Answer:
b. steepest slope
Step-by-step explanation:
The cumulative relative frequency curve also known as Ogive is used for reading the median, upper quartile, lower quartile from the curve and calculating the semi-interquartile range when needed.
From the cumulative relative frequency curve, the interval with the highest proportion of measurements is the interval with the steepest slope. This is because the cumulative relative frequency curve always have a positive slope, and given that the interval has the highest proportion, then the slope will be steepest.
Which of the following correctly shows the quotient of 80 divided by 5 ?
Answer:16
Step-by-step explanation:
Just divide 80 by 5 or skip count by fives.
PLEASE HELPPPPP!!!!!!!!!!!!!!!Which relationships have the same constant of proportionality between y and x as the following graph?Choose two answers!!
Answer:
B, E
Step-by-step explanation:
You can use these strategies to compare the given graph and the other representations.
A & B) See if the point (x, y) = (8, 6) marked on the first graph works in the given equation.
A -- 6y = 8x ⇒ 6(6) = 8(8) . . . FALSE
B -- y = (3/4)x ⇒ 6 = (3/4)8 . . . True
__
C) Compare this graph to the given graph. They don't match.
__
D & E) Plot a point from the table on the given graph and see where it falls.
D -- The point (x, y) = (3, 4) lies above the line on the given graph.
E -- The point (x, y) = (4, 3) lies on the given graph.
_____
Choices B and E have the same constant of proportionality as shown in the given graph.
Answer:
B and E
Step-by-step explanation:
A table has five bowls. None of the quantities in the bowls are prime, though the last two bowls are empty. Two of the quantities are squares, and when added to the remaining number, the sum is 21. What are the amounts in the first three bowls?
Since two of the quantities are squares and the sum of all of three is equal 21, then the possible values of those two quantities are: 1,4,9,16
Let's consider each possibility
1 and 4
21-1-4=16, but 16 is also square and there can be only two square so NO
1 and 9
21-1-9=11, but 11 is prime, so NO
1 and 16
21-1-16=4... 4 is a square ,so NO
4 and 9
21-4-9=8 , 8 is not prime and not a square, so YES
4 and 16
21-4-16=1, but 1 is a square ,so NO
9 and 16
9+16=25>21 so.. NO
Therefore, the amounts in the first three bowls are 4,8,9.
In the diagram, the vertices of the square lie at the centers of the four partial circles. What is the area of the entire shape? Use the value pi = 3.1416
The area of the entire shape is 33,562 square units
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
The figure is made up of a square and four 3/4 circles. So the total area will be equal to the sum of the area of the square and the sum of the 3/4 th circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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The area of the entire shape is 33,562 square units.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.
Here, we have,
The figure is made up of a square and four 3/4 circles.
So the total area will be equal to the sum of the area of the square and the sum of the 3/4 the circles.
Area of Square:-
= 100 x 100 = 10,000
Area of each circle
= π r² = 3.1416 x 50 x 50 = 7854
Area of each 3/4 circle
= 7854 x ( 3/4 ) = 5890.5
Area of all four 3/4 circles
= 5890.5 x 4=23562
The TOTAL area will be the sum of all the areas
A = 23562 + 10,000 = 33,562 square units
Therefore the area of the entire shape is 33,562 square units
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What is the midpoint of the segment below?
A.
(0, 0)
B.
(-1, 1)
C.
(0.5, 0.5)
D.
(0.5, -0.5)
Answer:
Step-by-step explanation:
(5+(-4))/2 = 1/2 or 0.5
(-7 + 6)/2 = -1/2 or -0.5
the solution is D
(0.5, -0.5)
Find the solution set of the inequality and the number: 12 − 6x > 24 A. , C. ≤, D. ≥, E. =
Answer:
x < -2
Step-by-step explanation:
12 − 6x > 24
Subtract 12 from each side
12-12 − 6x > 24-12
-6x > 12
Divide each side by -6, remembering to flip the inequality
-6x/-6 < 12/-6
x < -2
Answer:
x < -2
Step-by-step explanation:
12 − 6x > 24
12 - 12 − 6x > 24 - 12
-6x > 12
-6x/(-6) < 12/(-6)
x < -2
What is the third quartile?
Answer:
17
Step-by-step explanation:
The third quartile is positioned at the right end of the box, thus
third quartile = 17
Need help with the question below.
Answer:
A
Step-by-step explanation:
r=10 and the angle bln 5√3 and -5 is 330 or 11π/6
What is the value of 1 in 1,255 is what times the value of the 1 in 82,175
Answer:
100,000
You take 1,000 because it's in the thousandths place of 1,255. The value of that one is 1,000 so you multiply that times 100, which is the value of 1 in 82,175.
Answer:
Step-by-step explanation:
PLEASE HELP! (3/4) - 50 POINTS -
Answer:
C
Step-by-step explanation:
The set of data will only become more narrow when the standard deviation is decreased, so D isn't correct. The data isn't going to shift directions unless there's a translation, so A and B are both out. That leaves us with C. The opposite of answer D.
Answer:
C. It produces a wider range of probable values
Step-by-step explanation:
The set of data that we have cannot shift in directions unless there is a translation, so therefore, A and B are both out. The set of data would become smaller when the standard deviation is decreases so therefore, D isn't correct. So, that leaves us with only one answer.
C. It produces a wider range of probably values.
Consider the following case and determine whether there is sufficient information to solve the triangle using the low of sines. Two angles and the side included between them are known.
A. There is insufficient information because to use the law of sines, one side and the angle opposite it must be known.
B. There is sufficient information because if two angles and a side included between them are known, the third angle and the remaining two sides can be determined using the law of sines.
C. There is insufficient information because to use the law of sines, two angles and a side opposite one of them must be known.
D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
Answer:
D. There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
Step-by-step explanation:
A triangle is a plane shape that consists of 3 sides and 3 angles. There are different ways of solving for any unknown sides or angles of a triangle.
If any two angles and just one side of a triangle are known, then other angles and sides can also be determined using the sine rule.
For example, if a, b and c are the sides of the triangle and <A, <B and <C are the angles. The sine law is expressed as shown;
a/sinA = b/sinB = c/sinC
Any two can be equated to get any unknown sides and angles.
Also, if two of the angles are known, the third angle can be determined since the sum of angle in a triangle is 180°. If <A and <B are known for example, the third angle <C can be determined using the expression.
<C = 180°-(<A+<B)
Based on the explanation, option D is therefore the correct option i.e There is sufficient information because if two angles and a side included between them are known, the third angle can be determined using the angle sum formula and the remaining two sides can be determined using the law of sines.
Please help quick !
Answer:
vertical angles
Step-by-step explanation:
Angle 1 and 3 are vertical angles. The angles are made from the same lines and share a vertex. They are opposite it each other
List the angles in order from the largest to the smallest for ABC.
AB= 14, AC = 15, BC = 16
Answer:
B. ∠A, ∠B, ∠C
Step-by-step explanation:
1. Draw a model with AB as the shortest line and BC as the longest line.
∠A connects the two shortest lines, making it the largest angle.
∠B connects the shortest and the longest lines, making it the second largest angle.
∠C connects the two longest lines, making it the smallest angle.
Answer:
A > B > C
Step-by-step explanation:
Ypu probably wouldn't think about it unless someone pointed it out, but if you look at a triangle of any type you can see that the sizes of the sides are directly related to the sizes of the angles opposed to them.
By this I mean, the largest side will have the largest angle across from it and the smallest side will have the smallest angle.
Based off of my drawing, it looks like the order is angle A, then B, then, and then C.
Dan weighs 205 pounds but is only 5 feet 8 inches tall. Evan is 6 feet tall. How much would you expect Evan to weigh if they have the same height/weight ratio? WILL MARK BRAINLIST
Answer:
217.0588235294118
Step-by-step explanation:
Convert all height to inches.
5' 8" = 68 inches
6' = 72
205/68 = 3.014705882352941
Height/Weight Ratio * Evan's Height = 217.0588235294118
A regression analysis between sales (y in $1000) and advertising (x.in dollars) resulted in the following equation: ỹ= 30,000 + 4x
The above equation implies that an:________
a. increase of $l in advertising is associated with an increase of $4 in sales.
b. increase of $4 in advertising is associated with an increase of $4000 in sales.
c. increase of $1 in advertising is associated with an increase of $34,000 in sales.
d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Answer:
Correct answer is option d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Step-by-step explanation:
Given the equation of regression analysis is given as:
[tex]y= 30,000 + 4x[/tex]
where [tex]x[/tex] is the cost on advertising in Dollars.
and [tex]y[/tex] is the sales in Thousand Dollars.
To find:
The correct increase in sales when there is increase in the advertising cost.
Solution:
Suppose there is an increase of [tex]\$1[/tex] in the advertising cost.
Let the initial cost be [tex]x[/tex] then the cost will be [tex](x+1)[/tex].
Initial sales
[tex]y= 30,000 + 4x[/tex] ....... (1)
After increase of $1 in advertising cost, final cost:
[tex]y'= 30,000 + 4(x+1)\\\Rightarrow y' = 30,000+4x+4\\\Rightarrow y' = 30,004+4x ..... (2)[/tex]
Subtracting (2) from (1) to find the increase in the sales:
[tex]y'-y=30004+4x-30000-4x = 4[/tex]
The units of sales is Thousand Dollars ($1000).
So, increase in sales = [tex]4 \times1000 = \bold{\$4000}[/tex]
So, correct answer is:
d. increase of $1 in advertising is associated with an increase of $4000 in sales.
Please help. I’ll mark you as brainliest if correct!
Answer:
The system is dependent:
x=-3t-7
y=-5t-15
z=t
Step-by-step explanation:
I chose to use a matrix to solve this system of equations. Once put into matrix form, you need to row reduce the system into its simplest form (Row Reduced Echelon form). Doing this, we find that the system is dependent on the z variable. And following usual procedures, we let z equal some other letter; which is t in this case. Then we isolate each variable to get the answer.
Check the attachment for the work.
[The arrows indicate a row swap and the parenthesis indicates addition if a constant multiple of one row to another]
1. (a) Find the probability that a 90% free-throw shooter makes 10 consecutive free-throws, assuming that individual shots are independent.
Answer:
[tex]Probability = 0.35[/tex]
Step-by-step explanation:
Given
Probability of success free throw = 90%
Number of throw = 10
Required
Determine the probability of 10 consecutive free throws
Let p represents the given probability
[tex]p = 90\%[/tex]
Convert to decimal
[tex]p = 0.9[/tex]
Let n represents the number of throw
[tex]n = 10[/tex]
Provided that each throw is independent;
The probability of n consecutive free throw is
[tex]p^n[/tex]
Substitute 0.9 for p and 10 for n
[tex]Probability = 0.9^{10}[/tex]
[tex]Probability = 0.3486784401[/tex]
[tex]Probability = 0.35[/tex] (Approximated)
A professor of women's studies is interested in determining if stress affects the menstrual cycle. Ten women are randomly sampled for an experiment and randomly divided into two groups. One of the groups is subjected to high stress for two months while the other lives in a relatively stress-free environment. The professor measures the menstrual cycle (in days) of each woman during the second month. The following data are obtained.
High stress 20 23 18 19 22
Relatively stress free 26 31 25 26 30
Required:
1. The obtained value of the appropriate statistic is _______
a. tobt = -4.73
b. tobt = -4.71
c. tobt = -3.05
d. tobt = -.047
2. The df for determining tcrit are ____.
a. 4
b. 9
c. 8
d. 3
3. Using a = 0.052 tail, tcrit = ____.
a. +- 2.162
b. +- 2.506
c. +- 2.462
d. +- 2.306
4. Using a = .052 tail, your conclusion is ____.
a. Accept H0; stress does not affect the menstrual cycle
b. Retain H0; we cannot conclude that stress affects the menstrual cycle
c. Retain H0; Stress affects the menstrual cycle
d. Reject H0; stress affects the menstrual cycle
Answer:
1. a. tobt = -4.73
2. b. 9
3. a. +- 2.162
4. d. Reject H0; stress affects the menstrual cycle.
Step-by-step explanation:
The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted.
A city is holding a referendum on increasing property taxes to pay for a new high school. In a survey of 434 likely voters, 202 said that they would vote "yes" on the referendum. Create a 95% confidence interval for the proportion of likely voters who would vote "yes" on the referendum. Use a TI-83, TI-83 plus, or TI-84 calculator, rounding your answers to three decimal places.
Answer: 0.418 < p < 0.512
Step-by-step explanation: A 95% conifdence interval for a population proportion is given by:
[tex]p + z\sqrt{\frac{p(1-p)}{n} }[/tex]
where:
p is the proportion
z is score in z-table
n is sample size
The proportion for people who said "yes" is
[tex]p=\frac{202}{434}[/tex] = 0.465
For a 95% confidence interval, z = 1.96.
Calculating
[tex]0.465 + 1.96*\sqrt{\frac{0.465(0.535)}{434} }[/tex]
[tex]0.465 + 1.96*\sqrt{0.00057}[/tex]
0.465 ± 1.96*0.024
0.465 ± 0.047
Interval is between:
0.465 - 0.047 = 0.418
0.465 + 0.047 = 0.512
The interval with 95% of confidence is between 0.418 and 0.512.
the dot plot above identifies the number of pets living with each of 20 families in an apartment building .what fraction of families have more than two pets
Answer:
B. ⅕
Step-by-step explanation:
Fraction of families having more than 2 pets = families with pets of 3 and above ÷ total number of families in the apartment
From the dot plot above, 3 families have 3 pets, and 1 family has 4 pets.
Number of families with more than 2 pets = 3 + 1 = 4
Fraction of families with more than 3 pets = [tex] \frac{4}{20} = \frac{1}{5} [/tex]
The fraction of families that have more than two pets is B. [tex]\frac{1}{5}[/tex]
Calculations and ParametersGiven that:
Fraction of families having more than 2 pets = families with pets of 3 and above/total number of families in the apartment
From the dot plot above:
3 families have 3 pets, 1 family has 4 pets.Number of families with more than 2 pets
= 3 + 1
= 4
Fraction of families with more than 3 pets = [tex]\frac{4}{20} = \frac{1}{5}[/tex]
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Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not solve the equation.
x2+3x−18=0
Answer:
Step-by-step explanation:
Hello, "the constant term has been written on the right side", it means that we add 18 to both sides to get.
[tex]x^2+3x-18=0\\\\x^2+3x=18\\\\\text{We can see the beginning of } (x+\dfrac{3}{2})^2 \\\\x^2+3x=(x+\dfrac{3}{2})^2-\dfrac{3^3}{2^2}=18\\\\(x+\dfrac{3}{2})^2=18+\dfrac{9}{4}=\dfrac{18*4+9}{4}=\dfrac{81}{4}[/tex]
Hope this helps.
Thank you.
Answer:
2.25.
Step-by-step explanation:
x^2 + 3x - 18 = 0
First, we need to write the constant on the right of the equation. So, we add 18 to both sides.
x^2 + 3x = 18.
Now, we find the number that will complete the square. It will be [tex](\frac{b}{2} )^2[/tex].
In this case, b = 3.
[tex](\frac{3}{2} )^2[/tex]
= (1.5)^2
= 2.25.
So, the number that will complete the square to solve the equation is 2.25, or 2 and 1/4, or 9/4.
Hope this helps!
Write as an equation: The sum of a number and 12 is 78.
Answer:
x+12=78
Step-by-step explanation:
like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.
Answer:
n + 12 = 78
Step-by-step explanation:
Let n = number.
n + 12 = 78
Theresa bought 2 pineapples for $6. She wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part B
How much would 4 pineapples cost?
The yellow bar is the total cost of 2 pineapples. The black line in the middle of the yellow splits it equally in half and is located at the 3.
The constant bod proportionality would be 3, which means each pineapple cost $3
Answer:
first of all, brainly better not delete my answer again. (the answer is 3)
Step-by-step explanation:
you have to multiply to find the number of pineapples. but unlike me i did skip count and write down my number's and I tried to find "what number skips until it ends to 6?'' i found 3 as my answer! 3,6,9,12,15,18,21 etc..
In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠BTA ≅ ∠CTA ∠BAT ≅ ∠CAT
Answer:
The two choices are true by CPCTC. Are there other choices that were not posted?
How much will $1000 deposited in an account earning 7% interest compounded annually be worth in 20 years? (which formula do I use? I am confused...txs)
Answer:
$3870
Step-by-step explanation:
Hello, the initial deposit is $1000.
After one year, we will get 1000 + 7%*1000= 1000 * ( 1+7%) = 1000 * (1+0.07)
= 1000 * 1.07
And we want to compound it so the second year we will get
[tex]1000 * 1.07 * 1.07 = 1000 * 1.07^2[/tex]
And after n years, we will get
[tex]1000 * 1.07^n[/tex]
In that example, we want to know how much we will get after 20 years, so this is:
[tex]1000 * 1.07^{20}=3869.684462...[/tex]
Thank you.
When interest is compounded, it means that both the interest and the amount deposited will earn interest.
We are to determine the future value of $1000 with annual compounding.
The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = amount deposited = $1000
R = interest rate = 7%
N = number of years = 20
$1000 x ( 1.07)^20 = $3,869.68
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Figure out if the figure is volume or surface area.
(and the cut out cm is 4cm)
Answer:
Surface area of the box = 168 cm²
Step-by-step explanation:
Amount of cardboard needed = Surface area of the box
Since the given box is in the shape of a triangular prism,
Surface area of the prism = 2(surface area of the triangular bases) + Area of the three rectangular lateral sides
Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]
= [tex]\frac{1}{2}(6)(4)[/tex]
= 12 cm²
Surface area of the rectangular side with the dimensions of (6cm × 9cm),
= Length × width
= 6 × 9
= 54 cm²
Area of the rectangle with the dimensions (9cm × 5cm),
= 9 × 5
= 45 cm²
Area of the rectangle with the dimensions (9cm × 5cm),
= 9 × 5
= 45 cm²
Surface area of the prism = 2(12) + 54 + 45 + 45
= 24 + 54 + 90
= 168 cm²
Solve 2 - (7x + 5) = 13 - 3x (make sure to type the number only)
Answer:
x = -4
Step-by-step explanation:
2 - (7x + 5) = 13 - 3x
add the binomial (7x +5) to both sides
2 = (7x + 5) + 13 - 3x
combine like terms
2 = 4x + 18
subtract 18 from both sides
-16 = 4x
divide by 4
x = -4
Answer:
-4
Step-by-step explanation:
Distribute the negative signs to the values in the parentheses
2 -7x - 5 = 13 - 3x
Add like terms:
-7x - 3 = 13 - 3x
Add 3x to both sides:
-4x - 3 = 13
Add 3 to both sides:
-4x = 16
Divide both sides by -4:
x = -4
In the adjoining figure, in ΔABC, D is the midpoint of the side BC.Hence a) AD is ___________ A b) AM is ____________ c) Is BD = DC please help!!!!!!!!!!!!!!
Answer:
a) AD is Median
b) AM is Perpendicular Bisector
Step-by-step explanation:
c) Yes because the Median divides the line into two equal parts
1-What is the sum of the series? ∑j=152j Enter your answer in the box.
2-What is the sum of the series? ∑k=14(2k2−4) Enter your answer in the box.
3-What is the sum of the series? ∑k=36(2k−10)
4-Which answer represents the series in sigma notation? 1+12+14+18+116+132+164 ∑j=1712(j+1) ∑j=172j−1 ∑j=1712j+1 ∑j=17(12)j−1
5-Which answer represents the series in sigma notation? −3+(−1)+1+3+5 ∑j=155j−1 ∑j=15(3j−6) ∑j=15(2j−5) ∑j=15−3(13)j−1
Answer:
Please see the Step-by-step explanation for the answers
Step-by-step explanation:
1)
∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] 2j
The sum of series from j=1 to j=5 is:
∑ = 2(1) + 2(2) + 2(3) + 2(4) + 2(5)
= 2 + 4 + 6 + 8 + 10
∑ = 30
2)
This question is not given clearly so i assume the following series that will give you an idea how to solve this:
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²
The sum of series from k=1 to j=4 is:
∑ = 2(1)² + 2(2)² + 2(3)² + 2(4)²
= 2(1) + 2(4) + 2(9) + 2(16)
= 2 + 8 + 18 + 32
∑ = 60
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²
∑ = (2*1)² + (2*2)² + (2*3)² + (2*4)²
= (2)² + (4)² + (6)² + (8)²
= 4 + 16 + 36 + 64
∑ = 120
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²- 4
∑ = (2*1)²-4 + (2*2)²-4 + (2*3)²-4 + (2*4)²-4
= (2)²-4 + (4)²-4 + (6)²-4 + (8)²-4
= (4-4) + (16-4) + (36-4) + (64-4)
= 0 + 12 + 32 + 60
∑ = 104
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²- 4
∑ = 2(1)²-4 + 2(2)²-4 + 2(3)²-4 + 2(4)²-4
= 2(1)-4 + 2(4)-4 + 2(9)-4 + 2(16)-4
= (2-4) + (8-4) + (18-4) + (32-4)
= -2 + 4 + 14 + 28
∑ = 44
3)
∑[tex]\left \ {{6} \atop {k=3}} \right.[/tex] (2k-10)
∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)
= (6-10) + (8-10) + (10-10) + (12-10)
= -4 + -2 + 0 + 2
∑ = -4
4)
1+1/2+1/4+1/8+1/16+1/32+1/64
This is a geometric sequence where first term is 1 and the common ratio is 1/2 So
a = 1
This can be derived as
1/2/1 = 1/2 * 1 = 1/2
1/4/1/2 = 1/4 * 2/1 = 1/2
1/8/1/4 = 1/8 * 4/1 = 1/2
1/16/1/8 = 1/16 * 8/1 = 1/2
1/32/1/16 = 1/32 * 16/1 = 1/2
1/64/1/32 = 1/64 * 32/1 = 1/2
Hence the common ratio is r = 1/2
So n-th term is:
[tex]ar^{n-1}[/tex] = [tex]1(\frac{1}{2})^{n-1}[/tex]
So the answer that represents the series in sigma notation is:
∑[tex]\left \ {{7} \atop {j=1}} \right.[/tex] [tex](\frac{1}{2})^{j-1}[/tex]
5)
−3+(−1)+1+3+5
This is an arithmetic sequence where the first term is -3 and the common difference is 2. So
a = 1
This can be derived as
-1 - (-3) = -1 + 3 = 2
1 - (-1) = 1 + 1 = 2
3 - 1 = 2
5 - 3 = 2
Hence the common difference d = 2
The nth term is:
a + (n - 1) d
= -3 + (n−1)2
= -3 + 2(n−1)
= -3 + 2n - 2
= 2n - 5
So the answer that represents the series in sigma notation is:
∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] (2j−5)
For (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex] where j = 1 to j = 7, and for (5) the sigma notation is [tex]\rm\sum j = (2j-5)[/tex] where j = 1 to j = 5.
We have different series in the question.
It is required to find the sum of all series.
What is a series?In mathematics, a series can be defined as a group of data that followed certain rules of arithmetic.
1) We have:
[tex]\rm \sum j=2j[/tex] where j = 1 to j = 5
After expanding the series, we get:
= 2(1)+2(2)+2(3)+2(4)+2(5)
=2(1+2+3+4+5)
= 2(15)
=30
2) We have:
[tex]\rm \sum k=(2k^2-4)[/tex] where k = 1 to k = 4
After expanding the series, we get:
[tex]\rm = (2(1)^2-4)+(2(2)^2-4)+(2(3)^2-4)+(2(4)^2-4)+(2(5)^2-4)\\[/tex]
[tex]\rm = 2[1^2+2^2+3^2+4^2+5^2]-4\times5\\\\\rm=2[55]-20\\\\\rm = 90[/tex]
3) We have:
[tex]\rm \sum k= (2k-10)[/tex] where k = 3 to k = 6
After expanding the series, we get:
[tex]= (2(3)-10)+(2(4)-10)+(2(5)-10)+(2(6)-10)\\\\=2[3+4+5+6] - 10\times4\\\\=2[18] - 40\\\\= -4[/tex]
4) The series given below:
[tex]1, \frac{1}{2} ,\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},\frac{1}{64}[/tex]
It is a geometric progression:
[tex]\rm n^t^h[/tex] for the geometric progression is given by:
[tex]\rm a_n = ar^{n-1}[/tex]
[tex]\rm a_n = 1(\frac{1}{2})^{n-1}\\\\\rm a_n = (\frac{1}{2})^{n-1}\\[/tex]
In sigma notation we can write:
[tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex] where j = 1 to j = 7
5) The given series:
−3+(−1)+1+3+5, it is arithmetic series.
[tex]\rm n^t^h[/tex] for the arithmetic progression is given by:
[tex]\rm a_n = a+(n-1)d[/tex]
[tex]\rm a_n = -3+(n-1)(2)\\\\\rm a_n = 2n-5[/tex]
In sigma notation we can write:
[tex]\rm\sum j = (2j-5)[/tex] where j = 1 to j = 5
Thus, for (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex] where j = 1 to j = 7, and for (5) the sigma notation is [tex]\rm\sum j = (2j-5)[/tex] where j = 1 to j = 5.
Learn more about the series here:
https://brainly.com/question/10813422
do numbers ever stop
Nope, i dont think so
Answer:
no the numbers are infinite
Step-by-step explanation:
