Solve for x.
I need help with this geometry problem
Find the common ratio for each geometric sequence. 64,48,36,. . . . . .
The infinite geometric series has the general form a1 + a1r + a1r² + a1r³ +…, where r is the common ratio and a1 is the first term. The common ratio of the geometric sequence 64, 48, 36,.... is 3/4.
What is meant by geometric series?The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³ +…, where r is the common ratio and a1 is the first term.
The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.
Given: a1 = 64 and a2 = 48
The common ratio(r) is:
r = a2/a1 = 48/64
r = 6/8 = 3/4
Therefore, the common ratio of the geometric sequence 64, 48, 36,.... is 3/4.
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the stage wich is 35 feet wide in real life is 5 inches wide in the drawing . what is the scale of the drawing
Answer: 20 feet
Step-by-step explanation:
The scale is 3 inches to is to 2 feet
As a ratio, it would be:
The question is what is the actual length of the stage if the drawing is 30 inches. All we need to do is find a ratio proportional to the scale ratio:
Now to find the missing number, cross multiply the fractions first:
Then solve for x:
The answer is 20 feet
Determine the range of f(x) = |x + 5|.
if right ill award u pls need fast pretty pls
Answer:it
Step-by-step explanation:
it should be 10 i think
The statistical analysis of economic phenomena is defined as:_________
a) standard deviation.
b) econometrics.
c) confidence intervals.
d) variance.
The correct option out of all these is option B: Econometrics.
Now to clear our confusion further, we will look at the basic definitions of these concepts,
A confidence interval in statistics is the probability that a population parameter falls within a range of values for a specified percentage of the time.
Variance and standard deviation are very different measures from the mean, so we expect to see significant differences in how they are estimated.
Econometrics is a statistical and mathematical analysis of economic relations and is often the basis for economic forecasting. Governments may use such information to set economic policies and private companies to support pricing, inventory, and production decisions. However, economists mainly use it to study relationships between economic variables.
So, option B is Correct Econometrics.
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1. How would you write 2 × 2 × 2 using exponents?
(1 point)
02×3
023
032
2. Rewrite the following expression using exponents.
3×3 × 3× 3 × 3 x3
(1 point)
036
035
O
63
3. What is the value of 44? (1 point)
016
064
0256
4. What is the value of 92? (1 point)
018
081
0729
5. What is the value of 83? (1 point)
024
064
0512
PLEASE HELP ASAP
ykdlydkyskyskystksltsylelyellyslyspyslsu dyllglgzlgsls xlykx
Answer:
There is nothing to answer.
write 1875/100 in its lowest terms
Answer:
hii
Step-by-step explanation:
18.75 answer
is
correct
At a football game half time show the marching band was in 3 sections each with 8 rows of 8 players. The dancers were in 2 sections each with 6 rows of 7 dancers. What
is the total number of band members and dancers in the halftime show?
Answer:
276
Step-by-step explanation:
so since there is 3 section we know that it will be the same answer for the three sections then if it's 8 rows with 8 in each it would be 8x8=64 then since it's three sections 64 x 3= 192 that's the total of band then you repeat the process with dancers with will give you the total of 276
Your teacher invested 5000 in three funds. After a year they had 5450 . The growth fund had a return rate of 12% , the income fund had a return rate of 8% , and the money market fund had, a return rate of 5 \% . Your teacher invested twice as much in the income fund as in the money market fund. How much money was invested in each fund?
Using a system of equations, the amounts invested in each fund are given as follows:
Growth: $2,000.Income: $2,000.Market: $2,000.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: amount invested into the growth fund.Variable y: amount invested into the income fund.Variable z: amount invested into the market fund.The teacher invested 5000, hence:
x + y + z = 5000.
After a year, the amount was of $5,450, hence, considering the return rates:
1.12x + 1.08y + 1.05z = 5450.
The teacher invested twice as much in the income fund as in the money market fund, hence:
y = 2z.
