The derivative of S(t)= 1+e −t is S'(t) = S(t)(1 - S(t)). So, the correct answer is (iii).
To find S'(t), we can use the chain rule:
S'(t) = (d/dt) [1 + e^(-t/2)]^-2 * d/dt [1 + e^(-t/2)]
Using the chain rule again for the second derivative:
d/dt [1 + e^(-t/2)] = (-1/2)e^(-t/2)
d/dt [1 + e^(-t/2)]^-2 = -2(1 + e^(-t/2))^-3 * (-1/2)e^(-t/2) = (1/2) e^(-t/2) / (1 + e^(-t/2))^3
Substituting into the expression for S'(t), we have:
S'(t) = [(1/2) e^(-t/2) / (1 + e^(-t/2))^3] * [1 - (1/2)e^(-t/2)]
S'(t) = (1/2) e^(-t/2) / (1 + e^(-t/2))^3 * [2 - e^(-t/2)]
S'(t) = e^(-t/2) / (1 + e^(-t/2))^3 * [2 - e^(-t/2)]
Taking the derivative of S(t), we have:
S'(t) = e^(-t/2) / (1 + e^(-t/2))^2
Comparing this to the given choices, we can see that:
S'(t) = S(t) is not true, since S(t) = 1 + e^(-t/2) and S'(t) is a different function.
S'(t) = (S(t))^2 is not true, since (S(t))^2 = (1 + e^(-t/2))^2 is a different function from S'(t).
S'(t) = S(t)(1 - S(t)) is true, since we can substitute S(t) and S'(t) from above and simplify:
S'(t) = e^(-t/2) / (1 + e^(-t/2))^3 * [2 - e^(-t/2)]
S(t)(1 - S(t)) = [1 + e^(-t/2)] * [1 - (1 + e^(-t/2))] = e^(-t/2) / (1 + e^(-t/2))
Therefore, S'(t) = S(t)(1 - S(t)) is true.
S'(t) = -S(-t) is not true, since S(-t) = 1 + e^(t/2) and -S(-t) is a different function from S'(t).
So the correct choice is (iii): S'(t) = S(t)(1 - S(t)).
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Answer the Question attached. The person who gets it right will be given brainliest.
Answer:
Example of a function that satisfies the following conditions:
a. Domain and range are both all real numbers except 5:
f(x) =
{
x if x ≠ 5
0 if x = 5
}
b. Domain is all positive numbers greater than 1, including 1:
f(x) =
{
(x-1)^2 / (x-1) if x > 1
0 if x = 1 or x = 5
}
c. Domain is all positive numbers greater than 1, but not including 1:
f(x) =
{
(x-1)^2 / (x-1) if x > 1 and x ≠ 1
0 if x = 1 or x = 5
}
what should be added to 8a to get 12a ?
If the gradient of the equation 2x-ay+2=0 is 1. Then find the value of a.
Step-by-step explanation:
2x + ay + 2 = 0
the gradient or slope of the line is the factor m of x in the form
y = mx + b
so let's transform the given equation into that form :
ay = -2x - 2
y = (-2/a)x - 2/a
we know that m = 1.
so,
-2/a = 1
-2 = a
What would the slope of X -2, -1, 0, 1, 2. Y -12, -7, -2, 3, 8.
Answer:
slope = 5
slope = (y2 - y1) / (x2 - x1)
Using this formula, calculate the slope between pairs of points in the given set of data. For example, the slope between the first two points (-2, -12) and (-1, -7) is:
slope = (-7 - (-12)) / (-1 - (-2)) = 5 / 1 = 5
Calculate the slope between each pair of points as follows:
Between (-2,-12) and (-1,-7): slope = 5
Between (-1,-7) and (0,-2): slope = 5
Between (0,-2) and (1,3): slope = 5
Between (1,3) and (2,8): slope = 5
In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.
What is the expected mean for a sample of 150 women?
What is the standard deviation of the mean for a sample of 150 women?
What is the probability of 150 women having a sample mean below 160 pounds?
What is the probability of 150 women having a sample mean above 175 pounds?
What is the probability of 200 women having a sample mean below 160 pounds? Notice the change in sample size.
What is the probability of 200 women having a sample mean above 175 pounds?
Answer:
Notice the change in sample size.
Answer:
1. The expected mean for a sample of 150 women is 168.5 pounds.
2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.
3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.
4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.
5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.
6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.
The solution is given below. Notice the change in sample size.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
In 2016, the CDC estimated the mean weight of U.S. women over the age of 20 years old was 168.5 pounds with a standard deviation of 68 pounds.
so. we get,
1. The expected mean for a sample of 150 women is 168.5 pounds.
2. The standard deviation of the mean for a sample of 150 women is 6.8 pounds.
3. The probability of 150 women having a sample mean below 160 pounds is 0.0849.
4. The probability of 150 women having a sample mean above 175 pounds is 0.0305.
5. The probability of 200 women having a sample mean below 160 pounds is 0.0434.
6. The probability of 200 women having a sample mean above 175 pounds is 0.0153.
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Which function represents the following graph?
Oy=√√x-3+3
Oy=√√x+3+3
O y=3√√x-3+3
Oy-3√x+3+3
The correct option b) [tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.
What particular graph best illustrates a function?The graph οf a relatiοn is said tο reflect a functiοn if a vertical line drawn anywhere οn the graph οnly intersects the graph οnce. In the event when a vertical line can graph is nοt a representatiοn οf a functiοn if there are mοre than twο pοints οn it.
The graphs coordinate is at (-3, 3)
Lets put the value in all the given function to find the correct function
a. [tex]\rm y = \sqrt{x - 3} + 3[/tex]
Using (-3, 3) as x and y
[tex]\rm 3 = \sqrt{(-3) - 3} + 3[/tex]
[tex]\rm 3 = \sqrt{9} + 3[/tex]
[tex]\rm 3 \neq 3 + 3[/tex]
[tex]\rm y = \sqrt{x - 3} + 3[/tex] is not a function of graph.
b. [tex]\rm y = \sqrt{x+ 3} + 3[/tex]
Using (-3, 3) as x and y
[tex]\rm 3 = \sqrt{-3+ 3} + 3[/tex]
[tex]\rm 3 = \sqrt{0} + 3[/tex]
[tex]\rm 3 = 0 + 3[/tex]
[tex]\rm 3 = 3[/tex]
[tex]\rm y = \sqrt{x+ 3} + 3[/tex] is a function of the given graph.
The other two options are no the functions as cube root is used and the value of x wont satisfy there.
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3 g(n) = 80 . (-) 4 O Complete the recursive formula of g(n). g(1) = g(n) = g(n − 1). -
Answer:
Based on the given information, we know that:
g(n) = 80 - 4g(n-1)
Also, we have the initial condition:
g(1) = g(n) = g(n-1)
Putting everything together, we can write the recursive formula for g(n) as follows:
g(1) = g(n) = g(n-1) (initial condition)
g(n) = 80 - 4g(n-1) (recursive formula)
where n > 1.
(please mark my answer as brainliest)
Problem 2 (Vector and Matrix Refresh) Seven data points are arranged as columns of a data matrix X given as follows: 2 1 0 0 -1 0 -2 X = 2 0 1 0 0 -1 -2 a) Draw all data points on a 2D plane by hand. Properly label the two axes. Clearly provide important tick values to facilitate a precise graphical description of the data. b) Consider each point as a vector. Calculate the angle in between (2 27 and the five other points (excluding [0 07), respectively, using the inner/dot product formula that involves the angle. Note that the angle between two vectors can be negative. c) Calculate the matrix outer product for X, namely, R = XXT. Show the intermediate steps of calculating each element of the 2-by-2 matrix R. d) The matrix outer product can also be calculated via R =
a) The drawing of all data points on a 2D plane is illustrated below.
b) The angle in between the five other points is 27
c) The matrix outer product for X is R = XXT.
d) The matrix outer product can also be calculated via R is (2,27)
The data matrix X is a 2-by-7 matrix, where each column represents a data point with two components. We can visualize each data point as a vector in a two-dimensional plane, where the horizontal axis represents the first component and the vertical axis represents the second component.
To draw all data points on a 2D plane, we can plot each column of X as a vector starting from the origin. Proper labeling of the two axes and providing important tick values will facilitate a precise graphical description of the data.
Next, we can use the inner product formula to calculate the angle between the first data point (2, 27) and the other five data points, respectively.
The inner product, also known as the dot product, is a way to measure the similarity between two vectors by multiplying their corresponding components and summing the products.
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Question 4
Let us assume an original starting value of $4 trillion in 2033, but that the actual rate of
decline after 2033 was 10% greater than the 7.6% rate. (Notice that this refers to a 10%
relative increase over the 7.6% rate of decline that was originally estimated in the
lesson, and not an absolute increase of 10 percentage points.) In the questions below,
consider how this would affect the estimated value of the funds in 2038?
What is the new estimated value of the trust funds in 2038? Round to the nearest
The new estimated value of the trust funds in 2038 would be $2.5 trillion.
What is funds?Funds are resources of monetary value that can be used to acquire goods, services, or to meet financial obligations. They are usually obtained through the sale of goods and services or by borrowing. Funds can come from a variety of sources, including individuals, businesses, governments, and other organizations. Funds can be used to purchase assets such as stocks, bonds, real estate, or other forms of investments.
This is because a 10% relative increase over the original estimated 7.6% rate of decline means that the actual rate of decline is 8.36% (7.6% x 1.10 = 8.36%). Applying this rate to the original starting value of $4 trillion, the value of the trust funds in 2038 would be $4 trillion x 0.9164 (which is the equivalent of 1 - 0.0836) = $2.5 trillion.
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The new estimated value of the trust funds in 2038 would be $2.4 trillion.
What is trust fund?A trust fund is a legal arrangement in which a person or organization (the trustor) transfers assets to another person or organization (the trustee) to be managed and distributed for the benefit of a third party (the beneficiary). The trustor sets out a set of instructions (the trust deed) on how the trust funds should be handled, managed, and distributed. The trustee is legally bound to abide by these instructions, and is responsible for the management and distribution of the trust funds according to the trust deed. Trust funds can be used for a variety of purposes, such as providing for a beneficiary's education, medical care, or retirement.
This is because a 10% increase in the rate of decline would result in a rate of decline of 8.36% (7.6% plus 10% of 7.6%).
Using this new rate of decline, the value of the trust funds in 2038 would be $4 trillion multiplied by (1 - 0.0836)⁵,
which is equal to $2.4 trillion.
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T/F. To construct a confidence interval for sigma (or sigma squared), the population from which the sample was drawn must be normally distributed.
To construct a confidence interval for sigma the population from which the sample was drawn must be normally distributed. -
It is not necessary to make the normalcy assumption in order to build a confidence interval for sigma. To employ the central limit theorem, however, the sample size must be adequate which ideally enables the use of the normal distribution to approximate the sampling distribution of the sample variance. Alternative techniques, like t-distribution, can be employed if total sample size is limited.
It's also important to remember that, regardless of sample size, the distribution of sample variance will be normal if population is known and recognizable to have a normally distributed population. As long as the sample size is appropriate, the sample variance may still be utilized to create a confidence range for sigma even if the population is not normally distributed.
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any point on the parabola can be labeled (x,y), as shown. a parabola goes through (negative 3, 3)
The correct standard form of the equation of the parabola is:
[tex]y = -x^2 - 1[/tex].
To find the standard form of the equation of the parabola that passes through the given points (-3, 3) and (1, -1), we can use the general form of the equation of a parabola:
[tex]y = ax^2 + bx + c[/tex] ___________(1)
Substituting the coordinates of the two given points into this equation, we get a system of two equations in three unknowns (a, b, and c):
[tex]3 = 9a - 3b + c[/tex]
[tex]-1 = a + b + c[/tex]
To solve for a, b, and c, we can eliminate one of the variables using subtraction or addition. Subtracting the second equation from the first, we get:
[tex]4 = 8a - 4b[/tex]
Simplifying this equation, we get:
[tex]2 = 4a - 2b[/tex]
Dividing both sides by 2, we get:
[tex]1 = 2a - b[/tex]___________(2)
Now we can substitute this expression for b into one of the earlier equations to eliminate b. Using the first equation, we get:
[tex]3 = 9a - 3(2a - 1) + c[/tex]
Simplifying this equation, we get:
[tex]3 = 6a + c + 3[/tex]
Subtracting 3 from both sides, we get:
[tex]0 = 6a + c[/tex]
Solving for c, we get:
c = -6a __________(3)
Substituting this expression for c into the second equation, we get:
[tex]-1 = a + (2a - 1) - 6a[/tex]
Simplifying this equation, we get:
[tex]-1 = -3a - 1[/tex]
Adding 1 to both sides, we get:
[tex]-3a =0[/tex]
Solving for a, we get:
[tex]a = 0[/tex]
Substituting this value of a into the equation(3) for c, we get:
c = 0
Substituting a = 0 into the equation(2) for b that we found earlier, we get:
[tex]1 = 0 - b[/tex]
Solving for b, we get:
[tex]b = -1[/tex]
Putting the values of a, b and c in (1), we get
[tex]y = -x^2 - 1[/tex]
Therefore, the equation of the parabola that passes through the given points (-3, 3) and (1, -1) is:
[tex]y = -x^2 - 1[/tex]
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Complete question:
A parabola goes through (-3, 3) & (1, -1). A point is below the parabola at (-3, 2). A line above the parabola goes through (-3, 4) & (0, 4). A point on the parabola is labeled (x, y).
What is the correct standard form of the equation of the parabola?
The figure is in the image attached below
Which set of ordered pairs does not represent a function?
1. {(6,5), (3, 5), (−2, 8), (-9,4)}
2. {(-6, -1), (3, 1), (4, −4), (8, 1)}
3. {(-1,9), (-8, 5), (-1, 3), (-9, 1)}
4. {(5,9), (2,-5), (-1,-5), (0, 1)}
The set of ordered pairs does not represent a function is the one in the third option.
{(-1,9), (-8, 5), (-1, 3), (-9, 1)}
Which set of ordered pairs does not represent a function?A relation maps elements from one set, the domain, into elements of other set, the range.
Such that these mappings are of the form (x,y).
A function is a relation where each input is mapped into a single one output, then if you see a relation that has two points with the same value of x and different values of y, then that relation is not a function.
Particularly, if you look at the third option:
{(-1,9), (-8, 5), (-1, 3), (-9, 1)}
You can see that the first and second points have the same input and different outputs, then this is not a function, and that is the correct answer.
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What is the smallest possible average of five distinct positive even integers?
A. 10
B. 8
C. 6
D. 4
E. 0
Answer:
The smallest possible average of five distinct positive even integers will occur if we choose the five smallest even integers. Since we want the integers to be distinct, we start with 2 and add the next four even integers:
2, 4, 6, 8, 10
The average of these five integers is:
(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
Therefore, the smallest possible average of five distinct positive even integers is 6, which is answer choice C.
TRUE/FALSE. When calculating probabilities, combinations and permutations are used to find the number of outcomes in a sample space.
TRUE. Combinations and permutations are used in probability calculations to determine the number of possible outcomes in a sample space.
When calculating probabilities, combinations and permutations are used to find the number of outcomes in a sample space. Why?When order is important, permutations are utilized, and when order is not important, combinations are used. The formula P(n,r) = n!/(n-r)!, where n! signifies the factorial of n, and the expression C(n,r) = n!/r!(n-r)!, give the number of permutations of n items taken r at a time and the number of combinations of n objects taken r at a time, respectively.
It is possible to count the number of ways that a subset of items can be chosen from a larger set using both permutations and combinations. These ideas are crucial for estimating probabilities because they let us know how many different outcomes could satisfy a certain condition.
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Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P67, the 67-percentile. This is the temperature reading separating the bottom 67% from the top 33%.
P67 =
°C
Answer:
Step-by-step explanation:
To find the temperature corresponding to the 67th percentile, we need to find the z-score that has an area of 0.67 to the left of it in the standard normal distribution. We can use a table or a calculator to find this z-score.
Using a standard normal distribution table, we can look up the value that corresponds to an area of 0.67 to the left of the mean, which is 0.44. This means that P(Z ≤ 0.44) = 0.67, where Z is the standard normal random variable.
Next, we can use the formula for standardizing a normal random variable to convert this z-score to the corresponding temperature on the thermometer scale:
z = (x - μ) / σ
where μ is the mean, σ is the standard deviation, and x is the temperature we want to find.
Rearranging this formula, we get:
x = μ + z * σ
Plugging in the values, we get:
x = 0 + 0.44 * 1.00
x = 0.44
Therefore, the temperature corresponding to the 67th percentile is 0.44°C.
every nonzero real number has a reciprocal. zero does not have a reciprocal. therefore, zero is not a nonzero real number
The given argument is Valid because the conclusion follows the argument logically.
The argument is that "Every nonzero real number has a reciprocal. Zero(0) does not have a reciprocal. Therefore, zero is not a non-zero real number."
The argument can be expressed in logical form as:
⇒ Premise 1: For every nonzero real number x, there exists a reciprocal 1/x.
⇒ Premise 2: Zero does not have a reciprocal.
⇒ Conclusion: Therefore, zero is not a nonzero real number.
This argument is valid because the conclusion logically follows from the premises.
The premises establish that every nonzero real number has a reciprocal, and that zero does not have a reciprocal.
The conclusion then follows logically, as zero is explicitly excluded from the set of nonzero real numbers based on the definition of a reciprocal.
Therefore, the argument is valid.
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The given question is incomplete, the complete question is
Is The Following Argument Valid Or Invalid?
Every nonzero real number has a reciprocal. Zero does not have a reciprocal. Therefore, zero is not a nonzero real number.
If the average aggregate inventory value is $1,200,000 and the cost of goods sold is $600,000, which of the following is weeks of supply?
The inventory turnover ratio can be calculated by dividing the cost of goods sold by the average inventory value. In this case, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.
The inventory turnover ratio measures the number of times a company sells and replaces its inventory during a period. It can be calculated by dividing the cost of goods sold by the average inventory value.
The inventory turnover ratio = Cost of goods sold / Average inventory value
In this case, the cost of goods sold is $600,000 and the average inventory value is $1,200,000.
Inventory turnover ratio = $600,000 / $1,200,000 = 0.5
Therefore, the inventory turnover ratio is 0.5, and the correct answer is (D) 0.5.
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Complete question:
If the average aggregate inventory value is $1,200,000 and the cost of goods sold is $600,000, which of the following is inventory turnover?
A)60
B)10.4
C)2
D)0.5
E)None of these
point $p$ lies inside square $abcd$ such that triangle $abp$ is equilateral. find $\angle pcd$ in degrees.
The measurement of angle PCD in equilateral triangle is 67.38°.
Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.
Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.
Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.
Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.
Using the Pythagorean theorem in triangle $OCE$, we have
CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]
Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,
∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°
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Please figure out #3. I’ll mark brainliest for right answer.
Answer:
We are given the cost equations for Emma's and Madison's text message plans as:
Emma's Plan: y = 0.10x + 10
Madison's Plan: y = 0.15x
where y is the cost in dollars and x is the number of texts sent. We are also told that Emma and Madison paid the same amount in one month. Let's set the two equations equal to each other and solve for x:
0.10x + 10 = 0.15x
Subtracting 0.10x from both sides, we get:
10 = 0.05x
Dividing both sides by 0.05, we get:
x = 200
Therefore, Emma and Madison sent 200 text messages in one month to pay the same amount
Which of the following products is defined?
GH
FE
EH
FG
All of the above are undefined
Using matrices, we can find that the products of EH and FG are defined, the rest does not satisfy.
Define matrix?A matrix is a rectangular array of values that are defined for mathematical operations including addition, subtraction, and multiplication.
The quantity of rows and columns in a matrix—also referred to as the order of the matrix—determines its size. A 6 4 symbol and 6 by 4 reading are used to symbolise and denote the order of a matrix having 6 rows and 4 columns.
Here in the question,
When the matrices, E and H are multiplied, the resulting matrix is a defined matrix.
Similarly, we can see when F and G are multiplied, the resulting matrix is a defined matrix.
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Jim and Sally mow lawns in their neighborhood. Sally mows 5 less than twice the number of lawns Jim mows. Together they mow 25 lawns.
Which system of equations models this situation if j represents the number of lawns Jim mows and s represents the number of lawns sally mows?
Answer:
D
Step-by-step explanation:
Sallys= 2(Jims) -5
Sally's + Jim's = 25
Answer:
s = 2j -5s +j = 25Step-by-step explanation:
You want the system of equations that models, "Sally mows 5 less than twice the number of lawns Jim mows, and together they mow 25 lawns."
TranslationThe letters 's' and 'j' represent the number of lawns that Sally and Jim mow, respectively.
Then "twice the number of lawns Jim mows" is represented be 2j. And 5 less than that is represented by 2j-5. Since this is the number of lawns Sally mows, the equation is ...
s = 2j -5 . . . . . . . matches only one answer choice (D)
The equation for "together they mow 25 lawns" is ...
s +j = 25
In an effort to figure out why application rates are slipping, your college decides to set up an experiment to determine why students who are interested in the college decide to enroll or not. The college decides to send out a questionnaire to everyone who submitted an application to the college in 2017. What's the population for this study, and what's the sample?
A. The population is all college students everywhere, and the sample is all college students interested in your school.
B. The population is all college students everywhere, and the sample is the individuals who responded to the survey.
C. The population is all students who applied to your college, and the sample is the individuals who responded to the survey.
D. The population is all college students interested in your school, and the sample is everyone who decided to enroll.
The population of interest is the group of students who submitted an application to the college in 2017.
What is sample?A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.
According to question:The correct answer is C.
The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.
Option A is incorrect because the population is not all college students everywhere, only those who applied to the college in question.Option B is incorrect because the sample is not just the individuals who responded to the survey, but rather all students who submitted an application in 2017.Option D is incorrect because the sample is not just everyone who decided to enroll, but rather all students who submitted an application, regardless of whether they enrolled or not.To know more about sample visit:
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Last years freshman class at big state university totaled 5,303 students
URGENT
The 1,262 students who received a merit scholarship, the amount they received varied per student and totaled an average of $3,458 ($454). That amount is 78.2% of the full tuition cost of $4,400.
What is merit?Merit is a term used to describe the quality of something or someone that makes them worthy of recognition or respect. It is an indicator of worthiness and is usually based on a person's ability, effort, or accomplishments. Merit is often used when evaluating an individual or a group for a promotion, hiring, or award. Merit is subjective, as different people have different standards for what merits recognition.
Therefore, 21.8% of the students who received a merit scholarship did not receive enough to cover full tuition. Therefore, the percentage of students who received a merit scholarship and did not receive enough to cover full tuition is 21%.
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Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this order
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it turn when it changed direction? Show you Work.
answer: 175
Step-by-step explanation:
Answer:
71.9 degrees
Step-by-step explanation:
The find the value of x on the given diagram, we must first find the included angle between the two line segments labelled 94 mi and 119 mi in the triangle. To do this, we can use the Law of Cosines.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
The values to substitute into the formula are:
a = 119b = 94c = 173Solving for the angle C:
[tex]\begin{aligned}173^2&=119^2+94^2-2(119)(94)\cos C\\\\29929&=14161+8836-22372\cos C\\\\29929&=22997-22372\cos C\\\\6932&=-22372\cos C\\\\-\dfrac{6932}{22372}&=\cos C\\\\C&=\cos^{-1}\left(-\dfrac{6932}{22372}\right)\\\\C&=108.0502874...^{\circ}\end{aligned}[/tex]
As angles on a straight line sum to 180°, the value of x can be calculated by subtracting the found value of C from 180°:
[tex]x=180^{\circ}-108.0502874...^{\circ}[/tex]
[tex]x=71.9497125...^{\circ}[/tex]
[tex]x=71.9^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the ship turned 71.9 degrees north of west when it changed direction.
of the following people, who would be included in the survey conducted by the bureau of labor statistics?
The people who are included in the survey conducted by Bureau of Labor Statistics are (a) certain unpaid workers, (b) part-time workers and (c) workers on vacation, the correct option is (d).
The Bureau of Labor Statistics (BLS) is a unit of the US Department of Labor that is responsible for collecting, analyzing, and publishing data on labor market activity, working conditions, and price changes in the economy.
The Bureau of Labor Statistics (BLS) considers individuals to be employed if they meet any of the given criteria:
(i) Worked at least one hour as paid employees
(ii) Worked at least 15 hours as unpaid workers in a family-owned enterprise
(iii) Were temporarily absent from their regular jobs due to illness, vacation, strike, etc.
⇒ This means that certain unpaid workers, such as family members working in a family-owned business, would be considered employed by the BLS.
⇒ Part-time workers, who work less than 35 hours per week but are paid for their work, are also included in the employed category.
⇒ The Workers on vacation are considered employed by the BLS because they are temporarily absent from their job.
Therefore, all the options are correct , which is Option(d).
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The given question is incomplete, the complete question is
Who of the following are included in the Bureau of Labor Statistics "employed" category?
(a) certain unpaid workers
(b) part-time workers
(c) workers on vacation
(d) All of the above are correct.
Converting
What is 3.4 hours in hours and minutes?
By answering the presented questiοn, we may cοnclude that 0.4 οf an expressiοns hοur is 0.4 x 60 = 24 minutes in this situatiοn. As a result, 3.4 hοurs equals 3 hοurs and 24 minutes.
What is expressiοn ?An expressive in mathematics is a collection of numbers, variables, and complicated mathematical operations (such as addition, subtraction, multiplication, division, multiplicands, and others) that convey a quantity's value. Expressions can be as straightforward as "3 + 4" or as complex as "(3x2 - 2) / (x + 1)". They could also include functions like "sin(x)" or "lg(y)".
The real way to evaluate an expression is to insert the variables with their values and carry out the arithmetic operations in the order specified. For instance, the phrase "3x + 5" means 3(2) + 5 = 11 if x = 2. In mathematics, expressions are typically used to describe actual situations, build equations, and decompose challenging mathematical diagrams.
3 hοurs and 24 minutes is cοmparable tο 3.4 hοurs.
Yοu may separate the full number (which represents the hοurs) frοm the decimal tο cοnvert decimal hοurs tο hοurs and minutes (which represents the fractiοn οf an hοur in minutes).
0.4 οf an hοur is 0.4 x 60 = 24 minutes in th
is situation. As a result, 3.4 hours equals 3 hours and 24 minutes.
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let v be the set of all positive real numbers. determine whether v is a vector space with the following operations. x y
V is not a vector space, since at least one of the vector space axioms fails. Specifically, the axiom of closure under addition fails, since for any positive real numbers x and y, their sum xy may not be positive.
V is not a vector space, since some of the vector space axioms fail with the given operations.
Closure under addition fails For example, taking x=2 and y=3, we have xy = 6, but xy is not a positive real number, so xy is not in V.
Distributivity of scalar multiplication over vector addition fails For example, taking x=2, y=3, and c=-1, we have c(x+y) = cxy = -6, but cx + cy = -2 -3 = -5, which is not in V.
Other vector space axioms, such as associativity of addition, existence of additive identity and inverse, and compatibility of scalar multiplication with field multiplication, are still satisfied with the given operations.
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_____The given question is incomplete, the complete question is given below:
Let V be the set of all positive real numbers. Determine whether V is a vector space with the following operations. x + y = xy Addition cx = x Scalar multiplication If it is, then verify each vector space axiom; if it is not, then state all vector space axioms that fail. STEP 1: Check each of the 10 axioms. (1) U + v is in V. This axiom holds. This axiom fails. (2) U + V = V + u This axiom holds. This axiom fails. (3) U+ (v + w) = (u + v) + w This axiom holds. This axiom fails. STEP 2: Use your results from Step 1 to decide whether V is a vector space. O V is a vector space. O Vis not a vector space.
Letsha wants to produce 80 pages information books for school project. She can have this done at local printing company at R0.35 per page.
Answer:
if u want total price then,
=Rs.35×80=Rs.2800
PLEASE HURRY!!
Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle? Please show your work.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%
What is Conditional probability?
Conditional probability is the probability of an event occurring given that another event has occurred or is known to have occurred. It is denoted by P(A|B), which reads as "the probability of A given B."
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.
The total number of Plastic #2 bottles is 8 (correctly placed) + 5 (incorrectly placed) = 13.
The total number of Plastic #4 bottles is 5 (correctly placed) + 2 (incorrectly placed) = 7.
The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is given by:
(number of Plastic #4 bottles correctly placed) / (total number of bottles)
So the probability is:
5/20 = 1/4 = 0.25
Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.
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k is what or is it none for the equation?
The piecewise function will be continuous in its domain if k = 49/48
How to find the value of k such that the function is continuous?Here we have a piecewise function and we want to find the value of k suc that the function is continuous on the domain.
To get that, both piecese of the function must ahve the same value in the jump, then we will get:
f(7) = f(7)
Replacing the functions we will get:
k·7² = 7·7 + k
Let's solve that equation for k.
49k = 49 + k
49k - k = 49
48k = 49
k = 49/48
That must be the value of k such that the function is continuous in all its domain.
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