Rounding to the nearest whole number, the limits for a 'b' grade are 75 and 81
In this question we have been given a philosophy professor assigns letter grades on a test according to the given scheme.
We need to find the numerical limits for a b grade.
b: scores below the top 12 % and above the bottom 63 % which means scores between the 63th and 88th percentile.
Given that the scores on the test are normally distributed with a mean of 72 and a standard deviation of 8.1
μ = 72, σ = 8.1
z-score at the 63th percentile: 0.332
z-score at the 88th percentile: 1.175
The lower limit of a 'b' grade is:
0.332 = X - μ/σ
0.332 = (X - 72)/8.1
2.67 = X - 72
X = 74.67
X ≈ 75
The upper limit of a 'b' grade is:
1.175 = X - μ/σ
1.175 = (X - 72)/8.1
9.52 = X - 72
X = 81.52
X ≈ 81
Therefore, you get a 'b' if you have a grade between 75 and 81
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The digits in the product of 0.48 and a decimal number between 350 and 400 are 182136. Explain how to correctly place the decimal point without knowing the other factor. Then Place place the decimal point in the product.
The decimal point is to be placed three places to the left.
What are decimal numbers?
When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.
Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.
If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.
Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.
The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.
The decimal point is to be placed three places to the left.
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Which is an expression for the derivative P(x) = f(x) / —f(x)
the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².
What is derivative?
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.
given expression p(x)= f(x)/1-f(x)
The derivative of the given expression will be
p'(x) = f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))²
Hence the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².
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X² + 3x + y = 0
2x+y=5
Solve for x and y by substitution
The square root of a negative number is not a real number, this system of equations has no solution.
What is the system of equations?
A system of linear equations is a set of two or more equations that includes common variables. To solve a system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
To solve for x and y, we can start by solving one of the equations for one of the variables. Let's solve the second equation for y:
2x + y = 5
y = 5 - 2x
Now we can substitute this expression for y in the first equation to get an equation in terms of x:
x² + 3x + (5 - 2x) = 0
x² + 3x + 5 - 2x = 0
x² - x + 5 = 0
We can then solve this equation for x using the quadratic formula:
x = (-3 ± √(9 - 20))/2
x = (-3 ± √(-11))/2
Hence, the square root of a negative number is not a real number, this system of equations has no solution.
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6. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the initial
height of the rocket before it is launched?
h(t) = -5t² +42t +54
Answer:
Step-by-step explanation:
The initial height of the rocket before it is launched can be found by evaluating the function h(t) at t=0. To do this, you can substitute 0 for t in the function:
h(0) = -5(0)² + 42(0) + 54
h(0) = 0 + 0 + 54
h(0) = 54
Therefore, the initial height of the rocket before it is launched is 54 meters.
Answer: 54 meters.
Step-by-step explanation: The initial height of the rocket before it is launched is represented by the constant term in the quadratic function, which is 54. This means that the rocket's height at time t = 0 (before it is launched) is 54 meters.
To confirm this, you can plug in t = 0 into the quadratic function to get:
h(0) = -5(0)² + 42(0) + 54 = 54 meters
This means that the initial height of the rocket before it is launched is 54 meters.
Which diagram shows the rotation Rc, -90 (ABCD) = A'B'C'D'?
The diagram that shows the rotation of rectangle ABCD by -90 degrees is; Option A
What is the translation transformation rule?
When we rotate positive 90 degrees, the rotation is said to be counterclockwise but when we rotate negative 90 degrees, the rotation is said to be clockwise.
Now, we want to find the rotation that correctly describes rotation of the rectangle ABCD by negative 90 degrees.
Thus, looking at the options, the only one that has the negative 90 degrees rotation that is clockwise will be option A because we see that when we rotate to the right which is clockwise, the first point is A which is exactly what is in option A.
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. Solve for x: log₂ (x+4) + log₂ (x + 3) = 1. Pleasee
The value of x for the expression is equal to -5 and -2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the logarithmic expression is log₂ (x+4) + log₂ (x + 3) = 1. The value of x will be calculated as,
log₂ (x+4) + log₂ (x + 3) = 1
log₂ { (x+4)(x + 3) } = 1
x² + 7x + 12 = 2
x²+ 7x + 10 = 0
Solve the above quadratic equation,
x²+ 7x + 10 = 0
x² + 5x + 2x + 10 =0
x ( x + 5 ) + 2 ( x + 5 ) = 0
(x + 5 ) ( x + 2 ) = 0
x = -5 and -2
The values of x are -5 and -2.
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A sleep specialist wants to know if meditating before bedtime can help people fall asleep. In a study, he asked the subjects to meditate for various lengths of time just before going to bed.
The specialist tracked the subjects' meditation times, x, and how long it took them to fall asleep, y. Both times were recorded in minutes.
Answer:
whats the question?
Step-by-step explanation:
Two of the coordinates representing the corners of Maya's rectangular driveway are (-1, 1) and (1 1\2, -8 1\2
9. Plot the other two coordinates of Maya's rectangular driveway. What are the ordered pairs that you plotted?
Answer:
the coordinates of the other corner are (-10/3, -1 3/4).
The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).
Step-by-step explanation:
To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).
Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.
We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.
We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:
y = -3/17 * x + (-3 3/4)
x = (y - (-3 3/4))/(-3/17)
Substituting the coordinates of the corner we found earlier, we get:
x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3
So, the coordinates of the other corner are (-10/3, -1 3/4).
The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).
PLEASE HELP ASAP FOR MY FINALS
Answer:
A.86
is the answer will show how it's solved if necessary on comment.
hope it helps!!!
Solve for y
-x - 2y ≥ 7
Answer: [tex]y \leq -\frac{x}{2}-\frac{7}{2}[/tex]
Step-by-step explanation:
[tex]-x-2y \geq 7\\\\x+2y \leq -7\\\\2y \leq -x-7\\\\y \leq -\frac{x}{2}-\frac{7}{2}[/tex]
2 Fractions equivalent to 2/6
The fractions 1/12 and 1/4 are equivalent to 2/6.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Two fractions are equivalent to 2/6.
There can be many fractions which are equal to 2/6.
Let one fraction is 1/12,
And other fraction is x,
So, according to given condition,
x + 1/12 = 2/6
x = 2/6 - 1/12
x = 3/12
x = 1/4
The required fractions are 1/12 and 1/4.
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The statement for the expression 4x-10 is
Subtract 3
2y + 2xy – x + 4 from 9 - 7x + 3xy - 4
2y
The price of a coat is reduced by 17% in a sale.
The sale price is £78.85.
What was the original price of the coat?
Give your answer in pounds (£).
The required original price of the coat is given as £95.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95
Hence, the cost of the coat before the sale is £95.
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Please help, thank you!
suppose that, of people who undergo routine screening, for every two people who have colon cancer, there are 100 who do not. (that is, 2/102 people have it.) of those who undergo screening and do have colon cancer, all of them will have a positive test. of the people who undergo screening but don't have colon cancer, only 2 percent have a positive test. a random person undergoes routine screening and has a positive test. what is the probability (not odds) that this person has colon cancer? choose the range in which the answer lies.
The probability that a person has colon cancer given that they have a positive test result is approximately 0.98. The answer lies in the range [0.95, 1.00].
Let's call the probability that a person has colon cancer given that they have a positive test result "p". We can use Bayes' Theorem to find this probability.
Bayes' Theorem is: p(A|B) = (p(B|A) * p(A)) / p(B)
In this case, A is the event that the person has colon cancer, and B is the event that the person has a positive test result.
We are given that:
p(B|A) = 1 (all people who have colon cancer will have a positive test result)
p(B|~A) = 0.02 (2% of people who do not have colon cancer will have a positive test result).
We are also given that p(A) = 2/102 (2 out of 102 people who undergo routine screening have colon cancer) and p(~A) = 100/102 (100 out of 102 people who undergo routine screening do not have colon cancer).
Substituting these values into Bayes' Theorem, we get:
p(A|B) = (1 * (2/102)) / (1 * (2/102) + 0.02 * (100/102))
Simplifying, we get:
p(A|B) = 0.98
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show that 12cos30 + 2tan60 can be written in the form Vk where k is an integer
Answer:
√192
Step-by-step explanation:
12 cos 30° + 2 tan 60°
Substitute the trig functions of the special angles.
12 (½√3) + 2 (√3)
Simplify.
6√3 + 2√3
8√3
Move under the radical.
√(8² · 3)
√192
It takes 47 pounds of seed to completely plant a 5 -acre field. How many acres can be planted per pound of seed? (b)
Point E has the same y-coordinate as point D, but the x-coordinate of point D. Plot point E and write the coordinates of point E. Then describe the type of reflection you plotted.
The coordinates of Point E are (-4,2) and Point E is a reflection of point D across the X-axis.
What is the coordinate about?Point E has the same y-coordinate as point D, which is 2. However, the x-coordinate of point E is the opposite of the x-coordinate of point D. The x-coordinate of point D is 4, so the x-coordinate of point E must be -4. Therefore, the coordinates of Point E are (-4,2).
As for the reflection, you can imagine a mirror placed on the x-axis (horizontally) and Point D and E being on the same side of that mirror.
Therefore, As Point D is reflected on the mirror, it will be flipped and the x-coordinate changes its sign and becomes -4. Therefore Point E is a reflection of point D across the X-axis.
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Point E has the same y-coordinate as point D, but the x-coordinate of point E is the opposite of the x- coordinate of point D. Drag tiles to complete the statements. (4,2) (4,-2) (-4,2) (-4,-2) X-axis y-axis The coordinates of Point E are --- &Point E is a reflection of point D across the ---
Angela is following this recipe to make biscuits.
Angela uses 0.9 litres of syrup.
How much margarine is needed in kg?
Recipe: Makes 10 biscuits
150 g margarine
180 g sugar
225 ml syrup
225 g oats
40 g sultanas
The amount of margarine needed in Kg for making biscuits is 0.6kg
What is proportions?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.
How to find the amount of margarine needed in KgThe amount of margarine needed in Kg is calculated using proportions
If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require
0.225 l = 0.15 kg
0.9 l = ?
cross multiplying
0.225 * ? = 0.9 * 0.15
? = 0.135 / 0.225
? = 0.6
Angela will require 0.6 kg of margarine
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Which is the midpoint of segment AB with A(-1,5) and B(6,-3)
Answer:
(2½,1)
Step-by-step explanation:
(-1+6/2,5+-3/2)
(5/2,2/2)
(2½,1)
A line has a slope of 2 and includes the points (
–
7,
–
10) and (0,j). What is the value of j?
Answer:
j = 4
Step-by-step explanation:
calculate the slope of the line passing through the goven points and equate to 2
calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 7, - 10 ) and (x₂, y₂ ) = (0, j )
m = [tex]\frac{j-(-10)}{0-(-7)}[/tex] = [tex]\frac{j+10}{0+7}[/tex] = [tex]\frac{j+10}{7}[/tex] then equating gives
[tex]\frac{j+10}{7}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )
j + 10 = 14 ( subtract 10 from both sides )
j = 4
Solve. 3 x − 9 x 2 = − 10
Answer:
below
Step-by-step explanation:
9x^2-3x-10 = 0 Use quadratic Formula with a = 9 b = -3 and c = -10
to find the zeroes are x = 1/6 ± sqrt (41) / 6
Please help meee asap please !!!????
boston thinks that the domain is all positive real numbers between 0-4 while caleb thinks it is all whole numbers between 0-4. who do you agree with, and why?
0-4 can be the domain of positive real numbers but can not be the domain of whole numbers.
Numbers an arithmetical value used in counting and calculating that is expressed as a word, symbol, or figure that represents a specific quantity.
Let's understand what is positive real numbers.
That is all the real numbers that are greater than or equal to zero.
real numbers are numbers which include both rational and irrational numbers.
whole numbers are positive integers that mean only positive integers.
that means 0-4 can be the domain of positive real numbers but can not be the domain of whole numbers because 0.5 and 0.6 these numbers are not whole numbers.
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Find the vertex of the graph of 7(x) = 10.25x - 0.75|.
The vertex of the function f(x) = 10.25 |x - 0.75| will be at (0.75, 0).
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = | x - h| + k
The absolute function is given as,
f(x) = 10.25 |x - 0.75|
Compare the function f(x) with standard equation, then we have
h = 0.75
k = 0
The vertex of the capability f(x) = 10.25 |x - 0.75| will be at (0.75, 0).
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Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 5 ≤ x ≤9.
7
8
9
6
x
4
5
f(x)
4
8
16
32
64
medically explained PAINL X
128
Deltal/ath
The average rate of change, in simplest form, is -2/5.
What is average rate ?
Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.
The rate of change of the function is its gradient or slope.
The formula for calculating the gradient of a function is expressed as:
[tex]m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]
Using the coordinate points from the table (0,41) and (15,35)
Substitute the coordinate into the expression:
[tex]$$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$[/tex]
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A right triangle has a leg length of √ and a trypolenuse length of 7. Determine the length of the other leg of the right triangle.
03
O √59
O√43
The length of the other leg is (c) √43
How to determine the length of the other legFrom the question, we have the following parameters that can be used in our computation:
Hypotenuse = 7
One leg = √6
The length of the other leg can be calculated using
The length of the other leg = √(Hypotenuse^2 - One leg^2)
So, we have
The length of the other leg = √(7^2 - √6^2)
Evaluate
The length of the other leg = √43
Hence, the length is (c) √43
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Complete question
A right triangle has a leg length of √6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.
Express cos E as a fraction in simplest terms.
Answer: cos E=
E
10
24
C
0
The trigonometric ratio, cos E of the right triangle is 5 / 13.
How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
A right triangle is a triangle that has one of its angles as 90 degrees.
The sides and angles of a right triangle can be found using trigonometric ratios. The sides of a right triangle base on its sides are as follows;
opposite sideadjacent sidehypotenuse sideTherefore,
cos E = adjacent / hypotenuse
Hence,
let's find the hypotenuse side using Pythagoras theorem,
24² + 10² = c²
c = √576 + 100
c = √676
c = 26
cos E = 10 / 26
Therefore,
cos E = 5 / 13
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Translate: "five less than the product of a number and 6 is at least 8"
Answer:
yx6-5= greater than or equal to 8
Step-by-step explanation:
math brain
the population of a city was 250,000 in 1980, and it was 310,000 in 2000. what was the average rate of growth over this period?
Average rate of growth over this period is 0.4%.
Average rate of growth over a period is given by:
A=P[tex]e^{rT}[/tex] where,
A- Population at time T
P- Initial population
r-average rate of growth
T-Time period
Now, P=250,000, A=310,000 and T=21 (2000-1980+1)
therefore, putting values in the equation, we get:
310,000=250,000[tex]e^{21r}[/tex]
⇒ [tex]e^{21r}[/tex] = 1.24
⇒ 21r = log(1.24)
⇒ r = 0.0044 or 0.4%.
so, the average rate of growth over this time period is 0.4%.
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