The given series is convergent and the first term is 4 and the common ratio is -0.5 and the sum of the series is 8/3 .
The given series is 4 - 4/2+ 4/4 - 4/8 +...
We can see that the first term of the geometric series is 4
Hence a = 4
The second term is -4/2 and the third term is 4/4
Hence r = 4 ÷ (-4/2) = -4/2 ÷ 4/4 = - 1/2 or -0.5
Since the common ratio is less than 1 we can say that the series is convergent.
Now for a convergent series we know that the sum of the terms of the series is equal to
S = a / (1-r)
or, S = 4 / (1-(-0.5))
or, S = 4 / 1.5
or, S = 8/3
Hence the sum of the convergent series is 8/3 .
Both the ratio test and the root test are based on a comparison with a geometric series and hence function in comparable scenarios.
In fact, if the ratio test works (that is, if the limit exists and is not equal to 1), then so does the root test; the contrary is not true. The root test is thus more broad, although in practise, determining the limit for regularly encountered kinds of series is frequently challenging.
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The equation of line m is
5x - 3y = 2.
What is the slope of a line that is perpendicular to line m?
Enter your answer in the box as a fraction in simplest form.
Jack decides to estimate the volume of a coffee cup by modeling it as a right cylinder. Jack measures its radius as 2.2 cm and its volume as 117 cubic centimeters. Find the height of the cup in centimeters. Round your answer to the nearest tenth if necessary.
Please answer these questions!
Answer:
Step-by-step explanation:
1)
She takes medicine at the moment 0
24(1/2)^0
24 · 1
24 mg
2)
24 (1/2)^1
24 (1/2)
12 mg
5, Brittney is conducting an experiment in class to determine the probability of getting four heads when flip-
four coins. What is the sample space of her experiment?
Answer:
16 possible outcomes
Step-by-step explanation:
The sample space of Brittney's experiment is the set of all possible outcomes of flipping four coins. Since each coin can either land on heads or tails, there are two possible outcomes for each coin. Therefore, there are a total of 2^4 = 16 possible outcomes for the experiment. These outcomes can be represented as a list, with each outcome represented by a string of four "H"s and "T"s, where "H" represents a heads and "T" represents a tails. For example, one possible outcome of the experiment could be "HHHT" (two heads, one tails, one heads), and another could be "TTTT" (four tails). The complete sample space of Brittney's experiment would include all 16 possible outcomes.
pls help this is due in 5 minutes!!!!!
The answer is B & D
Answer:
Step-by-step explanation:
i'd say the 2nd one and the last one
Because the 2nd one is a straight line that is pointing up showing that it's increasing.
And the last one because the line is going up meaning it's increasing
If Ellie has 3 more quarters than nickels and they have a combined value of 195 cents, how many of each coin does she have?
Using system of linear equation, the number of quarter is 7 and nickel is 4
System of Linear EquationSystem of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
To solve this problem, we need to write a system of linear equation.
let;
x = quartersy = nickels1 nickel = 5 cent
1 quarter = 25 cent
25x + 5y = 195 ... eq(i)
x = 3 + y ...eq(ii)
Put eq(ii) into eq(i)
25(3 + y) + 5y = 195
75 + 25y + 5y = 195
75 + 30y = 195
30y = 195 - 75
30y = 120
y = 4
put y = 4 in equation (ii)
x = 3 + 4
x = 7
The number of quarter is 7 and nickel is 4
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This is a missing assignment please help.
Answer:
The answer is A:22
We can start by finding out 5^2 which is just 5 times 5 because it is 5 times itself 2 times (as the little two tells us how many times to multiply 5 by itself). The answer is 25. 25-3=22
5×5-3
=25-3
=22 is the answer
The history of melting point data for a certain product indicates that the long-term average melting point has been 95 degrees. It is desired to test to see if the average is still 95 degrees or whether it has changed. a) Set up the statistical test at a 0.01 significance level and draw the conclusion using the sample data that follows: the average of a sample of 16 randomly chosen melting points is 94.32 degrees. Assume that the distribution of melting points is normal with σ = 1.20 . b) What is the critical region for this test, both in terms of the sample average and the z-score?
