At a significance level of 0.05, the sample data is not consistent with the null hypothesis that the proportion of population who would respond "yes" is 0.5. The P-value of 0.0005 is less than 0.05, and also the sample proportion 0.4616 is not in the interval (0.477, 0.523) which we found as 95% Confidence interval.
Therefore, we reject the null hypothesis and conclude that the population proportion of "yes" responses is different from 0.5.
The P-value for a score test for H0: π = 0.5 can be found using the z-score and a standard normal table. The z-score is calculated as
[tex]z = \frac{x-0.5}{0.5\sqrt{\frac{x-0.5}{n} } }[/tex], that is
z = (x - 0.5) / (√(0.5(1 - 0.5) / n)
where x is the sample proportion of "yes" responses (842 / (842 + 982) = 0.4616), π is the population proportion of "yes" responses, and n is the sample size (842 + 982 = 1824).
[tex]z = \frac{0.4616-0.5}{0.5\sqrt{\frac{0.4616-0.5}{1824} } }[/tex]
= (0.4616 - 0.5)/ (√(0.5(1 - 0.5) / 1824)
This gives a z-score of -3.28.
To find the P-value, we can use the standard normal table to find the probability of observing a z-score less than -3.28. This P-value is approximately 0.0005, which is less than the commonly used significance level of 0.05. Therefore, we would reject the null hypothesis that π = 0.5.
To construct a 95% confidence interval for π, we can use the formula for a normal approximation interval:
π ± z×(√(π(1-π) / n)) that is
[tex]\pi \frac{+}{} z\frac{\pi (1 -\pi )}{n}[/tex]
Where π = 0.5, z = 1.96 (for a 95% confidence level), and n = 1824.
This gives a 95% confidence interval of (0.477, 0.523)
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A map of a playground can be represented on the coordinate plane below. The swings are located at (5, 7), the slide is located at (2, –4), and the sandbox is located at (0, 5). Jenny left the swings and walked 3 yards west and 2 yards south. Kent left the sandbox and walked 5 yards east and 4 yards north. If each square of the coordinate plane is equal to one square yard, how many yards north of the swings is Kent located? Help PLS
Answer:
2 yards
Step-by-step explanation:
The coordinates of the location of the swings = (5, 7)
The coordinates of the location of the slides = (2, -4)
The coordinates of the location of the sandbox = (0, 5)
The path through which Jenny walked = 3 yards west and 2 yards south from the swing
The path through which Kent walked = 5 yards east and 4 yards north from the sandbox
The coordinates of Kent's final location = (0 + 5, 5 + 4) = (5, 9)
Given that the coordinate of the location of the swing = (5, 7)
Kent is located at the coordinate (5 - 5, 9 - 7) = (0, 2) relative to the swing
Therefore, Kent is located 2 yards north of the swing.
42 kg in the ratio 4 : 2
Answer:
28 : 14
Step-by-step explanation:
4 : 2
4 + 2 = 6
42 ÷ 6 = 7
7 × 4 = 28
7 × 2 = 14
if you don’t help I could possibly die.
If $3,000 is loaned for 4 years at a
4.5% annual simple interest rate,
how much interest is earned?
Answer:
$540
Step-by-step explanation:
Interest = Principal x Rate x Time
I = 3000(.045)(4)
I = 540
Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
''By taking log'' on both side Mike solve this equation.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 37ˣ = 12
Now,
Since, The expression is,
⇒ 37ˣ = 12
Solve this expression as;
⇒ 37ˣ = 12
Taking log both side, we get;
⇒ log 37ˣ = log 12
⇒ x log 37 = log 12
⇒ x = log 12 / log 37
⇒ x = 1.08 / 1.57
⇒ x = 0.69
Thus, The value of x = 0.69
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Graph the system of equations on the grid below. Y=4x+7 and 2=x-y
The two lines intersect at (-3,-5) and thus a common solution.
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here, the system of linear equations as Y=4x+7 and 2=x-y
On solving these two equations we get that the two lines intersect at (-3,-5) and thus a common solution.
The two equations are plotted in the attachment below.
Hence, The two lines intersect at (-3,-5) and thus a common solution.
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Question 12
In the figure shown, if J, P, and L are the midpoints of KH, HM, and MK, respectively, find the values of x, y, and z.
Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility test for three.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
add all number
9+9+0 = 18
and 18/3 = 6
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On solving the provided question, we can say that in this triangle 2x-6 = 3 => 2x = 9 => x = 9/2 and 2z = 4 => z = 2
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here,
in this triangle
2x-6 = 3
2x = 9
x = 9/2
2z = 4
z = 2
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What is Destiny's hourly wage?
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
or in this case, hourly wage :)
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{200}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{200}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{10}-\underset{x_1}{0}}} \implies \cfrac{ 200 }{ 10 } \implies \cfrac{20}{1}\cfrac{dollars}{hour}\qquad \textit{\$20 per hour}[/tex]
Marking brainliest
Are you against animal testing? If so, why?
Answer:
I am against testing on animals.
