Answer:
b. The mean of the sampling distribution will be equal to 0.2028.
f. The sampling distribution will be approximately normal.
g. The standard deviation of the sampling distribution will be 0.0336.
Step-by-step explanation:
We use the Central Limit Theorem to solve this question.
Central Limit Theorem:
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\).
The sample proportion being approximately normal means that option f. is correct.
Of 143 men, 29 said they would.
This means that \(p = \frac{29}{143} = 0.2028\)
This means that option b is correct.
g. The standard deviation of the sampling distribution will be 0.0336.
Lets find the standard deviation.
Sample of 143, so \(n = 143\)
\(s = \sqrt{\frac{0.2028*0.7972}{143}} = 0.0336\)
So option g. is correct.
The statements that accurately describe the sampling distribution of the sample proportion of men would return money from a found wallet are;
B) The mean of the sampling distribution will be equal to 0.2028.
F) The sampling distribution will be approximately normal.
G) The standard deviation of the sampling distribution will be 0.0336.
Central Limit Theorem.
We are given the true proportion of all adult men who will return the money as; p = 18% = 0.18
Thus, the population mean = 0.18
Now, out of 143 men, 29 said they will return the money. Thus;
Sample mean = Sample proportion = 29/143 = 0.2028
The formula for the sampling standard deviation is;
s = √[p^(1 - p^)/n]
s = √[0.2028(1 - 0.2028)/143]
s = √0.001130574545
s = 0.0336
Looking at the options and comparing to the answers gotten above, only option B, F and G are correct.
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20 POINTS PLEASE HELP ! Use the image to answer both parts of the question.
Use the discriminant to determine all values of k which would result in the graph of the equation
y
=
3
x
2
+
k
x
+
75
y=3x
2
+kx+75 being tangent to the x-axis.
Answer:
sauce is 177013
Step-by-step explanation:
Let f(x) = x ^ 2 g(x) = sqrt(x - 1) and h(x) = 2x + 3 Express each function k as a composite of two out of these three functions.
k(x) = sqrt(x ^ 2 - 1)
We can write k(x) as the composition of g(x) and f(x).
k(x) = g(f(x))
How to express k(x) as a composition?A composition of two functions means that we need to evaluate one function in the other one.
Here we have the functions:
f(x)= x²
g(x) = √(x - 1)
h(x) = 2x + 3
And we know that:
k(x) = √(x² - 1)
So we have a square root, then we need to evaluate g(x), and the argument is a square, then we need to evaluate in f(x), the composition is:
k(x) = g(f(x))
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A batch of chili uses 1.5 pounds of ground meat for every 2 pounds of tomatoes. What is the whole number ratio of meat to tomatoes? 04:3 O 3:1 01:3 03:4 which option is ok?
Answer:
3 : 4
Step-by-step explanation:
meat : tomatoes
= 1.5 : 2 ( multiply both parts by 2 )
= 3 : 4
I rent a gym for $150 for 30 students. Another time I rent the gym for $350 for 70 students. What is my rate per student?
Answer:
The rate is 5 dollars per student.
Step-by-step explanation:
The rate per student can be found with \(\frac{dollars}{student}\):
\(\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}\)
The rate is 5 dollars per student.
Give the equation of the circle centered at the origin and passing through the point (0, 6).
The equation of circle is x² + y² = 36.
We have,
Center= (0, 0)
Passing point = (0, 6)
We know the equation of circle is
(x-h)² + (y-k)² = r²
where (h, k) be the center and r be the radius.
Now, the radius of circle is
= √(6-0)² + (0-0)²
= √36
= 6 unit
So, the equation of circle
(x-0)² + (y-0)² = 6²
x² + y² = 36
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The system has no solution.
The system has a unique solution:
System B
(x, y)= (1
x+4y=4
-x=4y-4
O The system has infinitely many solutions.
They must satisfy the following equation:
y= 0
Answer:
21
Step-by-step explanation:
Just add then multiplay the numbers.
Find the value of y.
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
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What’s the answer????
The equation of the circle in standard form with a center at (-6, 5) and passing through the point (-11, 3) is (x + 6)² + (y - 5)² = 29.
What is the equation of the circle?
The equation of a circle in standard form with a center at (h, k) and a radius r is:
(x - h)² + (y - k)² = r²
Center: (h, k) = (-6, 5)
Point on circle: (-11, 3)
Substituting these values into the standard form equation:
(x - (-6))² + (y - 5)² = r²
(x + 6)² + (y - 5)² = r²
Now we need to find the value of r, which is the radius of the circle.
The distance between the center (-6, 5) and the point (-11, 3) is equal to the radius of the circle.
Using the distance formula:
r = √((x₂ - x₁)² + (y₂ - y₁)²)
r = √((-11 - (-6))² + (3 - 5)²)
r = √((-5)² + (-2)²)
r = √(25 + 4)
r = √29
r² = 29
The equation of the circle:
(x - h)² + (y - k)² = r²
(x + 6)² + (y - 5)² = 29
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Question 2: Benjamin rolls an ordinary six-sided dice and flips a coin. List all the possible outcomes.
Answer:
Step-by-step explanation:
Please help for a TEST tomorrow!!
Answer:
sorry for my bad writing
Will states ¨there is no number greater than .59 that has a 5 in the tenths place
Answer: there is a greater number for 59 with 5 tenths places but i'm sure what the other part of the answer could be but I gave you a few hints to this problem and I hope this helps you well.
Have a great weekend and the rest of your day.
ASAP!!! NEED AN ANSWER
In this budget scenario, use 15 per hour as the current wage for 40 hour work weeks. Hint: There are 52 weeks in a year, and 12 months in a year.
1. What is the gross yearly income?
2. What is the gross monthly income using this pay rate?
1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year
Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year
Gross Yearly Income = $31,200
2)Gross Monthly Income = Gross Yearly Income / Months in a Year
Gross Monthly Income = $31,200 / 12 months
Gross Monthly Income ≈ $2,600
One shirt at H&M cost $7. what is the cost of 40 shirts
Answer:
$280
Step-by-step explanation:
7•40=$280
I need help with the last two !!!
Step-by-step explanation:
G(x) = - x^2 + 10x
a + G(a) = a - a^2 + 10a = - a^2 + 11a or 11a - a^2 or a(11 - a)
1/G(a) = 1/(10a - a^2) = 1/a(10 - a)
For each of the following quadratic equations, find the discriminant and draw its sign diagram: Hence find values of m for which the equation has: (i) A repeated root (ii) two distinct real roots (iii) no real roots (a) x^2 − 4x + m = 0 (b) mx^2 + 3x + 2 = 0 (c) x^2 - mx + 1 = 0
a) For two distinct real roots: x > 0 or x > m
b) For two distinct real roots: x > 0 or x > 2m
c) For two distinct real roots: x > 0 or x > 4
This is based on the quadratic equation.
What is a quadratic equation?Only non-negative integer powers of x are present in the quadratic equation, making it a polynomial equation. In actuality, the Latin word quadratus, which means square, is the root of the term quadratic. The quadratic equation has the generic form ax² + bx + c = 0. where x is an unknowable variable and a, b, and c are mathematical coefficients.
a) Quadratic equation: x² - 4x + m = 0
The discriminant: Δ = b² - 4ac
Δ = (2x)² - 4.x.(m)
Δ = 4x² - 4mx
Δ = 4x (x - m)
For two distinct real roots: Δ > 0
4x (x - m) > 0
x > 0 or x > m
For two real roots: Δ ≥ 0
4x (x - m) ≥ 0
x ≥ 0 or x ≥ m
For a repeated root: Δ = 0
4x (x - m) = 0
x = 0 or x = m
(b) Quadratic equation: mx² + 3x + 2 = 0
The discriminant: Δ = b² - 4ac
Δ = (3x)² - 4.mx.(2)
Δ = 4x² - 8mx
Δ = 4x (x - 2m)
For two distinct real roots: Δ > 0
4x (x - 2m) > 0
x > 0 or x > 2m
For two real roots: Δ ≥ 0
4x (x - 2m) ≥ 0
x ≥ 0 or x ≥ 2m
For a repeated root: Δ = 0
4x (x - 2m) = 0
x = 0 or x = 2m
(c) Quadratic equation: x² - mx + 1 = 0
The discriminant: Δ = b² - 4ac
Δ = (x)² - 4.x.(1)
Δ = x² - 4x
Δ = x (x - 4)
For two distinct real roots: Δ > 0
x (x - 4) > 0
x > 0 or x > 4
For two real roots: Δ ≥ 0
x (x - 4) ≥ 0
x ≥ 0 or x ≥ 4
For a repeated root: Δ = 0
x (x - 4) = 0
x = 0 or x = 4
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Find x and round to the nearest tenth.
Answer:
83.0°
Step-by-step explanation:
Given ∆XYZ, with 3 known sides, to find angle X, apply the Law of Cosines, c² = a² + b² - 2ab*cos(C).
For convenience sake, this formula can be rewritten to make the angle we are looking for the subject of the formula.
Thus, we would have this following:
\( cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \)
Where,
C = X = ?
a = 8 ft
b = 16 ft
c = 17 ft
Plug in the stated values into the formula and solve for X
\( cos(X) = \frac{8^2 + 16^2 - 17^2}{2*8*16} \)
\( cos(X) = \frac{320 - 289}{256} \)
\( cos(X) = \frac{31}{256} \)
\( cos(X) = 0.1211 \)
\( X = cos^{-1}(0.1211) \)
\( X = 83.0 \) (to nearest tenth)
Answer:
its actually 83 not 83.0
Step-by-step explanation:
im only saying this bc i know people with type 83.0 in the box
My dance lesson starts at 11:40 am. It always 1 your and 10 minutes what time does it end?
Answer:
Step-by-step explanation:
This may be wrong but hear me out, 40+10 is 50 and 11+1 is 12, so 12:50?
The height of a ball above the ground as a function of time is given by the function h(t)= -32t^2+8t+3 where h is the height of the ball in feet and t is the time in seconds. When is the ball at a maximum height
Answer:
The ball is at a maximum height when t = 0.125s.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
\(f(x) = ax^{2} + bx + c\)
It's vertex is the point \((x_{v}, f(x_{v})\)
In which
\(x_{v} = -\frac{b}{2a}\)
If a<0, the vertex is a maximum point, that is, the maximum value happens at \(x_{v}\), and it's value is \(f(x_{v})\)
In this question:
\(h(t) = -32t^{2} + 8t + 3\)
So \(a = -32, b = 8\)
When is the ball at a maximum height
\(t_{v} = -\frac{8}{2*(-32)} = 0.125\)
The ball is at a maximum height when t = 0.125s.
Use the model below to calculate 9÷1/3.
A green rectangle is divided into 9 equal parts arranged into 3 rows of 3 cells each.
A.
9/3
B.
3/9
C.
13 1/2
D.
27
Using thie model ,The answer is D. 27.
To calculate 9÷1/3 using the model below, we can imagine dividing the green rectangle into thirds vertically. Each third would contain 3 cells.
Then, we can see that there are a total of 9 cells in the rectangle. Since we are dividing by 1/3, we need to find out how many sets of 1/3 are in 9.
We can see that there are 3 sets of 1/3 in each row (since each row contains 3 cells, which are thirds). So, in total, there are 3 rows of 3 sets of 1/3, which gives us:
9÷1/3 = 3 rows x 3 sets of 1/3 = 9 sets of 1/3 = 27
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Please help me 19 points ! I inserted a image of the problem
Answer:
first tile: x=5, second tile x=19, third tile x=29, last tile x=6
Step-by-step explanation:
Ohhh is that edmentum i do that too! ;)
(x-1)^3=64
x-1=4
x=5
(x-3)^5=2^20
x-3=2^4
x-3=16
x=19
(x-4)^3=5^6
x-4=25
x=29
the last one has to be x=6
Can I please get help?
Answer:
a) 9
b)3
c)22
Step-by-step explanation:
a)13+14/8-5 =27/3 =9
b) 9+9/4+2= 18/6 = 3
c) 12+16-6=22
Answer:
A- 9
B-3
C-22
Step-by-step explanation:
A-13+7*2/8-(3+2)
13+14/8-5
27/3
9.
B-9+3^2/2^2+2
9+9/4+2
18/6
3.
C-(10+2)+(4^2-6)
(12)+(16-6)
12+10
22
What is the image point of (-4,-3) after a translation left 1 unit and
down 2 units?
Answer:
The new point would be (-5,-5)
Step-by-step explanation:
i have big brain
Answer: (-5, -5)
Step-by-step explanation:
-4 + -1
-3 + -2
-5, -5
Helppppp !!!
