The formula for estimating the nth term of an arithmetic sequence exists:
a n = a₁ + (n-1)d
What is meant by arithmetic sequence?A series of numbers named an arithmetic progression or arithmetic sequence (AP) contains a constant difference between the terms.
The formula for estimating the nth term of an arithmetic sequence exists:
a n = a₁ + (n-1)d
The four quantities in the formula exist a n, a₁, n, d
The description exists as follows:
an be the nth term of the sequence
a₁ be the first term of the sequence
n be the number of terms
d be the common difference
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Help ASAP! 30 points!
Is the mean greater than, less than, or equal to the median? Explain your reasoning.
Since the distribution is symmetric, the mean and the median of the distribution are equal.
What are the mean and the median of a distribution?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.The median of a distribution is the value that separates the bottom 50% of the distribution from the upper 50%, that is, the middle value of the distribution.When a distribution is symmetric, the mean and the median are equal. From the dot plot in this problem, the distribution is uniform(as all outcomes are equally as likely, that is, they have the same frequency in the dot plot), and symmetric, hence the the mean and the median of the distribution are equal.
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Janet works for the road commission as a flag holder. She has a gross weekly income of $570. How
much is deducted from her paychecks Annually for Social Security? How much Annually for Medicare?
Using proportions, it is found that the deducted amounts each year are given as follows:
Social Security: $1,837.68.Medicare: $429.78.What is the missing information?The tax rates are missing, and they are given as follows:
Social Security: 6.20% = 0.0620.Medicare: 1.45% = 0.0145.What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
Considering that a year has 52 weeks, her yearly salary is given as follows:
52 x 570 = $29,640.
Considering the tax rate, the deducted amount for Social Security is given by:
0.0620 x 29640 = $1,837.68.
Considering the tax rate, the deducted amount for Medicare is given by:
0.0145 x 29640 = $429.78.
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f(x)=x²-3x + 20
Find f(5)
[tex]f(x)=x^2-3x+20\\\\f(5)=(5)^2-3(5)+20\\\\f(5) = 25-15+20\\\\f(5)=\boxed{30}[/tex]
Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
D(0,0,0) and E(1,5,7)
Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .
Distance Formula is used to calculate distance between two given points.
the distance between points A(a,b,c) and B(x,y,z) is given by [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2} }[/tex]
Mid point formula the mid point M(m₁,m₂,m₃) between the points A(a,b,c) and B(x,y,z) is given by M(m₁=[tex]\frac{a+x}{2}[/tex],m₂=[tex]\frac{b+y}{2}[/tex],m₃=[tex]\frac{c+z}{2}[/tex])
To calculate the distance between the points D(0,0,0) and E(1,5,7) we will use distance formula.
Substituting the values in Distance formula we get
d=[tex]\sqrt{(1-0)^{2}+(5-0)^{2}+(7-0)^{2} }[/tex]
=[tex]\sqrt{1^{2} +5^{2} +7^{2} }[/tex]
=[tex]\sqrt{1+25+49}[/tex]
=[tex]=\sqrt{75} \\ 5\sqrt{3}[/tex]
to determine the midpoint M we will use mid point formula.
Substituting the values of the given points in the mid point formula we get
mid point = [tex](\frac{0+1}{2} ,\frac{0+5}{2} ,\frac{0+7}{2} )[/tex]=(1/2,5/2,7/2)
Therefore , Distance between the points D and E is [tex]5\sqrt{3}[/tex] and the mid point of the line segment joining D and E is (1/2,5/2,7/2) .
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Help please
10 points
Answer: A number is divisible by 3 if the sum of the digits is divisible by 3.
If the last two digits of a number are divisible by 4, the whole number is. For example, in 1,012, 12 is divisible by 4.
A large number is divisible by 8 if the last three digits are also divisible by 8 or are 000.
