For the geometric sequence, the common ratio is 2 and the 12th term is a12 =6144. What is the first term?
A. a1=2
B.a1=3
C.a1=4
D.a1=5
Answers
Answer:
B. a1 = 3
Step-by-step explanation:
Since we have the comon ratio and 12th term, we could just divide the 12th term (6144) by 2 11 times until we get to the 1st term:
[tex]6144 /2/2/2/2/2/2/2/2/2/2/2 = 3[/tex]
For a better understanding of the question, let's use the formula for geometric equations:
a(r)^(n-1)
1. Let's plug in the values we know
r = common ratio = 2 n = 12a(2)^(12-1)
2. Set equation equal to 6144 (Since we use n = 12) and solve for a
a = 6144/ (2^11) a = 3To confirm this, let's use the formula for geometric equations again:
a(r)^(n-1)
a = first term = 3
r = common ratio = 2
3(2)^(12-1) = 6144
Therefore, a1 = 3
Related Questions
Which cylinder will have a larger volume?
A. 3.5 in
8.5 in
________
B. 2.7 in.
11 in
Answers
explanation: 3.5x8.5= 29.75
2.7x11=29.70
Therefore a is larger.
A salesperson uses random digit dialing to call people and try to interest them in applying for a charge card for a large department store chain. From past experience, she is successful on 2% of her cals. in typical working, she makes 50 calls. Let X be the number of calls on which she is unsuccessful.
a. This is binomial distribution. Explain using the BINS method why this is so.
b. Find the mean and standard deviation of X. Leave answer to 4 d.p
c. Find the probablity of P(X>or equal to 48)
Answers
Answer:
a)
In this question, for each call, there are only two possible outcomes, either it is successful, or it is not, so binary outcomes. For each call, the probability of a success or failure is the same, which means that the trials are independent, having the same value of p. And the number of trials, which is 50, is fixed. This means that this is a binomial distribution.
b) The mean is 1 and the standard deviation is 0.9899.
c) [tex]P(X \geq 48) = 0[/tex]
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
From past experience, she is successful on 2% of her calls.
This means that [tex]p = 0.02[/tex]
50 calls.
This means that [tex]n = 50[/tex]
a. This is binomial distribution. Explain using the BINS method why this is so.
BINS: Binary outcomes, Independent Trials, n is fixed, and same value of p for all trials.
In this question, for each call, there are only two possible outcomes, either it is successful, or it is not, so binary outcomes. For each call, the probability of a success or failure is the same, which means that the trials are independent, having the same value of p. And the number of trials, which is 50, is fixed. This means that this is a binomial distribution.
b. Find the mean and standard deviation of X.
The mean is:
[tex]E(X) = np = 50*0.02 = 1[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.02*0.98} = 0.9899[/tex]
The mean is 1 and the standard deviation is 0.9899.
c. Find the probablity of P(X>or equal to 48)
This is:
[tex]P(X \geq 48) = P(X = 48) + P(X = 49) + P(X = 50)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 48) = C_{50,48}.(0.02)^{48}.(0.98)^{2} \approx 0[/tex]
[tex]P(X = 49) = C_{50,49}.(0.02)^{49}.(0.98)^{1} \approx 0[/tex]
[tex]P(X = 50) = C_{50,50}.(0.02)^{50}.(0.98)^{0} \approx 0[/tex]
So
[tex]P(X \geq 48) = 0[/tex]
What is the approximate circumference of the circle that has a center at (2, 1) and passes through the point (2, 5)?
A.) 8 units
B.) 13 units
C.) 25 units
D.) 50 units
Answers
Answer:
C. 25
Step-by-step explanation:
Have a great day!
You buy 4 pounds of steak at Store A for $25.50. Your friend buys 6 pounds
of steak at Store B for $40.25. Which store is cheaper?
O No answer text provided.
O They're the same
O Store A
O Store B
Question 3
Answers
Answer: To determine which store has the cheaper steak, you need to compare the price per pound of steak at each store. To do this, divide the total price by the number of pounds of steak at each store.
