The rejection region is given by: {F(x) ≤ c} ∪ {F(x) ≥ 1 - c} which is of the form {x ≤ x0} ∪ {x ≥ x1}, where x0 and x1 are determined by c.
To show that the rejection region is of the form {x ≤ x0} ∪ {x ≥ x1}, we can use the fact that the critical value c divides the sampling distribution of the test statistic into two parts, the rejection region and the acceptance region.
Let F(x) be the cumulative distribution function (CDF) of the test statistic. By definition, the rejection region consists of all values of the test statistic for which F(x) ≤ c or F(x) ≥ 1 - c.
Since the sampling distribution is symmetric about the mean under the null hypothesis, we have F(-x) = 1 - F(x) for all x. Therefore, if c is the critical value, then the rejection region is given by:
{F(x) ≤ c} ∪ {1 - F(x) ≤ c}
= {F(x) ≤ c} ∪ {F(-x) ≥ 1 - c}
= {F(x) ≤ c} ∪ {F(x) ≥ 1 - c}
This shows that the rejection region is of the form {x ≤ x0} ∪ {x ≥ x1}, where x0 and x1 are determined by c. Specifically, x0 is the value such that F(x0) = c, and x1 is the value such that F(x1) = 1 - c.
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Jada received a gift of $180. In the first week, she spent a third of the gift money. She continues spending a
third of what is left each week thereafter. Which equation best represents the amount of gift money g, in
dollars, she has after t weeks? Be prepared to explain your reasoning.
Answer:
180 minus 60 equals 120
Step-by-step explanation:
1/3 of 180 equals 60 so you would take 60 out of 180 to get 120 and 120 would be the amount that she spent the rest of the weeks
What is the complete factorization of the polynomial below? x3 + x2 + 4x + 4
Answer:
(x+1)(x+2/)(x-2/)
Step-by-step explanation:
solve the equation r4·r3 = _____
find the fourth proportional to 2,3,6
Answer:
9
Step-by-step explanation:
Let the fourth proportional be x Then
2 : 3 :: 6 : x
2/3 = 6 / x
2x = 3 * 6
x = 18 / 2
x = 9
Hope it will help :)
through (2,3); slope = -2
Answer:
y=-2x+7
Step-by-step explanation:
See image
whyyyyyy does math suck help meeee plzz
Answer:
3 1/2
Step-by-step explanation:
the equation is 7/8x4/1 and can be rewritten as 7x4/8x1 = 28/8 which simplifies to 3 4/8 or 3 1/2
Need help ASAP I will give you 10 points
Answer: x=18
Step-by-step explanation:
First distribute:
(18/6)-(x/6)=0
Isolate the x variable:
(18/6)=(x/6)
18=x
Mare has a monthly cell phone plan that has a fixed charge of $12 per month plus
$0.30 per text message. Marie wants to spend no more than $40 per month on her
call phone. Which inequality represents the number of text messages, X, that Marie
Please hurry
You need to multiply the cost per text message by the number of messages (x) add that to the fixed charge.
The total of those need to be less than or equal to the amount she wants to spend.
The equation would be written as:
0.30x + 12 <= 40
what 20,000 divided by 24 ?
Answer:
833.3333333
Step-by-step explanation:
hope this helps
Step-by-step explanation:
[tex]\qquad\sf\dashrightarrow 20000/24 [/tex]
[tex]\qquad\sf\dashrightarrow 10000/12 [/tex]
[tex]\qquad\sf\dashrightarrow 5000/6 [/tex]
[tex]\qquad\sf\dashrightarrow 2500/3 [/tex]
[tex]\qquad\sf\dashrightarrow 833.3 [/tex]
Jonathan says that when you add 7 2 3 to 2 2 3 , you must add the whole numbers together first ( 7 + 2 = 9 ). Then you just add the numerators together ( 2 + 2 = 4 ), and you add the denominators together ( 3 + 3 = 6 ). So the answer is 9 4 6 . Unfortunately, Jonathan's strategy is incorrect. Solve this problem, and then briefly explain the flaw in Jonathan's reasoning.
Answer:
9 4/3
Step-by-step explanation:
Jonathan working:
Add 7 2/3 to 2 2/3
Step 1: you must add the whole numbers together first ( 7 + 2 = 9 ).
Step 2: Then you just add the numerators together ( 2 + 2 = 4 ),
Step 3: you add the denominators together ( 3 + 3 = 6 ).
Step 4: Answer is 9 4/6
Correct workings:
Add 7 2/3 to 2 2/3
Step 1: you must add the whole numbers together first ( 7 + 2 = 9 ).
Step 2: Then you just add the numerators together ( 2 + 2 = 4 ),
Step 3: you pick one of the denominators because they are the same (3)
Step 4: Answer is 9 4/3
Need help!!!!!! this is for a grade
The Flightless Folly ship has 20 pirates aboard. 12 of those pirates wear an eye patch. What percentage of pirates wear an eye patch on the Flightless Folly?
Which point has the coordinates (2, 3)?
у
5
4
B.
С
3
2
D
A
1
0
1
2
з
4
х
5
ОА
ОС
OD
ОВ
Answer:
Point B
Step-by-step explanation:
The first number in the brackets is X while the second is Y (x, y).
X is the bottom line, while Y is the line going up.
Find 2 on the bottom line and 3 on the upright line. This gives us B.
I am sorry for the poor explanation.
20000 students took a standardized math test. The scores on the test are normally distributed, with a mean score of 85 and a standard deviation of 5. About how many students scored between 90 and 95?
Answer: 2718
Step-by-step explanation:
Given: Mean score = 85
Standard deviation = 5
Let x be the score of a random student that follows normal distribution.
Then, the probability that a student scored between 90 and 95 will be
[tex]P(90< x < 95)\\\\=P(\dfrac{90-85}{5}<\dfrac{x-\mu}{\sigma}<\dfrac{95-85}{5})\\\\= P(1< z< 2)\ \ \ \ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=P(z<2)-P(z<1)\\\\=0.9772-0.8413\\\\=0.1359[/tex]
The number of students scored between 90 and 95 = 0.1359 x (Total students)
= 0.1359 (20000)
= 2718
Hence, The number of students scored between 90 and 95 = 2718
PLS HELP 30 PTS!!!Use the coordinate plane to help you identify the length of each leg then use the Pythagorean Theorem to find the length of CD
Type your answer in the box.
Note: Type in only numeric part of the answer. Round your answer to the nearest hundredth.
Example: 12.70
Answer:
it says 15 points not 30
Step-by-step explanation:
Answer:
10.30
Step-by-step explanation:
Pythagorean Theorem is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]. The short leg(a) is 5 units long and the long leg(b) is 9 units long. CD is the hypotenuse, the longest side (c).
[tex]5^{2}[/tex] +[tex]9^{2}[/tex] =[tex]c^{2}[/tex]
25+81=[tex]c^{2}[/tex]
106=[tex]c^{2}[/tex]
[tex]\sqrt{106}[/tex] = [tex]\sqrt{c^{2} }[/tex]
10.29563014 = c
Rounded to the nearest hundredth, 10.30
To check this is correct, the hypotenuse is the longest side, and 10.30 is longer than 5 and 9.
find the tangents of the acute angle in the right triangle. write each answer as a fraction
Answer:
[tex]tanD=\frac{7}{24}[/tex]
[tex]tanF=\frac{24}{7}[/tex]
Step-by-step explanation:
We are given that
ED=24units
EF=7units
FD=25 units
We have to find the tangents of the acute angle in the right triangle
We know that
tangent=[tex]\frac{Perpendicular\;side}{Base}[/tex]
Using the formula
[tex]tanD=\frac{EF}{ED}[/tex]
[tex]tanD=\frac{7}{24}[/tex]
[tex]tanF=\frac{ED}{EF}[/tex]
[tex]tanF=\frac{24}{7}[/tex]
Suppose the radius of a circle is three units what is the circumference
Answer:
[tex]6\pi[/tex] or [tex]18.84[/tex] units
Step-by-step explanation:
The circumference of a circle can be found using the formula [tex]C=2\pi r[/tex], where [tex]C[/tex] is the circle's circumference and [tex]r[/tex] is the circle's radius. We know that [tex]r=3[/tex] and that we are solving for [tex]C[/tex]. Therefore:
[tex]C=2\pi r\\C=2*\pi *3\\C=6\pi[/tex]
Since [tex]\pi[/tex] is approximately [tex]3.14[/tex], [tex]6\pi =6*3.14=18.84[/tex] units. Hope this helps!
Write an equation and solve: At Trader Joes, Mrs.
Jacobs buys bananas for $0.65 per pound and a
frozen pizza for $4.99. The total for her purchase
was $6.94. How many pounds of bananas did
Mrs. Jacobs buy?
expand the following: 4(2x + 1)
Answer:
the equivalent expression is 8x + 4
Step-by-step explanation:
4(2x + 1) = 4x2 = 8 =
8x + 1 = 4x1 = 4 =
8x + 4
To check your work substitute 1
4(2(1) + 1) = 4(2 + 1) = 4(3) = 12
8(1) + 4 = 8+4 = 12
therefore they are both equivalent
hope this helped!
Please I’m desperate and tell me how you did it
Given:
Triangle EFG is similar to triangle HIJ.
To find:
The measure of side IJ.
Solution:
We know that, corresponding sides of similar triangles are proportional.
Triangle EFG is similar to triangle HIJ.
[tex]\dfrac{EF}{HI}=\dfrac{FG}{IJ}[/tex]
Putting the given values, we get
[tex]\dfrac{7}{32}=\dfrac{4}{IJ}[/tex]
[tex]7\times IJ=4\times 32[/tex]
[tex]IJ=\dfrac{128}{7}[/tex]
[tex]IJ=18.2857[/tex]
[tex]IJ\approx =18.3[/tex]
Therefore, the measure of side IJ is 18.3 units.
What is greater 100,000 cm or 1 mi PLEASE HELPPPPPPP
Answer:
1 mile
Step-by-step explanation:
1m =160934 cm
-2(3x-4)+3x=17 solve for x
Answer:
The answer will be -3
Step-by-step explanation:
Hope this Helped
Answer:
x= -3
Step-by-step explanation:
It is really Easy just Isolate the variable by dividing each factor that don't contain the variable
Find the value of 9x-5 given that – 2x-3=5.
Simplify your answer as much as possible.
Answer:
The value of 9x - 5 is -41.
Step-by-step explanation:
-2x - 3 = 5
-2x = 5 + 3
-2x = 8
x = -4
9x - 5
= 9(-4) - 5
= -36 - 5
= -41
Over the course of 3 days, Calvin spent 10 hours delivering newspapers. He spent the same amount of time each day delivering newspapers. Which of the following equations represents the amount of time Calvin spent delivering papers each day?
A: 3 ÷ 10
B: 10 ÷ 3 =
C:10 ÷ 7 =
D: 7 ÷ 10 =
On Monday ,bo saw 1/5 of birds listed in his guidebook. on Tuesday he saw 3/5 more of birds. what fraction of the birds in the guidebook did bo see in those two days ?
Answer:
4/5Step-by-step explanation:
That would be 1/5 + 3/5 which equals (1+3)/5 = 4/5
Someone plz help me I wil give brainliest
Answer:
The answer is three quarters, one nickel's dime, and a penny!
Step-by-step explanation:
Answer:
Dime- 4
Penny- 1
Half Dollar- 1
Step-by-step explanation:
A dollar is 100 cents and you have 91
91- 50 (half dollar)= 41
41- 1 (one penny)= 40
40- 40 (4 dimes)= 0
Is y=9 a horizontal line or vertical
Answer:
Horizontal
Step-by-step explanation:
Answer:
y = 9 is a horizontal line :)
Step-by-step explanation:
y=9 is the equation of a horizontal line. The slope is 0. This means that for any value of x that is chosen, the y-value is always 9 Hence y=9 .
I need help with this question.
Answer:
[tex]13 {z}^{8} [/tex]
Step-by-step explanation:
The perimeter of a square is represented by the expression 32x-12. . Write two equivalent expressions for the perimeter and explain how to find the length of one side. x=3
Answer:
P = 2(l+w) ----------(1)
P = 4l----------- (2)
P= 32x- 12
4l = 32x- 12
l = 8x- 3
One side will be equal to 21 units and the perimeter will be 84 units when x=3.
Step-by-step explanation:
The perimeter is given by the formula
P = 2(l+w) ----------(1)
where p= perimeter , l= length and w= width.
But a square has the length equal to the width so w= l and the formula becomes
P = 2( l+l)
P = 2 (2l)
P = 4l----------- (2)
The perimeter of the square is
P= 32x- 12
or
4l = 32x- 12
dividing the whole equation by 4 we get
l = 8x- 3
So the length of one side can be obtained by dividing the perimeter by 4.
If x= 3
then
l= 8(3)-3
l= 24- 3
l = 21
One side will be equal to 21 units and the perimeter will be 84 units.
P = 4l = 4(21)= 84
A circular cylinder has a curved surface area 1320cm square and the radius of its base is 10.5cm find the height and volume of cylinder.
Answer:
h=9.51
v=3293.89
Step-by-step explanation:
hope it helps :)
Answer:
h = 9.51
v = 3293.89
Step-by-step explanation:
please mark me as brainliest