Answer:
90% confidence interval for the difference between the two population means
( -23.4166 , -6.5834)
Step-by-step explanation:
Step(i):-
Given first sample size n₁ = 100
Given mean of the first sample x₁⁻ = 178
Standard deviation of the sample S₁ = 35
Given second sample size n₂= 100
Given mean of the second sample x₂⁻ = 193
Standard deviation of the sample S₂ = 37
Step(ii):-
Standard error of two population means
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }[/tex]
[tex]se(x^{-} _{1} -x^{-} _{2} ) = 5.093[/tex]
Degrees of freedom
ν = n₁ +n₂ -2 = 100 +100 -2 = 198
t₀.₁₀ = 1.6526
Step(iii):-
90% confidence interval for the difference between the two population means
[tex](x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})[/tex]
(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)
(-15-8.4166 , -15 + 8.4166)
( -23.4166 , -6.5834)
A box of chocolates contains five milk chocolates, three dark chocolates, and four white chocolates. You randomly select and eat three chocolates. The first piece is milk
chocolate, the second is white chocolate, and the third is milk chocolate. Find the probability of this occuring.
Answer:
60/220
Step-by-step explanation:
we use combination,
[tex] (\frac{5}{1} ) \times ( \frac{4}{1} ) \times ( \frac{3}{1} )[/tex]
[tex]5 \times 4 \times 3 = 60[/tex]
then, all divided by,
[tex] (\frac{12}{3}) = 220 [/tex]
[tex]60 \div 220[/tex]
The probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The sample contains five milk chocolates, three dark chocolates, and four white chocolates. Therefore, the probability that the first piece is milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{5}{12}[/tex]
Now, since the chocolate is been eaten the sample size will reduce from 12 chocolates in total to 11 chocolates in total (four milk chocolates, three dark chocolates, and four white chocolates). Therefore, the probability of the second piece being white chocolate is
[tex]\rm Probability=\dfrac{\text{Number of White choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{11}[/tex]
Now, as the chocolate is been eaten the sample size will reduce from 11 chocolates in total to 10 chocolates in total (four milk chocolates, three dark chocolates, and three white chocolates). Therefore, the probability of the third piece being milk chocolate is
[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]
[tex]\rm Probability=\dfrac{4}{10}[/tex]
Thus, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is
[tex]\rm Probability=\dfrac{5}{12}\times \dfrac{4}{11} \times \dfrac{4}{10} = \dfrac{80}{1320} = 0.06[/tex]
Hence, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.
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Line k has a slope of 2/3. Find the slope of a line parallel to line k.
Answer:
We have to remember
slope = m
if the slope of line is parellel so it will be the same with other slope
m1= m2
2/3= 2/3
so the answer is 2/3
hope it helps ^°^
Answer:
2/3
Step-by-step explanation:
Parallel lines have the same slopes. Therefore,
[tex]m_{k} =m_{p}[/tex]
The slope of line k ([tex]m_{k}[/tex]) will be equal to the slope of the line parallel to k ([tex]m_{p}[/tex]).
We know that the slope of line k is 2/3.
[tex]m_{k}=\frac{2}{3}[/tex]
Therefore, the slope of the line parallel to line k is also 2/3.
[tex]\frac{2}{3}=m_{p}[/tex]
The slope of a line parallel to line k is 2/3.
The sum of two numbers is 13. Two times the first number minus 3 times the second number is one. If your ex stand for the first number and why for the second number what are the two numbers
Answer:x = 8, y = 5
Step-by-step explanation:The sum of two numbers is 13. Two times the first number minus three times the second numberis 1. If you let x stand for the first number and y for the second number, the two numbers are: A. x = 8, y = 5
The height of the plant is given by the equation h = 0.5d + 4. Rewrite this as a function rule where f(x) is the height, in centimeters, and x is the time, in days. Use the rule to complete the table, and then use the drawing tools to create the graph representing this relationship.
Answer:
Here's what I get
Step-by-step explanation:
h = 0.5d + 4
A function rule tells you how to convert an input value (x) into an output value (y).
Your function rule is
ƒ(x) = 0.5x + 4
An easy way to represent your function is to make a graph.
The easiest way to make a graph is to make a table containing some inputs and their corresponding outputs.
Here's a typical table.
