What is tan(sin^-1(x/2))

with steps pls

The linear equation obtained is y = 0.3X + 18.3

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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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.

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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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:

Substitute 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.

The correct equation for a1(t) is dt -4a1 + e4t a1(0) = 0.

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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(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

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]

A rating/review would be much appreciated. Wish you a happy holiday season!

Answer:

---------------------------------

Given equation:

Fist, multiply both sides by 6 to clear the fraction:

Collect the terms with the variable and solve for x:

Thus, the required trig values corresponding to the cosФ = -3/5 have been shown,

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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Answer:

2/3x

Step-by-step explanation:

Answer:

------------------------------

The function f(x) is horizontally stretched when the function f(bx) has the value of b between 0 and 1.

We have a function y = - x - 4.

If we need to find the equation of horizontally stretch of this function by a factor of 5, then our b = 1/5.

So the function is:

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] ),

Therefore, the limit is = 1

Taking option b),

Therefore, the limit is = 0

Taking option c),

Therefore, the limit = 0

Therefore, the following limits are - a) 1, b) 0, c) 0

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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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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]

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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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

Answer:

(39 * 26)

Step-by-step explanation:

If (19 * 39) * 26

19 * (39 * 26)

Your answer is 39.

The probability that Luke will touch the target's inner ring fewer times than the mean of X out of five attempts is 0.40951.

Probability refers to possibility.

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

According to our question-

P(target) equals 0.90

Let the random variable X stand in for the number of times the arrow is fired at the target's ring.

The probability distribution of X is

  x:         0              1                2               3               4               5

P(x):    0.00001   0.00045  0.00810   0.07290   0.32805   0.59049

Hence, The probability that Luke will touch the target's inner ring fewer times than the mean of X out of five attempts is 0.40951.

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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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The volume of the solid is 250r³ when  the base of s is a circular disk with radius 5r.

Given that,

We have to discover the described solid's volume, v. The parallel cross-sections perpendicular to the base of s are squares, and the base of s is a circular disk with radius 5r.

We know that,

A cylinder is a solid with square cross sections parallel to the bases and circular bases. Its height is equal to the base circle's diameter.

The radius = 5r,

So the height = diameter = 10r

Volume of the cone is base × height= πr²×h

=π(5r)²×(10r)

=250πr³

Therefore, The volume of the solid is 250r³ when  the base of s is a circular disk with radius 5r.

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Answer:

A

Step-by-step explanation:

change 'its' to   it's    which is a contraction for 'it is'

On solving the provided question we can say that - correlation coefficient of the question is r = [tex]\frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }[/tex] =  -0.91

The Pearson's correlation coefficient, also known as the Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a statistical indicator of the linear relationship between two sets of data.

[tex]S_{xx} =[/tex]∑[tex]x^2[/tex] - (∑x[tex])^2[/tex] /n = 19300- ((420)^2 /10)= 1660

[tex]S_{yy} =[/tex] ∑[tex]y^2[/tex] (∑y[tex])^2[/tex]/n = 7454- ((270)^2 /10) = 164

[tex]S_{xy} =[/tex]∑[tex](xy)^2[/tex]/n -475

The correlation coefficient is:

r = [tex]\frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }[/tex] =  -0.91

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The frequency table with the classes is:

Category                        Frequency

85 99                                     7

100-114                                   8

115-129                                   13

130-144                                   7

145-159                                   5

In the given question,

The daily total number of students who used the state university swimming pool on 40 days during the summer is given.

A frequency table with the classes is 85 99, 100-114, 115-129, 130-144, and 145-159.

First we make table of given frequency and write the given number who lies in between that numbers.

Category                                         Numbers in interval

85-99                                          90, 93, 98, 89, 86, 97, 98

100-114                                 110, 107, 108, 110, 102, 105, 109, 104

115-129                  121, 119, 128, 129, 128, 115, 120, 129, 118, 122, 126, 118, 116

130-144                                      142, 132, 139, 137, 131, 132, 131

145-159                                            145, 149, 149, 152, 159

As we know that the frequency is the total numbers that cones between given interval.

Now the frequency is:

Category                        Frequency

85 99                                     7

100-114                                   8

115-129                                   13

130-144                                   7

145-159                                   5

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The right question is:

The daily total number of students who used the state university swimming pool on 40 days during the summer is as follows:

90 98 137 108 128 115 152 122 110 132 149 131 102 109 118 126 121 145 89 149 86 120 97 118 142 139 128 110 105 104 131 159 93 119 107 129 132 129 98 116

For a frequency table with the classes 85 99, 100-114, 115-129, 130-144, and 145-159.

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)

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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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.

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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The vertex and the range of y = |2x + 6| + 2 are (c) (-3, 2); 2 ≤ y < ∞

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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div( curl( grad f )) - scalar field; the divergence of a vector field is a scalar field

A quantity with both direction and magnitude, particularly when used to depict the distance between two points in space.

In a scalar field, each point in a space—possibly actual space—is assigned a single integer.

According to the given information

(a) You can only determine the curl of a vector field; curl f is meaningless.

(b) grad f - vector field; when you take a gradient of something , it results in a vector field

(c) div F - scalar field; take the divergence of a vector field, it results in a scalar field

(d) A vector field is produced by the operation curl(grad f) on a vector field.

(e) grad F - meaningless; gradients are only used for scalar fields

(f) grad( div F ) - vector field; the gradient of a scalar field is a vector field

(g) div( grad f ) - scalar field; if you take divergence of a vector field, the result is a scalar field

(h) Grad (div f) is useless; one cannot take a scalar field's divergence into account.

(i) vector field; a vector field is a vector field's curl (curl F).

(j) div(div F) is useless; it is impossible to calculate a scalar field's divergence.

(k) ( grad f ) x ( div F ) - meaningless; you cant cross a scalar field by a vector field !

(l) The divergence of a vector field is a scalar field, and its formula is div(curl(grad f))

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Answer:

-6 is your answer

Step-by-step explanation:

I hope that's right

Answer:

First son: 4

Second son: 3

Third son: 3

Sum ratio =10

First son= 4/10*4000=1600

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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