A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 76.5 and a standard deviation of 9. if 67.36% of his students received grades of c or above, what is the minimum score of those students receiving a grade of at least a c?
Using the properties of normal distribution and the Z-score related to the given percentile, it can be inferred that the minimum grade for a 'C' in this college statistics class is approximately 72.
Explanation:In this scenario, the professor's grades reflect a normal distribution, therefore, we can utilize the properties of normal distribution to answer your question. The probability given, 67.36%, corresponds to a Z-score of -0.45 (you can find this in standard statistical tables).
We'll utilize the formula Z = (X - μ) / σ, Z is the Z-score, X is the data point, μ is the mean, and σ is the standard deviation. Therefore, if we rearrange the formula to find X (the data point,or in this case, the lowest grades for students receiving a C or above), it will be X = Z * σ + μ. Substituting the given values in the equation gives X = -0.45 * 9 + 76.5. This results in a minimum score approximately equal to 72.45, or 72 if we consider only whole marks. Hence, our conclusion that the minimum grade for a 'C' is 72.
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The minimum score required to receive at least a grade of C in this normally distributed class is approximately 72.54.
To determine the minimum score that students need to receive at least a grade of C in a class where grades are normally distributed, we analyze the problem with a mean [tex](\mu)[/tex] of 76.5 and a standard deviation [tex](\sigma)[/tex] of 9.
We know that 67.36% of the students received a grade of C or above.
This corresponds to the top 67.36% of the distribution.
The bottom 32.64% of the distribution received less than a C.
The z-score associated with the 32.64th percentile can be found using z-tables or a standard normal distribution calculator:
z = -0.44
Next, we convert this z-score to the actual score using the formula:
[tex]X = \mu + z\cdot \sigma[/tex]
Substituting the given values:
X = 76.5 + (-0.44 * 9) = 76.5 - 3.96 = 72.54
Thus, the minimum score required for a grade of at least C is approximately 72.54.
Find the thirtieth term of the following sequence.
-6, -4, -2, 0, ...
Answer: 52
Step-by-step explanation:
To find the 30th number sequence with the given values of: -6,-4,-2,0.
Multiply 30 by 2 because we add 2 to the sequence every time we go up.
30*2 gives us 60, then we subtract however many 2's were in the given sequence.
From -6 to -4 to -2 to 0, we get 8.
60-8 = 52.
Thank you and I hope this helps. Even if my math is wrong somewhere, I got the answer right on my assignment so this is 100% correct.
Suppose that factory a produces 12 tables and 6 chairs an hour while factory b produces 8 tables and 4 chairs and hour. how many hours should each factory work to produce 48 tables and 24 chairs? how many different solutions are there to this problem?
Factory A should work for 4 hours, while factory B should work for 6 hours to produce 48 tables and 24 chairs
The rates of both factories are given as:
Factory A = 12 tables and 6 chairs in an hour
Factory B = 8 tables and 4 chairs in an hour
To produce 48 tables and 24 chairs, we make use of the following equation
[tex]h = \frac{Produce}{Rate}[/tex]
Where h represents time (in hours)
So, we have:
Factory A
[tex]h = \frac{48\ tables, 24\ chairs}{12\ tables, 6\ chairs}[/tex]
[tex]h = 4[/tex]
Factory A
[tex]h = \frac{48\ tables, 24\ chairs}{8\ tables, 4\ chairs}[/tex]
[tex]h = 6[/tex]
Hence, factory A should work for 4 hours, while factory B should work for 6 hours to produce 48 tables and 24 chairs
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Factory A should work for 0 hours and Factory B should work for 6 hours to produce 48 tables and 24 chairs. There is only one solution to this problem.
Explanation:To find out how many hours each factory should work to produce 48 tables and 24 chairs, we can set up a system of equations. Let's say that factory A works for x hours and factory B works for y hours. From the information given, we can write the following equations:
12x + 8y = 48 (equation 1, for tables)
6x + 4y = 24 (equation 2, for chairs)
We can solve this system of equations using substitution or elimination method. Let's solve it using the substitution method:
From equation 1, we can isolate x by subtracting 8y from both sides:
12x = 48 - 8y
x = (48 - 8y) / 12
Substituting this value of x in equation 2:
6((48 - 8y) / 12) + 4y = 24
Simplifying the equation:
3(48 - 8y) + 4y = 24
144 - 24y + 4y = 24
-20y = -120
y = (-120) / (-20)
y = 6
Substituting the value of y in equation 1:
12x + 8(6) = 48
12x + 48 = 48
12x = 0
x = 0
Therefore, factory A should work for 0 hours and factory B should work for 6 hours to produce 48 tables and 24 chairs. There is only one solution to this problem.
Draw cubes to show the number. Write the number different ways. Love has seven ones Nick has 5 ones they put all their once together what number did they make
What is the range of arcsinx
Final answer:
The range of the inverse sine function, or arcsin(x), is the set of angles from -π/2 to π/2 radians, which is the same as -90° to 90° degrees. This defines the possible output values of the function for all real numbers in the interval [-1, 1].
Explanation:
The question "What is the range of arcsinx" concerns itself with the inverse trigonometric function, specifically the inverse of the sine function. The range of a function is the set of all possible output values it can produce. For the inverse sine function, or arcsin(x), the range is the set of angles that can produce all possible sine values, which are within the closed interval [-1, 1].
The sine function itself has a range from -1 to 1, so the arcsine function, being its inverse, takes on values that are angles that correspond to these sine values. In terms of angles, the range of the arcsin function is [-π/2, π/2] or [-90°, 90°] in degrees. This means that for any input value x within [-1, 1], the output of arcsin(x) will always be an angle measured in radians (or degrees) that falls within this range.
In right triangle ABC, AB = 10, AC = 6 and BC = 8 units. What is the distance from C to the midpoint of segment AB?
Divide then check using multiplcation
1056÷37=
Benjamin solved the equation 3 + x over 2 = 10 and justified each step as shown.
Identify Benjamin’s error and fix his mistake
Step:
3 + x/2 = 10
X/2 = 7
X= 14
Justification:
Given
Multiplication Property of Equality
Subtraction Property of Equality
Answer:
The equation itself is fine but the justification looks wrong step2 is subtraction property of equality and step3 is Multiplecation property of equaliity
I could be wrong but im 95% sure
Good luck!
Reteach to build to understand 10-4
F=9/5C+32 What Does C And F represent
20.301_____ 20.31 is this equal or greater
Becky bought 4 pounds of grapes for $8.24.How much did the grapes cost per pound?
a baseball team plays 83 games in a season. if the team won 17 more than twice as many as they lost how many times did the did lose?
Final answer:
By creating an equation based on the information provided and solving for L, which represents the number of games lost, it was determined that the baseball team lost 22 games during the season.
Explanation:
To determine how many games the baseball team lost during the season, let us denote the number of lost games as L. The problem states that the baseball team won 17 more than twice the number of games they lost, which can be expressed as 2L + 17. Since the team played a total of 83 games in the season, we have the following equation to represent the total number of games played:
L + (2L + 17) = 83.
Combining like terms, we get:
3L + 17 = 83.
Now, subtract 17 from both sides of the equation:
3L = 66.
Then, we divide both sides of the equation by 3:
L = 22.
So, the baseball team lost 22 games during the season.
To find the number of times the team lost, set up an equation using the given information. The team won 17 more than twice the number of times they lost. The team lost 22 times.
Explanation:To find the number of times the team lost, we can set up an equation using the given information.
Let's assume the number of times the team lost is x.
According to the given information, the team won 17 more than twice the number of times they lost. So, the number of times the team won is 2x + 17.
The total number of games played is 83, which is the sum of the number of games won and lost.
So we have the equation 83 = x + (2x + 17).
Simplifying this equation, we get 83 = 3x + 17.
Subtracting 17 from both sides, we have 66 = 3x.
Dividing both sides by 3, we get x = 22.
Therefore, the team lost 22 times.
A 12 lb shankless ham contains 16 servings. What is the rate in servings per pound?
Which sentence explains the correct first step in the solution of this equation?
2(x−4)=12
A. Subtract 12 from both sides.
B. Add 4 to both sides.
C. Apply the distributive property to get 2x - 8 = 12
D. Apply the distributive property to get 2x - 4 = 12
Answer: like 5 years late but wtv
Step-by-step explanation:
The volume of a box of soup broth is 972 cubic centimeters. The box is 20 centimeters high and 10.8 centimeters long. How wide is the box?
The width of the rectangular prism will be 4.5 centimeters.
What is the volume of the rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
The volume of a box of soup broth is 972 cubic centimeters. The box is 20 centimeters high and 10.8 centimeters long.
Then the width of the rectangular prism is calculated as,
972 = 20 x W x 10.8
Simplify the equation, then we have
972 = 20 x W x 10.8
972 = 216W
W = 4.5 centimeters
The width of the rectangular prism will be 4.5 centimeters.
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A right triangle has sides 5.0 m, 12 m, and 13 m. the smallest angle of this triangle is nearest:
Final answer:
To find the smallest angle in a right triangle with side lengths of 5.0 m, 12 m, and 13 m, we use the inverse tangent function with the shortest leg over the adjacent leg, yielding an angle of approximately 22.6 degrees.
Explanation:
The subject of the question is mathematics, and it pertains to high school level geometry. The question is asking to determine the smallest angle in a right triangle with sides measuring 5.0 m, 12 m, and 13 m. To find the smallest angle, we can use trigonometry, specifically the inverse tangent function.
Step-by-Step Explanation
Identify the sides of the triangle. In this case, we know that the sides are 5.0 m, 12 m (which could be interpreted as legs), and 13 m (the hypotenuse).
Because we are looking for the smallest angle, we will use the smallest leg, which is 5.0 m, and the next largest leg, which is 12 m.
Use the tangent function, which relates the opposite side to the adjacent side in a right triangle. The smallest angle, which we will call θ, will have the opposite side of 5.0 m and an adjacent side of 12 m.
Calculate θ using the inverse tangent function (also known as arctangent). θ = tan-1(5.0/12).
Perform the calculation using a calculator to find the nearest degree. θ = tan-1(5.0/12) ≈ 22.6°.
Therefore, the smallest angle in the triangle is approximately 22.6 degrees.
A store discounts the price of a beanbag chair by 20%. The price of the beanbag chair is marked as $16. What was the original price of the beanbag chair?
original price of the beanbag chair was $20 before the 20% discount was applied.
To find the original price of the beanbag chair that has been discounted by 20%, we set up an equation. Let's denote the original price as P. A 20% discount on the original price means the chair is being sold for 80% (100% - 20%) of P. This is represented by the equation 0.80P = $16.
To find P, we simply divide both sides of the equation by 0.80:
P = $16 / 0.80
This gives us:
P = $20
Therefore, the original price of the beanbag chair was $20 before the 20% discount was applied.
what is 5879 rounded to the nearest hundredth
540 less than the product of 54 and a number is 918
how to solve x^2-4y^2=7
Find the dimensions of a rectangle with perimeter 100m area of 336
A recipe for krispy rice treats calls for 6 cups of rice cereal and 40 large marshmallows. You want to make a larger batch of goodies and have 9 cups of rice cereal. How many large marshmallows do you need? However, you only have the miniature marshmallows at your house. You find a list of substitution quantities on the internet that suggests 10 large marshmallows are equivalent to 1 cup miniatures. How many cups of miniatures do you need?
Lesley raised $25 for the food bank last year and she raised 8 times as much money this year how much money did she raise this year
The _______ form of a quadratic equation is written y = a(x - h)2 + k
Answer:
Correct Answer: vertex form
Step-by-step explanation:
"to find x in part a, you would need" to solve the equation x 2 – 25 =0. wh
A bag contains 1 gold marbles, 6 silver marbles, and 30 black marbles. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. You can expect to lose an average of ________ cents every time you play. (round to the nearest cent)
You are scheduled to receive $16,500 in three years. when you receive it, you will invest it for nine more years at 9.5 percent per year. how much will you have in twelve years?
The total amount you will have in twelve years is calculated by multiplying your initial amount of $16,500 with (1 + 0.095) raised to the power of 9 (years of investment). This is a demonstration of the future value concept in finance.
Explanation:This question is about the concept of future value in finance. First, you receive $16,500 after three years. Following this, you invest this amount at an interest rate of 9.5% for nine more years. To calculate the future value of an investment, you can use the formula: Future Value = Present Value * (1 + Interest rate)^numbers of years. In this case, it would be $16,500 * (1 + 0.095)^9. This calculation will give you the total amount you will have in twelve years after the investment.
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Estimate the area of the irregular shape. Explain your method and show your work. Can someone explain this to me?
Answer:
Approximate area: 27.5 square units
Step-by-step explanation:
The irregular shape is very similar to a trapezium with coordinates (-3,3), (2, 2), (2, -2) and (-3, -4).
Area of a trapezium: [(a+ b)/2]*h
where a and b refer to the two parallel sides and h is the distance between them. From the above coordinates: a = 7 length units, b = 4 length units and h = 5 length units. Therefore, approximate area = [(7+ 4)/2]*5 = 27.5 square units
Find the dimensions of a triangle given the following information. The perimeter is equal to 36cm, side 1 is 4 less than side 2 and side 3 is twice the length of side 2.