[tex]\begin{array}{cc}\textbf{x} &\textbf{y} \\0 & 4 \\2 & 5 \\4 & 6 \\6 & 7\\6 & 8 \\\end{array}[/tex]
The graph is like the one below.
Help me solve this and get marked branliest:
Answer:
75°
Step-by-step explanation:
Let's find the size of x°
BCFE has four sides so the sum of its angles sizes is 360°.
● CBE + 110 + 110 + CFE = 360
CFE is equal to 65° since they have the same vertex
● CBE + 220 + 65 = 360
● CBE + 285 = 360
● CBE = 360-285
● CBE = 75
CBE and x° have the same size since they share the same vertex.so:
● x° = 75°
Answer:
75°
Step-by-step explanation:
CBE = x (vertically opposite angles are equal)
CFR = 65° (vertically opposite angles are equal)
C+F+E+B= 360 (angles in a quadrilateral sum up to 360°)
110+65+110+x=360
x= 75°
Answer the questions attached about the given sequence: -33, -27, -21, -15, ...
Answer:
see below
Step-by-step explanation:
-33, -27, -21, -15,....
-33 +6 = -27
-27+6 = -21
-21+6 = -15
This is an arithmetic sequence
The common difference is +6
explicit formula
an=a1+(n-1)d where n is the term number and d is the common difference
an = -33 + ( n-1) 6
an = -33 +6n -6
an = -39+6n
recursive formula
an+1 = an +6
10th term
n =10
a10 = -39+6*10
= -39+60
=21
sum formula
see image
The sum will diverge since we are adding infinite numbers
In the diagram, the vertices of the square lie at the centers of the four partial circles. What is the area of the entire shape? Use the value pi = 3.1416
The area of the entire shape is 33,562 square units
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
The figure is made up of a square and four 3/4 circles. So the total area will be equal to the sum of the area of the square and the sum of the 3/4 th circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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The area of the entire shape is 33,562 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Here, we have,
The figure is made up of a square and four 3/4 circles.
So the total area will be equal to the sum of the area of the square and the sum of the 3/4 the circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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Find the distance between points P(5, 1) and Q(3, 4) to the nearest tenth.
3.6
5
9.4
13
Answer:
≈ 3.6
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (P(5, 1) and (x₂, y₂ ) = Q(3, 4)
d = [tex]\sqrt{(3-5)^2+(4-1)^2}[/tex]
= [tex]\sqrt{(-2)^2+3^2}[/tex]
= [tex]\sqrt{4+9}[/tex]
= [tex]\sqrt{13}[/tex] ≈ 3.6 ( to the nearest tenth )
Answer:
3.6
Step-by-step explanation:
Look above bru
If you have a piece of glass that is 12in X 12in - how many square feet is it?
Answer:
1 square foot is the answer
Answer:
1 ft^2
Step-by-step explanation:
We know 12 inches = 1 ft
12 inches by 12 inches
1 ft by 1 ft
The area is 1 * 1 = 1 ft^2
A hunter shot 7 ducks. The hunter's dog recovered 5/7 of the ducks. How many ducks were recover
Answer:
5
Step-by-step explanation:
Just multiply 5/7 by 7 since his dog retrieved 5/7 out of the 7 ducks he shot.
Answer:
5
Step-by-step explanation:
7*5/7
7 represents the # of ducks
5/7 represents the # of ducks that were recovered
The question asks the number of ducks that were recovered so you should multiply the total # of ducks there are by the fraction that were recovered.
These figures are similar. The area of one is given. Find the area of the other. PLZ HELP Plz ps the answer is not 12
==================================================
Explanation:
Dividing the side lengths, the scale factor is 6/3 = 2. This means the larger figure has a side length twice as long compared to its smaller counterpart.
How can we use this to figure out how the areas are connected? By simply squaring the scale factor to get 2^2 = 2*2 = 4, then we divide the larger area over 4 to get 24/4 = 6.
The longer side is 2 times longer
The larger area is 4 times larger
--------------------
Let's say we had a 3 by 3 square. It's area would be 9.
Also, let's say we had a 6 by 6 square. It's area is 36.
Notice the ratio of areas is 36/9 = 4, so the larger square is 4 times larger than the smaller. This 4 matches with what we got earlier.
