Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]Starting with the equation:
[tex]\tan (\theta)=1[/tex]take the inverse tangent function to both sides of the equation:
[tex]\begin{gathered} \arctan (\tan (\theta))=\arctan (1) \\ \Rightarrow\theta=\arctan (1) \\ \therefore\theta=\frac{\pi}{4} \end{gathered}[/tex]Yet another value can be found for this equation to be true since the period of the tangent function is π:
[tex]\begin{gathered} \theta_1=\frac{\pi}{4} \\ \theta_2=\frac{\pi}{4}+\pi=\frac{5}{4}\pi \end{gathered}[/tex]Starting with the equation:
[tex]7\tan (\theta)=-15[/tex]Divide both sides by 7:
[tex]\Rightarrow\tan (\theta)=-\frac{15}{7}[/tex]Take the inverse tangent to both sides of the equation:
[tex]\begin{gathered} \Rightarrow\arctan (\tan (\theta))=\arctan (-\frac{15}{7}) \\ \Rightarrow\theta=\arctan (-\frac{15}{7}) \\ \therefore\theta=-1.13416917\ldots \end{gathered}[/tex]The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:
[tex]\begin{gathered} \theta_1=-1.13416917\ldots+\pi \\ =2.007423487\ldots \end{gathered}[/tex]We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:
[tex]\begin{gathered} \theta_2=\theta_1+\pi \\ =5.14901614\ldots \end{gathered}[/tex]Therefore, for each equation we know that:
[tex]\begin{gathered} \tan (\theta)=1 \\ \Rightarrow\theta=\frac{\pi}{4},\frac{5\pi}{4} \end{gathered}[/tex][tex]\begin{gathered} 7\tan (\theta)=-15 \\ \Rightarrow\theta=2.007423487\ldots\text{ , }5.14901614\ldots \end{gathered}[/tex]karem drives his car 96 miles per hour 1 1/2 hours how many miles will he drive in 2 1/2 hours
a communication system consists of n components, each of which will, independently, function with probability p. the total system will be able to operate effectively if at least one-half of its components function. (a) let x denote the number of functioning components out of the n components. what is the distribution of x? (b) what is the probability that a 5-component system will function? (c) for what values of p is a 5-component system more likely to operate effectively than a 3-component system?
A Communication system consists of n components.
a) Binomial distribution,
P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾
b) For 5-component system,
P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5
c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.
Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .
(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.
(b) Now , 5-component system is function . That is n=5
Probability that 5-components system will function is P(X= 5)
= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)
(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is
⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵
Whereas the corresponding probability for a 3-components system
³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3
³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³
5-Component system is better than 3-Components system if
10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³
=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²
Which reduce to
3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0
either p> ½ or p <1
=> p belongs to ( 0.5, 1)
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which measure of variability is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean? group of answer choices iqv interquartile range variance standard deviation
Standard deviation is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean.
What is measure of variability?
Measures of variability provide descriptive information about the dispersion of scores within data.
Standard deviation uses all the values in the distribution in it's calculation hence the standard deviation provides the most information.
Therefore standard deviation is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean.
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Identify at least two pairs of congruent angles in the figure and explain how you know they are congruet
you didn't attach the figure....
Draw the preimage and image of the polygon with the vertices X(-1,4), Y (2,2), and Z(0,-1) translated using the vector <2,-37>
Answer:
12
Step-by-step explanation:
{(7, 3), (4, 8), (-6, -5), (6, 6), (-1, 9) }
Domain:
Range:
Answer:
Domain: -6,-1,4,6,7
Range: -5,3,6,8,9
Step-by-step explanation:
The domain is the first element in each ordered pair. It is the x value. The range is the second element in each ordered pair. It is the y values.
Martin, a carpenter wants to make a spice rack for the kitchen. He cuts a 16.24 feet long plank into 5 pieces of equal length. What is the length of each piece of wood ? Round to the nearest hundredth.
Solution
For this case we can solve the problem with the following operation:
[tex]\frac{16.24ft}{5}=3.248ft[/tex]And rounded the answer we got 3.25 ft
16.24*100 = 1624
5*100 = 500
And we can do this:
1624/500 = 812/250 = 406/125
003
_____
125 / 406
-0
____
-40
-0
____
406
-375
_____
31
Multiply and simplify completely ( 3x - 1 ) (3x + 1)
Answer:
9x^2-1
Step-by-step explanation:
Answer:
Step-by-step explanation:
Multiply (3x - 1) * (3x + 1)
= 9(x)^2 + 3x - 3x -1
= 9(x)^2 - 1
find the volume of a cone with a height of 100 feet and a radius of its base 100 feet use 3.14 for pi
The volume of a cone is given as follows;
[tex]\begin{gathered} \text{Vol}=\frac{1}{3}(\pi\times r^2\times h) \\ \text{The radius of the base r=100, h=100} \\ \text{Vol}=\frac{1}{3}\times3.14\times100^2\times100 \\ \text{Vol}=\frac{3.14\times10000\times100}{3} \\ \text{Vol}=1046666.67 \\ \text{Vol}\approx1046666.67ft^3\text{ (rounded to the nearest hundredth)} \end{gathered}[/tex]The volume of the cone with the given dimensions is
1,046,666.67 cubic feet (rounded to the nearest hundredth)
Without approximation, the answer would be,
1,046,666.6666 cubic feet
A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of careconomy luxury The charge E dollars) to rent an economy car is given by the function E = 15.95 + 0.60M where M is the number of miles drivenThe charge (dollars) to rent a luxury car is given by the function L = 18.20 + 1.25M be how much more it costs to rent a luxury car than an economy car (in dollars)an equation relating C to Simplify your answer as much as possible
C=34.15+0.65M
ExplanationGiven
[tex]\begin{gathered} E=15.95+0.60M \\ L=18.20+1.25\text{ M} \\ where \\ E\text{ is the cost to rental an Economy car} \\ Lis\text{ the total cost to rental an Luxury car} \\ M\text{ is the number of miles traveled} \end{gathered}[/tex]so
to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ \end{gathered}[/tex]so, replace and simplify
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ C=18.20+1.25M-(15.95+0.60M) \\ C=18.20+1.25M-15.95-0.60M \\ C=34.15+0.65M \end{gathered}[/tex]therefore, the answer is
C=34.15+0.65M
I hope this helps you
C=34.15+0.65M
ExplanationGiven
[tex]\begin{gathered} E=15.95+0.60M \\ L=18.20+1.25\text{ M} \\ where \\ E\text{ is the cost to rental an Economy car} \\ Lis\text{ the total cost to rental an Luxury car} \\ M\text{ is the number of miles traveled} \end{gathered}[/tex]so
to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ \end{gathered}[/tex]so, replace and simplify
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ C=18.20+1.25M-(15.95+0.60M) \\ C=18.20+1.25M-15.95-0.60M \\ C=34.15+0.65M \end{gathered}[/tex]therefore, the answer is
C=34.15+0.65M
I hope this helps you
Assume the given function is one to one.Find the indicated values
To solve this question, you have to look for the answers in the table.
Let's analise each part of the question to solve it:
(a) f(1) =
f(1) means the output of the function [f(x)] when x = 1.
Looking for x =1 in the table, you can see that f(x) = 0.
f(1) = 0.
(b) f(x) = 3, x =
Now, you have to find the input (x) when the outpout [f(x)] is 3.
Looking for f(x) = 3, you can see that x = 7.
f(x) = 3, x = 7.
(c) f⁻¹(0) =
Now, you have to evaluate the inverse function.
To look for the values of the inverse function, x will be the output and f⁻¹ will be the input.
To look for f⁻¹(0), look for f(x) = 0 (input) and the output will be 1
f⁻¹(0) = 1.
(d) f⁻¹(x) = 7; x =
Again, you have an inverse function. So, 7 will be the input in the table (x). x is 7 (output).
f⁻¹(x) = 7; x = 3.
What is the answer? Pls
Answer:
70
Step-by-step explanation:
f(1)=6, f(n)=f(n-1)+4
n = 1 → a1 = 6 ← given value
n = 2 → a2 = 6+4 = 10
n = 3 → a3 = 6+4+4 = 14
n = 4 → a4 = 6+4+4+4 = 18
n = 17 → a4 = 6+(4 * 16) =
(its 4 times 16 because 16 is 17 - 1 or n - 1)
n = 17 → a4 = 6+(64) = 70
socraticorg
Tony B
You had $21 to spend on five notebooks after buying them u had $6 dollars how much did each notebook cost.
Let x be the cost of each notebook. We know that we bought 5 of them, then the total cost of the notebooks is:
[tex]5x[/tex]We had 21 dollars and we spent 5x on the notebooks, this can be express as:
[tex]21-5x[/tex]Finally we know that this is equal to the six dollars we had at the end, then we have the equations:
[tex]21-5x=6[/tex]Solving for x we have:
[tex]\begin{gathered} 21-5x=6 \\ 21-6=5x \\ 5x=15 \\ x=\frac{15}{5} \\ x=3 \end{gathered}[/tex]Therefore each notebook cost $3
find regular and irregular polygons
Answer:
Regular Polygon:
D
Irregular Polygon:
A, B, F
Not a Polygon:
E, C
Step-by-step explanation:
Polygons are shapes with straight lines.
Regular polygons have uniform side lengths and angles.
All of the guests at a wedding choose one option for their dinner – the meat option, the fish option, or the vegetarian option. 65% of the guests chose the meat option. 210 guests chose the fish option. 5% of the guests chose the vegetarian option. How many guests chose meat as their dinner option?
Using the percentage of guests choose one option for their dinner , the number of guest chose meat as their dinner option are 455.
As given in the question,
Options given for dinner :
Meat, Fish and Vegetarian
Percent of guest having
Meat in dinner = 65%
Vegetarian = 5%
Number of guest chose fish =210
Percent of guest chose fish = 100 -(65 +5)
= 30%
Let x be the total number of guest
30% of x = 210
⇒ (30/100) × x = 210
⇒ x= (210 ×100) / 30
⇒ x = 700
Therefore, using the percentage of guests choose one option for their dinner ,the number of guest chose meat as their dinner option are 455.
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Linear equations
Which ordered pair is a solution of this equation, -2x+9y=-26
A. (4,4)
B. (-4,-4)
C. (-5,-4)
D. (-4,-5)
The ordered pair which is a solution to the given linear equation is (-5, -4)
What are linear equations?Linear equations are equations that has a leading degree of 1. The standard linear equation is given as Ax + By = C.
Given the linear equation below;
-2x+9y=-26
We need to determine the ordered pair that gives a solution to the linear expression.
For the coordinate point (4, 4)
-2(4) + 9y = -26
9y = -26 + 8
9y = -18
y = -18/9 = -2
This shows that (4, 4) is not a solution.
For the coordinate point (-4, -4)
-2(-4) + 9y = -26
9y = -26 - 8
9y = -34
y = -34/9
This shows that (-4, -4) is not a solution.
For the coordinate (-5, -4)
-2(-5) + 9y = -26
9y = -26 - 10
9y = -36
y = -4
This shows that (-5, -4) is a solution of the linear equation.
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helpppppp math its hard for me
Step-by-step explanation:
You would start off with solving inside, the parenthesis, and you would get -8/27.
Then, your would solve the 1 1/4 - 3/4 and get 1/2.
You then have to multiply -8/27*1/2, which is -4/27.
Lastly, you divide by negative 4.
-4/27 divided by -4.
You have to flip it to multiply the reciprocal, and you get -4/27*-1/4.
Since negative times negative is positive, the answer would be 1/27.
Answer:
1/27
Hope this helped! :)
The diagram below shows an equilateral triangle ABC, with each side 3 cm long. The side [BC] is extended to D so that CD = 4 cm.What is the length of side AD?Round your answer to two decimal places.
The triangle ABC is an equilateral triangle. This means that each angle equals 60°. Hence, the angle at B is 60°.
The length of each side of ABC is given to be 3 cm long.
We can get the length of side AD by solving the triangle ABD using the Cosine Rule given to be:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Since we're considering triangle ABD, and we have the measure of angle B, we can use the relationship:
[tex]b^2=a^2+d^2-2ad\cos B[/tex]Note that a, b, and d are the sides, such that:
[tex]\begin{gathered} a=BD=BC+CD=3+4=7\operatorname{cm} \\ b=AD \\ d=AB=3\operatorname{cm} \end{gathered}[/tex]Substituting these values, we have:
[tex]\begin{gathered} AD^2=7^2+3^2-2(7\times3\times\cos 60) \\ AD^2=49+9-42\cos 60 \\ AD^2=37 \\ AD=\sqrt[]{37} \\ AD=6.08\operatorname{cm} \end{gathered}[/tex]The length of AD is 6.08 cm to 2 decimal places.
due in an hour pls help!!
If the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2), then the coordinates of the M' = (4,1)
The point is M(4,3)
The translation rules is
(x, y) ⇒ (x, y-2)
The translation states that the movement of the graph either horizontally or vertically. When we translate the graph, the shape and size will not change, only the coordinates of the graph changes.
We know the values of
x = 4
y = 3
Substitute the values in the equation
The coordinates of the M' = (x, y-2)
= (4, 3-2)
= (4,1)
Hence, if the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2), then the coordinates of the M' = (4,1)
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Given that f(x)=x^2-3x-54and g(x)=x-9 find (x)(f⋅g)(x)
Answer: [tex]x^4 - 12x^3 - 27x^2 +486x[/tex]
Step-by-step explanation:
[tex](f \cdot g)(x)=f(x)g(x)\\\\=(x^2 -3x-54)(x-9)\\\\=x^3 - 9x^2 - 3x^2 + 27x - 54x + 486\\\\=x^3 -12x^2 -27x+486\\\\\therefore x(f \cdot g)(x)=x(x^3 -12x^2 -27x+486)\\\\=x^4 - 12x^3 - 27x^2 +486x[/tex]
what is the probability that a card drawn randomly from a standard deck of 52 cards is a red three? express your answer as a fraction in lowest terms or a decimal number rounded to three decimal places, if necessary.
Answer:
1/26
Step-by-step explanation:
If the cards are all there, you can count there are 2 red threes. And there are 52 cards. The fraction is 2/52 or 1/26
Given the image Q’(33, 36) and preimage Q(11, 12), by what scale factor was the point dilated?
22
3
24
1/3
Answer:
22
Step-by-step explanation:
Use spinner and color key to find the indicated probabilities. Landing on green or a vowelNot landing on yellow or a constant
Solution:
The spinner has a total of 8 sections.
There are two green sections and 4 four vowel sections where one of the vowels is also green.
Then, the probability of landing on green or a vowel is;
[tex]\frac{5}{8}=0.625[/tex]A manufacturer has been selling 1250 television sets a week at $450 each. a market survey indicates that for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
The demand function of the number of sets sold will increase by 130 per week is p(x) = (-1 ÷ 13)x + 550.
Determine the coordinates of two points mostly online. Estimate the difference in y-coordinates between these two places. Estimate the difference in x-coordinates between these two places. Divide the y-coordinate difference by the x-coordinate difference.
Let p(x) denote the demand function, with x denoting the number of TV sets desired. As stated in the issue, a $10 decrease in p(x) causes a 130 rise in x. As a result, the slope of the demand function graph is -13 ÷ 130 = -1 ÷ 10.
Given p(1250) = 450,
-1 ÷ 10 = (p(x) - 450) ÷ (x - 1250)
p(x) = (-1 ÷ 13)x + 550
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The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
Answer:
A) there are no outliers in this distribution.
Pleas help me !!!! Please!!!
The most appropriate choice for domain of a functions will be given by -
What is a domain of a function
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
The set of values for which the function is defined is called domain of the function.
Here, from the graph, the set of values of x axis for which the graph is drawn is [tex]-6\leq x \leq 6[/tex].
And values of x - axis represents the domain.
So domain of function is {x ∈ [tex]\mathbb{R}[/tex], [tex]-6 \leq x \leq 6[/tex]}
Third option is correct.
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Using positive integers between 1 and 9 and each positive integer at most once, fill in values
to get two constraints so that x = 7 is the only integer that will satisfy both constraints at
the same time.
☐ x+☐ < ☐ x + ☐
☐x+ ☐ > ☐ x+ ☐
Using positive integers between 1 and 9 and each positive integer at most once,
2 x+ 9 < 3 x + 1
6x+ 4 > 5 x+ 8
To get two constraints so that x = 7 is the only integer that will satisfy both constraints at the same time. Upon analysing it can be seen that to the coefficients of x in eaxh equation shouch be two consecutive number. The coefficient on the lesser than side should be lower than the coeffiecient present on the greater than side.
To make the equation in such a way that only 7 satisfy it, the lesser than sides are added with numbers higher than 7 that is 8 and 9.
Therefore, Using positive integers between 1 and 9 and each positive integer at most once,
2 x+ 9 < 3 x + 1
6x+ 4 > 5 x+ 8
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where is the center of dilation located in the image pictured below?
Answer:
V
Step-by-step explanation:
Which expression is equivalent to the given expression? (+2+6)-(- 2+3) x +9 O A I O B. - } +3 O C. x+3 OD. - *+9
Answer:
The equivalent expression is;
[tex]\frac{5}{7}x+3[/tex]Explanation:
We want to simplify the expression;
[tex](\frac{1}{7}x+6)-(-\frac{4}{7}x+3)[/tex]we will first multiply the negative by every term in the bracket, then simplify by collecting the like terms.
[tex]\begin{gathered} \frac{1}{7}x+6-(-\frac{4}{7}x)-(+3) \\ \frac{1}{7}x+6+\frac{4}{7}x-3 \\ \text{collecting the like terms we have;} \\ \frac{1}{7}x+\frac{4}{7}x+6-3 \\ \frac{5}{7}x+3 \end{gathered}[/tex]Therefore, the equivalent expression is;
[tex]\frac{5}{7}x+3[/tex]What is the area, in square centimeters, of the shaded part of the rectangle shown below
Answer:100 cm
Step-by-step explanation: first, you would find the area of the whole rectangle.
L x W = A
10x14=140
Next, find the area of the unshaded part. To do this, you would subtract 6 from 14
14-6=8
After that, times 8 by 10, then divide by 2
10x8=80
80÷2=40
Take 40 and subtract it from the area of the whole rectangle
140-40=100