Answer:
(a) S = {GH, GT, BH, BT, RH and RT}
(b) The value of P (A) is 0.15.
(c) A and B mutually exclusive.
(d) A and C are not mutually exclusive.
Step-by-step explanation:
There are 10 cards in a special deck of cards: 4 are green (G), 3 are blue (B), and 3 are red (R).
Also when a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin.
(a)
The sample space is:
S = {GH, GT, BH, BT, RH and RT}
(b)
A = a blue card is picked first, followed by landing a head on the coin toss
Compute the probability of event A as follows:
[tex]P(A)=P(B)\times P(H)[/tex]
[tex]=\frac{3}{10}\times\frac{1}{2}\\\\=\frac{3}{20}\\\\=0.15[/tex]
Thus, the value of P (A) is 0.15.
(c)
B = a red or green is picked, followed by landing a head on the coin toss.
The result of the coin toss is same for both events A and B.
So, consider the events,
A as a blue card is picked first
B as a red or green is picked
There is no intersection point for the two events.
Thus, events A and B mutually exclusive.
(d)
C = a red or blue is picked, followed by landing a head on the coin toss.
The result of the coin toss is same for both events A and C.
So, consider the events,
A as a blue card is picked first
C as a red or blue is picked
There is an intersection point for the two events.
Thus, events A and C are not mutually exclusive.
Part(a): The sample space can be written as shown below:
[tex]S=\{GH,GT,BH,BT,RH,RT\}[/tex]
Part(b): The required probability is [tex]P(A)=0.15[/tex]
Part(c): The events A and B are mutually exclusive because of [tex]P( A\ AND\ B ) = 0[/tex] are equal to zero.
Part(d): The events A and C are not mutually exclusive because [tex]P( A\ AND\ C ) = 0[/tex] are not equal to zero.
Samples Space:A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.
Part(a):
A special deck contains ten cards with colors red, green, and blue when the card is picked its color gets recorded, and after that coin will get tossed.
Then the sample space can be written as shown below:
[tex]S=\{GH,GT,BH,BT,RH,RT\}[/tex]
Part(b):
If A is the event that a blue card is picked first followed by landing ahead on the coin toss then the outcome it contains is 3 blue cards and 1 head.
Therefore the [tex]P(A)[/tex] is calculated below:
[tex]P(A):P(B)\timesP(H)\\=\frac{3}{10}\times\frac{1}{2}\\ =0.15[/tex]
Part(c):
Mutually exclusive events contain a probability [tex]P( A\ AND\ B ) = 0[/tex] that means there is no common outcome between them.
Here, it can be noticed that events A and B cannot happen at the same time. That means, the researcher cannot pick the same cards together. Either it could be red or green.
Hence, events A and B are mutually exclusive because of [tex]P( A\ AND\ B ) = 0[/tex] are equal to zero.
Part(d):
Mutually exclusive events contain a probability [tex]P( A\ AND\ C ) = 0[/tex] which means there is no common outcome between them.
Here, it can be noticed that events A and C can happen at the same time because event C can contain all outcomes of event A.
Hence, events A and C are not mutually exclusive because [tex]P( A\ AND\ C ) = 0[/tex] are not equal to zero.
Learn more about the topic samples space:
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2(3y+6)−3(−4−y) simplified
Answer:
9y+24
Step-by-step explanation:
2(3y+6)-3(-4-y)
Expand the brackets.
6y+12+12+3y
Rearrange.
6y+3y+12+12
Add like terms.
9y+24
Answer:
9y+24solution,
[tex]2(3y + 6) - 3( - 4 - y) \\ = 6y + 12 + 12 + 3y[/tex]
Collect like terms,
[tex]6y + 3y + 12 + 12[/tex]
Simplify
[tex]9y + 24[/tex]
hope this helps...
Good luck on your assignment..
In the diagram below, $RT:TS = 1:2$ and $SR = PQ = 20$. Find $UV$.
It's pretty easy not college levlel just some simple high school geomerty.
Answer: 12
Step-by-step explanation: Because $\overline{PQ}$, $\overline{UV}$, and $\overline{SR}$ are all perpendicular to $\overline{QR}$, we have $\overline{PQ} \parallel \overline{UV} \parallel \overline{SR}$. Therefore, we have $\angle UPQ = \angle UTS$ and $\angle UQP = \angle UST$, which means that $\triangle UPQ \sim \triangle UTS$. So, we have $UQ/US = PQ/ST$.
Because $ST/SR = 2/3$ and $PQ = SR$, we have
\[\frac{UQ}{US} = \frac{PQ}{ST} = \frac{SR}{ST} = \frac{3}{2}.\]Since $UQ/US = 3/2$, we have $UQ/QS = 3/5$.
We have $\triangle UQV \sim \triangle SQR$ by AA Similarity, so $UV/SR = UQ/QS = 3/5$. Therefore, we have $UV = (3/5)SR = \boxed{12}$.
What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?
Answer:
Step-by-step explanation:
Answer:
its b on edge
Step-by-step explanation:
Which expression is equal to -3b(6b^-8)
Answer:a^2/b
Step-by-step explanation:
(a^6b^−3)1^/3
a^6 ^ 1/3 b ^ -3 ^ 1/3
using the power of power rule we can multiply the exponents
a ^ (6*1/3) b ^ (-3* 1/3)
a^ 2 b ^ -1
the negative exponent flips it from the numerator to the denominator
a^2* 1/ b^1
a^2/b
Answer:
A. -18b^-4
second answer is B. -18/b^-4
Step-by-step explanation:
All applicants for admission to graduate study in business are given a standardized test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What fraction of applicants would you expect to have scores of 600 or above
Answer:
The probability that applicants would you expect to have scores of 600 or above = 0.0401 or 4%
Step-by-step explanation:
Explanation:-
Let "x" Scores are normally distributed
Given mean of the Population = 460
standard deviation of the population = 80
Let X = 600
[tex]Z = \frac{x -mean}{S.D} = \frac{600-460}{80} =1.75[/tex]
The probability that applicants would you expect to have scores of 600 or above
P( X≥600) = P( Z≥ 1.75)
= 1- P( Z≤1.75)
= 1- ( 0.5 + A(1.75)
= 1- 0.5 - A(1.75)
= 0.5 - 0.4599 (from Normal table)
= 0.0401
The probability that applicants would you expect to have scores of 600 or above = 0.0401 or 4%
in a church wing with 8 men and 10 women members find the probability that a 5 member committee chosen randomly will have.......
a).all men.
b).3men and 2 women
Answer:
a) Probability that a 5 member committee will have all men = 0.0065
b) probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
Step-by-step explanation:
Number of men = 8
Number of women = 10
Total number of members = 10 + 8 = 18
Probability = (Number of possible outcomes)/(Total number of outcomes)
Number of ways of selecting a 5 member committee from 18 people = [tex]^{18}C_5 = \frac{18!}{(18-5)!5!} = \frac{18!}{13!5!}[/tex] = 8568 ways
a) Probability that a 5 member committee will have all men
Number of ways of selecting 5 men from 8 men
= [tex]^8C_5 = \frac{8!}{(8-5)!5!} = \frac{8!}{3!5!}[/tex] = 56 ways
Probability that a 5 member committee will have all men = 56/8568
Probability that a 5 member committee will have all men = 0.0065
b)probability that a 5 member committee chosen randomly will have 3men and 2 women
Number of ways of selecting 3 men from 8 men
= [tex]^8C_3 = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!}[/tex] = 56 ways
Number of ways of selecting 2 women from 10 men
= [tex]^{10}C_2 = \frac{10!}{(10-2)!2!} = \frac{10!}{8!2!}[/tex] = 45 ways
Number of ways of selecting 3 men and 2 women = 56*45
Number of ways of selecting 3 men and 2 women = 2520
Probability of selecting 3 men and 2 women = 2520/8568 = 0.294
probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
The amount of money that is left in a medical savings account is expressed by the equation y = negative 24 x + 379, where x represents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it? 10 weeks 13 weeks 15 weeks 21 weeks
Answer: 13 weeks
Step-by-step explanation:
y = -24x + 379
67 = -24x + 379
24x = 379 - 67
x = 312 / 24
x = 13
Answer:
the answer is 13 weeks
Step-by-step explanation:
y = amount left
y = 67
67 = -24x+379
-312 = -24x
x = -312 / -24
x = 13
A restaurant borrows from a local bank for months. The local bank charges simple interest at an annual rate of for this loan. Assume each month is of a year. Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Complete Question:
A restaurant borrows $16,100 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. Assume each month is 1/12 of a year.
Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Answer:
a) Interest that will be owed after 4 months , I = $131.48
b) Amount owed by the restaurant after 4 months = $16231.48
Step-by-step explanation:
Note that the question instructs not to round any intermediate computations except the final answer.
Annual rate = 2.45%
Monthly rate, [tex]R = \frac{2.45\%}{12}[/tex]
R = 0.20416666666%
Time, T = 4 months
Interest, [tex]I = \frac{PRT}{100}[/tex]
[tex]I = \frac{16100 * 0.20416666666 * 4}{100} \\I = 161 * 0.20416666666 * 4\\I = \$131.483333333\\I = \$131.48[/tex]
b) If the restaurant doesn't make any payments, that means after four months, they will be owing both the capital and the interest ( i.e the amount)
Amount owed by the restaurant after 4 months = (Amount borrowed + Interest)
Amount owed by the restaurant after 4 months = 16100 + 131.48
Amount owed by the restaurant after 4 months = $16231.48
A random sample of n observations is selected from a normal population to test the null hypothesis that muμequals=10. Specify the rejection region for each of the following combinations of HSubscript aa, alphaα, and n. a. HSubscript aa: muμnot equals≠10; alphaαequals=0.010.01; nequals=1313 b. HSubscript aa: muμgreater than>10; alphaαequals=0.100.10; nequals=2323 c. HSubscript aa: muμgreater than>10; alphaαequals=0.050.05; nequals=99 d. HSubscript aa: muμless than<10; alphaαequals=0.100.10; nequals=1111 e. HSubscript aa: muμnot equals≠10; alphaα equals=0.050.05; nequals=2020 f. HSubscript aa: muμless than<10; alphaαequals=0.010.01; nequals=77 a. Select the correct choice below and fill in the answer box within your choice.
Answer:
Step-by-step explanation:
a) H0: μ = 10
Ha: μ ≠ 10
This is a two tailed test
n = 13
Since α = 0.01, the critical value is determined from the t distribution table. Recall that this is a two tailed test. Therefore, we would find the critical value corresponding to 1 - α/2 and reject the null hypothesis if the absolute value of the test statistic is greater than the value of t 1 - α/2 from the table.
1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995
The critical value is 3.012
The rejection region is area > 3.012
b) Ha: μ > 10
This is a right tailed test
n = 23
α = 0.1
We would reject the null hypothesis if the test statistic is greater than the table value of 1 - α
1 - α = 1 - 0.1 = 0.9
The critical value is 1.319
The rejection region is area > 1.319
c) Ha: μ > 10
This is a right tailed test
n = 99
α = 0.05
We would reject the null hypothesis if the test statistic is greater than the table value of 1 - α
1 - α = 1 - 0.05 = 0.95
The critical value is 1.66
The rejection region is area > 1.66
d) Ha: μ < 10
This is a left tailed test
n = 11
α = 0.1
We would reject the null hypothesis if the test statistic is lesser than the table value of 1 - α
1 - α = 1 - 0.1 = 0.9
The critical value is 1.363
The rejection region is area < 1.363
e) H0: μ = 10
Ha: μ ≠ 10
This is a two tailed test
n = 20
Since α = 0.05, we would find the critical value corresponding to 1 - α/2 and reject the null hypothesis if the absolute value of the test statistic is greater than the value of t 1 - α/2 from the table.
1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975
The critical value is 2.086
The rejection region is area > 2.086
f) Ha: μ < 10
This is a left tailed test
n = 77
α = 0.01
We would reject the null hypothesis if the test statistic is lesser than the table value of 1 - α
1 - α = 1 - 0.01 = 0.99
The critical value is 2.376
The rejection region is area < 2.376
PLEASE I NEED HELP ASAP sally drives for 2 hours at an average speed of 70 m/h. she then drives for half an hour at an average speed of 40 m/h work ot the total distance that sally has travelled
Answer:
Total Distance = 160 m
Average speed = 64 m/hr
Step-by-step explanation:
For first 2 hours:
Distance = Speed × Time
D = 70 × 2
D = 140 m
For the next half hour:
Distance = Speed × Time
Distance = 40 × 0.5
Distance = 20 m
Now total Distance:
Total Distance = 140+20
Total Distance = 160 m
After that,
Average Speed = Total Distance Covered/ Total Time taken
Average Speed = 160 m / 2.5 hours
Average speed = 64 m/hr
Solve the system of equations below by graphing them with a pencil and
paper. Enter your answer as an ordered pair.
y= -x+5
y=x-3
Answer:
X+5= -x-3
2x = 2
X=1
then y1 is 4
y2 is -1
Answer:
Answer is 4, 1. If you graph the lines, they intersect at 4, 1.
Step-by-step explanation:
Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ?
Answer:
980 intervals.
Step-by-step explanation:
For each interval, there are only two possible outcomes. Either it captures the population mean, or it does not. One interval is independent of other intervals. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
98% confidence interval
Has a 98% probability of capturing the population mean, so [tex]p = 0.98[/tex]
1000 intervals
This means that [tex]n = 1000[/tex]
How many of these 1000 intervals do you expect to capture the corresponding value of μ?
[tex]E(X) = np = 1000*0.98 = 980[/tex]
980 intervals.
Preciso de ajudaa! Resolução também! - Considere as funções f e g tais que f(x)= x³+1 e g(x)= x-2 Determine: a)(fog)(0) b)(gof)(0) c)(fof)(1) d)(gog)(1)
Answer:
(fog)(x) means that we have the function f(x) evaluated in the function g(x), or f(g(x)).
So, if f(x) = x^3 + 1 and g(x) = x - 2.
we have:
a) (fog)(0) = f(g(0)) = (0 - 2)^3 + 1 = -8 + 1 = -7
b) (gof)(0) = g(f(0)) = (0^3 + 1) - 2 = -1
c) (fof)(1) = f(f(1)) = (1^3 + 1)^3 + 1 = 2^3 + 1 = 8 + 1 = 9
d) (gog)(1) = g(g(1)) = (1 - 2) - 2 = -1 -2 = -3
Paolo is buying salad and pizza for a company lunch. Suppose that a bowl of salad costs $5.00, and slice of costs $2.00.Let E be the amount in dollars that Paolo spends on salad and pizza. If Paolo buys S bowls of salad and P slices of pizza, then the total amount of money he spends E can be represented by the equation _____.Now rearrange the equation you wrote above so that P is written in terms of E and S. The quantity of pizza he buys can be represented by the equation _____.Suppose Paolo has $40.00 to spend on salad and pizza; that is E = $40.00Complete the following table with values of S or P that make the equation true.To complete the first row, determine the number of pizza slices Paolo can purchase with $40.00, when the number of salad bowls he purchases is 0.Budget (Dollars) Salad (Bowls) Pizza (Slice)40.00 0 _____40.00 4 _____40.00 _____ 0
Answer:
E=5S+2PP=0.5(E-5S)[tex]\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|[/tex]
Step-by-step explanation:
Cost of a bowl of salad = $5.00
Cost of a slice of pizza = $2.00
If Paolo buys S bowls of salad and P slices of pizza, then the total amount of money he spends E can be represented by the equation:
E=5S+2PNext, we make P the subject of the equation above.
2P=E-5S
[tex]P=\dfrac{E-5S}{2} \\P=0.5(E-5S)[/tex]
Therefore, The quantity of pizza he buys can be represented by the equation:
P=0.5(E-5S)When E=$40, we are required to complete the table below.
[tex]\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&\\40.00&4&\\40.00&&0\end{array}\right|[/tex]
When S=0, E=$40
From P=0.5(E-5S)
P=0.5(40-5(0))=20
When S=4, E=$40
P=0.5(40-5(4))
=0.5(40-20)
=0.5*20
=10
When P=0, E=$40
P=0.5(E-5S)
0=0.5(40-5S)
40-5S=0
5S=40
S=8
Therefore, the completed table is:
[tex]\left|\begin{array}{c|c|c}$Budget (Dollars)& $Salad (Bowls) &$Pizza (Slice)\\40.00&0&20\\40.00&4&10\\40.00&8&0\end{array}\right|[/tex]
Which expanded expressions represent the exponential expression (–4)3 · p4? Select all that apply. (–4) · (–4) · (–4) · (–4) · p · p · p p · p · p · p · (–4) · (–4) · (–4) p · (–4) · (–4) · p · (–4) · p p · p · (–4) · (–4) · p · p · (–4) (–4) · p · p · p · (–4) · (–4) · (–4) (–4) · (–4) · p · (–4) · p · p · p
The expanded form of the given exponential expression is (-4)×(-4)×(-4)×p×p×p×p.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given expression is (-4)³·p⁴.
Here, (-4)³= (-4)×(-4)×(-4)
p⁴=p×p×p×p
So, (-4)×(-4)×(-4)×p×p×p×p
= -64×p×p×p×p
Therefore, the expanded form is (-4)×(-4)×(-4)×p×p×p×p.
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A sequence is defined recursively using the formula . If the first term of the sequence is 120, what is f(5)? −15 −7.5 7.5 15
Answer:
C. 7.5
Step-by-step explanation:
I took the quiz on EDGE
If the first term of the sequence is 120, then f(5) will be 7.5
What is recursively sequence?In mathematics and theoretical computer science, a constant-recursive sequence is an infinite sequence of numbers satisfying a linear recurrence relation: each number in the sequence is equal to a fixed linear combination of one or more of its immediate predecessors. A recursive sequence is a sequence of numbers formed by using previous terms to find the next terms, such as the Fibonacci sequence.How to solve this problem?The steps are as follow:
From the given conditions We knew the sequence is defined by the formula f(n + 1) = - 0.5f(n) and we know f(1) = 120So f(1 + 1) = f(2) = - 0.5f(1) = - 0.5 * 120 = f(2) = - 60Then f(2+1) = f(3) = -0,5 f(2) = -0,5x-60 f(3)=30f(3 + 1) = f(4) = - 0.5f(3) = - 0.5 * 30 = f(4)= -15f(4 + 1) = f(5) = - 0.5f(4) = - 0.5x - 15 = f(5) = 7.5So, f(5) = 7.5So if the first term of the sequence is 120, then f(5) will be 7.5
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The point (-7,1) when reflected across the origin maps onto
Answer:
(7,-1)
Step-by-step explanation:
common rule for reflections across the origin; im guessing you meant a reflection across the line y=x since it goes through the origin too.
for this make sure to add this transformation:
(x,y) --> (-x,-y)
Thursday is ladies night at the slurp in Burt bar and Grill. All adult beverages are $1.25 for women and $2.50 for men. A total of 211 adult beverages were sold last Thursday night. If the slip and burp sold a total of $365.00 in adult beverages last Thursday night, how many adult beverages were sold to women?
Answer:
130 women
Step-by-step explanation:
First set up a system of equations:
1.23W+2.50M=365.00
W+M=211
Using substitution you get:
1.25W+2.50(211-W)=365.00
Simplify:
-1.25W=-162.5
Divide:
W=130
What is the probability that 4 randomly selected people all have different birthdays? Ignore leap years, and round your final answer to four decimal places.
0.9729
0.9918
0.9891
0.9836
Answer:
(D)0.9836
Step-by-step explanation:
There are 365 days in a year.
Since each person has a different birthday:
We can choose a birthday for the first person 365 out of 365 days.We can choose a birthday for the second person 364 out of 365 days.We can choose a birthday for the third person 363 out of 365 days.We can choose a birthday for the fourth person 362 out of 365 days.Therefore,
P(4 randomly selected people all have different birthdays)
[tex]=\dfrac{365}{365} \times \dfrac{364}{365} \times \dfrac{363}{365} \times \dfrac{362}{365}\\\\=0.9836[/tex]
help i give u brainliest
It is a 4 : 1 ratio of color to white
or a 1 : 4 white to colored
Explanation:
1cm = 10mm
1.2cm = 12mm
12 : 48 --> 1 : 4
Answer:
1:4
Step-by-step explanation:
1.2 cm of white fabric per 48 mm of colored fabric:
1.2 cm : 48 mm= 12 mm: 48 mm= 1:4
The ratio is: 1:4
The next 3 options are:
A: x=1 or x= -3
A: x= -1 or x=3
B: Since the quadratic equation has two real solutions, the graph of the quadratic equation intercepts the x axis at (-1,0) and (3,0)
please please help. Thank you so much.
Answer:
A: x= -1 or x=3
B: Since the quadratic equation has two real solutions, the graph of the quadratic equation intercepts the x axis at (-1,0) and (3,0)
Step-by-step explanation:
x^2 -2x -3 =0
Factor
(x-3 )(x+1) =0
Using the zero product property
x-3 =0 x+1 =0
x=3 x=-1
The zeros are
(3,0) (-1,0)
It intersects the x axis at (3,0) (-1,0)
The diameter of a sphere is 4 centimeters, which represents the volume of the sphere?
Answer:
10 2/3π or 33.51
Step-by-step explanation:
the volume of a sphere is 4/3πr^3
if the sphere has a diameter of 4 the radius is half the diameter so it would be 2. 2^3 = 8 now multiply 8 by 4/3 to get 10 2/3. now multiply by pi to get 10 2/3 π or 33.5103 which rounds to 33.51
Answer:
32π/3 cubic cm
Step-by-step explanation:
The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs of the hypotenuse is 25 feet.
Answer:
9.233 ft, 23.233 ft
Step-by-step explanation:
If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...
x^2 + (x +14)^2 = 25^2
2x^2 +28x +196 = 625
x^2 +14x = 214.5
x^2 +14x +49 = 263.5
(x +7)^2 = 263.5
x = -7 +√263.5 ≈ 9.23268
The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.
Answer: 9 ft, 23 ft
Step-by-step explanation:
We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.
(x-14)²+x²=25²
(x²-28x+196)+x²=625
2x²-28x+196=625
2x²-28x-429=0
When we solve for x, we get [tex]x=\frac{14+\sqrt{1054} }{2}[/tex] and [tex]x=\frac{14-\sqrt{1054} }{2}[/tex].
Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.
add or subtract negative numbers
[tex]9+(-2)\\9-2\\=7[/tex]
[tex]-6+(-3)\\-6-3\\=-9[/tex]
[tex]4+(-9)\\4-9\\=-5[/tex]
Answer:
see below
Step-by-step explanation:
9 + -2 =
9 -2 = 7
-6 + -3
-6 - 3 =-9
4 + - 9
-9 +4 = -5
Consider the following sets of sample data: A: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312 B: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
Answer:
Dataset A
We have the following results:
[tex] \bar X_A = 359.786[/tex]
[tex]s_A= 60.904[/tex]
[tex] CV_A = \frac{60.904}{359.786}= 0.169 \approx 0.2[/tex]
Dataset B
We have the following results:
[tex] \bar X_B = 1.791[/tex]
[tex]s_B= 0.635[/tex]
[tex] CV_B = \frac{0.635}{1.791}= 0.355 \approx 0.4[/tex]
Step-by-step explanation:
For this case we have the following info given:
A: 431, 447, 306, 413, 315, 432, 312, 387, 295, 327, 323, 296, 441, 312
B: $1.35, $1.82, $1.82, $2.72, $1.07, $1.86, $2.71, $2.61, $1.13, $1.20, $1.41
We need to remember that the coeffcient of variation is given by this formula:
[tex] CV= \frac{s}{\bar X}[/tex]
Where the sample mean is given by:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
And the sample deviation given by:
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
Dataset A
We have the following results:
[tex] \bar X_A = 359.786[/tex]
[tex]s_A= 60.904[/tex]
[tex] CV_A = \frac{60.904}{359.786}= 0.169 \approx 0.2[/tex]
Dataset B
We have the following results:
[tex] \bar X_B = 1.791[/tex]
[tex]s_B= 0.635[/tex]
[tex] CV_B = \frac{0.635}{1.791}= 0.355 \approx 0.4[/tex]
Which of the following are point-slope equations of the line going through (3,
6) and (1,-2)? Check all that apply:
Answer:
y+2=4(x-1)
y-6=4(x-3)
Step-by-step explanation:
Slope between (3, 6) and (1, -2)
6-(-2)/3-1
8/2
4
y+2=4(x-1)
y-6=4(x-3)
HELP PLZ!! I NEED HELP!
Answer:
yes£18Step-by-step explanation:
The amount Lila and Wassim plan to save is ...
(£13 +13)(9) = £234
__
The charges they expect to incur are a per-person charge and a tent pitch charge. Since they expect to stay 10 nights, the special rate means they will only be charged for 8 nights.
per-person charge
per-person-per-night charge = (2 persons)(8 nights)(£6 per person-night)
= £96
tent pitch charge
To determine the tent pitch area required, we need to find the area of the tent:
A = LW = (4.2 m)(2.3 m) = 9.66 m²
This is less than 10 square meters, so we can expect the pitch charge to be £15 per night for 8 nights.
tent pitch charge = (£15/night)(8 nights) = £120
So, the total of camp site charges is expected to be ...
person charge + pitch charge = £96 +120 = £216
__
The expected savings exceeds the expected charges by ...
£234 -216 = £18
Lila and Wassim will have enough saved, with £18 extra.
According to Brad, consumers claim to prefer the brand-name products better than the generics, but they can't even tell which is which. To test his theory, Brad gives each of 199 consumers two potato chips - one generic, and one brand-name - then asks them which one is the brand-name chip. 92 of the subjects correctly identified the brand-name chip.
Required:
a. At the 0.01 level of significance, is this significantly greater than the 50% that could be expected simply by chance?
b. Find the test statistic value.
Answer:
a. There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
b. Test statistic z=-1.001
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion that correctly identifies the chip is significantly smaller than 50%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi<0.5[/tex]
The significance level is 0.01.
The sample has a size n=199.
The sample proportion is p=0.462.
[tex]p=X/n=92/199=0.462[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{199}}\\\\\\ \sigma_p=\sqrt{0.001256}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.462-0.5+0.5/199}{0.035}=\dfrac{-0.035}{0.035}=-1.001[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.001)=0.16[/tex]
As the P-value (0.16) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
A biologist conducting an experiment starts with a culture of 300 E. coli bacteria. 72 hours later the culture consists of 600,000 bacteria. What is the average increase in the number of E. coli bacteria per hour
Answer:
2,000
Step-by-step explanation:
if you divide 600,000 by 300 you get 2,000.
What is the solution for this inequality? 5x ≤ 45
A. x ≥ -9
B. x ≤ 9
C. x ≤ -9
D. x ≥ 9
Answer:
[tex]x\le \:9[/tex]
Step-by-step explanation:
[tex]5x\le 45[/tex]
[tex]\frac{5x}{5}\le \frac{45}{5}[/tex]
[tex]x\le \:9[/tex]
Answer:
B
Step-by-step explanation:
We divide the entire inequality by 5 to get rid of the coefficient of x. The ≤ stays the same so we get x ≤ 9.