Answers
Answer: see proof below
Step-by-step explanation:
[tex]x^a=y^b=z^c\ =k\\[/tex]
Then [tex]x^a=k\qquad \rightarrow \qquad x=k^{\frac{1}{a}}[/tex]
and [tex]y^b=k\qquad \rightarrow \qquad y=k^{\frac{1}{b}}[/tex]
and [tex]z^c=k\qquad \rightarrow \qquad z=k^{\frac{1}{c}}[/tex]
y³ = x · z
[tex](k^{\frac{1}{b}})^3=k^{\frac{1}{a}}\cdot k^{\frac{1}{c}}\\\\k^\frac{3}{b}}=k^{\frac{1}{a}+\frac{1}{c}}\\\\\\\bold{\dfrac{3}{b}=\dfrac{1}{a}+\dfrac{1}{c}}\quad \checkmark[/tex]
Related Questions
t/f) when calculating the standard error for p-hat, we use the p-hat not the p under h null. true false
Answers
The given statement when calculating the standard error for p-hat, we use the p-hat not the p under h null is false.
When calculating the standard error for p-hat (the sample proportion), we use the value of p under the null hypothesis (p₀) rather than the observed sample proportion (p-hat). This is because the standard error is an estimate of the variability or uncertainty in the sample proportion compared to the population proportion assumed under the null hypothesis.
The standard error formula for p-hat is:
SE(p-hat) = sqrt[(p₀ * (1 - p₀)) / n]
Here, p₀ represents the hypothesized population proportion under the null hypothesis, and n is the sample size. We use p₀ because it represents the proportion assumed to be true in the population when there is no evidence to reject the null hypothesis.
Using p-hat (the observed sample proportion) instead of p₀ would not accurately reflect the assumptions made under the null hypothesis and could lead to incorrect inference and conclusions.
for such more question on standard error
https://brainly.com/question/475676
#SPJ8
SHOW WORK PLEASE!!!!!!!!!!!
Answers
Answer:
(3x)/2+14=15-x
2*(3x/2+14)=2*(15-x)
3x+14*2=15*2-x*2
3x-2x=30-28
x=2
If f(x) = 3x + 2
Find f(x + 1)
Answers
Answer:
use symbolab
Step-by-step explanation:
Twice the sum of consecutive numbers n and n+1 is 510. What is the smaller number and the larger number?
Answers
Answer:
n is smaller, n + 1 is larger
Step-by-step explanation:
First, make the equation.
2(n + n+1) = 510
Then, simplify.
2(2n + 1) = 510
Distribute.
4n + 2 = 510
Solve.
n = 127
The smaller number is n (127) and the larger number is n + 1 (128).
Answer:
the correct answer is the smaller number is:127 and the bigger number is:128
Step-by-step explanation:
The number of hits per day on the Web site of a tool company is normally distributed with a mean of 510 and a standard deviation of 100 . a. What proportion of days have more than 650 hits? b. What proportion of days have between 580 and 650 hits? c. Find the number of hits such that only 15% of the days will have the number of hits below this number. Click the icon to view the standard normal table of the cumulative distribution function. a. The proportion of days with more than 650 hits is (Round to four decimal places as needed.) b. The proportion of days with between 580 and 650 hits is (Round to four decimal places as needed.) c. Only 15% of the days will have loss than hits
Answers
a. The proportion of days with more than 650 hits is approximately 0.0808.
b. The proportion of days with between 580 and 650 hits is approximately 0.6772.
c. The number of hits such that only 15% of the days will have fewer hits is approximately 406.36.
To solve these questions, we will use the standard normal distribution and the z-score.
a. To find the proportion of days with more than 650 hits, we need to calculate the z-score for 650 and find the area under the standard normal curve to the right of that z-score.
First, calculate the z-score:
z = (x - μ) / σ
z = (650 - 510) / 100
z = 1.4
Using the standard normal table or a calculator, we find the area to the right of the z-score 1.4 is approximately 0.0808.
Therefore, the proportion of days with more than 650 hits is 0.0808 (rounded to four decimal places).
b. To find the proportion of days with between 580 and 650 hits, we need to calculate the z-scores for 580 and 650 and find the area between these two z-scores under the standard normal curve.
First, calculate the z-score for 580:
z1 = (580 - 510) / 100
z1 = 0.7
Next, calculate the z-score for 650:
z2 = (650 - 510) / 100
z2 = 1.4
Using the standard normal table or a calculator, we find the area to the right of z1 (0.7) is approximately 0.7580, and the area to the right of z2 (1.4) is approximately 0.0808. To find the area between these two z-scores, we subtract the smaller area from the larger area:
0.7580 - 0.0808 = 0.6772
Therefore, the proportion of days with between 580 and 650 hits is 0.6772 (rounded to four decimal places).
c. To find the number of hits such that only 15% of the days will have fewer hits, we need to find the z-score that corresponds to the cumulative probability of 0.15 (15%).
Using the standard normal table or a calculator, we find that the z-score corresponding to a cumulative probability of 0.15 is approximately -1.0364.
Now, we can use the z-score formula to find the number of hits:
z = (x - μ) / σ
-1.0364 = (x - 510) / 100
Solving for x:
x - 510 = -1.0364 * 100
x - 510 = -103.64
x = 510 - 103.64
x ≈ 406.36
Therefore, the number of hits such that only 15% of the days will have fewer hits is approximately 406.36.
In summary:
a. The proportion of days with more than 650 hits is approximately 0.0808.
b. The proportion of days with between 580 and 650 hits is approximately 0.6772.
c. The number of hits such that only 15% of the days will have fewer hits is approximately 406.36.
Learn more about number from
https://brainly.com/question/27894163
#SPJ11
-3.3x + 1x + 8 = -10x
Answers
Answer:
x= -80/77
Step-by-step explanation:
-33x+x+8=-10x
-2.3x+8=-10x
-2.3x=-10-8
-2.3x+10x=-8
7.7x=-8
x=-80/77
Will give brainiest.
1. At the store, I purchased 3.25 lb of honey crisp apples. The apples cost $15.60. How much does it cost per pound
2. Mr. Santora got 4.3 gallons of gas at Wawa. His bill was $12.47. How much was each gallon of gas?
3. A grocery store sells fruit snacks that come in two different sizes. Box A has 8 snacks for $2.48. Box B has 12 snacks for $3.48. How much does it cost per snack in Box A? How much does it cost per snack in Box B? How much more does Box A cost than Box B?
4. Ashton works at a drop in day care center. She earned $68.25 for working 6 hours and 30 minutes. How much does Ashton make per hour? How many hours would it take Ashton to earn $126
5. The small poster in the gift shop has a width of 12 inches and a height of 15 inches. The largest poster has a width of 32 inches. What is the height of the largest poster?
6. Lauren took 12 hours to read a 360 page book. At this rate, how long will it take her to read a 400 page book? It will take Lauren _____ hours and ____ minutes.
Answers
Answer:
(Hope I got them correct I may have some mistakes)
1. $4.80 per pound
2. $2.90 per gallon
3. 31 cents or $0.31, 29 cents or $0.29, 2 cents
4. $10.50, 12 hours
5. 40 inches
6. 13 hours and 20 min
Step-by-step explanation:
1. $15.60/3.25=
$4.80 per pound
2. $12.47/4.3=
$2.90 per gallon
3. $2.48/8=
31 cents or $0.31
$3.48/12=
29 cents or $0.29
31 cents- 29 cents= 2 cents
4. $68.25/6hr 30 min=
$68.25/6.5=
$10.50
$126/10.5= 12 hours
5. Hope you are doing a ratio problem
12/32=15/x
15*32= 480
480/12=
40 inches
6. 360/12=
30
400/30=
13 1/3=
13 hours and 20 min
4. A plumber charges $75 for a house call plus $45 per hour, h. If he charged $210 for the plumbing work, which equation would represent the situation to find how many hours of work he did? I A. $210 = $75h +S45 B. $210 = $45h +$75 C. $210h = $75 +545 D. 575 = 5210 + 545h
Answers
Answer:
B
Step-by-step explanation:
In a class of 17 students, 3 are math majors. A group of four students is chosen at random.
(a) What is the probability that the group has no math majors?
(b) What is the probability that the group has at least one math major?
(c) What is the probability that the group has exactly two math majors?
Answers
Answer:
Step-by-step explanation:
Step1
Definition permutation (order is important):
P(n,r)= n!/(n−r)!
Definition combination (order is not important):
C(n,r) =( n/r )= n!/r!(n−r)!
Step2
a) The order of the students does not matter, because a different order results in the same students being selected, and thus we should use the definition of combination.
We are selecting 3 of the 17 students in the class (of which 3 are math majors and 14 are not math majors).
# of possible outcomes=(17,3)=17!/3!(17−3)!=17!/3!14!=680
There areC(14,3) ways to select 3 of the 14 no math majors.
# of favorable outcomes=C(14,3)= 14!/3!(14−3)! = 14!/3!11! =364
The probability is the number of favorable outcomes divided by the number of possible outcome.
P(no math majors)= # of favorable outcomes/# of possible outcomes
= 364/680= 91/170
≈0.5353=53.53%
Step 3
(b) By part (a):
P(no math majors)=91/170≈0.5353=53.53%
Use the Complement rule
Complement rule:
P(E’)=1−P(E)
P(at least one math major)=1−P(no math majors)=1−91/170
=79/170≈0.4647=46.47%
Step 4
(c) The order of the students does not matter, because a different order results in the same students being selected, and thus we should use the definition of combination.
We are selecting 3 of the 17 students in the class (of which 3 are math majors and 14 are not math majors).
# of possible outcomes=C(17,3)= 17!/3!(17−3)!=17! /3!14!=680
There areC(14,1) ways to select 1 of the 14 no math majors and there are
C(3,2) ways to select 2 of the 3 major majors.
# of favorable outcomes=C(14,1)⋅C(3,2)=14⋅3=42
P(2 math majors)= # of favorable outcomes/# of possible outcomes
= 42/680= 21/340=approx0.0618=6.18%
why does x^2 = 64 have two solutions but x^3 = 64 only has one?
Answers
Because if the exponent is an even number, x can also be -x. For example, -4^2=4^2 but -4^3 isn't the same as 4^3
The area of a rectangular painting is 6348 cm
cm.
If the length of the painting is 92 cm, what is its width?
Width of the painting: cn
cm
Answers
6348cm^2=92cm•w
6348/92=59, so that means that we now know all the components of this rectangle.
A=6348cm^2
l=92cm
w=59cm
Answer plz and do y’all wanan start a chat
Answers
Answer:
Sorry, no thanks
Step-by-step explanation:
The answer for the equation is A and B... I think
Answer:
A B that is what I think the answer is
A coin is tossed three times. Find the probability of the following events:
(1) A: getting at least two heads
(2) B: getting exactly two heads
(3) C: getting at most one head
Answers
Given, the coin is tossed three times.
Sample space: {HHH, HTH, THH, TTH, HHT, HTT, THT, TTT}
Number of positive outcomes = 8
Probability of
(1) A: Getting at least two heads
P(A) = P(Getting 3 heads) + P(Getting 2 heads)
= [tex]\frac{3}{8} +\frac{1}{8}[/tex] Since, P(event) = [tex]\frac{No. of favourable outcomes}{Total no. of possible outcomes}[/tex]
P(A) = [tex]\frac{1}{2}[/tex]
(2) B: Getting exactly two heads
P(B) = [tex]\frac{3}{8}[/tex]
(3) C: Getting at most one head
P(C) = P(Getting zero head) + P(Getting 1 head)
= [tex]\frac{1}{8} + \frac{3}{8}[/tex]
= [tex]\frac{4}{8}[/tex]
P(C) = [tex]\frac{1}{2}[/tex]
To learn more about probability of events:
https://brainly.com/question/26497828
a hotel manager asked each guest that checked in on may 15th if they were more likely to use the hotel pool, exercise room, or neither. identify the sampling method used.
a. voluntary response.
b. stratified
c. convenience
d. systematic
Answers
The sampling method used in this scenario is c. convenience sampling.
Convenience sampling involves selecting individuals who are readily available and easily accessible. In this case, the hotel manager asked each guest that checked in on May 15th about their preferences. The manager likely approached the guests based on convenience, as they were already present at the hotel.
Convenience sampling is a quick and convenient way to gather information, but it may introduce bias since the sample may not accurately represent the larger population. It's important to note that convenience sampling may not provide a representative sample and may not yield generalizable results.
The other sampling methods are not applicable in this case. Voluntary response sampling is a type of non-probability sampling in which individuals volunteer to participate in a study. Stratified sampling is a type of probability sampling in which the population is divided into groups (strata) and then a random sample is selected from each group. Systematic sampling is a type of probability sampling in which every nth individual is selected from the population.
Learn more about sampling methods here:
https://brainly.com/question/12902833
#SPJ11
BRAINLIEST IF RIGHT FOR SURE
the difference between a number is 12 is 30
show steps brainly if correct
Answers
Answer:
18
X + 12 = 30
-12. -12. Subtract 12
X = 18. Answer
Answer:
42
Step-by-step explanation:
V= 1/2bhw
solve for b
Answers
Answer:
uhmmm try to search on google ♂️
solve the inequality 8 < 12 + c < 12
Answers
Separate the inequalities by part.
[tex]8<12+c\\12+c<12[/tex]
We'll do 8 < 12+c first then 12+c<12 next.
[tex]8-12<c\\-4<c\\c>-4[/tex]
Then 12+c<12
[tex]12+c<12\\c<12-12\\c<0[/tex]
Then mix c<0 and c>-4 as we'll get [tex]-4<c<0[/tex] #
Given J(1,4) and the midpoint is M(2, 1), find the other endpoint K.
Answers
Which way is better?
Answers
Answer:
the best way is to follow the law, sales tax is not subject to discount by the seller.
Step-by-step explanation:
both ways result in the same outcome:
improper way, discount after tax
$50+$5(tax)=$55, after discount $55-$11(20%)=$44
proper way, discount before tax
$50-$10(20%)=$40+$4(tax)=$44
What is the additive inverse of the polynomial?
Answers
Answer:
Option A is the correct answer
Step-by-step explanation:
Where there is + sign it changes to - and where there is - sign it change to + sign for the additive inverse
Answer:
Its the first one <3
Step-by-step explanation:
Work out the product of
work out the product of 3 1/3 and 2 1/6
Give your answer as a mixed number.
Answers
Answer:
3⅓×2 1/6
10/3×13/6
5/3×13/3
65/3
21 2/3
f(x)=-2x + 2, find f(6)
Answers
Answer:
-10
Step-by-step explanation:
f(6)=-2(6)+2
f(6)=-12+2
f(6)=-10
Answer:
f(6) = - 10
Step-by-step explanation:
-2(6)+2
-12+2
= -10
Four friends are saving money to go on a vacation together. The table shows how much each has saved so far.
Friend
Part of Money Saved
Gabrielle
85%
Savanna
0.9
Katrina
4/5
Susan
5/6
Arrange the numbers in order from least to greatest.
Answers
Answer:
Katrina = 0.8
Susan = 0.833
Gabrielle = 0.85
Savannah = 0.9
Step-by-step explanation:
Change to decimal
Gabrielle = 85%
= 85/100
= 17/20
= 0.85
Savannah = 0.9
= 9/10
= 0.9
Katrina = 4/5
= 0.8
Susan = 5/6
= 0.833
Arrange from least to greatest
Katrina = 0.8
Susan = 0.833
Gabrielle = 0.85
Savannah = 0.9
.(2n + 4) + 6 = –9 + 4(2n + 1)?
Answers
Answer:
n = 5/2
Step-by-step explanation:
(2n + 4) + 6 = -9 + 4(2n + 1)
2n + 4 + 6 = -9 + 8n + 4
2n + 10 = 8n - 5
15 = 6n
n = 5/2
Hope this helps!
solve x/-4 ≥ –1, show your work
Answers
Answer:
x≤4
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
−1/4
x≥−1
Step 2: Multiply both sides by 4/(-1).
(4−1)*(−14x)≥(4−1)*(−1)
Answer:
1. multiply both sides of the equality by -4 and flip the equality sign
that makes the problem: -4×x/-4 >_ -4×(-1)
2.since you multiplied -4 the divisor cancels and you are left with : x<_ -4×(-1)
multiplying 2 negatives makes it a positive so now you get x<_4
What is the length of segment AB with point A and B located at (-4, 1) and (2, 9)
Answers
Answer:
The answer is 10 unitsStep-by-step explanation:
The distance between two points or a line segment can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-4, 1) and (2, 9)
The length of segment AB is
[tex] |AB| = \sqrt{ ({ - 4 - 2})^{2} + ({1 - 9})^{2} } \\ = \sqrt{( { - 6})^{2} + ({ - 8})^{2} } \\ = \sqrt{36 + 64} \\ = \sqrt{100} \: \: \: \: \: \: \: \: \\ = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
We have the final answer as
10 unitsHope this helps you
Answer:
The length of segment AB is 10
Step-by-step explanation:
The distance formula is d=[tex]\sqrt{ (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}[/tex]
With the points (-4,1) and (2,9) you know that [tex]-4=x_{1}, 2=x_{2}, 1=y_{1} ,9=y_{2}[/tex]
Now you put the numbers into the distance formula
d=[tex]\sqrt{(2-(-4))^{2}+(9-1)^2[/tex]
(2-(-4) turns into (2+4) because two negatives equal a positive.
After adding and subtracting you get d=[tex]\sqrt{6^2+8^2[/tex]
You then square [tex]6^2[/tex] and [tex]8^2[/tex] to get [tex]\sqrt{36+64[/tex]
After adding 34+64 you get [tex]\sqrt{100[/tex], which is 10
So the length of segment AB is 10
Question
Show that a language A is Turing recognizable if and only if there is a decider V such that for all x∈Σ∗, x∈A if and only if ∃y∈Σ∗ such that V accepts (x,y).
Answers
By proving both directions, we have established the equivalence between a language A being Turing recognizable and the existence of a decider V such that for all x ∈ Σ∗, x ∈ A if and only if ∃y ∈ Σ∗ such that V accepts (x, y).
To prove the statement, we need to show both directions of the "if and only if" statement.
First, let's assume that language A is Turing recognizable. This means that there exists a Turing machine M that recognizes A. We will construct a decider V based on M as follows:
V = "On input (x, y):
Simulate M on input x and y.
If M accepts, accept."
Now, let's analyze the behavior of V. If there exists y such that V accepts (x, y), it means that M accepts both x and y as inputs. Since M recognizes language A, this implies that x ∈ A. Therefore, if V accepts (x, y), then x ∈ A.
On the other hand, if x ∈ A, we know that there exists some string y such that M accepts (x, y). In this case, V will also accept (x, y) because it simulates M and accepts when M accepts. Therefore, if x ∈ A, there exists y such that V accepts (x, y).
We have shown that for all x ∈ Σ∗, x ∈ A if and only if ∃y ∈ Σ∗ such that V accepts (x, y). Hence, the existence of the decider V satisfies the condition for language A to be Turing recognizable.
Next, let's assume that there is a decider V such that for all x ∈ Σ∗, x ∈ A if and only if ∃y ∈ Σ∗ such that V accepts (x, y). We will construct a Turing machine M that recognizes A based on V as follows:
M = "On input x:
For each y in Σ∗, do the following:
Simulate V on input (x, y).
If V accepts, accept."
Now, let's analyze the behavior of M. If x ∈ A, then there exists some y such that V accepts (x, y) according to the assumption. In this case, M will eventually simulate V on input (x, y) and accept. Therefore, if x ∈ A, M will accept.
On the other hand, if x ∉ A, it means that for every y in Σ∗, V rejects (x, y). In this case, M will simulate V on all possible pairs (x, y) and reject for each of them. Therefore, if x ∉ A, M will reject.
We have shown that M recognizes language A based on the existence of the decider V.
By proving both directions, we have established the equivalence between a language A being Turing recognizable and the existence of a decider V such that for all x ∈ Σ∗, x ∈ A if and only if ∃y ∈ Σ∗ such that V accepts (x, y).
Learn more about directions from
https://brainly.com/question/30318208
#SPJ11
Please answer quickly
Answers
please help
What is the probability that either event will occur?
15
A
12
B
18
21
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Answers
Answer: 15
Step-by-step explanation:
The probability that either event A or event B will occur is approximately 0.9715.
To find the probability that either event A or event B will occur, we can use the formula P(A or B) = P(A) + P(B) - P(A and B). In this case, the probabilities of events A and B are given as 12/15 and 18/21, respectively. To find the probability of both A and B happening together, we can multiply their individual probabilities. Now we can plug these values into the formula to find the probability of A or B occurring.
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 12/15 + 18/21 - (12/15) * (18/21)
P(A or B) = 0.8 + 0.8571 - (0.8) * (0.8571)
P(A or B) = 0.8 + 0.8571 - 0.6856
P(A or B) = 0.9715
Therefore, the probability that either event A or event B will occur is approximately 0.9715.
Learn more about Probability here:
https://brainly.com/question/22962752
#SPJ2
One hundred less than a half of a number is five
Answers
Answer:
x/2-100=5
Step-by-step explanation:
