The probability that a household views television between 5 and 11 hours a day is approximately 0.7291, and that a household views television more than 3 hours a day is approximately 0.9830.
(a) To find the probability that a household views television between 5 and 11 hours a day, we need to find the area under the normal distribution curve between the values of 5 and 11, with a mean of 8.35 and a standard deviation of 2.5. We can use a standard normal distribution table or calculator to find the corresponding probabilities.
First, we need to standardize the values of 5 and 11 using the formula:
z = (x - μ) / σ
where z is the standardized score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
For x = 5: z = (5 - 8.35) / 2.5 = -1.34
For x = 11: z = (11 - 8.35) / 2.5 = 1.06
Using a standard normal distribution table, we can find the area under the curve between z = -1.34 and z = 1.06 to be approximately 0.7291.
Therefore, the probability that a household views television between 5 and 11 hours a day is approximately 0.7291.
(b) To find how many hours of television viewing a household must have in order to be in the top 3% of all television-viewing households, we need to find the z-score corresponding to the top 3% of the distribution, and then use the formula:
z = (x - μ) / σ
to solve for x, where x is the number of hours of television viewing and μ and σ are the mean and standard deviation of the distribution, respectively.
Using a standard normal distribution table, we can find that the z-score corresponding to the top 3% of the distribution is approximately 1.88.
Therefore, we can solve for x as follows:
1.88 = (x - 8.35) / 2.5
x - 8.35 = 4.7
x = 13.05
Therefore, a household must view more than 13.05 hours of television per day to be in the top 3% of all television-viewing households.
(c) To find the probability that a household views television more than 3 hours a day, we need to find the area under the normal distribution curve to the right of the value of 3, with a mean of 8.35 and a standard deviation of 2.5. We can again use a standard normal distribution table or calculator to find the corresponding probability.
First, we need to standardize the value of 3 using the formula:
z = (x - μ) / σ
where z is the standardized score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
For x = 3: z = (3 - 8.35) / 2.5 = -2.14
Using a standard normal distribution table, we can find the area under the curve to the right of z = -2.14 to be approximately 0.9830.
Therefore, the probability that a household views television more than 3 hours a day is approximately 0.9830.
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1. An Estate dealer sells houses and makes a commission of GHc3750 for the first house sold. He
receives GHc500 increase in commission for each additional house sold. How many houses must
she sell to reach a total commission of GHc6500?
If an Estate dealer sells houses and makes a commission of GHc3750 for the first house sold and receives GHc500 increase in commission for each additional house sold, for reaching a total commission of GHc6500, she must have sold 6.5 houses.
How is the number of houses sold determined?The number of houses the estate dealer sold to reach a total commission of GHc6500 can be determined using the mathematical operations of subtraction, division, and addition.
The total commission received = GHc6,500
The commission for the first house = GHc3,750
The commission for the remaining houses sold = GHc2,750 (GHc6,500 - GHc3,750)
The commission for additional sale of each house = GHc500
The number of additional houses sold = 5.5 (GHc2,750/GHc500)
The total number of houses sold = 6.5 (5.5 + 1 or the first house)
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There is a bag filled with 5 blue, 2 red and 3 green marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 the same colour?
Answer:
2/9 + 5/36 = 17/36
So the probability of getting 2 marbles of the same color is 17/36 or 0.472.
Answer:
17/36
Step-by-step explanation:
There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year
A function [tex]P(t) = 170.(1.30)^t[/tex] that gives the deer population P(t) on the reservation t years from now
We were told there were 170 stags on reservation. The number of deer is increasing at a rate of 30% per year.
We could see the deer population grow exponentially since each year there will be 30% more than last year.
Since we know that an exponential growth function is in form:
[tex]f(x) = a*(1+r)^x[/tex]
where a= initial value, r= growth rate in decimal form.
It is given that a= 170 and r= 30%.
Let us convert our given growth rate in decimal form.
[tex]30 percent = \frac{30}{100} = 0.30[/tex]
Upon substituting our given values in exponential function form we will get,
[tex]P(t) = 170.(1+0.30)^t[/tex]
⇒ [tex]P(t)= 170.(1.30)^t[/tex]
Therefore, the function [tex]P(t) = 170.(1.30)^t[/tex] will give the deer population P(t) on the reservation t years from now.
Complete Question:
There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.
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question 962946: if a triangle with all sides equal length has a perimeter of 15x 27, what is an expression for the length of one of it's sides?
If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).
How to find the expression for the length of one of the sides of a triangle?The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27.
Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).
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What is the area under the normal curve below the z- score of 1?
Answer:
One way is to realize that since the total area is 1, the area below z = 1 is equal to 1 minus the area above z= 1 which we know from before is 0.1587. So the area below 1 is 1 - 0.1587 = 0.8413.
10) Find the vertex form of the parabola.
Step-by-step explanation:
4x + y^2 + 2y = - 5
4x = - y^2 -2y - 5
4x = - (y^2 + 2y) - 5 'complete the square' for y
4x = - ( y +1)^2 + 1 - 5
x = - 1/4 ( y+1)^2 - 1 vertex is at -1, -1
-14x+2y^2-8y -20 = 0
14x = 2y^2 -8y-20
14x = 2 ( y^2 - 4y) - 20 complete the square for y
14x = 2(y-2)^2 -8 - 20
x = 1/7 ( y-2)^2 - 2 Vertex is at -2 , 2
I NEED HELP ON THIS ASAP!!
From the graph, the feasible region from the system of linear inequalities is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.
What is the system of linear inequalitiesa. Let x be the amount of loam soil (in tons) sold, and y be the amount of peat soil (in tons) sold. The system of inequalities representing the constraints of the problem situation is:
x ≥ 0 (non-negative amount of loam soil)
y ≥ 0 (non-negative amount of peat soil)
x + y ≤ 120 (total amount of soil sold is at most 120 tons)
x ≤ 60 (maximum amount of loam soil available is 60 tons)
y ≤ 90 (maximum amount of peat soil available is 90 tons)
To graph these inequalities, we can plot the feasible region (the region that satisfies all the inequalities) in the x-y plane, as shown below;
The feasible region is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.
b. The profit function P(x, y) for selling x tons of loam soil and y tons of peat soil is:
P(x, y) = 50x + 75y
To maximize profit, we need to find the values of x and y that satisfy the constraints of the problem situation and maximize the profit function P(x, y). One way to do this is to use the method of linear programming, which involves finding the corner points of the feasible region and evaluating the profit function at each corner point.
The corner points of the feasible region are (0, 0), (60, 0), (60, 60), (30, 90), and (0, 90). Evaluating the profit function at each corner point, we get:
P(0, 0) = 0
P(60, 0) = 3000
P(60, 60) = 9000
P(30, 90) = 6750
P(0, 90) = 6750
Therefore, the maximum profit is $9000, which occurs when the company sells 60 tons of loam soil and 60 tons of peat soil.
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If p and q vary invarsely and p is 11 when q is 28, determine q when p is equal to 4
77 is the value of Q in linear equation.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
P ∝ 1/Q
PQ = K
AT P= 11
Q = 28
11 * 28 = K
K = 308
AT P = 4
4Q = 308
Q = 77
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Solve by whatever method you prefer, using one or two variables. Edna Britten's income from two stocks each year totals 280.StockApaysdividendsattherateof5 5000, how much is invested in each stock?
The given information is inconsistent.
Answer: Let x and y be the amount invested in stocks A and B from the information given in the question, we have:x + y = total amount invested....(1)And also, the income from stock A and stock B are 5500 and (280-5500) = -5220 respectively.Now, if the income from a stock is negative, it means the investor loses money, i.e. invested more than the income received.So, we have:0.10x - 0.09y = 5500... (2)Multiplying equation (1) by 0.09 and subtracting from equation (2) multiplied by 10, we get:1.01x = 109900=> x = 108910Therefore, the amount invested in stock A is $108910, and the amount invested in stock B is:280 - 108910 = $(-108630)But since a negative value of investment doesn't make sense, it means there is no solution to this problem. So, the given information is inconsistent.
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Find the value of the the expression x+|x|, if x=7
x +|x|
= 7 + |7|
= 7 + 7
= 14
because determine of | 7 | is 7
at the local college, a study found that students used an average of 5.2 school books per semester. a sample of 39 students was taken. what is the best point estimate for the average number of school books per semester for all students at the local college?
The best point estimate for the average number of school books per semester for all students at the local college is 5.2.
The average number of school books per semester for all students at the local college is 5.2. A sample of 39 students was taken, i.e., n = 39. To find, The best point estimate for the average number of school books per semester for all students at the local college.
The best point estimate for the average number of school books per semester for all students at the local college is the sample mean which can be calculated.
Therefore, the best point estimate for the average number of school books per semester for all students at the local college is 5.2.
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alissa owns a lovely country store. she buys 6 jars of honey for $65 and the sells 5 jars for $72. how many jars would alissa have to buy and then sell to make a profit of $214 on the honey?
She must purchase and sell at least 61 jars to make a profit of $214.
How to determineFirst, calculate the cost per jar of honey that Alissa purchased:
$65/6 jars = $10.83/jar
Then, calculate the selling price per jar of honey:
$72/5 jars = $14.40/Jar
The profit per jar of honey is the selling price minus the cost price:
$14.40 - $10.83 = $3.57/jar
To find the number of jars that Alissa needs to sell to make a profit of $214, divide the total profit by the profit per jar:
$214 ÷ $3.57/jar ≈ 60.03 jars
Since Alissa cannot sell 0.03 of a jar of honey, she must purchase and sell at least 61 jars to make a profit of $214.
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A number subtracted from 80 gives — 30. Find the number
The number which, when subtracted from 80, results in -30 is equal to 110.
To solve this problem, we can use algebraic equations to represent the given information. Let x be the number that we want to find.
According to the problem, when we subtract x from 80, we get -30:
80 - x = -30
To solve for x, we can isolate it on one side of the equation by adding x to both sides, and then simplify:
80 - x + x = -30 + x
80 = -30 + x
Next, we can isolate x by subtracting -30 from both sides:
80 - (-30) = x
Simplifying the right-hand side:
80 + 30 = x
110 = x
Therefore, the number that was subtracted from 80 and gave -30 as the result is 110.
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[Pre-calculus honors, grade 11] The light from a lighthouse can be seen from an 18-mile radius. A boat is anchored so that it can just see the light from the lighthouse. A second boat is located 25 miles from the lighthouse and is headed straight toward it, making a 44° angle with the lighthouse and the first boat. Find the distance between the two boats when the second boat enters the radius of the lighthouse light.
Using trigonometry, the distance between the two vessels when the second boat enters the lighthouse's radius is 13.46 miles.
Trigonometry: What Is It?The relationships between angles and length ratios are investigated in the branch of mathematics known as trigonometry. The use of geometry in astronomical study led to the establishment of the field during the Hellenistic era in the third century BC.
The distance between the two boats when the second boat enters the radius of the lighthouse light is 13.46 miles using trigonometry.
Triangle - what is it?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the vertices A, B, and C is represented by the Δ ABC.
Any three points that are not collinear create a singular triangle and a singular plane in Euclidean geometry. (i.e. a two-dimensional Euclidean space). In other words, every triangle is a part of a plane, and that triangle is a part of only one plane. In the Euclidean plane, all triangles are contained within a single plane, but in higher-dimensional Euclidean spaces, this is no longer the case. This page covers triangles in Euclidean geometry, especially the Euclidean plane, unless otherwise specified.
In this question,
The side of the isosceles triangle is given by,
l=2a sin(θ/2)
where a= 18 miles
θ= 44°
l= 2*18*sin 22°
= 36*0.374
= 13.46 miles
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At the 2022 Winter Olympics, one country won a total of 150 medals. A circle graph of the medals is shown.
a circle graph titled 2022 Winter Olympic Medals, with three sections labeled gold 20 percent, silver 30 percent, and bronze 50 percent
How many silver and bronze medals were won?
40
80
100
120
The country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.
What is Medal?A medal is a small, flat, and usually round piece of metal that is awarded to individuals or groups as a symbol of recognition or honor for achievement, bravery, or other notable deeds. Medals can be made of various materials, such as gold, silver, bronze, or other alloys, and they often feature intricate designs or engravings that reflect the significance of the award.
According to question:According to the circle graph, gold medals make up 20% of the total medals, which means the country won 20% of 150 medals as gold, or 0.2 x 150 = 30 gold medals.
Similarly, silver medals make up 30% of the total medals, which means the country won 30% of 150 medals as silver, or 0.3 x 150 = 45 silver medals.
Finally, bronze medals make up 50% of the total medals, which means the country won 50% of 150 medals as bronze, or 0.5 x 150 = 75 bronze medals.
Therefore, the country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.
So the answer is 120.
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An account executive receives a base salary plus a commission. On $50,000 in monthly sales, the account executive receives $7000. On $70,000 in monthly sales, the account executive receives $7800.
(a) Determine a linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x
(b) Use this model to determine the account executive's compensation for $75,000 in monthly sales.
a: _____ b: _____
Answer:
(a) To find the linear function, we need to determine the slope and y-intercept of the line that passes through the two given points: (50000, 7000) and (70000, 7800).
Slope = (change in y)/(change in x) = (7800 - 7000)/(70000 - 50000) = 800/20000 = 0.04
Y-intercept = 7000 - slope * 50000 = 5000
So the linear function that gives the account executive's compensation y for a given amount of monthly sales x is:
y = 0.04x + 5000
(b) To find the account executive's compensation for $75,000 in monthly sales, we can plug x = 75000 into the linear function we found in part (a):
y = 0.04(75000) + 5000 = 8000
So the account executive's compensation for $75,000 in monthly sales is $8,000.
Jack's school is selling tickets to a spring Musical on the first day of ticket sales for school so 46 senior citizen tickets and 44 a child tickets for total of 362 the school took in 85 on the second day by selling two senior citizen tickets and 25 child tickets Bonnie price of a senior citizen ticket and the price of a child ticket.
On the first day of ticket sales for the school’s spring musical, 46 senior citizen tickets and 44 child tickets were sold, bringing the total number of tickets sold to 362.
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.
The second day saw a slightly lower number of tickets sold, with two senior citizen tickets and 25 child tickets purchased, for a total of 85. The price of a senior citizen ticket and a child ticket was likely the same on both days, and likely the same price as it is for the rest of the ticket sales.
The school likely has a set price for tickets, which would not change as the number goes up or down. It is common for schools to give discounts for senior citizens, so the price of their tickets is usually lower than the price of a child ticket. The school set the prices of the tickets in a way that would bring in the most money, while still being affordable for the community to attend.
The school likely had a plan in place for how many tickets they wanted to sell and what prices they wanted to set. They also likely had a goal of how much money they wanted to bring in from the ticket sales. After the two days of ticket sales, the school was able to see how many tickets were sold and how much money was collected. This can help the school to adjust their plan, if necessary, to reach their goal.
The money brought in from the ticket sales will likely help the school to cover the costs of putting on the musical. It may also help to pay for any other expenses associated with the production of the show. The school may also use the money to purchase new materials or supplies for the performing arts department.
Overall, the school was able to bring in a total of 447 from the two days of ticket sales. This money will help to ensure that the school’s spring musical is a success. The school was also able to offer discounted tickets to senior citizens, which allowed more people to attend the show.
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The price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.
Jack's school is selling tickets to a spring Musical. On the first day of ticket sales, the school sold a total of 362 tickets, 46 of which were senior citizen tickets and 44 of which were child tickets. On the second day of ticket sales, the school sold two senior citizen tickets and 25 child tickets, for a total of 85 tickets.
To calculate the price of each ticket, we can divide the total amount taken in by the number of tickets sold. For senior citizen tickets, the total amount taken in was 85, and two were sold, so the price of a senior citizen ticket is 85/2 = 42.50. For child tickets, the total amount taken in was 85, and 25 were sold, so the price of a child ticket is 85/25 = 3.40.
In conclusion, the price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.
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16/(8×2)=
16/8×2=
16-8/2=
Answer:
16/(8×2)=
16/8×2=
16-8/2=
8/2=
4
Step-by-step explanation:
first we subtract 8 from 16 and divide the result by 2.
What is the quotient of 6. 208 × 10^9 and 9. 7 × 10^4 expressed in scientific notation?
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
Quotient:
The quotient is the answer we get when we divide one number by another. For example, if we divide the number 6 by 3, we get 2, the quotient. The quotient can be integer or decimal. For an exact division like 10 ÷ 5 = 2, we have a whole number as the quotient, and for a division like 12 ÷ 5 = 2.4, the quotient is a decimal number. The quotient can be greater than the divisor, but always less than the dividend.
Based on the given conditions, Formulate:
6.208× 10⁹ /9.7×10⁴
Simply using exponent rule with same base:
[tex]a^n. a^m = a^(n+m)[/tex]
= 6.208 × 1/9.7
Now,
the sum or difference = [tex]6.208*\frac{1}{9.7}[/tex] × 10¹³
Now solving, we get:
6.208/9.7 × 10¹³
Converting fraction into decimal, we get:
0.64× 10¹³
⇒ 6.4 × 10¹²
Therefore,
The quotient of 6. 208 × 10⁹ and 9. 7 × 10⁴ expressed in scientific notation is 6.4 × 10¹².
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Given the function y = 4x + 3 do the following. Find its average rate of change: from x = 2 to x = 5
Answer: 4 is the average rate of change
Step-by-step explanation:
The equation to find the average rate of change is:
[tex]\frac{f(x_{2})-f(x_{1} ) }{x_{2}-x_{1} }[/tex]So f(2)= 11 and f(5)=23 then you plug these numbers in:
[tex]\frac{23-11}{5-2}[/tex] = [tex]\frac{12}{3}[/tex] = 4
A ball is thrown straight up into the air. The x-axis shows the time, in seconds, and the y-axis shows the height of the ball, in feet, at any time (x)
Based on the information in the graph, it can be inferred that the false sentence is: The ball landed 11 feet from the person (option C).
How to identify the false option?To identify the false option we must read all the options and check them with the information in the graph:
The first option is true because the highest point the ball reaches is between 11 and 12 feet high.The second option is true because the person drops the ball about 5 feet above the ground.The third option is false because the graph does not show the displacement of the ball with respect to the person who throws it. It only shows your height and the time elapsed in the launch.The fourth option is true because the ball falls between 0.7 and 1.45 seconds.According to the above, the correct answer to this question would be option C because the sentence is false with respect to the information in the graph.
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Solve the problems. a) The number a is 4/5 of the number b. What part of number a is number b?
Answer:
Solve the problems. a) The number a is 4/5 of the number b. What part of number a is number b?
Step-by-step explanation:
a) If a is 4/5 of b, then b is 5/4 of a.
To find what part of a is b, we divide b by a:
b/a = 5/4
This means that b is 5/4 times larger than a, or b is 125% of a.
To find what part of a is b, we subtract 1 from this fraction:
b/a - 1 = 5/4 - 1
b/a - 1 = 1/4
So, b is 1/4 of a, or b is 25% of a.
System of equations by elimination y=-7x-29 y=-3x-9
The solution to the system of equations y=-7x-29 and y=-3x-9 using elimination method is x = 5 and y = -64.
To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the two equations. In this case, we can eliminate y by subtracting the second equation from the first. This gives us:
y - y = -7x - 29 - (-3x - 9)
0 = -4x - 20
Simplifying this equation, we get:
x = 5
Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
y = -7x - 29
y = -7(5) - 29
y = -64
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Complete question is:
Solve the given System of equations by elimination method
y=-7x-29, y=-3x-9
In advance of the 1936 Presidential Election, a magazine titled Literary Digest released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent post cards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards. a. Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time. b. What effect does the low response rate have on the reliability of the sample? c. Are these problems examples of sampling error or nonsampling error? d. During the same year, George Gallup conducted his own poll of 30,000 prospective voters. His researchers used a method they called "quota sampling" to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?
Answer:
a. The sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time for several reasons. Firstly, in 1936, only a small fraction of the US population had magazine subscriptions or owned cars, telephones or club memberships. Hence, the sample was biased towards the more affluent and educated sections of society, and did not include a representative cross-section of the population. Secondly, the sample was limited to people who could read and write, which excluded many poor and illiterate people who may have had different political views.
b. The low response rate of 2,300,000 out of the 10,000,000 postcards sent out indicates a response rate of only 23%. This means that the sample was not a random sample, and that the respondents were not representative of the larger population. Low response rates tend to increase sampling error and decrease the reliability of the sample.
c. These problems are examples of nonsampling error, which occur due to factors other than the sample selection process. The bias in the sample resulted from the sampling frame, which was not representative of the population, and the low response rate.
d. Quota sampling is an example of non-probability sampling, where researchers select a specific number of participants from different subgroups of the population based on predetermined quotas. In this method, the goal is to obtain a sample that is representative of the population in terms of certain characteristics, such as age, gender, or ethnicity. Quota sampling was used by George Gallup in 1936, and is still used today in various forms, such as stratified sampling.
