Answer:
First Term = 6
Common Ratio = 3
Step-by-step explanation:
According to the Question,
Given, The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240 .Thus, [tex]S_{8} = 19680[/tex] & [tex]S_{4} = 240[/tex] .
The Sum of n-term of Geometric Mean is [tex]S_{n} = \frac{a(r^{n-1)} }{r-1}[/tex] Where, r>1 , a=First term of G.P & r=common Ratio .Now, on solving [tex]\frac{S_{8} }{S_{4} }[/tex] we get,
[tex]\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}[/tex]
[tex]82 = \frac{r^{8}-1 }{r^{4}-1 }[/tex]
[tex]82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0[/tex](r=1 is not possible so neglect [tex]( r^{4}-1) =0[/tex] )
So, r=3 Now Put this value in [tex]S_{4} = {\frac{a(r^{4-1)} }{r-1}}[/tex] We get a=6 .
Dr. Kang, a cognitive psychologist, conducts an experiment examining the effect of emotion on memory. He provides lists of 15 words to two groups of participants at his university. He puts the names of all the participants in a hat. The first 20 names he assigns to Group A and the last 20 he assigns to Group B. Group A is given a list of words that are very emotional in content (e.g., passion, murder). Group B is given a list of words that are neutral in content (e.g., houseplant, desk). He then measures how many words each group is able to remember after being distracted for 5 minutes by watching a video about the history of the university. He finds that Group A remembers 15% more words than Group B. Use the scenario to answer the following questions (A though C).
A. What is the dependent variable? [1 pt]
B. What is the independent variable? [1 pt]
C. Can Dr. Kang make a causal claim that "emotion enhances memory"? Why or why not?
Answer:
21
Step-by-step explanation:
best pickup line: Even if earth didn't have gravity i would still fall for you.
Please answer i will give brainliest
Answer:
sorry bro......sis
Step-by-step explanation:
don,t know its answer
20. A smaller rectangle is centered within a larger rectangle such that the shaded area is created as shown below. The dimensions of both rectangles are shown in terms of x.
i don´t know how to solve this
Step-by-step explanation:
please check the attachment
can you help me with the question pls it's about standard form/scientific notation.
I'm confused with the minuses on the indices.
Answer:
-3 squared means it is 0.1 for each -1, so it would be 0.001
Step-by-step explanation:
it is 0.003 for a and the rest you can figure out
answer choices:
a. 122
b. 102
c. 138
d. 85
Answer:
option b
Step-by-step explanation:
The sum of the interior angles of a quadrilateral is 360°.
That is,
120 + y + 85 + 53 = 360
y = 360 - 120 - 85 - 53
y = 102
Answer:
Option B is correct
Step-by-step explanation:
Hint :
Sum of angles in quadrilateral = 360°
Simplify :
[tex] {y}^{o} + {120}^{o} + {85}^{o} + {53}^{o} = {360}^{o} \\ {y}^{o} + {258}^{o} = {360}^{o} \\ {y}^{o} = {360}^{o} - {258}^{o} \\ {y}^{o} = {102}^{o} [/tex]
Hope it is helpful...x+y-6=0, x-y=0. What is the solution set of the system?
A. (3,3)
B. (-3,3)
C. (3, -3)
Answer:
A. (3,3)
Step-by-step explanation:
Simply and find the value of the following
Answer:
this is the answer of your question
Step-by-step explanation:
[tex]i) \: {(729)}^{ \frac{1}{6} } [/tex]
[tex] = {(3 \times 3 \times 3 \times 3 \times 3 \times 3)}^{ \frac{1}{6} } [/tex]
[tex] = \sqrt[6]{(3 \times 3 \times 3 \times 3 \times 3 \times 3)}[/tex]
= 3 (Ans)
[tex]ii) \: {(64)}^{ \frac{2}{3} } [/tex]
[tex] = \sqrt[3]{ {64}^{2} } [/tex]
[tex] = \sqrt[3]{(64 \times 64)} [/tex]
[tex] = \sqrt[3]{ {2}^{12} } [/tex]
[tex] = {(2)}^{ \frac{12}{3} } [/tex]
[tex] = {2}^{4} [/tex]
= 16 (Ans)
[tex]iii) \: {(243)}^{ \frac{6}{5} } [/tex]
[tex] = {( \sqrt[5]{ {243} })}^{6} [/tex]
[tex] = {3}^{6} [/tex]
= 729 (Ans)
Which value of “x” would satisfy the following equation 24x - 18 - 8x - 30 = 96?
Answer:
x = 9
Step-by-step explanation:
24x - 18 - 8x - 30 = 96
add or subtract like terms
16x - 48 = 96
shift - 48 to right hand side . when it goes to other side minus changes to plus
16x = 96 + 48
16x = 144
x = 144/16
x = 9
to prove that the value of x satisfy the given equation or not.
to prove that the value of x is 9 substitute 9 inplace of x and if it gives 96 then it satisfy
24x - 18 - 8x - 30 = 96
24*9 - 18 - 8*9 - 30 = 96
216 - 18 - 72 - 30 = 96
216 - 120 = 96
96 = 96
since both sides is equal to 96 it can be concluded that the value of x is 9.
Which value of “x” would satisfy the following equation 24x - 18 - 8x - 30 = 96?
AnswerX = 9Step by Step Explanation24x - 18 - 8x - 30 = 96
First let's just add/subract the following terms.
16x - 48 = 96
Second.. shift the 48 to the right side. after that change the minus sign into plus sign.
16x = 48 + 96
16x = 44
x = 144/16
x = 9
Explanation:
So we just prove that the value of x satisfy the equation true or not.To prove that the value of x is 9.. we just substitute the 9 in place of x and if it was 96 the result of the equation the problem must be true.So we begin to solve it!
24x - 18 - 8x - 30 = 96
24*9 - 18 - 8*9 - 30 = 96
216 - 18 - 72 - 30 = 96
216 - 120 = 96
Since that all both sides are equal to 96 it can be concluded that the value of x is 9.
#LearnwithBrainly
(4 × 5) × 7 = 7 × _________ (4 × 7) 20 (7 - 5) (5 + 7)
Answer:
I think the answer is 5 hope it helps
What's the area of this shape?
Answer:
[tex] 365.97\: cm^2[/tex]
Step-by-step explanation:
Area of the shape = Area of triangle with base 22 cm and height 16 cm + Area of semicircle with radius (22/2 = 11) 11 cm
[tex] = \frac{1}{2}bh + \frac{1}{2} \pi {r}^{2} \\ \\ = \frac{1}{2} \times 22 \times 16 + \frac{1}{2} \times \times 3.14 {(11)}^{2} \\ \\ = 11 \times 16 + 3.14 \times 60.5 \\ \\ = 176 + 189.97 \\ \\ = 365.97 \: {cm}^{2} [/tex]
Step-by-step explanation:
The radius would be 11 which is half of the width and the height is 16.
A= πr(r+√h²+r²)
A= π•11•(11+√16²+11²)
A≈ 1051.11836
ANSWER IS C
Which number line represents the solution to 2.5 – 1.2x < 6.5 – 3.2x?
1.) A number line from negative 5 to 5 in increments of 1. An open circle is at 4 and a bold line starts at 4 and is pointing to the left.
2.) A number line from negative 5 to 5 in increments of 1. An open circle is at 4 and a bold line starts at 4 and is pointing to the right.
3.) A number line from negative 5 to 5 in increments of 1. An open circle is at 2 and a bold line starts at 4 and is pointing to the left.
4.) A number line from negative 5 to 5 in increments of 1. An open circle is at 2 and a bold line starts at 4 and is pointing to the right.
Answer:
x <2
Step-by-step explanation:
2.5 – 1.2x < 6.5 – 3.2x
Add 3.2x to each side
2.5 – 1.2x+3.2x < 6.5 – 3.2x+3.2x
2.5 +2x < 6.5
Subtract 2.5 from each side
2.5+2x-2.5<6.5-2.5
2x<4
Divide by 2
2x/2 < 4/2
x <2
what is x?
0=3x² - 4x + 12
Answer:
x=0.66+1.88i
x=0.66-1.88i
Step-by-step explanation:
Given
3[tex]x^{2}[/tex]-4x+12=0
using the Quadratic Formula where
a = 3, b = -4, and c = 12
[tex]x=-b[/tex]±[tex]\sqrt{b^{2}-4ac } /2a\\[/tex]
x=-(-4)±[tex]\sqrt{(-4)^{2}-4(3)(12) } /2(3)[/tex]
x=4±[tex]\sqrt{16-144} /6[/tex]
x=-4±[tex]\sqrt{128} /6[/tex]
[tex]b^{2} -4ac<0\\[/tex]
x=-4±[tex]8\sqrt{2} i[/tex]/6
[tex]x=\frac{2}{3}[/tex]± [tex]\frac{4\sqrt{2}i }{3}[/tex]
Which becomes,
x=0.66+1.88i
x=0.66-1.88i
The value of x will be x=0.66+1.88i
x=0.66-1.88i
I don't understand help plz
ADD AND SKMPLIFY
will
Give
Brainlist
Answer:
37 5/8
Step-by-step explanation:
Hey buddy I am here to help!
*converting them into improper fraction*
13/8 + 149/8 + 139/8 = 13+149+139/8 = 301/8 = 37 5/8
Hope the answer helps!
Plz mark me brainliest
A
B
Peanut
Butter
Peanut Butter
150g
400g
$2.14
$6.50
Which of the jars shown above is the BETTER buy?
Answer:
I guess 400g good for your diet. and health
John can jog twice as fast as he can walk. He was able to jog the first 5 miles to his grandmothers house, but the he tired and walked the remaining 2 miles.If the total trip took 0.9 hours, then what was his average jogging speed?
10^ log 2 to the base 10
Answer:
the answer is 2
Step-by-step explanation:
It is like you are taking the antilogarithm of log 2
Answer:
2 is the answer of your question
hope it is helpful to you
Consider the polygon shown. Determine the value of y.
67
75
Answer:
70 degrees
Step-by-step explanation:
It's a right angle and have angles. The polygon is 5 sides. It's 540 degrees.
It's complementary.
Step-by-step explanation:
i don't know but i think it 157 because:
180-67=113
113-90=23 x
180-23-75=82 y
hope u can understand this
If the first three Fibonacci numbers are given as x, = 1, X2 = 1 and x3 = 2,
what is the value of n for which X, + Xp = 55?
Answer:
n=8
Step-by-step explanation:
Please help 50 points
Simplify the expression
Answer:
c
Step-by-step explanation:
Which point is located on the x-axis?
D
4
А
3
BE
2+
1
C
-4 -3 -2 -1
-1
1
2
3
4 X
-2+
-3+
4
Answer:
point C ad B located on the x axis
Dominic is deciding if he should become a member of his local ice rink. The $144 annual membership fee at the ice rink includes admission and parking, members pay $4.00 per visit to rent ice skates. Non-members pay $11 admissions, $5.00 for parking and they also pay $4.00 per visit to rent ice skates. 1. When is it better to be a member? After 4 visits how much would each pay? Member: $_________ Non-Member: $__________ After 6 visits how much would each pay? Member: $_________ Non-Member: $__________
Answer:
1. members = $ 160 , non members = $ 80
2. members = $ 168 , non members = $ 120
Step-by-step explanation:
For members
Annual membership = $ 144
rent per visit charges = $ 4
For Non members
parking charges = $ 5
admission charges = $ 11
rent per visit = $ 4
(1) for 4 visits
Members pay = $ 144 + 4 x $ 4 = $ 160
Non members pay = 4 x $ 11 + 4 x $ 5 + 4 x $ 4 = $ 80
So, non member ship is better.
(2) for 6 visits
Members pay = $ 144 + 6 x $ 4 = $ 168
Non members pay = 6 x $ 11 + 6 x $ 5 + 6 x $ 4 = $ 120
So, non member ship is better.
For what value of k will the relation y = kx² + 8x + 8 have only one zero? (3 marks)
Answer:
2
Step-by-step explanation:
2x^2 + 8x + 8
factor the 2 out : 2(x^2 + 4x + 4)
2(x + 2)^2
x = -2
According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 9X4 – 2x2 – 3x + 4?
1
2
1
O ,
4 2 4
3. +1, +3, +2, +4
0 +2, ++1, +3, 4, +3, +
9
*9
4
1 2 1 4 2
Ogg. 3.9. 3, 1, 3, 2, 4
1 1 3 3 9 9
O 4.2.2.1, 2, 7, 3, 2,9
Answer:A
Step-by-step explanation:
I JUST TOOK THE TEST ON EDGE
The possible root of the function are: ±1, ±1/3, ±1/9 , ±2, ±2/3, ±2/9, ± 4, ±4/3, ±4/9.
What is Rational Root Theorem?In algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the fraction's denominator and the constant term (the one without a variable) must be divisible by the fraction's numerator.
We have the function f(x) = 9[tex]x^4[/tex] - 2x² - 3x + 4.
For Polynomial Function
f(x) = p[tex]x^n[/tex] + ...... + q
So, The possible rational roots are calculated using
Roots = ± factors of p / factors of q
= ± factors of 4 / factors of 9
= ± 1, 2, 4 / 1, 3, 9
So, the possible rational roots are ±1, ±1/3, ±1/9 , ±2, ±2/3, ±2/9, ± 4, ±4/3, ±4/9.
Learn more about Rational Root Theorem here:
brainly.com/question/10937559
#SPJ7
negative 5 plus positive 5
Answer:
0
Step-by-step explanation:
Select the choice that follows the correct sequence of steps in solving this inequality.
-1/2y - 1 < or equal to 3
Answer:
what are the choices?? if you don't mind me asking
Convert to polar form
Please click on the above picture and view the full answer.
Step-by-step explanation:
Hope it helps you.^_^
Subtract (7x-3) from (5-3x)
Which class is better, math or science (in your opinion)
comment/answer your fav i need this for a survey
Answer:
Science is more interesting for me than math and fun!
Step-by-step explanation:
Answer:
Math is more fun for me because you get to learn more stuff in it. Plus, math can help you in everyday stuff like for example cooking.
Step-by-step explanation:
Everyone agrees that learning math can be difficult, but some people believe math is important and some people believe math is not important. Math is important for three reasons: math is everywhere, children need math, and God created math.
The first reason math is important is math is everywhere. Math is used in everyday life; it is useful, but it is more than just useful. Math is there to help us, to keep us well ordered, to help us learn new things, and to help us teach new things. Students will become adults who will use math in their jobs. All kinds of careers use math; for example, musicians, accountants, fashion designers, and mothers use math. However, math is not only used for things you do. It also brings order to everything around you; the world is organized essentially because it was made with math.
The second reason math is important is children need math. Now, as we all know, children are as chaotic as a volcanic eruption, but children, as they grow, need to learn patience. Patience is precisely what math teaches us. It also teaches us curiosity; for example, why is this rule used here? Why would that number be negative? Why is that equation set up like that? These are questions they will learn to ask if they are taught math. The parents’ job is to help their children grow up to become good people who are patient and wise, who want to learn even more about anything and everything. Their future depends on what they have learned and if they have learned mathematics, then they will be able to do many different things—maybe even anything—when they are adults.
The third reason math is important is God created it. This is a reason most adults use to convince their children that math is not boring and unimportant, so it may seem unoriginal. I believe, however, it is something that needs to be stated. God created the universe as well as math. The universe is full of math and it is orderly because of math. The sun is a certain distance from the earth; everything is organized in such a way that no matter what has happened we have always been safe. We need math. From this, you should be able to see how much we really do use and need math. We would not be able to process or even do everyday things without it. Math, in addition to these things, helps us to know God. God gave us math to live well and to serve Him. With everything we learn using math in science, we learn more about the world, which can help draw us closer to God.
Some people say math is unimportant because you don’t need math other than basic math principles—you can live without more complicated math. They say, if you need it, then simply use a calculator and leave the more complicated math to people who like math, the mathematicians. This, however, is not correct; you need math and could not live well without math, even including more complicated math concepts. God made us with a sense of curiosity so we can learn, do, and think about all sorts of things. Math is that thing that connects everything together, everything people love to do: music, cooking, painting, and everything else. Math is important.
Math is important because math is everywhere, children need math, and God created math. This matters to me and other children because math determines our future and how we choose to live.
express your answer as a polynomial in a standard form.