Answer: second option
Step-by-step explanation:
To find the inverse function of the given function f(x):
[tex]f(x)=2x[/tex]
You need to:
Substitute [tex]f(x)=y[/tex] into the function:
[tex]y=2x[/tex]
Now, you need to solve for "x", to do this, you must divide both sides of the function by 2:
[tex]\frac{y}{2}=\frac{2x}{2}\\\\\frac{y}{2}=x[/tex]
Now, replace "x" with "y" and replace "y" with "x":
[tex]\frac{x}{2}=y[/tex]
Therefore, substituting [tex]y=f^{-1}(x)[/tex] you get:
[tex]f^{-1}(x)=\frac{x}{2}[/tex] or [tex]f^{-1}(x)=\frac{1}{2}x[/tex]
Find the product. (A^3 + 8)(a^3 -8)
a^6-64
I used the foil method
(a^3+8)(a^3-8)
a^6-8a^3+8a^3-64 middles cancel out
a^6-64
A statistics student is doing a project for her class. She wants to make a prediction for the outcome of an upcoming national election. Since there are only two candidates, she decides that her question is "Which candidate do more people favor in the upcoming election?" She decides to randomly interview 100 students crossing the courtyard on campus about their preference. Is this sample good for drawing general conclusions about the results of the election?
Final answer:
Interpreting the preference of 100 college students on campus to predict an election result is unlikely to yield a representative sample of the national electorate. A more scientific poll requires a larger, random, and demographically diverse sample of the voting population.
Explanation:
The student's approach of interviewing 100 students on a college campus to predict the outcome of a national election may not provide a representative sample of the general voting population. A sample to make general predictions about national elections should reflect the demographics and political distribution of the entire nation, which is unlikely to be the case for a sample drawn solely from a college campus.
Furthermore, the sample may also suffer from selection bias if, for instance, those who choose to walk through the courtyard are not representative of the entire student body, let alone the country's electorate.
To conduct a more accurate and scientific poll, a larger and more diverse sample size would need to be chosen randomly from among all potential voters in the nation and it should include a mix of individuals with a history of voting and other demographic characteristics that align with the broader population.
If the first term of a geometric sequence is positive, and r>1, then the sequnce increases?
Answer:
Yes, if the first term of a geometric sequence is positive and r > 1, then the sequence increases
Step-by-step explanation:
* Lets talk about the geometric sequence
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric sequence:
# U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4
# Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms, and n is the position of
the number in the sequence
- V.I.N: The position of the number means the place of the
number like first , second , third , .......... so n must be positive integer
* Lets talk about the ratio r
- If r greater than 1 and a is positive, the sequence increases lets
take some different examples to explain that
# If the first term is 2 and the ratio between the consecutive
terms is 3/2, then the first four terms in the sequence are
∵ a = 2
∵ r = 3/2 ⇒ greater than 1
∴ First = a = 2
∴ Second = ar = 2 × 3/2 = 3
∴ Third = ar² = 2 × (3/2)² = 2 × 9/4 = 9/2 4.5
∴ Fourth = ar³ = 2 × (3/2)³ = 2 × 27/8 = 27/4 = 6.75
- From the answers the sequence increases
# If the first term is 1/2 and the ratio between the consecutive
terms is 4/3, then the first four terms in the sequence are
∵ a = 1/2
∵ r = 4/3 ⇒ greater than 1
∴ First = a = 1/2
∴ Second = ar = 1/2 × 4/3 = 2/3 ⇒ 2nd > 1st
∴ Third = ar² = 1/2 × (4/3)² = 2 × 16/9 = 8/9 ⇒ 3rd > 2nd
∴ Fourth = ar³ = 1/2 × (4/3)³ = 2 × 64/27 = 32/27 ⇒ 4th > 3rd
- From the answers the sequence increases
* Now we are sure if the first term of a geometric sequence is
positive and r > 1, then the sequence increases
Answer:
The given statement is TRUE.
Step-by-step explanation:
We are given that if the first term of a geometric sequence is positive, and r>1, then the sequence increases which is true.
If the first term of any geometric sequence is positive and its common ratio ( r ) is greater than 1 then the sequence will always increase.
[tex] a _ n = a r ^ n - 1 [/tex]
A cabin cruiser travels 48 miles upstream (against the current) and 48 miles downstream (with the current). The speed of the current is 4 miles per hour. Find the total time traveled if the cabin cruiser travels at 12 miles per hour in still water.
The answer is:
The total time traveled by the cabin cruiser is equal to 9 hours.
Why?To solve the problem, we need to write two equations using the given information about the travel upstream and downstream.
Then, we need to write two equations:
Let be "x" the speed of the cabin cruiser (12 mph in still water)
Let be "y" the speed of the current (4 mph).
So,
For the travel against the current (upstream), we have:
[tex](x-y)*t_{upstream}=48miles\\\\(x-y)*t_{upstream}=48miles\\\\(x-4mph)*t_{upstream}=48miles[/tex]
For the travel with the current (downstream), we have:
[tex](x+y)*t_{downstream}=48miles\\\\(x+y)*t_{downstream}=48miles\\\\(x+4mph)*t_{downstream}=48miles[/tex]
Also, we know from the statement that the speed of the cabin cruise traveling in still water is equal to 12mph.
So,
Calculating the time traveled upstream, we have:
[tex](x-4mph)*t_{upstream}=48miles(12mph-4mph)*t_{upstream}=48miles(8mph)*t_{upstream}=48milest_{upstream}=\frac{48miles}{8mph}=6hours[/tex]
Calculating the time traveled downstream, we have:
[tex](x+4mph)*t_{downstream}=48miles(12mph+4mph)*t_{downstream}=48miles(16mph)*t_{downstream}=48milest_{downstream}=\frac{48miles}{16mph}=3hours[/tex]
Now that we know the time traveled upstream and downstream, we need to calculate the total time traveled using the following equation:
[tex]TotalTime=t_{upstream}+t_{downstream}\\\\TotalTime=6hours+3hours=9hours[/tex]
Therefore we have that the total time traveled is equal to 9 hours.
Have a nice day!
Sam wrote these four expressions .
1 . n + n + n + n + 2
2 . n + n + n + 2
3 . 4n + 2
4 . 2n + 2n + 2n
PART A- Which expressions are equivalent? Write your answer in the space provided .
PART B- Choose two of Sam’s expressions that are not equivalent . Explain how you know they are not equivalent . Write your answer in the space provided .
Part A) the first and the third answer are equivalent because.
n+n+n+n+2= 4n+2 which is the same as the third answer.
Part B) 2 and 4 are not equivalent because
2) n+n+n+2= 3n+2
4) 2n+2n+2n= 6n
as we can see they are not the same. Therefore they are not equivalent.
hope this helps
More math help please im lazy ._.
there are no real square roots of 25,36
A rectangular swimming pool that is 10 ft wide by 16 ft long is surrounded by a cement sidewalk of uniform width. If the area of the sidewalk is 155 ft2, what is its width? A = lw 2.5 ft 5.0 ft 6.2 ft 15.5 ft
The pool has area [tex]160\,\mathrm{ft}^2[/tex].
Let [tex]x[/tex] be the width of the sidewalk. Then the combined area of the pool and sidewalk is [tex](10+x)(16+x)=160+26x+x^2[/tex], so that the area of the sidewalk alone is [tex]26x+x^2[/tex].
We're told this area is [tex]155\,\mathrm{ft}^2[/tex], so
[tex]26x+x^2=155\implies x^2+26x-155=(x-5)(x+31)=0\implies x=5[/tex]
Answer:
The width of the sidewalk is 5.0 ft.
Step-by-step explanation:
Given,
The dimension of the rectangular swimming pool is 16 ft × 10 ft,
So, the area of the pool = 16 × 10 = 160 ft²,
Let x be the uniform width of the cement sidewalk,
So, the dimension of the area covered by both swimming pool and sidewalk = (16+x) ft × (10+x) ft,
Thus, the combined area of the swimming pool and sidewalk = (16+x)(10+x) ft²
Also, the area of the sidewalk = The combined area - Area of the pool,
= (16+x)(10+x) - 160
According to the question,
[tex](16+x)(10+x)-160 = 155[/tex]
[tex](16+x)(10+x)=315[/tex]
[tex]160+16x+10x+x^2=315[/tex]
[tex]x^2+26x-155=0[/tex]
By the quadratic formula,
[tex]x=\frac{-26\pm \sqrt{676+620}}{2}[/tex]
[tex]x=\frac{-26\pm 36}{2}[/tex]
[tex]\implies x=5\text{ or } x = -31[/tex]
Side can not be negative,
Hence, the width of the sidewalk is 5.0 ft.
A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she
serves 6 times, what's the probability that she gets...
All 6 serves in?
Exactly 4 serves in?
At least 4 serves in?
No more than 4 serves in?
this is a binomial problem: p = 0.7 and q = 0.3
a) (0.7)^6
b) (6C4)(0.7)^4(0.3)^2
c) Pr ( at least 4) = Pr(4) + Pr(5) + Pr(6) = (6C5)(0.7)^5(0.3) + (0.7)^6
d) Pr (no more than 4) = 1 - Pr(at least 4) = 1 - (answer from c)
The question requires understanding of binomial probability. The probability of all 6 serves, exactly 4 serves, at least 4 serves, and no more than 4 serves can be calculated using binomial distribution when each serve is an independent event.
Explanation:The subject of this question relates to probability involved in binomial distribution. Binomial distribution applies when there is a fixed number of independent trials, each with a constant probability of success. Here, a tennis player making a successful serve can be considered a success, with a probability of 0.70.
For all 6 serves in, the calculation is simply the product of the successful probability raised to the power of 6, which is (0.70)^6.For exactly 4 serves in, the calculation uses a binomial probability formula P(x=k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where n is the total number of trials, k is the desired number of successes, and p is the probability of a single success. Here, C(6,4) * (0.70^4) * (0.30^2).For at least 4 serves in, it's the sum of the probabilities of getting exactly 4, 5, and 6 serves in.For no more than 4 serves in, it's the sum of the probabilities of getting exactly 0, 1, 2, 3, and 4 serves in.Learn more about Binomial Probability here:https://brainly.com/question/39666605
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What is the equation of the circle shown below?
A.
(x ‒ 4)2 + (y + 5)2 = 34
B.
(x ‒ 5)2 + (y ‒ 4)2 = 5.83
C.
(x + 4)2 + (y ‒ 5)2 = 34
D.
(x ‒ 5)2 + (y + 4)2= 5.83
I am definitely willing to assist you, but without an illustration is a tough challenge.
Find the value of x shown in the isosceles triangle shown below
40 POINTS!!
Answer:
x = √41 units
Step-by-step explanation:
Half the base length
= 8 ÷ 2
= 4
x² = 4² + 5²
x² = 16 + 25
x² = 41
x = √41
Answer:
x = sqrt(41)
Step-by-step explanation:
We have a right triangle with height 5 and a base that is 1/2 of 8 = 4
We can use Pythagorean theorem
a^2 + b^2 = c^2 to find the length of the hypotenuse
5^2 + 4^2 = x^2
25+16 = x^2
41 = x^2
Take the square root of each side
sqrt(41) = x
what is the area of this figure
Answer:
532 m²Step-by-step explanation:
We have a square with the side a = 18m and a triangle with the base
b = 18m + 8m = 26m and height h = 16m.
The formula of an area of a square:
[tex]A_{\square}=a^2[/tex]
The formula of an area of a triangle:
[tex]A_{\triangle}=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A_{\square}=18^2=324\ m^2\\\\A_{\triangle=\dfrac{(26)(16)}{2}=(26)(8)=208\ m^2[/tex]
The area of figure:
[tex]A=A_{\square}+A_{\triangle}\\\\A=324\ m^2+208\ m^2=532\ m^2[/tex]
Which kind of function best models the data in the table? Graph the data and write an equation to model the data.
a. linear; y = –x – 2
b. linear; y = x – 2
c. exponential; y = 3^x – 2
d. quadratic; y = x^2 – 2
Answer:
Option A, linear; y = -x - 2
Step-by-step explanation:
Example-
x = 3
y = ?
? = -3 - 2 (add the negative number if in the case of subtracting a negative number)
? = -5
A baseball player has had 5 hits in the last 25 times at bat. Based on this information, how many times can the player be expected to get a hit in the next 35 times at bat ?
Answer:
7 times
Step-by-step explanation:
5 times 5 is 25 so 5 times 7 is 35 and thats the answer
Calculate the value of x to the nearest degree
Answer:
x = 61.3°
Step-by-step explanation:
We are given the radius r = 9 cm and arc length l = 9.7 cm. We need to find the angle x in degrees.
The formula used is:
l = rФ
In our case Ф = x. So re writing the formula:
l= rx
9.7 = 9 x
=> x = 9.7 / 9
x = 1.07 radians
Converting radians into degree we need to multiply the value of x by
180/π where π = 3.14
x = 1.07 * 180/3.14
x = 61.3°
Jefferson played basketball in the park. He started playing basketball at 1:15 P.M and played for 1 hour and 25 minutes. What time did Jefferson play basketball until?
Final answer:
Jefferson played basketball until 2:57 P.M.
Explanation:
To find out what time Jefferson played basketball until, we need to add the duration of time he played to the starting time.
First, we convert the duration of time from minutes to hours. Since there are 60 minutes in an hour, 1 hour and 25 minutes is equal to 1.42 hours.
Next, we add 1.42 hours to the starting time of 1:15 P.M. This gives us the ending time of 2:57 P.M.
the measure of angle C
Answer:
75 degrees
Step-by-step explanation:
The two marks on the triangle sides mean they are the same length (congruent). Because of the Isosceles Triangle Theorem, the angles across from those two congruent sides are also congruent. That means that angle C also measures 3x. Because all the sides of a triangle add up to equal 180, then (x+5) + 3x + 3x = 180. 7x + 5 = 180, and 7x = 175. That means that x = 25. Take that 25 and sub it into 3x to get 3(25) = 75 degrees.
Are these permutation or combination problems?
1. Suppose you need to choose a new combination for your combination lock. You have to choose three numbers, each different and between 0 and 40. How many combinations are there?
2. You want to construct a 3 digit number from the digits 4,6,8,9. How many possible numbers are there?
Answer: You just bought a new briefcase and need to pick a four digit combination out of 10 possible numbers for the lock. If order does matter how many possible lock combinations can you choose from?
Step-by-step explanation:
For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed that 63 developed tissue abnormalities that might lead to cancer. Provide a descriptive statistic (to 1 decimal) that could be used to estimate the number of women out of 1,000 in this population who have tissue abnormalities.
Answer: 15.8 Women out of 1,000 have tissue abnormalities.
Step-by-step explanation:
It's pretty simple, all you need to do is set up a proportion with the variables you already have
63/3980 = x/1000
Do Cross products so
63000=3980x
Divide both sides by 3980 to get x by itself and you get 15.82914573 which reduced to 1 decimal is 15.8
Answer:
Answer is 16
Step-by-step explanation:
Given that for the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed that 63 developed tissue abnormalities that might lead to cancer.
From the given information, we find the proportion of women who took the drug and developed tissue abnormalities
Proportion p = [tex]\frac{63}{3980} =0.015829[/tex]
Assuming the same proportion continues constantly for any population, we find
the number of women out of 1,000 in this population who have tissue abnormalities, estimated = [tex]1000(0.015829)\\=15.829\\=16[/tex]
the lengths of two sides of a right triangle triangle are 3 and 5 what is the length of the hypotenuse
Answer:
√34
Step-by-step explanation:
3²+5²=9+25=34
√34=√34 because 34 cannot be simplified because no perfect square go into it
write the equation for the cosine function that has been compressed vertically by a factor of 2, stretched horizontally by a factor of 4, and shifted down one unit
Answer:
[tex]f(x)=\frac{1}{2}Cos(\frac{1}{4}x)-1[/tex]
Step-by-step explanation:
Consider the function f(x) = cos x. Noted below are the points of transformations of the cos function
The function f(x) = [tex]\frac{1}{a}[/tex] cos x is a vertical compression of the original by a factor of aThe function f(x) = cos [tex](\frac{1}{b}x)[/tex] is a horizontal stretch of the original function by a factor bThe function f(x) = cosx - c is the original function shifted down c unitsConsidering the points above, we can now write down the "transformed" cosine function's equation:
f(x) = [tex]\frac{1}{2}Cos(\frac{1}{4}x)-1[/tex]
Answer:
Hope this helps :)
Step-by-step explanation:
What is the total amount for an investment of $1000 invested at 7.25% for 15 years and compound continuously?
Answer:
[tex]\$2,966.85[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=15\ years\\ P=\$1,000\\ r=0.0725[/tex]
substitute in the formula above
[tex]A=\$1,000(e)^{0.0725*15}=\$2,966.85[/tex]
Final answer:
The total amount for a $1000 investment at 7.25% compounded continuously for 15 years is approximately $2972.70, demonstrating the power of compound interest.
Explanation:
To calculate the total amount from an investment that is compounded continuously, you use the formula for continuous compounding, which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial sum of money), r is the annual interest rate (decimal), t is the time the money is invested for, and e is the base of the natural logarithm, approximately equal to 2.71828.
Substituting our values into this formula we get:
A = 1000 * e0.0725*15
A ≈ 1000 * e1.0875
A ≈ 1000 * 2.9727
A ≈ $2972.70
This result shows us the power of compound interest and highlights starting to save money early in life as a key financial decision.
how many square feet of outdoor carpet will we need for this hole?
