Probability that S assumes a value between 280 and 320 inclusive is 0.853.
S = Σ[tex]X_{i}[/tex] where [tex]X_{i}[/tex] has a uniform distribution on 1, 2, 3, 4, 5, with mean 3 and variance (25 – 1)/12 = 2 (result known, or calculated via E[[tex]X^{2}[/tex]] = 11, or from book of formulae, p10, with a = 1, b = 5, h = 1).
So S ~ N(300, 200) approximately.
P(280 ≤ S ≤ 320) = [tex]P(\frac{279.5-300}{\sqrt{200} } < Z < \frac{320.5-300}{\sqrt{200} })[/tex]
= [tex]P(-1.450 < Z < 1.450)[/tex]
= 0.853.
Hence, probability is 0.853.
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2. (01.03 LC)
Landyn is comparing cell phone plans. He does not want to spend more than 10% of his net pay each month. If his current monthly net pay is $560.00, which
plan below fits into his budget? (2 points)
Plan A: 55+55(0.05) -
Plan B: 50+ 50(0.05) -
Plan C: 60+60(0.05) =
Plan A
O Plan B
Plan C
O No plans
The plan that fits to Landyn's budget is plan B
What is percentage and how to calculate it?
A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%." Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. Two methods exist for calculating a percentage. By adjusting the fraction's denominator to 100 and applying the unitary approach.
We are given that Landyn's current monthly net pay is $560
And he does not wish to spend more than 10% of his current net pay
That means not more that $56
Now we are given 3 choices
Out of which the third one is more than 60 hence this rules out the third option. Now the first option the value is 55+55(0.005) which again is more than $56
Consider the option B)
50 + 50(0.05)
= 52.5
Which is less than $56
Hence, The plan that fits to Landyn's budget is plan B
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4. A Bag of marbles has 4 yellow, 5 red, and 1 purple. Create a situation that would satisfy the following:
a) Something that is IMPOSSIBLE to
happen.
b) Something that is EQUALLY
LIKELY to happen.
c) Something that is LIKELY to
happen.
According to the solving Probability the value are as follows.
a) P(Blue)= 0/10
b) P(Red)= 5/10
c) P(Red or Yellow)= 9/10
What is probability?The definition of probability is "How likely something is to happen."
Probability is indeed a number ranging from 0 to 1 that expresses the likelihood that an event will take place as specified.
First, 0 P(E) 1 (where P(E) specifies the probability of an event E) and second, the sum of the probabilities of any collection of mutually and exclusive exhaustive occurrences equals 1 are the two characteristics that define a probability.
According to the given data:We have a Bag of marbles has 4 yellow, 5 red, and 1 purple.
Total balls in a bag= 4+5+1=10 balls.
Something that is IMPOSSIBLE to happen.
P(Blue)= 0/10
Something that is EQUALLY LIKELY to happen.
P(Red)= 5/10
Something that is LIKELY to happen.
P(Red or Yellow)= 9/10
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MODELING REAL LIFE The diagram shows the prices of two
types of ground-cover plants. A gardener can afford to buy 125
vinca plants and 60 phlox plants.
$1.20/plant Vinca $2.50/plant Phlox
a. Write an equation in standard form that models the possible
combinations of x vinca plants and y phlox plants the gardener
can afford to buy.
An equation that models the possible combinations is:
___ = 300.
Please help!
a.
A gardener can afford to buy 125 vinca plants and 60 phlox plants. $1.20/plant Vinca $2.50/plant Phlox.
The equation in standard form that models the possible combinations of x vinca plants and y phlox plants the gardener can afford to buy is
⇒ $1.20*x + $2.50*y
b.
