A furniture factory makes 5 recliners for every 3 couches. If the factory makes a total of 56 recliners and couches in a day, how many recliners were made? Select the correct proportion to solve this problem.
Answers
In ratios, 'things go with the same things', so recliners have to be both in the numerator or denominator. The 8 is misleading. That's the total, and the problem is all about recliners and couches only
Related Questions
Choice #1: Describe each of the following properties of the graph of the cosine function, f(theta) = cos(theta), and relate the property to the unit circle definition of cosine. Amplitude Period Domain Range x-intercepts
Answers
The Amplitude is the maximum distance from 0 the function can be. In the case of [tex]cos(\theta)[/tex] that maximum distance is 1, because the unit circle has a radius of 1 and is centered at the origin, so the x value of a point on the circle can't be greater than 1.
Period = [tex]2\pi[/tex]
The period is the distance required for the function to complete one cycle. It takes [tex]2\pi[/tex] radians to make a full round of the unit circle, and after that [tex]cos(\theta)[/tex] repeats, so it is the period.
Domain = [tex]\mathbb{R}[/tex]
When the function is given an angle it radians, it goes that distance around the unit circle, and then gives the x value of the point on the circle at that distance. There is no [tex]\theta[/tex] that would cause this function to be undefined, so it's domains is [tex]\mathbb{R}[/tex].
Range = [tex]\{\theta \: | \: -1 \leq \theta \leq 1 \}[/tex]
The unit circle has a radius of 1 and is located at the origin so the x value of any point on the unit circle has to be between -1 and 1.
X-Intercepts: [tex]\frac{n\pi}{2} \:\: where\: n\: is \:any \:odd \:integer[/tex]
X-intercepts occur where a function evaluates to 0. For [tex]cos(\theta)[/tex] this occurs at odd multiples of [tex]\frac{\pi}{2}[/tex], as these are locations on the unit circle where the x value of the corresponding point on the circle is 0.
The graph of the cosine function, f(theta) = cos(theta), has properties such as amplitude, period, domain, range, and x-intercepts, and these properties can be related to the unit circle definition of cosine.
Explanation:The graph of the cosine function, f(theta) = cos(theta), has several properties:
Amplitude: The amplitude of the cosine function is 1, which means that the graph oscillates between a maximum value of 1 and a minimum value of -1.Period: The period of the cosine function is 2π, which means that the graph repeats itself every 2π units of theta.Domain: The domain of the cosine function is all real numbers, as there are no restrictions on the values of theta for which the cosine function is defined.Range: The range of the cosine function is the interval [-1, 1], as the values of the cosine function range from -1 to 1.X-intercepts: The x-intercepts of the cosine function occur when the value of theta is equal to π/2 + nπ, where n is an integer. In the unit circle, these x-intercepts correspond to the points where the terminal side of theta intersects the x-axis.These properties can be related to the unit circle definition of cosine. The amplitude corresponds to the distance from the origin to the maximum or minimum value of cosine on the unit circle. The period corresponds to the distance traveled along the unit circle to complete one cycle of the cosine function. The x-intercepts of the cosine function correspond to the angles at which the terminal side of theta intersects the x-axis on the unit circle.
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Sat scores are distributed with a mean of 1,500 and a standard deviation of 300. you are interested in estimating the average sat score of first year students at your college. if you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?
Answers
To estimate the average SAT score of first-year students at a college with a 95% confidence interval and a margin of error of 25 points, you would need to sample approximately 554 students.
Explanation:This question involves using the concepts of mean, standard deviation, margin of error, and confidence intervals from probability and statistics. To determine the sample size needed to estimate the average SAT score with a certain margin of error, we'll use the formula for the sample size required for estimating a population mean in statistics:
n = (Z*σ/E)^2
Where:
n is the sample size Z is the Z-score (for a 95% confidence interval, Z is 1.96) σ is the standard deviation (300 in this case) E is the margin of error (25 in this case)
Plugging the values into the formula, we get:
n = (1.96*300/25)^2 ≈ 553.47
As we cannot have a fraction of a student, we always round up to ensure our margin of error requirement is met. Therefore, you would need to sample approximately 554 students.
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To limit the margin of error of your 95% confidence interval to 25 points, given the standard deviation is 300, use the formula for the margin of error for a confidence interval and solve for the sample size 'n'. Approximately 553 students should be sampled.
Explanation:For this question, we can use the formula for the margin of error for a confidence interval which is calculated as: Margin of Error = z * (σ/√n). Here, 'z' represents the z-score, 'σ' is the standard deviation, and 'n' is the sample size.
In this case, we wish to have a 95% confidence level. From z-tables, we know that the z-value for a 95% confidence level is approximately 1.96. We want a margin of error of 25 points. The standard deviation (σ) for the dataset is said to be 300.
So, we can rearrange our formula to solve for 'n', giving us: n = (z * σ / Margin of Error)². Substituting in our numbers, we get n = (1.96 * 300 / 25)². So, to limit the margin of error on your 95% confidence interval to 25 points, you will need to sample approximately 553 students.
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Find all solutions in the interval [0, 2pi): sin5x+sinx=sin3x
Answers
sin5x+sinx=sin3x
this can be written as:
(sinx)^5+sinx=(sinx)^3
dividing through by sin x we get:
(sinx)^4+1=(sinx)^2
let y=(sinx)^2
thus our expression will be given by:
y^2+1=y
y^2-y+1=0
solving the quadratic equation above we get:
y=(-1)^(1/3) or -(-1)^(2/3)
the above is a complex equation, therefore our expression has no defined answer
Name a pair of supplementary angles.
A. angle A E B and angle C E D
B. angle A E B and angle B E D
C. angle A E C and angle B E D
D. angle B E A and angle C E B
Answers
Answer:
B.angle AEB and angle BED.
Step-by-step explanation:
We are given that a diagram .
We have to find a pair of supplementary angles.
Supplementary angles:The pair of angles whose sum is 180 degrees is called supplementary angles.
From given diagram
[tex]\angle AEB+\angle BED=180^{\circ}[/tex]
[tex]\angle AEC+\angle CED=180^{\circ}[/tex]
Hence, option B is true.
Answer:B.angle AEB and angle BED.
What is the remainder when (4x3 + 2x2 − 18x + 38) ÷ (x + 3)?
2
12
96
110
Answers
Answer: First Option is correct.
Step-by-step explanation:
Since we have given that
[tex](4x^3+2x^2-18x+38)\div(x+3)[/tex]
We will apply the "Remainder Theorem ":
So, first we take
[tex]g(x)=x+3=0\\\\g(x)=x=-3\\\\and\\\\f(x)=4x^3+2x^2-18x+38[/tex]
So, we will put x=-3 in f(x).
[tex]f(-3)=4\times (-3)^3+2\times (-3)^2-18\times (-3)+38\\\\f(-3)=-108+18+54+38\\\\f(-3)=2[/tex]
So, Remainder of this division is 2.
Hence, First Option is correct.
The remainder of the given expression is 2 and this can be determined by using the factorization method.
Given :
Expression -- [tex]\rm \dfrac{4x^3+2x^2-18x+38}{x+3}[/tex]
The factorization method can be used in order to determine the remainder of the given expression.
The expression given is:
[tex]\rm =\dfrac{4x^3+2x^2-18x+38}{x+3}[/tex]
Try to factorize the numerator in the above expression.
[tex]\rm =\dfrac{4x^3+12x^2-10x^2-30x+12x+36+2}{x+3}[/tex]
[tex]\rm = \dfrac{4x^2(x+3)-10x(x+3)+12(x+3)+2}{(x+3)}[/tex]
Simplify the above expression.
[tex]\rm = (4x^2-10x+12) + \dfrac{2}{(x+3)}[/tex]
So, the remainder of the given expression is 2. Therefore, the correct option is A).
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Solve |x| + 7 < 4.
........................
Answers
|x| + 7 < 4.
|x| < 4.-7
|x| < -3
no reals solutions because for all reals x : |x| ≥ 0
Find the equation of the tangent line of f^-1(x) at the point where it intersects the x-axis
Answers
note :
1 ) f(X0) = Y0 equiv : X0 = f^-1(Y0)
2 ) ( f^-1(Y0) )' = 1/ f'(X0)
in this exercice : X0 = 0
he equation of the tangent line for graph of : f
Y - Y0 = f'(X0) (X- 0)
sp : he equation of the tangent line for graph of : f^-1(x) is :
X -X0 = f'(Y0) (Y -0)
Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n equals 123n=123, p equals 0.85
Answers
Variance = np(1-p) = (123)(0.4)(1-0.4) =(123)(0.4)(0.6) = 29.52
Standard. Deviation = √variance = √29.52 = 5.43
The mean of the binomial distribution is [tex]\( 104.55 \)[/tex], the variance is [tex]\( 15.6825 \)[/tex], and the standard deviation is approximately .
To find the mean, variance, and standard deviation of a binomial distribution with given values of [tex]\( n \)[/tex] and [tex]\( p \)[/tex], we use the following formulas:
Mean [tex](\( \mu \)) = \( n \times p \)[/tex]
Variance [tex](\( \sigma^2 \)) = \( n \times p \times (1 - p) \)[/tex]
Standard Deviation [tex](\( \sigma \)) = \( \sqrt{\text{Variance}} \)[/tex]
Given:
[tex]\( n = 123 \)[/tex]
[tex]\( p = 0.85 \)[/tex]
Let's calculate each of these:
Mean [tex](\( \mu \))[/tex]:
[tex]\( \mu = n \times p \)[/tex]
[tex]\( \mu = 123 \times 0.85 \)[/tex]
[tex]\( \mu = 104.55 \)[/tex]
Variance [tex](\( \sigma^2 \))[/tex]:
[tex]\( \sigma^2 = n \times p \times (1 - p) \)[/tex]
[tex]\( \sigma^2 = 123 \times 0.85 \times (1 - 0.85) \)[/tex]
[tex]\( \sigma^2 = 123 \times 0.85 \times 0.15 \)[/tex]
[tex]\( \sigma^2 = 104.55 \times 0.15 \)[/tex]
[tex]\( \sigma^2 = 15.6825 \)[/tex]
Standard Deviation [tex](\( \sigma \))[/tex]:
[tex]\( \sigma = \sqrt{\sigma^2} \)[/tex]
[tex]\( \sigma = \sqrt{15.6825} \)[/tex]
[tex]\( \sigma \approx 3.9599 \)[/tex]
Therefore, the mean of the binomial distribution is [tex]\( 104.55 \)[/tex], the variance is [tex]\( 15.6825 \)[/tex], and the standard deviation is approximately .
How much money should be deposited today in an account that earns 6% compounded monthly so that it will accumulate to $9000 in three years?
Answers
A=p (1+r/k)^kt
A future value 9000
P present value?
R interest rate 0.06
K compounded monthly 12
T time 3years
We need to solve for p
P=A÷(1+r/k)^kt
P=9,000÷(1+0.06÷12)^(12×3)
P=7,520.80
Assume that adults have iq scores that are normally distributed with a mean of 100100 and a standard deviation of 15. find the third quartile upper q 3q3, which is the iq score separating the top 25% from the others.
Answers
Final answer:
The third quartile (Q3) of IQ scores, which separates the top 25% of scores, is approximately 110.125 for a normal distribution with a mean of 100 and a standard deviation of 15.
Explanation:
To find the third quartile (Q3) of IQ scores, which is the value that separates the top 25% from the others in a normally distributed data set, we use the properties of the normal distribution. The mean IQ score is 100 and the standard deviation is 15. Q3 corresponds to the 75th percentile in a normal distribution.
To find the third quartile (Q3), we often refer to the z-score table or use a statistical software or calculator that can handle normal distribution calculations. The z-score corresponding to the 75th percentile is approximately 0.675. We can then use the formula for z-scores:
Q3 = mean + z*(standard deviation)
Q3 = 100 + 0.675*15
Q3 = 100 + 10.125
Q3 = 110.125
Thus, the third quartile IQ score, separating the top 25% of scores from the rest, is approximately 110.125.
To find Q3 for IQ scores (mean 100, SD 15), calculate 75th percentile: [tex]\( Q3 = 100 + 0.674 \times 15 = 110.11 \).[/tex]
To find the third quartile (upper Q3) of IQ scores, we need to determine the IQ score that separates the top 25% from the rest. Given that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution to find this value.
1. Identify the z-score corresponding to the third quartile (Q3):
- The third quartile (Q3) corresponds to the 75th percentile of the normal distribution.
- Using the standard normal distribution table or a calculator, the z-score for the 75th percentile is approximately 0.674.
2. Convert the z-score to an IQ score:
- Use the formula for converting a z-score to a value in a normal distribution:
[tex]\[ X = \mu + z \sigma \][/tex]
where:
- [tex]\( \mu \)[/tex] is the mean (100)
- [tex]\( \sigma \)[/tex] is the standard deviation (15)
- [tex]\( z \)[/tex] is the z-score (0.674)
3. Calculate the IQ score:
[tex]\[ Q3 = 100 + (0.674 \times 15) = 100 + 10.11 = 110.11 \][/tex]
Therefore, the third quartile (Q3) IQ score, which separates the top 25% from the others, is approximately 110.
If y = 4x + 3 were changed to y = -4x + 3, how would the graph of the new function compare with the original?
Answers
-4x-3 adding 6 moves the graph upwards by 6 units
-4x-3+6
-4x+3
Answer:
The graph of y=-4x+3 will be as a reflexion in a mirror of y=4x+3
Step-by-step explanation:
y=4x+3 y=-4x+3
. .
. .
. .
Tiffany put a $1550 item on layaway by making a 20% down payment and agreeing to pay $120 a month. How many months sooner would she pay off the item if she increased her monthly payment to $180?
A. 18 months sooner
B. 11 months sooner
C. 4 months sooner
D 7 months sooner
Answers
1550*0.8=1240
1240/120 = approximately 11 months to pay off
1240/180=approximately 7 months to pay off
11-7 =4
so it would be paid off 4 months sooner, so C is the answer
Option: C is the correct answer.
C. 4 months sooner.
Step-by-step explanation:Total amount of the item is: $ 1550
Also, Tiffany paid 20% of the amount by down payment.
Hence, the amount left to pay after the down payment is:80% of total amount.
i.e. 0.80 of total amount.
= 0.80×1550
= $ 1240
Now the number of month it will take if she pay $ 120 a month is:
[tex]=\dfrac{1240}{120}=10.3333[/tex]
which is approximately equal to 11 months.
Similarly, the number of month it will take if she pay $ 180 a month is:
[tex]=\dfrac{1240}{180}=6.8889[/tex]
which is approximately equal to 7 months.
Hence, the number of months sooner she will pay off is:
11-7=4 months.
Which statement about corresponding sides and angles of the two polygons is correct?
Answers
The first option is incorrect because, as seen in the graph, the two angles have the same measure.
The second choice and third choices are wrong because the two polygons are different sizes, as stated in the question and as shown in the attached graph.
Therefore, the last selection is the correct option.
Answer:
Option D. is the correct answer.
Step-by-step explanation:
In this graph, polygon PQRST has been dilated by a scale factor of 3 keeping origin as the center of dilation to form P'Q'R'S'T'.
We know when two polygons are similar, their angles will be same and their corresponding sides will be in the same ratio.
Therefore, option D.which clearly says that the ratio of side SR and S'R' is 1 : 3, will be the answer.
Write the equation in logarithmic form.
25 = 32
A. log32 = 5 • 2
B. log232 = 5
C. log32 = 5
D. log532 = 2
Answers
The equation in logarithmic form is B.log₂32 = 2.
To convert the equation 2⁵ = 32 into logarithmic form, you need to identify the base, the exponent, and the result. The given equation can be interpreted as 2 raised to the power of 5 equals 32.
The general form of a logarithmic equation is: log_base (result) = exponent
In this specific case, we have:
base = 2
result = 32
exponent = 5
Putting it into the logarithmic form, we get: log₂32 = 5
So, the correct option is: B.log₂32 = 2
write the equation of a line that is perpendicular to the line y= (-1/5)x + 2 and has a y-intercept that is 5 units larger that the y-intercept of y= (-1/5)x + 2.
a. y= -5x + 7
b. y= 5x + 7
c. y= (-1/5)x + 7
d. y= (1/5)x + 7
Answers
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Determine which ordered pair is NOT a solution of y=3x-8.
a.
(8, 16)
b.
(3, 4)
c.
(–6, –26)
d.
(–10, –38)
Answers
The coordinates (3, 4) are not of this function:
y = 3x - 8
x = 3:
y = 3(3) -8
= 9 - 8
= 1 ≠ 4
∴ (3, 4) does not lie on the line y = 3x - 8
If the length of a rectangle parking lot is 10 meters less than twice it's width, and the perimeter is 400 meters, find the length of the parking lot
Answers
The length of the rectangular parking lot is 130 meters.
What are the area and perimeter of a rectangle?The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
Given, The length of a rectangular parking lot is 10 meters less than twice it's width.
Assuming the width of the rectangle is x meters, therefore length would be
(2x - 10) meters and the perimeter is 400 meters.
We know the perimeter of a rectangle is 2(length + width).
∴ 2( x + 2x - 10) = 400.
2(3x - 10) = 400.
6x - 20 = 400.
6x = 420.
x = 70 meters and length is (2.70 - 10) = 130 meters.
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A bond payable is similar to which of the following?
Answers
A Bond payable is are likely similar to note payable. They are similar because they have both written premises to pay the interest and the principal amount on a specific futures dates. They are both liability and also the interest is accrued in current liability.
The answer to your question is "Notes Payable."
What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms?
Answers
9 - 3 = 6, 15-9 = 6 the difference is 6, So d = 6
First term: a1 = 3
Sn = n*(a1 + an)/2
Sn = n*(a1 + a1 + (n-1)*d)/2
Sn = n*(2*a1 + (n-1)*d)/2
substitute 26 for n
S26 = 26*(2*a1 + (26-1)*d)/2
substitute 3 for a1
S26 = 26*(2*3 + (26-1)*d)/2
substitute 6 for d
S26 = 26*(2*3 + (26-1)*6)/2
S26 = 2,028
S = n*(a_1+a_n)/2, that easy.
n is the number of terms, 26 in your case. a_n is a_26. We need to find the series!
a_n = a_1 + (n-1)*d, the difference, d, is 6.
So a_n = 3 + (n-1)*6 = 6*n-3 (check it works: 3, 9, 15, ...)
Now a_26 = 6*26-3 = 153, so finally:
S = 26*(3+153)/2 = 26*78 = 2028
2028 is the answer
For Jane's Uber business, she charges $5 initial fee and $0.10 a mile. Joe's Uber business charges $4 initial fee and $0.20 per mile.
1. Write a function for jane's Uber buisiness
2. write a function for joe's Uber business
Answers
Joe : y = 0.20x + 4...or f(x) = 0.20x + 4
The linear equations to calculate the earning by Jane and Joe's Uber business per ride, given the initial fee and charge per mile:
Jane: y = 5 + 0.1x
Joe: y = 4 + 0.2x
What is a linear equation ?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
For Jane's Uber business, she charges $5 initial fee and $0.10 a mile.
Let Jane's earning from a ride be $y.
Let the number of miles she drove in that ride be x miles.
Linear equation to calculate the earning from a ride given the number of miles rode: y = 5 + 0.1x
For Joe's Uber business, he charges $4 initial fee and $0.20 a mile.
Let Joe's earning from a ride be $y.
Let the number of miles he drove in that ride be x miles.
Linear equation to calculate the earning from a ride given the number of miles rode: y = 4 + 0.2x
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What are the amplitude, period, and midline of f(x) = −7 sin(4x − π) + 2?
Answers
This is an example of a sine wave function. A given sine wave function has a standard form of:
y = A sin [B (x + C)] + D
Where,
A = absolute value of amplitude
2 π / B = the period of the sine wave
D = is the midline of y
C = phase of the sine wave
Rewriting the given equation into this form will yield:
f (x) = -7 sin[4 (x – π / 4)] + 2
Therefore from this form, we can get the answers:
Amplitude = 7
Period = 2π / 4 = π / 2
Midline = 2
Which function represents g(x), a reflection of f(x) = 6(1/3)^x across the y-axis?
Answers
g(x)=6(1/3)^(-x)
this will give us the reflection of the f(x) along the y-axis because the only term that is affected upon this transformation is the x-term.
Answer:
its b
Step-by-step explanation:
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Four photographers are taking pictures at a school dance. Photographer A takes 2/5 of the pictures, Photographer B takes 4%, Photographer C takes 0.29, and Photographer D takes 27/100.
Which choice lists the photographers in order from least to greatest by the amount of pictures they take?
Answers
A 2/5 = 40/100
B 4% = 4/100
C .29= 29/100
D 27/100
in order from least to greatest
B
D
C
A
choice "A" is the correct answer or the first option
A) 2/5 = 0.4
B) 4% = 0.04
C) 0.29
D) 27/100 = 0.27
least = 0.04, then 0.27, then 0.29, then 0.4
so B, D, C A is the order
If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be
Answers
rope = 36 feet
first piece = x
2nd piece = 2x ( twice as long as the first piece)
3x=36
x=12
first piece = 12 feet
2nd piece = 2 x 12 = 24 feet
Line EF has an equation of a line y = −2x + 7. Which of the following could be an equation for a line that is perpendicular to line EF?
y = 2x − 3
y = 1 over 2x − 3
y = −2x − 3
y = −1 over 2x − 3
Answers
When a line is given in the form y=mx+n,
m is the slope of this line.
For example, the slope of the line y=-2x+7 is -2.
2.
If lines y=mx+n and y=kx+t are perpendicular, then the multiplication of their slopes is -1, that is
m*k = -1, so k=-1/m
3.
any line perpendicular to y=-2x+7 has slope = -1/(-2)=1/2
4.
Among the choices, y=(1/2)x-3 is a line perpendicular to the given line.
Answer:
b. y=(1/2)x-3
Answer:
[tex]y=\frac{1}{2} x-3[/tex]
Step-by-step explanation:
Step 1
Find the slope of the line EF
we have
[tex]y=-2x+7[/tex]
The slope of the line EF is equal to
[tex]m=-2[/tex]
Step 2
Find the slope of the line perpendicular to the line EF
we know that
If two lines are perpendicular, then the product of its slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
we have
[tex]m1=-2[/tex] -----> slope of the line EF
Find the value of m2
substitute
[tex](-2)*m2=-1[/tex]
[tex]m2=1/2[/tex]
therefore
the equation [tex]y=\frac{1}{2} x-3[/tex] could be an equation for a line that is perpendicular to line EF
Use these values to solve this problem. X=2,y=3,z=4. 21xy/x+z
Answers
21xy/x+z
Substitute x with 12, y with 3, z with 4
21xy/x+z
=21(2)(3)/(2+4)
=42(3)/16
=126/16
=21. As a result, 21 is your correct answer. Hope it help!
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Which equation does the graph below represent?
y = fraction 1 over 4x
y = 4x y
fraction negative 1 over 4x
y = −4x
Answers
Answer:
y=-4x
Step-by-step explanation:
WE need to write the equation for the given graph
In the graph y intercept is (0,0)
The equation of linear graph is y=mx+b
where m is the slope and b is the y intercept
From the given graph y intercept is 0 so b=0
to find slope pick two points from the graph
(0,0) and (1, -4)
slope = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-4-0}{1-0} = -4[/tex]
m=-4 and b=0
So the equation becomes
y= -4x+0
y= -4x
Find three consecutive odd integers with the sum of 51.
Answers
bear in mind that, if you multiply any integer, odd or even, by 2, you get an even, no matter how you slice it and dice it, you always get an even number, 17 *2, 34*2, or whatever * 2, is always an EVEN integer.
you can always get an ODD integer, by simply adding or subtracting 1 from any even, say 4 - 1, or 4 + 1, is 3 and 5 respectively, both odd ones.
and you can always get another consecutive odd integer, by simply jumping 2 units from any odd, so 3, 5, 7, 9, 11 and so on, notice, you simply hop two spots from one, on either direction back or forth, and you get another ODD integer.
alrite, with that in mind, let's pick a reference value, say "a" is our reference integer.
so, 2*a or 2a, we know is an EVEN integer, however, we also know that 2a + 1 is an ODD integer, well, there you have it, our first odd integer is 2a + 1.
now, let's hop twice from there to get our second consecutive odd one, (2a + 1) + 2, or 2a + 3, now, let's hop again to get the next consecutive odd one, (2a + 3) + 2, or 2a + 5.
there you have it, our reference integer is "a", our odd integers are those.
alrite... now, we know their sum gives 51, alrite
[tex]\bf (2a + 1) + (2a + 3) + ( 2a + 5) = 51 \\\\\\ 2a + 1 + 2a + 3 + 2a + 5 = 51 \\\\\\ 2a + 2a + 2a +1 + 3 ++ 5 = 51\implies 6a+9=51\implies 6a=51-9 \\\\\\ 6a=42\implies a=\cfrac{42}{6}\implies \boxed{a=7}[/tex]
now, recall, "a" is only our reference integer, so... if you want to get the consecutive odd integers, well, they're just 2a + 1, 2a + 3 and 2a + 5, and since you already know what "a" is, well, just plug it in to get the integers.
If there is a 0.3% chance of something happening one day, what is the possibility of it happening throughout twenty days?
Answers
Well if there is a 3/10 probability of it happening in any given day, there is a 7/10 probability of it not happening on any given day. The probability of it not happening at all in 20 consecutive days is:
(7/10)^20
So the probability of it happening at least once in 20 days is:
1-(7/10)^20≈9992/10000 (about 99.92%)
What is the formula for a finite geometric series and how can you use it in a practical situation?
Answers
Call r the ratio, An the nth term and An+1 the next term to n, then:
An+1 / An = r
For example, the geometric series, 1, 3, 9, 27, 81, ..
You can verify that
3 = 1* 3
9 = 3 * 3
27 = 9 * 3
81 = 27 * 3
So, the formula is An+1 = An * r, so if you know the first term you can find any other term.
For example, Find the fith term of a geometric series where the first term is 5 and the second term is 25.
r = secont term / first term = 25 / 5 = 5
=> Fifth term = First term * r * r * r * r = First term * r^4 = 25 * 5^4 = 15,625
From this you can also see this valid formula:
An = A1 * r^ (n-1).
So now you have two equivalent formulas:
An+1 = An * r, which is called recursive formula, and
An = A1 * r ^ (n-1), which is called explicit formula