Answer:
40
Step-by-step explanation:
12x4 = 48
3x2 = 6
2x1 = 2
6+2 = 8
48-8= 40
HOPE THIS HELPS!
Can you guys help my with this problem? thanks.
Answer:
$3,750
Step-by-step explanation:
Find how much 3% of 125,000 is. Divide 3 by 100 and then multiply that by 125,000. You get 3,750, which is how much interest Moran will earn.
Solved + 3d = 6.
isolate the variable
You can sum like terms:
[tex]d+3d=4d[/tex]
The equation becomes
[tex]4d = 6[/tex]
Divide both sides by 4:
[tex]d=\dfrac{6}{4}=\dfrac{3}{2}[/tex]
Please help will give brainliest
What’s a brainliest sorry I can’t help
This relation is a function because a function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs). So we have that:
[tex]\left[\begin{array}{cc}x & y\\1 & 0\\2 & 4\\3 & 8\\4 & 12\end{array}\right][/tex]
We have plotted all the points below. As you can see, this is a linear function. Therefore, with two points we can get the equation, so:
[tex]The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1}) \\ \\ \\ y-0=\frac{4-0}{2-1}(x-1) \\ \\ y=4(x-1) \\ \\ y=4x-4 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(1,0) \\ \\ (x_{2},y_{2})=(2,4)[/tex]
Finally, the equation is:
[tex]\boxed{y=4x-4}[/tex]
What is the value of a in the polynomial
Answer: a= 16
Step-by-step explanation:
We have the following expression:
[tex](y-4)(y^2 +4y +16)[/tex]
To find the value of the coefficient "a" you must use the distributive property to multiply the expression:
[tex](y-4)(y^2 +4y +16)[/tex]
until you transform it to the form:
[tex]y^3 +4y^2 +ay -4y^2 -ay-64[/tex]
Then we have
[tex](y-4)(y^2 +4y +16)\\\\(y^3 +4y^2 +16y -4y^2 -16y-64)\\\\[/tex]
Therefore the value of a in the polynomial is 16
which expressions are equivalent to 2-(-6+3)+4c
A..-8c+6
B.3(-4+2)+4c
c. None of the above
Answer:
c. none of the above
Step-by-step explanation:
(-6+3)= -3
2--3=2+3=5
5+4c cant add them since they arent like terms
final answer 5+4c and that option isnt here
44 is 55% of what number?
Enter your answer in the box.
|___|
Whoever answers it correctly gets branliest :)
Answer:
44 is 55% of 80
Step-by-step explanation:
44 is 55% of what number
LEt the unknown number be x
44 is 55% of x
Write the given sentence in equation form
[tex]44= 55 \ percent \ times \ x[/tex]
To remove percentage we divide by 100
55 divide 100 is 0.55
[tex]44=0.55 \cdot x[/tex]
Divide both sides by 0.55 to solve for x
[tex]80=x[/tex]
The value of x is 80. It means 44 is 55% of 80
The number is 80 and 44 is 55 percentage of the number 80
Given data ,
To find out what number 27 is 30 percent of, we can set up the equation:
55% of x = 44
To solve for x, we can divide both sides of the equation by 55% (or 0.55), which is the equivalent of dividing by 0.55:
x = 44 / 0.55
On dividing the numerator of the fraction by the denominator , we get
Evaluating the expression on the right side gives:
x = 80
Therefore , the value of the number is x = 80
Hence , 44 is 55 percent of number 80
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The frequency table below represents the 30 best batting averages for a semi-peo baseball league. Which range of batting averages was most common among the players?
Answer:
A. .350-.359
Step-by-step explanation:
It has the highest frequency of all the ranges (14).
Answer: [tex]0.350-0.359[/tex]
Step-by-step explanation:
From the given table, it can be seen that the largest frequency in the data table = 14
Thus, there are 4=14 players which have the common range.
The range corresponding to the frequency 14 = [tex]0.350-0.359[/tex]
Hence, the range of batting averages which was the most common among the players = [tex]0.350-0.359[/tex]
What is the square root of 9 plus the square root of 9 plus the square root of 9 plus the square root of 9, etc
[tex] \sqrt{9} + \sqrt{9} + \sqrt{9} + \sqrt{9} [/tex]
3+3+3+3
=18
hope that helped you
Answer: 18
Step-by-step explanation:
square root of 9 equals 3+3+3+3+3+ = 18 (3x6)