The vector sum [tex]\mathbf{u}+\mathbf{v}[/tex] is approximately equal to [tex]3.9\left < \cos 26^{\circ},,\sin 26^{\circ}\right > , 3.9⟨cos26∘, sin26∘⟩[/tex] in magnitude and direction form.
To find the sum of two vectors, we add their corresponding components. In this case, [tex]\mathbf{u}+\mathbf{v} = 7\left < \cos 0^{\circ},,\sin 0^{\circ}\right > + 4\left < \cos 135^{\circ},,\sin 135^{\circ}\right >[/tex]. Evaluating the x- and y-components separately, we get:
[tex]\mathbf{u}+\mathbf{v} = (7\cos 0^{\circ} + 4\cos 135^{\circ}),\mathbf{i} + (7\sin 0^{\circ} + 4\sin 135^{\circ}),\mathbf{j}[/tex]
[tex]\mathbf{u}+\mathbf{v} = 3.9,\left < \cos 26^{\circ},,\sin 26^{\circ}\right >[/tex]
To write the answer in magnitude and direction form, we can use the ormula [tex]\left|\mathbf{u}+\mathbf{v}\right| = \sqrt{(u_1+v_1)^2 + (u_2+v_2)^2}[/tex] for the magnitude, and [tex]\theta = \tan^{-1}\left(\frac{u_2+v_2}{u_1+v_1}\right)[/tex] for the direction. Plugging in the values, we get:
[tex]\left|\mathbf{u}+\mathbf{v}\right| \approx 3.9\theta \approx 26^{\circ}[/tex]
Therefore, the vector sum [tex]\mathbf{u}+\mathbf{v} is approximately equal to 3.9\left < \cos 26^{\circ},,\sin 26^{\circ}\right > , 3.9⟨cos26∘, sin26∘⟩[/tex] in magnitude and direction form.
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a researcher tests for a post-test versus pre-test difference. she gets a 95% confidence interval for the mean difference of (-0.5, 3.5). what is true about the p-value for the test of whether or not there is a difference between the post- and pre- tests?
We cannot determine the p-value for the test of whether or not there is a difference between the post- and pre-tests from the given information.
The confidence interval indicates the range of values that the true population mean difference is likely to fall within with 95% confidence. If the interval contains zero, then we cannot reject the null hypothesis that there is no difference between the post- and pre-tests. However, we don't know the exact p-value for this test based on the confidence interval alone.
To determine the p-value, we would need to know the sample mean difference, the standard error of the mean difference, and the sample size. With these values, we could calculate the test statistic and look it up in a t-distribution table or use software to find the p-value.
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a fact starts with a relationship followed by a list of arguments. the arguments of a fact group of answer choices must be variables. must be simple values. can have a structure similar to that of a rule. can have a structure similar to that of a fact.
A fact is a statement that is considered to be true based on evidence or experience. It starts with a relationship, which expresses a connection or correlation between two or more entities, and is followed by a list of arguments.
The arguments of a fact can be variables, which represent unknown values, or simple values, such as numbers or strings. In some cases, a fact can have a structure similar to that of a rule, which defines a set of conditions that must be satisfied for the fact to be true. However, unlike a rule, a fact is not conditional and is considered to be true at all times.
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Express the confidence interval 0.333 < p < 0.777 in the form p +-E.
p +- E= ___ +- ____
The confidence interval 0.333 < p < 0.777 can be expressed in the form p +- E as 0.555 +- 0.222.
The confidence interval 0.333 < p < 0.777 gives a range of possible values for the true population proportion, p, with a certain level of confidence. To express this interval in the form p +- E, we need to find the midpoint of the interval, which is (0.333 + 0.777)/2 = 0.555. This midpoint represents the best estimate of the true population proportion based on the sample data.
To find the margin of error, E, we need to calculate half of the width of the confidence interval, which is (0.777 - 0.333)/2 = 0.222. The margin of error represents the maximum amount by which the sample proportion may differ from the true population proportion.
Therefore, the confidence interval 0.333 < p < 0.777 can be expressed in the form p +- E as 0.555 +- 0.222.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. In this case, the confidence interval 0.333 < p < 0.777 gives a range of possible values for the true population proportion, p, with 95% confidence. This means that if we were to repeat the sampling process many times and construct a confidence interval each time, about 95% of the intervals would contain the true population proportion.
To express the confidence interval in the form p +- E, we need to find the midpoint of the interval, which is (0.333 + 0.777)/2 = 0.555. This midpoint represents the best estimate of the true population proportion based on the sample data.
The margin of error, E, represents the maximum amount by which the sample proportion may differ from the true population proportion. To find the margin of error, we need to calculate half of the width of the confidence interval, which is (0.777 - 0.333)/2 = 0.222. This means that the sample proportion could vary by up to 0.222 in either direction from the midpoint of the interval.
Therefore, the confidence interval 0.333 < p < 0.777 can be expressed in the form p +- E as 0.555 +- 0.222. This means that we are 95% confident that the true population proportion falls within the range of 0.333 to 0.777, with the best estimate of the true population proportion being 0.555 and a margin of error of 0.222.
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One day the school cafeteria sells 1380 lunches. 866 of those lunches included a fruit and 468 included a vegetable. 233 lunches included both a fruit and a vegetable. Brady sees this question: ""how many lunches included a fruit or a vegetable?""
Brady sees 1101 lunches included a fruit or a vegetable.
To find out how many lunches included a fruit or a vegetable, we need to add the number of lunches that included a fruit to the number of lunches that included a vegetable, and then subtract the number of lunches that included both a fruit and a vegetable (since we don't want to count these twice).
So, lunches that included a fruit or a vegetable = (lunches with fruit) + (lunches with vegetable) - (lunches with both fruit and vegetable)
lunches that included a fruit or a vegetable = 866 + 468 - 233
lunches that included a fruit or a vegetable = 1101
Therefore, 1101 lunches included a fruit or a vegetable.
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Solve for X using SOH-CAH-TOA
Answer:
The value of x is 10cm
Step-by-step explanation:
The triangle given is a right angled triangle.
so two angles of the triangle is known,
let it be a=45
b= 90
and c=45, since its a right angled triangle.
to find out the sides of the triangle, we use the formula
tan45= opposite side/ adjacent side= 10/x; value of tan 90 is 1
so, 1= 10/x
x= 10cm
This is basically using SOH CAH TOA method, that is, sine theeta cosine theeta and tangent theeta.
Mickey and Jenny Porter file a joint tax return, and they itemize deductions. The Porters incur $3,800 in investment expenses. They also incur $6,000 of investment interest expense during the year. The Porters’ income for the year consists of $186,000 in salary and $5,020 of interest income. B. What would their investment interest expense deduction be if they also had a ($2,840) long-term capital loss?
If the Porters also had a ($2,840) long-term capital loss, their investment interest expense deduction would be $5,160.
To calculate their investment interest expense deduction, we first need to determine their adjusted gross income (AGI). Their AGI is calculated by subtracting the investment expenses ($3,800) and the long-term capital loss ($2,840) from their total income, which is $186,000 + $5,020 = $191,020 - $3,800 - $2,840 = $184,380.
Next, we need to calculate their investment interest expense limitation. This is equal to their investment income, which is $5,020. Since their investment interest expense ($6,000) is greater than their investment income, their investment interest expense deduction is limited to the excess of investment interest expense over investment income, which is $6,000 - $5,020 = $980.
Finally, we need to adjust their investment interest expense deduction for the long-term capital loss. Since the Porters have a long-term capital loss, they can only deduct investment interest expense up to the amount of net investment income after taking into account the long-term capital loss. Their net investment income is $5,020 - $2,840 = $2,180. Therefore, their investment interest expense deduction is limited to $2,180, which is less than the amount of investment interest expense they incurred. Thus, their investment interest expense deduction is $2,180, plus the amount of investment interest expense they could not deduct due to the limitation, which is $980. Therefore, their total investment interest expense deduction is $3,160.
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help asap! i realy need help! i will give Who deserves the Brainliest award?!
The absolute value function that matches the graph is given as follows:
y = |x|
How to define the absolute value function?An absolute value function of vertex (h,k) is defined as follows:
y = a|x - h| + k.
The vertex of the function in this problem is at the origin, hence:
(h,k) = (0,0).
The leading coefficient is of a = 1, as when x = 1, y = 1.
Hence the absolute value function that matches the graph is given as follows:
y = |x|
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Calculating prices using discounts and tax rates
PLEASE HELP!! LIMITED TIME & WILL GIVE POINTS!
The grade distribution of the many students in a geometry class is as follows.
Find the probability that a student earns a grade of A
P( A ) = [?]
Answer:
The probability is 2/10 or 0.2
Step-by-step explanation:
Probability of student getting grade A=number of students who will get grade A/Total number of students grade
T(s)=28+35+56+14+7=140
P=28/140
P=2/10 or 0.2
Towns K and L are shown on a map.
a) Work out the actual distance between towns K and L.
b) A third town, M, is 150 km due
South of town K.
Mark Mon the map with X.
c) Measure the bearing of town L from town K.
a) The actual distance between towns K and L is: 100 km
b) As shown in the attached file
c) The bearing of town L from town K is 117 degrees.
How to Interpret the map?The scale of the map is given as:
1 cm to represent 50 km
Now, when we measure the distance between K and L on the map, we see that it gives us a distance of 2 cm.
Using the scale of 1 cm: 50 km, we can say that:
Actual distance between towns K and L = (2 * 50)/1 = 100 km
b) Using a compass and it’s 3cm aiming down {South} as seen in the attached photo. Then a line was drawn aiming {South} with a ruler. On the end of the line the (x) point was put there to get the mark.
c) Measuring the angle gives the bearing of town L from town K which is 117 degrees.
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I need to know the answer
The value of the angle m∠MQN of the given rectangle is: 76°
How to find the missing angle in the rectangle?Some of the properties of rectangles are:
A rectangle is defined as a quadrilateral that has four equal interior angles.
The opposite sides of a rectangle are equal and parallel to each other.
The interior angle of a rectangle at each vertex measures 90°.
The sum of all the interior angles of a rectangle is 360°.
The diagonals bisect each other.
The length of the diagonals is equal.
The length of the diagonals can be obtained using the Pythagoras theorem. The length of the diagonal with sides a and b is √( a² + b²).
Since the sides of a rectangle are parallel, it is also called a parallelogram.
All rectangles are parallelograms but all parallelograms are not rectangles.
We are given that m∠NQO = 104°.
Sum of angles on a straight line is 180°. Thus:
m∠MQN = 180 - 104
m∠MQN = 76°
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in one-way anova where there are x treatments and y observations, the degrees of freedom for the f statistic are:
In case of one-way anova where x are treatments and y are observations, the degrees of freedom for the f statistic are three and 20.
A one way analysis of variance refers to the technique that is used in knowing if there's significant difference between two samples means. ANOVA uses F-tests to statistically test the equality of means.
Now, if x and y are represented the number of treatments and observations then degree of freedom for f statistic is either 3 or 20. Because two separate samples are used to compute a F-score and the samples with different size, so, there are two separate degrees of freedom one for each sample, either it is three or twenty. Hence, required value either 3 or 20.
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A sphere of radius r has surface area A = 4πr2 and volume V = 4 3 πr3. The radius of sphere 2 is four times the radius of sphere 1. (a) What is the ratio of the areas, A2/A1? (b) What is the ratio of the volumes, V2/V1?
(a) The ratio of the areas, A2/A1, is (4π[tex]r^{2}[/tex])/π[tex]r^{2}[/tex] = 16.
(b) The ratio of the volumes, V2/V1, is (4/3)π[tex]4r^{3}[/tex] / (4/3)π[tex]r^{3}[/tex] = 64.
(a) Given that the radius of sphere 2 is four times the radius of sphere 1, let's denote their radii as r1 and r2 = 4r1. The surface areas A1 and A2 can be calculated as follows:
A1 = 4πr1^2
A2 = 4π(4r1)^2 = 4π(16r1^2) = 64πr1^2
To find the ratio A2/A1:
A2/A1 = (64πr1^2) / (4πr1^2) = 64/4 = 16
So, the ratio of the areas is 16:1.
(b) Similarly, let's calculate the volumes V1 and V2:
V1 = (4/3)πr1^3
V2 = (4/3)π(4r1)^3 = (4/3)π(64r1^3) = 64(4/3)πr1^3
To find the ratio V2/V1:
V2/V1 = (64(4/3)πr1^3) / ((4/3)πr1^3) = 64
So, the ratio of the volumes is 64:1.
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I forgor to add the options for the term part, please help!!! 45 points, please only choose from the options..
Zelda is a plant geneticist and needs to see the internal details of plant cells. She needs a very high power of resolution. Which microscope should she choose?
Compound light microscope
Common light microscope
Dissecting microscope
Scanning electron microscope
To see the internal details of plant cells with a very high power of resolution, Zelda should choose a Scanning Electron Microscope (SEM).
A Scanning Electron Microscope uses a beam of electrons to produce high-resolution images of the surface of an object.
It provides a much higher resolution than a compound light microscope or a dissecting microscope, allowing for detailed observations of the internal structures of plant cells at a subcellular level.
A compound light microscope and a dissecting microscope are both optical microscopes that use visible light to produce an image.
While they can be used to observe plant cells, they have a much lower resolution than an SEM and may not provide the level of detail required for Zelda's research.
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A machine used for filling plastic bottles with a soft drink has a known standard deviation of σ=0.05 liter. The target mean fill volume is μ=2.0 liters
(a) Describe the sampling distribution of the sample mean fill volume, for a random sample of 45 such bottles. Is the distribution normal? why/why not? Compute the mean and the standard deviation for a random sample of 45 bottles. Round 4 decimals (b) What is the probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters? Round 4 decimals
There is an 86.06% chance that the sample mean fill volume for a random sample of 45 bottles will fall between 1.98 and 2.02 liters.
The sampling distribution of the sample mean fill volume for a random sample of 45 bottles is approximately normal by the Central Limit Theorem, provided that the sample size is sufficiently large. The mean of the sample mean fill volume is equal to the target mean fill volume, μ=2.0 liters.
The standard deviation of the sample mean fill volume is equal to the standard error of the mean, which is σ/√n = 0.05/√45 ≈ 0.0075 liters.
To find the probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters, we need to standardize the values using the formula z = (x - μ) / (σ / √n), where x is the sample mean, μ is the target mean, σ is the standard deviation of the population, and n is the sample size.
Thus, we have z1 = (1.98 - 2.0) / (0.05 / √45) ≈ -1.79 and z2 = (2.02 - 2.0) / (0.05 / √45) ≈ 1.79.
Using a standard normal distribution table or calculator, we find that the probability is approximately 0.8606. Therefore, there is an 86.06% chance that the sample mean fill volume for a random sample of 45 bottles will fall between 1.98 and 2.02 liters.
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The probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters is approximately 0.9934 or 99.34%.
(a) The sampling distribution of the sample mean fill volume for a random sample of 45 bottles is approximately normal due to the Central Limit Theorem. The mean of the sampling distribution is equal to the target mean fill volume, which is μ = 2.0 liters. The standard deviation of the sampling distribution, also known as the standard error of the mean, is σ/√n, where σ is the standard deviation of the population and n is the sample size. Therefore, the standard error of the mean is:
SE = σ/√n = 0.05/√45 = 0.00746
So the mean and standard deviation of the sampling distribution are:
Mean = μ = 2.0 liters
Standard deviation = SE = 0.00746 liters
(b) We want to find the probability that the sample mean of 45 bottles is between 1.98 and 2.02 liters. We can standardize the values using the formula:
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error of the mean. Thus:
z1 = (1.98 - 2.0) / 0.00746 = -2.68
z2 = (2.02 - 2.0) / 0.00746 = 2.68
Using a standard normal distribution table or calculator, we can find the probability that z is between -2.68 and 2.68:
P(-2.68 < z < 2.68) = 0.9967 - 0.0033 = 0.9934
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Does a population have to be normally distributed in order to use the chi-square distribution? Choose the correct answer below. O A No, in order to use the chi-square distribution, the population must be exponentially distributed. OB. No, the population can have any distribution to use the chi-square distribution OC. No, in order to use the chi-square distribution, the population must have a standard normal distribution OD. Yes, in order to use the chi-square distribution, the population must be normally distributed.
Does a population have to be normally distributed in order to use the chi-square distribution? Choose the correct answer below B. No, the population can have any distribution to use the chi-square distribution.
The chi-square distribution is commonly used to test the goodness-of-fit between an observed distribution and an expected distribution (which can be any theoretical distribution). It is not necessary for the population to be normally distributed or follow any specific distribution to use the chi-square test.
The chi-square distribution can be used with any population distribution, not just the normal distribution or any other specific distribution.
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Select the expression equivalent to ( 4x + 3) + ( -2x + 4)
The given expression is (4x + 3) + (-2x + 4). To simplify the expression, we first combine like terms.
(4x + 3) + (-2x + 4) = 4x - 2x + 3 + 4 = 2x + 7
Therefore, the expression equivalent to (4x + 3) + (-2x + 4) is 2x + 7.
When adding or subtracting two expressions, we combine like terms by adding or subtracting the coefficients of the same variables. In the given expression, we have two terms, (4x + 3) and (-2x + 4).
We can first rearrange the terms by adding the coefficients of x and constants separately. By doing so, we obtain 4x - 2x and 3 + 4, which simplify to 2x and 7, respectively. Thus, we have the expression 2x + 7 as the simplified form of the given expression.
This is a useful technique when simplifying algebraic expressions and can be used to simplify more complex expressions involving multiple variables and terms.
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Your aunt gives you $50 to help buy the reflector telescope, you have $25.50 left. How much money did you have before your aunt gave you $50?
You had $24.50 before your aunt gave you $50 to help buy the reflector telescope
If your aunt gave you $50 and you now have $25.50 left after buying the reflector telescope, then you spent:
$50 - $25.50
Fifty minus twenty five point five
We get twenty four point five
= $24.50
Therefore, you had $24.50 before your aunt gave you $50 to help buy the reflector telescope
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A hot air balloon is descending with a constant velocity of 3 ms when somebody inside the balloon throws an apple downward with a velocity of 5 m.s¹. The apple strikes the ground after 2,5 8. Calculate:
a) the velocity with which the apple strikes the ground
The velocity with which the apple strikes the ground is 2 m/s.
In every case, we add the speed of the object (relative to the reference point) to the speed of the reference point (relative to the ground) to find the speed of the object relative to the ground. (We choose to use + to mean "up" or "forward".)
The hot air balloon is descending with a constant velocity of 3 ms. when somebody inside the balloon throws an apple downward with a velocity of 5 m.s¹ so the velocity with which the apple strikes the ground
... (3m/s) + (-5m/s) = -2m/s
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please help!!!!!! will mark brainlest
The given expressions are a+12, 7+a, a+7, & 5a.
The given values 1, 3 & 4 are substituted in the given expressions as follows
For value 1 the expressions will be given as follows
1+12=13, 7+1=8, 1+7=8 & 5*1=5
For value 3 the expressions will be given as follows
3+12=15, 7+3=10,3+7=10 & 5*3=15
For value 4 the expressions will be given as follows
4+12=16, 7+4=11,4+7=11 & 5*4=20
From the obtained results above it is clear that expressions a+7 & 7+a are equal for all possible values as the result obtained from them is same irrespective of the value substituted.
Similarly, the expressions a+12 & 5a are equivalent for a = 3 as the result obtained is same on substituting a=3 but it is not true for all other values.
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Hi, I need help with this question.
The value of the angles m∠A is 95 degrees, m∠BOT is 195 degrees, m∠ATO is 40 degrees and m∠PBQ is 40 degrees.
First, let's find the measure of angle m∠A. Since PT is tangent to circle O, we know that angle m∠T is a right angle (90 degrees). Since arc AB and arc BT add up to the whole circle (360 degrees), we can find their measures as follows:
m(arc AB) = m(arc OB) - m(arc OA)
= 360 - m(arc OA)
= 360 - 2m∠P (since m∠P = m(arc OA)/2)
= 360 - 2(40) = 280
m(arc BT) = 180 - m∠T (since arc BT is a minor arc and m(arc BT) = 180 - m∠T)
= 180 - 90 = 90
Therefore, m∠A = (m(arc AB) - m(arc BT))/2 = (280 - 90)/2 = 95 degrees.
Next, let's find the measure of angle m∠BOT. Since PT is tangent to circle O, we know that angle m∠T is a right angle (90 degrees).
This gives us:
m∠BOT = 1/2 (m(arc BA) - m(arc BT))
= 1/2 (m(arc OA) + m(arc AB) - m(arc BT))
= 1/2 (2m∠P + 280 - 90) (using the same arc measures as before)
= 1/2 (2(40) + 190)
= 135 degrees.
Next, let's find the measure of angle m∠ATO. This is the angle between the secant PBOA and the tangent PT, on the opposite side of point T from angle m∠BOT.
We can use the alternate segment theorem, which states that the angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment. In this case, angle m∠ATO is equal to angle m∠P.
Therefore, m∠ATO = 40 degrees.
Finally, let's find the measure of angle m∠PBQ. In this case, angle m∠PBQ is congruent to angle m∠P, which we have already found to be 40 degrees. Therefore, m∠PBQ = 40 degrees.
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help please today NOW
photo below help
Answer:
a) 15
b) 10
Step-by-step explanation:
a) [tex]3\sqrt{25}[/tex]
[tex]\sqrt{25}=5\\ 5(3)\\=15[/tex]
b) [tex]\sqrt{(2(50))}\\\sqrt{100}\\ =10[/tex]
Hope this helps! Let me know if you need clarification.
je suis un nombre entier compris entre 50 et 70 qui est un multiple de 6 et qui est divisible par 5 qui suis-je ?
Answer:
54 et 60 sont les multiples de 6 entre 50 et 70
Find the quotient if the dividend is 4.38 · 10^6and the divisor is 0.0024.
1.05 · 10 8
1.825 · 10 3
5.48 · 10 4
1.825 · 10 9
Question 12 of 25
The function f(x) = 4(2)* represents the number of people who share a cat
video x hours after it first appears on a website. How does the number of
people sharing the video change each hour?
OA. The number increases by 2 each hour.
OB. The number increases by 4 each hour.
OC. The number doubles each hour.
OD. The number increases by a factor of 4 each hour.
The number of people sharing the video doubles each hour.
Calculating how the number of people sharing the video change each hour?From the question, we have the following parameters that can be used in our computation:
f(x) = 4(2)ˣ
The above function is an exponential function
Where
x represents the number of hours after the first time it appears
An exponential function is represented as
f(x) = a(b)ˣ
Where
a = initial value = 4
b = rate = 2
This means that the number of the video doubles each hour i.e. b is correct
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how can we measure the opportunity cost of leisure? the opportunity cost of leisure is
The opportunity cost of leisure can be measured by calculating the cost of the next-best alternative that could have been pursued instead of leisure.
To measure the opportunity cost of leisure, follow these steps:
Step 1: Identify the alternatives to leisure time. These can include activities like working, studying, or doing household chores.
Step 2: Determine the value of these alternative activities. For example, if you choose to work instead of enjoying leisure time, the value can be the income you would earn during that time.
Step 3: Compare the values of the alternative activities to the value of leisure. The opportunity cost of leisure is the highest value among these alternatives that you give up by choosing leisure. For example, if someone decides to spend an hour watching TV instead of working on a freelance project that could earn them $50, the opportunity cost of leisure in this case would be $50.
In summary, the opportunity cost of leisure is the value of the best alternative activity you forgo when choosing to spend time on leisure activities.
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What does "Y" equal (m
The value of y is given as follows:
y = 12.
How to obtain the value of x?The value of x is obtained applying the angle bisection theorem, which divides an angle into two angles of equal measure, hence the opposite segments also have equal length.
The segments for this problem, along with their lengths, are given as follows:
AD = 3y + 6.CD = 5y - 18.Hence the value of y is obtained as follows:
5y - 18 = 3y + 6
2y = 24
y = 12.
(due to the angle bisection theorem, both segments have equal length, hence we equal their lengths to obtain the variable y).
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Construct triangle XYZ in which XY= 8.3xm, YZ= 11.9cm. ii, Construct M the midpoint of XZ where angle YXZ= 60. III, Measure YM.
The length of YM in triangle XYZ, where XY = 8.3 cm and YZ = 11.9 cm, is approximately 2.77 cm.
To construct triangle XYZ with XY = 8.3 cm and YZ = 11.9 cm:
i. Start by drawing a line segment XY with a length of 8.3 cm.
ii. From point X, draw a line segment in the direction of YZ, measuring 11.9 cm. Label the endpoint as Z.
iii. Connect points Y and Z to complete the triangle XYZ.
To construct the midpoint M of XZ with angle YXZ = 60 degrees:
i. Draw a ray from point Y, forming an angle of 60 degrees with line segment YZ. Label the point where the ray intersects XY as M.
ii. Construct a line segment from point M perpendicular to line segment XY. This line segment will intersect line segment XZ at the midpoint M.
The length of YM can be calculated using the Pythagorean theorem.
If we let XZ = a, then XZ/2 = XM = MZ = a/2.
Using the angle YXZ = 60 degrees, we can write the length of YM as:
YM = [tex]\sqrt{(XM^2 + YX^2)} = \sqrt{((a/2)^2 + (8.3-a)^2)[/tex]
We can solve for a by setting the derivative of YM with respect to a to zero and solving for a, which yields a value of a = 4.85 cm.
Therefore, the length of YM is:
YM = [tex]\sqrt{((4.85/2)^2 + (8.3-4.85)^2)[/tex] = [tex]\sqrt{(7.686)[/tex] ≈ 2.77 cm.
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at a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 750 milliliters of water. the technician dispenses 38 samples of water and determines the volume of each sample. the 38 samples have a sample mean volume of 751.1 ml. the machine is out of calibration if the mean volume differs from 750 ml. the technician wants to perform a hypothesis test to determine whether the machine is out of calibration. the population standard deviation of the dispensed volume is known to be 5.1. compute the value of the test statistic.
Answer:
Step-by-step explanation:
near 9000