----------------------
Another example:
square A is 7 by 7 with area 49
square B is 21 by 21 with area 441
ratio of areas is 441/49 = 9, which is exactly equal to 3^2, and the 3 comes from the ratio of the sides 21/7 = 3.
------------------------
So in short, you find the linear scale factor by dividing the sides. Then you square the result to get the area scale factor, which you use to find the smaller area.
linear scale factor = (new side)/(old side)
area scale factor = (linear scale factor)^2
smaller area = (larger area)/(area scale factor)
Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the early years but began to grow rapidly after 2005. But the iPod era is coming to a close. Smartphones with music and video
Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the
END OF THE IPOD ERA
players are replacing the iPod, along with the category of device it helped to create. Sales of the iPod worldwide from 2007
through 2011 (in millions) were
approximately
N(0= -165t2 + 13.13t+ 39.9 (0 < t< 4)
in year t, where t= 0 corresponds to 2007. Show that the worldwide sales of the iPod peaked sometime in 2009. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?
Answer:
a. t = 2.48 will be a period within 2009.
b. 56.16 million
Step-by-step explanation:
Here is the complete question
Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the early years but began to grow rapidly after 2005. But the iPod era is coming to a close. Smartphones with music and video
Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the
END OF THE IPOD ERA
players are replacing the iPod, along with the category of device it helped to create. Sales of the iPod worldwide from 2007
through 2011 (in millions) were
approximately
N(0= -2.65t2 + 13.13t+ 39.9 (0 < t< 4)
in year t, where t= 0 corresponds to 2007. Show that the worldwide sales of the iPod peaked sometime in 2009. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?
a. Show that the worldwide sales of the iPod peaked sometime in 2009
N(t) = -2.65t² + 13.13t + 39.9
To find the maximum value of N(t), we find dN(t)/dt and equate it to zero
dN(t)/dt = d[-2.65t² + 13.13t + 39.9]/dt
dN(t)/dt = -5.3t + 13.13 = 0
-5.3t = - 13.13
t = -13.13/(-5.3)
t = 2.477
t ≅ 2.48
d²N(t)/dt² =d[-5.3t + 13.13]/dt = -5.3 < 0. So, t = 2.48 is a maximum point
Since t = 2 is 2009 and t = 3 is 2010, t = 2.48 will be a period within 2009.
b. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?
The approximate largest number of ipods sold is when t = 2.48
N(2.48) = -2.65(2.48)² + 13.13(2.48) + 39.9
N(2.48) = -16.29856 + 32.5624 + 39.9
N(2.48) = 56.16384
N(2.48) ≅ 56.16 million
Which equation represents the data shown in the table provided in the image?
A. y = 2x + 1
B. y = 3x — 1
C. y = 2.5x
D. y = 2.5x + 1
Please include ALL work! <3
The correct answer is A. y = 2x +1
Explanation:
An equation is a statement that shows equality. In this context, the equation should lead to two equal numbers even if the values of y and x change. In this context, the correct equation is y= 2X + 1 because this is the only one, in which, the value of Y is always equivalent to 2x + 1. To prove this, let's replace y and x for the values of the table.
First column
5 = 2 · 2 + 1
5 = 4 + 1
5 = 5
Second Column
9 = 2 · 4 + 1
9 = 8 + 1
9 = 9
Third column
13 = 6 · 2 + 1
13 = 12 + 1
13 = 13
Fourth column
17 = 8 · 2 + 1
17 = 16 + 1
17 = 17
3-(-4) answer the question
Answer:
7Step-by-step explanation:
[tex]3-(-4) \\-\times - = +\\3+4 \\=7[/tex]
Answer:
7
Step-by-step explanation:
because you when multiply -1 by -4 u get positive 4 then 3 + 4 equals 7
Use technology to find the P-value for the hypothesis test described below. The claim is that for 12 AM body temperatures, the mean is F. The sample size is n and the test statistic is t.
Answer:
P value = 0.1575
Step-by-step explanation:
Data provided in the question
t = 1.021
n = 33
[tex]\mu[/tex] = 98.6° F
Based on the above information, the P-value could be determined by using the excel spreadsheet i.e. shown in the attachment
So, the P value is 0.1575
The 1.021 denotes the test statistic
32 denotes degrees of freedom
And,
1 denotes one tailed alternative hypothesis.
Find the value of x , 5x =625 , also find 3x and 2x-1
Answer:
That's your answer
x= 125
3x= 375
2x-1= 249
PLEASE HELP..............
Which of the following has no solution?
{x | x < 0} and {x I x > 0}
{x | x ≤ 0} and {x | x ≥ 0}
{x | x ≤ 0} or {x | x ≥ 0}
Answer:
{x | x < 0} and {x I x > 0} has no solution
Step-by-step explanation:
x cannot be less than zero AND more than zero at the same time, so the first inequality has no solution.
{x | x < 0} and {x I x > 0}
Answer:
A
Step-by-step explanation:
Choice A has the two options:
[tex]x<0 \text{ and } x>0[/tex]
In other words, x must be a number such that it is negative (left option) and positive (right option) at the same time.
There can't be such number (and 0 is not included in the answer choices since it is not less/more than or equal to). Thus, Choice A has no solution.
The keyword here is and. If instead of and it was or, then the choice does indeed have a solution.
What is the result of question?
Answer:
B
Step-by-step explanation:
x can not be greater than (1,325-270)/26 because $270 is fixed for the rental
Shawna finds a study of American men that has an equation to predict weight (in pounds) from
height (in inches): y = -210 + 5.6x. Shawna's dad's height is 72 inches and he weighs 182 pounds.
What is the residual of weight and height for Shawna's dad?
a. 11.2 pounds
b. -11.2 pounds
c. 193.2 pounds
d. 809.2 pounds
Answer:
-11.2 pounds
Step-by-step explanation:
It is given that,
Shawna finds a study of American men that has an equation to predict weight (in pounds) from height (in inches):
y = -210 + 5.6x
Height of Shawna's dad is 72 inches
Weight is 182 pounds
We need to find the residual of weight and height for Shawna's dad.
Predicted weight of 72 inches men,
y' = -210 + 5.6(72)
y' = 193.2 pounds
So, residual is :
Y = 182 - 193.2
Y = -11.2 pounds
So, the residual of weight and height for Shawna's dad is -11.2 pounds.
Answer:
-11.2 pounds
Step-by-step explanation:
Got it right on the test.
Just a little bit of math hw
Answer:
Put 0 in the box.
Step-by-step explanation:
The value x = 0 if replaced in the given equation will always make the denominator zero.
Best Regards!
PLEASE HELP ! (2/5) -50 POINTS -
Answer:
symmetric
Step-by-step explanation:
it kind of evenly falls to the left and right from the highest value in the middle
skewed would be different and would look like a straight line not a quadratic equation
I need help pls. Algebra
Answer:
The answer is option AStep-by-step explanation:
f(x) = (x+1)³ + 4
To find f-¹(x) equate f(x) to y
That's
y = (x+1)³ + 4
Next interchange the terms x becomes y and y becomes x
That's
x = ( y+1)³ + 4
Make y the subject
(y+1)³ = x - 4
Find the cube root of both sides
That's
[tex]y + 1 = \sqrt[3]{x - 4} [/tex]
Send 1 to the right side of the equation
That's
[tex]y = \sqrt[3]{x - 4} - 1[/tex]
So we have the final answer as
[tex]f ^{ - 1} (x) = \sqrt[3]{x - 4} - 1[/tex]
Hope this helps you
Answer:
option 1
Step-by-step explanation:
f(x)=(x+1)³+4
to find the inverse interchange the variable and solve for y
inverse f(x)=(y+1)³+4
x=(y+1)³+4
x-4=(y+1)³
y+1=∛x-4
y=∛x-4 -1
Residents of four cities are able to vote in an upcoming regional election. A newspaper recently conducted a survey to gauge support for each of the two candidates. The results of the poll are shown in the two-way frequency table below.
Answer:
3 only
Step-by-step explanation:
Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.
Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.
Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.
Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.
Therefore, the true statement is III only.
More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Data given in the table shows the data of elections between two candidates among the different cities.
What is Statistic?
Statistics is the study of mathematics that deals with relations between comprehensive data.
I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.
II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false
III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.
IV. Overall, more residents support candidate A than candidate B. it is also false.
Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
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Evaluate the function f(x)=x^2-2x+2. a.f(2)
Answer:
f(2) = 2
Step-by-step explanation:
f(x)=x^2-2x+2
Let x=2
f(2)=2^2-2*2+2
= 4 -4 +2
= 2
If Q(x)=x2−6x−2, find Q(−4).
Answer:
Q(-4) = 38Step-by-step explanation:
Q(x)=x² − 6x − 2
To find Q(−4) substitute the value of x which is - 4 into Q(x)
That's
Q(-4) = (-4)² - 6(-4) - 2
Q(-4) = 16 + 24 - 2
We have the final answer as
Q(-4) = 38Hope this helps you
If 7time the 7th of Ap. Is equal of 11 tomes its 11th term find 18th term
0 0
,
---------------
A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5. The test rejects the null hypothesis if either 0 or 10 heads are observed.
(a) What is the significance level of the test?
(b) If, in fact, the probability of heads is 0.1, what is the power of the test?
Answer:
(a) The significance level of the test is 0.002.
(b) The power of the test is 0.3487.
Step-by-step explanation:
We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.
The test rejects the null hypothesis if either 0 or 10 heads are observed.
Let p = probability of obtaining head.
So, Null Hypothesis, [tex]H_0[/tex] : p = 0.5
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.5
(a) The significance level of the test which is represented by [tex]\alpha[/tex] is the probability of Type I error.
Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.
Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;
P(Type I error) = [tex]\alpha[/tex]
P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true) = [tex]\alpha[/tex]
Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.
So, X ~ Binom(n = 10, p = 0.5)
P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true) = [tex]\alpha[/tex]
[tex]\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}[/tex] = [tex]\alpha[/tex]
[tex](1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})[/tex] = [tex]\alpha[/tex]
[tex]\alpha[/tex] = 0.0019
So, the significance level of the test is 0.002.
(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.
Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.
Also, the power of the test is represented by (1 - [tex]\beta[/tex]).
So, here, X ~ Binom(n = 10, p = 0.1)
[tex]1-\beta[/tex] = P(X = 0/[tex]H_0[/tex] is true) + P(X = 10/[tex]H_0[/tex] is true)
[tex]1-\beta[/tex] = [tex]\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}[/tex]
[tex]1-\beta[/tex] = [tex](1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})[/tex]
[tex]1-\beta[/tex] = 0.3487
Hence, the power of the test is 0.3487.
How dose this input and output table work?
Aswer:I am sure of the answer it is 6 and 42
Step-by-step explanation:
5+30=3512+30=4230+30=6036+30=6640+30=60Find the standard form of the equation of the ellipse with the given characteristics. center: (0, 0) focus: (3, 0) vertex: (4, 0)
Answer:
[tex]\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]
Step-by-step explanation:
Since the vertex of the parabola is at (4,0), it has the vertex on the x axis (horizontal axis). The standard equation of an ellipse with horizontal major axis is given by:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Where (h,k) is the center of the ellipse, a is the vertex and ±√(a²- b²) is the focus (c).
Since the ellipse center is at (0, 0), h = 0 and k = 0. Also the vertex is at (4, 0) therefore a = 0
To find b we use the equation of the focus which is:
[tex]c=\sqrt{a^2-b^2}\\ \\Substituing:\\\\3=\sqrt{4^2-b^2} \\4^2-b^2=3^2\\b^2=4^2-3^2\\b^2=16-9\\b^2=7\\b=\sqrt{7}[/tex]
Substituting the values of a, b, h and k:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{\sqrt{7} ^2}=1\\\\\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]
State the correct polar coordinate for the graph shown:
Answer:
Solution : ( - 5, 5π / 4 )
Step-by-step explanation:
There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. r is the directed distance from the pole, and theta is the directed angle from the positive x - axis. Let's start by listing coordinates when r is positive. r here is 5 units from the positive x - axis.
( 5, θ ) theta here is between 30 and 60 degrees, so we can say it's about 45 degrees.
( 5, θ ) theta here is the remaining negative side of 360 - 45 = 315. That would make it - 315.
And when r is negative ( r < 0 ),
( - 5, θ ) now the point is going to lie on the ray pointing in the opposite direction of the terminal side of theta. This will be 45 degrees more than 180, or 180 + 45 = 225 degrees.
Right away we know that ( - 5, 225° ) is our solution, we don't have to consider the second case. Converting 225 to radians in terms of π will be 5π / 4 radians, giving us a solution of ( - 5, 5π / 4 ) or option b.
