The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3
The quadratic function is
f(x) = [tex]-3x^2[/tex] + 18x + 3
The general form of the quadratic function is
y = [tex]ax^2[/tex] + bx + c
If a < 0, the quadratic function has maximum value
Here the value of a = -3
Therefore the function has maximum value.
Maximum value will be at x = -b / 2a
= -18 / 2(-3)
= -18 / -6
= 3
The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a
Substitute the value in the equation
(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3
= (-36 - 324 / -12
= -360 / -12
= 30
Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3
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A coin is weighted so that the probability of Heads is five times the probability of Tails. This coin is flipped
twice. What is the probability that both Heads and Tails are flipped?
A.5/36
B.8/25
C.5/24
D.None of the above
If a coin is weighted so that the probability of heads is five times the probabily of tails, that means :
+) P(head) + P(tail) = 1
+) P(head) = 5P(tail)
Therefore, P(head) = 5/6 ; P(tail) = 1/6
For both head and tail to be flipped, the events must happen together.
Therefore, we have the probabilty that both head and tail is flipped = 5/6 x 1/6 = 5/36.
This shows a triangle.
What is the value of x?
43
62
105
115
Answer:
105 degrees
Step-by-step explanation:
Find angle F:
the sum of angles of triangle =180
62+43+y=180
105+y=180
y=75
straight line = 180 degrees
75+x=180
x=105 degrees
Monica is 33 years old. Amanda is 18 years older than Brittany and 16 years older than Rita. Brittany is 23 years younger than Monica. How old is Rita?
please help
Which angles are congruent to <5
Answer:
1, 3, 7 (<5 is also congruent to <5, but this is not a choice.)
Step-by-step explanation:
The angles congruent to <5 are:
<1 by corresponding angles.
<3 by alternate interior angles.
<7 by vertical angles.
<5 by the theorem: congruence of angles is reflexive.
Hannah swims in a swimming pool of 25 metres long.
How many laps does she need to complete for a total distance of 0.5 kilometre?
She needs to complete 20 laps for a total distance of 0.5 kilometer.
1 kilometers = 1000 meters
0.5 kilometers = 500 meters
Length of swimming pool = 25 meters
That means, she covers 25 meters in 1 lap.
Laps to cover 500 meters = 500/25
= 20
Hence, she needs to do 20 laps.
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A salesman earns 9% commissions on all the merchandise that he sells.last month he sold $3000 worth of merchandise.how much commissions in dollars did he earn last month
The commission earned by selling the merchandise worth $3000 is $270
The percentage of the commission earned by the salesman is 9%
The worth of the merchandise is $3000
A sales commission is typically an amount paid to an employee upon completion of a task for the sale of a specified quantity of goods or services.
Therefore, the commission earned can be found using the formula,
Commission = SP x CP
where SP is the selling price and
CP is the commission percentage.
Let us substitute the known values in the above equation, we get
Commission = 3000 x 9%
= 3000 x 9/100
= 30 x 9
= $270
Therefore, the commission earned is $270
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Please help me (check the file attached)
According to the model, the value of -6(10b + 0.8) will be -60b - 4.8.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, this is illustrated as:.
= -6(10b + 0.8)
Open the parentheses
= -60b - 4.8
Therefore, the value is -60b - 4.8.
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(x+2)(x+3)(x+4) can be written in the form [tex]x^{3}[/tex] + a[tex]x^{2}[/tex] + bx c where a, b and c are positive integers.
Work out the values of a, b and c.
a = (Answer here) (1)
b = (Answer here) (1)
c = (Answer here) (1)
Answer:
a = 9 ; b = 26 ; c = 24
Step-by-step explanation:
(x^2+3x+2x+6)(x+4)
(x^2+5x+6)(x+4)
x^3+5x^2+6x+4x^2+20x+24
x^3+9x^2+26x+24
which of the following is a reason why a researcher might choose to conduct a double-blind placebo control group study? a. to control for regression to the mean b. to control for observer bias c. to eliminate testing effects d. to prevent attrition
A double-blind placebo control group study is used to control for observer bias and eliminate testing effects. So option c is correct.
A double-blind placebo control group study is one in which subjects are randomly assigned to either a control group, who receive a placebo, or an experimental group, who receive the treatment being studied. The researcher is not aware of which subjects are in which group, and neither are the subjects. This design is used to control for observer bias and eliminate testing effects.
This type of study is important because it allows researchers to test the efficacy of a new treatment without the risk of bias. By eliminating the possibility that the researcher or the subjects will know who is receiving the treatment and who is receiving the placebo, any expectations or preconceptions about the treatment can be avoided. This type of study is also important because it helps to control for the placebo effect, which is the phenomenon whereby subjects in the control group may experience some benefits from the placebo itself.
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Solve the inequality 4x-7<5
Answer:
x<3
Step-by-step explanation:
4x<5+7
4x < 12
4/4 x < 12/4
x < 3
Please help thank you
By comparing the fractions of rocks that skip over the poind for Jessica and Henry, we will see that Jessica gets more rocks to skip over the pond.
Who gets more rocks to skip over the pond?We know that for every 9 rocks that Herny throws, 5 skip over the pond. Then the fraction for Henry is:
H = 5/9
While for Jessica we know that for every 12 that she throws, 7 skip over the pond, so her fraction is:
J = 7/12
Now we only need to see which one of the fractions is larger.
If we simplify both we will get:
H = 5/9 = 0.556
J = 7/12 = 0.583
So we can see that Jessica's fraction is larger, which means that she will get more rocks.
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Complete the tasks to subtract the polynomials vertically. (1.3t3 0.4t2 â€"" 24t) â€"" (0.6t2 8 â€"" 18t) what is the additive inverse of the polynomial being subtracted? â€""0.6t2 (â€""8) (â€""18t) â€""0.6t2 (â€""8) 18t â€""0.6t2 8 â€"" 18t 0.6t2 (â€""8) 18t
The subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18) is given as follows:
1.3t³ - 0.2t² - 32t + 18.
How to subtract polynomials?Polynomials are subtracted subtracting the like terms, which are the terms that have the same symbolic variable and the same exponent.
For this problem, the subtraction is given by the expression presented as follows:
(1.3t³ + 0.4t² - 24t) - (0.6t² + 8t - 18).
The like terms of the expression are given as follows:
1.3t³ and 0t³ = 1.3t³.0.4t² - 0.6t² = (0.4 - 0.6)t² = -0.2t².-24t - 8t = (-24 - 8)t = -32t.0 - (-18) = 0 + 18 = 18.Hence the result of the subtraction of the polynomials is given as follows:
1.3t³ - 0.2t² - 32t + 18.
Missing InformationThe problem asks for the subtraction of the polynomials (1.3t³ + 0.4t² - 24t) and (0.6t² + 8t - 18).
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how many 4-letter passwords can be formed using the letters a, b, c, d, e, f, g if repetition of letters is not allowed and the first letter can only be a, b or c?
840 are 4-letter passwords can be formed using the letters by permutation .
What are some examples of permutation?
A permutation is a set up of things in a specific order. In this arrangement, the components or components of sets are organized in a linear or sequential order. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. The components of set A cannot be arranged in any other way, as you can see.We are to count all possible 4-letter passwords that can be generated from the letters a, b, c, d, e, f, g .
There are 7 letters in total.
n = 7 r = 4
P(n , r ) = 7!/( n - r )!
P( 7 ,4 ) = 7!/( 7 - 4)!
= 7!/3!
= 7 * 6 * 5 * 4 * 3 * 2 * 1/3!
= 7 * 6 * 5 * 4
= 840
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Line K is represented by the equation y = -3/2x + 1. Line L is perpendicular to line K and passes through the point (6,2). Determine the equation is line L.
Answer:
y = (2/3)y - 2
Step-by-step explanation:
Linear equations of the form y=mx+b, describe the slope, m, and the y-intercept, b (the value of y when x=0).
Line K
y = -(3/2)x + 1 tells us that it has a slope of -(3/2) and crosses the y axis (x=0) at y = 1.
Perpendicular Lines
Perpendicular lines have a useful property in that they have a slope that is the "negative inverse" of the line they are perpendicular to. If, for example, we were ever asked what is the slope of a line perpendicular to Line L (yes, it happens), we could, with minimal effort, respond "It is the negative inverse of -(3/2)," which is a slope of (2/3).
Line L
We just accidently answered a key question when we found the negative inverse of the slope for Line K, (2/3). That will be the slope of Line L that will make it perpendicular to Line K.
Line L will have the form y = (2/3)x + b
This line will be perpendicular to Line K, no matter the value of b. But we want a perpendicular line that goes through point (6,2), so we need to find a value of b that will force it to go through that point.
The role b has in our equation is simply moving it up or down. If b were 0, the line will go through the origin (0,0). If b were 5, it would interect the y axis at 5 (0,5). We could draw a graph and get a pretty good idea what b would have to be for the line to go throgh (6,2), but most prefer the easier route: Use the (x,y) value in the above equation and solve for b. Its easy, and works great:
y = (2/3)x + b for (6,2)
2 = (2/3)(6) + b
b = 2 - (2/3)*(6)
b = 2 - 4
b = -2
The equation for Line L is thus: y = (2/3)y - 2
See the attached graph. Included are equations [marked Demo Line 1 and 2] with 2 random values of b (1 and 0), in order to:
demonstrate how b impacts the line, andsuggest try using DESMOS as a free online graphing tool.
Sohan rolled a number cube 90 times. The outcome of ""6"" occurred 18 times. What is the experimental probability of rolling a 6?
The value of the experimental probability of rolling a 6 is found as 1/5.
Define the term experimental probability?A probability that has been established by a series of tests is called an experimental probability. To ascertain their possibility, a random experiment is conducted and iterated over a number of times; each iteration is referred to as a trial. The purpose of the experiment is to determine the likelihood that a particular occurrence will occur or not.For the given question-
Sohan made 90 turns of the number cube. There were 18 occurrences of the result of "6."Thus, by the definition of the probability-
Probability (getting 6) = number of occurred outcomes/ Total outcomes
Probability (getting 6) = 18/90
Probability (getting 6) = 1/5
Thus, the value of the experimental probability of rolling a 6 is found as 1/5.
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[tex]x-4/5-x+1/6=1/3[/tex]
The equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions.
What is an equation?
A equation in mathematics is a mathematical statement depicting that the values of two mathematical expressions are equal. Some examples representing equations are -
y = 5x + 4
2x + 3y = 5x + 8π
cos(ny) = sin(πx)
Given is the following equation -
x - 4/5 - x + 1/6 = 1/3
We have -
x - 4/5 - x + 1/6 = 1/3
x - x - 4/5 + 1/6 = 1/3
- 4/5 + 1/6 = 1/3
Now, [x] will cancel out for ever possible value of [x], therefore, it will have infinitely many solutions
Therefore, the equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions
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Factorise
(a) 4ab + 6abc + 8ac
(b) 9x2y + 6xy - 15xy²
(c) 10ab²-8ab + 2a²b
(d) 6xy - 7x²y + 3xy²
what is 1/1/2 x 2/23
Answer:
1/23
Step-by-step explanation:
Given in a plane the points A(-1,4),B(2,3),C(4,5),D(m,7)
Calculate m knowing that AB // CD
helppppp step by step
Answer:
m = -2
Step-by-step explanation:
slope of AB
(4-3)/(-1-2)= 1/-3 = -1/3
parallel lines have the same slope
slope of CD = -1/3
we can now find the line that passes through the point C
y-5= -1/3(x-4)
y = -1/3 x +4/3 +5
y = -1/3 x + (4+15)/3
y = -1/3 x + 19/3
this line must passes also through the point D
we know its y, so:
7 = -1/3 x + 19/3
(7 * 3) = (-1/3 x + 19/3) * 3
21 = - x + 19
x = 19 - 21
x = -2
you want to know the opinions of american school teachers about establishing a national test for high school graduation. you obtain a list of the members of the national education association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. by the deadline, 1347 teachers return the questionnaire. the population is
The list of the members of the national education association is the Population.
Given, that a list of the members of the national education association is obtained and the questionnaire is mailed to 2500 teachers chosen at random from the list.
1347 teachers from those 2500 teachers return the questionnaire.
So, as we know that
A population is the group that you want to draw conclusions about.
Here, we want to know the opinions of American school teachers about establishing a national test.
So, The list of the members of the national education association is the Population.
Also, 1347 responses which we got is the sample.
Hence, The list of the members of the national education association is the Population.
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3X + 4X - 2 = 12
Please help again I’m not very smart lol
[tex]{ \pink{ \boxed{ \blue{ \sf{x = 2}}}}}[/tex]
Step-by-step explanation:
[tex]{ \red{ \sf{3x + 4x - 2 = 12}}}[/tex]
[tex]{ \red{ \sf{7x = 12 + 2}}}[/tex]
[tex]{ \red{ \sf{7x = 14}}}[/tex]
[tex]{ \red{ \sf{x = \frac{14}{7}}}} [/tex]
[tex]{ \blue{ \boxed{ \green{ \sf{x = 2}}}}}[/tex]
The sequence below shows a certain company's expected net worth in millions of dollars after 1, 2, 3, 4 years, etc....
8.3, 10.4, 12.5, 14.6,...
Which function models the nth term of this sequence?
Responses
f(n) = 8.3 + 2.1nf(n) = 8.3 + 2.1n
f(n) = 8.3 − 2.1nf(n) = 8.3 − 2.1n
f(n) = 8.3 + 2.1(n+1)f(n) = 8.3 + 2.1(n+1)
f(n) = 8.3 + 2.1(n−1)
f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.
What is Sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given,
The sequence below shows a certain company's expected net worth in millions of dollars after 1, 2, 3, 4 years, etc....
8.3, 10.4, 12.5, 14.6,...
The given sequence is a arithmetic sequence.
The first term is 8.3
The common difference is 2.1
The nth term of arithmetic sequence aₙ=a+(n-1)d
the nth term of this sequence=8.3+(n-1)2.1
f(n)=8.3+(n-1)2.1
Hence, f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.
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create a table and graph using -2x + 1/2
Answer:
Open Canva — Launch the table and chart maker tool by going to Canva and searching for “table” or “table chart.” Choose a template — Explore our collection of pre-built, fully customizable templates. Narrow your search by style, theme, and color to find a layout that best fits your needs. Click your chosen template to start designing.
Linda had 45 fliers to post around town. Last week, she posted 1/3 of them. This week, she posted 3/5 of the remaining fliers. How many fliers has she still not posted?
Answer:
Step-by-step explanation:
The number of fliers that he has not posted is 9
What is proportion?
Proportion can be defined as the mathematical comparison of two elements or numbers.
From the information given, we have that;
• Total number of fliers is 45
• First week, 1/3 of the floors were posted
• This week, 3/5 of the remaining were posted.
To determine the number of fliers remaining, we have that;
Remaining fliers for the First week
= 45 × 1/3
Multiply and find the quotient
= 15 fliers
Fliers remaining after the last week
= 15 × 3/5
Multiply and find the quotient
= 45/5
= 9 fliers
Thus, the number of fliers the he has not posted is 9
PLSSSS HELPPPPP MEEE !!!!!
All the angles in a triangle add up to 180 degrees.
40 + x + (5x + 14) = 180
54 + 6x = 180
6x = 126
x = 21 degrees
Answer:
x=21
Step-by-step explanation:
a triangle adds up to 180 degree so to find x we will use the formula
(5x+14)+x+40=180
subtract 40 from each side so we have
(5x+14)+x=140
we have 2 terms with the same factor (x) so combine like terms
6x+14=140
subtract 14 from both sides
6x=126
divide both sides by 6
x=21
check your answer
5(21)+14
105+14=119
119+ 21+40=180
so x is equal to 21
Given g(x)=-3x-3 solve for x when g(x)=0
what is the probability that you will receive at most 30 winning tickets? (round to four decimal places.) 0.5484 what is the probability that you will receive more than 30 winning tickets? (round to four decimal places.) 1 what is the probability that you will receive fewer than 10 winning tickets? (round to four decimal places.) 0.2206 what is the probability that you will receive at least 10 winning tickets? (round to four decimal places.
Normal distributions are frequently employed in the natural and social sciences to describe real-valued regressors with uncertain distributions, normal distributions are essential to statistics.
The central limit theorem is one reason they are significant.
This claim argues that, in some circumstances, the average of many samples (observations) of a random variable with finite variance and mean is itself a random variable, whose distribution tends to become normal with an increase in sample size.
Because of this, distributions of physical quantities that are meant to be the culmination of multiple separate processes, such as error margins, frequently resemble normal distributions.
Only the normal distribution has additional cumulants after the first two that are zero. It is also the continuous distribution with the highest level of entropy for a given mean and variance.
Assuming that the mean and variance are finite, Geary has shown that the normal distribution is the only distribution in which the mean and variance calculated from a collection of independent drawings are independent of one another.
The normal distribution is a form of elliptical distribution. The normal distribution is symmetric about its mean and non-zero over the whole real line.
Consequently, it could not be an appropriate model for variables that are inherently positive or highly skewed, such as a person's weight or the value of a share.
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Which expression is equal to 6(r2 – 3) + 2(r2 + 1)?
8r squared - 20
6r squared -2
8r squared -16
6r squared +2r-16
pls, help 20 points!
Answer:8r squared -16
Step-by-step explanation:
Does the relation shown in the diagram below represent a function? Explain why or why not
The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.
Given that,
In the picture we can see the domain and range.
We have to find if the domain and range is function or not.
Each of the sets of domain values has precisely one range value, according to the mapping.
Every domain value in a relation must have precisely one range value in order for it to be referred to as a function. It is not recommended to assign or map a domain value to more than one range value.
Therefore, The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.
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a 3x3x3 cube is made of 27 small cubes of which one is blue and 26 are white. the surface of the cube is formed by 3x3 squares. the small cubes are arranged in such a way that the surface is as much white as possible. what fraction of the surface of the cube is white
The fraction of the surface of the cube which is white is 14/27
Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3
To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.
• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26
Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.
• Total number of cube surfaces exposed in blue = 9 * 6 = 54
• Therefore, the greatest fraction in blue= 26/54 = 13/27
Therefore the fraction of the surface of the cube is white is = 1-[tex]\frac{13}{27}[/tex]= 14/27
The fraction of the surface of the cube which is white is 14/27 is the answer
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The fraction of the surface area of the cube which is white is 14/27
Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3
To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.
• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26
Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.
• Total number of cube surfaces exposed in blue = 9 * 6 = 54
• Therefore, the greatest fraction in blue= 26/54 = 13/27
Therefore the fraction of the surface of the cube is white is = 1-(13/27)
= 14/27
The fraction of the surface of the cube which is white is 14/27 is the answer.
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