Step-by-step explanation:
Personally based on my faith humans are told to make the earth their dominion. To dominate doesn't only mean to use to one's advantage but to also take care of and replenish any loss caused by unintentioned damage. Animals do have feelings, both emotional and physical, and though those feelings may not be quite as developed as those of humans, they are undoubtedly existent. With how far technology has come when it comes to predictability and how calculated and concise science experiments have become, if as the most advanced species on earth we are still unable to determine how long a deodorant or lipstick or eyeliner would last without torturing other species, then what exactly have we achieved, and are we truly any more advanced than we were 10000 years ago? And for things that quite necessarily do need testing like vaccines and medicines it is to some extent understandable, but then again if the death sentence still exists for offenders of heinous crimes , why don't we instead of killing those criminals dedicate them to science and research for testing of vaccines and medicines. That way we all benefit from it. They don't have to die and neither do the animals and neither do we. It's a far stretch of a solution but alternatives can be made. Where there's a will there's a way.
helpp pleaaaaaaaaaseee
The linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)
6x + 2y = 60 (the equation representing the total cost of Rew)
and the solution would be x = 8, y = 6.
What is a system of linear equations?
A system of linear equations is a set of two or more linear equations that describe a relationship between multiple variables. The variables in each equation are related to each other, and the solution of a system of linear equations is the set of values that satisfy all of the equations in the system.
In this case, since Kent and Rew each bought the same amount of boondins and hopts, we can use the same variable names (x for boondins and y for hopts) for both of them. We can use this information to write two equations to model the relationship between the amounts of boondins and hopts that Kent and Rew bought:
4x + 5y = 62 (the equation representing the total cost of Kent)
6x + 2y = 60 (the equation representing the total cost of Rew)
This system of linear equations is called a system of two equations in two variables.
Hence, the linear equations would be
4x + 5y = 62 (the equation representing the total cost of Kent)
6x + 2y = 60 (the equation representing the total cost of Rew)
and the solution would be x = 8, y = 6.
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HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
A
Step-by-step explanation:
Y intercept means x=0. f(0)=0-3=-3
g(0)=4
y intercept for f(x) is-3,y intercept for g(x)is 4
Solve this system of equations. Explain how you determined your answer.
2x−4y=−14
−8x+4y=−4
Answer:
(3, 5 )
Step-by-step explanation:
Given the 2 equations
2x - 4y = - 14 → (1)
- 8x + 4y = - 4 → (2)
Adding (1) and (2) term by term will eliminate the y- term
- 6x + 0 = - 18
- 6x = - 18 ( divide both sides by - 6 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (2)
- 8(3) + 4y = - 4
- 24 + 4y = - 4 ( add 24 to both sides )
4y = 20 ( divide both sides by 4 )
y = 5
solution is (3, 5 )
how many four digit positive integers have exactly two even numbers?
Answer:
You will need to eaither choose 2 odd numbers and 1 even number or choose 2 even numbers and 1 odd number
Step-by-step explanation:
In both cases we will be choosing two from 5 and 1 from 4
Line M contains the points (-3,2) and (5,1) line n contains the points (2,7) and (1,-1) which statement is TRUE about lines m and n
Answer:
The lines are perpendicular
Step-by-step explanation:
Answer:
perpendicular
Step-by-step explanation:
Can someone figure out these for me.
Answer:
Algebra :(
Step-by-step explanation:
Anyway haiiiiiiii remember me Katie i saw your question lol haiii
I need help.
professional?
- needed
The equation of the linear function after a translation down 9 units is given as follows:
f(x) = x - 11.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the y-intercept, representing the value of y at which the graph cross the y-axis.The graph of the function crosses the y-axis at y = -2, hence the intercept b is given as follows:
b = -2.
When x increases by 2 units, from x = 0 to x = 2, y increases by 2 units, from y = -2 to y = 0, hence the slope is calculated as follows:
m = 2/2.
Then the function is of:
y = x - 2.
After the translation down 9 units, 9 is subtracted from the function, hence:
f(x) = x - 2 - 9
f(x) = x - 11.
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Help me Ive been asking for hours pls help
Is ∆MHT ≈ ∆TMA? If so, state the congruence property you used to make the determination and fully explain your reasoning. Be sure to cite all properties, definitions, or theorems used in your reasoning. You may use a flowchart if you wish. If they are not congruent, explain why they are not.
Please help
Answer:
Triangle MHT and Triangle TMA are congruent.
If you reflect over the dotted line, point H and A will be on the same point. The triangles are also the same shape and same size.
In an isosceles triangle ABC with AC = BC, point M is on the side BC , and point N is on the segment MC. It is known that MN=AM, and m∠BAM=m∠NAC. Find m∠MAC
The measure of angle MAC is 90°.
What is means of isosceles triangle?
An isosceles triangle is a type of triangle where two of its sides are congruent, or have the same length. This means that if you draw a line down the center of an isosceles triangle, it will split the triangle in half and both halves will have the same side lengths.
