n = 8
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a(1-r^{n )} }{1-r}[/tex]
where a is the first term and r the common ratio
here a = 16 and r = [tex]\frac{64}{-32}[/tex] = [tex]\frac{-32}{16}[/tex] = - 2
[tex]S_{n}[/tex] = ( 16( 1 - ( - 2 )^n )/1 - (- 2 )) = - 1360
[tex]\frac{16}{3}[/tex] ( 1 - (- 2 )^n ) = - 1360
multiply both sides by [tex]\frac{3}{16}[/tex]
1 - (- 2 )^n = - 255
- (- 2 )^n = - 256
)-2)^n = 256
note that [tex]2^{8}[/tex] and [tex](-2)^{8}[/tex] = 256
hence n = 8
You decide to start baby-sitting. You find out it is $42 for the CPR certification. Your
mom is going to charge you $1 for gas and use of her cell phone for each hour you
baby-sit as she has to drive you to all of your jobs. If you charge $8 an hour for each
hour you baby-sit, how many hours will you need to work to break even in your new
venture?
Paco, Jayden, Brett each made a stack of superheroes cards. Pacos stack was 0.342 meter high. Jaydens stack was 0.41 meter high. Brett stack was 0.405 meter high. Write a number sentence that compares Jayden stack of cards Brett stack of cards.
Jayden's stack of superhero cards, which is 0.41 meters high, is taller than Brett's stack of superhero cards, which is 0.405 meters high. The number sentence to compare them is 0.41 > 0.405.
The student is asking to write a number sentence that compares Jayden's stack of cards to Brett's stack of cards.
Jayden's stack was 0.41 meter high, and Brett's stack was 0.405 meter high. To compare these two stacks, we look at the decimal values given for the heights. Since 0.41 is greater than 0.405, the number sentence that compares the two stacks is:
Jayden's stack > Brett's stack
Or in terms of the specific values:
0.41 > 0.405
This shows that Jayden's stack of cards is taller than Brett's stack of cards.
two factors of 38 add up to 15 what are they
Answer: The answer to this problem is: no solution
Step-by-step explanation: The trick to solving this problem is listing out 38's factors:
1, 2, 19, 38. As you can see, none of these pairs add up to 15, so there is no solution (unless you are talking about fraction factors)
Using the figure below, identify two line segments that complete the given expression: Given: FLAG is GXYZ is XY | | Segment GF Segment AL Segment GZ Segment GX Segment FL
Answer:
Segment XY is || GZ & FL.
Step-by-step explanation:
If you look at the figure closely, you will see that the only two parallel segments are the above.
Hope this helps.
[tex] \frac{5}{12} \div \frac{2}{11} = [/tex]
Solve. To solve this equation, you must change the divide sign into a multiplication sign.
To do so, change it into a multiplication sign, and flip the second fraction
(5/12)/(2/11) = 5/12 x 11/2
Multiply across
5/12 x 11/2 = 55/24
55/24, or 4 7/12
hope this helps
~Rise Above the Ordinary
Answer:
55/24
Step-by-step explanation:
First you flip the second fraction because its division-
2/11=11/2
Therefor-
5/12*11/2=55/24
Use the method of completing the square to solve x2-8x+7=0
A should be your answer no 100 %
[tex]Solution, solve\:for\:x,\:x^2-8x+7=0\quad :\quad x=7,\:x=1[/tex]
Steps:
[tex]Solve\:with\:the\:quadratic\:formula, \mathrm{For\:}\quad a=1,\:b=-8,\:c=7:\quad x_{1,\:2}=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:7}}{2\cdot \:1},\\[/tex]
[tex]x=\frac{-\left(-8\right)+\sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:7}}{2\cdot \:1}:\quad 7[/tex]
[tex]x=\frac{-\left(-8\right)-\sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:7}}{2\cdot \:1}:\quad 1[/tex][tex]\mathrm{The\:final\:solutions\:to\:the\:quadratic\:equation\:are:} x=7,\:x=1[/tex]
The correct answer is B.
whats the answer to 2 2/8
2 2/8=10/8 22/8=2 6/8 or 2 3/4
if you are trying to make it an improper faction it would be 9/4
find the difference 572-284
Answer:
288
Step-by-step explanation:
The Jones family traveled 314 miles each day until they reached their destination, which is 1,256 miles away from their starting point. How many days did they drive until they arrived at their destination?
Ig yook yen 4 days to get to their destination.
A blueprint for a garage has a scale of 1.5 cm to 3 m. On the blueprint, the length of one wall is 8 cm. If w represents the length of the actual wall, what is w?
Answer:
16m
Step-by-step explanation:
Carol is given a 10% pay decrease. Her new wage is £306 per week. What would be her weekly wage if, instead, she had received a 10% pay increase?
To find Carol's weekly wage with a 10% increase, first calculate her original wage before the decrease, and then apply the 10% increase to this original wage to find the new increased wage.
Explanation:The question involves calculating Carol's original weekly wage prior to the 10% pay decrease to find out what her wage would be with a 10% pay increase instead. To calculate the original wage before the decrease, divide the current wage (£306) by 0.9 (since 10% decrease implies she's now getting 90% of her original wage). After finding the original wage, we can calculate what her wage would be with a 10% increase by multiplying the original wage by 1.10.
First, let's find the original wage: Original Wage = £306 / 0.9. Now that we have Carol's original wage, we can calculate the 10% increase: New Wage with 10% Increase = Original Wage × 1.10.
Following these steps, we can determine what Carol's wage would have been if her pay had been increased by 10% instead of decreased.
A car travels 150km on 12 L of gasonline. How many liters are there of gasoline needed to travel 500km
You can use the given distance to amount of gasoline used relationship to find how much gasoline is needed for 1 km of traveling. Then use that data to find the amount of gasoline needed to travel 500 km.
The amount of gasoline needed to travel 500 km is 40 L
How to find the gasoline used for 1 km of distance traveled?We can equate the 150 km figure to 12 L use of gasoline on the basis of usage.
Thus,
[tex]\rm 150 \: km = 12 \: L\\\\\\\text{Dividing both quantities in 150 parts}\\\\\\dfrac{150}{150} \: km = \dfrac{12}{150} \: L\\\\1 \: km = 0.08 \: L[/tex]
Thus, there will be use of 0.08 L gasoline for travelling 1 km by that same car.
Using that above derived relationship, we can find the amount of gasoline needed to travel 500 km by that same car.
[tex]1 \rm \: km = 0.08 \: L\\\\\text{Multiplying 500 on both the sides}\\\\500 \: km = 40 \: L[/tex]
Thus,
The amount of gasoline needed to travel 500 km is 40 L
Learn more about division here:
https://brainly.com/question/2689177
Write a system of equations with the solution (4,-3)
Answer:
y = 3x-15 and y = x-7
Step-by-step explanation:
We are asked to write a system of equations with the solution (4,-3)
It is sufficient if we find two lines passing through this point.
Let us take first line as with slope 3.
Then the equation would be of the form
y-y1 = m(x-x1)
y+3 = 3(x-4)
Or y = 3x-15 is one line
Let second line have slope 1
y+3 = 1(x-4)
y = x-7
Now we have two systems of equations as
y = 3x-15 and y = x-7
kendrick can finish a 240 page book in 2 hours. how many pages does he read per minute?
He reads 2 pages per minute. So Divide 2 hours in it's minute form by 240. So like this:
240÷120=2
Kendrick can read 2 pages per minute if he can finish a 240-page book in 2 hours.
The question asks how many pages Kendrick can read per minute if he can finish a 240-page book in 2 hours. First, we need to transform the hours into minutes. Since there are 60 minutes in an hour, 2 hours equate to 120 minutes. Next, to find out how many pages Kendrick reads per minute, we divide the total number of pages by the total number of minutes.
240 pages ÷ 120 minutes = 2 pages per minute.
Therefore, Kendrick reads 2 pages per minute.
please solve this i dont no how. im good at English how do you fail English if you speak the language
*(Step-By-Step)*
[tex]15.8+14.9+16.7+17.6+13.4=78.4[tex] Add all numbers
[tex]78.4/5=15.68[/tex] Divide 5 which is the number of data set to 78.4
*(Answer)*= The mean is 15.68
HELP PLEASE!!!!!!!!!!!!!! PLEASE!!!!!! I GIVE BRAINLIST <#3
11.)
x y
75 50
175 50
x y
10. it isn't a function because an x value was repeated
11. x= 1,2,3,4
y= 125, 175, 225, 275
this is a function
True or False? The following is an example of inductive reasoning: In your study of geometry, you notice that every square you have seen is also a rectangle. You conclude that this is true in all cases.
Answer:
true
Step-by-step explanation:
given the function f(x)=(x+2) find each if the following f(1), f(-10),f(0)
The sum of three consecutive even numbers is 174. What is the smallest of the 3 numbers?
The smallest value is 56.
First even number + second even number + third even number = 174
First even number: x
Second even number: x + 2
Third even number: x + 4
So, (x) + (x+2) + (x+4) = 174
3x + 6 = 174
3x = 168
x = 56
(56 + 58 + 60 = 174)
Final answer:
The smallest of the three consecutive even numbers whose sum is 174 is determined by setting up an equation and solving for x, which represents the smallest number. The solution reveals that the smallest number is 56.
Explanation:
The question asks for the smallest of three consecutive even numbers whose sum is 174. To find the numbers, we can set up an equation where x represents the smallest even number, x+2 represents the second number, and x+4 represents the third number. The equation will be x + (x+2) + (x+4) = 174. When we solve it, we combine like terms to get 3x + 6 = 174, then subtract 6 from both sides to get 3x = 168, and finally divide by 3 to get x = 56. Therefore, the smallest of the three consecutive even numbers is 56.
You and a friend each roll a standard die to see who goes first in a board game. What is the probability that at least one of you rolls a 6?
Answer:
2
--
6
Step-by-step explanation:
2 over 6
Answer:
the answer is 11/36
Step-by-step explanation:
Uncle Percy sold t-shirts at the show. Now he only has 10% of the t/shirts now, how many did he start with?
Answer: He started with 250 t-shirts.
Step-by-step explanation:
Let the total number of shirts he start with be 'x'.
He has only 10% of the t-shirts.
Number of t-shirts he has now = 25
According to question, it becomes,
[tex]\frac{10}{100}\times x=25\\\\0.1\times x=25\\\\x=\frac{25}{0.1}\\\\x=250[/tex]
Hence, he started with 250 t-shirts.
Thus, Second option is correct.
Approximately 3 out of every 25 Americans live in California. About 3 out of every 50 Americans live in New York, and about 2 out of every 25 Americans live in Texas.
A. Which state has the largest population?
b Which state has the smallest population?
C. About what percentage of Americans do not live in California, New York, or Texas?
Convert all statistics into percentages:
CA: 3/25=0.12 -> 12%
NY: 3/50=0.06 -> 6%
TX: 2/25=0.08->8%
(A) Out of the three states, California has the largest population
(B) Out of the three states, NY has the smallest population
(C) USA=100%, CA+NY+TX=26%, therefore 74% of USA do not live on those three states.
how to sovle this equation
Your answer is b
X^3-8= (x-2)(x^2+2x+4)
To check you multiply each term on first expression to the second expression .
(X-2)(x^2+2x+4)
X(x^2)+x(2x)+x(4) +(-2(x^2)-2(2x)-2(4))
Simplify
X^3+2x^2+4x-2x^2-4x-8
Subtract 2x^2 from 2x^2
X^3+4x+0-4x-8
Add x^3 And 0
X^3+4x-4x-8
Subtract x^3-0
X^3-8
I will give 80 points if u anwser this.
What is the equation of this line in standard form?
7x−6y=11
6x−5y=−13
6x−7y=11
6x−7y=−11
Answer:
[tex]6x-7y=11[/tex]
Step-by-step explanation:
we know that
The equation of the line in standard form is equal to
[tex]Ax+By=C[/tex]
step 1
Find the slope m
Let
[tex]A(-3,-1), B(1/2,2)[/tex]
[tex]m=\frac{2+1}{(1/2)+3}\\ \\m=\frac{6}{7}[/tex]
step 2
The equation of the line in point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
with the slope m and the point B find the equation of the line
[tex]y+1=\frac{6}{7}(x+3)[/tex] ------> multiply by 7 both sides
[tex]7y+7=6(x+3)[/tex]
[tex]7y+7=6x+18[/tex]
convert to standard form
[tex]6x-7y=18-7[/tex]
[tex]6x-7y=11[/tex]
For any three consecutive numbers, what can you say about odd numbers and even numbers?Explain
What does 3+3 (a) simplify to when a=5
Help with this please
Answer:
1. 26:5 or
[tex]\frac{26}{5}[/tex] or
5.2 as a decimal
2. 21:26 or
[tex]\frac{21}{26}[/tex] or
0.81 as a decimal
3. 21:5 or
[tex]\frac{21}{5}[/tex] or
4.2 as a decimal
4. 5:21 or
[tex]\frac{5}{21}[/tex] or
0.24 as a decimal
Step-by-step explanation:
A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.
To write a ratio, we count the number of each quantity we are comparing. A part to whole ratio for letters and vowels would be the part compared to the whole. For example, there are 21 consonants to 26 letters in the alphabet. We write 21:26 or [tex]\frac{21}{26}[/tex] or 0.81. We can also compare the number of vowels which is 5:26 or
A part to part ration compares a part to a part like the number of consonants is 21 with the number of vowels is 5. We write the ratio as consonants : vowels.
21:5 or
[tex]\frac{21}{5}[/tex] or
4.2 as a decimal.
We can reverse and write vowels : consonants.
5:21 or
[tex]\frac{5}{21}[/tex] or
0.24 as a decimal.
What is the equation of this line?
Y= 1/2x - 3
Y= -1/2x - 3
Y= -2x - 3
Y= 2x - 3
answer: y = 1/2x - 3
why?: if you go 1 unit up (which is positive) and go right 2 units (which is positive). you will get 1/2 as your slope. the y-intercept would be -3 because the line passes through the y-axis on -3.
Maya is on the swim team. Each day she swims 750 m. Use the facts to find how much this is in kilometers
Maya swims 0.75 kilometers each day because to convert 750 meters to kilometers, we divide by 1,000.
The student wishes to know how many kilometers Maya swims each day if she swims 750 meters. To convert meters to kilometers, we use the fact that 1 kilometer is equivalent to 1,000 meters. So, to find out how many kilometers 750 meters is, we divide the number of meters by 1,000.
750 meters \/ 1,000 = 0.75 kilometers
Therefore, Maya swims 0.75 kilometers each day.
Rubber band is 3 eanch long.its stretched to 24 inches.How many times longer is the rubber band now than it was stretched?
This would be 72 Inches. Or 6 feet.