Answer:
D. x(2x − 3)/ 7
Step-by-step explanation:
[tex]To- divide- by -a -fraction, multiply- by -its -reciprocal.\\\frac{2x-3}{x} *\frac{x^{2} }{7} \\Cancel- the- common -factor -of x\\(2x-3)\frac{x}{7}\\ Apply- the- distributive- property.\\2x\frac{x}{7} -3\frac{x}{7}\\ Multiply ; 2x\frac{x}{7}\\ \frac{2x^2}{7} -3\frac{x}{7}\\ Combine -3- and; \frac{x}{7} \\\frac{2x^2}{7} + \frac{-3x}{7}\\ Move- the- negative- in- front -of -the- fraction.\\\frac{2x^2}{7} - \frac{3x}{7} \\Simplify- terms.\\ x\frac{(2x-3)}{7}\\[/tex]
Answer:
8x
Step-by-step explanation:
Geometry: Similarity, Congruence, Proofs Question: Why are proofs so picky? Why can’t we just measure the two figures to see if they are congruent?
Answer:
Haha proofs are an interesting thing. Usually, nothing is to scale, which is why you can't measure anything. They are pretty annoying, but it helps to know why certain things are the way that they are and develop justification skills for higher level math.
Sorry to discourage you, but you're going to see "Justify" quite a lot in calculus and beyond which is basically a more informal version of a proof
you can never escape it tbh lol
We can't just measure the two figures to see if they are congruent as congruence is about shape and size.
What is congruence?It should be noted that congruence simply means that the shapes have identical length, angles, and size.
Therefore, we can't just measure the two figures to see if they are congruent as congruence is about shape and size.
Learn more about geometry on:
brainly.com/question/24375372
#SPJ9
Parallelogram V W Z X is shown. Point Y is at the bottom center of the shape. Lines are drawn from points V to X through point Y and from points W to Z through point Y. 4 triangles are formed by the lines. If VX = WZ = 40 cm and m∠ZVX = m∠XWZ = 22°, can ΔVZX and ΔWXZ be proven congruent by SAS? Why or why not? Yes, along with the given information, ZX ≅ ZX by the reflexive property. Yes, the triangles are both obtuse. No, the sides of the triangles intersect. No, there is not enough information given.
Answer:
It's D: No, there is not enough information given.
Step-by-step explanation:
just took the quiz
The correct answer option D which is No, there is not enough information given.
What is parallelogram?A parallelogram is a quadrilateral having four sides with two opposite sides parallel to each other. The sum of the angles suspended by all the four sides of the parallelogram is 360.
Using VX = WZ and m∠ZVX = m∠XWZ, we have a side and an angle. In order to prove the triangles congruent by SAS, we must have two sides and the angle between them. With the information we have now, we would have to have VZ = WX. However, we are not given that information.
We do have that ZX = ZX by the reflexive property, but this is not SAS, as the angle we have is not between the two sides.
Therefore correct answer option D which is No, there is not enough information given.
The complete figure is attached with the answer below.
To know more about parallelogram follow
https://brainly.com/question/970600
#SPJ5
The net of a solid figure is shown below: Four squares are shown side by side in a row. The second square has a square above it and a square below it. All the squares have side length equal to 5 inches Which calculation will give the total surface area of the solid figure? 5 × 6 × 6 square inches 6 × 5 × 5 square inches 6 × 5 × 5 × 5 square inches 5 × 6 × 6 × 6 square inchesv
Answer:
6 × 5 × 5 square inches
Step-by-step explanation:
The area of one of the figure's 6 squares is the product of its side length, so is ...
5 × 5 square inches
The area of all 6 of those squares is 6 times this, or ...
6 × 5 × 5 square inches
The British Department of Transportation studied to see if people avoid driving on Friday the 13th. They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations ("Friday the 13th," 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean difference in traffic count between the 6th and the 13th using a 90% level. Dates 6th 13th 1990, July 139246 138548 1990, July 134012 132908 1991, September 137055 136018 1991, September 133732 131843 1991, December 123552 121641 1991, December 121139 118723 1992, March 128293 125532 1992, March 124631 120249 1992, November 124609 122770 1992, November 117584 117263
Answer: The mean difference is between 799586.3 and 803257.9.
Step-by-step explanation: To estimate the mean difference for confidence interval:
Find the statistic sample:
d = value of 6th - value of 13th;Sample mean of difference: mean = ∑d / nSample standard deviation: s = ∑(d - mean)² / n - 1;For the traffic count, mean = 1835.8 and s = 1382607.3
The confidence interval is 90%, so:
α = [tex]\frac{1-0.9}{2}[/tex]
α = 0.05
The degrees of dreedom are:
df = n - 1
df = 10 - 1
df = 9
Using a t-ditribution table, the t-score for α = 0.05 and df = 9 is: t = 1.833.
Error will be:
E = [tex]t.\frac{s}{\sqrt{n} }[/tex]
E = 1.833.([tex]\frac{1382607.3}{\sqrt{10} }[/tex])
E = 801422.1
The interval is: mean - E < μ < E + mean
1835.8 - 801422.1 < μ < 1835.8+801422.1
-799586.3 < μ < 803257.9
The estimate mean difference in trafic count between 6th and 13th using 90% level of confidence is between 799586.3 and 803257.9.
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X>1), n=4, p=0.6.
Answer:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=4, p=0.6)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex] P(X >1)[/tex]
And for this case we can use the complement rule and we got:
[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]
[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]
And replacing we got:
[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]
A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2 comma 6402,640 firms, 709709 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 2929%? Use alphaαequals=0.100.10 to make your decision.
Answer:
Step-by-step explanation:
Using the one sample proportion test:
z = (p-P) / √{P (1-P)/n}
Where p = 709/2640= 0.27, P = 0.29, n= 2640
Thus z = (0.27-0.29) / √{0.29 (1-0.29) / 2640}
z = (-0.02) / √{0.29(0.71) /2640}
z = (-0.02) / √0.00007799
z = (0.02) / 0.0088
z = 2.27
To be able to draw a conclusion, lets find the p value at the 0.1 level of significant: p value is 0.2327. The result is significant as the p value is greater than 0.1 thus we will fail to reject the null and conclude that there is not enough statistical evidence to prove that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29%
you currently have 24 credit hours and a 2.8 gpa you need a 3.0 gpa to get into the college. if you are taking a 16 credit hours this semester. what gpa must you get in order to raise your gpa to the correct level? set up an equation and use algebra to solve.
Answer:
[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]
And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:
[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]
And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:
[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]
And from the previous result we got:
[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]
And solving we got:
[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]
And then we can find the mean with this formula:
[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]
So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0
Step-by-step explanation:
For this case we know that the currently mean is 2.8 and is given by:
[tex] \bar X = \frac{\sum_{i=1}^n w_i *X_i }{24} = 2.8[/tex]
Where [tex] w_i[/tex] represent the number of credits and [tex]X_i[/tex] the grade for each subject. From this case we can find the following sum:
[tex]\sum_{i=1}^n w_i *X_i = 2.8*24 = 67.2[/tex]
And for this case we want a gpa of 3.0 taking in count that in this semester he/ she is going to take 16 credits so then the new mean would be given by:
[tex] \bar X_f = \frac{\sum_{i=1}^n w_i *X_i+w_f *X_f }{24+16} = 3.0[/tex]
And we can solve for [tex]\sum_{i=1}^n w_f *X_f [/tex] and solving we got:
[tex] 3.0 *(24+16) =\sum_{i=1}^n w_i *X_i +\sum_{i=1}^n w_f *X_f [/tex]
And from the previous result we got:
[tex] 3.0 *(24+16) =67.2 +\sum_{i=1}^n w_f *X_f[/tex]
And solving we got:
[tex] \sum_{i=1}^n w_f *X_f =120 -67.2= 52.8[/tex]
And then we can find the mean with this formula:
[tex] \bar X_2 = \frac{\sum_{i=1}^n w_f *X_f}{16}= \frac{52.8}{16}=16=3.3[/tex]
So then we need a 3.3 on this semester in order to get a cumulate gpa of 3.0
if 25% or the person'so salary is $135.75 then what is the amount of his full salary?
Answer:
543
Step-by-step explanation:
let x= total salary
0.25x=135.75
x=543
Answer:
[tex]\$ \: 543.00[/tex]
Step-by-step explanation:
[tex]25\% \times x =135.75[/tex]
[tex]1/4 \times x =135.75[/tex]
[tex]0.25 \times x =135.75[/tex]
[tex]x=135.75 \times 4[/tex]
[tex]x=543[/tex]
can someone help please, it wont give me the last mark
Answer:
The explanation is:
All interior angles in an equilateral triangle are congruent, making them all 60° by the sum of angles in a triangle. Because alternate interior angles of parallel lines are congruent, x = 60°.
Algebra 1
Function Notation Worksheet Alternate
Name
For #I-8: Evaluate the following expressions given the functions below:
f(x) = x2 – 7
g(x) = -3x - 1
j(x)=2x-9
h(x) = 1
X=
1. g(10) =
2. What is the value of x if g(x) = 16
3. f(3) =
4. What is the value of x if f(x) = 23
X
5. h(-2) =
6. What is the value of x if h(x) = -2
X =
7. |(7) =
8. h(a) =
For #9-12: Translate the following statements into coordinate points:
9. S(-1) = 3
10. g(4) = -1
11. h(2) = 8
12. k(2) = 9
Answer:
None
Step-by-step explanation:
The answers are:
1. g(10) -31
2. x= -17/3
3. f(3)= 2
4.x= √30
5. h(-2)= 1
6. x= 0
7. h(a)= 1
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = x² – 7
g(x) = -3x - 1
j(x)= 2x-9
h(x) = 1
1. g(10)= -3(10) -1 = -30 - 1= -31
2. g(x) = 16
-3x- 1= 16
-3x = 17
x= -17/3
3. f(3)= (3)² – 7 = 9- 7= 2
4. f(x)= 23
x² – 7= 23
x² = 30
x= √30
5. h(-2)= 1
6. x= 0
7. h(a)= 1
8. S(-1) = 3
The value of function s(a) at a=-1 is 3.
10. g(4) = -1
The value of function g(a) at a=4 is -1.
11. h(2) = 8
The value of function h(a) at a=2 is 8.
12. k(2) = 9
The value of function k(a) at a= 2 is 9.
Learn more about function here:
https://brainly.com/question/21145944
#SPJ5
Which scenario is the best example of a deus ex machina?
Answer:
D.
Step-by-step explanation:
Deus ex machina is the plot device of using something very improbable to resolve a situation.
Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. Which value represents the probability that he will win the election?
Answer:
The probability is 1
Step-by-step explanation:
P ( Jamaal winning) = Jamaal / number of people running
= 1/1
= 1
Answer:
1
Step-by-step explanation: :-)
Use the Central Limit Theorem to find a mean given a probability Question A video game company sells an average of 132 games a month, with a standard deviation of 9 games. The company is looking to reward stores that are selling in the top 7%. How many video games must a store sell in order to be eligible for a reward if the company is only looking at 36 of their stores. Use the 2-table below: z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 1.1 0.864 0.867 0.869 0.871 0.873 0.875 0.877 0.879 0.881 0.883 1.2 0.885 0.887 0.889 0.891 0.893 0.894 0.896 0.898 0.900 0.901 1.3 0.9030.905 0.9070.908 0.910 0.911 0.913 0.915 0.9160.918 1.4 0.919 0.921 0.922 0.924 0.925 0.926 0.928 0.929 0.931 0.932 1.5 0.933 0.934 0.936 0.937 0.938 0.939 0.941 0.942 0.943 0.944 1.6 0.945 0.946 0.947 0.948 0.949 0.951 0.952 0.953 0.954 0.954
Round the z.score and a to two decimal places. Round up to the nearest whole number.
Answer:
The number of games must a store sell in order to be eligible for a reward is 135.
Step-by-step explanation:
Let the random variable X represent the number of video games sold in a month by the sores.
The random variable X has a mean of, μ = 132 and a standard deviation of, σ = 9.
It is provided that the company is looking to reward stores that are selling in the top 7%.
That is, [tex]P (\bar X > \bar x) = 0.07[/tex].
The z-score related to this probability is, z = 1.48.
Compute the number of games must a store sell in order to be eligible for a reward as follows:
[tex]z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}[/tex]
[tex]\bar x=\mu+z\cdot \sigma/\sqrt{n}[/tex]
[tex]=132+1.48\times (9/\sqrt{36})\\\\=132+2.22\\\\=134.22\\\\\approx 135[/tex]
Thus, the number of games must a store sell in order to be eligible for a reward is 135.
Answer:
1.48
1.5
135
Step-by-step explanation:
For a project in your statistics class you decide to make a histogram of the salary data for players in the National Basketball Association (NBA). Since most of the players in the NBA earn the league minimum based on their years of service and a few superstars earn very high salaries in comparison, which of the following would most likely be a characteristic of your histogram?
a. Skewed-right
b. Skewed-left
c. Symmetric, with a central peak
d. Uniform
Answer:
b. Skewed-left
Step-by-step explanation:
The histogram will be expressed with the x-axis representing the salaries, in growing amount to the right. The y-axis will represent the relative or absolute frequency.
We know that most of the players earn the minimum league wage. Then, we will have a high frequency in the low salaries classes, at the left of the histogram. A few players earn very high salaries, so we will have a right tail with high values for the salaries a little frequency.
There is no symmetry in this histogram and it is not uniform, as there is no representative mean salary.
As most of the data will be close to the left side, we can conclude that the histogram will be skewed-left.
The Histogram of salary data, with most having less salary is RIGHT Skewed
Given : Data of players' salary is concentrated towards towards most players having less ( minimum ) salary.
Right Skewness denotes a distribution where Tail is on the right side. This implies data is highly concentrated toward left side, ie lower independent variable (x - here 'salary') values.
Left Skewness denotes a distribution where Tail is on the left side. This implies data is highly concentrated towards right side, ie higher independent variable (x - here 'salary') values.
In this case : As more players have lower values of independent variable ie salary, so the data will be concentrated at left - having tail at right.
Hence, it will be Skewed Right
To learn more, refer https://brainly.com/question/3907939?referrer=searchResults
What number should be in the blank in the sequence? 7; 17; 37; 77; ___ ; 317
Answer:
the answer is 157
Step-by-step explanation:
7 +10= 17
17+20=37
37+40=77
77+80=157
157+160=317
At the beginning you add +10. Every sequence, you need to multiply that number x2. For example: 10 x 2=20...
9/8+7/40= and does the answer simplify
Answer:
1 3/10
Step-by-step explanation:
9/8 +7/40
Get a common denominator of 40
9/8 *5/5 + 7/40
45/40 + 7/40
52/40
Rewriting as
40/40 +12/40
1 + 3/10
1 3/10
Answer:
1 3/10
Step-by-step explanation:
First, you need to get a common denominator:
8x5=40 <-- common denominator
45/40+7/40= 52/40
yes you can simplify it.
your final answer will be: 1 3/10
66 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a spade? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
0.8397
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the cards are chosen is not important. Also, they are drawn without replacement. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the probability that at least one of the cards drawn is a spade?
Either none is a spade, or at least one is a spade. The sum of the probabilities of these outcomes is 1.
The standard deck has 52 cards, of which 13 are spades. So
Probability that none are spades:
Desired outcomes:
6 cards from a set of 52 - 13 = 39. So
[tex]D = C_{39,6} = \frac{39!}{6!33!} = 3262623[/tex]
Total outcomes:
6 cards from a set of 52. So
[tex]T = C_{52,6} = \frac{52!}{6!46!} = 20358520[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{3262623}{20358520} = 0.1603[/tex]
Probability that at least one is a spade:
1 - 0.1603 = 0.8397
The answer is 0.8397
Check all of the points that are solutions to the system of inequalities.
'X + y 2 2 +4
y< 4
Answer:
C. (5, 3)
D. (7, -1)
Step-by-step explanation:
The requirement that y < 4 eliminates points A, E, F. None of 7, 4, 5 are less than 4.
The requirement that x+y ≥ 6 eliminates point B. 1-1 = 0 is not at least 6.
Points C and D satisfy both inequalities.
Which of the following expressions is equal to -1?
sec90°
sin180°
csc270°
Answer:
csc 270° is the answer.
An ordinary deck of playing cards contains 52 cards, 26 red and 26 black. If a card is dealt to each of 2 players,.
Find in how many different ways this can be done if the following occur.
a. both cards are red. _____ ways
b. both cards are black _____ways
c. one card is black and the other is red. ________way
Answer:
(a)650 ways
(b)650 ways
(c)676 ways
Step-by-step explanation:
There are 26 red and 26 black cards.
If a card is dealt to each of 2 players, we want to find out how many different ways this can be done.
(a)Both cards are red
If both cards are red:
The first red card can be dealt in 26 ways.
The second red card can be dealt in 25 ways.
Therefore: Both Red cards can be dealt in: 26 X 25 = 650 ways
(b)Both cards are black
If both cards are black:
The first black card can be dealt in 26 ways.
The second black card can be dealt in 25 ways.
Therefore: Both black cards can be dealt in: 26 X 25 = 650 ways
(c)One card is black and the other is red.
The red card can be dealt in 26 ways.
The black card can be dealt in 26 ways.
Therefore: Both cards can be dealt in: 26 X 26 = 676 ways
Use the fundamental identities to simply the expression.
Answer:
[tex]\cos (\theta)[/tex]
Step-by-step explanation:
[tex]\dfrac{\tan (\theta) \cot (\theta)}{\sec (\theta)}= \\\\\\\dfrac{\dfrac{\sin (\theta)}{\cos (\theta)}\cdot \dfrac{\cos (\theta)}{\sin (\theta)}}{\dfrac{1}{\cos (\theta)}}= \\\\\\1\cdot \cos (\theta)=\\\\\\\boxed{\cos (\theta)}[/tex]
Hope this helps!
What is the sum of (4x2 – 10x + 3) and (-6x2 + 10x + 12)
Answer:
-2x² + 15
Step-by-step explanation:
Step 1: Add like terms
4x² - 6x² = -2x²
-10x + 10x = 0
12 + 3 = 15
Step 2: Rewrite
-2x² + 15
[tex](8 - 10x + 3) + ( - 12 + 10x + 12)[/tex]
[tex](11 - 10x) + (10x)[/tex]
[tex] 11 - 10x + 10x[/tex]
[tex] = 11[/tex]
Write a system of linear equations for the graph below
Answer:
y = -3x + 3
[tex]y=\frac{1}{3}x-7[/tex]
Step-by-step explanation:
Slope of a line passing through two points ([tex]x_1, y_1[/tex]) and [tex](x_2, y_2)[/tex] is determined by the formula,
Slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
If these points are (0, 3) and (3, -6),
Slope of the line passing through these lines = [tex]\frac{3+6}{0-3}[/tex] = (-3)
Equation of the line which passes through (0, 3) and slope = (-3),
y - y' = m(x - x')
y - 3 = (-3)(x- 0)
y - 3 = -3x
y = -3x + 3
Now slope of another line that passes through (3, -6) and (0, -7),
m' = [tex]\frac{(-6+7)}{(3-0)}[/tex]
m' = [tex]\frac{1}{3}[/tex]
Equation of the line that passes through (0, -7) and slope = [tex]\frac{1}{3}[/tex]
y - (-7) = [tex]\frac{1}{3}(x-0)[/tex]
y + 7 = [tex]\frac{1}{3}x[/tex]
y = [tex]\frac{1}{3}x-7[/tex]
Therefore, system of linear equations are,
y = -3x + 3
[tex]y=\frac{1}{3}x-7[/tex]
If the standard deviation of a population is 20 and we take a sample of size 16 from which to calculate a mean, the standard error (the standard deviation of the sample mean) is:
Answer:
36
Step-by-step explanation:
Find the slope through each pair of two points. Report answers in simplest form.
(-3,6) and (-5,9)
m =
Answer: m=-3/2
Step-by-step explanation:
To find the slope, we use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. With our given points, we can directly plug them into the formula.
[tex]m=\frac{9-6}{-5-(-3)} =\frac{3}{-2}[/tex]
Our slope is m=-3/2.
Can someone help me with this?
Answer:
poop
Step-by-step explanation:
poop
What is (14x2 + 19x - 3) = (2x+3)?
Answer:
Dear User
Answer to your query is provided below
X = 2/7 or X = -3/2
Step-by-step explanation:
Explanation for the same is attached in image
A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 218 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related
Answer:
Step-by-step explanation:
Hello!
Since you didn't upload the data, I'll use my own data to solve the example. The steps will be the same, only the results will change. (see attachment) The hypothesis test will be made using a 5% significance level.
The objective of this exercise is to test if there is an association between two variables:
X₁: The subject is vaccinated, categorized "Yes" and "No"
X₂: The subject got the disease, categorized "Yes" and "No"
These two variables of interest are qualitative categorical and each one of them has two categories.
To test if the variables are associated, considering the type of variables they are, you have to apply a Chi Square test of Independence, where the statistic hypotheses are:
H₀: [tex]P_{ij}= P_{i.} * P_{.j}[/tex] ∀ i= 1, 2 and j= 1, 2
H₁: The variables, vaccination and disease status, are not independent.
α: 0.05
The statistic is
X²= [tex]{r} \atop {i=1} \right.[/tex]∑[tex]{c} \atop {j=1} \right.[/tex]∑[tex]\frac{(O_{ij}-E_{ij})^2}{E_{ij}}[/tex]≈[tex]X^2_{(r-1)(c-1)}[/tex]
i= values in rows
j= values in columns
r= total number of rows
c= total number of columns
This type of test is always one-tailed to the right, meaning that you will reject the null hypothesis to high values of Chi Square. There is only one critical value:
[tex]X^2_{(r-1)(c-1);1-\alpha }= X^2_{(2-1)(2-1);1-0.05}= X^2_{1*1;0.95}= 3.841[/tex]
The decision rule will be:
If [tex]X^2_{H_0}[/tex] ≥ 3.841, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 3.841, do not reject the null hypothesis.
Using the p-value approach, the decision rule is always the same:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
Before calculating [tex]X^2_{H_0}[/tex], you have to calculate the expected frequencies for all categories using the formula:
Ê[tex]_{ij}[/tex]= [tex]\frac{O_{i.}*O_{.j}}{n}[/tex]
Ê₁₁= [tex]\frac{O_{1.}*O_{.1}}{n}= \frac{82*100}{200} = 41[/tex]
Ê₁₂= [tex]\frac{O_{1.}*O_{.2}}{n}= \frac{82*100}{200} = 41[/tex]
Ê₂₁= [tex]\frac{O_{2.}*O_{.1}}{n}= \frac{118*100}{200} = 59[/tex]
Ê₂₂= [tex]\frac{O_{2.}*O_{.2}}{n}= \frac{118*100}{200} = 59[/tex]
[tex]X^2_{H_0}= \frac{(42-41)^2}{41} + \frac{(40-41)^2}{41} + \frac{(58-59)^2}{59} + \frac{(60-59)^2}{59}= 0.0827[/tex]
The p-value for this test is the probability of obtaining a value as extreme as [tex]X^2_{H_0}[/tex]= 0.0827:
P(X₁² ≥ 0.0827)= 1 - P(X₁² < 0.0827)= 1 - 0.2264= 0.7736
Using the critical value approach: the value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.Using the p-value approach: the p-value is greater than the significance level, the decision is to not reject the null hypothesis.Ata 5% significance level, the decision is to not reject the null hypothesis. You can conclude that the vaccination and the disease status of the subjects are not related. The new vaccine does not affect the chances of the subjects getting the disease.
I hope this helps!
answer please anybody ???
Step-by-step explanation:
a) 2x = 8 x 3
2x = 24
x = 12
b) 3x = 12
x = 4
find the values of a and b such that x^2-4x+9=(x+a)^2+b
Answer:
a = -2; b = 5
Step-by-step explanation:
Expanding the right side of the given equation, we have ...
x^2 -4x +9 = x^2 +2ax +a^2 +b
Comparing coefficients, we see ...
-4 = 2a . . . . . coefficient of x term
9 = a^2 +b . . . constant term
The first of these tells us ...
-2 = a . . . . divide by 2
The second of these tells us ...
9 = (-2)^2 +b . . . substitute for a
5 = b . . . . subtract 4
The values of a and b are (a, b) = (-2, 5).
Answer:
a=-2
b=5
Step-by-step explanation:
type this on mathswatch and you will get it right