Answer:
[tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given:
[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}[/tex]
The sigma notation means to find the sum of the given geometric series where the first term is when n = 1 and the last term is when n = ∞.
To find the first term in the series, substitute n = 1 into the expression:
[tex]\implies a_1=4^{-1}=\dfrac{1}{4}[/tex]
The common ratio of the geometric series can be found by dividing one term by the previous term:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{4^{-2}}{4^{-1}}=\dfrac{1}{4}[/tex]
As | r | < 1 the series is convergent.
When a series is convergent, we can find its sum to infinity (the limit of the series).
Sum to infinity formula:
[tex]S_{\infty}=\dfrac{a}{1-r}[/tex]
where:
a is the first term in the seriesr is the common ratioSubstitute the found values of a and r into the formula:
[tex]S_{\infty}=\dfrac{\frac{1}{4}}{1-\frac{1}{4}}=\dfrac{1}{3}[/tex]
Therefore:
[tex]\displaystyle \sum^{\infty}_{n=1} 4^{-n}=\dfrac{1}{3}[/tex]
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Answer:
64 is the answer
Step-by-step explanation:
Mark me brainliest answer pls
At May 31, Lily Company has net sales of $395,000 and cost of goods available for sale of $268,000.
Compute the estimated cost of the ending inventory, assuming the gross profit rate is 35%.
The estimated cost of the ending inventory, assuming the gross profit rate is 35% is; $11250
How to find Estimated Cost?Let us first calculate the gross profit;
Gross Profit = Sales * Profit%
Gross Profit = 395000 * 35%
Gross Profit = $138250
Cost of goods sold = Sales - Gross Profit
Cost of goods sold = 395000 - 138250
Cost of goods sold = $256750
Cost of ending inventory = Cost of goods available for sale - Cost of goods sold
Cost of ending inventory = 268000 - 256750
Cost of ending inventory = $11250
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Assume that t varies jointly as r and q2². If t=320 when r=5 and q = 4, what is the value of q when r= 1 and t= 196?
q=
Step-by-step explanation:
[tex]t = k(r)( {q}^{2} )[/tex]
[tex]320 = k(5)( {4}^{2} )[/tex]
[tex]320 = 80k[/tex]
[tex]k = 4[/tex]
[tex]196 = 4(1)( {q}^{2} )[/tex]
[tex]49 = {q}^{2} [/tex]
[tex]q = 7[/tex]
Need help with this geometric question
Answer: 95 degrees (not an answer choice)
Step-by-step explanation:
Opposite angles of a parallelogram are congruent, so the left part of the angle is 40 degrees.
Adjacent angles of a parallelogram are supplementary, so the right part of the angle is 55 degrees.
Adding these together, we get 95 degrees.
Elian is placing a rectangle in the coordinate plane. He knows that the shorter side of the rectangle is half the length of the longer side. He places the longer side on the x-axis. What coordinates should he assign to the top-left vertex of the rectangle? Enter your answer in the boxes. ( , )
A rectangle is in the coordinate plane so that the bottom left vertex is at 0 comma 0, the top left vertex is on the positive side of the y-axis and is labeled question mark comma question mark, the top right vertex is in the first quadrant, and the bottom right vertex is on the positive side of the x-axis and is labeled 2 a comma 0.
Answer:
(0, a)
Step-by-step explanation:
We can start by imagining this rectangle as a square.
(This is written as if it is a square:)
The distance that a square reaches on the x-axis (assuming it has its lower left point at the origin, like this one does) is the same distance that it reaches on the y-axis.
meaning that we will have (length, 0) along the x-axis and (0, length) along the y-axis
so, if we are to treat this as a square, the point (2a, 0) means that our opposite vertex is (0, 2a)
However, because this length is only half of the length that it would be (if it were a square), we must divide our length by 2
2a ÷ 2 = a
So, the coordinates of the top-left vertex of this rectangle:
(0, a)
Answer:
coordinates of top left vertex: (0, a)
Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. As random sample of 20 Clarinex-D users is obtained, and the number of patients who experienced insomnia is recorded. Find and interpret probability that 3 or fewer experienced insomnia as a side effect.
Using the binomial distribution, it is found that there is a 0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect, which means that it is a highly likely event.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 20, p = 0.05.
The probability that 3 or fewer experienced insomnia as a side effect is given by:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.3585[/tex]
[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]
[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]
[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]
Then:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9842[/tex]
0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect.
Since this probability is greater than 95%, this is a highly likely event.
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A ship leaves port at 1 pm traveling north at the speed of 30 miles/hour .at 3 pm the ship adjusts its course20° eastward. Sketch a diagram to show the path the ship moved and the distance the ship is from the port. And how far the ship is from the port at 4pm?
The ship is 88.8 miles far from the port at 4 pm.
Given,
The displacement from 1 to 3 in the afternoon.
D1 = 30 miles/hr × 2 hr
= 60 miles to the north
The displacement from 3 till 4 in the afternoon.The ship changes its course 20 degrees eastward at 3 o'clock.
Therefore, D2 = 30 miles/hr × 1 hr
= 30 miles to the 20° north eastward
By combining two vectors, the resulting displacement:
D = √((D1 ₊ D2 × cos(20°))² ₊ (D2 × sin(20°))²
D = √((60 ₊ 30 × cos (20°))² ₊ (30 × sin(20°))²
D = 88.8 miles
Hence the ship is 88.8 miles far away from the port at 4 pm.
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Answer this please, thank you in advance :D
i) Student A used the property of the power of a power and student B used the definition of power and the property of the product of power with the same base. ii) Both were correct.
How to understand power properties
In this question we must analyze the procedure used by each student to simplify a power into the form rⁿ:
i) The student A used the property of the power of a power which states that [tex](r^{m})^{n} = r^{m\cdot n}[/tex]. In exchange, the student B used the definition of power and the property of the product of powers with the same base.
ii) Based on the description in i), both students used correct methods of simplifying.
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Solve the compound inequality .
2w-2<-8 and 4w+3<11
Write the solution in interval notation. If there is no solution, enter 0
Answer: [tex](-\infty, -3)[/tex]
Step-by-step explanation:
[tex]2w-2 < -8\\\\2w < -6\\\\w < -3[/tex]
[tex]4w+3 < 11\\\\4w < 8\\\\w < 2[/tex]
So, the solution is [tex](-\infty, -3)[/tex]
Leah wants to buy a home for
$380,000, but can only get a loan from the bank for $330,600. What percentage does Leah have to put down in order to pay for the home?
Leah have to put down 13% of the total money in order to pay for the home.
What is a Home Loan ?The amount of money a person borrows from a bank to buy a house is termed as Home Loan.
It is given that
Leah wants to buy a home for $380,000
The amount of money he can get from bank is $ 330,600
The amount of money Leah needs to have
= $ 380000 - $ 330600 = $49400
The percentage Leah have to put down in order to pay for the home is
=($49400 /$380000 ) * 100%
= 0.13 * 100 %
= 13%
Therefore Leah have to put down 13% of the total money in order to pay for the home.
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What amount would u have if u deposited 1800 a year for 30 years at 7% compounded annually
Answer: $183,731
Step-by-step explanation:
After 30 years, the interest is $183,731
[tex]\frac{1}{28} + \frac{1}{70} + \frac{1}{130} + \frac{1}{208} + \frac{1}{304} = ?[/tex]
Evaluate this expression.
Considering the least common multiple of the denominators, it is found that the result of the expression is given by:
[tex]\frac{9100}{138320}[/tex]
How do we add fractions?We place all the terms of the addition in "equivalent" fractions, with the same denominator, found from the last common multiple of all the denominators.
In this problem, the denominators are as follows: 28, 70, 130, 208, 304. Using a calculator, their lcm is of 138,320.
Considering equivalent fractions(the numerators are the division of the lcm by the previous denominator), the expression is:
[tex]\frac{4940}{138320} + \frac{1976}{138320} + \frac{1064}{138320} + \frac{665}{138320} + \frac{455}{138320} = \frac{4940 + 1976 + 1064 + 665 + 455}{138320} = \frac{9100}{138320}[/tex]
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What is the simplified form of StartRoot 100 x Superscript 36 Baseline EndRoot ?
10x Superscript 18
10x Superscript 6
50x Superscript 18
50
The simplified form of the expression √(100x³⁶) will be 10x¹⁸. Then the correct option is A.
What is simplification?Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The expression is given below.
⇒ √(100x³⁶)
Then the simplified form of the expression will be
⇒ √[(10x¹⁸)²]
⇒ 10x¹⁸
Then the correct option is A.
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Answer:
Step-by-step explanation:
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The simplified form of √(400x¹⁰⁰) is;
D; 20x⁵⁰
We want to find the simplified form of √(400x¹⁰⁰)
Now, according to laws of indices;
√ab = √a × √b
Thus;
√(400x¹⁰⁰) = √400 × √(x¹⁰⁰)
⇒ 20√(x¹⁰⁰)
Also according to law of indices;
a⁴ = a² × a²
Thus;
x¹⁰⁰ = x⁵⁰ × x⁵⁰
Thus;
√(x¹⁰⁰) = √(x⁵⁰ × x⁵⁰)
⇒ x⁵⁰
Our final answer is;
20x⁵⁰
. . . , , ,
help please
The system of inequalities of the graph is (a) y > x² + 2x - 3 and y > 2x + 3
How to determine the inequalities?The complete question requires that we determine the system of inequalities of the graph (the graph is attached)
Going by the list of options, the equation of the quadratic curve is:
y = x² + 2x - 3
From the graph, we can see that:
The curve uses a dotted lineThe upper part is shadedThe above means that the inequality is greater than i.e. >
So, we have:
y > x² + 2x - 3
The above eliminates options (b) and (c)
From the graph, we can see that the straight line has a positive slope, a dotted line and the upper part is shaded.
The linear inequality in option (a) has the above characteristics.
So, the inequality is:
y > 2x + 3
Hence, the system of inequalities of the graph is (a) y > x² + 2x - 3 and y > 2x + 3
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Factor the polynomial function.
G(v) - 196v² + 100
Answer:
4(49v²+25)
Step-by-step explanation:
[tex]196 {v}^{2} + 100[/tex]
[tex]4(49 {v}^{2} + 25)[/tex]
Based on statistics from a worldwide health organization, in there were million people worldwide living with a certain disease, and million deaths from the disease. By , the number of people living with the disease had grown to million, and million deaths were reported. Find the percent change for each statistic, and write any conclusions you can draw.
Based on the statistics from the worldwide health organization, the percentage change in those living with the disease is 19.7% and the change in those who have died is 70%.
This shows that the disease is getting worse and not being treated effectively.
What do the statistics on the disease show?The number of those living with the disease went from 71 million to 40 million:
= (85 - 71) / 71
= 19.7% increase
The percent change in those who have died is:
= (6.8 - 4) / 4
= 70% increase
This shows that the measures being implemented against the disease are not working because both the number of people who have the disease and have died from it has increased.
Full question is:
Based on statistics from a worldwide health organization, in 1999 there were 71 million people worldwide living with a certain disease, and 4 million deaths from the disease. By 2015, the number of people living with the disease had grown to 85 million, and 6.8 million deaths were reported. Find the percent change for each statistic, and write any conclusions you can draw.
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is the square root of 10 a rational number
Answer:
No
Step-by-step explanation
The square root of 10 is irrational because it isn't a fraction
A theme park had 1099 visitors in 3 days. There were twice as many visitors on saturday than on Friday. There were 234 more visitors on Sunday than on Saturday. How many visitors were there on Saturday?
Answer:
346
Step-by-step explanation:
Visitors on Friday(x)+Visitors on Saturday(2x)+Visitors on Suday(2x+234)
x+2x+2x+234=1099
5x+234=1099
5x=1099-234
5x=865
x=865/5
x=173
So, visitors on Saturday = 2x = 346
What are m and b in the linear equation 3+4x+6+2x=y
Answer:
m = 6, b= 9
Step-by-step explanation:
Simplifying the equation, we get y = 6x + 9.
Matching this up with y = mx + b, we get m = 6 and b = 9.
What are the similarities and differences between these data sets in terms of their centers and their variability?
Data Set A: 14, 21, 24, 28, 28, 35
Data Set B: 18, 19, 21, 25, 29, 32
Select from the drop-down menus to correctly complete the statements.
Comparing the centers of the data sets, the median for Data Set A is
Choose...
the median for Data Set B. The mean for Data Set A is
Choose...
the mean for Data Set B.
The median for Set A is (24+28)/2 = 26
The median for Set B is (21+25)/2 = 23
The mean for set A is (14+21+24+28+28+35)/6 = 25
The mean for set B is (18+19+21+25+29+32)/6 = 24.
Thus, the mean for Data Set A is greater than the mean for Data Set B.
Which table correctly shows all the sample spaces for tossing a coin to get heads and rolling a number on a six-sided number cube?
Using it's concept, the sample space for the experiment is given as follows:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
What is the sample space of an experiment?The sample space is the set that contains all possible outcomes for an experiment.
In this problem:
For the coin, there are 2 outcomes, H for heads and T for tails.For the number, there are 6 outcomes, which are the 6 numbers.Hence the sample space is given as follows:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
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(
Given that a = 7 cm and b = 8 cm,
work out the area of the triangle.
Give your answer rounded to 1 DP.
a
cm²
b
The diagram is not drawn accurately.
Answer:
28cm²
Step-by-step explanation:
The area of a triangle is given as:
= 1/2 × b × h
= 1/2 × 7 × 8
= 28cm²
Which number is irrational?
OA. 0.45
OB. 0.636363...
O C. √25
OD. √6
Answer:
D. Sqroot6
Step-by-step explanation:
6 is not a perfect square. So it is a non-repeating decimal that never ends
sqroot6 ~=
2.4494897428...
this is an irrational number.
The rest on the numbers can be written as a ratio:
0.45=45/100=9/20
0.63636363
= 63/99 = 7/11
sqrt25 = 5 = 5/1
that means they are rational.
Solve the equation x³ - 5x²+2x+8 = 0 given that - 1 is a zero of f(x)= x3 - 5x²+2x+8.
The solution set is? (Use a comma to separate answers as needed.)
Answer:
added in the picture
Step-by-step explanation:
added in the picture
Identifying Proportional Relationships
Which graph represents a proportional relationship?
Answer:
I can't answer this if you don't have the answer choices
I'm sorry
A major airline is planning to purchase new airplanes. It wants to borrow $800 million by
issuing bonds. The bonds are for a 10-year period with simple interest computed quarterly at
a rate of 2 percent per quarter. Interest is to be paid each quarter to bondholders.
How much (in millions) will the airline have to pay in quarterly interest? $
million
How much interest (in millions) will it pay over the 10-year period? $ million
Answer:
look at the picture
Step-by-step explanation:
look at the picture
Solve for x in the equation 4/x-3=x
Answer:
jenejebdjdndnr
r
r
r
r
r
r
Answer:
Step-by-step explanation:
Comment
Multiply through by x - 3
Then factor the result
4*(x - 3) / (x - 3) = x*(x - 3)
4 = x * (x - 3 ) Remove the brackets
4 = x^2 - 3x Subtract 4 from both sides
4-4 = x^2 - 3x - 4 Simplify
0 = x^2 - 3x- 4
This factors
0=(x - 4)(x + 1)
Answer
x - 4 = 0
x = 4
x+ 1 = 0
x = - 1
Please create an example using exponential growth and exponential decay
Answer:
f(x)=4^x exponential growth, -6^x exponential decay Step-by-step explanation:
Find the radius of a circle with area 345 square centimetres
30 pts need in like 10 mins!!
Please say the answer like-
… divided by … = ……
Or
… times … = …..
Answer:
5.9
Step-by-step explanation:
It's because area is 345
Formula , A=πr2Find the √ of 34518.6=3.14×f2fR = 5.9Write the mathematical expression for cost of each item if y items cost a
total of $25.00.