a) The test statistic for the two independent samples is 0.7
b) The p-value for the test sample is 0.483 , here p-value is greater than significance level.Thus, there is no sufficient evidence to reject null hypothesis.
Given,
significance level, \alpha = 0.04
From population 1,
Mean, [tex]x_1=13.2[/tex]
variance, [tex]\sigma^2_1=39[/tex]
standard deviation, [tex]\sigma_1 =6.24[/tex]
sample size,[tex]n_1=62[/tex]
From population 2,
Mean, [tex]x_2=11.5[/tex]
variance, [tex]\sigma^2_2 = 29[/tex]
standard deviation, [tex]\sigma_2=4.47[/tex]
Test hypothesis,
[tex]H_0:(\mu_1-\mu_2)=1.6\\\\H_a:(\mu_1-\mu_2)\neq1.6[/tex]
a)
The test statistic can be determined by formula,
[tex]z=\frac{(x_1-x_2)-d}{\sqrt{\frac{S^2_1}{n^2_1}+\frac{S^2_2}{n_2}}}[/tex]
[tex]d=\mu_1-\mu_2=1.6[/tex]
[tex]z=\frac{(13.2-11.5)-1.6}{\sqrt{\frac{6.24^2}{62^2}+\frac{4.47^2}{51}}}\\\\z=\frac{0.1}{\sqrt{0.01+0.007}}\\\\z=\frac{0.1}{0.13}=0.7[/tex]
b)
P-value can be calculated by the z-score table
as z=0.7 then from z-value table
p=0.483
A p-value greater than 0.04 (> 0.04) indicates strong support for the null hypothesis. This means that the null hypothesis is retained and the alternative hypothesis is rejected. It is important to note that you cannot accept the null hypothesis; we can only reject it or fail to reject it.
To learn more about test statistic refer here
https://brainly.com/question/14128303
#SPJ4
Write each of these numbers in base five as a sum of multiples of powers of five (5):
(a). 1012⁵
(b). 101⁵
(c). 1.1⁵
(d). 10.21⁵
(e). 210⁵
Answer:
Step-by-step explanation:
a) 1012⁵ can be written as:
1012⁵ = 15¹² + 05¹¹ + 1*5¹º
= 5¹² + 5¹º
= 3125 + 625
= 3750
(b) 101⁵ can be written as:
101⁵ = 15⁴ + 05³ + 1*5²
= 5⁴ + 5²
= 625 + 25
= 650
(c) 1.1⁵ can be written as:
1.1⁵ = 15¹ + 15º
= 5¹ + 5º
= 25 + 5
= 30
(d) 10.21⁵ can be written as:
10.21⁵ = 15² + 05¹ + 25º + 15⁻¹
= 5² + 2*5º + 5⁻¹
= 25 + 10 + 0.2
= 35.2
(e) 210⁵ can be written as:
210⁵ = 25⁴ + 15²
= 2*625 + 25
= 1250 + 25
= 1275
What is true about machine learning algorithms? A/Model is fitted using training dataset B/Performance of the model is assessed using test data C/Model is validated on validation dataset D/Model is calibrated on test dataset E/Validation dataset is used to minize model overfitting Select all what applies to traditional classification tree model: A/Group of answer choices B/Unsupervised learning method C/Requires categorical output(target) variable D/Does not require any output variables E/None of the above F/Supervised learning method
A. Model is fitted using training dataset and E. Validation dataset is used to minimize model overfitting are true about machine learning algorithms
The process by which an AI system completes its task—generally, forecasting output values from provided input data—is known as a machine learning algorithm. Classification and regression are the two key operations of machine learning algorithms.
Simple linear regression, decision trees, logistic regression, the KNN algorithm, and other well-known supervised learning techniques are some examples.
Machine learning is crucial because it helps businesses identify trends in customer behaviour and operational patterns and facilitates the creation of new goods.
According to the question,
Option A and option E are correct about the machine learning algorithms
To know more about machine learning algorithms here
https://brainly.com/question/28391243
#SPJ4
Find the measure of one exterior angle in each regular polygon. Round your answer to the
nearest tenth if necessary.
3)
45°
27.7°
51.4°
8.8 Use Runge-Kutta method of fourth order to solve numerically the initial value problem
10(dy/dx) = x²+y² , y(0)=1
and find y in the interval 0 ≤x ≤ 0.4 , taking h=0.1.
The value of y(0.4) is 1.04384484247985 using Runge-Kutta method of fourth order .