As per the desire to test to see if the average is still 95 degrees or whether it has changed. The results will be as follows:
a) The null hypothesis and the alternative hypothesis must be identified before we can set up the statistical test at a 0.01 significance level. The average melting point, which is still 95 degrees, has not altered, according to the null hypothesis. The other theory is that the average melting point, which was 95 degrees, has changed.
Next, we must establish the test's critical value. The critical value will be the amount that corresponds to a p-value of 0.01 because we are choosing a significance level of 0.01. We may use the usual normal distribution to determine the critical value because we are presuming that the melting point distribution is normally distributed with a standard deviation of 1.20.
Using the sample data, we discover that a sample of 16 melting points has an average temperature of 94.32 degrees. A one-sample z-test can be used to examine whether this sample average differs noticeably from the 95 degree long-term average.
where x is the sample average (94.32), is the long-term average (95), σ is the standard deviation of the melting points (1.20), and n is the sample size (16).
Plugging these values into the formula, we get:
z = (94.32 - 95) / (1.20 / √16) = -0.83
We are unable to rule out the null hypothesis because the z-score is smaller than the critical value. As a result, we draw the conclusion that 95 degrees still serve as the average melting point.
b) The range of values that would be deemed statistically significant at the 0.01 significance level constitutes the critical region for this test. The range of values that would be regarded as significantly different from the long-term average of 95 degrees is the critical zone in terms of the sample average. The range of values that would be associated with a p-value of less than 0.01 is known as the critical zone in terms of the z-score.
The required z-score value for a one-sided test with a significance level of 0.01 is 2.326. Therefore, any number more than 2.326 is the critical zone in terms of the z-score. This relates to a range of values that are significantly higher than 95 degrees based on the sample average.
The essential z-score values for a two-sided test with a 0.01 significance level are -2.326 and 2.326. Therefore, any value between -2.326 and 2.326 constitutes the key zone in terms of the z-score. This relates to a range of values that are significantly higher or lower than 95 degrees, based on the sample average.
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It is known that the probability p of tossing heads on an unbalanced coin is either 1/4 or 3/4. The coin is tossed twice and a value for Y , the number of heads, is observed. For each possible value of Y , which of the two values for p (1/4 or 3/4) maximizes the probability that Y = y? Depending on the value of y actually observed, what is the MLE of p?
On solving the provided question we can say that NILE is not unique for this case
What is Probability?Probability is the possibility or chance that something will happen. Probability = how many different paths there are to success/the total number of events that might occur. A coin flip, for instance, has a 50% chance of coming up heads since there is only one method to acquire a head and there are a total of two possible outcomes (a head or tail). P(heads) = 1/2 is the formula.
Note: the probability is equal to the mass function for Y :2
since, ML criteria, we choose p which maximizes the probability.
If Y 0, L (p) is maximized at p 0.25.
If Y 2, L (p) is maximized at p 0.75.
[tex]But if Y 1, L (p) has the same value at both as shown above; that is,[/tex]
L (0.25) L (0.75) for y — 1.
NILE is not unique for this case
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Afia bought shoes that were on sale for `30\%` off the regular price.
Afia saved `\$12`.
What was the regular price of the shoe
In case whereby Afia bought shoes that were on sale for 30% off the regular price and Afia saved $12` the regular price of the shoe is $40.
How can this be calculated?It should be noted that the Regular price can be described as the price at which the goods or services are openly and actively sold with the producer or supplier to the public with repect to the continuing basis for a substantial period of time.
The amount of savings can be divided by the percentage off to find the
Since the sale for 30% off the regular price, then regular price.
(12/0.30) = 40
hence the regular price was $40
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The population of a country increases at a rate proportional to the number of inhabitants. f is the population which doubles in 20 years, then the population will triple in approximately
The population of a country increases by 31 years approximately.
differentiation:
To differentiate is to identify the differences between things, and to discriminate among them. There are a number of simple rules which can be used to allow us to differentiate many functions easily.
If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the derivative of y (with respect to x) is written dy/dx, pronounced "dee y by dee x".
Let population =x, at time t years.
Given [tex]\frac{dx}{dt} \alpha X[/tex]
⇒ [tex]\frac{dx}{dt}=Kx[/tex]
where k is a constant of proportionality
or [tex]\frac{dx}{x} =Kdt[/tex]. Integrating, we get lnx=kt+lnc
⇒ [tex]\frac{x}{c}=e^{Kt}[/tex] or [tex]X=ce^{kt}[/tex]
If initially, i.e., when time t=0,x=x0 then xo=ce^0=c
[tex]X-Xoe^{kt}[/tex]
Given X=2Xo t=20 then,
[tex]2Xo=Xoe^{20k} \\\\= > 2=e^{20k} \\[/tex]
ln2=20k---(1)
To find t, when t triples X=3Xo
[tex]3Xo=Xoe^{kt} \\\\3=e^{kt}[/tex]
ln3=kt(2)---(2)
Dividing equation (2) by (1) then
[tex]\frac{t}{20} =\frac{ln3}{ln2}[/tex]
or
[tex]t=20*\frac{ln3}{ln2}[/tex]
t=20*1.5849
t=31 years (approx)
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what is the square root of 10
Answer:
3 or 3.16227766017
Step-by-step explanation:
multiply by 6, 7, 8, and 9 fill in the puzzle so that the product in each column and row is the same
Multiply by 6, 7, 8, and 9 fill in the puzzle so that the product in each column and row is the same is 3024.
What is Multiply?
Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.
[tex]\begin{aligned}& 6 \times 8=48 \\& 6 \times 9=54 \quad \text { find the common } \\& \text { multiple } \\& 9 \times 7=63 \quad 6 \times 7 \times 8 \times 9=3024 \\&\end{aligned}[/tex]
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One card is selected at random from a deck of cards. What is the probability that the card selected is a spade or a queen?
the probability that the card selected is a spade or a queen is given by P= 0.25
In a deck, there are:
total card = 52
spade = 13
Required
Determine the probability that a selected card is a spade
This is represented as: P(Spade) and it is calculated using:
P= card / spade
Substitute 13 for Spade and 52 for Cards
P = 13/52
= 0.25
Hence, the required probability is 0.25
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The distance between the points (10, -2) and (4, 6) is 10.
True
False
=
Answer:
True
Step-by-step explanation:
Use the distance formula: x^2 + y^2 = d^2; where d=distance
x = x2 - x1
y = y2 - y1
(10, -2), (4, 6) ==> (x1=10, y1=-2), (x2=4, y2=6)
x = 4 - 10 ==> plug in 4 for x2 and 10 for x1
x = -6
y = 6 - (-2) ==> plug in 6 for y2 and -2 for y1
y = 6 + 2
y = 8
(-6)^2 + (8)^2 = d^2 ==> plug in x and y back into the distance formula
36 + 64 = d^2
100 = d^2 ==> simplify
d = [tex]\sqrt{100}[/tex]
distance = 10 ==> True
If a+b=1, prove by induction that a^3+b^3 is bigger or equal to ¼.
To prove that a^3+b^3 is bigger or equal to ¼, we can use mathematical induction. This involves two steps:
Show that the statement is true for the base case of a and b (i.e., when a and b are equal to some specific values).Assume that the statement is true for some arbitrary values of a and b (i.e., the "inductive hypothesis"). Then, show that it must also be true for the next values of a and b (i.e., a+1 and b+1).To begin, let's consider the base case where a and b are equal to 0. In this case, a^3+b^3 is equal to 0^3+0^3, which is 0. Since 0 is greater than or equal to ¼, the statement is true for the base case.
Next, we can assume that the statement is true for some arbitrary values of a and b (i.e., the inductive hypothesis). That is, we can assume that a^3+b^3 is bigger or equal to ¼.
To complete the proof, we need to show that a^3+(b+1)^3 is also bigger or equal to ¼. To do this, we can use the fact that (a+1)^3 = a^3+3a^2+3a+1. Since the inductive hypothesis states that a^3+b^3 is bigger or equal to ¼, we can say that a^3+(b+1)^3 = a^3+b^3+3a^2+3a+1 is also bigger or equal to ¼.
Therefore, by mathematical induction, we have shown that a^3+b^3 is bigger or equal to ¼ for all values of a and b.
A particle moves along line segments from the origin to the points (2, 0, 0), (2, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field
F(x, y, z) = z2i + 3xyj + 5y2k.
Use Stokes' Theorem to find the work done.
Refer to the images uploaded. Please let me know if this answer works out for you. I also would appreciate a rate :)
Rewrite as equivalent rational expressions with denominator
assume that a wild-type sequence is 5'agcctac3'. which of the following sequences might be produced by a transversion? correct!
Transversion is known as point mutation in DNA.
Transversion is a term used in molecular biology. It refers to a point mutation in DNA in which a single (two ring) purine (A or G) is changed for a (one ring) pyrimidine (T or C), or vice versa. A transversion can be spontaneous, or it can be caused by ionizing radiation or alkylating agents. It can only be reversed by a spontaneous reversion.
So, here 5'AGCCTAC3' we can replace (A or G) with (T or C)
So, the answer should be :
5'ATCCTAC3'
Here we have replaced G with T and other things are same
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The full question will be like this
Assume that a wild-type sequence is 5'AGCCTAC3'. Indicate the sequence that might be produced by a transversion. Which of the following sequences might be produced by a transversion?
A) 5'AGTCTAC3'
B) 5'AGCCGCCGCCGCCTAC3'
C) 5'AGCCCAC3'
D) 5'ATCCTAC3'
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L'expression -6x + 8 est la forme réduite de :
-3x + 3x + 2 *4 ou 2x - 8x *5 + 3 ou 2x - (5x - 6) + (-3x + 2) ou - (3x + 5) + (-2x + 3) - x
Answer:
2x - (5x - 6) + (-3x + 2)
Step-by-step explanation:
L'expression -6x + 8 est la forme réduite de:
-3x + 3x + 2 *4
= 0x + 8
= 8
pas vrai
__________________________
2x - 8x *5 + 3
= 2x - 40x + 3
= -38x + 3
pas vrai
__________________________
2x - (5x - 6) + (-3x + 2)
=2x - 5x + 6 - 3x + 2
= -6x + 8
Corriger
__________________________
- (3x + 5) + (-2x + 3) - x
= - 3x - 5 - 2x + 3 - x
= - 6x + 2
pas vrai
(veuillez pardonner mon français.)
what is 24divided by 2
Answer:12
Step-by-step explanation:
24/2 = 12 bc 12*2=24
Find the solution of y = log(x + 3) and y = 1.
Answer:
x=7
Step-by-step explanation:
y = log(x + 3) and y = 1.
Substitute y =1 into the equation
1 = log(x + 3)
Raise each side to base 10 since log (x+3) has a base 10 implied
10^1 = 10^ log(x+3)
10 = x+3
Subtract 3 from each side
10-3 = x+3-3
7 =x
henry flips 10 coins then lays them on a desk. he then chooses one of the coins at random, and if it is tails, he flips it to heads.
As per the concept of probability, the probability of getting head is 99.5%.
The term probability in statistics is known as the possible way of getting the particular event.
Here we have given that
And we need to find the probability of getting head.
Here we know that the number of coins is 10.
So, the sample space for the 10 coins is calculated as,
Here we already know that for each of the 10 coin tosses, we have either a head (H) or a tail (T).
so, the total number of probability of 10 coins is 210 strings in the sample space.
Here we know that the only option of all tails doesn't have head in it.
So, the number tosses that have head in it is calculated as,
=> 210 - 1
=> 209
Therefore, the probability is calculated as,
=> P = 209/210
=> P = 0.995
Therefore, the probability in percentage is 99.5%
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I had to re-put the question for you shining dream
The equation that correctly represents the given problem is;
¹/₂p - 2 = 18
How to solve algebra word problems?We are told that p is the time it takes Tomás to bike to the park.
Now, we are given that;
Time taken by Tomás to bike to the community center = 2 minutes less than half the time it takes him to bike to the city park.
Time taken by Tomás to bike to the community center = 18 minutes
Thus, correct equation can be expressed as;
¹/₂p - 2 = 18
And if we need to solve p, we can just make p the subject of the equation and solve accordingly.
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The complete question is;
Which equation represents this problem?
The time it takes Tomás to bike to the community center is 2 minutes less than half the time it takes him to bike to the city park. It takes Tomás 18 minutes to bike to the community center.
Let p = the time it takes Tomás to bike to the park.
Prove that for any natural number n: The number 3^n+2 - 2^n+2 + 3^n - 2^n is divisible by 10.
Answer: (___)•10
By algebra properties, the power expression 3ⁿ⁺² - 2ⁿ⁺² + 3ⁿ - 2ⁿ is divisible by 10 as it is equivalent to (3ⁿ - 2ⁿ⁻¹) · 10.
How to determine if a given expression is divisible by a given number
According to number theory, a natural number is divisible by another natural number if the result is a natural number. In this case we must determine if a power expression is divisible by 10 according to algebra properties.
First, write the whole expression:
3ⁿ⁺² - 2ⁿ⁺² + 3ⁿ - 2ⁿ
Second, use algebra properties until the multiple is found:
(3ⁿ⁺² + 3ⁿ) + (- 2ⁿ⁺² - 2ⁿ)
3ⁿ · (3² + 1) + 2ⁿ · (- 2² - 1)
3ⁿ · 10 - 2ⁿ · 5
3ⁿ · 10 - 2ⁿ⁺¹⁻¹ · 5
3ⁿ · 10 - 2ⁿ⁻¹ · 10
(3ⁿ - 2ⁿ⁻¹) · 10
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What is 71/5 as a decimal
Answer:
Step-by-step explanation:
71/5 70/5 = 14 with 1/5 = .2 this together = 14.2
1. If a thief tried 80 combinations to open the safe lock the
first hour, then 40 every hour after, how many hours would it
?
take before trying them all?
The total number of hours [h] that it will take to try the possible combinations are → h = {(x/40) - 2} + 1.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a thief tried 80 combinations to open the safe lock the
first hour, then 40 every hour after that.
Assume that their are total of [x] possible combinations for the lock. Then we can write the expression for the total number of hours [h] that it will take to try the possible combinations as -
x = 80 + 40(h - 1)
(x - 80) = 40(h - 1)
(h - 1) = (x - 80)/40
(h - 1) = {(x/40) - 2}
h = {(x/40) - 2} + 1
Therefore, the total number of hours [h] that it will take to try the possible combinations are → h = {(x/40) - 2} + 1.
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Which of the following statements is true concerning f(x) = x2 - 22 - 24
Please help !
What is the inverse of this function f(x)=-1/2sqrtx+3, x>_-3
The inverse of the function f(x) = -1/2√x + 3, x ≥ -3 is y = (6 - 2x)²
How to determine the inverse of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x)=-1/2sqrtx+3, x>_-3
Express properly
So, we have
f(x) = -1/2√x + 3, x ≥ -3
Write out the function
f(x) = -1/2√x + 3
Express as an equation
y = -1/2√x + 3
Swap x and y
This gives
x = -1/2√y + 3
Subtract 3 from both sides
-1/2√y = x - 3
So, we have
√y = 6 - 2x
Take the square of both sides
y = (6 - 2x)²
Hence, the inverse is y = (6 - 2x)²
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alan booker's service charges: basic charge, 8 bills paid, a lost card replacement, and four atm transactions, 2 national and 2 out-of-network.
Total service charges is 23.45 when Alan Booker's service fees included a basic charge is 6.95.
Given that,
Alan Booker's service fees included a basic charge, the payment of eight bills, the replacement of a lost card, and four atm transactions—two in-network and two out-of-network.
We have to find the total service charges.
We know that,
Alan borker
Basic charge is 6.95
Bill payments is 3×0.5= 1.5
Card replacement is 5
ATM Transactions
National is 2×2 =4
Out of network is 2×3 =6
Total service charges is 23.45
Therefore, Total service charges is 23.45 when Alan Booker's service fees included a basic charge is 6.95.
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