Answer:
[tex]T_n =-\frac{8}{3} (-3)^{n}[/tex]
Step-by-step explanation:
Given
[tex]Sequence: 8, -24, 72[/tex]
Required
Determine the n term
The above sequence is geometric. So, we calculate the common ratio first:
[tex]r = \frac{T_2}{T_1}[/tex]
[tex]r = \frac{-24}{8}[/tex]
[tex]r = -3[/tex]
The equation is then calculated using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = T_1 = 8[/tex]
and
[tex]r = -3[/tex]
The equation becomes:
[tex]T_n =8 * (-3)^{n-1}[/tex]
Apply law of indices:
[tex]T_n =8 * (-3)^{n} * (-3)^{-1}[/tex]
[tex]T_n =8 * (-3)^{n} * \frac{1}{-3}[/tex]
[tex]T_n =-8 * (-3)^{n} * \frac{1}{3}[/tex]
[tex]T_n =-\frac{8}{3} * (-3)^{n}[/tex]
[tex]T_n =-\frac{8}{3} (-3)^{n}[/tex]
A utility company might offer electrical rates based on time-of-day consumption to decrease the peak demand in a day. Enough customers need to accept the plan for it to be successful. Suppose that among 50 major customers, 15 would accept the plan. The utility selects 10 major customers randomly (without replacement) to contact and promote the plan. a. What is the probability that exactly two of the selected major customers accept the plan
Answer:
0.2406 = 24.06% probability that exactly two of the selected major customers accept the plan
Step-by-step explanation:
The customers are chosen without replacement, which means that we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
50 major customers, 15 would accept the plan.
This means that [tex]N = 50, k = 15[/tex]
The utility selects 10 major customers randomly (without replacement) to contact and promote the plan.
This means that [tex]n = 10[/tex]
a. What is the probability that exactly two of the selected major customers accept the plan
This is P(X = 2).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,50,10,15) = \frac{C_{15,2}*C_{35,8}}{C_{50,10}} = 0.2406[/tex]
0.2406 = 24.06% probability that exactly two of the selected major customers accept the plan
What is the value of
2021
−
2223
+
2425
2021
−
2223
+
2425
?
Answer:
the answer is 2223 please mark as brainliest
Answer:
2223
Step-by-step explanation:
its a simple math issue
43 POINTS IF U DO THIS! + ILL MARK BRAINLIEST!
Answer:
The second one
210 lbs
Step-by-step explanation:
The difference between 7 and 4 is 3
90/3 = 30
30 times 7 = 210
Answer:
Second Diagram
Step-by-step explanation:
63 over 22 as a decimal
Answer:
Step-by-step explanation:
63/22 = 2.86363 = 2.86
NEED HELP ASAP PLEASE HELP
Answer:
the second one or b. :)
Step-by-step explanation:
B. What is the largest whole number to the left of 3.52?
Answer:
3
Step-by-step explanation:
<---------1-----------2---------3----3.52----4----->
You purchase a new mountain bike for $1,575. You put a 10% down payment and $65.56 per month on a 24 month purchase plan. Determine the total finance charge.
Answer:
c believe me
Step-by-step explanation:
Is the equation y=5x+90 proportional?
Answer:
yes, x does have an exact proportion of y
Step-by-step explanation:
Simplify
6sqrt20 + 8sqrt5 – 5sqrt45
Answer:
5√5Step-by-step explanation:
Simplify
6√20 + 8√5 - 5√45 = 6√4(5) + 8√5 - 5√9(5) =6(2)√5 + 8√5 - 5(3)√5 = (12 + 8 - 15)√5 =5√5A quality-control engineer samples 100 items manufactured by a certain process, and finds that 15 of them are defective. True or False:
a) The probability that an item produced by this process is defective is 0.15.
b) The probability that an item produced by this process is defective is likely to be close to 0.15, but not exactly equal to 0.15.
