The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.
What is the nth term of an arithmetic series?The nth term of an arithmetic sequence is calculated by the formula
aₙ = a + (n - 1) · d
Here the first term is 'a' and the common difference is 'd'.
Calculation:The given sequence is an arithmetic sequence.
3, 7, 11, 15, 19, ....
So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.
Thus, the required 21st term in the sequence is
a₂₁ = 3 + (21 - 1) × 4
⇒ a₂₁ = 3 + 20 × 4
⇒ a₂₁ = 3 + 80
∴ a₂₁ = 83
So, the 21st term in the given arithmetic sequence is 83.
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solve the equation -6=2(w+5)
which is true about the product of 10 and 2/3
A The product is less than 2/3
B The product is greater than 10
C The product is less than 10
D The product is between 2 and 3
i don't have anymore points this is all i have
The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The numbers are given below.
10 and 2/3
The product of the numbers 10 and 2/3 will be given as,
⇒ 10 x 2 / 3
⇒ 20 / 3
⇒ 6.67
The value of the product of the numbers 10 and 2/3 is less than 10. Then the correct option is C.
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What is the volume of a cube with side
lengths that are 30 inches? Use the formula
V = s³, where s is the length of one side.
60 in.³
900 in.³
2,700 in.3
27,000 in.³
Answer:
27,000 or D
Step-by-step explanation:
30 x 30 x 30 = the answer on edge <3 good luckkk
Math question
finding the slope
Answer:
y-intercept: -1
Step-by-step explanation:
The equation is y = mx + b
In this case, the y-intercept is -1
-1 is an integer, so my answer is correct!
Answer:
Slope: 1/3, [tex]y[/tex]-intercept: -1
Step-by-step explanation:
The [tex]y[/tex]-intercept of the line with equation [tex]y=mx+b[/tex] is [tex]b[/tex]. The slope is [tex]m[/tex].
how many of the natural numbers from $1$ to $600$, inclusive, contain the digit $5$ at least once? (the numbers $152$ and $553$ are two natural numbers that contain the digit $5$ at least once, but $430$ is not.)
There are 195 natural numbers from 1 to 600
The term integer is referred as the combination of zero, natural numbers and their additive inverse
Here we need to find how many of the natural numbers from 1 to 600, inclusive, contain the digit 5 at least once.
While we looking, into the given range of numbers 100 integers from 500 - 599 contain at least one 5
And here we know that in each of the 499 integers
=> _5, _15, _25, _35, _ 45, _55 , _65, _ 75, _ 85 , _ 95
And we also know that in each hundred from 1 to 499 contain at least one 5
Therefore, there are 5 sets of these = 5 * 10 = 50
So, in each hundred from 1 to 499 we have the integers
Therefore, _5_ where the last digit is not a 5
So, we have 9 of these in every hundred
Then here we have 5 * 9 = 45 of these
=> 100 + 50 + 45 = 195
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diseases tend to spread according to the exponential growth model. in the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9. in 1983, about 1700 people in the u.s. died of aids. if the trend had continued unchecked, how many people would have died from aids in 2005?
The number of people died from aids in U.S. in 2005 are 2,30,68,96,671
Given, diseases tend to spread according to the exponential growth model.
In the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9.
In 1983, about 1700 people in the U.S. died of aids.
we have to find the number of people died from aids in 2005.
Let the exponential function, be
P(x) = AB^x
where, A is the initial population of people died of aids in U.S.
B is the growth factor of aids in U.S.
as, B = 1.9
In 1983, x = 0
P(0) = AB^0
1700 = A
Now, P(x) = 1700(1.9)^x
and the number of years from 1983 to 2005 are, 22 years
The number of people died from aids in 2005 be,
P(22) = 1700(1.9)^22
P(22) = 2,30,68,96,671
So, 2,30,68,96,671 people died from aids in 2005.
Hence, 2,30,68,96,671 people died from aids in 2005.
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Find the equation of a line parallel to x −6y=−60−9xthat passes through the point ( − 6 , 9 ) (−6,9).
Answer:
Therefore, the equation of the line that is parallel to the given line and passes through the point ( − 6 , 9 ) (−6,9) is y = 4x + 33.
Step-by-step explanation:
To find the equation of a line that is parallel to a given line and passes through a given point, you can use the point-slope form of a linear equation. The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
Where (x1, y1) is the point through which the line passes, and m is the slope of the line.
The slope of a line is given by the difference in the y-coordinates of two points on the line, divided by the difference in the x-coordinates of those points. The slope of a line is also the coefficient of the x-term in the standard form of a linear equation (y = mx + b).
In this case, the given line is x − 6y = −60 − 9x. To find the slope of this line, you can rearrange the equation to standard form:
x − 6y = −60 − 9x
−9x + x − 6y = −60
−8x − 6y = −60
y = 4x + 15
The slope of this line is m = 4.
To find the equation of a line parallel to this line that passes through the point ( − 6 , 9 ) (−6,9), you can use the point-slope form of a linear equation with (x1, y1) = ( − 6 , 9 ) (−6,9) and m = 4:
y - 9 = 4(x - (-6))
y - 9 = 4(x + 6)
y - 9 = 4x + 24
y = 4x + 33
sky won a total of 480 tickets at the arcade. she choose a stuffed animal and wants to redeem her remaining tickets on sticky hands. Which represents the possible number of sticky hands she can choose?
The answer is 240 sticky hands. This is because each sticky hand costs 2 tickets, so if she has 480 tickets, she can buy 240 sticky hands.
What is cost?
Cost is the amount of money that is required to purchase, use, or produce something. It is an economic measure of the value of goods, services, or resources. Cost is typically associated with the purchase of goods and services and can include both the monetary and non-monetary costs associated with the acquisition. For example, when buying a car, the cost is the money spent on the purchase plus any additional costs such as taxes, registration fees, and insurance. Non-monetary costs can include the time and effort invested in researching and shopping for the car, as well as the opportunity cost of not using the money for something else.
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What is the polar form of ? 7(cos(30o) + i sin(30o)) 7(cos(330o) + i sin(330o)) 14(cos(30o) + i sin(30o)) 14(cos(330o) + i sin(330o)).
Polar form of complex numbers is z=a+bi is
z = r(cosθ + i sinθ) . So, first find the absolute value of r and then argument θ. Polar form of given expression are
a) 7(√3/2 + i/2 )
b) 7(√3/2 - i/2)
c) 14(√3/2 + i/2)
d) 14(√3/2 - i/2)
The polar form of complex numbers is a different way of representing complex numbers than the orthogonal form. Complex numbers are usually represented in the form z = x+iy. where "i" is an imaginary number. But in polar form, complex numbers are represented as a combination of modulus and argument.
Problems Algebra Convert to polar form
a) 7(cos(30°) + i sin(30°))
we simplify each term.
The exact value of cos(30°) = √3/2
=> 7((√3/2) + i sin(30°))
The exact value of sin(30°) = 1/2
=> 7(√3/2 + i/2 )
Combine all values we get, 7(√3/2 + i/2 )
7(cos(330°) + i sin(330°))
Using quadrant system
b) cos(330°) = cos(360°- 30°) = cos 30° = √3/2
sin(330°) = sin(360°- 30°) = - sin 30° = -1/2
so, 7 ((√3/2) + i(-1/2))
= 7√3/2 - 7i/2 = 7(√3/2 - i/2)
c) 14(cos(30°) + i sin(30°))
= 14 ((√3/2) + i (1/2)) = 14√3/2 + 14i/2=14(√3/2 - i/2)
d) 14(cos(330°) + i sin(330°))
= 14 (√3/2) + 14i(-1/2) = 14√3/2 - 14i/2
= 14(√3/2 - i/2)
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Answer:
14(cos(330o) + i sin(330o))
Step-by-step explanation:
A mountaineer is climbing on a cliff. She is 400 feet above the ground. If she climbs up, this will be a positive change. If she climbs down, this will be a negative change.
Complete the table.
Answer:
I added a picture, hope this helps!
Step-by-step explanation:
Let me know if you need to show work
in analysis of variance, what is measured by the ms values? group of answer choices the mean of the standard deviations the mean variability within conditions the mean variability between conditions the mean of the squared deviations
The mean of the squared deviations
What is Squared deviations?
The sum of all scores' squared deviations from the mean is lower than the sum of all scores' squared deviations from any other number. The least squares concept governs this.
What is Mean ?
The average of a group of values is referred to as the mean. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
The term "mean square" refers to the sample variance in the analysis of variance (ANOVA) table, which calculates the mean squared deviation.
The average of the deviations' squared
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Step 2: Look at the second part of the word problem.
Cadence has 16 more blue-eyed dolls than green-eyed dolls.
Let b represent the dolls with blue eyes.
Let g represent the dolls with green eyes.
Write an equation for this part of the word problem.
The equation part of the given word problem is x+y=52 and y=x+16.
a) Let x = number of green eyed dolls
And let y = number of blue-eyed dolls
Now we are told the following:
x+y=52 → eq1
and
y=x+16 → eq2
b) substitute y = x+16 from eq2 into eq1:
x+x+16 = 52 subtract 16 from each side
x+x+16-16 = 52-16 collect like terms
2x = 36 divide each side by 2
x = 18 → number of green-eyed dolls
substitute x = 18 into equation2
y = 18+16 =34 → number of blue-eyed dolls
18+34=52
52=52
and
18+16=34
34=34
THIS PROBLEM CAN ALSO BE SOLVED USING ONE EQUATION AND ONE UNKNOWN:
Let x = Number of green-eyed dolls
Then 52-x = Number of blue-eyed dolls
Now we are told that:
x+16 = 52-x add x to and subtract 16 from each side
x+x+16-16 = 52-16-x+x collect like terms
2x=36 → same as before
x = 18.
Hence, the equation part of the given word problem is x+y=52 and
y=x+16.
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consider the matrix : what is the minimal approximation error achievable by a rank-1 approximation to ?
The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is
||A - A1||₂=0 where A is 2×2 matrix.
We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]
note here that C₂= 3C₁
where Cᵢ --> iᵗʰ column
v = [ 5 ; 6 ; -1 ; -4 ; 2]
||v||² = 82 => ||v|| = √82
and A At v = 820 v
and A At = [ 82 246 ; 246 738]
AAt [1;3] = 820[1;3]
=> v1 = 1/√10(1,3)^t
Then the best rank of 1 approx
= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]
= A
Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0
Hence, the minimal Approx. ||A - A1||2 = 0 .
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Complete question:
Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?
Solve Proportion
y/32=16/10
Answer:
y = 51.2
Step-by-step explanation:
y/32=16/10
First, we time 32 on both sides to get y alone
y = 32(16/10)
y = 32(1.6)
y = 51.2
Let's check:
51.2/32 = 16/10
1.6 = 1.6
The answer y = 51.2 is correct!
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what's the probability you don't roll doubles on your first roll, then roll doubles on your second roll?
We have a 1/6 chance of rolling doubles on the first roll. The odds of rolling a double on the second turn but not the first are (5/6) x (1/6) = 5/36.
So we have a total of 36 outcomes over here. So we have 36 possibilities, and if we simplify this, 6/36 is 1/6. So the chance of rolling doubles on two six-sided dice numbered 1 to 6 is 1/6.
The odds of rolling a double on the second turn but not the first are (5/6) x (1/6) = 5/36.
We'll now look at the chances of getting out of jail by rolling doubles. Because there are more possibilities to examine, this probability is significantly more complex to compute.
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Please help me. It’s not that hard I’m just in a rush and dont have time to do it myself
Answer:D
Step-by-step explanation: 610/488= 1.25 or 5/4
A nursery owner buys 8 panes of glass to fix some damage to her greenhouse. The panes cost $21.20. Unfortunately, she breaks 3 more panes while repairing the damage. What is the cost of another 3
panes of glass
Cost of another 3 panes of class is 7.95
How to calculate the cost of another 3 panes of glass ?Given, Number of panes of glass bought = 8
Cost of 8 panes of glass = $21.20
Number of broken panes of glass = 3
We must determine the price of three glass panes.
By unitary method, If 8 panes of glass costs $21.20 , then the cost of one pane of glass will be as follows,
Cost of one pane of glass = 21.20/8
= $2.65
Therefore, cost of 3 panes of glass it would be $2.65×3 = 7.95
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.
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Find the area of a triangle whose sides are 4.5 cm and 1 cm and perimeter 10.5 cm.
The area of a triangle whose sides are 4.5 cm and 1 cm and perimeter 10.5 cm is 2.045 square cm
How to find the area of the triangleThe area for the triangle whose perimeter and side is given is solved by the formula
A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c))
where:
a, b, and c are the sides of the triangle
s = perimeter / 2
perimeter = a + b + c
10.5 = 4.5 + 1 + c
c = 10.5 - 5.5
c = 5
s = (a + b + c) /2
s = 10.5/2
s = 5.25
substituting for s a b and c
A= √(s(s ﹣ a) (s ﹣ b) ( s ﹣ c) )
A= √(5.25 (5.25 ﹣ 4.5) (5.25 ﹣ 1) (5.25 ﹣ 5) )
A = √4.18358
A = 2.045 square cm
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2) Ratio of basketballs to soccer balls
1)
2:1
OPEN ENDED QUESTION
In example #2, which quantity will you write first:
basketballs or soccer balls? Why?
The ratio of basketballs to soccer balls is 2 : 1
The quantity which would be written first if basketballs to soccer balls is 2 : 1 is basketball
What is ratio?This refers to a number representing a comparison between two or more named things.
If the ratio of basketballs to soccer balls = 2 : 1
This means,
Basketball : soccer ball = 2 : 1
Therefore, Basketball is the quantity which would be written first because it comes first in the given expression.
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Determine if the following are true or false: [Choose ] As n increases the t-distribution approaches the standard normal distribution. As n increases, the tails in the t- distribution become "fatter". [Choose ] [Choose ] The shape of a t-distribution depends on its degrees of freedom. [Choose ] We will always use a student'st distribution when we are given raw data to analyze, regardless if we know the population standard deviation or not. t-distributions are similar in shape to the standard normal curve. [Choose] [Choose ] We use the Student's t-distribution when we estimate the mean of a population that is normally distributed, has an unknown standard deviation, and small n.
Answer:
true i think
Step-by-step explanation:
you are bored at a lunch meeting and surreptitiously place a raisin in your glass of water. the raisin swells to twice its original size. relative to the water, the raisin must have been:
If the raisin swells to twice its original size, relative to the water, the raisin must have been a)hypertonic solution. So, correct option is a.
Hypertonic alludes to an answer with higher osmotic strain than another arrangement. At the end of the day, a hypertonic arrangement is one in which there is a more noteworthy fixation or number of solute particles outside a layer than there are inside it.
A hypertonic arrangement is one which has a higher solute fixation than another arrangement.An illustration of a hypertonic arrangement is the inside of a red platelet contrasted and the solute centralization of new water.At the point when two arrangements are in touch, solute or dissolvable moves until the arrangements arrive at harmony and become isotonic concerning one another.Hence, correct option is a.
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(Complete question) is:
You are bored at a lunch meeting and surreptitiously place a raisin in your glass of iced tea. The raisin shrinks to half its original size. The raisin must have been a __?__ solution.
a)hypertonic
b)aquatonic
c)hypotonic
d)isotonic
Let
ƒ(x) = (x + 2)² +3
g(x)=2x+6
Write the equation for the function.
Answer:
x³ -6x² +11x-6
Step-by-step explanation:
as there are three zeros visible, we assume the function is cubic. It can be written in the form ax³ +bx²+cx +d. Another form of writing a function is by making the brackets (x-x0), where x0 is the zero of the function (the value of the function for x0 is equal zero): a(x-1)(x-2)(x-3) (I assumed a is 1). By multiplying the brackets, you got the answer.
how do we specify the one-way anova model in the model statement of proc glm? select one: a. model response variable*grouping variable; b. model response variable; (the grouping variable is only specified in the class statement.) c. model grouping variable
We specify the one-way anova model in the model statement of proc glm is model response variable; (the grouping variable is only specified in the class statement.)
So option b. is the correct option of the given statement.
We define variables for what purpose?Information that needs to be accessed and changed by a computer program is stored in variables. In order to make our programs more understandable to ourselves and the reader, they also offer a mechanism to label data with a descriptive name.
How should variables be used?Values can be stored in variables. In order to use a variable, we must first declare it so the program is aware of it and then assign it so the program is aware of the value we are storing in the variable.
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Find the volume and the surface area of a cylinder where r:
= 8m, h = 15m
Answer:
volume = 960π m³ ; surface area = 368π m²
Step-by-step explanation:
base area = 8²π = 64π m²
base perimeter = 8 x 2 x π = 16π m
lateral area = 16π x 15 = 240π m²
surface area = 2 x 64π + 240π = 128π + 240π = 368π m²
Volume = 64π x 15 = 960π m³
If y = x-4, which point corresponds to the location where y = -7? (Hint: Keep in mind that this question gives you the
value of y, not x.)
The variable y takes the value -7 when we have x = -3.
For which value of x we have y = -7?
Here we have the linear equation:
y = x - 4
We want to find the value of x such that y = -7, to get that, we only need to replace the variable y by the number -7 in the linear equation above:
-7 = x - 4
Now we can solve the linear equation for x.
-7 = x - 4
-7 + 4 = x
-3 = x
That is the solution.
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Which of the following is a zero of 3x² + 5x - 2?
The zeros of the expression 3x² + 5x - 2 are 1/3 and -2
What is a quadratic equation?A quadratic equation can simply be defined as an algebraic equation having the second degree of x.
From the information given, we have that;
3x² + 5x - 2
Equate the expression to zero
3x² + 5x - 2 = 0
Find the pair factors of -6 that sum up to + 5, we get;
+ 6 and -1
Substitute the values into the equation;
3x² + 6x - x - 2 = 0
Enclose in brackets
(3x² + 6x) - ( x - 2) = 0
Factor the common terms
3x( x + 2) - 1( x + 2)
Then,
3x - 1 = 0
x = 1/3
x +2 = 0
x = -2
Hence, the values are 1/3 and -2
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Someone please help I can’t figure out 11, 13, or 15 I just need an explanation and how to set the equation up!!??
The solution to each of the system of equations is given as follows:
11. (1,-1).
13. (-6,-5).
15. (-4,3).
What are the solutions to the system of equations?For item 11, the system is given as follows:
5x = y + 6.5x + 2y = 3.The variable x can be isolated as follows:
5x = y + 6.5x = 3 - 2y.Then the solution for y is given as follows:
y + 6 = 3 - 2y
3y = -3
y = -1.
Then the solution for x is of:
5x = -1 + 6
5x = 5
x = 1.
Following the same procedure, in item 13, we have that:
3y = 6x + 21.3y = 4x + 9.Hence the solution for x is of:
6x + 21 = 4x + 9
2x = -12
x = -6.
The solution for y is of:
3y = 4(-6) + 9
3y = -15
y = -5.
For item 15, we have that:
x = 5 - 3y.x = -6y + 14.Hence the solution for y is of:
5 - 3y = -6y + 14
3y = 9
y = 3.
Then the solution for x is of:
x = 5 - 3(3)
x = 5 - 9
x = -4.
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se the given information to prove that m
By using the given information we can prove that m ∠ABC = m ∠EDC.
What are similar angles?
Polygons' corresponding sides and corresponding angles are compared as part of the geometric tests for congruence and similarity. With care taken to maintain the order of adjacency, each side and each angle in one polygon is paired with a side or angle in the other polygon in these tests.
Given:
m ∠1 = m ∠2
m ∠2 = m ∠4
We have to prove that m ∠ABC = m ∠EDC
Let, ∠ABC = ∠1 + ∠2
and ∠EDC = ∠3 + ∠4
So, m ∠ABC = m ∠1 + m ∠2
and m ∠EDC = m ∠3 + m ∠4
From the given information,
m ∠1 + m ∠2 = m ∠3 + m ∠4 (Since m ∠1 = m ∠3, m ∠2 = m ∠4)
⇒ m ∠ABC = m ∠EDC
Hence, by using the given information we can prove that
m ∠ABC = m ∠EDC.
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How do you find the derivative of 1/logx?
The derivative of 1/logx is With the chain rule.
1log(x)=log(x)−1 is ,= -1xlog(x)2 .
The by-product of logₐ x (log x with base a) is 1/(x ln a). Here, the thrilling issue is that we have "ln" withinside the by-product of "log x". Note that "ln" is referred to as the logarithm (or) it's miles a logarithm with base "e".
The by-product of 1/log x is -1/x(log x)^2. Note that 1/logx is the reciprocal of log.
[tex]With the chain rule. \\
1log(x)=log(x)−1 \\
So you follow the chain rule to the electricity after which to the log: \\
ddxlog(x)−1=−1⋅log(x) \\ \\−2⋅ddxlog(x)
\\ =−1log(x)21x
\\ =−1xlog(x)2 .[/tex]
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