An equation that models the possible combinations is
⇒ $1.20*125 + $2.50*60 = 300
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What is the function rule for the line?
f (x) = 2x - 4
f(x)=-4x - 2
f(x) = 4x - 2
f (x)= -2x + 4
Answer: f (x)= -2x + 4
Solve for x. Enter the solutions from least to greatest. (x + 6)^2 - 16=0 lesser x = greater x =
Answer:
x= -2, -10
Step-by-step explanation:
(x+6)^2-16=0
(x+6)(x+6)-16=0
x^2+6x+6x+36-16=0
x^2+12x+20=0
10+2=12
10(2)=20
(x+2)=0
(x+10)=0
x= -2, -10
If the original function is f(x)
What would be the function notation when the function was
Shifted Right 6
The function notation when the function was shifted right 6 is f(x-6).
Given that, the function was shifted right 6 units.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Rule: In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.
So, the transformation from the original function to new function is
f(x-6)
Therefore, the function notation when the function was shifted right 6 is f(x-6).
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HELP, ASAP PLEASE. 15 POINTS! ( Only 1 picture is attached)
The concentration of the type of antibiotic after 4 hours is; 11.04 parts per million
How to find the input values of functions?
We are told that the equation that models the concentration in parts per million of a type of antibiotic in a human's bloodstream after h hours is;
A(h) = -0.06h² + 2h + 4
where h is the time in number of hours after which the concentration is recorded.
Now, we want to find the concentration after 4 hours and as such we will input 4 for h in the equation to get;
A(4) = -0.06(4²) + 2(4) + 4
A(4) = -0.96 + 12
A(4) = 11.04 parts per million
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Which of the following has a graph that is wider than the graph of y = 5x² - 3?
-
y = 8x² - 10
y = 5x² + 2
y=-6x² + 1
y = 3x² + 4
The equations y = -6x² + 1 and y = 3x² + 4 both have graphs that are wider than the graph of y = 5x² - 3.To determine which equation has a graph wider than the graph of y = 5x² - 3, we need to compare the coefficients of x² in each equation.
A wider graph indicates a smaller coefficient in front of x², which means the parabola will be less steep and have a broader shape.Let's compare the coefficients:y = 8x² - 10: The coefficient is 8, which is larger than 5. Therefore, this equation does not have a wider graph than y = 5x² - 3.
y = 5x² + 2: The coefficient is 5, which is equal to the coefficient in y = 5x² - 3. Therefore, the graphs of these two equations will have the same width.
y = -6x² + 1: The coefficient is -6, which is smaller than 5. Hence, this equation has a wider graph than y = 5x² - 3.
y = 3x² + 4: The coefficient is 3, which is smaller than 5. Hence, this equation also has a wider graph than y = 5x² - 3.
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A line of best fit was drawn for 5 data points. What is the maximum number
of these data points that may not actually be on the line?
A. 5
B. 3
C. 2
D. 4
Answer:
Step-by-step explanation:
Correct answer is A 5
Louie is studying ceramics, and he was asked to submit 5 vessels from his collection to exhibit at the fair. He has 15 vessels that he thinks are show worthy. In how many ways can the vessels be chosen?
Louie can choose the vessel for exhibition using combination in 3003 ways
How to determine the number of Louie can choose the ceramicinformation from the question include
Louie is studying ceramics and he is to submit 5 vessels
He has 15 vessels
The problem will be solved using combination
combination is method of choosing or making selection when order does not matter
Louie can choose any 5 of his vessel with no particular order
The formula is ₁₅C₅
₁₅C₅ = 15! / {5!(15 - 5)! )
= 15! / {5! * 10!}
= 3003 ways
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Alma ran a marathon. The graph shows the distance she ran during the marathon. Use the drop-down menus to complete the statements based on the graph.
From the proportional relationship graphed, it is found that:
The labeled point means that in 2 hours she ran 16 miles.In 1 hour, Alma ran 8 miles.Her distance changed at a unit rate of 8 miles per hour, so Alma's speed was of 8 miles per hour.If Alma ran faster, the slope of the graph would be greater.What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0, meaning that the relationship passes through the origin.
When the two variables x and y are direct proportional, the output variable y is obtained multiplying the input variable x by the constant of proportionality k, according to the rule presented follows:
y = kx.
From point (2,16) in this problem, the constant is given as follows:
k = 16/2 = 8.
Hence the equation is:
y = 8x.
Meaning that her rate is of:
8 miles per hour.
If she ran faster, the slope = constant would increase, as it represents the velocity.
Missing InformationThe problem is given by the image at the end of the answer.
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What must be added to 4/9 to make a whole?
Answer:5/9
Step-by-step explanation:
Suppose we want to determine how long it takes on average for a typical adult to build four different styles of tables,
which are referred to as A, B, C, and D. To create four treatment groups, the researcher begins by writing the name
of each member of the population on a slip of paper. Next, the researcher puts all slips of paper into a hat and
shuffles them well. Finally, the researcher draws slips of paper from the hat to determine the participants in the
experiment. Identify the component missing from the researcher's process.
The researcher did not assign individuals to treatment groups.
* The researcher did not create the correct number of treatment groups
The researcher did not select the experimental units randomly.
* The researcher did not allow each experimental unit the chance of being chosen
Intro
Final
According to the given statement the correct option is A.
The researcher did not assign individuals to treatment groups.
What Do Researchers Actually Do?Typically, researchers are employed by either university or commercial organizations. To support future research, enlarge the body of academic literature, and enhance decision-making, researchers collect data over the course of a project, evaluate the data, and publish the results.
What aspect of a researcher's job is most crucial?Researchers have an obligation to share their findings, collaborate with others when needed, and transmit and use information for the good of their employer, the economy, and society at large. In the process of their research, researchers have an obligation to conduct themselves honestly and ethically.
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Josephine invests £3,500 in a bank account which pays annual compound interest of 4.5%. How much money will she have in the bank after: (a) 2 years, (b) 3 years?
Josephine have £3882.9 amount after 2 years and £3994.9 amount after 3 years.
Using the formula of compound interest we can find the amount after t years compounded annually at the r per cent rate.
The formula of compound interest is as follows,
[tex]A=p(1+\frac{r}{100} )^t[/tex]
Where P is the principal value, A is the amount, r is the rate and t is the time.
Here we have a principal value of £3,500 and a rate is 4.5%.
Now, finding the amount after 2 years by putting the values in the formula of compound interest,
[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^2\\\\A=3500(1+0.045 )^2\\A=3500(1.045)^2\\A=3500\times1.092025\\A=3882.0875[/tex]
So, After 2 years Josephine will have £3882.9.
Now, finding the amount after 3 years,
[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^3\\\\A=3500(1+0.045 )^3\\A=3500(1.045)^3\\A=3500\times1.141166125\\A=3994.0814375[/tex]
So, After 3 years Josephine will have £3994.9.
Therefore, After 2 years Josephine will have £3882.9 and after 3 years Josephine will have £3994.9 when 4.5% interest is compounded annually.
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What integer is closest to 4 √5?
Answer:
it's decimal value then it is 11.1803399.
The integer close to it is 11
Step-by-step explanation:
let's square this :
4² × 5 = 16 × 5 = 80
the closest squared integer is 81 (9²).
so, the closest integer to 4×sqrt(5) is 9.
1. research institute reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.5 weeks and that the population standard deviation is 4 weeks. Suppose you would like to select a random sample of 50 unemployed individuals for a follow-up study.
a. What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean of less than 1 week?
b. What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean?
The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:
X = N(17.5)
Where μ = 17.5 and σ = 4
Since the distribution for X is normal then, the distribution for the sample mean is given by:
X = N(17.5, σ/√n)
X =N(17.5.4/√50) = 0.566
We select a sample of n =50 people. And we want to find the following probability
P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )
And using the normal standard table or excel we find the probability:
P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92
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Given that (x - 5) is a factor of
x³ - 7x² + 2x + a, find the value of a
check your textbook for the remainder theorem, where it states that for a factor (x-5) of f(x) then the remainder will be 0, thus f(5) = 0, what the heck all that means?
well, it means that if we evaluate f(5) our result should be 0, so
[tex]\stackrel{factor}{(x-5)}\hspace{5em}f(5)=(5)^3-7(5)^2+(5)+a=0 \\\\\\ 0=(5)^3-7(5)^2+(5)+a\implies 0=125-175+10+a \\\\\\ 0=-40+a\implies \boxed{40=a}[/tex]
If you throw exactly two heads in three tosses of a coin you win $41. If not, you pay me $29. If you played this game 713 times how much would you expect to win or lose?
Two heads in three tosses is 3/8, 3/8x713=267.375. 267.375×41=10,962.375.
5/8x713=445.62, 445.62×29=12,923.125
So 10,962.375-12,923.125=-1960.75
Therefore if you played this game, you would statistically lose $1960.75
18. MULTIPLE CHOICE
(Lesson 2-6)
(A) X=-4
B) X= 4
Ox=8
(D) X = 20
Solve
3
x + 4
=
2
X-4
Answer:
Step-by-step explanation:
solving 3x+4=2x-4
now 3x-2x=-4-4
⇒ x=-8
(c) x=8 here you have given it as O thank you
Like terms 8x-12-10x-8
8x + 16x - 12 = 24x- 12
Does the equation have one,
none, or infinite solutions?
Explain why.
Answer:
Infinite solutions
Step-by-step explanation:
The equation is,
→ 8x + 16x - 12 = 24x - 12
Let's solve for the value of x,
→ 8x + 16x - 12 = 24x - 12
→ 24x - 24x = -12 + 12
→ [ 0 = 0 ]
Hence, it has infinite solution. Because, all the real numbers are suitable.
Answer:
infinite number.
Step-by-step explanation:
Comment
There is only the same letter (x) on both sides of the equation. None of the xs are raised to any power. The power is 1 for all of them. That being so, there is only ONE solution.
x^2 + 5x + 6 would give 2 solutions because the x is raised to the second power.
x^3 + x^2 + 4x + 9 would give 3 solutions.
Solution
8x + 16x - 12 = 24x - 12 This equation is a little different. Both sides are exactly the same -- 24x - 12. That means that there is an infinite number of solutions.
For example let x = 10
The right side = 240 - 12 = 228
The left side = 8*10 + 16*10 - 12 = 228
You can't come up with a number that will make the left side unequal to the right side.
What value of k will translate the graph of f(x) = 5x + 6 down by 1 when replaced by f(x) + k?
Step-by-step explanation:
"down by one" means that the y values (the function result values) are all decreased by 1.
so, k = -1
268 + 88 in the form of a(b+c)
Answer:
4(67 + 22)
Step-by-step explanation:
1. Find the greatest common factor(in this case it is 4)
2. Divide both 268 and 88 by 4 and you get 67 and 22
3. Put it in the requested format and you are left with 4(67 +22)
Differentiate the function with respect to x.
Differentiation of f(x) is [tex]-8x^{3} sinx^{4}[/tex].
Given,
f(x) = [tex]cos2x^{4}[/tex]
Now, we will differentiate f(x) with respect to x,
[tex]\frac{d}{dx}cos2x^{4} = (\frac{d}{dx}cos2x^{4})(\frac{d}{dx}2x^{4} )[/tex]
[tex]= (-sin2x^{4})(2*4x^{3})[/tex]
[tex]= -8x^{3}sin2x^{4}[/tex]
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HELPPPPP pleaseeeeeeeeeeeeeeeeeeeee
Use the properties of logarithms to rewrite the following expression as a single logarithm. Please see attached pic.
Answer:
log4 (70)
Step-by-step explanation:
log4(7) + log4(10) = log4(7 * 10 ) = log4(70)
Solve 5x² + 1 = 51 by finding square roots.
x = 50, -50
x = √10,-√10
x = 10, −10
x = √50,-√√/50
Answer:
x = √10,-√10
explanation:
5x2 + 1 = 51
you would carry the +1 to the other side making it
5x2=51-1
which is 5x2=50
this equation above can then be turned into
x2=50÷5
which goes on to form the equation
x2=10
this can then be turned into x=the square root of ten
and since it is know that when an equation is x2 whether it is negative or positive it would result in the same answer
but yeah I'm not smart or whatever but I hope this helps
not too sure it's correct though
lynn bought a new crash cymbal for her drum set. it costs 120$ but she received a 15% student discount. Roger bought the same crash cymbal from another store for$130 but he used a coupon for $25 off. who got the better deal
lynn got the better deal than Roger.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
lynn bought a new crash cymbal for her drum set. it costs 120$ but she received a 15% student discount.
Convert 15% to decimal form
15%=15/100=0.15
0.15×120=18
So 15% of 120 is 18.
Iynn bought crash cymbal for her drum set is 120-18=102
Roger bought the same crash cymbal from another store for$130
Roger applied coupon of $25.
So 130-25=$105
When we compare both Iynn and Roger, Iynn got the crash cymbal for a better deal.
Hence lynn got the better deal than Roger.
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A square floor is fitted with rectangular tiles of perimeter 220 cm. Each row carries 20 less tiles than each column. If the length of the floor is 9.6 m; calculate
(a) the dimensions of the tiles.
(b) the number of tiles needed.
(c) the cost of fitting the tiles if the tiles are sold in dozens at Kshs. 1500 per dozen and the labour cost is Kshs. 3000.
The 220 cm (2.2 m) perimeter of the tiles and the 9.6 meter side length of the square floor gives equations with the following solutions;
(a) The dimensions of the tiles are;
Width = 0.3 meters
Length = 0.8 meters
(b) 384 tiles are needed
(c) The fitting cost of the tiles is Kshs 51,000
What is an equation?An equation is a mathematical statement that consists of two expressions connected with an equals sign
Shape of the floor = Square
Shape of the tiles = Rectangular
Perimeter of the tiles = 220 cm = 2.2 m
The number of tiles in each row = 20 + The number of tiles in each column
Length of the floor = 9.6 m
(a) Let w represent the width of the tiles, the length l is found using the equation;
[tex]l = \dfrac{2.2 - 2\cdot x}{2} = 1.1 - x[/tex]
Let n represent the number of tiles in each row, which gives;
The number of tiles in each column = 20 + n
(20+n)·x = n·(1.1 - x)
Which gives;
[tex]x = \dfrac{1.1\cdot n}{2\cdot n+20}[/tex]
The side length of the square floor, s = 9.6
(20+n)·x = n·(1.1 - x) = 9.6
Which gives;
[tex]n\cdot \left(1.1 - \dfrac{1.1\cdot n}{2\cdot n+20}\right) = 9.6[/tex]
Which gives;
0.55·n² - 1.4·n -96 = 0
n = 12 or n ≈ -14.5
The number tiles in each roe, n = 20
Which gives; n·(1.1 - x) = 9.6
20 × (1.1 - x) = 9.6
x = 0.3
The width of each tile, x = 0.3 m
The length of each tiles = 1.1 m - 0.3 m = 0.8 m
(b) The number of tiles in each row, n = 20
The number of tiles in each column = n + 20, which gives;
Number of tiles in each column = 12 + 20 = 32
The number of tiles needed = 12 × 32 = 384
(c) The cost of a dozen tiles = Kshs 1,500
The labour cost = Kshs 3,000
Number of dozens of tiles = 384 ÷ 12 = 32
The cost of the tiles C = Kshs 1500 × 32 = Kshs 48000
The total cost = Kshs 48,000 + Kshs 3,000 = Kshs 51,000
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A+(-7)=-17 I don’t know
Answer:
a = -10
So your answer is a = -10, I hope this helps!
Step-by-step explanation:
a + (-7) is the same as a - 7, so you could rewrite it as
a - 7 = -17
+ 7
