all the students in an algebra class took a 100-point test. five students scored 100, each student scored at least 60, and the mean score was 76. what is the smallest possible number of students in the class?
The smallest possible number of students in the algebra class is 13.
What is meant by the word inequality?Inequalities define the connection between two non-equal values. Inequality means being unequal. If two values really aren't equal, we use the "not equal symbol (≠)".Let n≥5 be the number of students.
The sum of their scores must be at least 5×100 + (n - 5).
Simultaneously, we must achieve the mean 76, which is equivalent to achieving the mean sum 76n.
As a result, we have a sufficient precondition on n: we should have 5×100 + (n - 5) ≤ 76n.
This can be reduced to 200 ≤ 16n. This is true for the smallest integer n = 13.
To complete our solution, we must now determine how 13 students might have scored just on test.
We have 13×76 = 988 points to distribute to them. Because five 100s equal 500, we must distribute the remaining 488 points as among remaining eight students.
This can be accomplished, for example, by awarding each of them 61 points.
Thus, the smallest possible number of students in the class is 13.
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4/5÷3/4 i need to know it
To divide two fractions, simply cross-multiply as following:
The population of a city increases by 3.1% per year. If this year's population is
290,000, what will next year's population be, to the nearest individual?
Answer:
the next year population is 122,689
Step-by-step explanation:
The computation of the next year population is as follows:
= This year population × increase percentage
= 119,000 × (1 + 0.031)
= 119,000 × 1.031
= 122,689
Hence, the next year population is 122,689
The above formula is applied so that the correct value of the population could come
and the same is relevant
A, B, C, D, E, F, G & H form a cuboid.
AB= 3.2 cm, BC = 1.6 cm & CG = 7.7 cm.
Find AG rounded to 1dp
The length of AG=8.5 cm that is diagonal. There are four body diagonals of cuboid and twelve face diagonals. A body diagonal is referred to as the diagonal of cuboid. The diagonal of cuboid formula is √(l² + b² + h²) units.
What is cuboid?A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid means "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces.
What is diagonal?A diagonal in geometry is a line segment that connects two polygonal vertices when they are not on the same edge. Any sloping line is known as a diagonal informally.
A, B, C, D, E, F, G & H form a cuboid. AB= 3.2 cm, BC = 1.6 cm & CG = 7.7 cm. That is l=3.2 cm, b=1.6 cm, h=7.7 cm.
√(l² + b² + h²) units.
=√(3.2²+1.6²+7.7²)
=8.49 cm
≈8.5 cm
A body diagonal is referred to as the diagonal of cuboid. The diagonal of cuboid formula is √(l² + b² + h²) units. The length of AG=8.5 cm that is diagonal. There are four body diagonals of cuboid and twelve face diagonals.
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Please look at the image below. This is my homework by the way.The figure shown are congruent. Find a sequence of transformations for the indicated mapping. Give coordinate notation for the transformations you use.
Coordinates of PQRSTU
P = (-2, -6)
Q = (-4, -6)
R = ((-4, -2)
S = (2, -4)
T = (2, -8)
U = (0, -10)
They changed to ABCDEF
A = (4, 4)
B = (2, 4)
C = (2, 8)
D = (8, 6)
E = (8, 2)
F = (6, 0)
Transformations used = (x + 6, y + 10)
Jesse recorded a temperature of 75 degrees Fahrenheit this morning for science class. The temperature increased by 4 1/2 degrees Fahrenheit in the afternoon, before decreasing 2.6 degrees Fahrenheit in the evening. What was the temperature in the evening?
The temperature in the evening is 79.5 degrees Fahrenheit.
What is basic algebra?The area of mathematics known as algebra aids in the representation of issues or circumstances into mathematical statements. Creating a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including coordinate geometry, calculus, and trigonometry. 2x + 4 = 8 is a basic algebraic expression.When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement.
Jesse recorded a temperature in the morning of 75 degrees Fahrenheit
The temperature increased by [tex]4\frac{1}{2}[/tex] degrees Fahrenheit in the afternoon
75 + [tex]4\frac{1}{2}[/tex] =[tex]\frac{159}{2}[/tex]
=79.5 degrees Fahrenheit
Before decreasing by 2.6 degrees Fahrenheit in the evening. The temperature in the evening is 79.5 degrees Fahrenheit.
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Given A-
2 2
1 3
what is A-¹?
The inverse of matrix A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex] is [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
The given matrix is A = [tex]\left[\begin{array}{cc}2&2&1&3\\\end{array}\right][/tex]
The inverse of a matrix is given by
[tex]A^{-1} = \frac{1}{|A|} adjA[/tex] ...(1)
Now, determinant of matrix A is
|A| = [tex]\left|\begin{array}{cc}2&2&1&3\\\end{array}\right|[/tex]
= (3)(2) - (2)(1)
= 6 - 2
= 4
Now, adjoint A will be
[tex]A_{11}[/tex] = 3
[tex]A_{12}[/tex] = -1
[tex]A_{21}[/tex] = -2
[tex]A_{22}[/tex] = 2
AdjA = [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
Now, substituting the values of |A| and AdjA in equation (1), we get
[tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
Therefore, [tex]A^{-1} = \frac{1}{4}[/tex] [tex]\left|\begin{array}{cc}3&-2&-1&2\\\end{array}\right|[/tex]
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Would the image be categorized as a function or as a relation? Use at least one sentence to explain your answer.
Answer:
This is a relation, not function.Step-by-step explanation:
The attached graph is NOT a function, since it doesn't pass the vertical line test.
If a vertical line cuts the graph more than once, then this relation is not a function.
how do you make y squared equal 169
Answer:
13
Step-by-step explanation:
A number squared is a number multiplied by itself.
13 x 13 = 169.
The answer is 13.
Hope this helps!
P.S, Brainliest please! Thanks!
Answer:
[tex]y^{2}[/tex] = 169
Meaning that
[tex]\sqrt{y^2}[/tex] = [tex]\sqrt{169}[/tex]
Simplify...
y = 13
A polygon is shown on the graph: A polygon is shown on a coordinate plane. The vertices are A at negative 6 comma 5, B at negative 6 comma 2, C at negative 2 co If the polygon is translated 4 units down and 5 units right, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates. (5 points)
The coordinates of the image of polygon A'B'C'D' after a translation of 4 units down and 5 units right would be A' (-1, 1), B' (-1, -2), C' (3, -2), D' (3, 2).
What is a translation?In Geometry, the translation of a geometric figure to the right simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image and translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
By translating the pre-image of polygon ABCD vertically down 4 units and horizontally right 5 units, the coordinates of the image of polygon A'B'C'D' include the following:
(x, y) → (x + 5, y - 4)
Coordinate A = (-6, 5) → Coordinate A' (-6 + 5, 5 - 4) = (-1, 1)
Coordinate B = (-6, 2) → Coordinate B' = (-6 + 5, 2 - 4) = (-1, -2)
Coordinate C = (-2, 2) → Coordinate C' = (-2 + 5, 2 - 4) = (3, -2)
Coordinate D = (-2, 6) → Coordinate D' = (-2 + 5, 6 - 4) = (3, 2)
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24. mrs. piatt, the math teacher, has six black, nine yellow and two blue calculators. what is the probability that she will hand out a blue calculator to the first student, then hand out a yellow calculator second?
The likelihood or probability that she will give the first student a blue calculator and the second student a yellow calculator is 6.6%.
The math teacher Mrs. Piatt has six black, nine yellow, and two blue calculators.
Therefore, the total number of calculators is 17.
The probability that she hands out a blue calculator to the first student is:
P₁ = Number of blue calculators/ Total number of calculator
P₁ = 2/17
Now, as a calculator is handed out to a student. Then the remaining number of calculators is 16.
Therefore, the probability that the second student gets a yellow calculator will:
P₂ = Number of yellow calculators/ Total number of calculators.
P₂ = 9/16
Therefore, the probability that she will hand out a blue calculator to the first student, then hand out a yellow calculator second will be:
P = P₁ × P₂
P = 2/17 × 9/16
P = 18/272
P = 0.06617647058
P = 6.6%
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Look at question 23 please help! I'm giving out the brainliest!!!!!!
The expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y are equivalent .
In the question ,
two expressions are given as
8x²+3(x²+y) and 7x²+7y+4x²-4y .
Simplifying the first expression
we get ,
= 8x²+3(x²+y)
= 8x² + 3x² + 3y
adding the like terms , we get
= 11x² + 3y
Simplifying the second expression
we get ,
= 7x²+7y+4x²-4y
adding and subtracting the like terms ,
we get
= 11x² + 3y
We can see that both the expressions are giving the final answer as 11x² + 3y .
hence , both the expressions are equivalent .
Therefore , the expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y are equivalent .
The given question is incomplete , the complete question is
Are the expressions 8x²+3(x²+y) and 7x²+7y+4x²-4y equivalent ? Explain your reasoning .
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What is the equation in slope-intercept form of a line that passes through the point (−2, −6) and has a slope of 12?
Answer:
y = 12x + 18
Step-by-step explanation:
Equation of line in slope-intercept form: y =mx +b
Here, m is the slope and b is the y-intercept.
m = 12
Substitute m =12 in the above equation,
y = 12x + b
This line passes through (-2,-6). So, plugin the point in the above equation.
-6 = 12*(-2) + b
-6 = -24 + b
-6 + 24 = b
b = 18
Equation of the line:
[tex]\sf \boxed{\bf y = 12x + 18}[/tex]
a binomial experiment with probability of success and trials is conducted. what is the probability that the experiment results in exactly successes? do not round your intermediate computations, and round your answer to three decimal places. (if necessary, consult a list of formulas.)
The probability that the experiment results in exactly successes is; [tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Consider that we have random variable X about binomial distribution with parameters n and p, then it can be written as;
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there be x successes is given as;
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are given as:
[tex]E(X) = np\\Var(X) = np(1-p)[/tex]
Hence, the probability that the experiment results in exact success are;
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
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Determine which answer in the solution set will make the equation true.
2p + 9 = 4p − 13
S: {−11, 0, 11, 22}
Answer:
11
Step-by-step explanation:
If you input the number and then solve, you should get that #=#
2(11)+9=4(11)-13
22+9=44-13
31=31
Answer: 11
Step-by-step explanation: 2(11)+9=4(11)-13, 22+9=44-13, 31=31
{x>2}∩{x|x≤4}
please solve
GOOD LUCK! ????????????????????????????????????????????????????????????????????????????????////
A street has the coordinates (-2, -5) and (5, 9). What is a parallel street to that one? (Write answer in slope-intercept form)
The parallel street to that one lines on the equation y = 2x -1
Slope of a LineTo find the parallel street to the one we have the points given, we have to first of all, find the slope of the given point and then pick a coordinate.
Point A = (-2, -5)Point B = (5, 9)Using the value above, let's find the slope of the line.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\[/tex]
Let's substitute the values into the equation and solve.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\\\m = \frac{9 - (-5)}{5 - (-2)} \\m = \frac{14}{7} \\m = 2[/tex]
The slope of the line is equal to 2.
Let's use this to find the equation of the line
[tex]y = mx + c[/tex]
Using one of the points,
[tex]y = mx + c\\9 = 2(5) + c\\9 = 10 + c\\c = - 1\\[/tex]
The equation of the line is
[tex]y = 2x - 1[/tex]
From the calculation above, the equation of the line is y = 2x - 1
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PLEASE HELP ASAP!! THANK YOU
The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.
First 585 - 50% = ?Then, add or subtract 50% from the first total and then, I believe, add (or it might be the other way around) to get your actual total. We would want it because it shouldn't affect the cost of the first machine. I'm sorry, but I haven't done any math in a long. use a calculator if necessary
The selling price determinedCalculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. To determine the ultimate price, use the selling price formula: Cost price + profit margin = selling price.
How is a 20% profit margin determined?Use the decimal representation of 20%, which is 0.2.To get 0.8, subtract 0.2 from 1.Your product's original cost should be divided by 0.8.You should charge this amount in order to make a 20% profit margin.To Learn more About long division, Refer:
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Jamie is 5 years older than her sister amy. If the sum of their ages is 19. how old is Jamie?
Considering the age of Amy and sum of their ages, Jamie is 12 years old.
Let the age of Amy be x years. Thus, the age of Jamie be (x + 5) years. Forming equation as per the age -
x + x + 5 = 19
Performing addition on Left Hand Side of the equation
2x + 5 = 19
Shifting 5 to Right Hand Side of the equation
2x = 19 - 5
Performing subtraction on Right Hand Side of the equation
2x = 14
Shifting 2 to Right Hand Side of the equation
x = 14 ÷ 2
Performing division to Right Hand Side of the equation
x = 7
The age of Amy = 7 years
The age of Jamie = 7 + 5
Performing addition
The age of Jamie = 12 years
Thus, the age of Jamie is 12 years old.
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This is easy but I just don’t have time please answer.
The nearest degree of the measure of the angle having trigonometric ratios are answered below.
What are trigonometric ratios?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others. Review the sine, cosine, tangent, cotangent, secant, and cosecant trigonometric ratios. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.
Given Data
Trigonometry Ratios:
1) cosine x = 0.8988
cos⁻¹ = 26.103°
2) sine x = 0.6691
sine⁻¹ x = 41.99°
3) tangent x = 2.50
tan⁻¹ x = 68.2°
4) tan x = 20
tan⁻¹ x = 87.14°
5) sin x = [tex]\frac{6}{11}[/tex]
sin⁻¹ x = 0.518
6) cos x =[tex]\frac{7}{9}[/tex]
cos⁻¹ = 0.7
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If f(x) = (x-4)(x+3), determine the x-intercepts of each function.
a) y=f(x)
b) y=-2f(x)
c) y=f(-1/2x)
d) y=f(-(x+1))
a) The x-intercepts of y=f(x) is (-3,0) (4,0)
b) The x-intercepts of y=-2f(x) is (-3,0) (4,0)
c) The x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)
d) The x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)
What is x-intercept?A line's x-intercept is the distance in x coordinates from the line's intersection with the x-axis at its origin. A location on the graph where y is 0 is known as the x-intercept. The x-intercept of a line that is perpendicular to the y-axis is undefined.
Here to determine the x-intercept put y=0,
Given f(x)=(x-4) (x+3)
a) y=(x-4) (x+3)
Replacing y by 0 we get,
(x-4) (x+3) =0
x=-3, 4
Therefore, x-intercepts of y=f(x) is (-3,0) (4,0)
b) y = -2(x-4) (x+3)
Replacing y by 0 we get,
-2(x-4) (x+3) =0
x=-3, 4
Therefore, x-intercepts of y=-2f(x) is (-3,0) (4,0)
c) y= (-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3)
Replacing y by 0 we get,
(-[tex]\frac{1}{2x}[/tex]-4) (-[tex]\frac{1}{2x}[/tex]+3) =0
By solving the above equation
(-[tex]\frac{1}{2x}[/tex]-4) =0 and (-[tex]\frac{1}{2x}[/tex]+3) =0
-1/2x=4 and -1/2x=-3
x=-1/8 and x=1/6
Therefore, x-intercepts of y=f(-1/2x) is (-1/8,0) (1/6,0)
d) y=(-(x+1)-4) (-(x+1) +3)
Replacing y by 0 we get,
(-(x+1)-4) (-(x+1) +3) =0
By solving the above equation
(-(x+1)-4) =0 and (-(x+1) +3) =0
-(x+1) =4 and -(x+1) =-3
x=-5, 2
Therefore, x-intercepts of y=f(-(x+1)) is (-5,0) (2,0)
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If f(x) = kx^3+ x^2 − kx + 2, find a number k such that the graph of f contains the point (2, 12).
Answer:
k = 1
Step-by-step explanation:
since the graph contains the point (2, 12 ) then the coordinates of the point make the equation true.
substitute x = 2 and f(x) = 12 into the equation and solve for k
12 = k(2)³ + 2² - k(2) + 2 , that is
12 = 8k + 4 - 2k + 2
12 = 6k + 6 ( subtract 6 from both sides )
6 = 6k ( divide both sides by 6 )
1 = k
Given f(x) = (x-7)(x + 4) and g(x) = x + 4, find (f/g)(x)
20/24 equals 45/50 true or false
bring the fractions to a common denominator
[tex]undefined[/tex]what is the different between 5,781 and 57.81
Answer: 5,723.19
Step-by-step explanation:
to find the answer you subtract 57.81 from 5781 to get 5,723.19
Is that what you were asking? I hope so.
Given mn, find the value of x.
Answer:
(2x+5)° (8x+5)°
Submit Answer
m
00
Step-by-step explanation:
2x+(-8x) +5-5
-5=0. u Wii collect like terms and if u do that that's the answer if am wrong let me know
PLEASE HELP!!! Ignore the small text at the bottom.
The equation that represents the miles of the car's odometer after 2020 is y = 14000x
Odometer:
Basically Odometer is the instrument used for measuring the distance traveled by a vehicle, such as a bicycle or car.
Given,
An odometer shows that a car has traveled 56,000 miles by January 1, 2020. The car travels 14,000 miles each year.
Here we need to write an equation that represents the number y of miles on the car's odometer x years after 2020
Through the given question we know that,
x represents the year
y represents the miles
We know that, for one year it will travels 14,000 miles.
Then the equation is written as,
miles = number of years x 14000
Therefore, the equation is,
y = 14000x
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The mean birth weights of infants born at an area hospital in the month of Aprill is 128 oz. with a standard deviation of 10.2 oz. Given an interpretation of
this situation.
The distance between each infant's weight when they were bonded in April is the proper interpretation of the standard deviation in this situation. And the average weight was 10.20 pounds.
What is standard deviation ?The variance's positive square root is the standard deviation. One of the foundational strategies in statistical analysis is standard deviation. The term "standard deviation," often shortened as "SD," tells us how far a value deviates from the mean value. It is represented by the symbol "."
Given that : The mean birth weights of infants born at an area hospital in the month of April is 128 oz. with a standard deviation of 10.2 oz.
So let's look at this and see what the correct interpretation of a standard deviation is, which is the distance between each person's actual way of being born and a braille and the main way it was, which is typically about 10 points two oh. From this, we can deduce what the question Act is. The distance between each infant's weight when they were bonded in April is the proper interpretation of the standard deviation in this situation. And the average weight was 10.20 pounds.
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find the measure of each angle only need numbers 22, 24, and 26
22) 68
24) 90
26) 158
Melinda has a goal of donating at least $300 to charity this year. Her mother and father each gave her $25 to help and she is selling ribbons for $5 each. What is the least number of ribbons Melinda must sell to reach her goal?
Answer:
50
Step-by-step explanation:
25x2=50
300-50=250
250/5=50
50 ribbons needed :) hope this helped