=============================================
Work Shown:
a = 3 is the first term
r = 2 is the common ratio
Sn = a*(1-r^n)/(1-r) ... sum of the first n terms
S8 = 3*(1-2^8)/(1-2) ... sum of the first 8 terms
S8 = 3*(-255)/(-1)
S8 = 765
----------
We can generate the first 8 terms to get 3, 6, 12, 24, 48, 96, 192, 384. Each new term is found by multiplying the previous one by 2.
Then add them up to get 3+6+12+24+48+96+192+384 = 765. We get the same result.
Answer: Answer: 765
Work Shown:
a = 3 is the first term
r = 2 is the common ratio
Sn = a*(1-r^n)/(1-r) ... sum of the first n terms
S8 = 3*(1-2^8)/(1-2) ... sum of the first 8 terms
S8 = 3*(-255)/(-1)
S8 = 765
The measure of an interior angle of a regular octagon is how many degrees greater than the measure of an interior angle of a regular hexagon?
Answer:
Step-by-step explanation:
Sum of interior angle of any polygon = 180* (n- 2 )
Here, n= number of sides
Sum of interior angles of regular octagon = 180 * ( 8-2) = 180 * 6 = 1080°
In regular octagon, all the angles are congruent,
So, measure of an interior angle of regular octagon = 1080/8 = 135°
Sum of interior angles of regular hexagon = 180 * ( 6-2) = 180*4 = 720°
In regular hexagon, all the angles are congruent,
So, measure of an interior angle of regular hexagon = 720/6 = 120°
The measure of an interior angle of a regular octagon is greater than the measure of an interior angle of a regular hexagon by 15°
Answer:
15
Step-by-step explanation:
The sum of the angle measures in a polygon with n sides is 180(n-2) degrees. So, the sum of the octagon's angles is 180(8-2) = 1080 degrees. The polygon is regular, so all the angles have the same measure, which means each is 1080/8 = 135. Similarly, the sum of the angles of a hexagon is 180(6-2) = 720 degrees, which means each angle in a regular hexagon has measure 720/6 = 120.
Therefore, the desired difference is 135 - 120 = 15
Algebra 1
a car can travel 78 miles on 13 gallons of gasoline. How much gasoline will it need to go 150 miles
a. 13
b. 78
c. 50
d. 25
Answer:
D
Step-by-step explanation:
First we need to find out how many miles we can travel using 1 gallon of gasoline. We can easily find that by dividing 78/13 which equals 6. Now we just need to multiply all of the given answers by 6. To be reasonable, since we already know 13*6=78, we should look at the next smallest number and go up from there.
The next smallest number given is 25. 25*6=150.
Hope this helps!! <3 :)
Answer the following questions: 2/3 is what percent of 1/6 ? 0.2 is what percent of 1 3/5 ?
Answer:
a. 4 %b. 0.125%Step-by-step explanation:
Let the missing percent be 'x'
[tex] x \: \times \: \frac{1}{6} = \frac{2}{3} [/tex]
Use the commutative property to reorder the terms
[tex] \frac{1}{6} x = \frac{2}{3} [/tex]
Multiply both sides of the equation by 6
[tex] \frac{1}{6} x \times 6 = \frac{2}{3} \times 6[/tex]
Calculate
[tex]x = 4 \:[/tex] %
b. [tex]x \: \times 1 \frac{3}{5} = 0.2[/tex]
Convert the mixed number into improper fraction
[tex]x \times \frac{8}{5} = 0.2[/tex]
Use the commutative property to reorder the terms
[tex] \frac{8}{5} x = 0.2[/tex]
Multiply both sides of the equation by [tex] \frac{5}{8} [/tex]
[tex] \frac{8}{5} x \times \frac{5}{8} = 0.2 \times \frac{5}{8} [/tex]
Calculate
[tex]x = 0.125 \: [/tex] %
Hope this helps..
Best regards!!
Answer:
1) 2/3 is 400% of 1/6
2) 0.2 is 12.5% of 1 3/5
Step-by-step explanation:
1) First, let's switch these two fractions to a low common denominator. I used sixths, and got 4/6 and 1/6. then, noticing that 4/6 is 4x bigger than 1/6, and 100% means all of the 1/6, and 4/6 is 4x that, 4x 100% is 400%, that's the answer ;-)
2) First, let's convert these both to fractions, 1/5 and 1 3/5, which converts to 8/5. 8/5 is 8x as much as 1/5, which means that it is 12.5%
hope this helps and gives a clear answer!
Find the slope of the line graphed. A)1/2 B)1 C)2 D)4
Answer:
Slope is 2. Y-intercept is -2
Step-by-step explanation:
To find slope look how many it goes up and right. So 2 up and 1 right will give a slope of 2. The y-intercept is -2 because it touches the y-axis.
Answer:
2
Step-by-step explanation:
To find this you would just look at two points that the line will cross. The 2 pairs or coordinates that are the most obvious to me are (0,-2) and (1,0) so then we would do an equation that is [tex]y_{2}[/tex] (which is the second y in this case 0) minus [tex]y_{1}[/tex](First y in this case -2) over or / [tex]x_{2}[/tex](second x in this case 1) minus [tex]x_{1}[/tex](first x in this case 0) so when we plug in into the equation is is [tex]\frac{0-(-2)}{1-0}[/tex] which will be simplified to [tex]\frac{2}{1}[/tex] so the slope would be 2.
Another simpler way to solve this is to is just to count the distance between the 2 slopes so we would go up 2 to get to 0 and over 1 which would be [tex]\frac{2}{1}[/tex] or 2.
You are having a small party and the Pizza driver drops
off 5 Pizza's. They are all cut into eighths. You also
have 3 slices left over in your fridge from the night
before. Write how much pizza you have as an
improper fraction(Remember that an improper
fraction has the numerator larger than the
denominator)
Answer:
[tex]\frac{43}{8\\}[/tex]
Step-by-step explanation:
Since there are 8 slices in each of the 5 boxes, we will multiply. 8 x 5 = 40
So there are 40 slices of pizza from the delivery. And because there are 3 extra slices from the night before in fridge, add those. 40 + 3 = 43.
8 will be the denominator because it is the common number of slices in a box of pizza, 43 will be the numerator to make the improper fraction.
So the amount of pizza as an improper fraction is [tex]\frac{43}{8\\}[/tex]
Can someone help with this.... thanks!
Answer:
3244.5
Step-by-step explanation:
LxW=A
Let f(x) = 5x + 4 and g(x) = −2x + 1. Find the indicated value f(-2) plz respond quickly
Answer:
f(-2) = -6
Step-by-step explanation:
f(x) = 5x + 4
Let x=-2
f(-2) = 5*-2 +4
= -10+4
= -6
Answer:
[tex]\boxed{f(-2) = -6}[/tex]
Step-by-step explanation:
[tex]f(x) = 5x-4[/tex]
Put x = -2
[tex]f(-2) = 5(-2)+4\\f(-2) = -10+4\\f(-2) = -6[/tex]
Which equation represents a line that has a slope of Negative one-half and passes through point (4, –5)? y = negative one-half x + three-halves y = negative one-half x + StartFraction 13 Over 2 EndFraction y = negative one-half x minus 7 y = negative one-half x minus 3
Answer:
y = (-1/2)x - 3
Step-by-step explanation:
Please present the equation symbolically instead of in words:
m = -1/2, passing through (4, -5):
Using the slope-intercept formula y = mx + b, and using m = -1/2, x = 4 and y = -5, we get:
-5 = (-1/2)(4) + b, or -5 = -2 + b. Then b = -3 and the desired equation is:
y = (-1/2)x - 3
y = -x/2 - 3 equation represents a line that has a slope of -1/2 and passes through point (4, –5)
What is the equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Given that a line has slope -1/2 and passes through point (4, -5)
The standard equation of a line is y = mx + c where m is the slope of the line.
Solving for c,
-5 = -1/2*4 + c
c = -3
Hence, y = -x/2 - 3 equation represents a line that has a slope of -1/2 and passes through point (4, –5)
For more references on the equation, click;
https://brainly.com/question/10413253
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Susan placed $9900 in a savings account which compounds interest continuously at a rate of 1.9 %. How much will she have in the account after 6 years?
Answer:
$11095.45
Step-by-step explanation:
This is a problem in continuous compounding, for which the formula is
P = Ae^rt, r being the annual interest rate as a decimal fraction and t being the time in years. Here we have:
P = $9900e^(0.019)(6) = $11095.45
Answer:
11095
Step-by-step explanation:
Rounding to the nearest dollar
solve for x plz: |5x|=3
Answer:
x = 3/5 or x = -3/5
Step-by-step explanation:
| 5x | = 3
Solve for absolute value.
There are two possibilities.
First possibility:
5x = 3
x = 3/5
Second possibility:
5x = -3
x = -3/5
Answer:
x= 3by 5
or 3/5
i tried my best
stay at home stay safe
and
kepp rocking
3) Y-3=4(n=2)
*to draw graph
Answer:
[see below]
Step-by-step explanation:
I am assuming that you mean: [tex]y-3=4(x-2)[/tex].
The equation is in point slope form...
[tex]y-y_1=m(x-x_1)[/tex]
The point used in the equation is (2, 3). 2 replaces 'x1' and 3 replaces 'y1'.
If you convert the equation in to slope intercept form:
[tex]y-3=4(x-2)\\\\y-3=4x-8\\\\y-3+3=4x-8+3\\\\\boxed{y=4x-5}[/tex]
You get -5 as the y-intercept.
So, the line you draw would pass through points (2,3) and (0,-5).
Hope this helps.
1. A man decided to buy new furniture from Futuristie Purniture for $2600, Futuriste Vurniture
gave the man two choices pay the entire amount in one payment with cash, or pay $1000 as a dews
payment and 1120 per month for two full years in the finanong plan. If the man chooses the
financing plan, how much more would he payl
Answer:
Also, there seem to be many typos in this question, I am trying my best to decipher them all :) next time maybe double check the wording thx!
Step-by-step explanation:
the question doesn't make sense because if you were to pay $1120 per month, for 2 years, you would go over the amount that you bought. I also am not sure what a dews payment is. Try wording it differently/check you spelling.
what is 149 scaled down by a factor of 1/10
Answer:
14.9
Step-by-step explanation:
Given
149
Required
Scale factor of ⅒
The result of a scale factor is the product of an expression by its scale factor.
The result of 149 scale factor of 10 is the product of 149 by 10
In other words;
149 * ⅒
= (149 * 1)/10
= (149)/10
Remove bracket
= 149/10
= 14.9
Hence, 149 scaled down by a factor of ⅒ is 14.9
posts does Tom need and what are the
dimensions of the fence?
I postdyards Therefore, Dimensions are
A bag of marbles can be shared equally among 3,
or 6 students with none left over. What's the least
amount of marbles that can be in the bag?
If there are 150 people born in the world every
minute; how many are bom every Hour? Day?
Year?
Answer:
1) 3 marbles
2) The number of people born every hour is 9000 people
The number of people born every day is 216,000 people
The number of people born every year = 78,840,000 people
Step-by-step explanation:
1) The given information are;
The number of students = 3 or 6
Amount of marbles remaining after sharing = None
Least amount of marbles that can be shared equally among the students = Condition each student gets one marble = 1 × 3 = 3 marbles
The least amount of marbles that can be shared equally among the students = 3 marbles
2) The number of people born int eh world every minute = 150 people
The number of minute in one hour = 60 minutes
∴ The number of people born every hour = 150 × 60 = 9000 people
Given that the number of hours in one day = 24 hours
∴ The number of people born every day = 9000 × 24= 216,000 people
Given that the number of days in one year = 365 days
∴ The number of people born every year = 216,000 × 365= 78,840,000 people
Jane will draw one card from the regular deck of 52 cards. In how many ways can she choose
a
a king, or a queen?
Answer:
8
Step-by-step explanation:
Find the different numbers of kings and queens there are in a deck.
If each suit has a king and queen respectively, and there are four suits in total, then 2 * 4 means that there are 8 total cards you can get.
Put the steps of storm formation in the correct order.
Ice and water droplets fall
The Sun heats the
Water vapor condenses
Water droplets freeze.
Warm air rises into the
to the surface
surface
upper atmosphere.
Answer:
The Sun heats the surface
Warm air rises into the upper atmosphere
Water Vapors condenses to the surface
Water droplets freeze
Ice and water droplets fall.
Step-by-step explanation:
Clouds are formed when invisible water vapors condenses into air and droplets or ice crystals are formed. Water enters into the air through evaporation process. The are few necessary steps for storm formation. The sun heats the surface of the earth and warm air rises into the upper most atmosphere where temperature is lowered. Water vapors condenses from the surface and rises to the upper atmosphere water droplets freeze in upper atmosphere because of reduce temperature and then ice or water droplets fall.
Answer:
The Sun heats the surface
Warm air rises into the upper atmosphere
Water Vapors condenses to the surface
Water droplets freeze
Step-by-step explanation:
Trust me on this, also can I have brainiest please?
Hope you do well! :D
PLEASE HELP!!!! I WILL GIVE BRAINLIEST AND LOTS OF POINTS!!! Please provide an explanation and answer only if you know the answer for sure. In the following diagram, BC is parallel to DE. What is the measure of angle х? **Angles are not necessarily drawn to scale.**
Answer:
x = 29
Step-by-step explanation:
If the lines are parallel
< CBA = < DAB due to the fact that they are alternate interior angles
42 = DAB
We also know that
DAB + BAC + CAE = 180 since they form a straight line
Substituting the given values
42+ 109 + x = 180
Combine like terms
151 + x = 180
151+x-151 = 180-151
x = 29
whats 1,112,433 rounded to nearest ten thousand
Answer:
1,110,000
Step-by-step explanation:
1,112,433
↑ this is the digit in the ten thousand place
We look at the digit below to determine if we need to round up
2 is less than 5 so we leave the digit in the ten thousands place alone
1,110,000
Answer:
1110000
Step-by-step explanation:
2 is smaller than 5 so it will round to 0 and so will everything under it.
Circle O is shown. 2 tangents intersect at a point outside of the circle which is labeled Satellite. The angle formed is 20 degrees and the measure of the first arc formed is x. One tangent intersects the circle at a point labeled Earth. A satellite views the Earth at an angle of 20°. What is the arc measure, x, that the satellite can see? 40° 80° 160° 320°
Answer:
The arc measure, x, that the satellite can see is 160°
Step-by-step explanation:
Given that the two tangents intersect at a point outside the with circle center O
The angle formed between between the two tangent = 20°
The first arc formed is measured as x°, which is the arc opposite the point where the two tangents meet = The arc the satellite can see
The angle x is given by the relationship;
x = 2 × (90 - v/2)
Where;
v = The angle formed at the point where the two tangent meet = 20°
Therefore;
x = 2 × (90 - 20/2) = 2 × (90 - 10) = 2 × 80 = 160°
The arc measure, x, that the satellite can see = 160°.
Answer:
160
Step-by-step explanation:
edge
Solve the system of equations by substitution y=-2x+18 and 4y-x+9=0
x = 9
y = 0
Step-by-step explanation:y = -2x + 18
4y - x + 9 = 0
4(-2x + 18) - x + 9 = 0
- 8x + 72 - x + 9 = 0
- 9x + 81 = 0
81 = 9x
x = 81 : 9
x = 9
y = - 2×9 + 18
y = - 18 + 18
y = 0
Help me out :O What is the volume of three cubes, each with a side length of fraction 1 over 3 foot? V = s3, where s is the side length.
Answer:
Step-by-step explanation:
[tex]s = \frac{1}{3}ft\\[/tex]
Volume of a cube = s³ ft³
Volume of 3 cubes = 3 * s³
[tex]= 3 * \frac{1}{3} * \frac{1}{3} *\frac{1}{3}\\\\= \frac{1}{3} *\frac{1}{3}\\\\=\frac{1}{3*3}\\\\=\frac{1}{9} ft^{3}[/tex]
Please help will mark brainly
Answer:
$10.10
Step-by-step explanation:
We are told that she bought 3 CDs of the same price. Her total was $34.20 with $3.90 tax. We want to find the price of a CD before tax.
Since we are finding the price before tax, we need to subtract the tax from the total.
total - tax
We know she paid $34.20 with the tax of $3.90
$34.20 - $3.90
Subtract
$30.30
The total before tax was $30.30
Now we must find the price of a CD. Each CD is the exact same price, and she bought 3. Therefore, we can divide the total before tax ($30.30) by 3.
$30.30 / 3
Divide
$10.10
Each CD costs $10.10 before tax.
Answer:
10.1 $
Step-by-step explanation:
The total price Lella paid was 34.20 $ wich includes the Cd's price and the taxes
The taxes value is 3.9 $
So we need to substract 3.9 $ from 34.20 $ to get the price of the Cds
34.20 -3.9 = 30.3
The total price of the cds is 30.3 $
There are 3 cds with the same price
To get the price of each Cd divife the total of cds by 3
30.3÷3 = 10.1
The price of 1 cd is 10.1$
Inspired by election season, Evan decided to run for class president. He earned 80% of the votes in his class. If he earned 24 votes, how many students were in his class?
Answer:
16
Step-by-step explanation:
Just took test
Answer:30
Step-by-step explanation: Let s represent the number of students in the class. Evan earned 80% of these votes, which came to 24 votes. 0.80=24votes so total number of votes is 30.
0.8
Find how many quarts of 6% butterfat milk and 1% butterfat milk should be mixed to yield 75 quarts of 3% butterfat milk.
The mixture should contain quarts of the 6%
Answer:
30 gallons of 6% milk, and 45 gallons of 1% milk.
Step-by-step explanation:
x=quarts of 6% butterfat
First, write an equation.0.06x+0.01(75-x)=0.03*75
Multiply both sides by 100.0.06x*100+0.01*100(75-x)=100*0.03*75
Simplify6x+75-x=3*75
6x+75-x=225
Solve5x=225-75=150
5x=150
x=30
75-30=45
So, we need 30 gallons of 6% milk, and 45 gallons of 1% milk.
So, the mixture contains 60 quarts of 6% milk and 15 quarts of 1% milk
Linear Equation:The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1
Let [tex]x[/tex] quats and [tex]y[/tex] quats of 6% and 1% butterfat milk then,
[tex]x+y=75...(1)[/tex]
And
[tex]\frac{6x}{100} +\frac{y}{100} =375\\6x+y=375...(2)[/tex]
Now, solving equations (1) and (2) we get,
[tex]x=60\\y=15[/tex]
Learn more about the topic linear equations:
https://brainly.com/question/16740131
What is the difference between a Rate and a Ratio? Explain *
Answer:
Step-by-step explanation:
A ratio is a comparison of two numbers. A ratio can be written using a colon, 8:12 , or as a fraction 8/12 . A rate is a comparison of two quantities which can have different units. For example 8 miles per 4 hours is a rate.
(08.01 MC)
A cone has a volume of 24 cubic inches. What is the volume of a cyinder that the cone fits exactly inside of? (1 point)
Select one:
b. 24 in
c. 48 in
d. 72 in
Answer:
d. 72 in³
Step-by-step explanation:
To find the volume of a cylinder that a cone of volume 24 cubic inches fits in exactly inside of, we will follow the steps below:
From the question volume of the cone = 24 cubic inches
volume of a cone = [tex]\frac{1}{3}[/tex] πr²h
and volume of a cylinder = πr²h
This implies
volume of a cone = [tex]\frac{1}{3}[/tex] πr²h
= [tex]\frac{1}{3}[/tex] (volume of a cylinder)
volume of a cone = [tex]\frac{1}{3}[/tex] (volume of a cylinder)
24 = [tex]\frac{1}{3}[/tex] (volume of a cylinder)
multiply both-side of the equation by 3
24×3 = [tex]\frac{1}{3}[/tex] (volume of a cylinder)
72 =volume of a cylinder
Therefore volume of the cylinder that the cone fits exactly inside of is 72 cubic inches
ordered pair for this point?
Answer:
(-1,-1)
Step-by-step explanation:
Go across the X axis first then the y axis
Write an equation of the line passing through the given point and satisfying the given condition. Give the equation (a) in slope-intercept form and (b) in standard form.
(8,6); perpendicular to 2x - y = 4
(a) Write the equation of the line in slope-intercept form.
Answer:
y = -[tex]\frac{1}{2}[/tex]x + 10
Step-by-step explanation:
To find the equation of a line that passes through the point (8,6) and perpendicular to the equation 2x - y = 4, we will follow the steps below:
first write the equation 2x - y = 4 in a standard form
we will find the slope of our equation using this equation
2x - y = 4
y = 2x -4
comparing the above with
y = mx + c
m = 2
[tex]m_{1}[/tex][tex]m_{2}[/tex] = -1 ( slope of perpendicular equations)
2[tex]m_{2}[/tex] = -1
[tex]m_{2}[/tex] = -1/2
our slope m = -1/2
We can now go ahead and form our equation
[tex]x_{1}[/tex] =8 [tex]y_{1}[/tex] =6
y-[tex]y_{1}[/tex] = m (x-[tex]x_{1}[/tex])
y-6 = -[tex]\frac{1}{2}[/tex](x-8)
y-6 = -[tex]\frac{1}{2}[/tex]x + 4
y= -[tex]\frac{1}{2}[/tex]x+4+6
y = -[tex]\frac{1}{2}[/tex]x + 10
50 points, show your work. This table shows the battery life of 4 different mobile phones: Phone A: 20 hours Phone B: 25 hours Phone C: 10 Hours Phone D: 18 hours. If 8.45% of the battery life of each mobile phone is used in a day by a typical user, for which mobile phone is 0.8 hour of battery life used in a day? Phone A Phone B Phone C Phone D
Answer:
phone c :)
Step-by-step explanation:
Adam and three friends go on holiday together for a week.
The costs of the holiday will be shared equally between the 4 friends.
These are:
• £1460 for 4 return plane tickets
• £720 for the accommodation
• £180 for the car hire for a week
How much does Adam have to pay for his share of the costs?
Answer:
590
Step-by-step explanation:
1,460+720+180=2,360
2,360/4=590
HOPE THIS HELPS!!!! :)