Answer: b) The probability that an item produced by this process is defective is likely to be close to 0.15, but not exactly equal to 0.15.
Step-by-step explanation:
Given that:
Number of samples = 100
Number of defective samples = 15
Proportion =number defective samples / total samples
P = 15 / 100 = 0.15
Hence, the probability that an item produces is defective is 0.15.
However, due to sampling Variations, the probability will be corrected for these variations. Hence, probability that an item produced by this process is defective is likely to be close to 0.15, but not exactly equal to 0.15.
POINTS PLZ HELP
A baker determined the annual profit in dollars from selling pies using p n( ) = 52n − 0.05n2 , where n is the number of pies sold. What is the annual profit if the baker sells 400 pies?
F $20,780
G $12,800
H $28,800
J $20,760
Answer:
G
Step-by-step explanation:
Answer:$12,800
Step-by-step explanation:
Add 400 to every n in the equation, I’ll be using y for the “p(n)” part cus it always confuses me like that.
Y=52(400)-0.05 x 400^2
=20,800 - 0.05 x 160,000
=20,800 - 8,000
=12,800
How do you use Trigonometric Ratios to solve Real-world problems
9514 1404 393
Explanation:
Obviously, the way you use trig ratios will depend on the problem. The problems you see in algebra and trig courses are a good sampling of the kinds of problems you run across in the real world. Some of them include ...
finding height or widths based on a measure and an angle (SOH CAH TOA)
finding areas based on side lengths and an angle (area formula)
finding unknown sides or angles of a triangle (law of sines/cosines)
finding bearing and/or distance (spherical trig relations, law of cosines)
__
As with solving problems of any kind, you choose the appropriate formula(s), fill in the known values, and solve for the unknown values. Sometimes a real-world problem will require solution of intermediate problems before the answer to the original question is found.
Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the form a b c , where abc
This question is incomplete, the complete question is;
Determine if the described set is a subspace. Assume a, b, and c are real numbers.
The subset of R³ consisting of vectors of the form [tex]\left[\begin{array}{ccc}a\\b\\c\end{array}\right][/tex] , where abc = 0
The set is a subspaceThe set is not a subspace
Answer:
Therefore; The set is not a subspace
Step-by-step explanation:
Given the data the question;
the subset R³;
S = { [tex]\left[\begin{array}{ccc}a\\b\\c\end{array}\right][/tex] , where abc = 0 }
we know that a subset of R³ is a subspace if it stratifies the following properties;
it contains additive identityit is closed under additionit is closed under scales multiplicationLooking at the properties, we can say that it is not a subspace
As;
u = [tex]\left[\begin{array}{ccc}1\\1\\0\end{array}\right][/tex] ∈ S and v = [tex]\left[\begin{array}{ccc}0\\1\\1\end{array}\right][/tex] ∈ S
As 1×1×0=0 0×1×1=0
But u+v = [tex]\left[\begin{array}{ccc}1+0\\1+1\\0+1\end{array}\right] =[/tex] [tex]\left[\begin{array}{ccc}1\\2\\1\end{array}\right][/tex] ∉ S as 1×2×1 ≠ 0
Hence, it is not closed under addition.
Therefore; The set is not a subspace
Consider a square-based straight pyramid. Suppose that the base is a square with sides 10 km long, and all other edges are 17 km long. Find an approximate value of the angle formed between the base and a triangular face. Present your answer in degrees, accurate up to four or more decimal places.
Answer:
72.06
Step-by-step explanation:
Given that :
Side Lenght, a = 10
Edge length, b = 17
Using Pythagoras :
h = height of pyramid
h = sqrt (b² - 1/2a²)
h = sqrt(17^2 - 10^2/2)
h = sqrt(289 - 50)
h = 15.46
Slant height :
L = sqrt(h² + a²/4)
L = sqrt(15.46² + 25)
L = sqrt(239 + 25)
L = sqrt(264)
L = 16.25
Sinα = h/L
α = sin^-1 (15.46/16.25)
α = 72.060933
= 72.06
The approximate value of the angle formed between the base and a triangular face is 72.0775°.
