The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.
The given arithmetic series is 10+7+4+ . . .
The summation notion of given series is ∑10-3n , here n starts from 0.
The sum of arithmetic series can be written as,
[tex]S_{n}[/tex] = [tex](n(a_{1} + a_{n}))/2[/tex]
n is the number of terms, [tex]a_{1}[/tex] is the first term and [tex]a_{n}[/tex] is the last term.
We have, n=5, [tex]a_{1}[/tex] = 10
To calculate sum of arithmetic series, we need to find [tex]a_{5}[/tex] .
[tex]a_{5} = a_{1} + (n-1)d[/tex]
d = -3 for the given series. On substituting value of n, [tex]a_{1}[/tex] and d in equation1, we get
[tex]a_{5}[/tex] = 10 + (5-1)(-3)
[tex]a_{5}[/tex] = 10-12 =-2
On substituting values in sum of arithmetic series formula, we get
[tex]S_{5}[/tex] = (5(10 + (-2)))/2 = 20
The summation notion of given series is ∑10-3n , here n starts from 0 and the sum of given arithmetic series is 20.
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Write the equation of the line that is perpendicular to x + 4y = 12 and passes through the point (-8, 5) in slope-intercept form.
y = mx + b
m=
b=
The equation of the line is: y = 4x + 37
m = 4
b = 37
How to Write the Equation of a Line in Slope-intercept Form?The equation of the line that is perpendicular to x + 4y = 12, will have a slope that is the negative reciprocal of the its slope.
Rewrite the equation, x + 4y = 12 in slope-intercept form:
4y = -x + 12
y = -x/4 + 3
The slope is -1/4. Therefore, the slope of the perpendicular line would be 4.
Substitute m = 4 and (a, b) = (-8, 5) into y - b = m(x - a)
y - 5 = 4(x - (-8))
y - 5 = 4x + 32
y = 4x + 32 + 5
y = 4x + 37
The equation of the line is: y = 4x + 37
m = 4
b = 37
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please help
please good graph
You can see the graphs in the attached image. The order is the same as on page. Note that 7. and 8. give us an infinite number of solutions, and no solutions, respectively.
From 125 yards away, a marksman hit 55.6 of the targets last year.
From 125 yards, a marksman hit 55.6 of the targets last year, which is equal to (55.6 × 100)% that is 5560%
What is percentage?A percentage (from Latin: per centum, "by a hundred") is a number or ratio stated as a fraction of 100 in mathematics. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A percentage is a dimensionless (pure) number; it does not have a unit of measurement.
A percentage is a fraction or a ratio in which the full number is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of a possible 100. It is written as 30/100 in fraction form and 30:100 in ratio form.
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Full question
Rewrite the decimal in the sentence below as a percentage.
From 125 yards away, a marksman hit 55.6 of the targets last year.
Which expression has a value of -5?
A: (-3) -8
B: (-8) - (-3)
C:(-3) - (-8)
D: 8-(-3)
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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find the value of each expression
16.2 + (-8.4) =
2/5 - 3/5 =
-9.2 - 7 =
(-4 3/8) - (-1 1/4) =
WILL GIVE OUT BRAINLIEST !
Answer:
1. 7.8
2. -1/5
3. -16.2
4. -25/8
Step-by-step explanation:
-
Answer:
7.8
-0.2
-16.2
-3.125
I really hope it helps
ps: from ultra instinct Giga Chad
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x) = (2/9)x - (9/2) for x=9
f (9) = - 5/2 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= (2/9)x - (9/2)
Put x = 9 ⇒ (2/9) * 9 - (9/2)
⇒ 2 - 9/2
⇒ -5/2
Therefore f (9) = - 5/2
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please help!!!!!!!!!!!!!! show your work and try to have the right answer
Answer:
Step-by-step explanation:
Jared has completed a controlled scientific experiment in which he found a strong
positive correlation between hours of daylight and pea plant growth. He calculates that
the correlation coefficient is 0.93. Does Jared's experiment suggest that sunlight causes
pea plant growth? Why or why not?
OYes; if the correlation coefficient is close to 1, then there is a cause-and-effect relationship.
Yes; finding a strong correlation in a controlled scientific experiment suggests a cause-and-effect
relationship.
O No; cause-and-effect relationships always have a correlation coefficient of 1 or -1.
No; cause-and-effect relationships can be established only by collecting observations from
nature, not from a controlled experiment.
In Jared's experiment, we can conclude that; No, cause-and-effect relationships can be established only by collecting observations from
nature, not from a controlled experiment.
How to Interpret Correlation Coefficient?
The correlation coefficient is simply the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis. It varies from -1 to 1.
Now, we are told that the correlation coefficient is 0.93. This means that it is close to 1. Now, we know that when the correlation coefficient is near 1 or −1, the linear relationship is strong; when it is near 0, the linear relationship is weak.
We also know that correlational studies allow researchers to detect the presence and strength of a relationship between variables, while experimental studies allow researchers to look for cause and effect relationships.
Thus, in Jared's experiment, we can conclude that; No, sunlight doesn't cause pea plant growth because cause-and-effect relationships can be established only by collecting observations from
nature, not from a controlled experiment.
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determine whether the following graph represents a function
1. one to one function
2. Not a function
3. Function, but not one to one
Answer:
3. function, but not one to one
Step-by-step explanation:
If you do a vertical line test anywhere you draw a vertical line will only hit in one spot
If you do a horizontal line test to check If the line is one to one it hits in multiple spots therefore the line that is graphed is a function but not one to one
Ana has 8 stamps. Together, Ricky and ana have 23 stamps. The equation 23 = r + 8 represents this situation,where r is the number of stamps Ricky has. Solve the equation to find the number of stamps ricky has
Ricky has the number of stamps in the number of 15 stamps.
According to the question, the given parameters can be used to form the expression by using simplification method and the parameters are as follows:
Stamps for Ana: 8
Stamps for Ricky and Ana: 23
Given equation: 23 = r + 8
The equation formed by the simplification method is: r + a = 23
Solving above two equations, we get a = 8 stamps and r = 15 stamps.
Hence, Ricky has the number of stamps in the number of 15 stamps.
What is simplification?
The word simplification is the procedure in which complicated expression can be written in a simpler form to make the calculation easy. This method is used to calculated the answers for the unknown quantity.
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Simplify the expression. Write your answers using integers or improper fractions.
− 3/2(1/2 n+2n−3)+4n
The expression is simplified to n - 16/ 4
What are algebraic expressions?
Algebraic expressions are expressions comprising of terms, variables, factors, constants and coefficients.
They are also made up of mathematical operations such as addition, subtraction, multiplication, division, bracket, etc.
Given the expression;
− 3/2(1/2 n+2n−3)+4n
Solve the variables in the bracket, we have;
- 3/ 2 { n + 4n - 6 / 2} + 4n
-3/2 { 5n - 6/ 2 } + 4n
expand the bracket
- 15n - 18/ 4 + 4n
Fin the LCM
-15n - 16 + 16n /4
n - 16/ 4
Thus, the expression is simplified to n - 16/ 4
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Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.Prove that the triangle with vertices (3,5),(-2,6) , and (1,3) is a right triangle.
Using the definition of slope, the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle.
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.
m = (y2 - y1)/(x2 - x1)
To prove that the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle, there should be a pair of adjacent lines perpendicular with each other(forms 90 degree angle). The slope of this pair of adjacent lines must be negative reciprocal of one another.
let A = (3 , 5)
B = (-2 , 6)
C = (1 , 3)
Determine the slope of each line of the triangle: AB, BC, AC.
AB : m = (6 - 5)/(-2 - 3) = 1/-5 = -1/5
BC : m = (3 - 6)/(1 - -2) = -3/3 = -1
AC : m = (3 - 5)/(1 - 3) = -2/-2 = 1
-1 is the negative reciprocal of 1. The slope of BC is the negative reciprocal of the slope of AC, hence, side BC is perpendicular with each other.
Therefore, the triangle with vertices (3 , 5), (-2 , 6), and (1 , 3) is a right triangle.
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Find the area
(Simplify your answer)
Answer:
why isnt there a backround base? it wouldnt be area if isnt so
Step-by-step explanation:
The area is 960 m
because 48*15=720
and 10*24=240
720+240= 960
A city has 73,400 voters. According to a survey, 96% of them will vote to support a local measure. How many people will vote
for this measure?
Answer: 70,464 people
Step-by-step explanation:
We will write an equation to help us solve. Note that a percent divided by 100 becomes a decimal and that "of" means multiplication in mathematics. Let x be the number of people who will support the measure.
96% of 73,400 voters will support the local measure.
(0.96)(73,400) = x
70,464 people = x
Solve by completing the square. Express answer in a simplified radical form when possible. When not possible, round to nearest hundredth.
x^2+6x+2=0
Answer:
[tex]{ \tt{ {x}^{2} + 6x + 2 = 0}} \\ { \tt{ {x}^{2} + 6x = - 2 }}[/tex]
- Add the square of the half of the sum on either sides:
[tex]{ \tt{ {x}^{2} + 6x + ( { \frac{6}{2}) }^{2} = - 2 + {( \frac{6}{2}) }^{2} }} \\ \\ { \tt{ {x}^{2} + 6x + 9 = - 2 + 9}} \\ { \tt{ {(x + 3)}^{2} = 7}} \\ { \tt{x + 3 = \sqrt{7} }} \\ { \tt{x = - 3 \pm2.648}} \\ { \tt{x = ( - 3 \pm \sqrt{7} )}}[/tex]
Determine whether each infinite geometric series diverges or converges.
If the series converges, state the sum. 4+2+1+ . . . .
Determine whether each infinite geometric series diverges or converges.
The series converges.
If the series converges, state the sum. 4+2+1+ . . .
The sum of the infinite series is 8
What is the sum of the infinite series?
Given:
[tex]a(\text{ the first term})=4\\\\r(\text{ the common ratio})= \frac{a_2}{a_1} = \frac{2}{4}=\frac{1}{2}[/tex]
Since , [tex]\vert r\vert < 1[/tex] , the infinite series converges.
The sum of infinite geometric series is:
[tex]S_\infty=\frac{a}{1-r} ; -1 < r < 1\\\\S_\infty=\frac{4}{1-\frac{1}{2} } =\frac{4}{\frac{1}{2} }=8[/tex]
The sum of the infinite series is 8
What is an infinite geometric series?
The result of an endless geometric sequence is an infinite geometric series.There would be no conclusion to this series.The total of all finite geometric series can be determined.However, if the common ratio of an infinite geometric series is bigger than one, the terms in the sequence will grow steadily larger, and adding the larger numbers together will not yield a solution.To learn more about infinite geometric series, refer:
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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:
when slolved please show steps.
The expression for h in the information illustrated will be h = 2r.
How to illustrate the information?It should be noted that the expression is given as:
2πr³ = πr²h
In this situation, the information is that we should make h the subject of the formula.
This will be:
2πr³ = πr²h
Divide both side by πr²
2πr³/πr² = πr²h/πr²
2r = h
Therefore h = 2r
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Given g(x)=-2x^(2)+1, find the indicated values. g(0)
Answer:
[tex]g(x) = 2 {x}^{2} + 1 \\ g(0) = 2 ({0})^{2} + 1 \\ = 2(0) + 1 \\ = 1[/tex]
does someone mind helping me with this? Thank you!
Answer:
32
Step-by-step explanation:
Sorry for not neat explanation but i hope u understand
Answer:
32?
Step-by-step explanation:
when i did it with a Pythagorean theorem calculator i got 32
Caroline rewrote a quadratic equation in vertex form by completing the square, but her work has errors.
f(x)
-2x² + 12x15
-2(x² - 6x) — 15
-2(x² - 6x + 9) - 9 - 15
-2(x - 3)²9 - 15
-2(x - 3)² - 24
Identify the first error in her work.
The required error in Caroline's quadratic equation in vertex form by completing the square is -2(x² - 6x + 9) - 9 - 15 is should be -18 in place of -9.
Given that,
To figure out the error made by Caroline in the calculation of a quadratic equation in vertex form by completing the square.
His calculation,
= -2x² + 12x - 15
= -2(x² - 6x) — 15
= -2(x² - 6x + 9) - 9 - 15-2(x - 3)²9 - 15
= -2(x - 3)² - 24
Correct calculation,
= -2x² + 12x - 15
= -2(x² - 6x) - 15
= -2(x² - 6x + 9) - 18 - 15
= -2(x - 3)² - 18 - 15
= -2(x - 3)² - 33
Thus, the required error in Caroline's quadratic equation in vertex form by completing the square is -2(x² - 6x + 9) - 9 - 15 is should be -18 in place of -9.
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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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help please
The cost of having a window fixed is $125 plus $25 per hour of labor. Using h for the number of hours of labor, write an expression that represents the total cost.
25 + 125h
125 + 25h
150h
125+25 over h
I believe the answer would be Y=125+25(h
Answer: 125 + 25h
Step-by-step explanation:
The total amount of money is the cost of the window plus the amount of hours.
Write equations for the horizontal and vertical lines passing through the point (1,8)
Answer:
Vertical: x = 1
Horiz: y = 8
Step-by-step explanation:
The equation of a
vertical line is always:
x = anumber
The equation of a horizontal line is in the form:
y = anumber
In the question a point is given, the point (1,8) is in the form (x,y) So x is 1 and y is 8.
We can fill in this given information to complete the equations.
Vertical: x = 1
Horizontal: y = 8
Use your results from Exercise 13 to determine whether the given measures define 0,1, 2, or infinitely many obtuse triangles. Justify your answers.
a=13, b=17, m
When two sides are provided without an angle measurement, such as a = 13m and b = 17m , we can create an infinite number of obtuse triangles.
As an example:
How many different obtuse triangles can we make if our side lengths are 13m and 17m, and our angle value ranges from 90 to 360 degrees?
Make a triangle with sides of 13m and 17m metres, a 120 degree angle, and a third side that can be protractored to the length you desire. You've constructed a triangle.
We may create a whole different triangle that is identical to this one by altering the third side's length and angle.
You must always remember to select the side lengths and angles. It's hinted that you could choose another course of action. There are an infinite amount of distinct triangles that can be created by using the same angles.
Thus, we can make an infinite number of triangles by employing a single angle and a single side length.
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The length of a bacterial cell is about 4 x 10−6 m, and the length of an amoeba cell is about 2.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
6.25 x 102
2 x 102
6 x 101
16 x 101
the bacterial cell is 6.25*10 times smaller than the amoeba cell.
How many times smaller is the bacterial cell than the amoeba cell?
To find how many times smaller is the bacterial cell than the amoeba cell, we need to take the quotient between the amoeba cell's length and the bacterial cell's length
We know that:
bacterial cell's length = 4*10^(-6) m
amoebas cell's length. = 2.5*10^(-4) m
The quotient gives:
Q = ( 2.5*10^(-4) m)/(4*10^(-6) m) = (2.5/4)*(10^(-4)*10^6) = 0.625*10^(-4 + 6)
Q = 0.625*10^2
Now we want this in scientific notation, so we need to have a digit in the left fo the decimal point, so we can rewrite this as:
Q = 0.625*10^2 = 6.25*10^1 = 6.25*10
Then the bacterial cell is 6.25*10 times smaller than the amoeba cell.
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Help Please
A woman has a total of $9,000to invest. She invests part of the money in an account that pays 7%per year and the rest in an account that pays 9%per year. If the interest earned in the first year is $710, how much did she invest in each account? She invested $ ____at 7%and $_____at 9%.
Answer:
5000.00 gives us 350
4000.00 gives us 360
Is the distance from the center of a circle to a point in the interior of a circle sometimes, always, or never less than the radius of the circle? Explain.
The distance from the center of a circle to a point in the interior of a circle is always less than radius of the circle.
It is given that there is a point inside the circle.
We have to find that whether its distance from center of circle is sometimes, always, or never less than the radius of the circle.
What is the radius of a circle ?
The distance between the center of a circle and any point on the circle is called the radius of circle.
We know that ;
Radius is the distance between the center of a circle and any point on the circle.
Let's assume three points which are A, B, and C, where A is a point inside circle, B is a point on circle, and C is a point outside circle.
Also ;
O is the center of circle.
So ;
OA = the length of the line from center to point inside the circle.
OB = radius of the circle.
OC = the length of the line from center to the point outside the circle.
So ;
We can conclude that ;
OA<OB<OC.
or
The length of the line from the center of a circle to any point inside the circle will be always less than it's radius.
Thus , the distance from the center of a circle to a point in the interior of a circle is always less than radius of the circle.
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Points P, Q, R, and S are collinear Point Q is between P and R, R is between Q and S, and PQ congruent RS. If PS=23 and PR= 18, what is the value of QR?
The value of QR when points P, Q, R and S are collinear is .13
We are given that:
Points P, Q, R and S are collinear points.
Also,
PS = 23
PR = 18
We need to find the value for QR.
Now, we have that PQ is congruent to RS.
So, This means that PQ = RS
This can also be written as:
PR - QR = RS
18 - QR = RS
Also,
PR + RS = PS
Substituting the values, we get that:
18 + ( 18 - QR ) = 23
18 - QR = 23 - 18
18 - QR = 5
QR = 18 - 5
QR = 13
Therefore, we get that, the value of QR when points P, Q, R and S are collinear is .13
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