For the given geometric sequence the seventh term is equal to 19/81 and the 12th term is equal to "-57" the value of the 15th term is 1539.
What is a geometric sequence?
One particular sort of sequence is a geometric sequence. It is a sequence in which each term, with the exception of the first, is multiplied by a fixed integer to obtain the following term. The common ratio must be multiplied by the current term in the geometric sequence to obtain the next term, and the common ratio must be divided by the current term to obtain the previous term.
Solution Explained:
We know, a7 = 19/81, a12 = -57
So, ar^7 = 19/81 and ar^12 = -57 (r= common ratio)
Since r< a15 < 0 [the sign alternate]
Ignoring the signs,
r^12 = r^7 X r^5
57 = 19/81 X r^5
(57 X 81)/19 = r^5
243 = r^5
r = the fifth ratio of 243 = 3
therefore, r = -3
So, a15 = a12 X r^3
= -57 X (-3)^3
= 1539
Hence, the value of the 15th term is 1539.
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What is the equation of this graphed line
Answer: y = -9/8 + 7
Step-by-step explanation:
point a = (0,7), point b = (8,-2)
y = mx + b
b = 7
y = mx + 7
-2 = 8m + 7
-9 = 8m
m = -9/8
y = -9/8 + 7
Answer:
y= -9/8x+7
Step-by-step explanation:
find the slope
y2-y1/x2-x1
-2-7/8-0
-9/8
y=mx+b
m=slope
b=y intercept
y= - 9/8x + b
y= -9/8x+7
Determine the point estimate of the population mean and margin of error for the confidence interval.
Lower bound is 19, upper bound is 25.
The point estimate of the population mean is 22 and margin of error for the confidence interval is 3.
How to find the point estimate?1. Point estimate
Point estimate = Upper bound+ Lower bound/2
Point estimate = (25+19) /2
Point estimate = 44/2
Point estimate = 22
2. Margin error
Margin error = Upper bound - Lower bound/2
Margin error = ( 25-19) /2
Margin error = 6 /2
Margin error = 3
Therefore the point estimate is 22.
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NO LINKS!! Please help me with this probability question Part 3j
Answer:
b) 64 to 76 inches.
Step-by-step explanation:
In a normal distribution, 95% of the population is within 2 standard deviations of the mean.
Given values:
[tex]\textsf{Mean}\; \mu=70\; \sf inches[/tex][tex]\textsf{Standard deviation}\; \sigma=3\; \sf inches[/tex]Given that the mean height is 70 inches and the standard deviation is 3 inches:
[tex]\implies \mu -2 \sigma = 70-2(3)=64[/tex]
[tex]\implies \mu+2 \sigma = 70+2(3)=76[/tex]
Therefore, an appropriate height range for 95% of all people in the sample would be:
64 to 76 inches.Determine which integer will make the inequality 4x + 6 < 2x + 12 false.
Answer:
x>=3 make the inequality false
Step-by-step explanation:
4x-2x<12-6
2x<6
x<3
Answer:
Any number higher than 3
Ex. 4, 5, 6, 7, 8, 9, 10, etc
Step-by-step explanation:
4x + 6 < 2x + 12
-2x -2x
---------------------
2x + 6 < 12
-6 -6
------------------
2x < 6
÷2 ÷2
-----------
x < 3
Since x is less than 3, any number higher than 3 will make the inequality false. For Ex. 4
4(4) + 6 < 2(4) + 12
16 + 6 < 8 + 12
22 < 20 (false)
I hope this helps!
August hosted two dinner parties for his friends. Twenty guests attended the first party, and twenty-seven guests attended the second party. What is the percentage increase of the number of guests from the first party to the second party?
A.
35%
B.
30%
C.
65%
D.
70%
Answer:
A 35%
Step-by-step explanation:
take the higher number (27) and subtract the smaller number (20) from it. there's your difference. afterwards, take the difference (7) and divide it by the smaller number (20). this gives you .35. convert it into percentage move the decimal point to the right two spots and slap a percentage sign onto it (shift+3). giving you 35%, or A.
Answer:
a) 35%
Step-by-step explanation:
Given information,
→ 20 guests attended the 1st party, and 27 guests attended the 2nd party.
Now we have to,
→ find the % increase of number of guests from first party to second party.
Let's solve the problem,
→ ((27 - 20)/20) × 100
→ (7/20) × 100
→ 0.35 × 100
→ 35%
Hence, the answer is 35%.
A farmer owns a total of 8 4/5 acres of land. The land is separated into 4 equally sized sections. How many acres are in each section?
Write your answer as a mixed number or simplest form
Answer:
2 1/5
Step-by-step explanation:
8 4/5=44/5
(44/5)/(4)=(44/5)*(1/4)
(44/5)*(1/4)=44/20
44/20=2 1/5
ms.folk at least 250 candies to reward her students she has 50 candies already and will buy more candy in bags with 20 candies in each write an inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies
50 + 20x ≥ 250 is the inequality that can be used to find how many bags of candy Ms. Folk needs to buy to have at least 250 candies.
How to solve equations in word problems?
Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:i) There are two separate numbers at play, such as the total number of adults and children, the total number of large boxes and little boxes, etc.(ii) Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.Let x be the number of bags she bought:
50 + 20x ≥ 250
3x ≥ 200
x ≥ 200/3
x ≥ 66.67
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Find the difference between the sums to ten terms of the AP and GP whose first two terms are-2 and 4.
The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
What is Arithmetic Progression and Geometric Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
First term = -2
Second term = 4
A)
For Arithmetic Progression
First term a = -2
Second term = 4
Common difference d = Second term - First term
= 4 - ( -2 )
= 6
And Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
n = 10 terms
Sₙ = ( 10/2 ) [ (2x- 2) + ( 9 ) x 6]
Sₙ = 5 [ -4 + 54 ]
Sₙ = 5 x 50
Sₙ = 250
Therefore , Sum of first 10 terms of an AP is 250
B)
For Geometric Progression
First term a = -2
Second term = 4
Common ratio = Second term / First term
= 4 / -2
= -2
And Sum of first n terms of an GP : Sₙ = a( 1 - rⁿ ) / ( 1 - r )
n = 10
Sₙ = 2( 1 - ( -2 )¹⁰ ) / 1 - ( -2 )
Sₙ = 2 ( 1 - 1024 ) / 3
Sₙ = ( 2 x (-1023) ) / 3
Sₙ = 2 x ( - 341 )
Sₙ = - 682
Therefore , Sum of first 10 terms of an GP is -682
The difference between the sum of first 10 terms of AP and GP is GP - AP
= -682 - 250
= -932
Hence , The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
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There are 207 public libaries in New York City. The population in New York City is 8.805 million. What was the rate of libraries per 100,000? Give your answer to the nearest hundredth.
The rate of libraries per 100000 is 88.05 .
In the question ,
it is given that ,
the number of public libraries in New York City = 207 libraries
the population of the New York City = 8.805 million
we have to find the rate of libraries per 100000 .
for this we first have to express the population in numbers .
the population 8.805 million expressed in numbers is 8805000 ,
the rate of libraries per 100000 is
= 8805000/100000
On further simplification ,
we get ,
= 88.05
Therefore , The rate of libraries per 100000 is 88.05 .
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A house was valued at $321,000. Over several years, the value decreased by 9%, giving the house a new value.
Answer:
The new value is $292,110
Step-by-step explanation:
321,000 - (1 - 0.09) = 292,110
If WX equals to XY , what is the length of WZ?
Answer:
the length of WZ is 10
Step-by-step explanation:
Given the equation negative 26 equals y over 13, solve for y.
−2
2
−338
388
pls help I exam!
Answer:
y = -338
Step-by-step explanation:
[tex]-26 = \dfrac{y}{13}[/tex]
Multiply by 13 on both sides.
[tex]-26 \cdot 13 = y[/tex]
[tex]-338 = y[/tex]
y = -338
Answer:
-338
Step-by-step explanation:
-26=y/13
cross multiplying
y=-26×13
y=-338
2.1 & 2.2 Assessment: Vertex & Standard Form of Quadratic Functions
What is the equation, written in vertex form, of a parabola with a vertex of (1, -9) that
passes through the point (2, -7)?
Work to Support Your Answer (Required for Credit!)
The equation of the parabola, in vertex form is
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2 - 9\qquad \textit{we also know that} \begin{cases} x=2\\ y=-7 \end{cases} \\\\\\ -7=a(2-1)^2-9\implies 2=a(1)^2\implies 2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 -9 \end{array}} ~\hfill[/tex]
You can add and subtract fractions with different denominators. trite or false
Answer:
False
Step-by-step explanation:
The denominators have to be the same for you to be able to add or subtract a fraction.
What does the Big Bang Theory explain?
Answer:
The big bang is how astronomers explain the way the universe began. It is the idea that the universe began as just a single point, then expanded and stretched to grow as large as it is right now—and it is still stretching!
Step-by-step explanation:
In 1927, an astronomer named Georges Lemaître had a big idea. He said that a very long time ago, the universe started as just a single point. He said the universe stretched and expanded to get as big as it is now, and that it could keep on stretching The universe is a very big place, and it’s been around for a very long time. Thinking about how it all started is hard to imagine. Some More Information
Just two years later, an astronomer named Edwin Hubble noticed that other galaxies were moving away from us. And that’s not all. The farthest galaxies were moving faster than the ones close to us. This meant that the universe was still expanding, just like Lemaître thought. If things were moving apart, it meant that long ago, everything had been close together.
Everything we can see in our universe today—stars, planets, comets, asteroids—they weren't there at the beginning. Where did they come from?
A Tiny, Hot Beginning
When the universe began, it was just hot, tiny particles mixed with light and energy. It was nothing like what we see now. As everything expanded and took up more space, it cooled down.
The tiny particles grouped together. They formed atoms. Then those atoms grouped together. Over lots of time, atoms came together to form stars and galaxies.
The first stars created bigger atoms and groups of atoms. That led to more stars being born. At the same time, galaxies were crashing and grouping together. As new stars were being born and dying, then things like asteroids, comets, planets, and black holes formed!
Suppose 57% of the doctors in a hospital are surgeons.
If a sample of 465 doctors is selected, what is the probability that the sample proportion of surgeons will differ from the population proportion by greater than 6%? Round your answer to four decimal places.
The probability that the proportion of surgeons will differ from the population proportion by greater than 6%-22.22%
How to solve for the probabilityP of 6%
= P (p > 0.06)
we would have to use the formula that is given below
[tex]P[z > \frac{p-P}{\sqrt{} \frac{PQ}{n} }[/tex]
where we have n = 465
p = 6%
P = 0.57
Q = 1 - 0.57 = 0.43
We would have to put the values into the equation that we have here as:
0.06 - 0.057 = -0.51
0.57 x 0.43 / 465 = 0.000527
√0.000527 = 0.022956
The probability = -0.51 / 0.022956
= -22.22%
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What must be added to 3/8 to make a whole?
Answer:1/2
Step-by-step explanation:
A number cube with faces labeled from 1 to 6 will be rolled once.
The number rolled will be recorded as the outcome.
Give the sample space describing all possible outcomes.
Then give all of the outcomes for the event of rolling a number greater than 3.
If there is more than one element in the set, separate them with commas
The Sample space for number greater than 3= {4, 5, 6}
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.
Given:
A number cube with faces labeled from 1 to 6 will be rolled once.
so, Sample Space = { 1, 2, 3, 4, 5, 6}
sample space for number greater than 3= {4, 5, 6}
Thus, the probability is 3/6 or 1/2.
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Express the number as a ratio of integers.
0.46 = 0.46464646
Answer:
3.45
Step-by-step explanation:
this is how it is supposed to be
The diameter of a semicircle is 4 yards. What is the semicircle's perimeter?
Use 3.14 for x.
d=4 yd
The diameter of a semicircle is 4 yards. The perimeter for a semicircle having a diameter of 4 yards is 10.28 yards.
The perimeter of a shape is the distance of the path or boundary that surrounds the shape.
The formula for the perimeter of a semicircle is πr + 2r
π(pie)=3.14
r(radius)=2 yards (∴ radius=1/2diameter)
∴ the perimeter of a semicircle = πr + 2r
= 3.14×2+2×2
=10.28 yards.
∴ The perimeter of a semicircle with a diameter of 4 yards is 10.28 yards.
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the set of the sets of odered pairs shown represents a function of f. {(-5,3), (4,9), (3,-2). give an orderd pair that could be added to the set so that it remains a function
The three ordered pairs that could be added to the set so that f remains a function is D) (-3, -2), (1, 6), and (2, 3)
How to get the ordered pairs?We are told that the displayed set of ordered pairs represents a function f.
{(-5,3),(4,9),(3,-2),(0,6)}
We must determine which three ordered pairs can be added to the set while the function remains unchanged. It is a mapping between elements of two sets A and B, with each element of set A uniquely mapped to each element of set B.
Alternatively, we can say that each element has only one image. For D,(-3,-2),(1,6) and (2,3) (2,3)
The image of f -3 is -2.
The image of one is six.
3 is the image of 2
It is correct because each element has a unique image while maintaining the same function.
As a result, option D is correct.
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Complete question
The set of ordered pairs shown represents a function f. {(-5, 3), (4, 9), (3, -2), (0, 6)} Which three ordered pairs could be added to the set so that f remains a function? a. (-3, -2), (4, 0), and (0, -1) B) (1, 6), (2, 3), and (-5, 9) C) (4, 0), (0, -1), and (-5, 9) D) (-3, -2), (1, 6), and (2, 3)
Simplify the expressions
a) (30+10 ÷ 2)-5-10
b) (30 + 10) = 2.5-10
c) 30 + 10 = 2(5-10)
(d) 30+ (10 ÷ 2·5)-10
The solution of the expressions are
(a) (30+10 ÷ 2)-5-10 = 20
(d) 30+ (10 ÷ 2·5)-10 = 24
What is meaning of expressions?
An expression is a combination of operations, variables, and numbers.
What is BODMAS rule?
According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by 'order' (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right.
Given expression is
(30+10 ÷ 2)-5-10
Applying BODMAS rule:
= (30 + 5) - 5 - 10
= 35 - 5 - 10
= 30 - 10
=40
Second expression is:
30+ (10 ÷ 2·5)-10
= 30 + (10 ÷ 10) - 10
= 30 + 1 - 10
= 31 -10
= 21
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Tater and Pepper Corp. reported free cash flows for 2021 of $47.1 million and investment in operating capital of $30.1 million. Tater and Pepper incurred $14.4 million in depreciation expense and paid $30.5 million in taxes on EBIT in 2021.
If Tater and Pepper incurred $14.4 million in depreciation expense and paid $30.5 million in taxes on EBIT in 2021. The EBIT is $93.3 million.
How to find EBIT?First step is to find the operating cash flow
Operating cash flow =$47.1 million + $30.1 million
Operating cash flow = $77.1 million
Now let find the EBIT
EBIT = Operating cash flow + Depreciation expenses - taxes
EBIT = $77.1 million + ($30.5 million - $14.4 million)
EBIT = $93.3 million
Therefore the EBIT is $93.3 million.
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A 800 g of rock was analysed and
found to contain 58 g of gold. What
percentage of the rock is the gold?
Answer:
7.25 %
Step-by-step explanation:
58 out of 800g is 58 / 800 = .0725 which is 7.25 %
How much must be deposited today into the following account in order to have $50,000 in 7 years for a down payment on a house? Assume no additional deposits
are made.
An account with quarterly compounding and an APR of 5.9%
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$50000\\ P=\textit{original amount deposited}\\ r=rate\to 5.9\%\to \frac{5.9}{100}\dotfill &0.059\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]50000=P\left(1+\frac{0.059}{4}\right)^{4\cdot 7} \implies 50000=P(1.01475)^{28} \\\\\\ \cfrac{50000}{(1.01475)^{28}}=P\implies 33183.05\approx P[/tex]
A house on the market was valued at $365,000. After several years, the value increased by 8%. By how much did the house's value increase in dollars? What is
the current value of the house?
Answer:
394,200
Step-by-step explanation:
You have to multiply the house value by 1.08 or 108%
365,000*1.08=394,200
The sUm of the measures
of the interior angles of
polygon is 2,880°. How
many sides does the
polygon have?
Which value of x makes the following statement true? 1.4 - x = a positive number
Answer:1.4<x
math math math
Answer:daddy
Step-by-step explanation:gay
Mike has some t-shirts. 1/4 of the
t-shirts are pink, 1/2 of the
remaining tshirts are white and the rest are
purple. What fraction is purple?
Mike has some t-shirts. 1/4 of the t-shirts are pink, 1/2 of the remaining t-shirts are white and the rest are purple, then the fraction of purple is 3/8
Mike has some t-shirts
The fraction of pink t-shirts = 1/4
The remaining t-shirts = 1 - (1/4)
= 3/4
1/2 of the remaining t-shirts are white
Then the fraction of white t-shirt = 3/4 × 1/2
= 3/8
The fraction of purple t-shirt = 1 - (1/4 + 3/8)
= 3/8
Hence, Mike has some t-shirts. 1/4 of the t-shirts are pink, 1/2 of the remaining t-shirts are white and the rest are purple, then the fraction of purple is 3/8
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I know this is easy for some, but I have no idea what happened here. Can someone explain to me? These are congruent triangles.
8x -13 = 5x + 17
3x = 30
x = 10
The x value we get is 10 when the sides are 8x-13 and 5x+17 in a congruent triangle.
Given that,
The sides as 8x-13 and 5x+17
We have to find the x value.
If two or more triangles are congruent, it depends on how big their sides and angles are. The three sides and three angles of a triangle determine its size and shape, accordingly. Two triangles are said to be congruent if the pairings of respective sides and corresponding angles are equal.
We say now,
8x-13 = 5x+17
8x-5x=17+13
3x=30
x=30/3
x=10
Therefore, The x value we get is 10 when the sides are 8x-13 and 5x+17 in a congruent triangle.
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