Then, replacing y = 2z in the first two equations:
x + 3z = 5000 -> x = 5000 - 3z.1.12x + 3.21z = 5450.Replacing the first equation into the second.
1.12(5000 - 3z) + 3.21z = 5450.
0.15z = 150
z = 150/0.15
z = 1000.
Hence:
y = 2z = 2000.x = 5000 - 3z = 2000.The amounts invested in each fund are given as follows:
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Determine whether each sequence is arithmetic. If so, identify the common difference. 100,10,1,0.1, ...........
The given sequence 100,10,1,0.1, ........... does not form an AP as the common difference is not same.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between two mathematical orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come across a few key concepts in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be referred to in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows:Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the stated sequence is; 100,10,1,0.1, ...........
The series comprises of four defined terms.
Consider the initial term be 'a₁' = 100.
Consider the second term be 'a₂' = 10.
Consider the third term be 'a₃' = 1.
And, consider the fourth term is 'a₄' = 0.1.
The AP must have the equal common difference. So,
d₁ = a₃ - a₂
Substitute the values.
d₁ = 1 - 10
d₁ = -9
Thus, the computed common difference is -9.
or d₂ = a₄ - a₃ (Substitute the values)
d₂ = 0.1 - 1
d₂ = -0.9.
As, for the result it is clear that the value of both common difference is not same. That is,
d₁ ≠ d₂.
Therefore, the given sequence doesn't not form an arithmetic sequence.
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215,36,6 find the seventh term
Pls help
Answer: 216, 36, 6, 1, 1/6, ...
Step-by-step explanation:
216, 36, 6, ...
[tex]b_1=216\\b_2=36\\b_3=6\\\displaystyle\\q=\frac{b_2}{b_1} \\\\q=\frac{36}{216} \\\\q=\frac{1}{6} \\\\q=\frac{b_3}{b_2} \\\\q=\frac{6}{36} \\\\q=\frac{1}{6} \\\\Hence,\\\\b_n=b_1q^{n-1}\\\\b_5=216*(\frac{1}{6})^{5-1}\\\\b_5=216*(\frac{1}{6} )^4\\\\b_5=216*\frac{1}{6^4}\\\\b_5=6^3 *\frac{1}{6^4} \\\\b_5=\frac{6^3}{6^4} \\\\b_5=6^{3-4}\\\\b_5=6^{-1}\\\\b_5=\frac{1}{6}[/tex]
normal body tem varies by the time of day. a series of readings was taken of the body temperature of a subject. the mean reading was found to be 36.5 C with a standard deviation of 0.3 C. if you wanted to convert the temp to the Fahrenheit scale, what would the new mean and standard deviation be?
Answer: 97.7 F 32.54 F
Step-by-step explanation:
So the equation to go from Celsius to Fahrenheit is 9/5(C)+32
So it would be 9/5(36.5)+32=97.7 F
And 9/5(0.3)+32=32.54 F
The new mean is 97.7 F and new standard deviation is 32.54 C.
what is Standard Deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean.
Given:
Mean = 36.5 C
Standard deviation = 0.3 C
Now, converting Celsius to Fahrenheit as
= 9/5(C)+32
So, the new mean is
=9/5(36.5)+32
=97.7 F
and, new standard deviation is
= 9/5(0.3)+32
=32.54 F
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Simplify (1+1/3)^2-2/9
The simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.
What is the simplified form of the given expression?Given the expression in the question;
( 1 + 1/3 )² - 2/9
Add the two terms inside the parenthesis
( (3+1)/3 )² - 2/9
( 4/3 )² - 2/9
Apply product rule to 4/3
4²/3² - 2/9
Raise 4 and 3 to the power of 2
16/9 - 2/9
Combine the numerators over common denominator
( 16 - 2 ) / 9
14/9
Therefore, the simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.
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The diameter of the trunk of a bush is 7.62 × 10^-2 meters. The diameter of the trunk of a tree is 3.81 × 10^–1 meter. How many times larger is the diameter of the trunk of the tree?
2 times larger
3 times larger
4 times larger
5 times larger
The diameter of the trunk of a tree is 5 times larger than the diameter of the trunk of a bush.
How to find the number of times larger the diameter of the trunk of the tree is when compared with the diameter of the trunk of a bushGiven data
diameter of the trunk of a bush is 7.62 × 10^-2 meter
diameter of the trunk of a tree is 3.81 × 10^–1 meter
To achieve the comparison we divide the diameter of the trunk of a tree with the diameter of the trunk of a bush, as follows:
= 3.81 × 10^–1 meter ÷ 7.62 × 10^-2 meter
= 5
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Show ur work please and thank you I’ll give brainilest
Answer:
7
Step-by-step explanation:
If he made 6 in the first game and 34 total, then we cant subtract 34 from 6 to find how many he made in the 4 remaining games.
34 - 6 = 28
Now simply divide 28 by 4 to figure out how much he made in each game
28 / 4 = 7
Graph the line with the equation y = -4/3x+1
Answer: coordinates would be 0,1 and 3,-3
Step-by-step explanation:
FIND x
log(x)+ log (x+3)=1
What is £40 shared in the ratio of 1:4
Complete the square. x² +14 x+ ____
The complete expression of the given quadratic function is:
x² + 14x + 49
What is an algebraic expression?An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:
(a + b)² = a² + 2ab + b²
x² + 14x + ?
where:
x² = a²14x = 2abb = ?Substitute and find b
14x = 2xb
2b = 14
b = 7
Let's complete the square
x² + 14x + 7²
x² + 14x + 49
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For the geometric sequence 3,12,48,192, . . . . . , find the indicated term.20 th term
The 20th term of the given geometric sequence, 3, 12, 48, 192, . . . , is 8.246337208 x 10^11.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
r = ratio
Given the geometric sequence 3, 12, 48, 192, . . .
Find the ratio,
r = a(n)/a(n-1)
r = a(2)/a(1)
r = 12/3
r = 4
Notice that the ratio between two succeeding terms is always 4.
Use the formula to find the 20th term of the geometric sequence.
a(20) = a r^(20-1)
a(20) = 3[4^(20-1)]
a(20) = 3(4^19)
a(20) = 8.246337208 x 10^11
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Please help I don't understand!!
1. Use the graph at right to answer the following questions. (Hint: rate of change = slope).
Calculate the average rate of change from x = 1 to x = 4
2. Use the graph at right to answer the following questions. (Hint: rate of change = slope).
Calculate the average rate of change from x = 2 to x = 5
1. Average rate of change = -1/3
2. Average rate of change = 4/3
How to the Average Rate of Change?Average rate of change = change in y /change in x.
1. Average rate of change from x = 1 to x = 4
When x = 1, y = 5
When x = 4, y = 4
Average rate of change = (4 - 5)/(4 - 1)
Average rate of change = -1/3
2. Average rate of change from x = 2 to x = 5
When x = 2, y = 3
When x = 5, y = 7
Average rate of change = (7 - 3)/(5 - 2)
Average rate of change = 4/3
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Identify the slope of the line that passes through the given points.
(1,3) and (6,1)
The slope of the line that passes through the given points,
(1,3) and (6,1)= -0.4
How slope is calculated?
The formula of the slope of a line between two points:[tex]\text{slope of a line between }(x_{1} ,y_{1} ) \text{ and } (x_{2} ,y_{2})=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substituting the given values,[tex]\text{slope of a line between }(1,3 ) \text{ and } (6,1)=\frac{1-3}{6-1}=-\frac{2}{5}=-0.4[/tex]
What is a slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's and Todhunter's versions of the equation for a straight line, respectively, where they are written as y = mx + b and y = mx + c.To learn more about slope, refer:
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the ratio of tomatoes to red apples is2:5 if there are 20 tomatoes how many red apples are there
Answer:
50 red apples
Step-by-step explanation:
If the ratio is 2:5
20 tomatoes ( 2 ratio)
20 ÷ 2 = 10 ( 1 ratio)
5 x 10 = 50 (5 ratio)
then there would be 50 red apples.
(o´▽`o)ﾉ x
Answer:
50 red apples
Step-by-step explanation:
the 2 part of the ratio applies to tomatoes of which there are 20, then
20 ÷ 2 = 10 ← value of 1 part of the ratio, then
5 parts = 5 × 10 = 50 red apples
Explain how to do long division within 5 minutes.
Let's say 125 / 5
5 can't go into 1 so we move on to 12(if it doesn't work for twelve you move on to the next number). 5 goes into 12 twice because 5*2=10.
So the first number to our answer is 2 and we do 12-10=2. Then we bring down the 5 in 125 to make 25(from 12-10=2).
Since we are dividing by 5, 5 goes into 25 five times, so the next number to our answer is 5. 25-25=0 which means we can't divide by 5 any further so our answer is 25.
I think it's confusing but just for the points :)
.............................................
Answer:
The value would be 100
Step-by-step explanation:
I now understand how to get y.. But how do I get x?
Answer:
x = 3.6
Step-by-step explanation:
since the 2 figures are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{AD}{EH}[/tex] = [tex]\frac{AB}{EF}[/tex] ( substitute values )
[tex]\frac{x}{2.4}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
2x = 7.2 ( divide both sides by 2 )
x = 3.6
a₁ is the first term of a sequence, r is a common ratio, and d is a common difference. Write the first five terms. a₁=3, d=7
The first five terms of an arithmetic sequence with first term 3 and common difference 7 are 3, 10, 17, 24, 31
The given parameters:
a₁ = 3, d = 7
d is the common difference, hence, the given sequence is an arithmetic sequence.
In an arithmetic sequence, the formula for the nth term is given by:
a(n) = a(1) + (n - 1) . d
We can also find the terms using recursive formula. The nth term of an arithmetic sequence is equal to the (n-1)th term plus the common difference, d. Mathematically,
a(n) = a(n -1) + d
Let us start from n = 1
a(1) = 3 (given)
a(2) = a(1) + d = 3 + 7 = 10
a(3) = a(2) + d = 10 + 7 = 17
a(4) = a(3) + d = 17 + 7 = 24
a(5) = a(4) + d = 24 + 7 = 31
Thus, the first five terms are 3, 10, 17, 24, 31
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A bee flies at 6 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 11 minutes, and then flies directly back to the hive at 4 feet per second. It is away from the hive for a total of 15 minutes. a. What equation can you use to find the distance of the flowerbed from the hive? b. How far is the flowerbed from the hive?
Answer:
576 feet
Step-by-step explanation:
The bee is at the flowerbed for 11 minutes so we can subtract that form the 15 minutes. The bee travels for 4 minutes.
So now we have that it flew to the flowerbed at 6 feet per second and back at 4 feet per second.
We have a total of 4 minutes or 240 seconds. we now have two speeds where one is 50% faster than the other. We then find the two percents that one is 50% greater than the other percent and both add up to 100. 40% +50% of 40% is 60. 60%+40% is 100%
We know it spent 40% of 240 seconds flying to the flowerbed at 6 feet per second.
40% of 240 is 96
96 seconds at 6 feet per second is 576 feet
Write an equation of a circle with the given center and radius. Check your answers.
center (-4,-6) , radius 7
The equation of the circle with radius 7 and center at (-4 , -6) is (x + 4)^2 + (y + 6)^2 = 49.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-4 , -6)
r = 7
(x - -4)^2 + (y - -6)^2 = 7^2
(x + 4)^2 + (y + 6)^2 = 49
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