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the prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. the manager at one of the stores randomly selects 10 pairs of pants. which of the following best describes the sampling distribution of all possible samples of size 10? a. skewed left with a mean of 32 and standard deviation of 6.32 b. skewed left with a mean of 32 and a standard deviation of 20 c. approximately normal with a mean of 32 and a standard deviation of 20 d. approximately normal with a mean of 32 and a standard deviation of 6.32
Sampling distribution of sample means with size 10, drawn randomly from a population with unknown mean and standard deviation, is approximately normal. It has a mean of 32 and a standard deviation of 6.32 (standard error of the mean). Option D is correct.
The sampling distribution of the mean of a large enough sample size follows a normal distribution, even if the underlying population is skewed.
The formula for the standard deviation of the sampling distribution of the mean is( σ / [tex](\sqrt(n))[/tex] ) ,
where sigma is the standard deviation of the population and n is the sample size.
Substituting the values, we get:
standard deviation of sampling distribution =[tex]20/(\sqrt(10))[/tex]= 6.32
Therefore, the sampling distribution of all possible samples of size 10 is approximately normal with a mean of 32 and a standard deviation of 6.32.
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Where did my dad go? He went to get milk but never came back
The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.
The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.
However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.
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two people standing at different locations are looking at a tall building. person a angle of elevation to the building is 35 degrees. person b angle of elevation is 77 degrees. the building is 8 miles away from person b. how far away is person a from the building?
Therefore, Person A is approximately 95.17 miles away from the building.
To find out how far person A is from the building, we'll need to use trigonometry. The diagram below shows the situation.
Given that Person A's angle of elevation to the building is 35 degrees, we'll let angle BAC be 35 degrees.
Similarly, since Person B's angle of elevation is 77 degrees, we'll let angle ABC be 77 degrees. We'll also let AB be x, the distance from Person A to the building, and BC be 8 miles, the distance from Person B to the building.
First, we'll use the tangent function to find the height of the building. In triangle ABC, tan(77) = height/8. Solving for the height, we get:
height = 8tan(77) ≈ 61.23 miles.
Next, we'll use the tangent function again to find x. In triangle ABC, tan(35) = height/x + 8. Solving for x, we get:
x = (height)/(tan(35)) - 8
≈ 103.17 miles - 8
≈ 95.17 miles.
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A relation contains the points (1, -4), (3, 2), (4, -3), (x, 7), and (-4, 6). For which values of x will the relation be a function?
In response to the stated question, we may state that To conclude, the function problem's relation is a function for all x values except x between 3 and 4.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.
If and only if each input has precisely one output, a relation is a function. To determine whether the connection stated in the issue is a function, we must examine whether any x values have more than one output.
We may achieve this by putting the specified points on a graph and looking for vertical lines that cross the graph more than once. If so, the relationship is not a function.
We may create the following graph with the supplied points:
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8 |
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7 | ●
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6 | ●
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5 |
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4 | ●
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3 | ●
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2 | ●
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1 |
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0 |
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-1 |
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-2 |
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-3 |
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-4 |
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|_____________________
-4 -3 -2 -1 0 1 2 3 4
Apart for the line travelling through the points (3, 2) and (4, 2), there is no vertical line that intersects the graph in more than one spot (4, -3). As a result, if x is between 3 and 4, the relation specified in the issue is not a function.
To conclude, the problem's relation is a function for all x values except x between 3 and 4.
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company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H, :p = 0.08 versus H, :p > 0.08 at the significance level of a = 0.01. The test yielded a p-value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion?А. The p-value is greater than a, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.B. The p-value is greater than a, and the null hypothesis is rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.C. The p-value is greater than a, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.D. The p-value is less than a, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.E The p-value is less than a, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
The conclusion which is correct about given situation is D) The p-value (0.001) is less than the significance level (0.01), which means we reject the null hypothesis that the proportion of boxes with broken glass is equal to or less than 8%.
We have convincing evidence to suggest that the actual proportion of boxes with broken glass is greater than 8%. Therefore, we can conclude that the glass manufacturer's belief is supported by the sample data.
This conclusion is based on the fact that the p-value is less than the significance level, indicating that the observed data is unlikely to have occurred by chance alone assuming the null hypothesis is true.
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The expression tan(0) cos(0) simplifies to sin(0) . Prove it
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