Find the first, fourth, and eighth terms of the sequence. A(n) = −5 ∙ 2x − 1
Answers
Answer:
The answer is option AStep-by-step explanation:
The rule for the sequence is
[tex]A(n) = 5. {2}^{x - 1} [/tex]
where x is the number of terms
For the first term
x = 1
That's
[tex]A(1) = 5. {2}^{1 - 1} [/tex]
[tex]A(1) = 5. {2}^{0} [/tex]
A(1) = 5(1)
A(1) = 5For the fourth term
x = 4
[tex]A(4) = 5. {2}^{4 - 1} [/tex]
[tex]A(4) = 5. {2}^{3} [/tex]
A(4) = 5(8)
A(4) = 40For the eighth term
x = 8
[tex]A(8) = 5. {2}^{8 - 1} [/tex]
[tex]A(8 ) = 5. {2}^{7} [/tex]
A(8) = 5(128)
A(8) = 640Hope this helps you
Answer:
The first option.
Step-by-step explanation:
The first term of the sequence would be...
A(1) = -5 * 2^(1 - 1)
= -5 * 2^0
= -5 * 1
= -5
The fourth would be...
A(4) = -5 * 2^(4 - 1)
= -5 * 2^3
= -5 * 8
= -40
The eighth would be...
A(8) = -5 * 2^(8 - 1)
= -5 * 2^7
= -5 * 128
= -640
So, the correct answer is the first option.
Hope this helps!
Related Questions
Randomly pick 5 points from a sphere. Show that you can always find a closed semi-sphere (half a sphere and boundary) that contains 4 points.
Answers
A teacher has 1,425 marbles to divide equally among 9 groups of students to use in an experiment. What is the least number of marbles he could have left after the marbles are distributed?
Answers
Answer:
3
Step-by-step explanation:
Basically we need to find out whats the remainder of 1425 when you divide by 9.
1425/9 = 158 R3
R3 is 3 marbles left, so the answer is 3.
PLEASE HELP I WILL GIVE BRAINLIEST!!!!! The box plots below show attendance at a local movie theater and high school basketball games: Two box plots are shown. The top one is labeled Movies. Minimum at 100, Q1 at 130, median at 165, Q3 at 185, maximum at 200. The bottom box plot is labeled Basketball games. Minimum at 135, Q1 at 225, median at 248, Q3 at 275, maximum at 300. Which of the following best describes how to measure the spread of the data? The IQR is a better measure of spread for movies than it is for basketball games. The standard deviation is a better measure of spread for movies than it is for basketball games. The IQR is the best measurement of spread for games and movies. The standard deviation is the best measurement of spread for games and movies.
Answers
Correct option is Option B: The standard deviation is a better measure of spread for movies than it is for basketball games.
Visual analysis for movies:
Movies data is more centric to mean and not skewed on a particular side.
Visual analysis for Basketball games:
Basketball games data is not centric to mean but is skewed or say more dense in right then left.
Property of standard deviation and its limitation:
Standard deviation just measures the deviation or spread with respect to mean of collected data. It is non- sensible for skewness of the data and thus more information is needed in such case.
Property of IQR and its limitation:
IQR is interquartile range. IQR generally is less powerful than standard deviation, but more powerful if the data is skewed and its variability has to be measured. It measures the range or say difference between [tex]Q_3 \: and \: Q_1[/tex]
In the movies data, the data is more collected and barely visible to be skewed. Thus standard deviation is best suited for this dataset.
In the basketball data, the standard deviation will fail to give good information about the data. The IQR, is better here since we've to measure variability or dispersion of data which is skewed.
Thus, option B: The standard deviation is a better measure of spread for movies than it is for basketball games; is correct option.
Learn more here:
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Use the clues in the sentences to determine the best meaning for each bolded word
"He was a tenacious worker, and by sticking firmly to his plan, he succeeded."
"Students planning to become scientists must select a science major, such as biology, chemistry, or physics."
"I want to take a class in calligraphy, or artistic writing, at the community center."
Done
Answers
Answer:
1. Determined
2. area of study
3. artistic writing
Step-by-step explanation:
Hope this helps! <3
Answer:
✔ determined
✔ area of study
✔ artistic writing
Explanation:
-15 POINTS PLS HURRY- Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 4.5 cm to 4 cm
Answers
Hi there! :)
Answer:
[tex]\huge\boxed{\frac{9cm}{8cm}}[/tex]
We can disregard the units temporarily to create a ratio for 4.5 to 4:
4.5 is not a whole number- we can convert this number in the ratio to a whole number by multiplying both numbers by 2:
2 · (4.5 : 4) = 9 : 8
Express as a fraction:
[tex]9cm : 8cm = \frac{9cm}{8cm}[/tex]
!50 POINTS! GIVE REAL ANSWER OR I REPORT PLZ NO TROLLS! An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. The executive then boarded the helicopter and flew to the corporate offices at an average speed of 78 mph. The entire distance from his home to the office was 169.5 miles. If the executive spent the same amount of time in the car as he did the helicopter, how long did it take the executive to get to work?
Answers
Answer:
it took him 3 hours to get to work
Step-by-step explanation:
For the first part of the trip, the executive covered a distance "d" in time 't" at 35 mph, therefore we can write that the time it took to get to the helicopter was:
[tex]t-\frac{d}{35}[/tex]
which if the distance is in miles, will render the time in hours.
We can write something similar for the second part of the trip", using the same "t" since it took the same time as for the first one, and using for distance 169.5 - d (since it is the distance to complete the total traveled distance :
[tex]t=\frac{169.5-d}{78}[/tex]
Now we equal those two equations because the time "t" is the same, and solve for "d":
[tex]\frac{d}{35} =\frac{169.5-d}{78} \\78\,d=35\,(169.5-d)\\78\,d=5932.5-35\,d\\(78+35)\,d=5932.5\\d=\frac{5932.5}{113} \\d=52.5[/tex]
Now, knowing the distance covered in the first trip, we can find the time of that first trip:
[tex]t=\frac{52.5}{35} =1.5\,\,hours[/tex]
Therefore, the time it took for thye total trip is: 1.5 h + 1.5 h = 3 hours
Veronica wants to buy a house that costs $249,900. She is going to make a 20% down payment. How
much is her down payment in dollars?
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
$49,980
▹ Step-by-Step Explanation
[tex]\frac{20}{100} * $249,900 \\\\= $49,980[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
49,900
Step-by-step-explanation
go two across and place the decimal there, so 20% will be turned into 0.20 and multiply 0.20 by the 249,900. When you are done you will get the amount.
Hope this helped!
I am getting headache In this question!! Can you solve it please!!? Please answer. Will mark brainliest!!
Answers
Answer:
Step-by-step explanation:
Find the quotient:
9/10 / 1/3
=> Take the reciprocal
=> 9/10 X 3/1
=> 27/10 = 2.7
Jennie spent 2h studying for exams.....
2 / 2/3
=> Take the reciprocal
=> 2/1 X 3/2
=> 6/2 = 3 subjects.
Calculate:
5 1/2 / 3
=> 11/2 / 3
=> Take the reciprocal\
=> 11/2 X 1/3
=> 11/6
A farmer has 9 1/2 ha of land.......
=> 9 1/2 / 1 1/4
=> 19/2 / 5/4
=> Take the reciprocal
=> 19/2 X 4/5
=> 76/10
=> 7.6 crops.
I don't know the answer to the question named: Draw a picture to show how many 1/5 s are there in 7/10.
I know the answer to the other 4 questions. They are correct.
Figure B is a scaled copy of Figure A.
9
3.6
3.6
9
Figure A
1.2
3
1.2
3
Figure B
What is the scale factor from Figure A to Figure B?
Answers
Answer:
1/3
Step-by-step explanation:
We are going to a small shape from a big shape, so the scale factor must be less than 1.
3 (which is a side on the blue figure) and 9 (a side on the green figure)
3 and 9 are easy numbers (for me...) so 3:9 is smaller than 1.
3:9 simplified is 1:3 = 1/3
so 1/3 is the scale factor.
Let's make sure it's right....
9 * 1/3 (green figure to blue figure) is = 3.
3.6 * 1/3 = 1.2
you can check it yourself on a calculator if you don't believe me
I hope this helps have a great day!!!!
Help pls! Will give brainliest to first person who answers correct
Answers
Answer:
a) x greater than or equal to 10
b) x = 9
Step-by-step explanation:
a)
[tex]x + 5 \geqslant 15 \\ x \geqslant 15 - 5 \\ x \geqslant 10[/tex]
b)
[tex]2x < 18 \\ x = \frac{18}{2} \\ x = 9[/tex]
Please help being timed!!! Given: △ABC AB=BC=AC Area of △ABC= 25 3 4 cm2 Find: The perimeter
Answers
Answer:
15 cm
Step-by-step explanation:
The area of an equilateral triangle is:
[tex]\frac{\sqrt{3} }{4}a^2[/tex], where a is the length of one side.
We can find the value of a (the length) by:
[tex]\frac{25\sqrt{3} }{4} = \frac{\sqrt{3} }{4}a^2[/tex]
[tex]a^2 = 25[/tex]
a = 5, so the side length of this triangle is 5 cm.
The perimeter of an equilateral triangle will be 3 times the length.
[tex]3\cdot5=15[/tex]
Hope this helped!
Simplify.
sin x cot x
Use algebra and the fundamental trigonometric identities. Your answer should be a number or use a single trigonometric function.
(please help, no idea how to solve this problem)
Answers
Answer:
cos x
Step-by-step explanation:
sin x = (sin x) / (1) and cot x = (cos x) / (sin x)
Put those fractions next to each other and multiply them out (numerator times numerator, denominator times denominator).
Cancel out the (sin x) in the numerator and denominator
You should be left with just (cos x) / (1), whoch equals just (cos x).
Hope this helps!
My brother said that’s it
hello can plzz help me with this question wil mark u brainlest and its for 18 points the file is down below thank u :)
Answers
Answer:
a rectangular prism
Step-by-step explanation:
consists of 6 faces which are rectangles
Directions: Calculate the percent increase or decrease between the starting and ending
quantities below. Round your answer to one decimal place.
1. Start: 3
End: 10
Answers
Answer:233.333%
Step-by-step explanation:
1. 10-3=7 subtract end by start
2.7/3=2.333 divide difference by absolute value of start
32.333x100=233.333% multiply by 100 if negative its decreasing if positive it increasing
hoped this helped
Jerome currently has an account balance of $1,859.55. His initial deposit on the account was $825 and it earned 5.7% simple interest. How long has Jerome held the
account?
Answers
Answer:
22 years
Step-by-step explanation:
Well we know the formula for simple interest is
I = PRT
I = interest earned
P = initial balance
R = rate
T = time
We want to solve for time here....so rearrange for T
T= I/(PR )
We have
P = 825
R = .057
And I = current balance - initial balance = 1859.55 - 825 = 1034.55
So plugging all those in we have
T = 1034.55/(825×.057 )
T = 1034.55/47.025
T = 22
It was held for 22 years.
Write as an inequality "The difference of a number squared and three is at least twelve"
Answers
Answer:
using the equilateral formula of solution
Answer:
[tex]x^2-3\geq 12[/tex]
Step-by-step explanation:
[tex]x^{2} -3[/tex] is the difference of a number squared and three
is at least 12, means that is greater but not less
[tex]x^2-3\geq 12[/tex]
Clare has 150$ in her bank account. She buys a bike for 200$. What is Clares account balance now?
Answers
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The amount left in the bank account is -$50.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Amount in the bank account = $150
Cost of the bike = $200
The amount left in the bank account.
= 150 - 200
= -$50
Thus,
The amount left in the bank account is -$50.
Learn more about expressions here:
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the standard form: four and sixty-eight hundredths
Answers
Answer:
4 17/25
Step-by-step explanation:
68
four and sixty-eight hundredths => 4 ------- or 4 34/50 or 4 17/25
100
Answer:
you would need to use decimals
Step-by-step explanation:
what is the right answerrrr??
Answers
Answer:
C. Two lines are perpendicular if they have opposite slopes
Step-by-step explanation:
Hey there!
Well 2 lines that are perpendicylar have reciprocal slopes for example,
2 and 1/2 are 2 slopes that are perpendicular.
Hope this helps :)
In a certain country, the heights and depths of a road are measured in relation to sea level. Sea level has a value of 0. The lowest point of the country lies at −8 feet. The highest point of the country lies at +107 feet. Which of the following statements best describes the lowest and the highest points?
The lowest point is 8 feet above sea level, and the highest point is 107 feet below sea level.
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
The lowest point is 8 feet below sea level, and the highest point is 107 feet above the lowest point.
The lowest point is 8 feet above sea level, and the highest point is 107 feet below the lowest point.
Answers
A negative value would mean it is below sea level. A positive value would be above sea level.
-8 is 8 feet below sea level
+107 is 107 feet above sea level.
The answer Is:
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
Answer:
Step-by-step explanation:
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
The Greenbaum family agreed to pay for 3 months of an online TV service in exchange for a $5 credit on the bill each month. If the Greenbaums spend a total of $11.85 on the service over the 3 months, what is the normal price of one month of online TV service?
$5.00
$6.85
$8.95
$30.55
Answers
divide $11.85 by 3 and you get 3.95 then add the $5
Look at the graph in the image. 1. What are the coordinates of point P? A. (4,3) B. (4,30) C. (4,90) D. (40,90) 2. What is the independent variable? A. Bike A B. Bike B C. Time D. Distance Please include work!
Answers
Answer:
1.C (4,90) 2.C.Time
Step-by-step explanation:
the answer to number 1 is C because the x coordinate is 4 and the y coordinate is 90. The answer to 2 is c because the independent variable represents x, which is time in this case because it is labeled on the coordinate plane.
Which property is shown by -6 + 0 = -6? A. Commutative Property of Addition B. Identity Property of Addition C. Distributive Property D. Associative Property of Addition
Answers
Answer:
C
Step-by-step explanation:
It is c because you are adding. the 6 and o.
Answer:
Would be C.
Step-by-step explanation:
Just adding the 6 and the 0 basically.
Alexander bought a box of crackers at the store. He ate half of the crackers in the box on Monday, and he ate 1/2 of what was left on Tuesday. On Wednesday, he ate 1/3 of what was left after he was finished eating the crackers on Tuesday.
1) What fractional part of the total crackers originally in the box did Alexander
eat on Wednesday?
2) what fractional part of the total crackers originally in the box are left. 3) if there are 4 crackers left in the box after Alexander finished eating crackers on wensday, how many crackers were in the box before it was opened. (Please help!)
Answers
Answer:
Given the equivocal nature of this question, I will need to draw an assumption: I will assume that Ali ate from the cake and so did Jason — not Ali ate from the cake and Jason ate from Ali’s slice.
With that being said, the first approach is make both of these fractions have a common denominator, so that we can find how much each respective person ate from the total amount of slices. Intuitively, the common denominator is 12
12
, so this must be true:
Ali ate 4/12
4
/
12
of the cake;
Jason ate 3/12
3
/
12
of the cake
Adding these two fractions will give us 7/12
7
/
12
— the total amount eaten. Now, to find the amount left, we need only subtract 7/12
7
/
12
from 12/12
12
/
12
(the total amount of the cake). Doing so will give us
Step-by-step explanation:
1/3 = 4.
1/3 < 1/2
3/3 = 2/2
4 x 3 = 12.
if there were still 4 crackers AFTER eating 1/3 on wednesday, you add 12 + 4 = 16
find the x value for this problem
Answers
180 = 75 + 25 + x
x = 180 - 75 - 25
x = 80°
Answer:
x = 80
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
25+x = 105
Subtract 25 from each side
25+x-25 = 105-25
x = 80
colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?
Answers
Answer: 24
Step-by-step explanation:
Colleen painted 7 windows, some of which were her mother's.
Her dad painted 7+1 (8) windows, and that is twice as much as what her mother was supposed to do. Her mother was supposed to do 4 windows. That means Colleen's share was 3 windows.
If all the kids had to do an equal amount of windows, than each kid had to do 3 windows.
8+7+3+3+3=24
The total windows in the house are 21.
What is an algebraic expression?It is an expression contains a relation between different parameters (variables). It contains variable and constant values, along with algebraic operations.
In our given problem, the algebraic relation between different members work output and total windows can be expressed as:
Windows painted by colleen and her mother = 7
Windows painted by father = (Windows painted by colleen and her mother + 1)
= (7 + 1) = 8
∴ Windows painted by father = 8
Now, as given,
2 Windows painted by mother = Windows painted by father
∴ Windows painted by mother = [tex]\frac{8}{2}[/tex] = 4
and Windows painted by colleen = 7 - 4 = 3
Colleen and her 2 brothers paint equal windows;
∴ They painted 3 windows each.
The total windows in the house is equal to total painted windows by mother, father, colleen and her two brothers:
⇒ 4 + 8 + 3 x 3 = 12 + 9 = 21
Hence the total windows in the house are 21.
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Dave loves a bargain and buys a feather boa which
has been reduced in price by 70%. If the sale price
is £2.85, what was the original price of the boa?
Answers
Answer:
£9.50
Step-by-step explanation:
if the price was reduced 70%, then Dave is paying 30% of the original.
0.3 of £ = 2.85
£ = 2.85 / 0.3
£ = 9.5
£9.50
Answer:
$4.84
Step-by-step explanation:
2.85*.70=1.99
2.85+1.99=4.84
PLS HELP ME I NEED THIS FOR HOMEWORK!!!!
Answers
Answer:
36 degrees
Step-by-step explanation:
Because it's a right angle, AOB and BOC are complementary, meaning they add up to 90 degrees.
(3x+30)+(6x-12)=90
9x+18=90
9x=72
x=8
AOB = 6x-12, so substituting
8 in for x gives us 48-12=36
Savannah is currently one more than twice the age of her cat, Selena Gomez. In thirteen years, Savannah will be 1.5 times as old as Selena. What is Savannah's current age?
Answers
Answer:
23 years old
Step-by-step explanation:
Savannah's age = x
Selena's age = y
Right now, x = 2y + 1
In 13 years, x = 1.5y
Here, we must use simultaneous equations to work it out.
x = 2y + 1
x + 13 = 1.5 x (y + 13) --> x + 13 = 1.5y + 1.5 x 13 --> x + 13 = 1.5y + 19.5
x + 13 = 1.5y + 19.5
- 13
x = 1.5y + 6.5
x = 1.5y + 6.5 = 2y + 1
1.5y + 6.5 = 2y + 1
- 1
1.5y + 5.5 = 2y
- 1.5y
5.5 = 0.5y
x 2
11 = y
We know that y = 11
Savannah is currently twice her cat's age plus 1, so...
11 x 2 + 1 = 22 + 1 = 23 years old
Hope this helps!
P.S. If the cat lives 13 more years after this, it will be a very old cat lol :)
What is the name of a number that can be written in the form a+bi where a and b are nonzero real numbers?
