Thus, angle q can either measure approximately 65.1 degrees or approximately 114.9 degrees.
To find all possible measures for angle q in triangle PQR, we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab cos(C)
where c is the length of the side opposite the angle we are trying to find (in this case, side q), and a and b are the lengths of the other two sides.
Plugging in the given values, we get:
85^2 = 45^2 + b^2 - 2(45)(b) cos(37°)
Simplifying and solving for b, we get:
b = 81.5 cm or b = 128.5 cm
However, we can only accept the solution b = 81.5 cm since the other value (b = 128.5 cm) would result in side b being longer than side c (which is not possible in a triangle).
So, the possible measures for angle q are:
q = 65.1° or q = 114.9°
Therefore, angle q can either measure approximately 65.1 degrees or approximately 114.9 degrees.
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Each chair that is added to this stack makes it 8cm taller. One chair is 55cm tall. Use your knowledge of patterns to find how high a stack of chairs will be that has 8 chairs in it. 1.5.1 Write down the constant difference 1.5.2 Using the general rule, determine how many chairs would there be if the stack was 127cm high?
Answer:
1.5.1 : constant difference is 8
1.5.2: When there are 10 chairs stacked, it's 127 cm tall.
Step-by-step explanation:
There is a linear relationship between the height of the stack and the number of chairs.
1 chair = 55 cm + 0 extra cm = 55cm
2 chairs = 55cm + 8cm = 63 cm
3 chairs = 55cm + 8(2)cm = 71 cm
4 chairs = 55cm + 8(3)cm = 79 cm
1.5.1 the constant difference between all the underlined numbers above is 8.
1.5.2 You could just keep calculating above until you get 127 cm. (Your teacher might not like that, but it's an option!)
You can find the equation & either solve for the number of chairs OR graph it.
So if we let C = the number of stacked chairs, our equation for H (height) would be:
H = 55 + 8(C-1)
If we substitute H = 127, solve for C.
127 = 55+ 8(c-1)
127 = 55+ 8c-8
127 = 47 + 8c
127 -47 = 8c
80 = 8c
10=c
When there are 10 chairs stacked, it's 127 cm tall.
Check that the answer works:
55 cm (1st chair) + 8*9 (8cm for each additional chair) = 55+ 72 = 127 cm
Two dice are rolled. What is the probability that at least one dice is showing a 2, given that the sum of the numbers on the dice is no more than 6?
The probability that at least one die is showing 2 and the sum of the two dice is 6 is 1/18
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it equivalent to 100% in percentage.
Probability = sample space /total outcome
The possible total out come for rolling two dice is 36.
For two dice two have a sum of 6 and at least one must show 2, the result must either be 2,4 or 4,2. Therefore the sample space is 2
Therefore the probability of at least one die showing 2 and sum of 6 = 2/36 = 1/18
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The number line below shows the
number of days Amaya spends
practicing the guitar every week.
0 1
2 3 4 5 6 7
Which inequality BEST represents the
number of days, d, she practices?
A d≤ 5
B d≥ 5
© d < 5
D d > 5
Answer:
The answer to your question is B) d≥ 5 because the best inequality that represents the number of days Amaya practices the guitar is "greater than or equal to 5". This is because Amaya practices the guitar at least 5 days a week, so the inequality that represents this would be d≥ 5.
Answer:
B
Step-by-step explanation:
Based on the given number line, we can see that the number of days Amaya practices the guitar falls on and to the right of the number 5. Since the number line is inclusive of 5, it means that Amaya practices for 5 days or more in a week.
Therefore, the inequality that BEST represents the number of days, d, she practices is:
B) d ≥ 5
This inequality indicates that the number of days Amaya practices (d) is greater than or equal to 5.
PLEASE HELP URGENT!!!
The exponential regression of the data is y = 3.143 * 6.064ˣ
What is the exponential regression equation for the following data?Exponential regression is a statistical technique used to model and analyze data that follows an exponential trend. It involves finding the equation of an exponential function that best fits a set of data points. The exponential regression equation has the general form:
y = abˣ
where y is the dependent variable, x is the independent variable, and a and b are the regression coefficients to be determined.
From the given data;
The regression equation is y = 3.143 * 6.064ˣ
The correlation of the data (r) = 0.9941
The r-squared of the data (r²) = 0.9883
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it is known that the population variance (σ2) is 144. at 95onfidence, what sample size should be taken so that the margin of error does not exceed 5?
A sample size of at least 139 should be taken to ensure that the margin of error does not exceed 5, with a population variance of 144 and a 95% confidence level.
Margin of error = Z-score * (σ / √n)
where Z-score is the critical value for the level of confidence (in this case, 95%), σ is the population standard deviation (which is equal to the square root of the variance, so σ = 12), and n is the sample size.
We want the margin of error to be less than or equal to 5, so we can set up the following inequality:
5 ≥ Z-score * (σ / √n)
To find the value of the Z-score for 95% confidence, we can use a standard normal distribution table or calculator. The Z-score for 95% confidence is approximately 1.96.
Substituting the values we have into the inequality, we get:
5 ≥ 1.96 * (12 / √n)
Solving for n, we get:
n ≥ ((1.96 * 12) / 5)²
n ≥ 138.2976
Since we cannot have a fractional sample size, we need to round up to the nearest whole number:
n = 139
Therefore, a sample size of at least 139 should be taken to ensure that the margin of error does not exceed 5, with a population variance of 144 and a 95% confidence level.
In summary, the long answer to your question is that we used the formula for the margin of error, substituted the given values, solved for n, and rounded up to get a sample size of 139.
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Use your knowledge of complementary and vertical angles to hit
this shot.
54°
B=
The value of the complementary angle of 54° is determined as B = 36°.
What is a complementary angle?Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.
So if the measure of one angle is 54°, the value of its complementary angle is calculated as follows;
Mathematically, the formula for calculating the complementary angle of 54° is given as;
B + 54° = 90
B = 90 - 54°
B = 36°
Thus, the value of the complementary angle of 54° is determined as 36° since both angles will add up to 90 degrees.
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The complete question is below:
Use your knowledge of complementary and vertical angles to hit
this shot.
If angle A is 54° and angle B is its complementary angle. Angle B = ?
A 3-phase, 6-pole induction motor runs on no-load at 1160 rpm. Determine the slip and frequency of rotor currents on no-load.
The frequency of the rotor currents on no-load is fr = 0.033 * 60 = 1.98 Hz.
The synchronous speed of the motor is given by
Ns = (120f) / P,
where Ns is the synchronous speed in revolutions per minute (RPM), f is the supply frequency in hertz (Hz), and P is the number of poles.
For the given motor, the synchronous speed is
Ns = (120 * 60) / (6 * 2) = 1200 RPM
On no-load, the rotor speed is equal to the synchronous speed, i.e., N = Ns = 1200 RPM.
The slip of the motor is given by
s = (Ns - N) / Ns,
where N is the rotor speed in RPM.
Thus, the slip of the motor is
s = (1200 - 1160) / 1200 = 0.033 or 3.3%
The frequency of the rotor currents on no-load is given by
fr = s * f,
where f is the supply frequency.
Thus, the frequency of the rotor currents on no-load is
fr = 0.033 * 60 = 1.98 Hz
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A solid is made from a hemisphere and a cylinder
The plane face of the hemisphere coincides with the upper plane face
of the cylinder
The hemisphere and the cylinder have the same radius. The ratio of the Radius at the cylinder to the
height of the cylinder is 1:3 given that the solid has volume 792 pi cm^3 . work out the height of the solid
Let's denote the radius of both the hemisphere and the cylinder as "r" and the height of the cylinder as "h".
The volume of the solid is given as 792π cm^3.
The volume of the hemisphere is (2/3)πr^3, and the volume of the cylinder is πr^2h. Since the solid is made up of a hemisphere and a cylinder, we can write the equation:
(2/3)πr^3 + πr^2h = 792π
We can simplify the equation by dividing both sides by π:
(2/3)r^3 + r^2h = 792
Given that the ratio of the radius to the height is 1:3, we can write r = 3h.
Substituting this value into the equation, we get:
(2/3)(3h)^3 + (3h)^2h = 792
Simplifying further:
(2/3)(27h^3) + 9h^3 = 792
18h^3 + 9h^3 = 792
27h^3 = 792
Dividing both sides by 27:
h^3 = 792/27
h^3 = 29.333...
Taking the cube root of both sides:
h ≈ 3.080
Therefore, the height of the solid is approximately 3.080 cm.
Kindly Heart and 5 Star this answer, thanks!Solve for x. Options are: 3,4,5,and 6.
Answer:
[B] 3
Step-by-step explanation:
We can set up a proportion to solve for x:
[tex]\frac{15}{10} =15+\frac{x}{12}[/tex]
[tex]10(15 + x) = 15(12)[/tex] >> Distribute
[tex]150 + 10x = 180[/tex] >> Subtract 150 from both side
[tex]10x = 30[/tex] >> Divide both side by 10
[tex]x=3[/tex] >> Solution
~ Lenvy ♥~
A cup has some coins in it.
The cup tips over and 1 coin falls out. What is the probability of a penny falling out?
The probability of a penny falling out is,
⇒ 3 / 11
We have to given that;
A cup has some coins in it.
And, The cup tips over and 1 coin falls out.
Here, By given table;
Total number of coins are,
⇒ 3 + 5 + 2 + 1
And, Number of penny coins are,
⇒ 3
Hence, The probability of a penny falling out is,
⇒ P = number of penny / total number of coins
⇒ P = 3 / 11
So, The probability of a penny falling out is,
⇒ 3 / 11
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What is the area of the regular hexagon shown below?
Hint:
Central angle = 360/n where n is the number of sides
Area= (n) 1/2 (r2)sin(central angle)
10 pts
Ahmed used to be happy, but seemingly overnight he
changed. For the past three weeks, Ahmed has had
feelings of sadness and despair. What term BEST
describes the disorder Ahmed has?
a. generalized anxiety
b. borderline personality disorder
c. major depression
d. panic attacks
The term that best describes the disorder that Ahmed has is given as follows:
c. major depression.
Why the disorder is major depression?What differs depression from the other disorders cited in this problem is the length of the duration of the symptoms.
Ahmed has been feeling the symptoms for the past three weeks, which is a large time, as the other disorders such as anxiety and panic attacks have an alternance of time where the person feel the symptoms with times where the people is feeling good, without the symptoms.
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for the data x 1 2 3 5 y 0 5 26 164 (a) fill in the lagrange form
The Lagrange form of the polynomial that fits the given data is L(x) = (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3.
To find the Lagrange form of the polynomial that fits the given data, we can use the following formula:
Lagrange form:
L(x) = ∑ [y * l_i(x)], i=0 to n
where
l_i(x) = ∏ [(x - x_j)/(x_i - x_j)], j=0 to n, j ≠ i
In this formula, x and y are the given data points, n is the number of data points (n+1 is the degree of the polynomial), and L(x) is the polynomial that fits the data.
Using the given data x = {1, 2, 3, 5} and y = {0, 5, 26, 164}, we can compute the Lagrange form as follows:
l_0(x) = (x - 2)(x - 3)(x - 5)/(1 - 2)(1 - 3)(1 - 5) = -(x^3 - 10x^2 + 31x - 30)/4
l_1(x) = (x - 1)(x - 3)(x - 5)/(2 - 1)(2 - 3)(2 - 5) = (x^3 - 9x^2 + 23x - 15)/2
l_2(x) = (x - 1)(x - 2)(x - 5)/(3 - 1)(3 - 2)(3 - 5) = -(x^3 - 8x^2 + 13x - 6)/2
l_3(x) = (x - 1)(x - 2)(x - 3)/(5 - 1)(5 - 2)(5 - 3) = (x^3 - 6x^2 + 11x - 6)/4
L(x) = 0l_0(x) + 5l_1(x) + 26l_2(x) + 164l_3(x)
= (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3
Therefore, the Lagrange form of the polynomial that fits the given data is L(x) = (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3.
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On his recent free-throw attempts, Lamar made 4 shots and missed 6 shots. Considering this data, how many of his next 20 free-throw attempts would you expect Lamar to miss?Of the last 18 trains to pull into Castroville Station, 12 were full. Considering this data, how many of the next 12 trains would you expect to be full?
For Lamar's free-throw attempts, we can find the proportion of shots he made as 4/10 or 0.4. We can use this proportion to estimate how many of his next 20 free-throw attempts he would expect to make by multiplying the proportion by the number of attempts:
Expected number of missed free-throws = (1 - 0.4) x 20 = 12
Therefore, we would expect Lamar to miss 12 of his next 20 free-throw attempts based on his recent performance.
For the trains at Castroville Station, we can find the proportion of trains that were full as 12/18 or 0.67. We can use this proportion to estimate how many of the next 12 trains we would expect to be full by multiplying the proportion by the number of trains:
Expected number of full trains = 0.67 x 12 = 8
Therefore, we would expect 8 of the next 12 trains to be full based on the recent pattern of trains at Castroville Station.
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why can we consider the sample mean in random samples of size n from a given population to be a random variable? group of answer choices because the outcome is unpredictable. we can't, because only data collected on individuals can be a random variable. because n varies at random.
Consider the sample mean in random samples of size n from a given population to be a random variable because the outcome of the sample mean is unpredictable.
Outcome of the sample mean can vary from one random sample to another.
The sample mean is computed as the sum of the values in the sample divided by the sample size.
And since the sample is a random sample, the values in the sample are random variables themselves.
This implies, the sample mean is a function of those random variables and, as a result, it is also a random variable.
In other words, the sample mean is not a fixed quantity.
But rather a value that varies depending on the particular random sample that is chosen from the population.
This randomness in the value of the sample mean makes it a random variable.
Therefore, sample mean from a random sample can be random variable because the outcome is unpredictable.
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The function C(x) = 7,200 + 52x models the cost to produce x number of sheets of metal. The function R(x) 500x represents the revenue earned on the sale of each sheet of metal. Waich function, P(x), represents the
= Revenue profit the company earns on sheet metal production? (Profit=revenue-Cost)
The profit function of the company is P(x) = 448x - 7200
How to determine the profit function of the companyFrom the question, we have the following parameters that can be used in our computation:
Cost function. C(x) = 7200 + 52x
Revenue function. R(x) = 500x
the profit function of the company is calculated as
P(x) = R(x) - C(x)
substitute the known values in the above equation, so, we have the following representation
P(x) = 500x - 7200 - 52x
Evaluate
P(x) = 448x - 7200
Hence, the profit function of the company is P(x) = 448x - 7200
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in the process of a statistical investigation, we often take information from a sample from the population because:
We often take information from a sample from the population in the process of a statistical investigation because it is often impractical or impossible to collect data from the entire population.
In statistical investigation, a sample is a subset of a population that is selected for study. Collecting data from an entire population can be impractical or impossible due to cost, time, or other constraints. By studying a representative sample, statistical inferences can be made about the entire population with a certain degree of confidence.
The size and selection of the sample are important factors that affect the accuracy of the statistical inference. Generally, larger samples are more representative of the population and lead to more accurate estimates of population parameters.
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When testing the goodness of fit for the logistic regression model, if the obtained chi-square is less than the critical value, one would:None of the aboveAccept the alternative hypothesisAccept the null hypothesisReject the null hypothesis
When testing the goodness of fit for the logistic regression model, if the obtained chi-square is less than the critical value, one would " Accept the null hypothesis". The correct option is c.
In the goodness of fit test for the logistic regression model, the null hypothesis states that there is no significant difference between the observed and expected values. If the obtained chi-square value is less than the critical value, it means that the difference between the observed and expected values is not significant, and hence, we fail to reject the null hypothesis. Therefore, we accept the null hypothesis and conclude that the model fits the data well. On the other hand, if the obtained chi-square value is greater than the critical value, we reject the null hypothesis and conclude that the model does not fit the data well.
The correct option is c.
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data refers to the data that are collected specifically for the particular research project at hand when research questions are still unanswered after seeking all reasonable secondary data sources. question 17 options: derived primary referential syndicated cohort
The term that best describes the type of data collected specifically for a particular research project is derived from primary data.
This type of data is collected directly from the source, such as through surveys or experiments, and is tailored to answer specific research questions that have not been satisfactorily addressed by existing secondary data sources. Derived primary data is typically more expensive and time-consuming to collect than secondary data, but it can provide valuable insights that are not available elsewhere.
It is important to note that derived primary data should be collected using sound research methods to ensure its validity and reliability. This includes careful consideration of sampling methods, data collection techniques, and data analysis procedures. Researchers should also be transparent about the limitations of their data and any potential sources of bias or error that could affect their findings.
In contrast, referential data refers to data that are collected from existing sources, such as databases or published reports, and syndicated data refers to data that are collected by third-party research firms and sold to multiple clients. Cohort data refers to data that are collected from a specific group of individuals over time to track changes and trends. While each of these types of data can be useful for research, derived primary data is often the most valuable for answering specific research questions and generating new insights.
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The amount of money an employee earns monthly before taxes, in dollars, after selling n products is $1,500 + $225n. Which statement is correct? A. For every product sold, the employee's earnings increase by $1,275. B. For every product sold, the employee's earnings increase by $1,500. C. For every product sold, the employee's earnings increase by $225.
For every product sold, the employee's earnings increase by $225.
Option C is the correct answer.
We have,
The expression for the amount of money an employee earns monthly after selling n products is given as:
$1,500 + $225n.
Here,
$1,500 is the fixed monthly earning, and $225n represents the earning from selling n products.
Thus,
For every product sold, the earning increases by $225.
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Choose all of the expressions that are equivalent to 7
7 20
(49³) (7)
( 7³ ) ( 7 )
7³ ( 7 = =)
10 27
0 17
The option that would have the same value as required is option A.
What are equivalent exponents?Equivalent exponents are any two or more exponents that, when added to a base number, produce the same value or result. In other words, equivalent exponents are various ways of expressing the same exponentiation-based mathematical action.
We now have that;
[tex](49^2/5) (7^- 3/4)\\(7^2)^2/5 (7^-3/4)\\(7^4/5) (7^-3/4)\\7^ (4/5 - 3/4)\\7^ 1/20[/tex]
Thus the correct expression is the one that is shown in option A above here.
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If a = 11 cm, b = 28 cm, c = 15 cm, and d = 20 cm, what is the area of the poster?
Answer:
Step-by-step explanation:
Question 9 of 25
This table shows values that represent an exponential function.
1
2
3
4
5
y
7
9
13
21
37
What is the average rate of change for this function for the interval from x = 1
to x = 3?
Answer:
Step-by-step explanation:
To find the average rate of change for an exponential function over an interval, we can use the formula:
average rate of change = (f(b) - f(a)) / (b - a)
where “a” and “b” are the endpoints of the interval, and “f” is the exponential function.
In this case, the interval is from x = 1 to x = 3, so a = 1 and b = 3. We are given the values of the function for these inputs:
f(1) = 7
f(2) = 9
f(3) = 13
Substituting these values into the formula, we get:
average rate of change = (f(3) - f(1)) / (3 - 1)
average rate of change = (13 - 7) / 2
average rate of change = 3
Therefore, the average rate of change for this function over the interval from x = 1 to x = 3 is 3.
use the laplace transform to solve the given initial-value problem. dy dt − y = 1, y(0) = 0
The solution to the initial value problem is y(t) = -1 + e^t, y(0) = 0.
To solve the initial-value problem using the Laplace transform, we first apply the transform to both sides of the differential equation, using the linearity and derivative properties of the transform:
L{dy/dt} - L{y} = L{1}
sY(s) - y(0) - Y(s) = 1/s
sY(s) - Y(s) = 1/s
Next, we solve for Y(s):
Y(s) = 1/(s(s-1))
We can simplify this expression using partial fractions:
Y(s) = A/s + B/(s-1)
1/(s(s-1)) = A/(s) + B/(s-1)
Multiplying both sides by s(s-1), we get:
1 = As - A + Bs - B
Setting s=0, we get:
1 = -A
A = -1
Setting s=1, we get:
1 = B
B = 1
Therefore, the Laplace transform of the solution y(t) is:
Y(s) = (-1/s) + (1/(s-1))
Taking the inverse Laplace transform, we get:
y(t) = -1 + e^t
Therefore, the solution to the initial-value problem is:
y(t) = -1 + e^t, y(0) = 0
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Can someone help me quick? Thanks.
A city wants to place a lamppost on the triangular parkway shown so that the lamppost is the same distance from all three streets. Should the lamppost be located at the circumcenter or incenter of the triangular parkway? Explain your reasoning.
The light should be placed in the middle of the triangle parkway in order to meet the aim of having it at the same distance from each of the three roadways.
Since we want the light to be equally far from all three streets in this scenario, that means we want it to be equally far from each side of the triangle parkway.
In light of this requirement, the lamppost ought to be put in the middle of the triangle parkway. This is due to the incenter's equidistant location from all three sides, which ensures that the distance between the lamppost and each side of the triangle is equal.
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The base of an isosceles triangle is x units. The sum of the lengths of the other two sides is one unit less than the length of the base. If the perimeter of the triangle is 67 units or less, which inequality describes all possible lengths of the
base?
A) x ≤ 34
B) x ≤ 16.5
C) x ≥ 34
D) x ≥ 16 5
The expression that represents the perimeter of the triangle is 5x - 2.
Writing an expression
From the question, we are to write an expression that represents the perimeter of the triangle
From the given information,
"The length of the base of the triangle is represented by x"
and
"The legs are 1 unit less than twice the length of the base"
∴ One leg of the triangle = 2x - 1
The perimeter of a rectangle is the sum of all the sides
Thus,
Perimeter of the isosceles triangle = 2x - 1 + 2x - 1 + x
Perimeter of the isosceles triangle = 2x +2x + x - 1 - 1
Perimeter of the isosceles triangle = 5x - 2
Hence, the expression that represents the perimeter of the triangle is
5x - 2
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complete question:
In an isosceles triangle (a triangle where two of the three sides called legs are equal), the legs
are 1 unit less than twice the length of the base. If the length of the base of the triangle is
represented by x, create an expression that represents the perimeter of the triangle.
Please help me out. Finding event "A and B", event "A or B", and complement.
(a) Event "X and Y": F
(b) Event "X or Y": A, B, C, D, F
(c) The complement of the event X: E, F, G
(a) Event "X and Y": F
The letter "F" satisfies both conditions: it comes before "E" (Event X) and it is found in the word "FACE" (Event Y).
(b) Event "X or Y": A, B, C, D, F
The letters A, B, C, D, and F satisfy either condition: they come before "E" (Event X) or they are found in the word "FACE" (Event Y).
(c) The complement of the event X: E, F, G
The complement of Event X includes all the letters that do not come before "E". In this case, the letters E, F, and G do not satisfy the condition of coming before "E".
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Find the critical value
t/α2
needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places.
Part 1 of 4
(a) For level
95%
and sample size
7
Criticalvalue=0
To construct a confidence interval, we need to determine the critical value based on the confidence level and sample size. For a 95% confidence level and a sample size of 7, the critical value is 2.571.
The critical value is used to calculate the margin of error for a confidence interval. It is based on the confidence level and sample size, and it is determined from a t-distribution table or a calculator.
For a 95% confidence level and a sample size of 7, we can find the critical value by looking at the t-distribution table with 6 degrees of freedom (df = n - 1). The 95% confidence level corresponds to a two-tailed test with an alpha level of 0.05, and the critical value for a t-distribution with 6 degrees of freedom and an alpha level of 0.025 (half of 0.05) is 2.571.
Therefore, to construct a 95% confidence interval for a sample size of 7, we can use the formula:
sample mean ± (critical value) x (standard error of the mean)
where the standard error of the mean is calculated as the sample standard deviation divided by the square root of the sample size.
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solve this and I will give u brainlist.
Answer:
See below!
Step-by-step explanation:
For angle Z:Hypotenuse = 20
Opposite = 16
Adjacent = 12
Using trigonometric ratios to solve this question.
Solution:sin ratio:sin θ = opposite / hypotenuse
sin Z = 16 / 20
sin Z = 4 / 5
tan ratio:We know that,
tan θ = opposite / adjacent
tan Z = 16 / 12
tan Z = 4 / 3
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