The reading of the angle sec θ in the second quadrant of the given problem is; Negative
How to interpret trigonometric ratios?There are 6 main trigonometric ratios and if we can use which are;
sin θ
cos θ
tan θ
secθ
cotan θ = sin θ/cosθ
cosec θ = 1/sin θ
sec θ = 1/cos θ
Now, we are told that sec θ is in the second quadrant and we know that in the second quadrant only sin θ and cosecθ are positive and as such sec θ will be negative.
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a sphere and a cylinder have the same radius length and the same volume. what is the ratio of the radius to the height of the cylinder? express your answer as a common fraction.
Therefore , the solution of the given problem of ratio comes out to be 2:3 for the following cylinder and sphere.
what is a ratio?An order pair of values "a" and "b" can be expressed with the straightforward formula "a / b," with "b" must be no bigger than zero. A ratio is created by adding two ratios together. In the event when there was only one guy and three women, the proportion might be shown as 1:3. 1/4 of the group are guys, and 3/4 are girls. A part can be a statistic, a portion of a thing's volume, or a division among two or more things.
Here,
Here, a sphere is engraved within a cylinder of height h=2r.
Sphere volume =>
4/3πr³.
and Cylinder Volume =πr²h = πr²(2r) = πr³
Volume of the sphere divided by the volume of the cylinder is equal to or greater than
=>4πr³/ 3×2πr³
=>2:3
Therefore , the solution of the given problem of ratio comes out to be 2:3 for the following cylinder and sphere.
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Find the curvature ofr(t) = 9t, t2, t3at the point(9, 1, 1)
The curvature of the curve r(t) = (9t, t², t³) at the point (9, 1, 1) is (3/ 800)√(91/ 94).
The curvature of a curve at a given point is a measure of how much the curve is bending at that point. In order to find the curvature of a curve, we need to first find the unit tangent vector, the unit normal vector, and the unit binormal vector at the point in question.
Given r(t) = (9t, t², t³) at the point (9, 1, 1). Thus t = 1 at (9, 1, 1).
The unit tangent vector at the point (9, 1, 1) is given by the derivative of r(t) with respect to t, evaluated at t = 1
r'(t) = (9, 2t, 3t²)
so T(t) = r'(1) = (9, 2, 3)
The magnitude of T(1) = √(9² + 2² + 3²) = √(94)
The unit tangent vector at (9, 1, 1) is T(1) = (9/√(94), 2/√(94), 3/√(94))
The unit normal vector, N(1), is given by the derivative of T(1) with respect to t, evaluated at t = 1
T'(t) = (0, 2, 6t)
T'(1) = (0, 2, 6)
The magnitude of T'(1) = √(0² + 2² + 6²) = √(40)
The unit normal vector at (9, 1, 1) is N(1) = (0, 2/√(40), 6/√(40))
The unit binormal vector, B(1), is given by the cross product of T(1) and N(1)
B(1) = T(1) × N(1)
= (18/√(40×94), 6/√(40×94), -54/√(40×94))
|B| = (3/2)√(91/ 235)
Finally, the curvature, k, at the point (9, 1, 1) is given by the magnitude of T'(1)
[tex]k = \frac{|B|}{|T|^3}[/tex]
k = (3/2)√(91/ 235)/ (√40)³ = (3/ 800)√(91/ 94)
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suppose the average number of hours worked per week for high-school aged teens in the united states is 17 hours per week with a standard deviation of 4 hours. a high school teacher working at an inner city high school is concerned about the time students spend working at after school jobs. she randomly selects 15 of her students and calculates their average work hours to be 14.3 hours per week. identify the population and sample.
suppose the average number of hours worked per week for high-school aged teens in the united states is 17 hours per week with a standard deviation of 4 hours. So, the number of people selected from the public for a research is known as a sample.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.
For the given details the correct matching will be:
Parameter - 17 hrs per week
Population - All high-school-aged teens in the US
Statistic - 14.4 hours per week
Sample - 15 students
Population is everything that is taken into account for an experiment since parameters reflect population characteristics and statistics state sample parameters.
The number of people selected from the public for a research is known as a sample.
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We prefer the t procedures to the z procedures for inference about a population mean because a. z requires that you know the population standard deviation. b. z requires that you can regard your data as an SRS from the population. c. z can only be used for large samples. d. the t distribution has less variation.
The right answer is: Z requires that you know the population standard deviation, which can be erroneous.
what is standard deviation ?The standard deviation calculates how much the data vary from the mean value. The mean of the following two numbers, for instance, is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. But the second is obviously more dispersed. It expresses the deviation of each observed value from the mean.
given
Both distributions must meet a number of requirements in order to be used. The prerequisites that must be met in order to execute a hypothesis test for employing a z-distribution are: The population has a normal distribution. We are aware of the population standard deviation.
The scope of the sample is broad.
The prerequisites that must be met in order to conduct a hypothesis test for employing a t-distribution are:
The population has a normal distribution. The chosen sample was chosen at random.
Use the t-distribution to conduct the test for the population mean in cases where the population standard deviation is unknown and the sample standard deviation must be computed.
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Suppose a farmer wants to create a four-sided rectangular pen with an area of 144 square feet. what is the length and width of the rectangular pen that uses the smallest perimeter possible to enclose this area? what is the perimeter of this pen?
pls help asap
According to the formula of area of rectangle, the smallest perimeter possible to enclose this area is 60 and the length is 24 and the breadth is 6.
The general formula to calculate the area of rectangle is written as
A = l x b
And the perimeter of rectangle is written as.
P = 2(l + b)
Where l refers the length of the rectangle and b refers the breadth of the rectangle.
Here we know that the four-sided rectangular pen with an area of 144 square feet.
So, here we have to substitute the value of the formula, then we get,
=> l x b = 144
=> b = 144/l --------------------(1).
Here we have to substitute this one on the perimeter then we get,
=> 2(l + b) = 30
=> 2(144/l + l) = 30
=> 144/l + l = 15
=> l² - 15l + 144 = 0
When we factorize this one then we get the value of l as 24.
Then the value of the width is calculated as,
=> l = 144/ b
=> b = 144/24
=> 6
Then the perimeter us calculated as,
=> P = 2(24 + 6)
=> P = 60.
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Monte todo página 108 quiero las respuestas porfa
Answer:
no abla espanol
Step-by-step explanation:
each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. when the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. there are 2 red-white pairs. how many white pairs coincide?
7 white pairs coincide when upper half is folded over the centerline.
What is triangle ?
A triangle is a three-sided polygon that has three straight sides and three angles. The sum of the angles in a triangle is always 180 degrees. Triangles are classified based on their side lengths or angle measures.
We know that each half of the figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles.
When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. there are 2 red-white pairs.
So, 2 red triangles + 3 blue triangles + 2 red-white pairs = 7 pairs of triangles that coincide
The total number of triangles in each half of the figure is 3 red triangles + 5 blue triangles + 8 white triangles = 16
If 7 pairs of triangles coincide, then 16 - 7 = 9 pairs do not coincide.
And since 2 red-white pairs coincide, then the remaining 9 - 2 = 7 pairs must be white pairs.
So 7 white pairs coincide when upper half is folded over the centerline.
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decimals that are equal to 3 1/40
A circle is circumscribed around $ABCD$ as follows:How many degrees are in $\angle CAB \angle ACD$
The measure of [tex]$\angle CAB = 180^{\circ} - \angle ACD$[/tex]
What is the circumscribed circle?
A circumscribed circle is a circle that is drawn around a polygon such that the circle touches all the vertices of the polygon. In other words, the vertices of the polygon lie on the circumference of the circle.
Given that a circle is circumscribed around a quadrilateral ABCD, it is clear that the circle passes through all four vertices of the quadrilateral, A, B, C and, D. Also, the diameter of the circle is the diagonal AC of the quadrilateral.
The angles formed by the diameter with the tangents from the non-adjacent vertices are supplementary. That is [tex]$\angle CAB + \angle ACD = 180^{\circ}$[/tex]
Therefore, the measure of [tex]$\angle CAB = 180^{\circ} - \angle ACD$[/tex]
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What is 1 2 as a division?
Answer:
Hence, 1 divided by 2 is 0.5. So, the correct answer is “0.5”
plse mark me as a brainalist
How do you find the domain and range of a linear line?
A graph when plotted, we get a straight line and it is called linear graph. Linear graph is a graph of linear function.
Domain refers to all the possible input values, it is the values in the x-axis of the graph. A range means all the output values, when each domain is used in a function. It is the y-axis values.
To determine the domain identify all the X- coordinates in the linear function graph. To determine the range, identify all Y-coordinates in the functions graph. The domain and range are usually represented as a set of values.
If the domain have values from 0-6, it is represented as {0<x<4}
If the range is values between -1 to 10, then it is represented as {-1<x<10}.
Lets consider the linear function y= 3x, the domain is between 0 and 10, and range above are,
Function y= 3x
Domain 0 1 2 3 4 5 6 7 8 9 10
Range 0 3 6 9 12 15 18 21 24 27 30
So domain is the X-coordinates, and range the Y-coordinates.
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Function g is a transformation of the parent function f(x)=x2. The graph of f is reflected across the x-axis and then translated left 4 units and down 2 units to form the graph of g. Write the equation for g in the form y=ax2+bx+c.
The equation of g(x), after the translations, is given as follows:
g(x) = x² + 8x + 14.
What are the translation rules?There are four translation rules that can be applied to a function, and they are listed as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
f(x) = x².
The translations, along with their effects, are given as follows:
Left 4 units: x -> x + 4.Down 2 units: y -> y - 2.Hence the function g(x) is defined as follows:
g(x) = (x + 4)² - 2
g(x) = x² + 8x + 16 - 2
g(x) = x² + 8x + 14.
Which is in the standard form as is desired for this problem.
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consider randomly selecting a student at a large university, and let a be the event that the selected student has a visa card and b be the analogous event for mastercard. suppose that p(a) 5 .6 and p(b) 5 .4. a. could it be the case that p(a > b) 5 .5? why or why not? [hint: see exercise 24.] b. from now on, suppose that p(a > b) 5 .3. what is the probability that the selected student has at least one of these two types of cards? c. what is the probability that the selected student has neither type of card? d. desc
The relationship between p(a), p(b) and p(a > b) is that p(a) + p(b) - p(a > b) = 1, meaning the probability of having at least one of the two types of cards is equal to the sum of the individual probabilities minus the probability of having both.
A. No, it could not be the case that p(a > b) = 0.5. This is because
p(a) + p(b) = 1,
so p(a > b) = 1 - p(a) - p(b)
= 1 - 0.6 - 0.4
= -0.1, which is not a valid probability.
B. The probability that the selected student has at least one of these two types of cards is
p(a) + p(b) - p(a > b)
= 0.6 + 0.4 - 0.3
= 0.7.
C. The probability that the selected student has neither type of card is 1 - (p(a) + p(b) - p(a > b))
= 1 - 0.7
= 0.3.
D. The relationships among p(a), p(b), and p(a > b) can be summarized by the equation p(a) + p(b) - p(a > b) = 1. This equation states that the probability of having atleast one type of card is equal to the sum of the probabilities of having a Visa card and a Mastercard minus the probability of having both types of card.
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write the following numbers in words 2740253535
Answer:
Two billion, seven hundred forty million, two hundred fifty-three thousand, five hundred thirty-five is the right answer...
8. 4. G.SRT.3 For what value of x is AABC ~ADEF?.
The value of x which makes ΔABC congruent to ΔDEF is 12.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
ΔABC is congruent to ΔDEF
This means,
∠A = ∠D ____(1)
∠B = ∠E ____(2)
∠C = ∠F _____(3)
Now,
From (1),
42 = 4x - 6
42 + 6 = 4x
48 = 4x
x = 48/4
x = 12
From (2),
7x + 10 = 94
7x = 94 - 10
7x = 84
x = 12
Thus,
The value of x is 12.
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How do you find the domain domain and range of a function?
To find the domain and range, the function we simply solve the equation y=f(x) to determine the values of the independent variable x and obtain the domain.
Domain: In simple words, the domain is the set of values of x for which function f(x) is defined, and also the set of values of x for which we can calculate the value of f(x)
Range: The range of function can define as the set of values of f(x) for the value of its domain
For finding the domain of any function f(x) ..find the value of all x for which function f(x) is defined
For finding the value of the range of function f(x), calculate the value of f(x) for all values of x in the set of domains of f(x)
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Zack deposited $4,533 in an account earning 5.9% interest compounded annually.
To the nearest cent, how much will he have in 1 year?
If Zack deposited $4,533 in an account earning 5.9% interest compounded annually. The amount he will have in 1 year is: $4,807.79.
How to find the compounded amount?Using this formula to find the compounded amount
A = P(1+r/n)^nt
Where:
A = Amount = ?
P = Principal = $4,533
R = Interest rate = 5.9% or 0.059
n = Number of months = 12
t = Time = 1 years
Let plug in the formula
A = $4,533 (1+ 0.059/12)^1×12
A = $4,533 (1+.004916)^12
A = $4,533 (1.004916)^12
A = $4,533 (1.0606)
A = $4,807.79
Therefore the amount he will have in 1 year is: $4,807.79.
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If a quadratic equation [tex]ax^{2} + bx + c = 0[/tex] has equal roots , then the value of b , is :
(a) ± 2√ac
(b) √ac
(c) 4ac
(d) -√ac
If a quadratic equation ax² + bx + c = 0, has equal roots , then the value of b , is : (a) ± 2√ac
How to Interpret Quadratic Formula?The general form of a quadratic equation is;
ax² + bx + c = 0
The quadratic formula used to solve this quadratic equation is;
x = [-b ± √(b² - 4ac)]/2a
The quadratic equation ax² + bx + c = 0 has equal roots if its discriminant b² - 4ac = 0.
Thus;
b² = 4ac
b = ±√4ac
b = ±2√ac
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Nolan and his children went into a grocery store and he bought $9 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. He bought 2 more apples than bananas. By following the steps below, determine the number of apples, x, and the number of bananas, y, that Nolan bought.
Determine three ways to have 2 more apples than bananas:
Nolan and his children went into a grocery store and he bought $9 worth of apples and bananas, The three ways are explained below
What are equations?Generally, One way to determine the number of apples, x, and the number of bananas, y, that Nolan bought is to use the equation:
x + y = a (total number of apples and bananas)
0.75x + 0.5y = 9 (total cost of apples and bananas)
Another way is to use the equation:
x = y + 2 (number of apples is 2 more than the number of bananas) 0.75x + 0.5y = 9 (total cost of apples and bananas)
A third way is to use the equation
y = x - 2 (number of bananas is 2 less than the number of apples)
0.75x + 0.5(x-2) = 9 (total cost of apples and bananas)
You can then solve for x and y using either of the above equations.
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Please help me I don’t understand math 2
Answer:
3rd choice
a rotation of 90° counterclockwise about the origin and a translation down 1 unit
Step-by-step explanation:
This is just asking you what operations you need to perform to get figure N from figure M. Such a set of operations is called a transformation.
In this case we see that to get figure N we have to rotate figure M 90° in a counterclockwise direction. That would be the first transformation
From the choices you can eliminate the first two choices which deal only with clockwise rotation
Translation transformation is one where the figure is shifted horizontally or vertically
All we have to do is figure out if, after 90° counterclockwise rotation of M whether it was shifted 1 unit up or 1 unit down
Look at the point (-3, 1) in figure M.
When a figure is rotated 90° counterclockwise, each if its original coordinates (x, y) become new coordinates (-y, x)
In other words the coordinates are interchanged in the transformed figure and the sign of the new x-coordinate is changed from the original y value
So (-3, 1) should become (-1, -3)
But in figure N, that point has become (-1, -4) which is (-1, -3-1). This indicates the figure has been shifted down which corresponds to a translation down by 1 unit
Answer: 3rd choice
a rotation of 90° counterclockwise about the origin and a translation down 1 unit
The two images I have attached may help you understand better. First one is just the rotation of M. Second one is the rotated figure shifted down which results in figure N
A park has t tables spread equally among the 3 picnic areas.Write an expression that shows how many picnic tables are at each picnic area.
Answer:
8000
Step-by-step explanation:
bc if its 3 picnic its its 8000
ghout-replacement-and-write-them-in-the-order-picked-assume-there-are-no-repeats-of-digits-in-your-phone-number-what-is-the-probability-that-you-have-written-the-first-6-digits-of
Therefore , the required probability is therefore 1/151200, which is the answer to the probability problem.
What is the process of probability?The probability that a happening will happen or that the proposition is true is determined by a field of mathematics known as probability theory. A probability is a number between 0 and 1, where 1 represents certainty and 0 roughly represents the likelihood that an event will occur. A probability is a numerical expression of a certain event's likelihood or chance of happening. The percentages 0% - 100% and 0 to 1 can also be used to express probabilities. the percentage of times in an ideal collection of equally likely alternatives that an event occurs compared to all possible outcomes.
Here,
The six numbers can only be chosen in one way if the order chosen must match my phone number.
In 10P6 methods, six random digits from a possible total of ten can be chosen.
So the necessary probability is equal to 1/P. (10,6).
Alternative: Probability = 1/151200
The required probability is therefore 1/151200, which is the answer to the probability problem.
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. mrs. elliott, a teacher at durham school of the arts, studies the effect of "personal narratives" on people's behavior. for example, if the "story" you have about your academic ability is positive, you do better in school than if your "story" is negative. something as simple as hearing older students describe overcoming challenges similar to yours can help you change your story and improve your performance. (a) suppose you have 40 college freshman who have volunteered to be part of a study. design a completely randomized experiment that tests the hypothesis that hearing older students talk about overcoming challenges improves academic performance. be sure your design addresses how randomization will be incorporated. (b) suppose you have reason to believe that students with a history of strong academic performance respond differently than those with a history of modest performance. describe how you would change the experimental design to address this difference.
Answer:
(a) There are 2 groups. The treatment group will hear older students describe overcoming challenges. The control group won't hear anything.
Label each student with a different integer from 01 to 40. Go to a line in Table D and read two-digit groups moving from left to right. The first 20 different labels between 01 and 40 identify the 20 students who hear older students talking. The remaining 20 students don't hear anything. Ignore groups of digits from 41 to 00.
(b) Separate the 40 freshmen into 2 groups according to their history of academic performance. Carry out treatment separately in each block to account for the variation due to the history of academic performance.
Step-by-step explanation:
(a) We want to infer the cause and effect between hearing older students talking about their challenges and the students' academic performance.
Claim the 2 groups first;
Clarify the random assignment of people.
(b) The differences between the two kinds of students are expected to affect the response to the treatments in some ways. Randomized block designs are to eliminate the effect.
10001000 students took a test and the scores are normally distributed, with a mean of 7676 and standard deviation of 55. approximately how many students scored between 8181 and 8686?
The number of students who scored between 8181 and 8686 can be calculated using the z-score formula to find standard deviation.
How is this calculated?z1 = (8181-7676)/55 = 1.89
z2 = (8686-7676)/55 = 3.04
Using a standard normal table, the area under the curve between these two z-scores is approximately 8.5%. So, we can estimate that about 850,085 students scored between 8181 and 8686. We find the z-score of 8181 and 8686 and calculate the area under the standard normal distribution curve between these z-scores.
What is the difference between a standard normal distribution and a non-standard normal distribution?A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, while a non-standard normal distribution has a different mean and/or standard deviation. The z-score formula is used to convert a non-standard normal distribution to a standard normal distribution, so that the properties of the standard normal distribution can be applied, such as using a standard normal table to find areas under the curve.
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Please help me! :(
I need these answers soon! :(
I will give Brainliest!
I've provided a picture.
a) The mean and the standard deviation of the proportion of 50 randomly-selected songs that are Beatles songs are given as follows:
Mean: 0.26.Standard deviation: 0.062.b) The probability that more than 30% of the 50 songs are Beatles songs is given as follows: 0.2594 = 25.94%.
c) The mean and the standard deviation of the proportion of 40 randomly-selected songs that are Beatles songs are given as follows:
Mean: 0.33.Standard deviation: 0.074.How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule 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, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].For item a, the sample size and the proportion are given as follows:
n = 50, p = 0.26.
Hence the mean and the standard error are given as follows:
[tex]\mu = 0.26[/tex][tex]s = \sqrt{\frac{0.26(0.74)}{50}} = 0.062[/tex](using the third bullet point, about the Central Limit Theorem).
