Complete the table for the arithmetic sequence.
Answers
Airthemetic Sequence : arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
It express as :
[tex]a_n=a_1+(n-1)d[/tex]In the given question the 88 term is ( 25)
Substitute the value in the expression of n terms
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for : n =25, a}_n=88,a_1=(-8) \\ a_n=a_1+(n-1)d \\ 88=(-8)+(25-1)d \\ 88=-8+24d \\ 88+8\text{ =24d} \\ 24d=96 \\ d=\frac{96}{24} \\ d=4 \end{gathered}[/tex]In the given Airthmetic sequence the constant difference, d = 4
Now for the position of term 8
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for a}_n=8,a_1=(-8),\text{ d =4} \\ 8=-8+(n-1)4 \\ 16=4(n-1) \\ 4=n-1 \\ n=5 \end{gathered}[/tex]for n= 5 terms is 8
Now for the term of position 8:
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for n=8, a}_1=(-8),d=4 \\ a_n=-8+(8-1)4 \\ a_n=-8+7\times4 \\ a_n=20 \end{gathered}[/tex]So, the term with position 8 is 20
Now for the position of term 36 :
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for :a}_n=36,a_1=(-8),\text{ d = 4} \\ 36=-8+(n-1)4 \\ 36+8=4(n-1) \\ 44=4(n-1) \\ n-1=\frac{44}{4} \\ n-1=11 \\ n=10 \end{gathered}[/tex]Thus, for n = 10, an = 36
Now, for the term of position 19
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{for n=19, d=4, a}_1=(-8) \\ a_n=-8+(19-1)4 \\ a_n=-8+(18)4 \\ _{}a_n=-8+72 \\ a_n=64 \end{gathered}[/tex]Thus at n = 19 the term i 64
Related Questions
4. Find the length of a cylinder of volume 2 litres and radius 10 cm.
5. Find the radius of a cylinder of volume 45 cm³ and length 4 cm.
Remember 1
Answers
length of a cylinder of volume 2 litres and radius 10 cm is 0.0064cm and the radius of a cylinder of volume 45 cm³ and length 4 cm is 1.8928cm.
PART A
Volume of Cylinder = 2 Litres
Radius of cylinder = r = 10 cm
We need to find the length of a cylinder .
We know , Volume of Cylinder = π[tex]r^{2} h\\[/tex]
On substituting the values of Volume of Cylinder and r , we get
2 = π( [tex]10^{2}[/tex])h
h = 2 / 100π = 0.0064 cm
Here h = length of a cylinder
The length of a cylinder is 0.0064cm .
PART B
radius of a cylinder = r
volume of cylinder = 45 cm³
length of cylinder = h = 4 cm
Volume of Cylinder = π[tex]r^{2} h\\[/tex]
45 = 3.14 [tex]r^{2}[/tex] (4)
[tex]r^{2}[/tex] = 3.5828
r = 1.8928
Radius of a cylinder is 1.8928cm.
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Directions: write an appropriate equation for the given graph using your knowledge of parent functions and (h,k)
Answers
The parent functions are defined with all coefficients with value 1.
They can be linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent...
Then we can pick a function and transform it in order to include the point (-1,5) in the function definition.
We will use the quadratic parent function:
[tex]y=x^2[/tex]We will adjust the coefficient a of the quadratic function in order to include (-1,5)
[tex]\begin{gathered} y=a\cdot x^2 \\ 5=a(-1)^2=a \\ a=5 \end{gathered}[/tex]Then, our transformed function is:
[tex]y=5a^2[/tex]
Graph the compound function
Answers
Consider the function f(x) = -2/3x +5.
What is ƒ ( − 1/2 ) ?
Answers
After substituting x = -1/2 in f(x), the value of the function f(-1/2) is found to be 5.333.
What exactly is function?A function from a set X to a set Y assigns exactly one element of Y to each element of X.
What is the function's domain and codomain?The set X is known as the function's domain, and the set Y is known as the function's codomain.
The given function is f(x) = -2/3x +5.
To obtain f(-1/2), we must substitute the value of x with -(1/2).
f(x) = -2/3x +5
f(-1/2) = -2/3×(-1/2) + 5
f(-1/2) = (2/6) + 5
f(-1/2) = 0.333 + 5
∴ f(-1/2) = 5.3333
Therefore, the value of the function f(-1/2) obtained after substituting x = -1/2 is 5.333.
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create an inequality expression with square root 8 and square root 16/2 thats shows how they compare
Answers
We are given the following two numbers to compare
[tex]\sqrt[]{8}\quad and\quad \frac{\sqrt[]{16}}{2}[/tex]Let us simplify them
[tex]\begin{gathered} \frac{\sqrt[]{16}}{2}=\frac{4}{2}=2\quad (\text{this is smaller)} \\ \sqrt[]{8}=2.828\quad (\text{this is greater)} \end{gathered}[/tex]So, we can compare them as
[tex]\sqrt[]{8}>\frac{\sqrt[]{16}}{2}[/tex]The quantity on the left side is greater than the quantity on the right side.
10 less than the quotient of a number and 2 is -18"
Answers
The representation of the expression is x/2 - 10 = -18
How to translate the algebraic expression?The mathematical statement is given as
"10 less than the quotient of a number and 2 is -18"
In expressions, quotient mean divide i.e. /
So, we have the following representation
"10 less than the quotient of a number and 2 is -18" ⇒ 10 less than a number/2 is -18"
Let the number be x
So, we have
"10 less than the quotient of a number and 2 is -18" ⇒ 10 less than x/2 is -18"
Less than as used here means minus
So, we have
"10 less than the quotient of a number and 2 is -18" ⇒ x/2 - 10 is -18
Rewrite as
"10 less than the quotient of a number and 2 is -18" ⇒ x/2 - 10 = -18
Hence, the expression represented by "10 less than the quotient of a number and 2 is -18" is x/2 - 10 = -18
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Which of the following is equivalent to −4(2x + 3y) − 6(3q + 7p)?
ill give coins or whatever its called...
Answers
Answer: −8x − 12y − 18q − 42p
Step-by-step explanation:
i did the exam xD
The quantity of six and a number, times
five
Answers
solve for x
8x=4x−32
Answers
Substract 4 on each side
4x=-32
divide -32/4
X = 8
Answer:
[tex]x = - 8[/tex]
Step-by-step explanation:
[tex]8x = 4x - 32 \\ 8x - 4x = - 32 \\ 4x = - 32 \\ x = - 8[/tex]
which value of a make the solution of the equation 3(2x-4) = 4(ax-2)
Answers
The value of a that makes the solution of the equation is 1/2.
Given,
The equation: 3(2x - 4) = 4(ax - 2)
Solve,
3(2x - 4) = 4(ax - 2),
Open the bracket and multiply:
6x - 12 = 4ax - 8
Add 12 to both sides
6x -12 + 12 = 4ax + 12 - 8
We get,
6x = 4ax + 4
Add - 4ax to both sides:
6x - 4ax = 4ax - 4ax + 4
We get,
6x - 4ax = 4
Take x = 1
Then,
6 × 1 - 4a × 1 = 4
6 - 4a = 4
Now,
Add - 6 to both sides
6 - 6 - 4a = 4 - 6
We get,
-4a = -2
That is,
4a = 2
a = 2/4 = 1/2
That is,
The value of a that makes the solution of the equation is 1/2.
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To pay for a $22,800car, Mai made a down payment of $3,800and took out a loan for the rest. On the loan, she paid monthly payments of $420for 4 years. (a) What was the total amount Mai ended up paying for the car (including the down payment and monthly payments)? (b) How much interest did Mai pay on the loan?
Answers
1. The total amount that was paid for the car will be $23960.
2. The interest that Mai pay on the loan will be $1160.
How to calculate the value?1. From the information, in order to pay for a $22,800 car, Mai made a down payment of $3,800 and took out a loan for the rest and on the loan, she paid monthly payments of $420for 4 years.
The total amount that was paid for the car will be:
= $3800 + ($420 × 4 years)
= $3800 + ($420 × 48)
= $3800 + $20160
= $23960
2. The interest that Mai pay on the loan will be:
= $23960 - $22800
= $1160
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Match the polar equations to their rectangular forms-
Answers
Applying the rules for the polar equations, the correct pairs are given in the image at the end of the answer.
What are polar equations?
The most well known polar equation rules are given as follows:
For the first pair, when x = 2, we have that:
rcos(θ) = 2.
r = 2/cos(θ)
r = 2 sec(θ), as one divided by the cosine is the secant.
For the second pair, we have that:
x² + y² = 36.
x² + y² = r², hence:
r² = 36
r = 6.
For the third pair, we have that:
x² + y² = 2y
r² = 2rsin(θ).
r²/r = 2sin(θ).
r = 2sin(θ).
For the fourth pair, we have that:
[tex]x = \sqrt{3}y[/tex]
[tex]\frac{y}{x} = \frac{1}{\sqrt{3}}[/tex]
[tex]\frac{y}{x} = \frac{\sqrt{3}}{3}[/tex]
Then the angle theta is given as follows:
θ = arctan(sqrt(3)/3) = pi/6.
For the fifth pair, we have an angle in which the sine and the cosine are equal, hence this angle is of 45º = pi/4.
The image at the end of the answer shows all the matched pairs.
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The set of all numbers greater than or equal to -10 and less than 9
Answers
The The set of all numbers greater than or equal to -10 and less than 9 will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
How to illustrate the information?It should be noted that from the information, we are to find the set of all numbers greater than or equal to -10 and less than 9.
This simply means the numbers from -10 to 8.
Therefore, the numbers will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
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7. Write a biconditional for the following conditional. Determine the truth value
of the new statement. If two lines have the same slope, then they are parallel.
Answers
Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.
How do parallel lines work?
Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.Only if the slopes of two lines are equal can they be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel. In a plane, parallel lines are two lines that never cross (meaning they will continue on forever without ever touching). The equal slopes of parallel lines are a distinctive feature. The rise (change in Y coordinates) over the run (change in X coordinates) of a line, or its steepness, is referred to as the slope of a line. The most typical way to depict parallel lines is with two vertical lines (ll). Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.Learn more about parallel lines
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It cost Angel $6.75 to send 75 text messages. How much does it cost to send one text?
Answers
0.09x75=6.75 it costs ¢9 to send one text
To know how much each message sent costs, knowing that 75 messages cost $6.75, we only have to divide the cost of the total of 75 text messages by the total number of the cost of the message,
So that:
$ 6.75 ➗75 text message = 0.09 $/text messagesWe say, that the cost of each text message is $0.09.
Statistics
Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria?
Speed-- Number of cars
0-29 4
30-59 16
60-89 60
90-119 20
No, the distribution is not symmetric THIS ONE
No, the frequency do not increase from the low frequency to a maximum frequency
Yes, all the requirements are met
Answers
Answer:
The answer to your question is: B
Explanation:
based on the statistics given, this answer best fits the Queston.
Question 1 options:
Is the relation in this set of points a function?
{(-2, 6) , (4, 5) , (3, -3) , (6, 9), (4, -4)}
State whether the statement is true of false.
1. The relation is a function.
2. An element from the domain is paired with more than one element from the range.
Answers
Answer:
1.4 Relations and Functions
A relation is a correspondence between two sets. If x and y are two
elements in these sets and if a relation exists between x and y, then x
corresponds to y, or y depends on x.
DEFINITION OF A FUNCTION:
Let X and Y two nonempty sets. A function from X into Y is a relation that
associates with each element of X, exactly one element of Y.
However, an element of Y may have more than one elements of X
associated with it.
That is for each ordered pair (x,y), there is exactly one y value for each x,
but there may be multiple x values for each y. The variable x is called the
independent variable (also sometimes called the argument of the
function), and the variable y is called dependent variable (also
sometimes called the image of the function.) x = y2 is not a function from X into Y, because there
is not exactly one y value for each x.
Solving for y, you get y =
which means there are two possible values for y
Step-by-step explanation:
The table below shows the probability distribution of a random variable Z. Z P(Z) -13 0.69-12 0.18 -11 0.04 -10 0.01 -9 0.01 -8 0.04 -7 0.03 What is the expected value of Z? Write your answer as a decimal.
Answers
To be able to get the expected value of Z, we will be using the following formula:
[tex]\text{ Expected Value = }\mu=Z_1P_1+Z_2P_2+Z_3P_3\text{ + }\ldots Z_nP_n[/tex]We get,
[tex]\text{ Expected Value = }\mu=Z_1P_1+Z_2P_2+Z_3P_3\text{ + }\ldots Z_nP_n[/tex][tex]\text{ = (-13)(0.69) + (-12)(0.18) + (-11)(0.04) + (-10)(0.01) + (-9)(0.01) + (-8)(0.04) + (-7)(0.03)}[/tex][tex]\text{ = (-8.97) + (-2.16) + (-0.44) + (-0.1) + (-0.09) + }(-0.32)\text{ + (-0.21)}[/tex][tex]\text{ = -8.97 - 2.16 - 0.44 - 0.1 - 0.09 }-0.32\text{ - 0.21}[/tex][tex]\text{ Expected Value = }\mu\text{ = -12.29}[/tex]Therefore, the expected value of Z is -12.29.
Evalúe the limit. Show steps
Answers
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex] as x approaches ∞- is 1
What is limit?The value that a function, sequence, or index approaches as an input, or an index, approaches a particular value is known as a limit in mathematics. Limits, which are essential to calculus and mathematical analysis, are required by the definitions of continuity, derivatives, and integrals.
In addition to being closely related to the concepts of limit and direct limit in category theory, the idea of a limit of a sequence is further generalised to encompass the idea of a limit of a topological network.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit we will use L'Hôpital's Rule
Find the derivative
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex]
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x +0}[/tex]
⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x }[/tex]
Evalue -∞ as x
⇒ [tex]\frac{2(-\infty)}{2(-\infty)} }[/tex]
⇒ 1
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Geometry help please
Answers
Given
A right angle triangle is removed from the rectangle to create the shaded region.
That is,
To find: The area of the shaded region.
Explanation:
It is given that,
That implies,
The area of the shaded region is,
[tex]\begin{gathered} Area\text{ }of\text{ }the\text{ }shaded\text{ }region=Area\text{ }of\text{ }the\text{ }rectangle-Area\text{ }of\text{ }the\text{ }triangle \\ =l\times b-\frac{1}{2}\times b\times h \\ =5\times9-\frac{1}{2}\times4\times3 \\ =45-6 \\ =39ft^2 \end{gathered}[/tex]Hence, the area of the shaded region is 39ft^2.
Use the drawing tools to form the correct answer on the number line
Graph the solution set to this inequality.
-2(x + 6) > -4x
Answers
Answer:
Step-by-step explanation:
Answer:
x > 6 with an open point
Hope this helps!
Step-by-step explanation:
-2 ( x + 6 ) > -4x
-2x - 12 > -4x
-(-4x) - 2x > -(-12)
4x - 2x > 12
2x > 12
x > 6
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y = -x² + 64x - 292
Answers
Answer:
what
Step-by-step explanation:
i think maybe like… actually
Find the missing integer that makes the following addition statement true.
+ 3 = 2+3=2
Answers
The missing integer that makes the following addition statement true is -1.
What is the commutative law of addition?The commutative law of addition is also known as the law of cumulative addition and it states that when two numbers are added together, then, the outcome is equal to the addition of their interchanged position because addition is considered as a binary operation.
Mathematically, the commutative law of addition can be represented using the following formula:
A + B = B + A.
What is an integer?An integer can be defined as a whole number that may either be positive, negative, or zero such as -1, 0, 1, 2, 3, etc.
Now, we would determine the missing number:
x + 3 = 2
x = 2 - 3
x = -1.
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Complete Question:
Find the missing integer that makes the following addition statement true.
+ 3 = 2
A contractor hired 150 workers to pave 30 miles of highway how many workers will they need to hire to pave 20 miles of highway in the same amount of time?
Answers
Answer: 100
Step-by-step explanation:
First, we need to know how many workers must be hired to pave one mile.
Which is 5 workers per 1 mile ( 150 / 30 )
Then you can either do
(5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5) + (5 + 5 +5 +5 + 5)
OR
5 x 20 = 100
( if I'm wrong it's like 3 am so I'm a bit slow but I hope I helped )
given: P(A) = 0.45, P(B) = 0.65, and P(A and B) = 0.35.
Find:
P (A or B)
P(A OR B) ( line on top)
P(A|B)
P(B|A)
Answers
Answer:
P(A or B) = 0.75P(A or B)' = 0.25P(A|B) = 0.54P(B|A) = 0.78Step-by-step explanation:
Normally we use the symbols U for set union corresponding to or and ∩ for set intersection corresponding to and.
But here i will use and and or
By the rules of probability
P(A or B) = P(A) + P(B) - P( A and B)
So P(A or b ) = 0.45 + 0.65 - 0.35 = 0.75
The complement of a set A is all the elements not in A
P(A') = 1 - P(A)
If we denote the complement of a set A as A' then your second expression is asking What is the complement of A or B or P(A or B)'
P(A and B)' = 1 - P(A or B) = 1- 0.75 = 0.25
P(A|B) = P(A and B)/P(B) = 0.35/0.65 = 0.54
P(B|A) = P(A and B)/P(A) = 0.35/0.45 = 0.78
Convert the following phrase into a mathematical expression use x as the variable combine like terms when possible A number multiplied by -8 subtracted from the sum of 8 and two times the number
Answers
ANSWER:
[tex]-8x-(8+2x)[/tex]STEP-BY-STEP EXPLANATION:
We must convert the following statement "A number multiplied by -8 subtracted from the sum of 8 and two times the number" into a mathematical expression.
We know that "a number" would be x.
Therefore:
[tex]-8x-(8+2x)[/tex]Find k with the given information.
m=-3/5 (k,-9) and (1,-6
Answers
Using the slope formula, the value of k in the coordinates of the point given is: k = 6.
How to Find the Slope of a Line?If we are given two points that lie on a line, (x1, y1) and (x2, y2), the formula that is used to find the slope (m) of the line is given as:
Slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = change in y / change in x..
Given the following:
(k, -9) = (x1, y1)
(1, -6) = (x2, y2)
Slope (m) = -3/5
Plug in the values into the formula used for calculating the slope of a line:
(-6 -(-9))/(1 - k) = -3/5
3/(1 - k) = -3/5
Cross multiply and solve for the value of k
-3(1 - k) = 3(5)
-3 + 3k = 15
Add 3 to both sides
-3 + 3k + 3 = 15 + 3 [subtraction property of equality]
3k = 18
Divide both sides by 3
3k/3 = 18/3 [division property of equality]
k = 6
The value of k is: 6. Therefore, the points on the line that have a slope of -3/5 are (6, -9) and (1, -6).
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Select the correct answer. Based on these segment lengths, which group of segments can form a triangle? A. 3, 10, 14 B. 8, 7, 13 C. 3, 2, 5 D. 20, 7, 13
Answers
Answer:
B
Step-by-step explanation:
By the triangle inequality theorem, the sum of the lengths of the two shorter sides needs to be greater than the length of the longest side.
What is the largest five-digit multiple of 15 whose digits are all distinct and nonzero?
Answers
The largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.
How can we express numbers belonging to decimal numeral system?Suppose that the number is abcd.efg and belongs to the decimal numerical system. Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more. Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more. We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.
WE need to find the five-digit multiple of 15 whose digits are all distinct and nonzero.
Thus, we can see that the largest five-digit multiple of 15 could be ;
12345
Since it must be all distinct and nonzero. so the correct digit is 12345.
Hence, the largest five-digit multiple of 15 whose digits are all distinct and nonzero is 12345.
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Hi, I need to send you the question as I have written
Answers
recall the formula for velocity, which involves distance and time:
velocity = distance / time
since the woman's velocity is: 4.5 Km/h, then in order to cover 10 km, we need to find the time in the equation:
4.5 km/h = 10 km / t
multiply both sides by the time (t)
4.5 * t = 10
divide both sides by 4.5 in order to isolate t completely
t = 10 / 4.5
then
t = 2 hours and 0.2222 hours which can be translated into minutes by multiplying this by 60: 40/3 = 13 minutes and 0.33333 minutes. which can be converted into seconds by multiplying it by 60: 20 seconds
Then she will cover that distance in 2 hours, 13 minutes and 20 seconds.