Let [tex]h[/tex] be the distance between the center of the square base and the midpoint of the side of the square and let [tex]H[/tex] the height of the triangular face of the pyramid. By properties of the square and the Pythagorean theorem we derive expressions for [tex]h[/tex] and [tex]H[/tex], respectively:
Square base
[tex]h = 0.5\cdot L[/tex] (1)
Triangular face
[tex]H = \sqrt{l^{2}-0.25\cdot L^{2}}[/tex] (2)
Where:
[tex]L[/tex] - Side length of the square base, in kilometers.[tex]l[/tex] - Remaining side length of the triangular face, in kilometers.Finally, by trigonometry we can derive an expression for the angle between the base and a triangular face ([tex]\theta[/tex]), in sexagesimal degrees:
[tex]\theta = \cos^{-1} \frac{h}{H}[/tex] (3)
If we know that [tex]L = 10\,km[/tex] and [tex]l = 17\,km[/tex], then the angle between the base and a triangular face is:
[tex]h = 5\,km[/tex]
[tex]H = \sqrt{17^{2}-5^{2}}[/tex]
[tex]H \approx 16.248\,km[/tex]
[tex]\theta = \cos^{-1} \frac{5\,km}{16.248\,km}[/tex]
[tex]\theta \approx 72.0775^{\circ}[/tex]
The approximate value of the angle formed between the base and a triangular face is 72.0775°.
We kindly invite to check this question on pyramids: https://brainly.com/question/16303112
5. Five-eighth of a number is 15. What is the number?
Your answer
Answer:
I think it is 24
Step-by-step explanation:
15÷5=3
3×8=24
Answer:
24
Step-by-step explanation:
divide 15 by 5 to get 3 which is equal to 1/8 of the number. then just multiply 3 by 8 to get 24.
What is true about the domain of the following two graphs
Answer:
the domain for both graphs is infinity
Step-by-step explanation:
both graphs are absolute value graphs, which means there is an infinite amount of possible x values in positive and negative directions.
edit: actually, if there are no arrows of the ends of the graphs, then what i just said is not true. a possible answer if that's the case may be both graphs have domains that include negatives
Please help me with this. I give brainliest and give ratings. Don't answer just to take my points or you're getting reported
Answer:
3/4
Step-by-step explanation:
You have to Subtract 6 ¼ by 5 ½
in which equation is y a nonlinear function of x ? will Mark brainiest is for the correct answer please help me
9514 1404 393
Answer:
(B)
Step-by-step explanation:
The power of x is 1 everywhere except equation (B), where it is 1/2.
Equation B is a nonlinear function of x.
Answer:
Step-by-step explanation: D
PLEASEEEEEEEEEEEE HELPPPPPPPPPP :(
will give brainliest
32,300 is 85% of what
Answer:
27455
Step-by-step explanation:
32300per of 85
is 27455
Jay's allowance is reduced $1.25 every time he forgets to clean his room. If he forgets to clean his room 7 times this month, how much is Jay's allowance reduced?
Answer:
$8.75
Step-by-step explanation:
1.25 times 7 equals 8.75 so it is reduced by 8.75
Which statement about the reflection below is true?
Answer:
A
Step-by-step explanation:
took le test review and got that question right
Answer:
A
Step-by-step explanation:
got it right edge2021
The prom committee has no more than $600 to spend on centerpieces for the prom. If each centerpiece costs $25, what is the maximum number of centerpieces the committee can buy?
Answer:
600/25 = 24
Brainiest plz :)
Answer:
600/25 = 24
Have a good day I hope this helps.
Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 12 of which have electrical defects and 13 of which have mechanical defects. (a) How many ways are there to randomly select 6 of these keyboards for a thorough inspection (without regard to order)
Answer:
There are 177,100 ways.
Step-by-step explanation:
Since there is no regard to order, we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 keyboards from a set of 25. So
[tex]C_{25,6} = \frac{25!}{6!(25-6)!} = 177100[/tex]
There are 177,100 ways.
The University of South Texas is interested in determining if there is a difference in the average weight gain between male students (group 2) and female students (group 1) during their freshman year. They take a random sample of 10 male students and 10 female students. Find the confidence interval with 95% confidence. The 95% confidence interval is (2.4, 20.4). A. We are 95% confident that the population mean weight gain for male University of South Texas students is 2.4 more to 20,4 more than female University of South Texas students. B. We are 95% confident that the population mean weight gain for female University of South Texas students is 2.4 more to 20.4 more than male University of South Texas students. C. We are 95% confident that the sample mean weight gain for female University of South Texas students is 2.4 more to 20.4 more than male University of South Texas students. D. We are 95% confident that the sample mean weight gain for male University of South Texas students is 2.4 less to 20.4 more than female University of South Texas students.
Answer: A. We are 95% confident that the population mean weight gain for male University of South Texas students is 2.4 more to 20,4 more than female University of South Texas students.
Step-by-step explanation:
Given a 95% confidence interval of : (2.4, 20.4)
The lower boundary of the interval = 2.4
The upper boundary of the interval = 20.4
Male = group 2, Female = group 1
P2 - P1 is between lower boundary more and upper boundary more ;
Hence
Population mean weight for male is 2.4 more to 20.4 more than female
A pet store has 40 freshwater fish. Of all the fish in the store, 80% are freshwater fish. How many fish does the store have in all?
Answer:
50 fish
Step-by-step explanation:
80% 40 fish :8
10% 5 fish x10
100% 50 fish
What is the average rate of change between:
x= 1 and x = 2?
x = 2 and x = 3?
x= 3 and x = 4?
Answer:
The average rate of change between x = 1 to x = 2 is 2, from x = 2 to x = 3 is 4 and from x = 3 to x = 4 is 8.
Step-by-step explanation:
An equation for a line is 3x + 3y = 18.
What are the slope and Y -intercept point?
Answer:
y = -1x + 6
slope ^ ^ y-intercept
Step-by-step explanation:
3x + 3y = 18
3y = -3x + 18
y = -1x + 6
hope this helps
Answer:
y int: 6 slope: -1
Step-by-step explanation:
Convert to y=mx+b format
3x + 3y - 18 = 0
3x - 18 = -3y
-1x + 6 = y
in mx+b format, m is the slope and b is the y-int:
m = -1
b = 6
All the teachers at a school are either left footed or right footed.
At the school
the number of left footed teachers:the number of right footed teachers = 3:13
At the school, there are 18 left footed teachers.
How many right footed teachers are there?
Answer:
78
Step-by-step explanation:
Ratio of left-footed teachers to right-footed teachers = 3:13
18 left-footed teachers; 3x6 = 18 (3:13 is a simplified ratio and to get 18, you have to multiply 3 by 6)
13x6 = 78 (whatever you do to one side, you have to do the other)
78 right-footed teachers
The are 78 teachers are right footed.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The ratio of the number of left footed teachers: the number of right footed teachers = 3:13
Total left footed teachers = 18
let the Common ratio be x.
Then , number of left footed teachers= 3x
and, number of right footed teachers= 13x
So, 3x= 18
x= 6
Hence, there are 78 teachers are right footed.
Learn mor about algebra here:
https://brainly.com/question/24875240
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From $5 to $8 in percent
Answer:
Step-by-step explanation:
That would be 8/5 = 1.3 = 130/100 = 130%
PLEASE HELP ME!!!!!!!!
Answer:
x = 50
Step-by-step explanation:
x = 180 - 130 = 50
Answer:
x=50
Step-by-step explanation:
