The four Quantities are a1 , r, n , [tex]S_{n}[/tex]
What is a Series:
A series can be highly generalized as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.
Arithmetic progression
an = a1 + ( n-1) d
a1 is the first term
d =common difference
an is the nth term
an can be found out if we know the a1 , d and n
b) Arithmetic progression
a1 is the first term
an is the nth term
sn is the sum of the n terms of the series
Sn = n/2 ( a1 + an)
we can calculate sn if we know a1 , an and n
c)Geometric progression
an = a1rn-1
a1 is the first term
an is the nth term
r is the common ratio
we can calculate an if we know a1 , r and n
d)Geometric progression
Sn = a1( 1- rn) / 1 - r
a1 is the first term
r is the common ratio
sn is the sum of the n terms of the series
If we know a1 , r and n we can calculate [tex]S_{n}[/tex].
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Simplify. 3/10 . 2/9
Answer:1/15
Step-by-step explanation:
Assuming it is multiplication, multiply the numerators: 3 * 2 = 6
Multiply the denominators: 10 * 9 = 90
Put them together for 6/90 and simplify for 1/15
Which expression is equivalent to 2
4√/23
√√25
O 4/43
√45
1
- IN
N
MI4
2
?
Answer:
√2⁵
Step-by-step explanation:
✅️✅️✅️✅️✅️✅️✅️✅️♀️♀️♀️
Answer:
[tex]\sqrt{2^{5} }[/tex]
It's B
Step-by-step explanation:
Look at the image
I hope this helps.
Mark me brainliest, please.
Multiply. Write your answer in scientific notation.
(1×103)(8×10-7)
I am so close to getting it but i am second guessing my answer
Answer:
7.519*10 power 3 is the answer.
PLEASE HELP ME IF YOU ARE GOOD AT MATH!!!
Use the symmetric property of congruence to complete the following statement.
If ∠UPR≅∠FSJ, then ? ≅∠UPR.
By the symmetric property of congruence is ∠FSJ ≅∠UPR.
It is required to find the solution.
What is symmetry ?Symmetry is defined as a proportionate and balanced similarity that is found in two halves of an object, that is, one-half is the mirror image of the other half. A 2D shape is symmetrical if a line can be drawn through it and either side is a reflection of the other.
Given:
The symmetric property is if y = x then x = y. The order of what is on the left or right side of the equation does not matter. It's like saying 2+3 = 5 is the same as 5 = 2+3.
According to given question we have,
This idea can be extended to congruences because congruent angles have the same measure.
Congruent angles are two or more angles that are identical to each other. Thus, the measure of these angles is equal to each other.
So, ∠UPR ≅∠FSJ, then ∠FSJ ≅∠UPR.
Therefore, by the symmetric property of congruence is ∠FSJ ≅∠UPR.
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Length of leg b = . pls help me
Answer:
20
Step-by-step explanation:
We can solve for the unknown base using Pythagorean's theorem.
Remember Pythagorean's theorem goes as such:
[tex]a^2+b^2=c^2[/tex]
Where a and b are the two legs and c is the hypotenuse. We know one leg and the hypotenuse so we can insert our known values and solve for the unknown.
[tex]15^2+b^2=25^2\\225+b^2=625\\b^2=400\\b=20[/tex]
Or using trigonometry:
Note this is a 45-45-90 triangle, therefore all angles are known.
I'll use the sin function with the B angle.
[tex]sin(45)=\frac{b}{25} \\25*sin(45)=b\\17.67=b[/tex]
I'm assuming this problem was not made for trig, although the answer is still close.
find the equation of the line shown
The length of a rectangle is 4 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the dimensions of the rectangle.
The dimensions are 3 inches, 10 inches, and 13 inches.
How to compute the value?It should be noted that the diagonal is the longest side. This will be solved by using Pythagoras theorem.
Therefore,
(2x + 6)²
4x²+ 24x + 36
Reduce to lowest term
x² + 6x + 9
x² + 3x + 3x + 9
x(x + 3) - 3(x + 3)
(x - 3) = 0
x = 0 + 3 = 3
Therefore x = 3
Therefore the dimensions will be:
x = 3
2x + 4 = 2(3) + 4 = 10
2x + 6 = 2(3) + 6 = 12
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4= 3/2+c pleaseeeeee
Do the columns of b span r4? does the equation bx d y have a solution for each y in r4?
Answer: Theorem 4 says that the columns of B do NOT span R4. Further, using Theorem 4, since 4(c) is false, 4(a) is false as well, so Bx = y does not have a solution for each y in R4.
Step-by-step explanation:
Yes, the column b span r4. Yes, the equation has a solution for each y in r4.
Matrix is defined as a set of numbers consisting of rows and columns elements.
It consists of rows and columns.
The dimensions of the matrix are determined by m×n.
Given matrix,
[tex]\begin{bmatrix} &1 &3 &-2 &2\\ &0 &1 &1 &-5\\ &1 &2 &-3 &7\\ &-2 &-8 &2 &-1\\\end{bmatrix}[/tex]
R3 → R1
R3→R4+2R1
[tex]\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-1 &1 &5 \\ &0 &-2 &-2 &3\\\end{bmatrix}[/tex]
R3→R3+R2
R4→R4+2R2
[tex]\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-0 &2 &0 \\ &0 &-0 &0 &7\\\end{bmatrix}[/tex]
This is the row echelon form of B. It has four independent columns and the dimension of r4 is 4.
column of B spans r4.
Row of matrix = 4
No of columns of matrix = No of rows of the matrix.
and the columns of B span r4.
thus we can conclude that the columns of b span r4 and the equation
bx =d y have a solution for each y in r4.
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20
f(x) = 4(x + 1)
(a) Write down the value of x when f¯¹(x) = 2.
(c) Find g(x).
(b) Find fg(x). Give your answer in its simplest form.
g(x)
2
Answer(a) x =
- 1
Answer(b) fg(x)=
[1]
[2]
Answer:
The value of x is 12 if the value of f^-1(x) = 2.
Step-by-step explanation:
It is given that f(x) = 4(x + 1), which is an inverse function.
Now,
First of all, let us understand what is a function and an inverse function;
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
On the other hand;
A function that may reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "f-1" or "F-1." Here, (-1) should not be confused with an exponent or a reciprocal.
Now, let us consider the first part of the question;
We have to calculate the value of x when f^-1(x) = 2 given that f(x) = 4(x+1) is the function;
=> f(x) = 4(x + 1)
=> 4(y + 1) = x
=> x = 4y + 4
=> y = (x - 4)/4
=> f^-1(x) = (x - 4)/4
Hence, f^-1(x) = (x - 4)/4 is the inverse of f(x).
Now, let us put the value of f^-1(x) = 2 in the equation so obtained;
=> f^-1(x) = (x - 4)/4
=> 2 = (x - 4)/4
=> 8 = (x - 4)
=> x = 12
Hence, the value of x is 12 if the value of f^-1(x) = 2.
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Compare the graphs. Which statement describes the comparison correctly.
A. There is a gap in the data and an outlier in both graphs.
B. There is a gap in the data and no outlier in both graphs.
C. There is a gap in the data in one graph and no gap in the other graph.
D. There is an outlier and a gap in one graph but only a gap in the other graph.
(pic attached is both graphs being referenced in the answers)
Answer: its A. ^^
Step-by-step explanation:
The statement describing the comparison correctly is "There is a gap in the data and an outlier in both graphs" option (A) is correct.
What are statistics?Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.
It is given that:
The two-bar graph is given in the picture.
From the data given in the picture.
Both plots contain an outlier and a data gap.
Thus, the statement describing the comparison correctly is "There is a gap in the data and an outlier in both graphs" option (A) is correct.
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You find a book that costs
$16.75. You must pay 4% sales
tax. You use a $25 gift card.
How much is left on the gift
card after you buy the book?
You find a book that costs $16.75 and you must pay 4% sales
tax. You use a $25 gift card then only $7.58 is left on the gift card after you buy the book.
What is sales tax?A sales tax is a government-imposed consumption tax levied on the purchase of goods and services. A traditional sales tax is assessed at the point of sale, collected by the retailer, and passed on to the government. A firm is liable for sales taxes in a given jurisdiction if it has a nexus there, which can be a physical location, an employee, an affiliate, or some other presence, depending on the rules in that country.
We must 4% sales tax on $16.75 book
Sales tax = 16.75 × 0.04
= 0.67
The total cost = 16.75 + 0.67
= $17.42
He uses a $25 gift card, so he is left with
= 25 - 17.42
= 7.58
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Type the correct answer in the box. Use numerals instead of words.
Jack and his friends are going hiking next week. There are four trails they can hike: Grayson Pass, Giant’s Ridge, Three Summits, and Elderberry. To make a decision, they use a spinner divided into four colors. They spin it 60 times to check the fairness of their model and record the results in this table
The Spinners landing on green is 10%, blue is 40%, yellow is 15% and red is 35%.
Given,
Green–6: The spinner lands on green with a relative frequency of 6/60.
Blue – 24: Spinners landing on blue have a relative frequency of 24/60.
Yellow – 9: The spinner's relative landing frequency on yellow is 9/60.
Red – 21: The spinner lands on red with a relative frequency of 21/60.
Then the simplified fraction, decimal, and percentage are as follows:
When the spinner lands on green, it does so relatively often, especially 6/60
Simple Fraction: 1/10
0.1 in decimal
percent equals 10%
The spinner's landing on blue occurs with a relative frequency of 24/60
Simple Fraction: 2/5
Decimal: 0.4.
percent equals 40%
The spinner's relative frequency of landing on yellow is 9/60
Simple Fraction: 3/20
Decimal: 0.15
Percentage equals 15%
The spinner typically lands on red with a relative frequency of 21/60
Simple Fraction: 7/20
Decimal: 0.35
Percentage: 35%
Hence, the spinners landing on green is 10%, blue is 40%, yellow is 15% and red is 35%.
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A card is drawn randomly out of 12 cards which are numbered from 1 to 12. What is the
probability that the card drawn has a composite number written on it ?
a) 2 / 3
b) 7 / 12
c) 1 / 3
d) 1 / 2
The probability that the card drawn has a composite number written on it is 1/2
What is the probability that the card drawn has a composite number written on it?The sample space is given as
S = {1, 2....3}
The list of composite numbers from 1 to 12 is 4, 6, 8, 9, 10, 12
So, we have
Composite = 6
The probability that the card drawn has a composite number written on it is
P = Composite/Sample size
So, we have
P = 6/12
Simplify
P = 1/2
Hence, the probability that the card drawn has a composite number written on it is 1/2
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Was wondering how to do this im confused.
A) The equation for a line that passes through the points (8, 2) and (6, 10) is:
y = -4*x + 34
B) line that has a slope of -2 and that passes through the point (-3, 5)
y = -2*x - 1
How to write the linear equations?
A) First we want to find the equation for a line that passes through the points (8, 2) and (6, 10).
Remember that a general linaer equation is of the form:
y = m*x + s
Where m is the slope and s is the y-intercept.
If the line passes through (a, b) and (c, d), then the slope is given by:
m = (d - b)/(c - a)
Then in this case, the slope is:
m =(2 - 10)/(8 - 6) = -8/2 = -4
Replacing that we get:
y = -4*x + s
To find the value of s we use the fact that the line passes through (8, 2), this means that:
2 = -4*8 + s
2 + 32 = s
34 = s
The linear equation is:
y = -4*x + 34
B) Now we want to find a line that has a slope of -2 and that passes through the point (-3, 5)
Here we already know the slope, so we can write:
y = -2*x + s
Again, to find the value of s, we replace the values in the point in the linear equation:
5 = -2*-3 + s
5 = 6 + s
5 - 6 = s = -1
We conclude that this linear equation is:
y = -2*x - 1
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An accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes. Which of the following equations can be used to describe this problem?
The equation when the accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes is 120 + 40h.
How to calculate the valueFrom the information, it should be noted that the
accountant charges a fee of $120 to complete a company's taxes. The accountant also charges an additional $40 per hour to complete the taxes.
Let the number of hours be represented by h.
Therefore, the expression to describe the problem will be:
= 120 + (40 × h)
= 120 + 40h
The equation is 120 + 40h.
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Help me with my assignment please.
Factor the ff.
1.) x² + 4x + 3
2.) y² - 5y + 6
3.) x² - 5x - 36
4.) y² + 5y - 14
Answer:
see explanation
Step-by-step explanation:
1
x² + 4x + 3
consider the factors of the constant term (+ 3) which sum to give the coefficient of the x- term (+ 4)
the factors are + 1 and + 3 , since
1 × 3 = + 3 and 1 + 3 = + 4 , then
x² + 4x + 3 = (x + 1)(x + 3)
2
y² - 5y + 6
consider the factors of the constant term (+ 6) which sum to give the coefficient of the y- term (- 5)
the factors are - 3 and - 2 , since
- 3 × - 2 = + 6 and - 3 - 2 = - 5 , then
y² - 5y + 6 = (y - 3)(y - 2)
3
x² - 5x - 36
consider the factors of the constant term (- 36) which sum to give the coefficient of the x- term (- 5)
the factors are - 9 and + 4 , since
- 9 × 4 = - 36 and - 9 + 4 = - 5 , then
x² - 5x - 36 = (x - 9)(x + 4)
4
y² + 5y - 14
consider the factors of the constant term (- 14) which sum to give the coefficient of the y- term (+ 5)
the factors are - 2 and + 7 , since
- 2 × 7 = - 14 and - 2 + 7 = + 5 , then
y² + 5y - 14 = (y - 2)(y + 7)
Answer:
Step-by-step explanation:
[tex]1)\\x^2+4x+3=\\x^2+3x+x+3=\\(x)(x+3)+(1)(x+3)=\\(x+3)(x+1)[/tex]
[tex]2)\\y^2-5y+6=\\y^2-3y-2y+6=\\(y)(y-3)-(2)(y-3)=\\(y-3)(y-2)[/tex]
[tex]3)\\x^2-5x-36=\\x^2-9x+4x-36=\\(x)(x-9)+(4)(x-9)=\\(x-9)(x+4)[/tex]
[tex]4)\\y^2+5y-14=\\y^2+7y-2y-14=\\(y)(y+7)-(2)(y+7)=\\(y+7)(y-2)[/tex]
Find the quadratic polynomial if its zeroes are 0, √5."
A quadratic polynomial can be written using the sum and product of its zeroes as: x² + (α+β) + αβ = 0 Where α and β are the roots of the equation. ☛ x² + ( 0+√5)x + 0 = 0 .
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Cual es el 35% de 900
The percentage is the hundredth of any digit or value between 1 to 100 so 35% of 900 will be 315.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The x percentage of any random y digit is given as;
⇒ (x/100) × y
Therefore,
35% of 900 →
(35/100) × 900
⇒ 35 × (900/100)
⇒ 35 × 9
⇒ 315
Hence " The 35% percentage of the amount 900 will be 315".
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The given question is not in English, English translation follows;
What is 35% of 900?
Write an equation in point-slope form of the line having the given slope that contains the given point.
m=2,(4,-9)
The equation in point-slope form of the line having the given slope m = 2 that contains the given point (4, -9) is 2x - y = 17
It is given that,
Slope is the measure of the steepness of a line.
Equation is the mathematical statement made up of two expressions joined together by the equal sign. For instance 3x - 5 = 16
The slope of a one point line = m = 2
The point through which the line passes = (4, -9)
We need to find the,
The equation in point-slope form of the line having the given slope that contains the given point
The formula which will be used,
(y-y1) = m(x-x1)
where, (x1,y1) = (4, -9) and m = 2
putting the values in the formula, we get
[y - (-9)] = 2. (x-4)
y + 9 = 2x - 8
y - 2x = -17
2x - y = 17
Hence, the equation in point-slope form of the line having the given slope that contains the given point is 2x - y = 17
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When I triple my number and add ten, I get my number plus `36.` What is my number?
Based on the information given, the number is 13
How to determine the numberFrom the information given;
Let the number be x
We have that;
3(my number) + 10 = my number + 36
Substitute the number as x, we have;
3x + 10 = x + 36
collect like terms
3x - x = 36 - 10
2x = 26
Make 'x' the subject of formula
x = 26/ 2
x = 13
The number is 13
Thus, based on the information given, the number is 13
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A store owner wants to develop a new snack mix by mixing chocolate and trail mix. how many pounds of chocolate costing $20.10 per pound should be mixed with 25 pounds of trail mix costing $2.80 per pound to create a mixture worth $8.41 per pound.
If a store owner wants to develop a new snack mix by mixing chocolate and trail mix, then the number of pounds of chocolate costing $20.10 per pound that should be mixed with 25 pounds of trail mix costing $2.80 per pound to create a mixture worth $8.41 per pound is equal to 11.99.
The pounds of chocolate needed to create a mixture worth $8.41 per pound can be calculated using an algebraic expression.
An algebraic expression can be defined as an expression consisting of both numbers and letters.
If x = the unknown pounds of chocolate
An algebraic expression can be given as,
20.10x + 2.80(25) = 8.41(x + 25)
Solving for x,
20.10x + 70 = 8.41x + 210.25
Rearranging,
20.10x - 8.41x = 210.25 - 70
11.69x = 140.25
x = 140.25 ÷ 11.69
x = 11.99
Hence, 11.99 pounds of chocolate costing $20.10 per pound should be mixed with 25 pounds of trail mix costing $2.80 per pound to create a mixture worth $8.41 per pound.
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If JK = 3x + 16, KL = 18x 5, and JL = 19x + 19, what is JK?
If we identify the points as follows, what are
the inputs to the slope formula?
(-1, -2) and (3, 0)
X1 У1. X2 Y2
hi
slope formula is : y2-y1 / x2-x1
you can reverse it if you want. : y1-y2 / x1 -x2
m = 0- (-2) / 3 - (-1) = 2/ 4 = 1/2
what is the coordinates of one point in the solution set.
The coordinates of one point in the solution set are (0, 0)
How to give the coordinates of one point in the solution set?The system of inequality is given as
y < 5/6x + 4
-5x + 6y >-6
The graph that completes the question is added as an attachment
From the question, we also have the graph that represents the inequalities in the above system of inequality
As a general rule, the shaded region in a system of inequality represents the solution set
From the attached graph, the point (0, 0) is in the shaded region
Hence, the coordinates of one point in the solution set are (0, 0)
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simplify 8(x+5)-4(x+4)
2x and 72
Step-by-step explanation:
pls don't use this I don't want you to get a bad grade if it is wrong
Answer: 4x+24
Step-by-step explanation: 8x+40-4x-16
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.
The three types of congruence transformations are rotation, reflection, and translation is TRUE.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
Reflection is a mirror image of a graph about any axis.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
A triangle will remain congruent if we rotate it by any angle in either a clockwise or counterclockwise manner.
If we transform by any amount either horizontal or vertical then it will remain the same so it will be congruent.
A triangle will remain the same if we mirror it on any axis, making it congruent.
Hence "The three types of congruence transformations are rotation, reflection, and translation is TRUE".
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3v+2v=25+v=25
what is v?
Answer: see explanation
Step-by-step explanation:
The answer is very simple, you first do 3v + 2v which is 5v then you do 25 / 5 which is 5. This is your v (5). So the answer would be 5, you can ignore the 25+v this is there to confuse you.
Write an explicit formula for each geometric sequence. 1,2,4,8, . . .
The explicit formula for a geometric sequence is [tex]a_{n}[/tex] =[tex]a_{1}^{r-1}[/tex]
The sequence is:
1, 2, 4, 8..........
The formula for a geometric sequence,
[tex]a_{n}[/tex] = [tex]a_{1}^{r - 1} }[/tex]
a, ar, [tex]ar^{2}[/tex], [tex]ar^{3}[/tex]
r = common ratio
n = number of sequences in a series.
Let us understand by the sequence,
Here r = 2 , a = 1
Therefore by putting these values in the equation we get,
[tex]a_{n}[/tex] = [tex]a_{1}r^{n-1} }[/tex]
= a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex], ........
1, 2, 4, 8 .........
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Find the total tax deductions for each of the following weekly paychecks.
weekly pay
$198.00
$340.00 $250.00
FICA (7.65%)
and
tax percentage = 7.65%Find amount of tax against each paycheck:
$198*7.65/100 = $15.15 ((rounded to the nearest cent))$340*7.65/100 = $26.01$250*7.65/100 = $19.13 (rounded to the nearest cent)