Answer:
heterozygous (Aa) are 0.085 = or 8.54%
Step-by-step explanation:
The heterozygous individuals are carriers of the sickle cell trait. They have a genotype of Aa and are represented by the 2pq term
in the H-W equilibrium equations.
According to the question 0.2% of the population is affected with sickle cell anemia, thus q^2
= 0.2% = 0.002 in decimal. So, q =
sqr(q^2)
or sqr(0.002) =
0.04472
and p + q = 1, thus p = 1 – q = 1 – 0.04472 = 0.96
Thus, A allele has a frequency of 0.96 and the a allele has a frequency of 0.04472. Therefore, the
percentage of the population that is heterozygous (Aa) and are carriers is = 2pq = 2× 0.04472× 0.96 =0.085 = or 8.54%
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the equation or formula for the indicated variable. T= 2 r π h + 2 π r ^2; for h
For this case we have the following equation:
[tex]T = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]
We must solve the equation for the variable "h":
We subtract [tex]2 \pi * r ^ 2[/tex] from both sides of the equation:
[tex]T-2 \pi * r ^ 2 = 2 \pi * r * h[/tex]
We divide by [tex]2 \pi * r[/tex] on both sides of the equation:
[tex]\frac {T-2 \pi * r ^ 2} {2 \pi * r} = h\\h = \frac {T} {2 \pi * r} - \frac {2 \pi * r ^ 2} {2 \pi * r}\\h = \frac {T} {2 \pi * r} -r[/tex]
Answer:
[tex]h = \frac {T} {2 \pi * r} -r[/tex]
Francis invested $20,000. Some was invested in bonds that made a 4% profit, and the rest was put into stocks that made an 8% profit. How much did Francis invest in bonds if his total profit on both types of investments was $1,120?
Answer:he invested $12000 in bonds and $8000 in stocks.
Step-by-step explanation:
Let x represent the amount that was invested in the bond that made 4% profit.
Let y represent the amount that was invested in the stock that made 8% profit.
Francis invested $20,000. Some was invested in bonds that made a 4% profit, and the rest was put into stocks that made an 8% profit. This means that
x + y = 20000
Profit made from the amount invested in the bond is
4/100 × x = 0.04x
Profit made from the amount invested in stock is
8/100 × y = 0.08y
if his total profit on both types of investments was $1,120, it means that
0.04x + 0.08y = 1120 - - - - - - - - - - 1
Substituting x = 20000 - y, it becomes
0.04(20000 - y) + 0.08y = 1120
800 - 0.04y + 0.08y = 1120
- 0.04y + 0.08y = 1120 - 800
0.04y = 320
y = 320/0.04 = 8000
x = 20000 - y = 20000 - 8000
x = $12000
Francis invested $12,000 in bonds.
Let's denote the amount invested in bonds as B and the amount invested in stocks as S.
We can set up a system of equations based on the given conditions:
1. B + S = 20,000 (Equation 1) - Total investment amount
2. 0.04B + 0.08S = 1,120 (Equation 2) - Total profit
We can solve this system of equations to find the amount invested in bonds B.
From Equation 1, we can express S in terms of B:
S = 20,000 - B
Now, substitute this expression for S into Equation 2:
0.04B + 0.08(20,000 - B) = 1,120
Let's solve for B:
0.04B + 1,600 - 0.08B = 1,120
-0.04B = 1,120 - 1,600
-0.04B = -480
Now, divide both sides by -0.04:
[tex]\[B = \frac{-480}{-0.04} \][/tex]
B = 12,000
So, Francis invested $12,000 in bonds.
Calculate the following derivatives. Assume y is a function of t . Use Y for the derivative of y . (a) d dt y7= Incorrect: Your answer is incorrect. (b) d dt y3e4t= Incorrect: Your answer is incorrect. (c) d dt t7 cos(y6)=
Answer:
(a) d dt y7=7Y^6
(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}
(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5
Step-by-step explanation:
We calculate the following derivatives. Since these are complex derivatives, we also calculate the formula for complex derivatives. We use Y for the derivative of y . Therefore, we calculate and we get
(a) d dt y7=7Y^6
(b) d dt y3e4t=3Y^2e^{4t}+4Y^3e^{4t}
(c) d dt t7 cos(y6)=7t^6 cos(y6)+t^7(-sin(y^6))·6Y^5
Classify each number below as a rational number or an irrational number. −17.6 , 81 , 15π , (square root −29), 13/14
Answer:
Rational Numbers
−17.6 (-176/10)
81
13/14
Rational Numbers
15π
square root −29
Step-by-step explanation:
Rational Numbers are those numbers which can be written as Ratio of two numbers.
