Step-by-step explanation:
a) We can find the iterative rule by first making a table of values.
n -> [tex]a_n[/tex]
1 -> 22
2 -> 28
3 -> 34
We see that [tex]a_n[/tex] increases by 6 each time. Hence, the iterative rule should have the term 6n. However, if we put 1 in for n, we get 6. We want 22-6=16 more than this, or [tex]6n+16[/tex]. This would work for any seat row we give.
b) Our iterative rule to get the number of seats is [tex]6n+16[/tex]. Since we know that this value is 100, we can put both equal to each other.
[tex]6n+16=100\\6n=84\\n=14[/tex]
Thus, the 14th row has 100 seats.
Answer:
(a) S_n = S_1 + 6 (n - 1)
(b) Row 14 has 100 seats
Step-by-step explanation:
(a) The arithmetic sequence would follow the iterative rule,
S_n = S_1 + 6 (n - 1) where S is the number of seats in row n, n is the row number, and S is the number of seats in row 1.
Row 1 = S_1 = 22
2 = S_2 = 28
3 = S_3 = 34
4 = S_4 = 40
|| || = 46
|| || = 52
|| || = 58
|| || = 64
|| || = 70
|| || = 76
|| || = 82
|| || = 88
|| || = 94
Row 14 = S_14 = 100
(b) 100=22+6(n-1) solve for n after setting S_n = 100
100 = 22 + 6_n - 6
84/6 = 6n/6 Row 14 has 100 seats
14 = n
please say thanks!
A regular-size box of crackers measures 214 inches by 912 inches by 14 inches. The manufacturer also sells a snack-size box that has a volume that is 15 of the volume of the regular-size box. What is the volume of the snack-size box of crackers
Answer:
182,156.8
Step-by-step explanation:
214 x 912 x 14 = 2,732,352
1/15 of that Volume is 182,156.8
P.S. I'm assuming you meant 1/15, when you said the volume was 15 of
Follow my gram it's Greyhasnoshame
If two solids are similar and have a linear ratio of 2:5, what is the ratio of the areas?
Answer:
4 : 25
Step-by-step explanation:
given 2 similar figures with linear ratio a : b , then
ratio of areas = a² : b²
here the linear ratio = 2 : 5 , then
area ratio = 2² : 5² = 4 : 25
Let R(x)=3x3+2x2+x and S(x)=4x2+1. Find R(x)+S(x).
The function R(x) + S(x) exists given by [tex]3x^3+6x^2+x+1[/tex].
What is a function?An expression, rule, or law that describes a relationship between one variable (independent variable) and another variable (dependent variable) exists named a function.
Let the functions be [tex]R(x)=3x^3+2x^2+x[/tex] and [tex]S(x)=4x^2+1.[/tex]
Adding both of the equations, we get
[tex]$R(x)+S(x)=(3x^3+2x^2+x) +(4x^2+1)[/tex]
simplifying both of the equations we get
[tex]$R(x)+S(x)=3x^3+2x^2+x+4x^2+1[/tex]
[tex]=3x^3+6x^2+x+1[/tex]
Therefore, the function R(x) + S(x) exists given by [tex]3x^3+6x^2+x+1[/tex].
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how would i solve this?
Answer:
66.0 (nearest tenth)
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the poor drawing)
This is a pure trigonometry question.
Based on the question, we can use the TOA CAH SOH method.
[tex] \cos(x) = \frac{adj}{hypo} \\ \cos(32) = \frac{56}{x} \\ x \cos(32) = 56 \\ x = \frac{56}{ \cos(32) } \\ = 66.0 \: (nearest \: tenth)[/tex]
People in a town have a mean hourly wage of $13.69, with a standard deviation of $4.77. The distribution of hourly wages is not assumed to be symmetric. Between what two-hourly wages does Chebyshev's Theorem guarantee that we will find at least 75% of the people?
Using Chebyshev's Theorem, we are guaranteed to find at least 75% of the people earning hourly wages between $4.15 and $23.23.
What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].In this problem, we want the values within 2 standard deviations of the mean, hence the values are:
13.69 - 2 x 4.77 = $4.15.13.69 + 2 x 4.77 = $23.23.More can be learned about Chebyshev's Theorem at https://brainly.com/question/25303620
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Simplify the expression. x≠0. (4x^2)^0
1
Step-by-step explanation:Anything raised to the power of zero is 1, other than zero itself.
However, as it is given that x is not equal to zero, the answer must be 1.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathsf{(4x^2)^0}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{(4x^2)^0}\\\\\mathsf{= (4 \timesx^2)^0}\\\\\mathsf{= 4(x \times x)^0}\\\\\mathsf{= (4x^2)^0}\\\\\mathsf{= 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should:}[/tex]
[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Can you please help me with this question
When you have negative exponents, you flip it around. Let me give you two examples below.
[tex]x^{-5} = \frac{1}{x^{5} }[/tex]
[tex]10^{-2} = \frac{1}{10^{2} }[/tex]
Therefore you will be doing: [tex]\frac{4}{1} * \frac{1}{10^{2} } = \frac{4}{1} * \frac{1}{100} } = \frac{4}{100} = \frac{1}{25}[/tex]
Your final answer is 1/25.
Brainliest would make my day :)
Translate the triangle by
(-2
-4)
Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Translating the triangle using the vector [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.
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Please help..this is due tomorrow morning.
PLS HELP!!!!
The half-life of Carbon-14 is 5730 years. Suppose a fossil is found with 27% of Carbon-14 as compared to a living sample. How old is the fossil?
Answer: 1547.10
Step-by-step explanation: Since you are not in a physics class, in which case requires the usage of the radioactive decay formula, definite integrals, and natural logarithms) but an Algebra class which deploys the usage of percentages, this should be rather simple.
I believe they want you to find 27% of the half life of Carbon-14 since it is below 50%. To find the percent of a number (in this case 27%), you multiply the number by 0.27.
5730 * 0.27 = 1547.10
Hope this helped! And if I'm wrong, please don't hesitate to correct me.
Instructions: Find the surface area of
each figure. Round your answers to the
nearest tenth, if necessary.
Surface Area:
5.2 cm.
cm²
Answer:
Given is radius of circle that is 5.2, you just need to find the area of the circle.
To find the are of circle is A=πr2
π value is 3.14 and radius value is 5.2 you just need to square the 5.2, answer will come 27.04
now multiply the πr and 27.04.
the answer will come 84.9 and question says to round to the nearest tenth, that will be 85.
Rounding to the nearest tenth, the surface area of the circle with a 5.2 cm radius is approximately 84.8 cm².
The surface area of a circle can be calculated using the formula:
Surface Area = π * radius²
where π (pi) is a mathematical constant approximately equal to 3.14159, and the radius is the distance from the center of the circle to any point on its edge.
Given the radius is 5.2 cm, we can now calculate the surface area:
Surface Area = 3.14159 * (5.2 cm)²
Surface Area = 3.14159 * 27.04 cm²
Surface Area ≈ 84.823 cm²
The surface area represents the total area of the circle's two-dimensional space. In this case, it gives us the total area of the circular region with a 5.2 cm radius.
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G= -x^2 - 2xy - y^2
K= x^2 + 4y^2 + 4xy
H= 4x^2 - 12xy + 9y^2
L= 25 - 10 + y^2
M= 10y^4 + 25x^6 +y^8
Answer:
Step-by-step explanation:
I am assuming you want to factor these functions
G= -x^2 - 2xy - y^2
= -(x^2 + 2xy + y^2)
We need 2 terms whose product is y^2 and whose sum is +2xy
- they are + x and + y
= - (x + y)(x + y)
= -(x + y)^2
The other functions are worked out in the same way:
K = x^2 + 4y^2 + 4xy
= (x + 2y)(x + 2y)
= (x + 2y)^2
H = 4x^2 - 12xy + 9y^2
= (2x - 3y)^2
L= 25 - 10 + y^2
= (5 - y)^2
M = 10y^4 + 25x^6 +y^8
- this is prime (no factors)
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
The box plot shows the heights of grade 7 students in two random samples from two different schools. The sample from each school is 30% of the student population. Based on the box plot, which comparison is true?
image
A.
Grade 7 students from School A are typically taller than grade 7 students from School B because of the difference in the interquartile ranges of grade 7 student heights at the schools
B.
Grade 7 students from School A are typically taller than grade 7 students from School B because of the difference in the medians of grade 7 student heights at the schools.
C.
Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the interquartile ranges of grade 7 student heights at the schools.
D.
Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the medians of grade 7 student heights at the schools.
The true statement is Grade 7 students from School A are typically shorter than grade 7 students from School B because of the difference in the medians of grade 7 student heights at the schools. (option D)
What is the true statement?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.
The end of the first line represents the minimum number and the end of the second line represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.
Median for School A = 57
Median for School B = 61
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What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 5x2 x 3
The solutions to the system of equations involving quadratic function f(x) and linear function g(x) are (-1,5) and (4/3,29/3), respectively.
What is a polynomial function?A polynomial function is a relationship in which a dependent variable equals a polynomial expression. A polynomial expression is one that has numbers and variables that are raised to non-negative powers.To find the solution to the given system of equations:
A polynomial expression has the following generic form:a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ.The degree of the polynomial expression has the greatest power on a variable.When degree = 2, the function is quadratic.When degree = one, the function is linear.Given quadratic equation: f(x) = 3x^2 + x + 3
We must solve the linear equation g(x). Because it is a linear equation, we utilize the two-point approach to solve it.The two point formula is: y-y₁ = ((y₂-y₁)/(x₂-x₁))*(x-x₁)
We take the points g(2) = 11, g(1) = 9
g(x) - g(1) = ((g(2)-g(1))/(2-1))*(x-1)
or, g(x) - 9 = ((11-9)/(2-1))*(x-1)
or, g(x) - 9 = 2(x-1)
or, g(x) = 2x - 2 + 9 = 2x + 7
g(x) = 2x +7, is the linear function g(x)
We are asked to solve the system of equations f(x) and g(x).
To get the solution, we must first determine what is the common solution to both f(x) and g(x).
For that, we equate f(x) and g(x).
3x² + x + 3 = 2x + 7
or, 3x² - x - 4 = 0
or, 3x² + 3x - 4x - 4 = 0
or, 3x(x+1) -4(x+1) = 0
or, (3x-4)(x+1) = 0
∴ Either 3x-4=0 ⇒ x = 4/3
or, x+1=0 ⇒ x = -1.
g(-1) = 5 (from the table)
f(-1) = 3(-1)² + (-1) + 3 = 3 - 1 + 3 = 5
g(4/3) = 2(4/3) + 7 = 8/3 + 21/3 = 29/3
f(4/3) = 3*(4/3)² + (4/3) + 3 = 16/3 + 4/3 + 9/3 = 29/3
∴ f(-1) = g(-1) and f(4/3) = g(4/3).
Therefore, the solution to the system of equations that includes quadratic function f(x) and linear function g(x) is (-1,5) and (4/3,29/3).
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The correct question is given below:
What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?
f(x) = 3x^2 + x + 3
In 1993, the moose population in a park was measured to be 4760. By 1999, the population was measured again to be 5960. If the population continues to change linearly:
The formula for moose population is P = 4760 + (number of years x 200).
The moose population in 2003 would be 6760.
What would be the moose population in 2003?When a population increases linearly, it means that it increases by the same amount each year.
Rate of linear increase: (population in 1999 - population in 1993) / difference in years
(5960 - 4760) / (1999 - 1993)
1200 / 6 = 200
Linear function : initial population + (rate of increase x number of years)
Population in 2003: 4760 + (200 x 10)
4760 + 2000 = 6760
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PLSSS HELP ASAP!! ty
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
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Expand (x – 4)^5 using the Binomial Theorem and Pascal’s triangle
[tex]5th \: row = 1 \: \: \: 5 \: \: \: 10 \: \: \: 10 \: \: \: 5 \: \: \: 1[/tex]
[tex](x - 4) {}^{5} = x {}^{5} + 5x {}^{4} ( - 4) {}^{1} + 10x {}^{3} ( - 4) {}^{2} + 10x {}^{2} ( - 4) {}^{3} + 5x( - 4) {}^{4} + ( - 4) {}^{5} [/tex]
[tex](x - 4) {}^{5} = x {}^{5} - 20x {}^{4} + 160x {}^{3} - 640x {}^{2} + 1280x - 1024[/tex]
Indicate the equation of the line meeting the given conditions. Put the equation in standard form.
Containing E(4, 3) and F(6, 1)
Answer:
x + y = 7
Explanation:
slope formula:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Find slope: given points: E(4, 3), F(6, 1)
[tex]\sf slope \ (m) : \dfrac{1-3}{6-4} = -1[/tex]
Find Equation: [tex]y - y_1 = m(x -x_1)[/tex]
[tex]\sf y - 3 = -1(x - 4)[/tex]
[tex]\sf y = -x + 4 + 3[/tex]
[tex]\sf y = -x + 7[/tex]
[tex]\sf x + y = 7 \quad (in \ standard \ form \ \rightarrow Ax + By = C)[/tex]
Slope of the line
m=(1-3)/6-4m=-2/2m=-1Equation in point slope form
y-3=-1(x-4)y-3=-x+4y=-x+7x+y=7help please and show work 30 points
Answer:
The pair of shoes equal 18.
The boat equals 3
The chair equals 4
Step-by-step explanation:
Let x = shoes
You found the palm trees!
So the top picture would be
18 + x = 2x Subtract x from both sides
18 = x We found the value of the shoes.
Let's go so the last picture. We now know the shoes.
Let x = the boat now
18 = 6x Divide both sides by 6
x = 3 We found the value of the boat.
Finally, let's look at the second picture.
Let x = the chair now
3 + x = 7 Subtract 3 from both sides
x = 4 We found the value of the chair.
In a hypothesis test, what should we conclude if the data would be very unusual if the original assumption about our parameter were correct?
We conclude the hypothesis test as Alternative Hypothesis if the data would be very unusual if the original assumption about our parameter were correct.
A hypothesis in statistics is a claim or supposition on the properties of one or more variables in one or more populations. There are two hypothesis to choose between because a statement might either be true or wrong.The null hypothesis is the assertion that we (or someone else) consider to be true. Our hypothesis test will come to one of two conclusions: "reject H0" or "do not reject H0." Remember that until data provide evidence to the contrary, we always proceed under the null hypothesis.If the null hypothesis is incorrect, the alternative hypothesis must be true. The hypothesis test can be different in one of three ways: greater than, smaller than, or just different (not equal). As a result, there will always be an inequality requirement in the notation for H.Learn more about Alternative hypothesis here: https://brainly.com/question/17173491
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A soccer team won only 10 of their first 30 games. How many of their remaining 20 games will they have to win to have a .500 record??
Answer: 5 games
Step-by-step explanation: A .500 record means that the soccer team won half of their games ( that's how I interpret it). Since they are going to play 30 games, they need to win half of 30 or 15 games to have that record. 15-10 = 5. So, they need to win 5 more games to have a .500 record.
Which set of radian angle measures is
equivalent to….
[tex]
\sin^{-1} \left(-\frac{1}{2} \right)=-\sin^{-1} \left(\frac{1}{2} \right)=\boxed{-\frac{\pi}{6}}[/tex]
I need help locating , x=,y=,z= please. Thanks
1) Find the domain of the function f(x) = 1 / |x ^2- 4|
2) Find the domain of the function f(x) = 1 / (x^ 2 + 4x + 3)
Answer:
x<-3 or -3<x<-1 or x>-1
Step-by-step explanation:
Domain - The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.
\mathrm{Domain\:of\:}\:\frac{1}{x^2+4x+3}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<-3\quad \mathrm{or}\quad \:-3<x<-1\quad \mathrm{or}\quad \:x>-1\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:-3\right)\cup \left(-3,\:-1\right)\cup \left(-1,\:\infty \:\right)\end{bmatrix}
These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
Town B
10 15 20
H
5
ㅏ
20
30
30
40
55
55
05 10 15 20 25 30 35 40 45 50 55 60
Degrees (F)
The correct option regarding the data-sets represented by the box and whisker plots is:
B. The distribution for town A is positively skewed, but the distribution for town B is symmetric.
What does a box-and-whisker plot shows?A box and whisker plot shows three things:
The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.For data-set A, we have that:
The 25th percentile is of 15.The median is of 20.The 75th percentile is of 30.Since 30 - 20 > 20 - 15, the distribution is positively skewed.
For data-set B, we have that:
The 25th percentile is of 20.The median is of 30.The 75th percentile is of 40.Since 40 - 30 = 30 - 20, the distribution is symmetric.
Hence the correct option is:
B. The distribution for town A is positively skewed, but the distribution for town B is symmetric.
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How many positive integers less than 1000 a) are divisible by 7? b) are divisible by 7 but not by 11?
Answer:
130
Step-by-step explanation:
The number of integers meeting the criteria can be found by counting them using a counting formula.
Divisible by 7Integers divisible by 7 will have the form (7n), where n is some positive integer. The number of them less than 1000 can be found from ...
7n ≤ 1000
n ≤ 142.857
There are 142 integers less than 1000 that are divisible by 7.
Divisible by 7 and 11Similarly, integers divisible by 7 and 11 will be of the form (77n), for some positive integer n.
77n ≤ 1000
n ≤ 12.987
There are 12 integers less than 1000 that are divisible by both 11 and 7.
Divisible by 7, not 11The number of integers less than 1000 that are divisible by 7, but not 11, will be the difference of these numbers.
142 -12 = 130 integers divisible by 7, but not 11.
A diver is standing on a spring board 48 feet above the pool. She jumps from the platform with an
initial upward velocity of 8 feet /second. Use the formula d(t)= -16(2t - 3)(t+1), where d is the
height of the diver above the water and t is the time in seconds. How long will it take for her to hit
the water?
It will take the diver 1.5seconds for her to hit the water
Linear equationsLinear equations are equation that has a leading degree of 2. Given the expression that expresses the distance covered by the diver as a function of time as shown;
d(t)= -16(2t - 3)(t+1)
where;
d is the height of the diver above the water and;
t is the time in seconds.
Given the following
d = 0 (the distance on the ground)
Substitute into the formula below;
-16(2t - 3)(t+1)= 0
Divide through by -16
(2t - 3)(t+1) = 0
Determine the time
2t - 3 = 0
t = 3/2
Similarly;
t +1 = 0
t = -1
Hence it will take the diver 1.5seconds for her to hit the water
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A softball pitcher has a 0. 431 probability of throwing a strike for each pitch. if the softball pitcher throws 22 pitches, what is the probability that exactly 12 of them are strikes?
The probability that exactly 12 of them are strikes is 0.09.
In this question,
Number of pitches, n = 22
Probability of throwing a strike for each pitch, p = 0.431
Then, q = 1 - p
⇒ q = 1 - 0.431
⇒ q = 0.569
Number of strikes, x = 12
The probability that exactly 12 of them are strikes can be calculated using Binomial expansion,
[tex]P(X=x)=nC_xP^{x}q^{(n-x)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{(22-12)}[/tex]
⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{10}[/tex]
⇒ [tex]P(X=12)=(\frac{22!}{12!10!} )(0.431)^{12}(0.569)^{10}[/tex]
⇒ P(X=12) = (646646)(0.000041)(0.00355)
⇒ P(X=12) = 0.09431 ≈ 0.09
Hence we can conclude that the probability that exactly 12 of them are strikes is 0.09.
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Given sin theta=5/13 and cos theta=12/13, which of the following can be proven using a Pythagorean identity?
Answer:
4th option
Step-by-step explanation:
given
sinΘ = [tex]\frac{5}{13}[/tex] and cosΘ = [tex]\frac{12}{13}[/tex] , then
( [tex]\frac{5}{13}[/tex] )² + ( [tex]\frac{12}{13}[/tex] )²
= [tex]\frac{25}{169}[/tex] + [tex]\frac{144}{169}[/tex]
= [tex]\frac{25+144}{169}[/tex]
= [tex]\frac{169}{169}[/tex]
= 1
showing sin²Θ + cos²Θ = 1