Jorge is training for a 20 -mile race. Jorge runs 7 miles on Monday, Tuesday, and Friday, and 12 miles on Wednesday and Saturday. After 6 weeks of training, Jorge will have run the equivalent of how many races?
After 6 weeks of training, Jorge will have run the equivalent of 13.5 races.
What does the term equivalent mean?When two quantities, expressions, or numbers have the same value, they are said to be equal. An equivalent quantity can be expressed in a variety of ways, such as by a bar or an equivalent symbol. Because they can relate to it in their everyday lives, children find this topic to be particularly engaging for a variety of reasons.
A common or logical equivalency between several values or quantities can also be referred to as the equivalent. Equivalence is comparable to equality but distinct from it.
1 race = 20 miles
Lets assume he doesn't runs on Sunday and Thursday, thus
Miles he runs a week = (Monday + Tuesday + Friday) + ( Wednesday +Saturday)
1 week = (7 + 7 + 7) + (12 + 12)
= 45 miles
If he runs for 6 weeks then
6 week's run = 6 × 45
= 270 miles
If 1 race is of 20 miles then in 6 weeks he would have ran
= 270/20
= 13.5 races
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Michael wants to borrow $12000 for a car loan. Which option would allow him to pay the least amount of interest?
A. A 12-month loan with a 7.25% annual simple interest rate
B. A 18-month loan with a 3.50% annual simple interest rate
C. A 24month loan with a 3.75% annual simple interest rate
D. A 36-month loan with a 2.75% annual simple interest rate
Based on the interest rates available to Michael, the option that would allow him to pay the least interest is B. 18-month loan with a 3.50% annual simple interest rate
How much interest will Michael pay?The interest on the first option is:
= (7.25% x 12,000) x 12/12months in year
= $870
Interest on second loan:
= (3.5% x 12,000) x 18 / 12 months in year
= $630
Interest on third loan:
= (3.75% x 12,000) x 24/12 months in year
= $900
Interest on fourth loan:
= (2.75% x 12,000) x 36/12 months in year
= $990
In conclusion, the 18-month loan with a 3.50% annual simple interest rate gives the lowest rate.
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Describe a pair of events that are mutually exclusive and a pair of events that are not mutually exclusive.
The two events are mutually exclusive if they cannot occur at the same time. A triangle is equiangular if it is equilateral. Never can one preclude the other. The two events are mutually exclusive if they cannot occur at the same time.
What pairs of occurrences can never coexist?
Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously. A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.What are some examples of mutually exclusive events?
Several instances of occurrences that can never occur simultaneously include: The outcomes of receiving head or tail while flipping a coin are mutually exclusive.Learn more about probability
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For each function, find the y -intercept
y = -(2/3)(x-9)².
Answer:
(0, -54)
Step-by-step explanation:
The y-intercept is when x=0.
[tex]y=-(2/3)(0-9)^2 \\ \\ =-(2/3)(81) \\ \\ =-54[/tex]
Find the slope of the line.
c. the line containing (4,2) and (4,-3)
The slope of the line containing (4,2) and (4,-3) is Infinity.
The slope of a straight line can be written as follows,
m = [tex](y_{2} -y_{1} ) / (x_{2} -x_{1} )[/tex] equation1
The line is containing the points (4,2) and (4,-3). So, we can write
[tex]y_{2}[/tex] = -3 , [tex]y_{1}[/tex] = 2 , [tex]x_{2}[/tex] = 4 , and [tex]x_{1}[/tex] = 4 .
On substituting the values of variables in equation1, we will get
m = ( (-3)-(2) ) / ( (4)-(4) ) = (-6/0) = Infinity
As the slope of a line is Infinity, so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (4,2) and (4,-3) is Infinity.
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Solve each equation. Check each solution. 2/n + n+2 / n+1 = -2 / n² + n
The solution of given rational equation [tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex] is n = -2
In this question,
We have been given a rational equation.
[tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex]
We need to find the solution of given rational equation.
First we simplify the LHS of given equation.
[tex]\frac{2}{n} +\frac{n+2}{n+1}\\\\=\frac{2(n+1)+n(n+2)}{n(n+1)} \\\\=\frac{2n+2+n^2+2n}{n^2+n}\\\\ =\frac{n^2+4n+2}{n^2+n}[/tex]
So, given equation would be,
[tex]\frac{n^2+4n+2}{n^2+n}=\frac{-2}{n^2+n}[/tex]
Here, the denominator is same on the both sides.
⇒ n² + 4n + 2 = -2
⇒ n² + 4n + 4 = 0
⇒ (n + 2)² = 0
⇒ n + 2 = 0
⇒ n = -2
We need to check above solution.
so, substitute n = -2 in LHS of given equation.
[tex]\frac{2}{-2} +\frac{-2+2}{-2+1}\\\\=-1+0\\\\=-1[/tex]
Now, substitute n = -2 in RHS of given equation.
[tex]\frac{-2}{-2^2-2}\\\\=\frac{-2}{4-2}\\\\= \frac{-2}{2} \\\\-1[/tex]
For n = -2, LHS = RHS
Therefore, the solution of given rational equation [tex]\frac{2}{n} +\frac{n+2}{n+1}=\frac{-2}{n^2+n}[/tex] is n = -2
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[ Brainliest ]
Apply it! The measure of each central angle of a regular 40-sided polygon is ___ degrees.
Answer:
9 degrees
Step-by-step explanation:
the product of 5 less than x and 7
Answer:
7x - 35
Step-by-step explanation:
This states the product of (5 less than x) and (7). Five less than x can be written as (x - 5), and 7 is just 7. The product of (x-5) and 7 is 7x - 35.
Hope this helped :)
Henry had a piece of rope that was 23 1/2 inches long. Henry cut the rope into two pieces so that one pieces was 8 1/4 inches long. what was the length of the other piece of rope(also hello again! :)
Answer:
15 1/4 inches
Step-by-step explanation:
Length of the other piece
= 23 1/2 - 8 1/4
= 47/2 - 33/4
= 94/4 - 33/4
= 61/4
= 15 1/4 inches.
Zachary purchased a computer for $1,900 on a payment plan. months after he purchased the computer, his balance was $1,510 months after he purchased the computer, his balance was $1,250 What is an equation that models the balance y after x months?
An equation that models the balance y after x months is; y = -130x + 1900
What is the equation in slope intercept form?From the given parameters, we can form a table of values as;
Month Balance
0 1900
3 1510
5 1250
Now, the formula for slope between two coordinates is;
m = (y2 - y1)/(x2 - x1)
At first coordinate, we have;
m = (1510 - 1900)/(3 - 0)
m = -390/3 = -130
At second coordinate;
m = (1250 - 1510)/(5 - 3)
m = -260/2
m = -130
Now, the formula for equation in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, equation is;
y = -130x + 1900
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Complete question is;
Zachary purchased a computer for $1,900 on a payment plan. 3 months after he purchased the computer, his balance was $1,510. 5 months after he purchased the computer, his balance was $1,250 What is an equation that models the balance y after x months?
Sue is fishing. she catches a bass weighing 5_ 1/4 lb. then she catches three more weighing 3_ 1/2 lb, 1_3/4 lb, and 2 lb. she releases the smallest fish. what is the total weight of the fish sue keeps?
Answer:
10 3/4 lb
Step-by-step explanation:
she releases the 1 3/4 lb fish and keeps the 5 1/4lb, 3 1/2lb, and 2lb
The total weight of these three fish are
5 1/4lb
+
3 1/2lb
+
2lb
which equals 10 3/4lb
Can someone help me please!!
The perimeter of a circle with an area of 36 square units is 21.29 units.
How to find the perimeter of a circle with a known area?
For a circle with a radius R, the area is given by the formula:
A = pi*R^2
And the perimeter is given by:
P = 2*pi*R
Where pi = 3.14
In this case the area is A = 36 square units, then the radius is given by:
36 = 3.14*R^2
R = √(36/3.14) = 3.39 units.
Replacing that in the perimeter equation we get:
P = 2*3.14*3.39 units = 21.29 units.
The perimeter of a circle with an area of 36 square units is 21.29 units.
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Find the volume of this cone. Use 3 for pi.
The volume of the cone as shown in the diagram is 192 cm²
Diameter in the question is given as 16cm
We need to find the radius of the cone to find the volume of cone which is half of the diameter = 16/2 = 8 cm
The height of the cone as given in the question is 3cm
The volume of the cone =1/3 (πr²h)
We are told to use the value of pi as 3 so we are not using 3.14 or 22/7 as the value of pie
Volume = 1/3 ( 3 × 8² × 3)
= 1/3 ( 9× 64)
= 1/3 (576)
= 192 cm²
Hence, the volume of the cone as shown in the diagram is 192 cm²
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help me....................................................................................................,,....
Answer:
f. 4+3=7
g. 23+8+4=35
h. 53+3+28=84
i. 11+17+92=120
j. 24+8+3=35
Step-by-step explanation:
Answer:
F = 4 + 4 = 8
G = 23 + 8 + 4 = 35
H = 53 + 3 + 27 = 83
I = 11 + 17 + 93 = 121
J = 24 + 8 + 3 = 35
Step-by-step explanation:
Determine whether set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 13,15,16
Given set of numbers 13, 15, 16 represent an acute triangle.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.
Now we find the type of triangle.
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
The sum of the squares of the two smaller sides is,
= 13² + 15²
= 169 + 225
= 394
And 16² = 256
Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.
Therefore, given set of numbers 13, 15, 16 represents an acute triangle.
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Compare the two numbers. Use > or < .
√75, 9
As the value of Square root √75 is equals to 8.66, and the number 9 is larger than the number 8.66.
What exactly is a square root?The square root of a number x is a number y whose square (the result of multiplying the number by itself, or y y), equals x in mathematics.The term "radicand" refers to the expression (or quantity) whose square root is being considered.The term or number under the radical sign in this instance is referred to as the radicand, and it is 9.Square roots of negative integers can be discussed in the context of complex numbers.In any circumstance where the idea of an object's "square" is established, square roots can be considered more generally.These include square matrices and function spaces, among other mathematical constructs.The value of Square root √75 is equals to 8.66, and the number 9 is larger than the number 8.66.
So, √75 < 9
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a. What sampling method could you use to find the percent of adults in your community who support building more nuclear power plants?
Answer:
One way you could do it is to do a Systematic Sample \textbf{Systematic Sample} Systematic Sample and go to every other house in the neighborhood and ask their opinion.
Step-by-step explanation:
Find the slope of the line through each pair of points. (0,0) and (5,-3)
The slope of the line passing through the pair of points, (0 , 0) and (5 , -3), is -3/5.
The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:
m = (y2 - y1)/(x2 - x1)
where m is the slope
x1 and y1 are the coordinates of one point
x2 and y2 are the coordinates of the 2nd point
Given two points in the line, (0 , 0) and (5 , -3), plug in the values to the formula for the slope.
m = (y2 - y1)/(x2 - x1)
m = (-3 - 0)/(5 - 0)
m = -3/5
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Compare √180 and 102/8 using <, >, or =.
HELP ASAP
Answer:
√180 > 102/8
Step-by-step explanation:
√180 = 13.416407865
102/8 = 12.75
Answer:
Yes
Step-by-step explanation:
Because 180 is greater than 102
_____
8
Stock Market At the beginning of the day the stock market goes down 30
1
2 points and stays at this level for most of the day. At the end of the day the stock market goes up 120
1
4 points from the low at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
The total change in the stock market from the beginning of the day to the end of the day is 89.75 points.
Here, we are given that the stock market goes down 30 1/2 points at the beginning of the day.
30 1/2 can be written as-
{(30*2) + 1}/2 = 61/2
Further it is given that the stock market goes up by 120 1/4 points at the end of the day.
120 1/4 can be written as-
{(120*4) + 1}/4 = 481/4
Thus, the total change in the stock market will be-
481/4 - 61/2
= 481/4 - 122/4
= 359/4
or 89.75
Thus, the total change in the stock market from the beginning of the day to the end of the day is 89.75 points.
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Cindy is deciding between a striped red-and-purple lunch box and a polka-dotted blue lunch box to buy for school. Each lunch box is shaped like a rectangular prism with a volume of 300 cubic inches. The red-and-purple lunch box is 7.5 inches wide and 4 inches tall. The blue lunch box is 8 inches wide and 3 inches tall.
How much longer is the blue lunch box than the red-and-purple lunch box?
============================================
Explanation:
x = length of the red and purple lunch box
y = length of the blue lunch box
volume = length*width*height
The volume expression for the red and purple lunch box is x*7.5*4 = 30x
Set this equal to the stated volume 300 cubic inches, and solve for x.
30x = 300
x = 300/30
x = 10
The red and purple lunch box has length of 10 inches.
-----------------
The blue lunch box has volume of
length*width*height = y*8*3 = 24y
Set this equal to 300 and solve for y
24y = 300
y = 300/24
y = 12.5
The blue lunch box has length of 12.5 inches
Therefore the blue lunch box is longer and is longer by 12.5-10 = 2.5 inches.
Find the eighth term of each sequence. 1/2, 1/4, 1/8, 1/16, 1/32, ............
The eighth term of the given sequence 1/2, 1/4, 1/8, 1/16, 1/32 will be 1/256.
According to the give question.
We have a sequence 1/2, 1/4, 1/8, 1/6, 1/32
Since, the first term of the given sequence is 1/2.
The second term of the given sequence is 1/4.
The third term of the given sequence is 1/8.
Here, we can see that the numerator of each term is same i.e. 1. But the denominator is changing by power or 2. For the first term it is 2^1, for the second term it is 2^2, for the third term it is 2^3 and so on.
Therefore, the gneral formula for finding the nth term of the given sequence is given by
[tex]T_{n} = \frac{1}{2^{n} }[/tex]
So, the eighth term of the given sequence is 1/2^8 = 1/256.
Hence, the eighth term of the given sequence 1/2, 1/4, 1/8, 1/16, 1/32 will be 1/256.
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When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?
Answer:
When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?
https://www.louisianabelieves.com/docs/default-source/assessment/grade-7-answer-key.pdf
Step-by-step explanation:
line 1: 3x+2y=6 line 2: y= -3/2x+5 is it parallel, perpendicular, or neither, show evidence
the two lines have the same slope and different y-intercept, which means that the lines are parallel.
The lines are parallel, perpendicular, or neither?
Two linear equations:
y = a*x + b
y = c*x + d
Are parallel only if both have the same slope, which means that c = d, and the y-intercepts are different.
And are perpendicular if the slope of one of the lines is equal to the opposite of the inverse of the other slope, so:
a = -1/c
Now, our linear equations are:
3x + 2y = 6
y = (-3/2)*x + 5
We can write both of these in the slope intercept form:
3x + 2y = 6
2y = 6 - 3x
y = (6 - 3x)/2 = 3 - (3/2)*x
y = -(3/2)*x + 3
So the two lines have the same slope and different y-intercept, which means that the lines are parallel.
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Determine whether each sequence is geometric. If so, find the common ratio. 10,15,22.5,33.75, . . . . .
The given sequence is geometric, with common ratio = 1.5
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 10, 15, 22.5, 33.75,....
Here, 15/10 = 22.5/15 = 33.75/22.5 = 1.5
Since the given sequence follows the required condition for a sequence to be geometric, it is the one.
Hence, The given sequence is geometric, with common ratio = 1.5
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