Irrationational Numbers are those which cannot be written as ratio of two numbers. such as recurring numbers.
e.g 0.26262626.........
Select the graph of the solution set that would represent the following expression. 2 ( x + 1 ) > 3 x − 2
Answer:
B
Step-by-step explanation:
x>4
Answer:
None of the options are right. The correct answer is x < 4
Step-by-step explanation:
2(x + 1) > 3x - 2
2x + 2 > 3x - 2
2 > x - 2
4 > x
x < 4
While performing intravenous drug injections, it is necessary to decrease the angle of the needle once a flashback is seen in the intravenous catheter to?
Answer: avoid passing through the vein.
Step-by-step explanation:
Identify the type of sampling used. A statistics student is trying to determine the proportion of all people who own cell phones. He interviews everyone in his apartment building to determine who owns a cell phone. What sampling technique was used?
Answer:
Convenience Sampling
Step-by-step explanation:
The given situation indicates the non-probability sampling because the sampling units are not selected at random and every unit in population has unequal chance of being selected. Convenience sampling is a type of non-probability sampling in which the sampling unit close to interviewer are selected. In the situation statistics student interviews the individual that resides in his building, so it is a convenience sampling.
Final answer:
The statistics student used convenience sampling, a non-probability method, by interviewing individuals in his apartment building to determine cell phone ownership. This method is subject to sampling bias and does not provide generalizable results.
Explanation:
The type of sampling used in the scenario where a statistics student interviews everyone in his apartment building to determine who owns a cell phone is called convenience sampling. This non-probability sampling method involves choosing participants because they are convenient to the researcher, not because they are randomly selected or necessarily representative of the larger population. Therefore, while it is easy and cost-effective, the results of convenience sampling cannot be reliably generalized to the wider population due to potential sampling bias.
40 points!! What is the limit of the infinite series?
As n goes onto infinity, the expression [tex]\frac{3n^5}{4n^5+1}[/tex] will approach [tex]\frac{3}{4}[/tex]. Note the 3 and 4 come from the leading coefficients of the numerator and denominator respectively. This only works because the degrees for the numerator and denominator are both the same (both are 5).
Since [tex]\frac{3n^5}{4n^5+1}[/tex] is not approaching 0 when n gets really large, adding on successive terms of these values will have the infinite sum diverge. After some very large n, we are effectively adding on 3/4 each time and that just makes the overall sum keep growing forever.
Answer: The sum divergesFinal answer:
The limit of an infinite series depends on whether it converges or diverges. If it converges, the limit is the value the series approaches as the number of terms approaches infinity. If it diverges, it does not have a finite limit.
Explanation:
The limit of the infinite series depends on the specific series being referred to. To find the limit of an infinite series, you need to determine if it converges or diverges. If the series converges, then the limit is the value that the series approaches as the number of terms goes to infinity. If the series diverges, then it does not have a finite limit.
For example, consider the series 1/2 + 1/4 + 1/8 + ... This is a geometric series with a common ratio of 1/2. It converges to the value of 1, so the limit of this series is 1.
Some various tests and properties can be used to determine if a series converges or diverges. Some common ones include the ratio test, the root test, and the comparison test.
The Cookie Monster stole 4 cookies before getting caught by grandma Cookie Monster.He continues stealing cookies when he gets caught. If he steals no less than 10 cookie how many more cookies does he need to steal?
Answer:
Cookie monster needs to steal at least 6 cookies more.
Step-by-step explanation:
Given:
Number of cookies already stole = 4
Total number of cookies he wants to steal [tex]\geq 10[/tex]
We need to find how many cookie he needs to steal more.
Solution:
Let number of cookies he needs to steal more be 'x'.
Now we can say that;
Number of cookies already stole plus number of cookies he needs to steal more should be greater than or equal to Total number of cookies he wants to steal
framing in equation form we get;
[tex]4+x\geq 10[/tex]
Now using Subtraction property of Inequality we will subtract both side by 4 we get;
[tex]4+x-4\geq 10-4\\\\x\geq 6[/tex]
Hence Cookie monster needs to steal at least 6 cookies more.
The Cookie Monster needs to steal at least 6 more cookies after getting caught.
Explanation:The Cookie Monster stole 4 cookies initially before getting caught. If he steals no less than 10 cookies each time, we need to determine how many more cookies he needs to steal. Let's represent the number of cookies he needs to steal as x. The equation to represent this situation is: x >= 10 - 4.
Simplifying the equation, we have x >= 6. Therefore, the Cookie Monster needs to steal at least 6 more cookies after getting caught.
Learn more about Cookie Monster steals cookies here:https://brainly.com/question/14543986
#SPJ12
Each person in a group of twenty people at a hotel orders one meal chosen from oatmeal, eggs, or pancakes and one hot beverage chosen from coffee or tea. One person will be selected at random from the twenty people. What is the sample space for the meal and beverage for the person selected?
1. {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)}2. {(oatmeal, pancakes), (oatmeal, eggs), (eggs, pancakes), (coffee, tea)}3. {(coffee, tea, oatmeal), (coffee, tea, eggs), (coffee, tea, pancakes)}4. {oatmeal, coffee, pancakes, eggs, tea}5. {(oatmeal, eggs, pancakes), (coffee, tea)}
Answer:
{(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)
Step-by-step explanation:
Sample space is the set of all possible outcomes of an experiment.
Here a person should choose one meal and a hot drink. Hence, each element in the set includes one meal and one beverage, which eliminates 2,because it indicates person choses oatmeal and pancakes which has no beverage. Sets should have elements in pairs so ,We should eliminate 3 ,4,5.
As a result person can choose
oatmeal as meal and coffee as drink
oatmeal as meal and tea for drink
eggs for meal tea for drink
eggs for meal coffee for drink
pancakes for meal tea for drink finally
pancakes for meal and coffee for drink
The sample space of a distribution is the list of possible options.
The sample space for the meal and the beverage is (a) {(oatmeal, coffee), (oatmeal, tea), (eggs, coffee), (eggs, tea), (pancakes, coffee), (pancakes, tea)
From the question, the meals are:
Meals: Oatmeal, Eggs, Pancakes
And the beverages are:
Beverages: Coffee, Tea
This means that, the available selections are:
Oatmeal and CoffeeOatmeal and TeaEggs and CoffeeEggs and TeaPancakes and CoffeePancakes and TeaHence, the sample space is (a)
Read more about sample space at:
https://brainly.com/question/14372246
A bag contains 5 red marbles, 10 blue marbles, and 14 yellow marbles. If Jen selects a marble from the bag without looking, what is the probability that she will not pull a red marble
Answer:
The answer to your question is 0.83 or 83%
Step-by-step explanation:
Data
5 red marbles
10 blue marbles
14 yellow marbles
Process
1.- Calculate the total amount of marbles
Total amount = 5 red + 10 blue + 14 yellow
Total amount = 29 marbles
2.- Calculate the amount of marbles that are not red
No red marbles = 10 + 14
= 24 marbles
3.- Calculate the probability
Probability of not pulling a red marble = [tex]\frac{no red marble}{total amount of marbles}[/tex]
Probability of not pulling a red marble = [tex]\frac{24}{29} = 0.83 or 83%[/tex]
I need help with this!!!!
Options are,
A: 1/3
B: 3/1
C: 1/4
D: 2/4
Answer:
D: 2/4
Step-by-step explanation:
Usually when we talk about a point partitioning a segment, we are interested in the ratio of the first segment to the second:
BC : CD = 2 : 2 = 1 : 1
Since this is not an answer choice, we need to "reverse engineer" the answer list to see if we can find an answer that corresponds to a reasonable interpretation of the question.
__
None of the segments is 3 units long, so neither of answer choices A or B makes any sense.
While segment BD is 4 units long, there is no segment that is 1 unit long, so answer choice C makes no sense, either.
There are segments that are 2 units long and a segment that is 4 units long, so if we interpret the question to be "what is the ratio of BC to BD?" then answer choice D is appropriate.
Assume that the following statements are true.
A. If Trisha is drinking water, then it is dinnertime.
B. If it is lunchtime, then Rob is drinking milk and nothing else.
C. If it is dinnertime, then Anna is drinking iced tea and nothing else.
D. If it is breakfast time, then Sarah is drinking milk and nothing else.
E. Trisha is drinking water.
Using only the information given above, determine if "Anna is drinking iced tea" must be true, may be true, or is not true. Explain your reasoning. Assume that the following statements are true.
A. If Trisha is drinking water, then it is dinnertime.
B. If it is lunchtime, then Rob is drinking milk and nothing else.
C. If it is dinnertime, then Anna is drinking iced tea and nothing else.
D. If it is breakfast time, then Sarah is drinking milk and nothing else.
E. Trisha is drinking water.
Based on the provided conditional statements, if Trisha is drinking water, then it's dinnertime. Additionally, if it's dinnertime, then Anna is drinking iced tea. Given that Trisha is drinking water, we can conclude that Anna is drinking iced tea.
Explanation:The question here is dealing with conditional statements in logic. It's important to understand that if a conditional statement is true, and the first part (the condition) is true, then the second part must be true as well. In this case, Statement A states that if Trisha is drinking water, then it is dinnertime. So, if Trisha is drinking water (which is confirmed by Statement E), then it is dinnertime.
Statement C further adds to our understanding by stating that if it is dinnertime, then Anna is drinking iced tea and nothing else. Since based on Statements A and E, we know it is dinnertime, then following the logic from Statement C, we can conclude that Anna is drinking iced tea.
Learn more about Conditional Statements here:https://brainly.com/question/36974334
#SPJ3
Suppose the following are given to you: D ( q ) = − 0.00029 q 2 − 0.0716 q + 557 C ( q ) = 81 q + 18300 Find the profit function.
Profit function= 81q +18300+0.00029q2+0.0716q-557
Step-by-step explanation:A profit function shows the relationship between a company's total profit and output.
The profit function is equal to the company's total rebenue(TR) minus total cost of the company(TC).
Mahemathically,Profit = TR-TC.
Let D(q)= TC=-0.00039q2-0.0716q+557C(q)
Let TR= 81q +18300.
Profit=TR-TC
Profit =81q+18300-(-0.00029q2-0.0716q+557)
Profit=81q+18300+0.00029q2+0.0716q-557.
Which expressions are equivalent to 8 (negative 10 x + 3.5 y minus 7)? Select two options. Negative 80 x + 24.5 y minus 56 Negative 80 x + 28 y minus 56 80 x + 28 y + 56 4 (negative 20 x + 7 y minus 14) Negative 4 (negative 20 x + 7 y minus 14)
Answer:
B. Negative 80 x + 28 y minus 56
This is equivalent to -80x + 28y - 56
C. 4 (negative 20 x + 7 y minus 14)
This is equivalent to -80x + 28y - 56
Step-by-step explanation:
Let's find out the options that are equivalent to:
8 (negative 10 x + 3.5 y minus 7)
8 ( - 10x + 3.5y - 7) =
-80x + 28y - 56
Options:
A. Negative 80 x + 24.5 y minus 56
This is not equivalent.
B. Negative 80 x + 28 y minus 56
This is equivalent to -80x + 28y - 56
C. 4 (negative 20 x + 7 y minus 14)
-80x + 28y - 56
This is equivalent to -80x + 28y - 56
D. Negative 4 (negative 20 x + 7 y minus 14)
80x - 28y + 56
This is not equivalent.
Answer:
B. Negative 80 x + 28 y minus 56
This is equivalent to -80x + 28y - 56
C. 4 (negative 20 x + 7 y minus 14)
Step-by-step explanation:
Find the value of x. Round to the nearest degree.
Answer:
The answer to your question is 32.64°
Step-by-step explanation:
Data
hypotenuse = 19
adjacent side = 16
x = ?
Process
1.- To solve this problem use trigonometric functions.
The function that relates the adjacent side and the hypotenuse is cosine.
cos x = [tex]\frac{adjacent side}{hypotenuse}[/tex]
2.- Substitution
cos x = [tex]\frac{16}{19}[/tex]
3.- cos x = 0.842
4.- cos ⁻¹x = x = 32.64°
Consider the numbers 0, 10, 20, 30, and 40. Multiply each by 4 and compare the result to 60 to determine into which of the following intervals? What number can you multiply by 4 and then add 8 to the product to get?
a. 0 to 10.b. 10 to 20.c. 20 to 30.d. 30 to 40.
Answer:
Option (b) 10 to 20
Step-by-step explanation:
Let the number obtained between the interval be 'x'
Therefore,
according to the question:
multiplying the number with 4 and then adding 8 to it to get 60
thus,
mathematically, we get
4x + 8 = 60
or
4x = 60 - 8
or
4x = 52
or
x = 13
Hence,
The 13 lies between the interval 10 to 20
Option (b) 10 to 20
Help please! 10 pts
Find the missing side length in the right triangle below. Show your work.
Answer:
i think it is 18 or something
Step-by-step explanation:
Answer:
Side length B is 17.
Step-by-step explanation:
Use the Pythagorean Theorem a^2 + b^2 = c^2. if one of the legs is 8, and another is 15, the hypotenuse will be 17.
In Canada, $1 and $2 bills have been replaced by coins. When Marissa returned home to San Fran from a trip to Canada, she found that she had acquired 37 of these coins, with a total value of 51 canadian dollars. How many coins of each denomination did she have?
Answer:
$1 coin is 23
$2 coin is 14
Step-by-step explanation:
We need to form mathematical equations that we can solve from this Long citation.
Firstly, let the numbers of $1 coins be a and that of $2 be b.
We know that there are 37 coins. Hence
a + b = 37
Now, total is 51 Canadian dollars.
a + 2b = 51
Let’s now solve this simultaneously
From 2 , a + b + b = 51
Let’s say this is 3. Now substitute 1 into 3.
37 + b = 51, b = 51 - 37 = 14
Since a + b = 37
a = 37 - 14 = 23
D = {x|x is a whole number} E = {x|x is a perfect square between 1 and 9} F = {x|x is an even number greater than or equal to 2 and less than 9} The number 4 is D ∩ (E ∩ F).
1. True
2. False
Answer: 1. True
Step-by-step explanation:
Given : D = {x|x is a whole number} = { 0, 1 , 2, 3, 4, 5, ..................}
E = {x|x is a perfect square between 1 and 9} = {4 }
F = {x|x is an even number greater than or equal to 2 and less than 9} ={4 , 6 , 8}
Since intersection of sets contains all the values they have common.
Then, E ∩ F= {4}
Now , D∩ (E ∩ F) = { 0, 1 , 2, 3, 4, 5, ..................} ∩ {4} = {4}
Hence , The number 4 is D ∩ (E ∩ F).
Thus , the given statement is 1 . true.
In 12 games last season the school baseball team scored 5, 11, 2, 0, 4, 8, 9, 6, 7, 4, 1, and 2 runs. What is the average number of runs scored per game? Round to the nearest tenth.
Answer:
For Plato users the Answer is C
Step-by-step explanation:
What is the difference? StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction StartFraction 2 (x + 6) Over (x + 4) (x minus 4) EndFraction StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction StartFraction x minus 3 Over (x + 5) (x minus 4) EndFraction StartFraction negative 2 (x minus 6) Over (x + 4) (x minus 4) EndFraction
Answer:
D
Step-by-step explanation:
[-2(x-6)] / [(x+4)(x-4)]
To simplify the given expression, we can break it down into fractions and multiply them together step by step.
Explanation:The given expression is quite complex, but we can simplify it step by step. Let's break it down:
Simplify the first fraction: StartFraction \frac{x}{x^2 - 16} \EndFractionSimplify the second fraction: StartFraction \frac{3}{x - 4} \EndFractionMultiply the two fractions together: StartFraction \frac{2(x + 6)}{(x + 4)(x - 4)} \EndFractionMultiply the result by the third fraction: StartFraction \frac{-2(x + 6)}{(x + 4)(x - 4)} \EndFractionMultiply the result by the fourth fraction: StartFraction \frac{x - 3}{(x + 5)(x - 4)} \EndFractionMultiply the result by the fifth fraction: StartFraction \frac{-2(x - 6)}{(x + 4)(x - 4)} \EndFractionBy following these steps, we have simplified the given expression.
Learn more about Simplifying fractions here:https://brainly.com/question/14693420
#SPJ3
The duck pond games at the carnival has a pool with 75 toy ducks twenty five of these ducks are marked underneath as winners. To play you pick up a duck do not replace it then pick up another what is the probability that both ducks picked are winners?
Answer:
50?
Step-by-step explanation:
Answer:
Step-by-step explanation:
need help ASAP
Solve the equation by factoring x^2+6x-27=0
a. {-3,9}
b. {-9,3}
c. {3,9}
d. {-3,-9}
Answer:
b. {-9, 3}.
Step-by-step explanation:
x^2 + 6x - 27 = 0
We need 2 numbers whose product is -27 and whose sum is + 6.
These are + 9 and - 3. So the factors are:
(x - 3)(x + 9) = 0
(x - 3) = 0 or (x + 9) = 0
x = 3 or -9.
Answer: option b is the correct answer.
Step-by-step explanation:
The given quadratic equation is expressed as
x^2+6x-27=0
In order to solve the equation by factorization, the first step is to find two numbers such that their sum or difference is 6x and their product is
- 27x^2. The two numbers are 9x and - 3x. Therefore,
x^2 + 9x - 3x - 27 = 0
x(x + 9) - 3(x + 9) = 0
x - 3 = 0 or x + 9 = 0
x = 3 or x = - 9
The distance between Quebec City and New York City is 520 miles. If Kate leaves Quebec and will leaves New York at 9 am and the drive towards each other at 55 mph and 75 mph respectively at what time will they meet
Answer:they would meet at 1 pm
Step-by-step explanation:
The distance between Quebec City and New York City is 520 miles.
At the point where Kate and Will meet, they would have travelled 520 miles.
Let t represent the time it takes Kate to travel a certain distance before they met.
Distance = speed × time
If Kate drives at 55mph, the distance covered would be
55 × t = 55t.will drives at 75 mph
Since Will left same that that Kate left, distance travelled by Will in t hours would be
75 × t = 75t
Since the total distance covered is 520 miles, it means that
55t +75t = 520
130t = 520
t = 520/130 = 4
9 am + 4 hours = 1 pm
Answer:
1 pm
Step-by-step explanation:
Their combined speed is 55 + 75 = 130 miles per hour. That is the rate at which the distance between them is decreasing. The time it takes for the distance between them to become zero is found from the relation ...
time = distance/speed
time = (520 mi)/(130 mi/h) = 4 h
4 hours after 9 am, Kate and Will will meet. That time is 1 pm.
HELP!Please solve! this!!
Answer:
Recursive formula for geometric sequence
[tex]a_{n}=a_{n-1}\times r[/tex]
is [tex]a_{n}=a_{n-1}\times 6[/tex]
and explicit formula for geometric sequence [tex]a_{n}=a_{1}^{r-1}[/tex] is
[tex]a_{n}=(\frac{1}{2})^{6-1}[/tex]
Step-by-step explanation:
Given sequence is [tex]\frac{1}{2},3,18,108,648,...[/tex]
To find the recursive and explicit formula for this sequence:
Let [tex]a_{1}=\frac{1}{2},a_{2}=3,a_{3}=18,a_{4}=108,a_{5}=648,...[/tex]
To find the common ratio r:
[tex]r=\frac{a_{2}}{a_{1}}[/tex]
[tex]=\frac{3}{\frac{1}{2}}[/tex]
[tex]=3\times 2[/tex]
[tex]=6[/tex]
Therefore r=6
[tex]r=\frac{a_{3}}{a_{2}}[/tex]
[tex]=\frac{18}{3}[/tex]
[tex]=6[/tex]
Therefore r=6
Therefore the common ration r=6
Therefore the given sequence is geometric sequence
Recursive formula for geometric sequence is [tex]a_{n}=a_{n-1}\times r[/tex]
[tex]a_{n}=a_{n-1}\times 6[/tex]
and explicit formula is [tex]a_{n}=a_{1}^{r-1}[/tex]
[tex]a_{n}=(\frac{1}{2})^{6-1}[/tex]
[tex]=(\frac{1}{2})^{5}[/tex]
[tex]=\frac{1}{32}[/tex]
Therefore [tex]a_{n}=\frac{1}{32}[/tex]
Answer:
Recursive: a(n) = 6a(n-1)
Explicit: a(n) = (6^n)/12
Step-by-step explanation:
3 = 6 × ½
18 = 6 × 3
.
.
.
Recursive formula:
a(n) = 6a(n-1)
Explicit:
a(n) = a × r^(n-1)
a(n) = ½ × 6^(n-1)
a(n) = (6^n)/12
Traviling upstream on the Mississippi River, a barge travels 56 mi in 7 h. Downstream, it travels the same distance in 4 h. Find the rate of the barge in still water and the rate of the current
Answer:the speed of the barge in still water is 11 mph
the speed of the current is 3 mph
Step-by-step explanation:
Let x represent the speed of the barge in still water.
Let y represent the speed of the current.
Traveling upstream on the Mississippi River, the barge travels 56 mi in 7 h. This is against the water current. It means that the total speed of the barge would be
x - y mph
Distance = speed × time
Therefore,
56 = 7(x - y)
8 = x - y - - - - - - - - - - - -1
Downstream, it travels the same distance in 4 h. This is in the same direction with the water current. It means that the total speed of the barge would be
x + y mph
Therefore,
56 = 4(x + y)
14 = x + y - - - - - - - - - - - -2
Adding equation 1 and equation 2, it becomes
22 = 2x
x = 22/2 = 11
Substituting x = 11 into equation 2, it becomes
14 = 11 + y
y = 14 - 11 = 3
Find an equation of the line that
a. has the same y-intercept as the line y+7x+3=0 and
b. Is parallel to the line -11x-12y=-7
Write your answer in the form y=mx+b
Answer:
y = (-11/12)x - 3
Step-by-step explanation:
Recall that for a linear equation in the form y = mx + b,
m = slope and b = y-intercept.
hence to satisfy parts (a) and (b) of the questions, we need to extract the y-intercept from the equation in part (a) and the slope from part (b)
For part (a)
given: y+7x+3=0 (rearrange this to get slope-intercept form)
y+7x+3=0 (subtract 3 from both sides)
y + 7x = -3 (subtract 7x from both sides)
y = -7x - 3
we can see that the y-intercept is -3.
For part (b)
given: -11x -12y=-7 (rearrange this to get slope-intercept form)
-11x -12y=-7 (add 11x toboth sides)
-12y = 11x - 7 (divide both sides by -12)
y = (-11/12) - (7/12)
we can see that the slope is (-11/12).
combining the y-intercept from part (a) and the slope from part (b) into the general equation given in the first line above,
y = (-11/12)x - 3 (answer)
Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on one day a week for a given year on one day a week for a given year, and the average (mean) value is 144.3 volts. Choose the correct answer below. A. The given value is a parameter parameter for the year year because the data collected represent a population population. B. The given value is a parameter parameter for the year year because the data collected represent a sample sample. C. The given value is a statistic statistic for the year year because the data collected represent a sample sample. D. The given value is a statistic statistic for the year year because the data collected represent a population population.
Answer:
C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.
Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
Step-by-step explanation:
The sample mean obtained was :
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}= 144.3[/tex]
A. The given value is a parameter parameter for the year year because the data collected represent a population population.
False. The data colected represent a sample of the population of interest, so for this case is not a parameter because we don't have the information about all the population of interest.
B. The given value is a parameter parameter for the year year because the data collected represent a sample sample.
False. First the sample average is not a parameter, and second the population mean is not equal to the sample mean most of the times.
C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.
Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
D. The given value is a statistic statistic for the year year because the data collected represent a population.
False. If is an statistic can't represent the population, since the parameter represent the population not the statistic.
In this exercise we have to use the knowledge of statistics to be able to identify the correct statement, so I can say that it is:
The letter C
So knowing the statistics topics we can recognize the true alternative:
A. False. The information in visible form colected show a sample of the inhabitants of a place of interest, so for this case exist not a limit cause we forbiddance bear the facts about all the inhabitants of a place of interest.
B. False. First the sample average exist not a limit, and second the inhabitants of a place mean happen inadequate the average value most of the opportunity.
C. Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
D. False. If exist an detail of action can't represent the inhabitants of a place, because the limit represent the inhabitants of a place not the detail of action.
See more about statistics at brainly.com/question/10951564
Find the area of the sector of a circle with radius 4 inches formed by a central angle of [tex]\frac{5\pi}{4}[/tex] radians. Give your answer correct to 3 decimal places.
Answer:
10in²
Step-by-step explanation:
5π/4 is 62.5% of a circle if you look at the unit circle.
So just find the area of a circle and take 62.5% of it.
A = πr²
A = π(4)²
A = 16π
16π(.625) = 10