What is Runge-Kutta method of fourth order ?
The RK4 method, also known as the fourth-order Runge-Kutta method, is the Runge Kutta technique most frequently employed to get the answer to a differential equation. For a given point x, the Runge-Kutta technique returns an approximation of the value of y. The Runge Kutta RK4 method can only be used to solve first order ODEs.
The step size is h = 0.1
f(x,y) = (x²+y²)/10
Step 1:
x₁ = 0 + 0.1 = 0.1
k₁ =f(0,1) = 0.1
k₂ = f(1/20, 1.005) = 0.1012525
k₃ = f(1/20, 1.005062625) =0.101265088017189
k₄ = f(1/10, 1.01012650880172) = 0.103035556378395
y₁ = 1+ (1/10)/6 +(0.1 + 2⋅0.1012525 + 2⋅0.101265088017189 + 0.103035556378395) = 1.01013451220688
Step 2:
x₂ = x₁ + h = 1/5
k₁ =f(1/10,1.01013451220688)=0.103037173275143
k₂ = f(3/20,1.01528637087064) = 0.105330641487567
k₃ = f(3/20, 1.01540104428126) = 0.105353928072747
k₄ = f(1/5, 1.02066990501415) = 0.10817670550016
y₂ =1.01013451220688 + (1/10)/6 +(0.103037173275143 + 2⋅0.105330641487567 + 2⋅0.105353928072747 + 0.10817670550016) = 1.02067756250514
Step 3:
x₃ = x₂ + h = 3/10
k₁ =f(1/5, 1.02067756250514)=0.108178268660144
k₂ = f(1/4,1.02608647593815)=0.111535345610318
k₃ = f(1/4, 1.02625432978566)=0.111569794940382
k₄ = f(3/10, 1.03183454199918)=0.115468252206266
y₃ =1.02067756250514 + (1/10)/6 (0.108178268660144 + 2⋅0.111535345610318 + 2⋅0.111569794940382 + 0.115468252206266) = 1.03184184253794
Step 4:
x₄ = x₃ + h = 2/5
k₁ =f(3/10, 1.03184184253794) = 0.115469758801209
k₂ = f(7/20,1.037615330478)=0.119914557404297
k₃ = f(7/20, 1.03783757040816)=0.119960682255071
k₄ = f(2/5, 1.04383791076345)=0.1249597583947
y₄ = 1.03184184253794 + (1/10)/6 (0.115469758801209 + 2⋅0.119914557404297 + 2⋅0.119960682255071 + 0.1249597583947) = 1.04384484247985
y(0.4) ≈ 1.04384484247985
To learn more about Runge-Kutta method of fourth order, click on below link:
https://brainly.com/question/13514876
#SPJ1
Can someone help me?
Answer:
Y=6x-12
Step-by-step explanation:
whenever the X is at zero the number across from it is the Y-intercept. and to find the slope just count how much they are increasing or decreasing by.
Which of the following is an example of a combination?
O A. The number of ways 3 people can sit on a couch.
O B. Picking 4 sets of towels out of 20 different sets.
• C. The number of ways 12 picture frames can be arranged on a shelf.
• D. Selecting a first, second and third place winner at a beauty
competition.
Answer: A or D
Step-by-step explanation: It can be A. But it can also be D. I would try D tho because with D, your combining 3 people together.
Answer to this required:
Answer:
9
Step-by-step explanation:
3.4^0 = 1
9^1 = 9
1 * 9 = 9
Which variable has a binomial distribution?
When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws.
When tiles are drawn, without replacement, from a bag of lettered tiles, X is the number of times it takes to get a vowel.
When tiles are drawn, without replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws.
When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of times it takes to get a vowel.
When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws variable has binomial distribution
The possibility that a value would take one of two independent values given a particular combination of factors or assumptions is summarised by the statistical distribution known as the binomial distribution.
The basic presumptions of the binomial distribution are:
each trial has a single possible outcome each trial has an equal chance of success each trial is either independent of the others or mutually exclusive.As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.
The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.
The result is then multiplied by the sum of the number of attempts and the number of successes.
To know more about binomial distribution here
https://brainly.com/question/14565246
#SPJ4
Select the best answer. The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean (a) if the sample size is reasonably large (for any population). (b) if the population is Normally distributed and the sample size is reasonable large. (c) if the population is Normally distributed (for any sample size). (d) if the population is Normally distributed and the population standard deviation is known (for any sample size). (e) if the population size is reasonably large (whether the population distribution is known or not).
The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.
Given that,
The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean,
In layman's words, the theorem asserts that regardless of the form of the initial population distribution, the sampling distribution of the mean tends to resemble a normal distribution as the sample size rises.
Statistics benefits from the Central Limit Theorem because it makes it safe to assume that the sampling distribution of the mean will be typically normal. As we will see in the next section, this means that we can benefit from statistical methods that presume a normal distribution.
The distribution of people's heights within a population is one illustration of how the central limit theorem is put to use. Even though the population's distribution of heights is not normal, when we sample this population, the distribution of the sample averages will be roughly normal.
Therefore,
The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.
To learn more about Central limit theorem visit :
brainly.com/question/18403552
#SPJ4
A game show host is going to draw a random number from 1 to 10. If the number is odd, you win $17. If the number is even, you win nothing. If you play the game, what is the expected payoff?
You are solving the equation √x+2= 12 and decide to start by squaring both sides. Which equation results if you
square both sides as your first step?
Ox+2=12
Ox+2=144
O² + 4 = 144
Oz² + 2x + 4 = 144
The equation that result if you square both sides of the equation √x+2 = 12 is x + 2 = 144.
How to solve equations?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Therefore, the equation √x+2= 12 can be solved as follows;
The first step to solve the equation is by squaring both sides of the equation as follows:
√x+2 = 12
square both sides of the equation
Hence,
(√x+2)² = 12²
The square root will cancel the square on the left side of the equation. Therefore,
(√x+2)² = 12²
x + 2 = 12 × 12
Hence,
x + 2 = 144
learn more on equation here: https://brainly.com/question/15595229
#SPJ1
I kinda need help
x + 19 -x + 10
Answer:x+19-x+10 is equal to 29.
Use the matrices below to perform matrix multiplication.
B=[2−1060311], C=⎡⎣⎢4−251068⎤⎦⎥
The matrix resulting from the multiplication of matrices B and C is given as follows:
[-92, -730; 3350, 19648]
How to multiply the matrices?The matrices in this problem are defined as follows:
B = [2, -10; 60, 311]. (; represents new line, the comma separates elements on the same line).C = [4, -25; 10, 68].For the product of the matrices, the row of matrix B multiplies the column of matrix C.
Then the element at the first row and the first column of the product matrix is given as follows:
2 x 4 - 10 x 10 = -92
The element at the first row and the second column of the product matrix is given as follows:
2 x -25 - 10 x 68 = -730.
The element at the second row and the first column of the product matrix is given as follows:
60 x 4 + 311 x 10 = 3350.
The element at the second row and the second column of the product matrix is given as follows:
60 x -25 + 311 x 68 = 19648.
More can be learned about multiplication of matrices at https://brainly.com/question/24274686
#SPJ1
How many different ways can the 11 letters in
the word PROBABILITY be arranged?
Answer: 1
Step-by-step explanation:
Use a sign chart to solve the inequality. Express the solution in inequality notation and in interval notation. X2 - 5x - 36 < 0 The solution expressed in inequality notation is.
The solution in inequality notation and in interval notation is (-∞ . -√5]∪[√5,36)
The term inequality refers the a relationship between two expressions or values that are not equal to each other is called 'inequality.
Here we have given the inequality (x² - 5)/ (x - 36) < 0
And we need to find the solution in inequality notation and in interval notation.
In order to find the inequality notation, we have to solve the given inequality, then we get.
(x² - 5)/ (x - 36) < 0
(x² - 5) < 0
x² < 5
x < √5
While we looking into the inequality we must know that the denominator must not be 0.
So, the interval notation can be written as,
=> (-∞ . -√5]∪[√5,36)
To know more about Inequality here.
https://brainly.com/question/28823603
#SPJ4
For rhombus LMNO, m∠LON = 102° and NP = 5 units.
Rhombus L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. All sides are congruent.
Use the diagram of rhombus LMNO to find the missing measures.
The measure of ∠LPM is
°.
The measure of ∠PMN is
°.
The length of LN is
units.
the measure of ∠LPM is 90°
the measure of ∠PMN is 102°
the length of LN is 10 units.
Define Rhombus.
A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal.
For a Rhombus, LMNO
∠LON = 102°
NP = 5 units
By the properties of Rhombus, we know that
All sides of a rhombus are congruent (equal)
So, LM = MN = NO = OL
and
Opposite angles are equal and the opposite sides are parallel.
So, ∠LON = 102° = ∠LMN
Since Adjacent angles add up to 180°.
Therefore ∠L + ∠M = 180°
∠M + ∠N = 180°
∠N + ∠O = 180°
∠O + ∠L = 180°
So, ∠N = 180° - ∠O = 180° - 102° =78°
∠L = 180° - ∠O = 180° - 102° =78°
∠M = 180° - ∠L = 180° - 78° =102°
Diagonals bisect each other at 90° or we can also say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.
So, ∠LPM = ∠NP0 = ∠MPN = ∠LPO =90°
Thus, the measure of ∠LPM is 90°
the measure of ∠PMN is 102°
the length of LN is 10 units.
Learn more about Rhombus properties by:
https://brainly.com/question/12189679
#SPJ1
Answer:
Lpm= 90
PMN=51
LN= 10
Step-by-step explanation:
Help me!!!
Graph the equation:
y - 2 = 3 (x - 2)
Answer:
See below and attached graph
Step-by-step explanation:
If you are using a graphing calculator it is a breeze. You write down the equation as it is and it should plot it, depending on what calculator you use.
If you are doing this manually here are the steps
We are given y - 2 = 3(x-2)
Expand the brackets on the right hand side
3(x - 2) = 3x - 6
So the original equation becomes
y - 2 = 3x - 6
Adding 2 to both sides
y - 2 + 2 = 3x -6 + 2
y = 3x - 4 [1]
This form of equation is known as a slope-intercept form of the line
We need two points to plot a line. This can be done by choosing a value for x, finding the y value which gives one point. Then repeat for another value of x to get y for that value giving another point. Draw a straight line through both points
Point 1
Let's choose x = 2 and plug this into the equation [1]
y = 3·2 - 4 = 6- 4 = 2.
So (2, 2) is one point on the graph
Point 2
Choose another value for x, say x = 4
y = 3·4 - 4
y = 12-4
y = 8
So (4, 8) is another point
Draw a line through these two points
expressions equivalent to 9 2/3
The equivalent expression for the given expression is 29/3.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given mixed fraction [tex]9\frac{2}{3}[/tex].
There are equivalent improper fractions for all mixed numbers. By multiplying the integer by the denominator and then adding the numerator, they are transformed. The numerator will not change.
Convert mixed fraction to improper fraction as follows
Improper fraction = [(Numerator × Denominator)+Numerator]/Denominator
[(9×3)+2]/3
=[27+2]/3
= 29/3
Therefore, the equivalent fraction for the given mixed fraction is 29/3.
To learn more about an equivalent expression visit:
https://brainly.com/question/28170201.
#SPJ1
Which statement correctly applies mathematical reasoning to find the possible values for x in the equation x − 1.2 = 1.6 and you get this
Answer:
2.8
Step-by-step explanation:
x-1.2=1.6
x=1.2+1.6
x=2.8
Solve ABC using diagram and the given measurement A=64 a=7.4
Answer:
Hope this helps!
3 QUESTIONS
Company 1 charges $2500 for the first 100 feet of fence, and $25 for each
additional foot. Write an equation and determine the cost of Company 1 to
complete the fencing job.
Company 2 charges $39 per foot of fence. Write an equation and determine
the cost of Company 2 to complete the fencing job.
if both companies charge 7% sales tax, which company would you choose?why?
I would select company 2 because it has lower cost and tax amount for complete fencing job.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Let, f = Total feet of the fence
For company 1 :
Given that 25 $
eq : (f-1)x25 + 2500
= (100 -1)25 + 2500
= 99 x 25 = 2500
= 4975 $
For company 2 :
Given that 39 $
Now if company 1 charges 7 % taxes then,
4975 x 7%
= 4975 + 348.25
= 5323.25$
and for company 2
39 x 7%
= 39 + 2.73
= 41.93 $
To know more about linear equations:
Brainly.com/question/24469790
#SPJ1
Which ordered pair lies on the graph of the function y = -2x + 1? (0, -2) (2, -2) (3, -5) (5, 2
So, the ordered pair which lies on the graph of the function y = -2x + 1 is (3,-5)
We will use the substitution method and check for all the ordered pair which are given
If the ordered pair lies on the graph, then it should satisfy the function.
So,
Given,
y = -2x+1
First check for (0,-2)
x=0, y=-2
Substitute the values,
y = -2x+1
-2=-2(0)+1
-2=1
It is false.
Next check for (2,-2)
x=2, y=-2
Substitute the values,
y = -2x+1
-2=-2(2)+1
-2=-3
It is false.
Next check for (3,-5)
x=3, y=-5
Substitute the values,
y = -2x+1
-5=-2(3)+1
-5=-5
It is true.
Next check for (5,2)
x=5, y=2
Substitute the values,
y = -2x+1
2=-2(5)+1
2=9
It is false.
To learn more about ordered pair, visit:
brainly.com/question/11139505
#SPJ1
I need help with my Geo hw!-
Answer:
listed below
Step-by-step explanation:
5.) x=77 and y=63
6.)y=60 and x= 1230
7.)y=65 and x=92
8.)y=69 and x=175
Here is a linear equation: y= 1 4x+2. What is the x-intercept of the graph of the equation?
As per the linear equation, the x-intercept of the graph of the equation will be (-8, 0).
What is slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the information given in the question,
The given equation is,
y= -1/4 x + 2
Now, let's take y = 0 for x- intercept,
So, the equation will be,
0 = 1/4x + 2
1/4x = -2
x= -8
The x-intercept is (-8, 0).
To know more about Slope:
https://brainly.com/question/3605446
#SPJ1
The question sees incomplete, your question may be:
Here is a linear equation: y = 1/4x + 2 What is the x-intercept of the graph of the equation?
researchers randomly select a married couple in which both spouses are employed. let x be the income of the husband and y be the income of the wife. suppose that you know the means mx and my and the variances s2x and s2y of both variables.
It is reasonable to take the variance of the total income to be [tex]\sigma_x^2 + \sigma_y^2[/tex].
How to obtain the variance of the distribution of the sum?When two variables are added, we have that:
The mean of the sum variable is given by the sum of of the means of each variable.The standard deviation of the sum variable is given by the square root of the sum of the variances of each variable.The variances for each variable are given as follows:
Income of husband: [tex]\sigma_x^2[/tex].Income of wife: [tex]\sigma_y^2[/tex].Then the standard deviation of the total income, which is the combination of the income of the husband and of the wife, is calculated as follows:
[tex]\sigma = \sqrt{\sigma_x^2 + \sigma_y^2}[/tex]
The variance is the square root of the variance, hence it is obtained as follows:
[tex](\sigma)^2 = (\sqrt{\sigma_x^2 + \sigma_y^2})^2 = \sigma_x^2 + \sigma_y^2[/tex]
Which means that it is reasonable to take the variance of the total income to be [tex]\sigma_x^2 + \sigma_y^2[/tex].
Missing InformationThe problem asks if it is reasonable to take the variance of the total income to be [tex]\sigma_x^2 + \sigma_y^2[/tex].
More can be learned about the addition of statistical variables at https://brainly.com/question/3764906
#SPJ1
What is the end behavior of the graph of the polynomial function f(x) = –x5 + 9x4 – 18x3?
The end behavior of the graph of the polynomial function:
As x approaches ∞, y approaches -∞
As x approaches -∞, y approaches ∞
What is an end behavior?
The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f.
Here, we have
f(x) = –x⁵ + 9x⁴ – 18x³
F(x) is a fifth-degree (odd function ) with a negative leading coefficient
If the exponent is odd and the leading coefficient is negative then the end behavior is
As x approaches ∞, y approaches -∞
As you go on the right, f(x) goes down
As x approaches -∞, y approaches ∞
As you go on the left, f(x) goes up.
Hence, the end behavior of the graph of the polynomial function: As x approaches ∞, y approaches -∞
As x approaches -∞, y approaches ∞
To learn more about the end behavior from the given link
https://brainly.com/question/27983072
#SPJ1
Find tan(0), if cot(0) = -2.6
According to Trigonometric Identity , tan(theta) = -5 / 13
What are Trigonometric Identities ?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. The relationship between a triangle's side length and angle is expressed by a variety of specific trigonometric identities.
Sin, cos, and tan are the three fundamental trigonometric ratios. The reciprocals of sin, cos, and tan are represented by the three additional trigonometric ratios sec, cosec, and cot in trigonometry, respectively.
According to the given information
We know that
tan(theta) = 1/cot(theta)
= 1 / -2.6
= -1 / 2.6
= -10 / 26
= -5 / 13
According to Trigonometric Identity , tan(theta) = -5 / 13
To know more about Trigonometric Identities
https://brainly.com/question/24377281
#SPJ1
Please help and explain this simple mathematics to me.
Thank you
I'll go over problem 9 part (a) to get you started.
The sine rule, aka law of sines, is this
[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}[/tex]
where the uppercase letters A,B,C are the angles and the lowercase letters a,b,c are the sides opposite those respective angles. Eg: angle B is opposite side b.
Some textbooks may have the lowercase letters up top, but it doesn't matter since it's the same ratio. All that matters is things stay consistent. The lowercase letters must be together on the same level, and same goes for the uppercase letters on their own separate level.
We can then break up that equation into these 3 separate equations, to make things more bite-sized so to speak.
[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\\\\frac{\sin(B)}{b} = \frac{\sin(C)}{c}\\\\\frac{\sin(A)}{a} = \frac{\sin(C)}{c}\\\\[/tex]
Let's focus on the 3rd equation and do a bit of algebraic manipulation like so
[tex]\frac{\sin(A)}{a} = \frac{\sin(C)}{c}\\\\\sin(A) = \frac{a\sin(C)}{c}\\\\\frac{\sin(A)}{\sin(C)} = \frac{a}{c}\\\\[/tex]
Through similar steps, we can say:
[tex]\frac{\sin(B)}{b} = \frac{\sin(C)}{c}\\\\\sin(B) = \frac{b\sin(C)}{c}\\\\\frac{\sin(B)}{\sin(C)} = \frac{b}{c}\\\\[/tex]
-------------------------------------------
To summarize the previous section, we found that:
[tex]\frac{\sin(A)}{\sin(C)} = \frac{a}{c}\\\\\frac{\sin(B)}{\sin(C)} = \frac{b}{c}\\\\[/tex]
It then allows us to do the following steps for problem 9, part (a)
[tex]\frac{a+b}{c} = \frac{\sin(A)+\sin(B)}{\sin(C)}\\\\\frac{a+b}{c} = \frac{\sin(A)}{\sin(C)}+\frac{\sin(B)}{\sin(C)}\\\\\frac{a+b}{c} = \frac{a}{c}+\frac{b}{c}\\\\\frac{a+b}{c} = \frac{a+b}{c}\\\\[/tex]
We have confirmed that the equation in problem 9 part (a) is indeed an identity. Take note how I kept the left hand side the same the entire time while the right hand side transformed into the left side.
Similar steps will be taken for problem 9, part (b). I'll let you do that part.
The pair of points (−6, y) and (4, 8) lie on a line with a slope of 5/2. Set up and solve for the missing y-value using the slope formula. Show all work!
We know that the required value of y is -17 using the slope formula.
What is the slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
The slope of a line can be used to gauge how steep it is.
The slope is theoretically determined as "rise over run" (change in y divided by change in x).
So, we have the slope 5/2.
The points are: (−6, y) and (4, 8)
The slope formula: m = y2 - y1/x2 - x1
Now, insert the values and calculate y as follows:
m = y2 - y1/x2 - x1
5/2 = 8 - y/4 + 6
5/2 = 8 - y/10
5/2 * 10 = 8 - y
25 = 8 - y
-y = 25 - 8
-y = 17
y = -17
Therefore, we know that the required value of y is -17 using the slope formula.
Know more about the slope here:
https://brainly.com/question/29280886
#SPJ1
A professor wanted to know what proportion of college students believe in ghosts. She polled 200 students and found that 58% said they believe in ghosts. Create a 99% confidence interval for the true proportion of college students believing in ghosts. a. (0.5116, 0.64840 b. (0.2074, 0.3727) c. (0.4901, 0.6699) d. (0.2271,0.3529)
A 99% confidence interval for the true proportion of college students believing in ghosts is Option(c) (0.4901, 0.6699)
According to the question,
A professor wanted to know what proportion of college students believe in ghosts.
For that he drawn a sample from the college.
Sample size : n = 200
Proportion of students that believed in ghosts in sample = 58%
=> p = 0.58
Proportion of students who does not believe in ghost : q = 1 - p
=> q = 0.42
We have to create a 99% confidence interval for a true proportion of college students believing in the ghosts
Formula of C.I = [tex]p \pm ( z_{\alpha} \sqrt{\frac{pq}{n}})[/tex]
Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size
C.I at 99% = 0.58 ± 2.576 √0.58×0.42/200
=> 0.58 ± 2.576 √0.001218
=> 0.58 ± 2.576 × 0.035
=> 0.58 ± 0.08958
C.I = ( 0.58 - 0.08958 , 0.58 + 0.08958)
=> C.I = (0.4901, 0.6699)
Hence, Option (c) is correct
To know more about Confidence interval here
https://brainly.com/question/29680703
#SPJ4
Answer:
41%
Step-by-step explanation:
