Answer:
A. {(-8,-14), (-7,-12), (-6,-10), (-5,-8)}
Step-by-step explanation:
A function has no repeated values of the independent variable. Only choice A meets that requirement.
___
B: (-9, 12) and (-9, 8) both have -9 as a first value; not a function.
C: (8, -2) and (8, -10) both have 8 as a first value; not a function.
D: (-2, 0) and (-2, 3) both have -2 as a first value; not a function.
Answer:
A.
{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}
Step-by-step explanation:
In mathematics, a function [tex]f[/tex] is a relationship between a given set [tex]x[/tex] (domain) and another set of elements [tex]y=f(x)[/tex] (range) so that each element x in the domain corresponds to a single element [tex]f(x)[/tex] of the range. This can be expressed as:
[tex]f:x \rightarrow y\\\\a \rightarrow f(a)\\\\Where\hspace{3}a\hspace{3}is\hspace{3}an\hspace{3}arbitrary\hspace{3}constant[/tex]
So according to that, the only set that satisfies the definition of a function is:
A.
{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}
This is because:
In B.
-9 is the first element in more than one ordered pair in this set.
In C.
8 is the first element in more than one ordered pair in this set.
In D.
-2 is the first element in more than one ordered pair in this set.
Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?
Answer:
If the mean of the sample standard deviations is equal to the population standard deviation, then the sample standard deviations target the population standard deviation and are called an unbiased estimator.
If the mean of the sample standard deviations is not equal to the population standard deviation, then the sample standard deviations target the population standard deviation and are called a biased estimator.
A biased estimator regularly underestimates or overestimates the parameter.
An unbiased sample statistics are good estimators A biased sample statistics are not good estimators.Final answer:
Sample standard deviations do not target the population standard deviation but serve as estimators. The accuracy of the estimation depends on the sample size.
Explanation:
The sample standard deviations do not target the exact value of the population standard deviation. Instead, they serve as estimators of the population standard deviation. In general, sample standard deviations can be good estimators of population standard deviations, but the accuracy of the estimation depends on the sample size. When the sample size is large, the sample standard deviation tends to be close to the population standard deviation. However, when the sample size is small, the sample standard deviation may not accurately estimate the population standard deviation.
The length of a rectangle is five times its width.
If the area of the rectangle is 405 in^2, find its perimeter.
Answer:
The answer to your question is: Perimeter = 108 in
Step-by-step explanation:
Data
Length (l) = 5 width (w)
A = 405 in²
Perimeter = ?
Formula
Area = l x w
Perimeter = 2w + 2l
Process
405 = 5w x w
405 = 5w²
405/5 = w²
w = √81
w = 9 in
l = 5(9) = 45 in
Perimeter = 2(9) + 2(45)
= 18 + 90
= 108 in
Which of the following is the solution to 9 | x + 4 | >= 54?
PLEASE HELP
Answer:
your selection is correct
Step-by-step explanation:
You can divide by 9 to get ...
| x+4 | ≥ 6
This resolves to two inequalities:
-6 ≥ x +4 ⇒ -10 ≥ xx +4 ≥ 6 ⇒ x ≥ 2These are disjoint intervals, so the solution set is the union of them:
x ≤ -10 or 2 ≤ x
Answer:
Step-by-step explanation: A is correct
2(x + 1 ) - 3(x + 5) ≥ 0
answer is x is less than or equal to -13
hope this helps:-)
Answer:
x ≤ -13.
Step-by-step explanation:
2(x + 1 ) - 3(x + 5) ≥ 0 Distribute the 2 and -3 over the parentheses:
2x + 2 - 3x - 15 ≥ 0
-x ≥ 15 - 2
-x ≥ 13
x ≤ -13 Note: when dividing by a negative the inequality sign is flipped .
Use the formula to estimate the temperature when n = 52 chirps/min. Round to the nearest whole number, if necessary. The formula F equals n divided by 4 plus 37 estimates the temperature F in degrees Fahrenheit when crickets chirp n times per minute. A. 58°F B. 52°F C. 53°F D. 50°F
Answer:
The answer to your question is: d) 50°F
Step-by-step explanation:
Data
n = 52 chirps/min
Formula
F = n/4 + 37
Substitution
F = 52/4 + 37
F = 13 + 37 simplifying
F = 50 °F result
The tallest living man at one time had a height of 230 cm. The shortest living man at that time had a height of 91.3 cm. Heights of men at that time had a mean of 170.53 cm and a standard deviation of 5.91 cm. Which of these two men had the height that was more extreme?
Answer: The shortest living man at that time had the height that was more extreme.
Step-by-step explanation:
We will z scores to solve this exercise. The formula we need is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where [tex]x[/tex] is the raw score, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
We know at that time heights of men had a mean of 170.53 centimeters and a standard deviation of 5.91 centimeters, then:
[tex]\u=170.53\\\\\sigma=5.91[/tex]
Knowing that the tallest living man at that time had a height of 230 centimeters, we get:
[tex]z=\frac{230-170.53}{5.91}\approx10.07[/tex]
And knowing that the shortest living man at that time had a height of 91.3 centimeters, we get:
[tex]z=\frac{91.3-170.53}{5.91}\approx-13.40[/tex]
Based on this, we can conclude that the shortest living man at that time had the height that was more extreme.
Suppose f left parenthesis x right parenthesis right arrow 150f(x)→150 and g left parenthesis x right parenthesis right arrow 0g(x)→0 with g(x)less than<0 as x right arrow 3x→3. Determine modifyingbelow lim with x right arrow 3 startfraction f left parenthesis x right parenthesis over g left parenthesis x right parenthesis endfractionlimx→3 f(x) g(x).
Final answer:
The limit of f(x)/g(x) as x approaches 3 is negative infinity, since f(x) approaches 150 and g(x) approaches 0 with g(x) < 0.
Explanation:
We are given that as x approaches 3, f(x) approaches 150, and g(x) approaches 0 while being less than zero. The question is to determine the limit of f(x)/g(x) as x approaches 3.
To find this limit, we should consider the behavior of both f(x) and g(x) as x approaches 3.
Since f(x) approaches a finite number and g(x) approaches 0, the limit of the quotient could potentially be infinity or negative infinity, depending on the sign of g(x).
Since g(x) is less than 0 as x approaches 3, the quotient f(x)/g(x) will approach negative infinity.
Hence, the limit limx→3 f(x)/g(x) = -∞.
The value of a collector's item is expected to increase exponentially each year. The item is purchased for $500 and its value increases at a rate of 5% per year. Find the value of the item after 4 years. $578.81 $607.75 $1687.50 $2531.25
Answer:
$607.75
Step-by-step explanation:
As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.
The appropriate answer choice is $607.75.
_____
The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...
$500 × 1.21550625 = $607.753125 ≈ $607.75
Answer:
Answer: $607.75
Step-by-step explanation:
Answer:
$607.75
Step-by-step explanation:
As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.
The appropriate answer choice is $607.75.
_____
The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...
$500 × 1.21550625 = $607.753125 ≈ $607.75
Susan needs to buy apples and oranges to make fruit salad. She needs 15 fruits in all. Apples cost $3 per piece, and oranges cost $2 per piece. Let m represent the number of apples. Identify an expression that represents the amount Susan spent on the fruits. Then identify the amount she spent if she bought 6 apples.
Answer:
Step-by-step explanation:
$3x6=18 the six represents the apples and the 3 is the cost of each apple, 18 is the cost.
$2x9=$18 the nine is the oranges and the two is the money spent on each one. The total would be $36 in total for all the fruit.
So (9x2)+(3x6)=$36
Answer with Step-by-step explanation:
Susan needs to buy apples and oranges to make fruit salad.
She needs 15 fruits in all.
Let m represent the number of apples.
Number of oranges= 15-m
Apples cost $3 per piece, and oranges cost $2 per piece.
Amount spent= $ (3m+2(15-m))
= $ (3m + 2×15 - 2m)
= $ (m+30)
If she bought 6 apples.
i.e. m=6
Amount spent =$ (6+30)
= $ 36
Hence,
Expression that represents the amount Susan spent on the fruits is:
m+30
The amount Susan spent if she bought 6 apples is:
$ 36
When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 54s to walk from your gate to the baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 83s to travel the same distance. How long will it take you to travel from the gate to baggage claim if you walk while riding of the moving sidewalk?
Answer:
Your travel time will be 32.71 secs.
Step-by-step explanation:
Let the total distance be x feet.
Speed while walking = [tex]\frac{x}{54}[/tex] feet per second
Speed on the sidewalk = [tex]\frac{x}{83}[/tex] feet per second
Therefore, total speed while walking on moving sidewalk =
[tex]\frac{x}{54} +\frac{x}{83y}[/tex]
= [tex]\frac{83x+54x}{54\times83}[/tex]
= [tex]\frac{137x}{4482}[/tex]
= [tex]\frac{x}{32.71}[/tex]
Hence, your travel time will be 32.71 secs.
In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was $2.25. Give your answer as a percentage value. Find the percent increase of the bus fare in Chicago.
Answer:
The bus fair is 50% increases.
Step-by-step explanation:
The percentage is the proportion of the relation to the whole.
Percentage increase is calculate as ratio of difference of original and new value to the original value. i.e.
[tex]\frac{ Percentage\ increase\ \ =\ \ new\ value - original \ value}{original\ \ value}[/tex]
∴ [tex]\frac{ Percentage\ increase\ \ =\ \ 2.25 - 1.50 }{1.50}[/tex]
⇒ Percentage increase = 50%
By using percentage, the result obtained is-
Percentage increase in bus fare in Chicago = 50%
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100.
Here,
Bus fare in the year 1995 in Chicago= $1.50
Bus fare in the year 2008 in Chicago = $2.25
Increase in bus fare = $(2.25 - 1.50) = $0.75
Percentage increase in bus fare in Chicago = [tex]\frac{0.75}{1.50}\times 100[/tex]
= 50%
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3. Suppose that you initially have $100 to spend on books or movie tickets. The books start off costing $25 each and the movie tickets start off costing $10 each. For each of the following situations, would the attainable set of combinations that you can afford increase or decrease?
a. Your budget increases from $100 to $150 while the prices stay the same.
b. Your budget remains $100, the price of books remains $25, but the price of movie tickets rises to $20.
c. Your budget remains $100, the price of movie tickets remains $10, but the price of a book falls to $15.
Answer:
Suppose that you initially have $100 to spend on books or movie tickets.
The books start off costing $25 each and the movie tickets start off costing $10 each.
a. Your budget increases from $100 to $150 while the prices stay the same.
Increase
b. Your budget remains $100, the price of books remains $25, but the price of movie tickets rises to $20.
Decrease
c. Your budget remains $100, the price of movie tickets remains $10, but the price of a book falls to $15.
Increase
Please please help me out! :)
Answer:
x = 24
Step-by-step explanation:
Given that y varies directly with x the the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 10 when x = 8, then
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{8}[/tex] = 1.25, thus
y = 1.25x ← equation of variation
When y = 30, then
30 = 1.25x ( divide both sides by 1.25 )
x = 24
A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10. How many individuals participated in each study?
Answer: 11
Step-by-step explanation:
We know that the degree of freedom for a t-distribution is given by :-
[tex]df=n-1[/tex], where n is the sample size.
Given : A repeated-measures experiment and a matched-subjects experiment each produce a t statistic with df = 10.
Then, the number of individuals participated in each study = [tex]df+1=10+1=11[/tex]
Hence, the number of individuals participated in each study =11.
Find the average rate of change.
p(x) = 6x + 7 on [2, 2 + h] , h ≠ 0
The average rate of change of a function is found with the formula (f(b) - f(a)) / (b - a). When applying this formula to the function p(x) = 6x + 7 over the interval [2, 2 + h], we find that the average rate of change is 6.
Explanation:In Mathematics, the average rate of change of a function on the interval [a, b] is given by the formula (f(b) - f(a)) / (b - a). In this case, our function is p(x) = 6x + 7, and the interval is [2, 2 + h]. So, we can plug these values into the formula to get an expression for the average rate of change.
First, calculate p(2 + h) and p(2). Here they are:
p(2 + h) = 6 × (2 + h) + 7 = 12 + 6h + 7 = 19 + 6hp(2) = 6 × 2 + 7 = 12 + 7 = 19Substitute these expressions into the average rate of change formula:
(P(2 + h) - P(2)) / (2 + h - 2) = (19 + 6h - 19) / (h) = 6h / h = 6.
So, the average rate of change of the function p(x) = 6x + 7 on the interval [2, 2 + h] is 6.
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You are going to make three shelves for your father and have one piece of lumber 14 feet long. Your plan is to make the top shelf a foot shorter than then middle shelf and to have the bottom shelf a foot shorter then twice the length of the top shelf. How long is each shelf?
Answer:
The lengths of the shelves are 3.5 feet , 4.5 feet , 6 feet
Step-by-step explanation:
* Lets explain how to solve the problem
- There are 3 shelves
- You have one piece of lumber 14 feet long
- Your plane is:
# The top shelf is 1 foot shorter than the middle shelf
# The Bottom shelf a foot shorter than twice the length of the top shelf
* Assume that the length of the middle shelf is x feet
∵ The length of the middle shelf = x
∵ The top shelf is shorter by 1 foot
∴ The length of the top shelf = x - 1
∵ The length of the bottom shelf is 1 less than twice the length of
the top shelf
- That means multiply the length of the top shelf by 2 and subtract
1 from the product
∵ The length of the top shelf is x - 1
∴ The length of the bottom shelf = 2(x - 1) - 1
- Simplify it by multiplying the bracket by 2 and add like terms
∴ The length of the bottom shelf = 2x - 2 - 1
∴ The length of the bottom shelf = 2x - 3
* The sum of the lengths of the 3 shelves equal the length of lumber
∵ The length of the lumber is 14 feet
∵ The length of the 3 shelves are x - 1 , x , 2x - 3
∴ x - 1 + x + 2x - 3 = 14
- Add like terms in the left hand sides
∴ 4x - 4 = 14
- Add 4 for both sides
∴ 4x = 18
- Divide both by 4
∴ x = 4.5
- Lets find the length of each shelf
∵ The length of the top shelf is x - 1
∴ The length of the top shelf = 4.5 - 1 = 3.5 feet
∵ The length of the middle shelf is x
∴ The length of the middle shelf = 4.5 feet
∵ The length of the bottom shelf is 2x - 3
∴ The length of the bottom shelf = 2(4.5) - 3 = 9 - 3 = 6 feet
* The lengths of the shelves are 3.5 feet , 4.5 feet , 6 feet
Final answer:
To find the length of each shelf, a system of equations is created based on the conditions given. Solving this system shows the middle shelf to be 4.5 feet, the top shelf to be 3.5 feet, and the bottom shelf to be 6 feet long.
Explanation:
The question involves using a piece of lumber that is 14 feet long to make three shelves with specific relative lengths. We can let the length of the middle shelf be x feet. Therefore, the top shelf will be x - 1 feet long, and the bottom shelf will be 2(x - 1) - 1 feet long, which simplifies to 2x - 3 feet. Adding together the lengths of the three shelves gives us the total length of the lumber:
x (middle shelf)x - 1 (top shelf)2x - 3 (bottom shelf)So: x + (x - 1) + (2x - 3) = 14.
Solving the equation:
x + x - 1 + 2x - 3 = 144x - 4 = 144x = 18x = 4.5Therefore, the middle shelf is 4.5 feet long, the top shelf is 3.5 feet (4.5 - 1), and the bottom shelf is 6 feet (2(3.5) - 1).
A solid lies between planes perpendicular to the x-axis at x=0 and x=3. The cross-sections perpendicular to the axis on the interval 0≤x≤3 are squares whose diagonals run from the parabola y=−x‾‾√ to the parabola y=x‾‾√.Find the volume of the solid.
Answer:
V = 9
Step-by-step explanation:
You can see it in the picture.
The side length of the square is found using the diagonal, which is the distance between the two parabolas. The area of each square cross section is then integrated from 0 to 3 to find the solid's volume, which is 9 cubic units.
Explanation:For these types of volume problems, you'll need to integrate. However, first you have to find the area of the square formed by the diagonals. The distance between the parabolas y=-√x and y=√x forms the square's diagonal. This distance, or length of the diagonal, can be obtained by adding the y-values of the two parabolas which gives 2√x. Given the diagonal, the side length of the square (s) can be obtained from the diagonal using Pythagoras theorem: s=diagonal/√2 => s=2√x/√2 => s=√2* √x => s=√2x. The area of the square is the side length squared, A=s² => A= 2x. Now, integrate the area function from 0 to 3 to get the volume of the solid: Volume= ∫ from 0 to 3 [2x dx] = [x²] from 0 to 3 = 9 - 0 = 9 cubic units.
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You are adding air to a tire the air pressure in the tire should be 32 27/200 pounds per square inch. What decimal should you watch for not the digital pressure gauge
Answer:
24
Step-by-step explanation:
The air pressure in tire should be 32.135 pounds per square inch. Hence, Rounding of to nearest tenths, we get 32.1 pounds per square inch.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
The air pressure in the tire should be pounds per square inch. This pressure is in the form of a mixed fraction. It is required to convert this pressure into a decimal form. We can convert it as follows;
The air pressure in tire =32 27/200
It is given in the form of a mixed fraction.
32 27/200 = ( 32 x 200) 27/200
First we, convert this mixed fraction into unlike fraction and then convert it into a decimal number;
32 27/200 = ( 32 x 200) 27/200
= 6427 /200
= 32.135
Therefore, the air pressure in tire should be 32.135 pounds per square inch.
Hence, Rounding of to nearest tenths, we get 32.1 pounds per square inch.
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Evaluate the radical
Answer:
5 1/2
Step-by-step explanation:
Your calculator can give you the correct answer.
___
[tex]\sqrt[3]{343}+\dfrac{3}{4}\sqrt[3]{-8}=7+\dfrac{3}{4}(-2)=7-\dfrac{3}{2}=5\frac{1}{2}[/tex]
Suppose in a society where there are equal numbers of men and women. There is a 50% chance for each child that a couple gives birth to is a girl and the genders of their children are mutually independent. Suppose in this strange and primitive society every couple prefers a girl and they will continue to have more children until they get a girl and once they have a girl they will stop having more children, what will eventually happen to the gender ratio of population in this society?
Answer:
eventually the gender ratio of population in this society will be 50% male and 50% female.
Step-by-step explanation:
For practical purposes we will think that every couple is healthy enough to give birth as much children needed until giving birth a girl.
As the problem states, "each couple continue to have more children until they get a girl and once they have a girl they will stop having more children". Then, every couple will have one and only one girl.
This girl would be the n-th child with a probability [tex](0.5)^n[/tex].We will denote for P(Bₙ) the probability of a couple to have exactly n boys.
Observe that statement 1 implies that:
[tex]P(B_{n-1})=(0.5)^{n}[/tex].
Then, the average number of boys per couple is given by
[tex]\sum^{\infty}_{n=1}(n-1)P(B_{n-1})=\sum^{\infty}_{n=1}(n-1)(\frac{1}{2} )^n=\sum^{\infty}_{n=2}n(\frac{1}{2} )^n=\\\\=\sum^{\infty}_{m=2}\sum^{\infty}_{n=m}(\frac{1}{2} )^n=\sum^{\infty}_{m=2}(\frac{1}{2} )^{m-1}=\sum^{\infty}_{m=1}(\frac{1}{2} )^{m}=1.\\[/tex]
This means that in average every couple has a boy and a girl. Then eventually the gender ratio of population in this society will be 50% male and 50% female.
When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel:
F=kR4(This is known as Poiseuille’s Law;) A partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter is inflated inside the artery in order to widen it and restore the normal blood flow. Show that the relative change in F is about four times the relative change in R. How will a 5% increase in the radius affect the flow of blood?
Answer:
[tex]\frac{dF}{F}=4\frac{dR}{R}[/tex]
So a 5% relative increase in R would mean a 20% relative increase in F
Step-by-step explanation:
First we need to remind the definition of relative increase of a variable.
For a variable A its relative increase is given by [tex]\frac{dA}{A}[/tex].
Using this, the relative increase in F is [tex]\frac{dF}{F}[/tex] and similarly the relative increase in R is given by [tex]\frac{dR}{R}[/tex].
Let's then start by deriving F with respect to R:
[tex]\frac{dF}{dR}=4kR^3[/tex]
thus
[tex]dF=4kR^3dR[/tex]
[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{F}[/tex]
[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{kR^4}[/tex]
[tex]\implies \frac{dF}{F}=4\frac{dR}{R}[/tex].
If we plug the value 5% [tex]\left( \frac{5}{100}\right)[/tex] in [tex]\frac{dR}{R}[/tex] we get
[tex]\frac{dF}{F}=4\times5\%=20\%[/tex]
According to Poiseuille's Law, the flux of blood through a blood vessel is proportional to the fourth power of the vessel's radius. By differentiating both sides of the equation, it can be shown that a small relative change in radius corresponds to four times that change in flux. Therefore, a 5% increase in radius results in a 20% increase in blood flow.
Explanation:Poiseuille’s Law states that the flux (F), which is the volume of blood flowing per unit time through a given point in a blood vessel, is proportional to the fourth power of the blood vessel's radius, R. In terms of an equation, F = kR4, where k is a constant of proportionality.
To show that the relative change in F is approximately four times the relative change in R, consider a small change in R (expressed as ΔR), and the corresponding change in F (ΔF). The relative change in F is ΔF/F and the relative change in R is ΔR/R.
By differentiating both sides of the equation, you get ΔF/ΔR = 4kR3. Therefore, ΔF/F = 4(ΔR/R), proving the statement. A 5% increase in the radius would therefore result in a 20% increase in the flux, or the blood flow rate.
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Upon joining the Girl Scouts a member receives 4 patches. Karen has been in the girls scouts for quite awhile and has a total of 70 patches. If Karen earns 3 patches each month,how many months has Karen been a member of the girls scouts?
Answer:
Karen has been a member of Girl Scouts for 22 months
Step-by-step explanation:
Let
x -----> the time in months
we know that
The total number of patches must be equal to the number of months multiplied by 3 patches each month plus 4 patches
so
[tex]70=3x+4[/tex]
Solve for x
Subtract 4 both sides
[tex]70-4=3x\\66=3x[/tex]
Divide by 3 both sides
[tex]22=x[/tex]
Rewrite
[tex]x=22\ months[/tex]
therefore
Karen has been a member of Girl Scouts for 22 months
Karen has been a member of the Girl Scouts for 22 months.
Explanation:To determine the number of months Karen has been a member of the Girl Scouts, we can set up an equation using the information given.
Let's assume that Karen has been a member for x months.
Since she earns 3 patches each month, the total number of patches she has earned is 3x.
Adding the initial 4 patches she received upon joining, we have the equation 3x + 4 = 70.
To solve for x, we can subtract 4 from both sides of the equation: 3x + 4 - 4 = 70 - 4, which simplifies to 3x = 66.
Finally, we can divide both sides of the equation by 3 to solve for x: x = 66 ÷ 3 = 22.
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Simon is factoring the polynomial. x2−4x−12 (x−6)(x+______) What value should Simon write on the line? −6 −2 2 6
Answer:
2
Step-by-step explanation:
You have to find a number that added with -6 equals -4, and multiplied equals -12.
Just have to do the opperations and that is all!
[tex](x-6)(x+2)=x^2+2x-6x-12=x^2-4x-12[/tex]
Hope you like it!
Answer:
Option C is the answer.
Step-by-step explanation:
Simon is factorizing the polynomial x² - 4x - 12 = (x - 6)( x + ......)
We will factorize the left hand side of the given expression
x² - 4x - 12
= x² - 6x + 2x - 12
Now we will break 12 into the factors so that sum of the factors should equal to 4
{ 6 × 2 = 12 and 6 - 2 = 4]
= x(x - 6) + 2(x - 6)
= (x + 2)(x - 6)
Therefore, the blank space should be replaced by 2.
Option C is the answer.
An octave contains twelve distinct notes (on a piano, five black keys and seven white keys). How many different eight-note melodies within a single octave can be written if the black keys and white keys need to alternate?
To determine the number of different eight-note melodies that alternate between black and white keys within a single octave, you calculate the permutations starting with either type of key and add them together, resulting in 141,120 possible melodies.
Explanation:The question asks: How many different eight-note melodies within a single octave can be written if the black keys and white keys need to alternate? To solve this, we need to understand the structure of a piano octave, which consists of seven white keys and five black keys. Since melodies must alternate between black and white keys, starting with a white key will always result in a pattern of white-black-white-black, and so on, until eight notes are reached. Conversely, starting with a black key follows a black-white pattern.
If we start with a white key, we have 7 options for the first note. The next note (a black key) gives us 5 options. This alternating pattern continues, decreasing the number of options by 1 for each type of key used, until we have selected all eight notes. Mathematically, this calculates as 7 × 5 × 6 × 4 × 5 × 3 × 4 × 2. Similarly, starting with a black key would result in a calculation of 5 × 7 × 4 × 6 × 3 × 5 × 2 × 4.
However, since an eight-note melody can start with either a white or a black key, we calculate both scenarios and add them together for the total amount of possible melodies. The sum of the series for both starting options gives us 141,120 possible eight-note melodies that alternate between black and white keys within a single octave.
A university found that 30% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. Compute the probability that 2 or fewer will withdraw (to 4 decimals). Compute the probability that exactly 4 will withdraw (to 4 decimals). Compute the probability that more than 3 will withdraw (to 4 decimals). Compute the expected number of withdrawals.
Step-by-step explanation:
a) Compute the probability that 2 or fewer will withdraw
First we need to determine, given 2 students from the 20. Which is the probability of those 2 to withdraw and all others to complete the course. This is given by:
[tex](0.3)^2(0.7)^{18}[/tex].
Then, we must multiply this quantity by
[tex]{20\choose2}=\frac{20!}{18!2!}=\frac{20\times19}{2}=190,[/tex]
which is the number of ways to choose 2 students from the total of 20. Therefore:
the probability that exactly 2 students withdraw is [tex]190(0.3)^2(0.7)^{18}[/tex].Following an analogous process we can determine that:
The probability that exactly 1 student withdraw is [tex]{20\choose1}(0.3)(0.7)^{19}=20(0.3)(0.7)^{19}.[/tex] The probability that exactly none students withdraw is [tex]{20\choose 0}(0.7)^{20}=(0.7)^{20}.[/tex]Finally, the probability that 2 or fewer students will withdraw is
[tex]190(0.3)^2(0.7)^{18}+20(0.3)(0.7)^{19}+(0.7)^{20}=(0.7)^{18}(190(0.3)^2+20(0.3)(0.7)+(0.7)^2)\approx0.0355[/tex]
b) Compute the probability that exactly 4 will withdraw.
Following the process explained in a), the probability that 4 student withdraw is given by
[tex]{20\choose4}(0.3)^4(0.7)^{16}=\frac{20\times19\times18\times17}{4\times3\times2} (0.3)^4(0.7)^{16}=4845(0.3)^4(0.7)^{16}\approx 0.1304.[/tex]
c) Compute the probability that more than 3 will withdraw
First we will compute the probability that exactly 3 students withdraw, which is given by
[tex]{20\choose3}(0.3)^3(0.7)^{17}=\frac{20\times19\times18}{3\times2} (0.3)^3(0.7)^{17}=1140(0.3)^3(0.7)^{17}\approx 0.0716.[/tex]
Then, using a) we have that the probability that 3 or fewer students withdraw is 0.0355+0.0716=0.1071. Therefore the probability that more than 3 will withdraw is 1-0.1071=0.8929
d) Compute the expected number of withdrawals.
As stated in the problem, 30% of the students withdraw, then, the expected number of withdrawals is the 30% of 20 which is 6.
This problem involves using the binomial distribution to compute probabilities of student withdrawal and the expected number of withdrawals. Probability values are computed using the binomial probability formula and the expected number of students withdrawing from the course is given by n*p.
Explanation:To solve the probability and expected value questions, we need to use the binomial distribution since the event (a student withdraws or not) is independent and repeated a fixed number of times.
1. The probability that 2 or fewer will withdraw is [tex]P(X < =2) = P(0)+P(1)+P(2) where P(x) = C(n, x) * (p^x) * (q^(n-x)). For n=20, p=0.3, q=0.7.[/tex]
2. The probability that exactly 4 withdraw is given by the binomial probability formula P(X=4). Again, use the same values of n, p, and q.
3. The probability that more than 3 will withdraw is P(X > 3) which is 1 - P(X<= 3). Compute P(X<=3) similar to the first situation and subtract it from 1.
4. The expected number of withdrawals, or the expectation of a binomial distribution, is given by n*p.
Calculations using these formulas will give you the desired probabilities to the accuracy you require.
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Given m< LOM = 3x +38 m< MON= 9x+28 find m< LOM:
PLEASE HELP ME !!!
Answer:
The answer to your question is: m∠LOM = 44°
Step-by-step explanation:
Data
m< LOM = 3x +38
m< MON= 9x+28
m< LOM = ?
Process
They are complementary angles
m∠LOM + m∠MON = 90°
3x + 38 + 9x + 28 = 90°
12x + 66 = 90°
12x = 90 - 66
12x = 24
x = 24/12
x = 2
m∠LOM = 3(2) + 38
= 6 + 38
= 44°
m∠ MON = 9(2) + 28
m∠MON = 18 + 28
m∠MON = 46°
The data from an independent-measures research study produce a sample mean difference of 4 points and a pooled variance of 18. If there are n = 4 scores in each sample, what is the estimated standard error for the sample mean difference?
Answer: 3
Step-by-step explanation:
Given : Pooled variance : [tex]\sigma^2=18[/tex]
Sample sizes of each sample = [tex]n_1=n_2=4[/tex]
We know that the standard error for the sample mean difference is given by :-
[tex]S.E.=\sqrt{\sigma^2(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\\\=\sqrt{(18)(\dfrac{1}{4}+\dfrac{1}{4})}\\\\=\sqrt{(18)(\dfrac{1}{2})}=\sqrt{9}=3[/tex]
Hence, the estimated standard error for the sample mean difference =3
Mary and tom park their cars in an empty parking lot with n ≥ 2 consecutive parking spaces (i.e, n spaces in a row, where only one car fits in each space). mary and tom pick parking spaces at random. (all pairs of distinct parking spaces are equally likely.) what is the probability that there is at most one empty parking space between them?
Answer:
p(at most one space between) = (4n-6)/(n(n-1))
Step-by-step explanation:
There are n-1 ways the cars can be parked next to each other, and n-2 ways they can be parked with one empty space between. So, the total number of ways the cars can be parked with at most one empty space is ...
(n -1) +(n -2) = 2n-3
The number of ways that 2 cars can be parked in n spaces is ...
(n)(n -1)/2
So, the probability is ...
(2n-3)/((n(n-1)/2) = (4n -6)/(n(n -1))
___
If the cars are considered distinguishable and order matters, then the number of ways they can be parked will double. The factor of 2 cancels in the final probability ratio, so the answer remains the same.
__
Check
For n=2 or 3, p=1 as you expect.
For n=4, p=5/6, since there is only one of the 6 ways the cars can be parked that has 2 spaces between.
The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.
We have,
To find the probability that there is at most one empty parking space between Mary and Tom's cars, we need to consider two scenarios:
Mary and Tom park their cars in adjacent spaces.
Mary and Tom park their cars in spaces with one empty space in between them.
Scenario 1: Mary and Tom park their cars in adjacent spaces.
In this case, there are (n - 1) ways for them to pick adjacent spaces out of the n spaces. Since there are n spaces to choose from initially, the probability for this scenario is (n - 1) / n.
Scenario 2: Mary and Tom park their cars with one empty space between them.
In this case, there are (n - 2) ways to pick two parking spaces with one empty space in between them. Again, since there are n spaces to choose from initially, the probability for this scenario is (n - 2) / n.
Now, we add up the probabilities of both scenarios because they are mutually exclusive:
Total Probability = Probability of Scenario 1 + Probability of Scenario 2
Total Probability = [(n - 1) / n] + [(n - 2) / n]
To make these fractions have a common denominator, we can rewrite them as:
Total Probability = [(n - 1) + (n - 2)] / n
Total Probability = [2n - 3] / n
Thus,
The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.
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What is the equation of the axis of symmetry?
Answer:
x = 2
Step-by-step explanation:
Since the parabola is opening vertically up then the equation of symmetry is vertical and of the form x = c
The axis of symmetry passes through the vertex (2, 0), thus
equation of axis of symmetry is x = 2
In the equation left parenthesis x squared plus 14 x right parenthesis plus left parenthesis y squared minus 18 y right parenthesisequals5, complete the square on x by adding _______ to both sides. Complete the square on y by adding _______ to both sides.
Answer:
Complete the square on x by adding 49 to both sides.
Complete the square on y by adding 81 to both sides.
Step-by-step explanation:
We have been given an equation [tex](x^2+14x)+(y^2+18y)=5[/tex]. We are asked to complete the squares for both x and y.
We know to complete a square, we add the half the square of coefficient of x or y term.
Upon looking at our given equation, we can see that coefficient of x is 14 and coefficient of y is 18.
[tex](\frac{14}{2})^2=7^2=49[/tex]
[tex](\frac{18}{2})^2=9^2=81[/tex]
Now, we will add 49 to complete the x term square and 81 to complete y term square on both sides of our given equation as:
[tex](x^2+14x+49)+(y^2+18y+81)=5+49+81[/tex]
Applying the perfect square formula [tex]a^2+2ab+b^2=(a+b)^2[/tex], we will get:
[tex](x+7)^2+(y+9)^2=135[/tex]
Therefore, We can complete the square on x by adding 49 to both sides and the square on y by adding 81 to both sides.