The percentile scores for a distribution with a mean of 100 and a standard deviation of 15, the z-scores for 112 and 82 are 0.8 and -1.2, respectively.
Calculating Percentile Scores
To determine percentile scores for the values given in the original student question, we need to calculate the z-scores for 112 and 82 from a distribution with a mean of 100 and a standard deviation of 15.
To find the z-score, use the formula:
Z = (X - mu) / sigma
Where X is the raw score, \\mu is the mean, and \\sigma is the standard deviation.
For 112:
Z = (112 - 100) / 15
Z = 12 / 15
Z = 0.8
For 82:
Z = (82 - 100) / 15
Z = -18 / 15
Z = -1.2
Once the z-scores are calculated, we can look up the corresponding percentiles in a standard normal distribution table.
A z-score of 0.8 corresponds to approximately the 78.81st percentile, meaning about 78.81% of the scores are below 112.
A z-score of -1.2 corresponds to approximately the 11.54th percentile, meaning about 11.54% of the scores are below 82.
Find last year’s salary if after. 2% pay rate, this year’s salary is $35,700
Suppose an ant is sitting on the perimeter of the unit circle at the point (1,0). if the ant travels a distance of 2π3 in the counter-clockwise direction, then the coordinates of the point where the ant stops will be
After traveling a distance of 2π/3 on the unit circle in the counter-clockwise direction from (1,0), the ant stops at the coordinates (-1/2, √3/2), which are found using the unit circle's parametric equations.
Explanation:The question asks about finding the coordinates of a point on the unit circle after traveling a certain distance in the counter-clockwise direction. The distance given is 2π/3, which, when considering the circumference of the unit circle (2π), represents an arc that is a third of the full circle. The unit circle is centered at the origin (0,0) and has a radius of 1, with points on it defined by cos(θ) and sin(θ) for any angle θ measured in radians from the positive x-axis.
Traveling 2π/3 radians from (1,0) in the counter-clockwise direction lands us at an angle of 2π/3 radians from the positive x-axis. The coordinates of the point on the unit circle at this angle can be found using the circle's parametric equations x = cos(θ) and y = sin(θ). Substituting θ with 2π/3, we obtain:
x = cos(2π/3) = -1/2y = sin(2π/3) = √3/2Therefore, the coordinates of the point where the ant stops are (-1/2, √3/2).
which of the following are the factors of 4b^2-16?
Z = x4 + x2y, x = s + 2t − u, y = stu2; ∂z ∂s , ∂z ∂t , ∂z ∂u when s = 1, t = 4, u = 5
two hundred eighty-four thousand, one hundred eighty-seven in expanded form
One 50 pound bag of fertilizer will cover 75 square feet of lawn.how many pounds of fertilizer will tawny need to cover 120 square feet of lawn
80 pounds of fertilizer will be needed to cover 120 square feet of lawn.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
To write a proportion.
50/75 = x/120.
Then Cross multiply to get;
6,000/75x.
Now, divide each side by 75 to isolate the “x”.
x = 80.
Therefore 80 pounds of fertilizer will cover 120 square feet of lawn.
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The total cost for office expenses to run the organic strawberry farm varies directly with the number of months it is used. Which equation represents this scenario?
https://coststudyfiles.ucdavis.edu//uploads/cs_public/c5/a1/c5a181af-8e1b-474a-9509-443c3cb223ed/strawberry2ndyrcc2011.pdf
pages 15-16
Answer:
There are so many little things that go into organic farming and each of them adds additional costs.
Some of these additional costs are listed in the article located here.
Use the data table at the end of the document to answer the questions.
Which cost category in the table shows an example of direct variation?
Weed-Hand
The total cost for office expenses to run the organic strawberry farm varies directly with the number of months it is used. Which equation represents this scenario?
y = 63x
What would be the total cost for office expenses for 24 months?
$1,512.00
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380 students increase 5% what is the new amount of students
Effie's store has 10,908 more comic book than Brody's. Brody's store has 45,607 coming books. How many books do Effie's and Brody's store have together?
Show your work...
Keith has p pennies, n nickels, and d dimes in his pocket. The total number of coins is 9. The expression 0.01p+0.05n+0.10d represents the value of the coins, which is equal to $0.44. He has one more dime than nickels. How many pennies does Keith have? Keith has _____ pennies.
he has 4 pennies
2 nickels=10 cents
3 dime=30 cents
20 cents
40 +4 pennies =44 cents
Answer:
Keith has 4 pennies, 3 dimes and 2 nickels.
Step-by-step explanation:
Let the pennies be = p
Let the nickels be = n
Let the dimes be = d
Total coins Keith has = 9
So, 1st equation form :
[tex]p+n+d=9[/tex] ....(1)
Keith has one more dime than nickels, means [tex]d=n+1[/tex] .....(2)
Total value of these coins is $0.44
So, third equation forms:
[tex]0.01p+0.05n+0.10d=0.44[/tex] .....(3)
Substituting (2) in (1)
[tex]p+n+n+1=9[/tex]
[tex]p+2n=8[/tex] .....(4)
Similarly substitution (2) in (3)
[tex]0.01p+0.05n+0.10(n+1)=0.44[/tex]
[tex]0.01p+0.05n+0.10n+0.10=0.44[/tex]
[tex]0.01p+0.15n=0.34[/tex] ....(5)
Now multiplying (4) by 0.01 and subtracting by (5)
[tex]0.01p+0.02n=0.08[/tex] subtracting this from (5) we get
[tex]0.13n=0.26[/tex]
So, we get n = 2
[tex]p+2n=8[/tex]
[tex]p+2(2)=8[/tex]
[tex]p+4=8[/tex]
p = 4
[tex]p+n+d=9[/tex]
[tex]4+2+d=9[/tex]
[tex]6+d=9[/tex]
d = 3
-------------------------------------------------------------------------------------
Therefore, Keith has 4 pennies, 3 dimes and 2 nickels.
The sum of 3 less than 5 times a number and the number increased by 9 is 24. what is the number?
The population of rabbits in a national forest is modeled by the formula P= 12,000 + 1000 (t+1) where t is the number of years from the present. How many rabbits are now in the forest?
The current population of rabbits in the forest can be found by substituting t = 0 into the given formula P = 12,000 + 1000(t+1).
Explanation:To find the number of rabbits currently in the forest, we can substitute the value of t = 0 into the given formula. The formula P = 12,000 + 1000(t+1) represents the population of rabbits in the forest at any given year, where t is the number of years from the present. Since we want to find the current population, we substitute t = 0:
P = 12,000 + 1000(0+1)
P = 12,000 + 1000(1)
P = 12,000 + 1000
P = 13,000
Therefore, there are currently 13,000 rabbits in the forest.
The price of a technology stock was $ 9.69 yesterday. Today, the price fell to $ 9.58 . Find the percentage decrease.
A null hypothesis can only be rejected at the 5% significance level if and only if:
The lateral area of the right regular triangular prism is 18cm2. find the total surface area. give your answer in decimal form rounded to 2 decimal places
A picture has a width that is 17 inches shorter than the length, and its total area is 480 square inches. Find the dimensions of the picture.
Final answer:
To find the dimensions of the picture, set up an equation using the length and width. Solve the equation to find the dimensions: length = 32 inches, width = 15 inches.
Explanation:
To find the dimensions of the picture, let's assume the length is x inches. According to the problem, the width is 17 inches shorter than the length, so the width would be (x - 17) inches. The total area of the picture is given as 480 square inches. We can set up an equation using the length and width: x(x - 17) = 480. Solve this quadratic equation to find the dimensions of the picture.
Expanding the equation, we get x^2 - 17x - 480 = 0. Factoring the quadratic equation, we find (x + 15)(x - 32) = 0. Therefore, the possible values for x are -15 and 32. Since the length cannot be negative, we discard -15. Thus, the length of the picture is 32 inches and the width is (32 - 17) = 15 inches.
Final answer:
The dimensions of the picture are 32 inches in length and 15 inches in width.
Explanation:
To find the dimensions of the picture, we need to establish equations based on the information provided. Let the length of the picture be L inches and the width be W inches.
Given that:
The width is 17 inches shorter than the length: W = L - 17.The total area of the picture is 480 square inches: L × W = 480.Plug the width expression from step 1 into the area equation from step 2 to form a quadratic equation:
L(L - 17) = 480
Solving this quadratic equation will give us the value of L. Once we have L, we can use the first equation to get W. Let's solve the quadratic equation:
L² - 17L - 480 = 0
Factoring the quadratic, we find that (L - 32)(L + 15) = 0. So L can be either 32 or -15. Since a length cannot be negative, L must be 32 inches, and W, therefore, is 32 - 17 = 15 inches.
The dimensions of the picture are therefore 32 inches by 15 inches.
Compare 249 and 271 write the greater number in word form
The local home improvement store wants to increase their inventory. Last year 40 lawn mowers cost them $4,776.
At the same cost, how much would 120 lawn mowers cost them this year?
Answer:14,328
Step-by-step explanation:
Suppose that in a population of 1000 there are 300 defective items and 700 items that are not defective. if you are selecting two items at random from this population, what is the probability they will both be defective?
If the pattern continues, how many cups of milk does George need to make 6 batches of muffins? Explain how you found your answer.
To make 6 batches of muffins, George needs 3 cups of milk, which is found by multiplying the ratio of 1/2 cup of milk per batch by 6.
Explanation:The question is asking to determine the quantity of an ingredient needed for a recipe, specifically milk for pancakes, according to a given ratio. The question is based on a proportion where 1/2 cup of milk is needed for one batch of pancakes. To find out how many cups of milk are needed for 6 batches of muffins (assuming muffins and pancakes require the same amount of milk which appears to be a minor typo in the scenario), we multiply the 1/2 cup required for one batch by 6.
Thus, the calculation is: 1/2 cup of milk × 6 batches = 3 cups of milk.
To find out how many cups of milk George needs to make 6 batches of muffins, we first need to determine the number of cups needed for one batch. Let's assume that each batch requires 3 cups of milk. Therefore, to make 6 batches, George would need 3 cups x 6 batches = 18 cups of milk
Farmer Jack needs 1,800 square feet of garden space to have enough corn for a year. His garden space is currently 10 5⁄6 feet by 18 feet. How much more land does farmer Jack need to plant the rest of his corn?
Farmer Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.
Explanation:To find out how much more land Farmer Jack needs to plant the rest of his corn, we need to calculate the area of his current garden and subtract it from the required area of 1,800 square feet. Farmer Jack's garden is 10 5/6 feet by 18 feet, so we can multiply these two dimensions to get the area of his current garden. Then, we subtract this area from 1,800 to find out how much more land he needs:
Area of Farmer Jack's garden: 10 5/6 feet * 18 feet = 197 1/3 square feet
More land needed by Farmer Jack: 1,800 square feet - 197 1/3 square feet = 1,602 2/3 square feet
Farm Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.
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Assume f(x) = g(x). Which of the following two functions may be used to represent the function 3x = x – 4?
Which item would most likely appear on a culturally fair test?
Brianna built a rectangular flower garden. The garden is 10 feet long and 8 feet wide. What is the area of Briannas flower garden?.
The table shows the outputs y for different inputs x:
Input (x) 5 6 7 8
Output (y) 2 5 8 11
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 75?
Answer:
A. yes...it is a function because there is no repeating x values.
B. (5,2)(6,5)...slope = (5 - 2) / (6 - 5) = 3
y = mx + b
slope(m) = 3
(5,2)...x = 5 and y = 2
now we sub
2 = 3(5) + b
2 = 15 + b
2 - 15 = b
-13 = b
so the equation is : y = 3x - 13
when x = 7
y = 3(7) - 13....y = 21 - 13....y = 8
f(x) = 2x + 13...when x = 7
f(7) = 2(7) + 13...f(7) = 14 + 13.....f(7) = 27
the function has a greater value
C. f(x) = 2x + 13....when f(x) = 75
75 = 2x + 13
75 - 13 = 2x
62 = 2x
62/2 = x
31 = x
Step-by-step explanation:
Ursula bought 9 dozen rolls of first aid tape for the health office. The rolls were divide equally into 4 boxes. How many rolls are in each box?
What is the concentration of nitrate ions in a 0.125 M Mg(NO3)2 solution
We have that the concentration of the nitrate ions is mathematically given as
M= 0.250M
The concentration of the nitrate ionsQuestion Parameters:
Generally the equation for the Reaction is mathematically given as
Mg(NO₃)₂ --> Mg²⁺ + 2NO₃⁻
Each mole of the Mg(NO₃)₂ will dissociate into 2 moles of NO₃⁻.
the concentration of the nitrate ions is
M = (0.125M)(2)
M= 0.250M
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A cube has an edge if 4 feet. The edge is increasing at a rate of 2 feet per minute. Express the volume of the cube as a function
To find the volume of a cube with an edge length that is increasing with time, express the edge length as a function of time and substitute this into the volume formula. In the given problem, the edge length is increasing 2 feet per minute, thus the volume V of the cube at any given time can be expressed as V = (4 + 2t)³.
Explanation:The volume of a cube is calculated by raising the edge length to the power of three (V = e³). For this problem, we know that the edge e is increasing at a rate of 2 feet per minute. Therefore, we can express e as a function of time t, where e = 4 + 2t. Substituting this back into our volume equation, we receive the volume V of the cube as a function of time t: V = (4 + 2t)³.
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The width of a rectangle is 3 4 the length. The perimeter is 252 cm. What is the width of the rectangle? A) 36 cm B) 48 cm C) 54 cm D) 72 cm
Terms that have the same variables raised to the same powers are called ___ terms.
Like terms are terms with the same variables raised to the same powers, allowing them to be combined by addition or subtraction.
Explanation:Terms that have the same variables raised to the same powers are called like terms.
In mathematics, particularly algebra, like terms are terms that contain the same variables to the same power, which allows them to be combined through addition or subtraction. An example of like terms would be 3x2y and 7x2y. Both contain the variable x raised to the second power, and y raised to the first power, thus they can be combined to form 10x2y.
Terms that have the same variables raised to the same powers are called "like" terms. In algebraic expressions, like terms are essential for simplifying and combining expressions efficiently. The concept is rooted in the understanding that terms with identical variable factors, such as x^2 or y, can be grouped together. This simplification aids in solving equations, factoring, and performing various algebraic operations.
Identifying and combining like terms streamline mathematical processes, providing a clearer and more concise representation of expressions. Ultimately, the recognition of like terms is a fundamental aspect of algebraic manipulation, contributing to the coherence and simplicity of mathematical expressions.
Final answer:
Terms that have identical variables raised to the same powers are called like terms. They can be added or subtracted as they represent the same quantities of variables to the same exponent powers.
Explanation:
Terms that have the same variables raised to the same powers are called like terms.
Like terms can be combined (added or subtracted) because they represent the same types of quantities raised to the same power. For example, in the expression 3x2 + 5x2, both terms are like terms because they both involve the variable x raised to the second power, which means that these two terms can be added together to get 8x2.
Raising a number to an exponent, such as squaring (raising to the second power) or cubing (raising to the third power), is a way to express repeated multiplication of the number by itself. For instance, the expression 52 = 5 x 5 = 25 shows that 5 is being squared, and the result is 25.