At Store A, the price per pound of steak is $6.38 because 25.50 / 4 = <<25.50/4=6.375>>6.375.
At Store B, the price per pound of steak is $6.71 because 40.25 / 6 = <<40.25/6=6.708>>6.708.
Therefore, Store A is cheaper because it has a lower price per pound of steak. The correct answer is Store A.
Step-by-step explanation:
A combination lock has four wheels in a row. Each wheel has the digits from 0 to 9 on it. How many different combinations are there?
(b)How many different combinations are there if we can only use each digit once?
Answers
Answer:
Step-by-step explanation:
a.10^4=10000
b.10×9×8×7=5040
50points! Select the correct answer.
The function is given by the table of values.
x: 1, 2, 3, 4
f(x): 5, 7, 11, 19,
If f(x) is shifted 5 units down to obtain g(x),
which table of values represents the function g?
A. x: -4, -3, -2, -1
g(x): 0 , 2, 6, 14
B. x: -4, -3, -2, -1
g(x): 5, 7, 11, 19
C. x: 1, 2, 3, 4
g(x): 0, 2, 6, 14
D. x: 1, 2, 3, 4
g(x): 10 , 12, 16, 24
Answers
Answer: B
Step-by-step explanation:
its B
Find the product
(b+2)(-b^2+4b-3b)
Answers
Step-by-step explanation:
=>(b*-b²)+(b*4b)-(b*3b)-(2*-b²)+(2*4b)-(2*3b)
=>-b³+4b²-3b²-2b²+8b-6b
=>-b³+b²-2b²+2b
=>-b³-b²+2b
Which sentence is incorrect?
A. -3 > -8
B. -4 > -7
C. -2/5=0.4
D. -5/2=0.4
Answers
Answer:
D
Step-by-step explanation:
Set V Is all do you need three digit numbers using the digits 1,2,3,4 and 5. Which set would be considered a subset V
Answers
The set that would be considered as subset V = {1,3,5} i.e set of odd numbers
What is a subset?A set A is a subset of another set B if all elements of the set A are elements of the set B. In other words, the set A is contained inside the set B. The subset relationship is denoted as A⊂B. A set is a collection of objects or elements, grouped in the curly braces, such as {a,b,c,d}. If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.
In the set 1,2,3,4,5 contains odd numbers and even numbers. But there are just 2 even numbers and 3 even numbers.
But the subset V of the numbers above must contain 3 numbers, this means that subset V will contain odd numbers from 1 to 5.
Therefore, This means that subset V = { 1,3,5}
learn more about subset from
https://brainly.com/question/13265691
#SPJ1
You have a four color spinner and a six color spinner. Both are spun at the same time. What are the total number of possible outcomes?
Answers
Answer:
24
all u have to do is draw out a tree diagram or multiply 6*4
write the product using exponents. 1/5 x 1/5 x 1/5 x 1/5 x 1/5
Answers
Answer: 1/5 with an exponent of 5.
hope this helps :)
1. Which of the following is a composite number?
A.47
B. 43
C. 41
D.49
Answers
Answer is D. 49
Answer:
D. 49
Step-by-step explanation:
Cooper has $200 in a savings account. The interest rate is 10% per year and is not compounded. How much interest will he earn in 1 year? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
Answer:
The interest is $20 per year
Step-by-step explanation:
Answer:
$20
Step-by-step explanation:
using the formula you gave, you can plug in the numbers, i=200 * .10 * 1 since you start with 200 dollars, have a 10% interest rate, and it has been one year, then solve to get 20
if you have any questions, leave them in the comments and i will try to answer them, if this helped, pls give brainliest
An Uber company charges $7.50 for the first mile and $1.10 for each additional mile. What is the Uber rate for 9 miles? Use r for the total rate and m for total miles.
Answers
Answer:
r = 7.50 + (1.10 × (m - 1))
r = 7.50 + (1.10 × (9 - 1))
r = 16.40
The total uber rate for 9 miles is $16.3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First-mile charge = $7.50
Additional charges after the first mile = $1.10
The total charge for 9 miles.
r = 7.50 + 1.10 x 8
r = 7.50 + 8.8
r = $16.3
Thus,
The total rate for 9 miles is $16.3.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
ype your answer ihto the box.
Ben bakes 30 cupcakes
A box holds 4 cupcakes
How many full boxes of cupcakes are there?
Answers
Answer:
7
Step-by-step explanation:
4 x 7 is 28
7 full boxes
random characters so I can submit this anwser to you
Answer:
90x+(-7y)=x+y
Step-by-step explanation:
i think
1. This week Tony practiced basketball 2 hours on Tuesday, 1 hours Wednesday, and 2 hours on Friday. Next
week Tony will practice basketball for the same number of hours Tuesday, Wednesday, and Friday. What is
the total number of hours Tony will practice basketball over the 2 weeks?
Answers
For 2 weeks tony will spent time for practice basketball is 10 hours.
How do you find time in math problems?The equation for calculating time is [Time = Distance Speed]. The distance may be calculated using the time formula [Distance = Speed Time].Work completed equals Time x Rate of Work. Work Rate is equal to One/Time. Time = 1 divided by the rate of work. If a task is completed across x days, then the amount of work completed in a single day is equal to 1/x.The Greenwich hour angle, abbreviated GHA, is used to define the Equation of Time as E = GHA (apparent Sun) - GHA (mean Sun) (1). E = right ascension of the fictional mean Sun - right ascension of the apparent (real) Sun is a different formula that is frequently used in textbooks.Given data :
1st week
= Tuesday = 2 hours
= Wednesday = 1 hour
= Friday = 2 hours
same for 2nd week
so total hours = 1st week + 2nd week
= 2 + 1 + 2 + 2 + 1 + 2
= 10 hours
Learn more about time refer to :
https://brainly.com/question/17146782
#SPJ1
Please complete part A.+ B. And show all work. Thank you for your help.
Answers
As part of a demographic study, a college administrator needed to survey a sample of students from the college. From each major offered at the college, the administrator randomly selected 5 percent of the students with that major to participate in the survey.
Required:
What is the best description of the type of sample selected by the administrator?
Answers
Answer:
Option D is correct
Step-by-step explanation:
The options for the question is
a)cluster sample
b)convenience sample
c)simple random sample
d)stratified random sample
e)systematic random sample
Solution
The sampling here comprises of students from all the major of college. Here the major can be considered as "strata" of the educational institute. Out of these, strata or majors five students are selected on random basis.
This is a form of stratified random sample
Hence, option D is correct
what do I do here..?
Answers
Answer:
Baking a cake is a chemical change.
Step-by-step explanation:
The baking powder or baking soda will undergo a chemical reaction. The heat helps baking powder or soda produce tiny bubbles of gas which makes the cake light and fluffy. That's why chemical reactions are involved in baking a cake.
verify the following -12/5 + 2/7 = 2/7 + -12/5
Answers
Answer:
yeah they are the same
Step-by-step explanation:
-2.11428571429
Step-by-step explanation:
By using the commutative property, regardless of how the numbers are listed using addition or multiplicaton, they will equal the same thing.
So, a+b=b+a, which is what is present for your question.
In the table, Pattern A uses the rule "add 12" and Pattern B uses the rule "add 3." Pattern A 0 12 24 36 48 Pattern B 0 3 6 9 12 Which statement is true? Every term in Pattern B is 4 times the corresponding term in Pattern A. Every term in Pattern B is 13 the corresponding term in Pattern A. Every term in Pattern B is 9 less than the corresponding term in Pattern A. Every term in Pattern B is 14 the corresponding term in Pattern A.
Answers
Answer:
D. Every term in Pattern B is 1/4 the corresponding term in Pattern A.
Step-by-step explanation:
Given
[tex]A:0\ 12\ 24\ 36\ 48[/tex]
[tex]B: 0\ 3\ 6\ 9\ 12[/tex]
Required
The true statement
Option D is true, and the proof is as follows.
The interpretation of D is:
[tex]B = \frac{1}{4}A[/tex]
When [tex]A = 0[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 0 = 0[/tex]
When [tex]A = 12[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 12 = 3[/tex]
When [tex]A = 24[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 24 = 6[/tex]
When [tex]A = 36[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 36 = 9[/tex]
When[tex]A = 48[/tex]
[tex]B = \frac{1}{4}A = \frac{1}{4} * 48 = 12[/tex]
Compare the calculated values with the given values of B, we have:
[tex]B: 0\ 3\ 6\ 9\ 12[/tex] --- Calculated
[tex]B: 0\ 3\ 6\ 9\ 12[/tex] --- Given
Hence, (d) is correct
Answer:
d yw
Step-by-step explanation:
i took the test
you can use a calculator if you want. No links please help this is very important i will give you brain thing if its correct
Answers
Answer:
6.36
Step-by-step explanation:
42.40x0.15=6.36
....
Answer:
$6.36
Step-by-step explanation:
42.4 x 0.15 = 6.36
Finding area of composite figure
Answers
Answer:
73
Step-by-step explanation:
so basically this process is rather easy, okay what u have to do is find the area but since u cant u just have to try your best and go over the answer with a friend, oh you have none? Sorry for assuming, so just ask siri if you have 0 friends, the formula should look a little like this:
A=l*w or A=b*h
which than u would have to add up the circumference (sorry for not mentioning that earlier) so the new formula would be a little like this
A+C=
than thats your answer (it should be 12.)
need help asappppppp
Answers
Answer:
what do you need help with
Step-by-step explanation:
in order for me to answer you need to pit the problem
Which ordered pair is not graphed below? Choose 1 answer
Answers
Answer:
D. (7, -7)
Step-by-step explanation:
The only coordinates on the coordinate plane are:
(1, 7 ), (-7, 1 ), and (-7, 7).
Dale has $1,000 to invest. He has a goal to have $2,400 in this investment in 12 years. At what annual rate compounded continuously will Dale reach his goal?
Answers
Answer:
9%
Step-by-step explanation:
Given that
The invested amount is $1,000
The future value is $2,400
The time period is 12 years
We need to find out the annual rate that compounded continously
So,
As we know that
Amount = Present value × e^(rate × time)
$2,500 = $1,000 × e^(rate × 12)
2.5 = e^(rate × 12)
ln 2.5 = 10r
ln 2.5 ÷ 10 = r
r = 9%
The access code of a garage door consists of 4 digits (0 through 9). All digits can be repeated.
Find the number of possible access codes.
Find the probability of randomly selecting the correct access code on the first try.
Find the probability of not selecting the correct access code on the first try.
Answers
Answer:
1
Step-by-step explanation:
a) The number of possible access codes is 1000.
b) The probability of randomly selecting the correct access code on the first try is 1/1000
c) The probability of not selecting the correct access code on the first try is 999/1000.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
a) There are 10 digits from 0 to 9.
First digit= 10 ways
Second digit= 10 ways
Third Digit = 10 ways
Then, possible outcomes
= 10 x 10 x 10
= 1000
b) Exactly 1 out of 1000 codes will be correct
Favorable outcomes= 1
so, probability of randomly selecting the correct access code on the first try
= 1/1000
c) The probability of not selecting the correct access code on the first try.
=1- 1/1000
= 999/1000
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ2
Subtract the sum of 9 3/4 and 3 1/8 from 18 7/16
A. 5 9/16
B. 5 3/4
C. 6 9/16
D. 6 3/4
help pls
Answers
Answer:
A
Step-by-step explanation:
hope you have a great day!!
(0.4+ 1.6) x 6 what is it please help
Answers
Answer:
12
Step-by-step explanation:
(0.4+ 1.6) x 6 = 2 x 6 = 12
Answer:
12
Step-by-step explanation:
(0.4 + 1.6) x 6
(2) x 6
12
If 10x =5 what is x
Answers
Answer:
1/2
Step-by-step explanation: