Find the area of a regular 12-gon inscribed in a unit circle.
Answers
The required area of the regular 12-gon is obtained as 3 square units.
What is a regular polygon?A regular polygon can be defined as a polygon having all of its sides and angles equal to one another. The expression for each angle of a regular polygon is 180(n - 2)/n.
The angle between two sides of regular 12-gon is given as below,
180(12 - 2)/12 = 150°.
Now, the area of regular 12-gon is equivalent to the area of sum of 12 triangles.
The angle for the triangle will be 150/2 = 75°.
The diagram for such a triangle is given as below,
Now, OC = 1 × Sin B
⇒ OC = Sin 75°
And, BC = 1 × Cos B
⇒ BC = Cos 75°
Then, AB = 2BC = 2Cos 75°
Area of the triangle is given as,
1/2 × base × height
⇒ 1/2 × Sin 75° × 2Cos 75°
⇒ 0.25
Now, the area of the regular 12-gon inscribed in a unit circle is given as,
12 × 0.25 = 3 square units.
Hence, the area of a regular 12-gon inscribed in a unit circle is 3 square units.
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Related Questions
indicate if dijkstra's algorithm will be able to find the shortest path for this particular graph. (assume the source vertex is m) yes no it will loop forever the algorithm will never start
Answers
By using Dijkstra's algorithm, it can be concluded that-
It will loop forever.
Third option is correct
What is Dijkstra's algorithm?
Dijkstra's algorithm is used to find the shortest path between the nodes of a graph.
Here, a node is fixed which is called the source node and the distance from the source node to all other nodes are calculated.
The minimum distance gives the shortest path.
For the first option,
The first option is incorrect because the shortest path will not be obtained. There does not exist path between every pair of vertices
For the second option
The second option is incorrect because all the conditions of Dijkstra's algorithm are fulfilled but here, infinite looping takes place.
For the fourth option
The fourth option is incorrect because there exist a path between the point M and every other vertex in the graph.
So the third option is correct
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Complete Question
The complete question has been attached
Calculate the difference and enter below. 3-9
Answers
Answer:
-6 is your answer
Step-by-step explanation:
I hope that's right
let x be a continuous random variable. we know that it takes values between 0 and 3, but we do not know its distribution or its mean and variance. we are interested in estimating the mean of x, which we denote by h. we will use 1.5 as a conservative value (upper bound) for the standard deviation of x. to estimate h, we take n i.i.d. samples x1,x2,...,xn, which all have the same distribution as x, and compute the sample mean
Answers
The randomized variable's sample distribution would be as follows: H+/- 1.96 * √3)/√n
A random variable in mathematics would be a variable for whom the value is the numerical result of an unpredictable event and a random number generator X on a sample space. S denotes the rule that gives each of the outcomes S in a collection a numerical value.
In this case, we have assumed that x is a constant random variable with values ranging from 0 to 3, but we are unsure of its distribution, mean, or variance.
The mean of x, which we designate by the letter h, is what we're now interested in estimating. To provide a conservative estimate (upper bound), we'll choose 1.5 for the standard deviation of x.
In this case, we must estimate h. To do this, we select the sample size n, the samples x1, x2,.., xn, all of which share the same dissemination as x, and accurately measure the sample mean.
Therefore, we have used a normal distribution to determine the variation of x as (0,6),
And it equals to 3, then apply CLT resulting in
=> H+/- 1.96 * √3)/√n
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Messages arrive to a computer server according to a Poisson distributionwith a mean rate of 17 per hour. Determine the length of an interval oftime such that the probability that no messages arrive during this intervalis 0.94.
Answers
The length of an interval of time such that the probability that no messages arrive during this interval is 0.94 is 56.88 seconds.
We have to find the length of the time interval that the probability of no messages arrive during this interval is 0.94
Let X be the no.of messages arrive to the server
X follows the poisson distribution with mean λ = 17
Let t be the time interval
The probability of no messages arrive during this interval is 0.94
Then P(0) = 0.94
e⁻⁽λt⁾ = 0.94
λt = ln0.94
17 t = ln(0.94)
t = ln(0.94)/17
t = 0.026872 / 17 hrs
t = 0.0158
Convert 0.0158 hours to seconds
That is t=0.0158(60)(60)
=56.88seconds
Hence in 56.88 seconds the time interval that the probability of no messages arrive during this interval is 0.94 .
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Determine the slope of the line that contains the points with coordinates (1, 5) and (-2, 7).
Answers
Answer:
2/3x
Step-by-step explanation:
transformation(s) can map APQR onto ASTU?
Which
O translation only
O rotation only
O rotation, then reflection
O reflection, then translation
Answers
D.) reflection, then translation
Explanation:
The triangles shown are congruent by the SSS congruent theorem.
Hopes this helps <3
Add a department store a coat that normally sells for $50 it's on sale for $35 what is the percent of the decrease? HELP
Answers
Answer: 30%
Step-by-step explanation: To find the percent of decrease, you have to subtract the greater number from the smaller one, then divide it by the first number that comes in the sentence x 100. So, using that formula, we subtract 35 from 50 to get 15, then we do 15/50 x 100 to get 30 or 30%. I hope this helped you understand a little more about the percentage decrease.
A man distributes his savings of 4000 among his three sons in the ratio 4:3:3. Find the amount received by his first son.
Answers
Answer:
First son: 4
Second son: 3
Third son: 3
Sum ratio =10
First son= 4/10*4000=1600
Find the solution to the system by elimination:
3x - 5y = 8
2x+ 3y = -1
Answers
Answer: x = 1, y = -1
Step-by-step explanation:
To solve this system by elimination, we will set it up so both of the y, or x, variables have opposite coefficients.
3x - 5y = 8
2x+ 3y = -1
3(3x - 5y = 8)
5(2x+ 3y = -1)
9x - 15y = 24
10x + 15y = -5
The 15y and -15y cancel each other out, so we're left with 9x + 10x on the left side and 24 - 5 on the right side of the equation.
19x = 19
x = 19/19
x = 1
Now, we will plug this back into one of the equations to solve for y.
3x - 5y = 8
3(1) - 5y = 8
3 - 5y = 8
-5y = 5
y = -1
Could I have some help with the question below:
In each part, find the two unit vectors in R^2 that satisfy the given conditions:
The two unit vectors parallel to the line y=5x+5 are: _ and _
The two unit vectors parallel to the line 2x+4y=1 are: _ and _
The two unit vectors perpendicular to the line y=2-5x are: _ and _
Answers
The two unit vectors parallel to the line y=5x+5 are [tex]u_{+}[/tex] =⟨1, 5⟩/√26 and [tex]u_{-}[/tex] =⟨1, 5⟩/√26.
What are vectors?Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.
Part A:
The given equation of line is y=5x+5.
It's all about slope. The vectors parallel to the line must have the same slope as the line. The line here is y=5x+5., and has slope 5. We can say the rise is 5 and the run is 1 and write the vector.
[tex]u_{\pm}[/tex] =⟨1, 5⟩
Magnitude =|u| =√(1²+5²)
= |±√26|
= √26
So, the two unit vectors are
[tex]u_{+}[/tex] =⟨1, 5⟩/√26 and [tex]u_{-}[/tex] =⟨1, 5⟩/√26
Part B: 2x+4y=1
x+2y=1/2
y=-x/2+1/4
Here slope is -1/2, where rise is -1 and run is 2
[tex]u_{+}[/tex]= ⟨2, -1⟩ and [tex]u_{-}[/tex]= ⟨-2, 1⟩
Magnitude =|u| =√(2²+(-1)²)
= √5
So, the two unit vectors are
[tex]u_{+}[/tex] =⟨2, -1⟩/√5 and [tex]u_{-}[/tex] =⟨-2, 1⟩/√5
Part C: The given equation is y=2-5x
Here slope is -5, slope perpendicular to line is -1/5
So, rise is -1 and run is 5
[tex]u_{\pm}[/tex] =⟨5, -1⟩
Magnitude =|u| =√(5²+(-1)²)
= √26
So, the two unit vectors are
[tex]u_{+}[/tex] =⟨5, -1⟩/√26 and [tex]u_{-}[/tex] =⟨-5, 1⟩/√26
Therefore, the two unit vectors parallel to the line y=5x+5 are [tex]u_{+}[/tex] =⟨1, 5⟩/√26 and [tex]u_{-}[/tex] =⟨1, 5⟩/√26.
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Triangle Congruence: Question 3
In the proof, what is the reason for (5) ?
Given: V W║Z Y
W X=Y X
Prove: ΔVWX ΔXYZ
Select one:
SSA
H
SAS
ASA
SSS
Answers
In the proof the reason for (5)ΔVWX ≅ ΔXYZ is ASA , the correct option is (d) .
In the question ,
it is given that ,
Given: VW parallel to ZY and WX = YX
to Prove: ΔVWX ≅ ΔXYZ .
the statement to prove ΔVWX ≅ ΔXYZ are given as
(1) VW parallel to ZY ....given
(2) m∠W = m∠Y ...alternate interior angle .
(3) WX = YX ...given
(4) m∠VXW = m∠ZXY .....vertically opposite angle
(5) ΔVWX ≅ ΔXYZ
In statement (5) , Since two angles and 1 side is included in proving the given two triangles congruent ,
the reason will be ASA congruence , that is option (d) .
Therefore , the reason for (5) is ASA .
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Given m = 2 and the point (6, 8), what is the point-slope form of the equation?
Answers
Answer:
y - 8 = 2 (x - 6)
Step-by-step explanation:
The point-slope equation is ...
y - y1 = m ( x - x1 )
In the coordinate (6,8)
x = 6 and y = 8
m = 2
Plug in values to find the point-slope form
y - 8 = 2 (x - 6)
We are done!
*for the `babies` (**usingr**) data set, the variable `age` contains the recorded mom's age and `dage` contains the dad's age for several cases in the sample. do a significance test of the null hypothesis of equal ages against a one-sided alternative that the dads are older in the sampled population\.\*
Answers
On solving the provided question we can say that - mean of x mean of y
27.37136 30.73706
what is alternative hypothesis?
In statistical inference studies, an alternative hypothesis is a statement. This is represented by Ha or H1, which conflicts with the null hypothesis. It only serves as a zero replacement. The claims that researchers are investigating in hypothesis testing are alternative theories.
[tex]t = -11.067, \\df = 2301.5, \\p-value < 2.2e-16[/tex]
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
[tex]-Inf -2.865266[/tex]
sample estimates:
mean of x mean of y
27.37136 30.73706
Conclusion:-
Here   p-value = 2.2e-16 < 0.05(Level of significance)
Therefore we reject at 5% Loss
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help me solve this please
Answers
Thus, the required trig values corresponding to the cosФ = -3/5 have been shown,
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
cosФ = -3/5
cosФ = -3/5 = base / hypotenuse,
perpendicular = √5² - 3² = 4
sinФ = perpendicular / hypotenus
= 4/5
Simultaneously,
cosecФ = 5/4
secФ = -5/4
tanФ = -4/3
cotФ = -3/4
Here,
sin and cosec are positive because this function as a positive positive value between π/2 and π, while else trigonometric function as a negative value for π/2 to π.
Thus, the required trig values are shown above.
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What are the vertex and range of y = |2x + 6| + 2? (0, 2); 2 < y < ∞ (0, 2); −∞ ≤ y < ∞ (−3, 2); 2 < y < ∞ (−3, 2); −∞ ≤ y < ∞
Answers
The vertex and the range of y = |2x + 6| + 2 are (c) (-3, 2); 2 ≤ y < ∞
How to determine the vertex and the range?From the question, we have the following parameters that can be used in our computation:
y = |2x + 6| + 2
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
y = |2x + 6| + 2
This gives
y = 2|x + 3| + 2
This means that the vertex is
Vertex = (-3, 2)
Remove the x value
y = 2
Because the leading coefficient is positive, then the vertex is a minimum
i.e. y ≥ 2
So, the range is 2 ≤ y < ∞
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[tex]2 \frac{3}{5} \div 5\frac{3}{8} [/tex]
in its simplest form:?
Answers
The expression 2 3/5 ÷ 5 3/8 given is written in simplest form as 104/215
How to write the expression in simplest formThe problem is a division problem in mixed numbers
converting to improper fractions we have
= 2 3/5 ÷ 5 3/8
= 13/5 ÷ 43/8
inverting the divisor to change to multiplication
= 13/5 ÷ 43/8
= 13/5 * 8/43
= 104/215
The division problem is simplest form give 104/215
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In order to understand the relation between smoking and hypertension (HT), a tea of researchers designed a study that looks at the numbers of smokers and nonsmokers with no HT, pre-HT, stage 1 HT, and stage 2 HT. Which one of the following statements is correct? a. A chi-square test of independence should be run for the study, because the outcome smoker vs. nonsmoker-is a continuous variable, and the grouping variable-no HT, pre-HT stage 1 HT, and stage 2 HT-categorizes the sample into four independent groups. b. A chi-square test of independence should be run for the study, because the outcome smoker vs. nonsmoker-is a dichotomous variable, and the grouping variable-no HT, pre-H stage 1 HT, and stage 2 HT-categorizes the sample into four independent groups. c. An independent samples t test should be run for the study, because the outcome-smoker vs. nonsmoker-is a categorical variable, and the grouping variable no HT, pre-HT, stage 1 HT, and stage 2 HT-categorizes the sample into four independent groups. d. An independent samples t test should be run for the study, because the outcome-smoker vs. nonsmoker-is a continuous variable, and the grouping variable no HT, pre-HT, stage 1 HT, and stage 2 HT-categorizes the sample into matched (or dependent) groups.
Answers
Correct option is C
In order to understand the relation between smoking and hypertension (HT) a tea of researchers designed a study that looks at the numbers of smokers and nonsmokers with no HT, pre-HT, stage 1 HT, and stage 2 HT.
An independent samples t test should be run for the study because the outcome smoker vs nonsmoker is a categorical variable and the grouping variable no HT, pre-HT, stage 1 HT, and stage 2 HT-categorizes the sample into four independent groups.
Variables
In Maths, a variable is an alphabet or term that represents an unknown number or unknown value or unknown quantity. The variables are specially used in the case of algebraic expression or algebra. For example, x+9=4 is a linear equation where x is a variable, where 9 and 4 are constants.
Probability
Probability is simply likely something is to happen. Whenever unsure about the outcome of an event, we can talk about the probabilities of certain outcome. The analysis of events governed by probability is called statistics.
Correct option is C
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brainliest for first right answer in minutes 40 points I swear
Answers
The value of the missing angle of the triangle is; x = 31°
What is the missing angle of the triangle?Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
Now, from the diagram, we can tell that ∠GAB is congruent to ∠CBA by alternate angles theorem.
Thus, ∠GAB = 28°
Similarly, sum of angles on a straight line = 180°. Thus;
∠EDA = 180 - (4x + x)
∠EDA = 180 - 5x
Also, sum of angles in a triangle is 180 degrees. Thus;
∠CAB = 180 - (90 + 28)
∠CAB = 62°
Thus;
62 + 3x + 180 - 5x = 180
62 - 2x = 0
2x = 62
x = 62/2
x = 31°
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8.) Graph f(x)=-x-3
a.) Evaluate f(-4).
b.) Evaluate f(5).
c.) Evaluate f(0).
d.) Circle any ordered pairs that are included in the function:
(-3,0) (-10,7) (13,10)
Answers
From the the graph f(x) = -x-3
Part a
The value of f(-4) = 1
Part b
The value of f(5) = -8
Part c
The value of f(0) = -3
The function is given that
f(x) = -x-3
The function is the mathematical statement that shows the relationship between the independent variable and dependent variable. The function consist of the different variables, numbers and mathematical operator.
The function is
f(x) = -x - 3
Part a
The value of f(-4)
Substitute the value of x in the function
f(-4) = - (-4) - 3
= 4 - 3
= 1
Part b
The value of f(5)
f(5) = -5 - 3
= -8
Part c
The value of f(0)
f(0) = -0 - 3
= -3
Therefore, the value of f(-4), f(5) and f(0) are 1, -8 and -3 respectively
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What is 19x( _________X26)=(19X39)X26
Answers
Answer:
(39 * 26)
Step-by-step explanation:
If (19 * 39) * 26
19 * (39 * 26)
Your answer is 39.
A forest covers 41000acres. A survey finds that 0.2% of the forest is old-growth trees. How many acres of old-growth
trees are there?
Answers
the scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. complete a linear equations that fits the data for tree 1, where x is the year and y is the trunk diameter, in inches. click on the variables and number you want to select and drag them into the boxes.
Answers
The linear equation obtained is y = 0.3X + 18.3
What is linear equation?A linear equation is an equation that can be written in the form ax + b = 0, where a and b are real numbers and x represents an unknown variable. The solutions of linear equations are often graphed on a coordinate plane, forming a straight line. Linear equations can be used to model many real-world situations, such as population growth, the rate of change of a physical quantity, or the total cost of an item. Linear equations can also be used to solve systems of equations, where several equations must be solved simultaneously.
Given that data :
x = year ;
y = trunk diameter, in inches
Year ________trunk diameter
1 __ 18.6
3 __ 19.2
5 __ 19.8
7 __ 20.4
9 ___21.0
11 __ 21.6
13 __ 22.2
Using the linear regression calculator :
The linear equation obtained is :
y = 0.3X + 18.3
Where ;
Slope = 0.3 ; intercept, c = 18.3
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Find the area of this triangle. Round to the nearest tenth. PLEASE HELP
Answers
Answer:
74.8 m²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Area of a triangle} \\\\$A=\dfrac{1}{2}ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides enclosing the angle. \\\end{minipage}}[/tex]
From inspection of the given triangle:
C = 115°a = 11 mb = 15 mSubstitute the values into the formula and solve for area:
[tex]\implies A=\dfrac{1}{2} \cdot 11 \cdot 15 \cdot \sin 115^{\circ}[/tex]
[tex]\implies A=\dfrac{165}{2} \sin 115^{\circ}[/tex]
[tex]\implies A=74.77039243[/tex]
[tex]\implies A=74.8\; \sf m^2\;(nearest\;tenth)[/tex]
Therefore, the area of the triangle is 74.8 m² rounded to the nearest tenth.
form differential equations for all circles in the xy plane
Answers
The differential equation that can represent all circles in the xy plane is given as follows:
[tex]\frac{dy}{dx} = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]
How to obtain the differential equations for a circle?The equation of a circle of center (h,k) and radius r is given as follows:
(x - h)² + (y - k)² = r².
The equation can be arranged to isolate the variable y as follows:
(y - k)² = r² - (x - h)²
y - k = square root (r² - (x - h)²)
y = square root (r² - (x - h)²) + k
To obtain the differential equation, then this equation must be differentiated towards variable x as follows:
[tex]\frac{dy}{dx} = \frac{d}{dx}(\sqrt{r^2 - (x - h)^2} + k)[/tex]
Applying the chain rule, along with the derivative for the square root, we have that:
[tex]\frac{d}{dx}(\sqrt{r^2 - (x - h)^2} + k) = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]
Meaning that the differential equation is given as follows:
[tex]\frac{dy}{dx} = -\frac{x - h}{\sqrt{r^2 - (x - h)^2}}[/tex]
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Suppose that you were trying to use the Putzer method to exponentiate the matrix A which has eigenvalues dı = 4 and A2 = 6, in that order. ao(t) is always the function et. Choose the correct equation for a1(t) da1 О (а) 6a1 + e4t a1(0) = 1 dt da1 : 4a1 + e4t P (g) da1 a1(0) = 1 (c) dt -4a1 + ett a1(0) = 0 da1 (d) dt 4a1 + et a1(0) = 0 da1 (e) : 6a1 + e4t a1(0) = 0 dt da1 (f) dt — 4а, + e# a,(0) — 1
Answers
The correct equation for a1(t) is dt -4a1 + e4t a1(0) = 0.
What is equation?An equation is a mathematical expression that shows the relationship between two values or variables. It typically consists of an equal sign (=), two expressions separated by an operator, and sometimes additional symbols like parentheses, fractions, or exponents. Equations are used to describe physical laws and conditions, solve problems, and make predictions. For example, the equation for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width.
This is because the eigenvalue of A which corresponds to the coefficient of a1(t) is 4, so the equation should contain e4t. The initial condition is a1(0) = 0, since the initial value of a1(t) is 0.
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let sn be the number of successes in n independent bernoulli trials, where the probability of success for each trial is 1/2. evaluate the following limits.
(a) n→[infinity]lim P( 2n− 3n ≤S n ≤ 2n + 3n)
(b)n→[infinity] lim P( 2n− 4n ≤S n ≤ 2n+ 4n)
(c) n→[infinity]lim P(2n−20≤Sn ≤ 2n+20)
Answers
The following limits -
Option a) = 1
Option b) = 0
Option c) = 0
According to the question given,
The probability of success of each trial is = [tex]\frac{1}{2}[/tex]
Let us consider options a),
n→[infinity]lim P( [tex]2n - 3n \leq S n \leq 2n + 3n[/tex] ),
We could conclude that if n tends to infinity, the probability of having [tex]2n - 3n[/tex] successes in n number of trials = the probability of having [tex]2n - 3n[/tex] successes in n number of trials.Since in the question, the probability of success for each trial is 1/2, so we could say that, [tex]2n - 3n[/tex] successes = [tex]2n - 3n[/tex] successesTherefore, the limit is = 1
Taking option b),
We could conclude that if n tends to infinity, the probability of having [tex]2n - 4n[/tex] successes in n number of trials = 0Since in the question, the probability of success for each trial is 1/2, so we could say that, [tex]2n - 4n[/tex] successes = 0Therefore, the limit is = 0
Taking option c),
We could conclude that if n tends to infinity, the probability of having [tex]2n - 20[/tex] successes in n number of trials = 0Since in the question, the probability of success for each trial is 1/2, so we could say that, [tex]2n - 20[/tex] successes = 0Therefore, the limit = 0
Therefore, the following limits are - a) 1, b) 0, c) 0
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Solve the equation. *Will give Branliest!*
-1/6x-5=2/3x
Answers
Answer:
[tex]x=-6[/tex]
Step-by-step explanation:
Solve for x.
Combine [tex]x[/tex] and [tex]\frac{1}{6}[/tex].
Combine [tex]x[/tex] and [tex]\frac{2}{3}[/tex].
[tex]-\frac{x}{6} -5=\frac{2x}{3}[/tex]
Move all terms containing x to the left side of the equation.
Subtract [tex]\frac{2x}{3}[/tex] from both sides of the equation.
[tex]-\frac{x}{6} -5-\frac{2x}{3}=0[/tex]
To write [tex]-\frac{2x}{3}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex].
[tex]-\frac{x}{6}-\frac{2x}{3}*\frac{2}{2}-5 =0[/tex]
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
[tex]-\frac{x}{6}-\frac{2x*2}{6}-5 =0[/tex]
Combine the numerators over the common denominator.
[tex]\frac{-x-2x*2}{6}-5 =0[/tex]
Simplify the numerator.
Factor [tex]x[/tex] out of [tex]-x-2x*2[/tex].
[tex]\frac{x(-1-2*2)}{6}-5 =0[/tex]
[tex]\frac{x(-1-4)}{6}-5 =0[/tex]
[tex]\frac{x*-5}{6}-5 =0[/tex]
Move the negative in front of the fraction.
[tex]-\frac{5x}{6} -5=0[/tex]
Add 5 to both sides of the equation.
[tex]-\frac{5x}{6}=5[/tex]
Multiply both sides of the equation by [tex]-\frac{6}{5}[/tex].
[tex]-\frac{6}{5}(-\frac{5x}{6})=-\frac{6}{5}*5[/tex]
Simplify the left side by cancelling the common factors of 5 and 6.
[tex]x=-\frac{6}{5} *5[/tex]
Move the leading negative in [tex]-\frac{6}{5}[/tex] into the numerator.
[tex]x=\frac{-6}{5} *5[/tex]
Cancel the common factor of 5.
[tex]x=-6[/tex]
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Answer:
x = - 6---------------------------------
Given equation:
-1/6x - 5 = 2/3xFist, multiply both sides by 6 to clear the fraction:
6(-1/6)x - 6(5) = 6(2/3)x- x - 30 = 4xCollect the terms with the variable and solve for x:
4x + x = - 305x = - 30x = - 30/5x = - 6a survey of 800 randomly selected adults in a certain country found that 82% believed that protecting the right of those with unpopular views is a very important component of a strong democracy. verify the central limit theorem conditions
Answers
On solving the question - At α = 0.05, two tailed critical value, Lower Bound =[tex]0.757[/tex], Upper Bound = 0.803, (0.757, 0.803)
What is 95% Confidence interval?An estimation range for an unknowable parameter is referred to as a confidence interval in frequentist statistics. The most popular confidence level is 95%, however other levels, such 90% or 99%, are occasionally used for computing confidence intervals. A constant that indicates the intended degree of significance based on the normal distribution is multiplied by the standard error once it has been calculated to get the confidence interval. Intervals with 95% certainty have a constant value of 1.96.
The number of people in the sample that felt protecting the rights of those with unpopular views is a very important component of a strong democracy is 1200*.78 = 936
Yes, the sample size is large enough, since the expected number of successes is 936, and the expected number of failures is 1200-936= 264, both of which are greater than or equal to 10.
95% Confidence interval :
At α = 0.05, two tailed critical value
Lower Bound =[tex]0.757[/tex]
Upper Bound = 0.803
(0.757, 0.803)
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What do I have to fill out in the blanks?
Answers
Opposite sides of a parallelogram are equal.
Opposite sides of a parallelogram are equal in the second case
RT is congruent to RT is obvious.
ΔRST and ΔRUT are congruent because a diagonal of a parallelogram divides it into two congruent triangles.
We know pair of interior alternate angles are equal.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given, Line segment TU is congruent to line segment RS because in a parallelogram opposite are equal same reason for line segment RU and ST.
We also know that the diagonal of a parallelogram divides the parallelogram into two equal triangles hence ΔRST and ΔRUT are congruent.
We also know that the pair of alternating angles are equal hence,
∠RST and ∠TRU are congruent.
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Los Angeles workers have an average commute of 27 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 15 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N(,)
b. Find the probability that a randomly selected LA worker has a commute that is longer than 35 minutes.
c. Find the 70th percentile for the commute time of LA workers. minutes
Answers
(a) Distribution of X is a bell curve with mean of 27 min
(b) The probability of a randomly selected LA worker has a commute that is longer than 35 minutes is 79.81%
(c) 70th percentile for the commute time of LA workers is 34.866
Given,
Mean = 27 minutes
Standard Deviation = 15 minutes
a. The distribution is a bell curve, with the peak of the curve corresponding to the mean = 27 minutes.
b. We have to find the probability that a randomly selected LA worker will have a commute of over 35 minutes. This value will fall on the right hand side of the bell curve, i.e, on the right side of the mean. For that, we need to find the z-score for 35.
z score, z = [tex]\frac{35-27}{15} = 0.53[/tex]
Using the z-tables, we get the z-value to the left of 0.53 as 0.2019, and therefore, the z-value to the right will be 1 - 0.2019 = 0.7981, which gives us a probability percentage of around 79.81%.
c. Here, we have to find the 70th percentile for the commute time for the LA workers. Let us take the marker as 0.70 on the bell-curve, so a z-score that gives us a value of 0.70 should be the right answer.
The answer to that is 0.5244.
Now, a little calculation:
0.5244 x 15 = 7.866 = x - 27
x = 34.866
Final answers:
a. A bell curve
b. 0.7981
c. 34.866
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a. The distribution is a bell curve, with the peak of the curve corresponding to the mean = 27 minutes.
b. Using the z-tables, we get the z-value to the left of 0.53 as 0.2019, and therefore, the z-value to the right will be 1 - 0.2019 = 0.7981, which gives us a probability percentage of around 79.81%.
c. Here, we have to find the 70th percentile for the commute time for the LA workers. Let us take the marker as 0.70 on the bell-curve, so a z-score that gives us a value of 0.70 should be the right answer.
The answer to that is 0.5244.
0.5244 x 15 = 7.866 = x - 27
x = 34.866