified value. Try it. Drag any vertex of the triangle and watch how the angle C is determined using the arccos() function. Meaning: A 30 degree angle is one whose cosine is 0.866.
What is the sine of two?The inverse cosine function is the arccosine. The arccosine function's input values range from -1 to 1, matching the cosine function's output range of -1 to 1. So, for x=2, arccos x is undefined.
From the given figure, we can see that:
cos A = 28/53
sin A = 45/53
Therefore, the expressions that give the measure of angle A are:
(B.) arccos (45/53)
(D.) arcsin (45/53)
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3901 of the original wordle's 10657 allowed guess words have at least one letter repeat, or 36.6%. we can also see that 749 of its 2315 solution words have at least one letter repeat, or 32.3%. how many of the possible 5-tuples of 26 letters (q3.1) have at least one letter repeat? remember: gradescope can evaluate expressions with , -, *, /, ^, ( ), but not factorial.
The original wordle has 10657 allowed guess words. Of which 3901 words have at least one letter repeat. In other words, the probability of the word having at least one letter repeat is 36.6% 749 solution words have at least one letter repeat out of a total of 2315 solution words. the number of possible 5-tuples of 26 letters that have at least one letter repeat is "3987776."
In other words, the probability of a solution word having at least one letter repeat is 32.3%To find the number of possible 5-tuples of 26 letters with at least one letter repeat
Step 1: We will find out the number of 5-tuples that do not have any repeated lettersFor the first letter, we have 26 options. As there can be no repetitions, we have 25 options for the second letter. Similarly, for the third, fourth, and fifth letter we have 24, 23, and 22 options respectively.Therefore, the number of 5-tuples that do not have any repeated letters is given by26 × 25 × 24 × 23 × 22 = 7893600
Step 2: We will find out the number of 5-tuples that have at least one repeated letterTotal number of 5-tuples = 26^5Using the formula for finding the number of 5-tuples without any repetition, we can find the number of 5-tuples that have no repetition:26 × 25 × 24 × 23 × 22 = 7893600 Therefore, the number of 5-tuples that have at least one repeated letter is given by the total number of 5-tuples – the number of 5-tuples that have no repetitions= 26^5 - 7893600= 11881376 - 7893600= 3987776Therefore, the number of possible 5-tuples of 26 letters that have at least one letter repeat is 3987776.
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factorise (x-3)²-(x-3)²
Step-by-step explanation:
(x-3)²-(x-3)²
=(x2-6x+9) - (x2-6x+9)
=x2-6x+9-x2+6x-9
=0
Weight: 20kg Order: 10 mg q6 hours Therapeutic range : 2-3 mg/kg/day. What is daily dose? Is it safe? Is it therapeutic?
The daily dose is 40mg, this dose per kilogram per day is within the therapeutic range of 2-3mg/kg/day, which means that the medication is within the safe and effective range for this patient's weight.
The weight of the patient is 20kg, and the prescribed dosage is 10mg every 6 hours. To calculate the daily dose, we need to multiply the prescribed dosage by the number of doses per day. Since the medication is prescribed every 6 hours, this means that the patient will take it 4 times a day.
=> (10mg x 4 doses) = 40 mg
The therapeutic range is the range of doses at which the medication is most effective and safe. In this case, the therapeutic range is 2-3mg/kg/day. To determine if the daily dose is within the therapeutic range, we need to divide the daily dose (40mg) by the patient's weight (20kg) to get the dose per kilogram per day, which is 2mg/kg/day.
However, it's important to note that the therapeutic range is a general guideline and may vary depending on the patient's individual circumstances and medical history.
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25 out of 68 students have vanilla ice cream and the rest have chocolate. What is the ratio of the number of students who have vanilla to the total number of students?
Answer: The total number of students is the sum of the number of students who have vanilla and those who have chocolate:
Total = 25 + (68 - 25) = 43
The ratio of the number of students who have vanilla to the total number of students is:
Vanilla : Total = 25 : 43
This ratio cannot be simplified any further because 25 and 43 do not have any common factors other than 1. Therefore, the ratio of the number of students who have vanilla to the total number of students is:
25 : 43
Step-by-step explanation:
how many legs does it take to make 109657 spiders
Assuming each spider has 8 legs, it would take 877,256 legs to make 109,657 spiders