In an isosceles triangle, the angles opposite the congruent sides are congruent. Therefore, in triangle ABC, m∠BAM = m∠CAB = m∠NAC.
Since angle BAM and angle NAC are congruent, and they are both supplementary to angle MAC, it follows that angle MAC is congruent to itself.
Therefore, m∠MAC = m∠MAC = 180 - m∠BAM = 180 - m∠NAC.
Since m∠BAM = m∠NAC, we can conclude that
m∠MAC = 180 - m∠NAC = 90°
Hence, the measure of angle MAC is 90°.
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Answer quickly IF u love god i do please
Answer:
The answer is 11
Step-by-step explanation:
The answer is 11 because you need to add the sides up that the points are on point P is 5 Point Q is 3 and point R is 3 5+3 is 8 8+3 is 11
Answer:
19.56
Step-by-step explanation:
PR = [tex]\sqrt{3^{2} + 3^{2} }[/tex] = [tex]\sqrt{18}[/tex] = 3[tex]\sqrt{2}[/tex]
RQ = [tex]\sqrt{5^{2} +5^{2} }[/tex] = [tex]\sqrt{50}[/tex] = 5[tex]\sqrt{2}[/tex]
QP = [tex]\sqrt{8^{2} +2^{2} }[/tex] = [tex]\sqrt{68}[/tex] = 2[tex]\sqrt{17}[/tex]
Perimeter = sum of the sides = 3[tex]\sqrt{2}[/tex] + 5[tex]\sqrt{2}[/tex] + 2[tex]\sqrt{17}[/tex] = 19.56
Break the triangle PQR into 3 right triangles, with each leg being a hypotenuse. Then you can use the Pythagorean theorem to find the length of each leg. Add them all together to get the perimeter.
PLEASE HELP BETS ANSWER GETS CROWN THERE ARE 2 QUESTIONS
ANSWER LIKE THIS
Q1. ANSWER
Q2. ANSWER.
NO LINKS OR FILES PLEASEEEE. (btw this is my last one)
Answer:
I am sorry but I can not answer as you have forgotten part of the question. Please repost and make sure you have everything there before you post the question!
It’s about solving systems of equations does anyone know the answer please
Answer:
A
Step-by-step explanation:
One Solution
A= v-u/ t
v = 37. 6 correct to 3 significant figures.
u = 11. 3 correct to 3 significant figures.
t = 8. 4 correct to 2 significant figures.
Work out the upper bound for the value of a.
Show your working clearly
The upper bound of a is 3.13.
Upper Bound
The smallest amount that would round up to the following anticipated value is the upper bound.
Significant FiguresThe number of digits that contribute to a value's level of precision is known as significant figures and is typically found in measurements. As soon as a digit is non-zero, we begin calculating significant numbers.
Given in the question
v = 37. 6
u = 11. 3
t = 8. 4
To find:- a = (v - u)/t
Solution: -
Since finding the upper boundary for a
Upper boundary = (upper v - lower u) / (lowest t)
So putting the value values of v, u, t in we get the value
a = (37.6 - 11.3) / 8.4
Therefore the value of a = 3.13
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These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
15 20
30
40
45
Town B
15 20 25 30
58
0
5
10
15
20
SO
55 60
25 30 35 40 45
Degrees (F)
Which statement is the most appropriate comparison of the centers?
A. The median temperature for both towns is 30°
B. The mean for town A, 30°, is greater than the mean for town B, 25
ОО O
C. The median temperature for both towns is 20°
D. The median for town A, 30°, is greater than the median for town B.
Answer: D
Step-by-step explanation:
What the answer too 3(-8+f)=57
The Answer is ...
f = 27
ILL BRAINLIEST YOU PLEASE HELP ME
Remember SohCahToa
For this let's use sine.
SinA = opposite/adjacent
SinA = x/c
We know c = 8 and A = 21
Sin21 = x/8
x = (sin21)8
Put that in the calculator:
x = 2.87 (rounded)hope this helps :D
-1.8 × (-9.3)
How do I find this with the whole equation written out show your work of how you do this please
Answer:
16.74
Step-by-step explanation:
-1.8 times -9.3 will have a positive answer because 2 negative numbers will have a positive sum
-1.8
x -9.3
---------
5 4
1 6 2 0
---------
1 6 7 4 ||| add two decimal spaces
16.74
Does the point (6, 2) satisfy the equation y = x - -4?
HELP, I need to find out this question!
How do you find the angles of an isosceles triangle given three sides and no angles?
The Law of Cosines can be used to calculate the angles of an isosceles triangle given three side lengths. Two of the angles are equal, while the third can be found by subtracting the two known angles from 180°.
Since you are given three sides of an isosceles triangle, you can use the Law of Cosines to calculate the angles of the triangle. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following equation holds:
c² = a² + b² - 2abcosC
Therefore, you can rearrange the equation to solve for angle C:
C = arccos((a² + b² - c²) / (2ab))
For an isosceles triangle, two of the angles will be equal, so you can calculate those two angles using the equation above, and the third angle can be found by subtracting the two known angles from 180°.
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