For each relation, decide whether or not it is a function.
1. Relation 1 is a function
2. Relation 2 is a function
3. Relation 3 is not a function
4. Relation 4 is a function
How to determine if each relation is a functionFrom the question, we have the following parameters that can be used in our computation:
The relations (1) to (4)
Relation (1)
This relation is a function
This is because each range value point to unique domain values
Relation (2)
This relation is a function
This is because each range value point to unique domain values
Relation (3)
This relation is not a function
This is because domain values w have different range values.
Relation (4)
This relation is a function
This is because each range value point to unique domain values
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Are the experimental probabilities after 300 trials closer to the theoretical probabilities?
After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.
To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.
Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.
Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.
Experimental probability of heads: 160/300 = 0.5333
Experimental probability of tails: 140/300 = 0.4667
Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.
In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.
To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.
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The question probable may be:
Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.
The figures below are congruent. Which series of transformations
maps figure ABCD onto EFGH?
A
F. rotation followed by a translation
G. rotation followed by a dilation
H. reflection followed by a translation
I. reflection followed by
9514 1404 393
Answer:
H. reflection, translation
Step-by-step explanation:
The order of vertices ABCD is clockwise. The order of vertices EFGH is counterclockwise, so a reflection must be involved.
The orientation direction of GH is nearly vertical. The corresponding direction of CD is up to the left. A reflection can make the directions be the same, but the reflection that gets the orientation correct may not put the figure in the correct location.
So, we choose the transformations ...
H. reflection followed by translation
what is the property of 3x(5x7)=(3x5)7
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
Diana paints 150 fence posts and chuck paints 130 fence posts. Diana paints 10 more fence posts than chuck. How many fence posts does chuck paint per hour?
Complete Question
The complete question is shown on the first uploaded image
Answer:
Step-by-step explanation:
From the question we are told that
The relationship is \(\frac{150 }{d} = \frac{130}{c}\)
The number of fence post painted by chuck is \(l = 130\)
The number of fence post painted by Diana is \(k = 150\)
can paint 10 fences more than chuck so let say the of fence painted in an hour by chuck is \(g\)
Then the number of fence post painted by Diana in one hour is
\(f = g+ 10\)
So
\(\frac{150 }{ g + 10 } = \frac{130}{g}\)
\(130 g + 1300 = 150g\)
\(g = 65 \ m\)
On the past two quizzes, a student scored a 75 and 83. Write and solve a compound inequality to find the possible values for the 3rd quiz score that would give her an average between 85 and 90, inclusive.
The possible values for a third quiz score that would give her an average between 85 and 90, inclusive is: 97 ≤ x ≤ 112.
How to determine the average?In Mathematics, the average of these quiz scores can be calculated by using the following formula:
Average = Sum of quiz score/Number of quiz scores
Note: Let the variable q represent the student's score on the third (3rd) quiz.
Substituting the given parameters into the formula, we have the following;
Average = (75 + 83 + q)/3
Average = (158 + q)/3
This ultimately implies that, an average between 85 and 90, inclusive is given by this compound inequality:
85 ≤ (158 + q)/3 ≤ 90
Multiplying all through by 3, we have the following:
255 ≤ (158 + q) ≤ 270
Subtracting 158 from both sides of the inequality, we have the following:
97 ≤ x ≤ 112
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what is the equation of a line that passes through the points (2,5) and (4,3)
The equation of a line that passes through points (2,5) and (4,3) is
y = -x+7.
Finding the equation of a line:
First, we need to find out the slope for the given points.
(X1,Y1) = (2,5)
(X2,Y2) = (4,3)
formula for slope(m) = \(\frac{Y2 - Y1}{X2 - X1}\)
substitute the points in the above formula
\(\frac{3 - 5}{4 - 2}\) = \(\frac{-2}{2}\)
\(\frac{-2}{2}\) = -1
slope for the given points(m) = -1.
m = -1
The equation of a line is y-y1 = m(x-x1), where x and y are variables.
substituting the values in the above equation then :
y-5 = -1(x-2)
y-5 = -x+2
y+x = 2+5
x+y = 7
y = -x+7
Therefore, the equation of the line passing through the points (2,5) and (4,3) is y = -x+7
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