The probability that the proportion is above 30% is one subtracted by the p-value of Z when X = 0.3, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (0.3 - 0.26)/0.062
Z = 0.645.
Z = 0.645 has a p-value of 0.7406.
(halfway between Z = 0.64 and Z = 0.65 on the z-table appended at the end of the answer).
1 - 0.7406 = 0.2594 = 25.94%.
For item c, the sample size and the proportion are given as follows:
n = 40, p = 0.33.
Hence the mean and the standard error are given as follows:
[tex]\mu = 0.33[/tex][tex]s = \sqrt{\frac{0.33(0.67)}{40}} = 0.074[/tex]More can be learned about the normal distribution at https://brainly.com/question/25800303
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Help would be greatly appreciated!
Items 3-4. AABC and
ACDE are shown.
3. What is m/BAC?
4. What is m/CDE?
-1/2x-2y=4
Solve for X and y pls
Answer:
The image attached
Step-by-step explanation:
Put the equation into slope-intercept form
[tex]y=mx+b[/tex]
The equation should look like this
[tex]y=-\frac{1}{4}x-2[/tex]
Graph the equation with the slope being [tex]-\frac{1}{4}[/tex] and [tex]-2[/tex] being the y-intercept.
9. An observer in a lighthouse sees a sailboat out at sea. The angle of depression from the
observer to the sailboat is 6°. If the observer is 104 ft up in the lighthouse, how far is the boat
from the base of the lighthouse?
The required distance from the base of the lighthouse to the sailboat is 11 feet.
Let x be the distance from the base of the lighthouse to the sailboat.
We know that the angle of depression is 6° and the height of the observer is 104 ft. We can use the tangent function to find the ratio of the opposite side (x) to the adjacent side (104 ft).
tan(6°) = x / 104
To find x, we can multiply both sides by 104:
x = 104 × tan(6°)
x = 104 × 0.10510
x = 10.9308
x ≈ 11
The value of x ≈ 11 is the distance from the base of the lighthouse to the sailboat.
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Using banker's algorithm what is safe sequence.(A) P2, P3, P1 (B) P1, P2, P3 (C) P3, P2, P1 (D) None of the above
P2, P3, P1 is a safe sequence according to the banker's algorithm.
What is banker's algorithm?The banker's algorithm gets its name from the fact that it determines whether or not a person should be granted a loan amount in order to assist the bank system in securely simulating resource allocation. In this part, we'll go through the Banker's Algorithm in depth. The Banker's Algorithm is primarily used in the banking system to avoid stalemate. It assists you in determining whether or not a loan will be granted. This procedure is used to assess the allocation for securely replicating the maximum amount available for all resources.
Here,
According to the banker's algorithm, the sequence P2, P3, P1 is secure.
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Evaluate the line integral, where C is the given curve.∫C xyds, C:x = t^2,y = 2t, 0 ≤ t ≤ 3
On solving the provided question, we can say that integral = [tex]\int\limits^a_b \,[/tex]t√9 + 16t² dt = [tex]\int\limits^a_b \,[/tex]√9 + 16t² d (9 + 16t²)
what is integral?In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas. The main goal of calculus is to work with derivatives and integrals. Primitives and inverse derivatives are other terms for integral. Integration is essentially utilized to determine the area of 2D space and determine the volume of 3D objects. As a result, calculating an integral of a function with respect to x entails calculating the area between the curve and the x-axis.
integral
Curves, x = t³ or,
= 3t²
y = t⁴ or,
= 4t³
Now, the line integral along C will be:
→ = [tex]\int\limits^a_b \,[/tex]√(3t²)² + (4t³)² dt
= [tex]\int\limits^a_b \,[/tex]√9t⁴ + 16t⁶ dt
= [tex]\int\limits^a_b \,[/tex]√9 + 16t² dt
= [tex]\int\limits^a_b \,[/tex]√9 + 16t² dt
= [tex]\int\limits^a_b \,[/tex]t√9 + 16t² dt
= [tex]\int\limits^a_b \,[/tex]√9 + 16t² d (9 + 16t²)
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