The expression 2^4 \u00b7 2^{-7} simplifies to 2^{-3}, which is the same as 1/2^3 or 1/8.
Explanation:The expression 2^4 \u00b7 2^{-7} can be simplified using the properties of exponents, specifically the law that states when multiplying expressions with the same base, you add the exponents. Here, we are multiplying 2 raised to the power of 4 with 2 raised to the power of -7. Therefore, we add the exponents 4 and -7 together to get 2^{4-7} = 2^{-3}.
To simplify further, remember that a negative exponent indicates the reciprocal of the base raised to the positive of that exponent. Hence, 2^{-3} = 1/2^3 = 1/8. Therefore, 2^4 \u00b7 2^{-7} simplifies to 1/8.
Find the sum of 2x 2 + 3x - 4, 8 - 3x, and -5x 2 + 2.
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x^2-3*x-(2)=0
2.1 Factoring 2x2-3x-2
The first term is, 2x2 its coefficient is 2 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 2 • -2 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -3 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 1
2x2 - 4x + 1x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-2)
Add up the last 2 terms, pulling out common factors :
1 • (x-2)
Step-5 : Add up the four terms of step 4 :
(2x+1) • (x-2)
Which is the desired factorization
express $15 for 10 gallons a unit rate
The area of a rectangular wall of a barn is 42 ft. Its length is 8 feet longer. Than twice its width. Find the length and width of the wall of the barn.
x divided by 7 equals 12
Solve For x
I can type 225 minutes in 5 minutes.at that speed,how many words can I type
how many 1/4 pound hamburgers can you make from 3 1/2 pounds of ground beef
How many packages of diapers can you buy with $36 when on package costs $9?
Based on the calculations, the number of diapers which can be bought with $36 is equal to $4.
Given the following data:
Cost of diaper = $9.Amount for packages = $36.How to calculate the number of diapers?In order to determine the number of diapers that can be bought with $36, we would set up a direct proportion equation as follows:
$9 = 1 diaper
$36 = X diapers.
Cross-multiplying, we have:
9X = 1 × 36
9X = 36
X = 36/9
X = $4.
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I need help with this problem
The shanghai maglev train is one of the fastest trains in the world, traveling about 2144 miles in 8 hours. How many miles does it travel in one hour? The distance between columbus ohio and new york city is about 560 miles.how many hours would it take the train to travel between the cities
Answer:
The train travels 268 miles in 1 hour. It would take 2.0896 hours to travel between the cities.
Step-by-step explanation:
Consider the provided information.
The shanghai maglev traveling about 2144 miles in 8 hours.
This can be written as:
2144 miles = 8 hours
Divide both sides by 8.
2144/8 miles = 8/8 hours
268 miles = 1 hours
Thus, the train travels 268 miles in 1 hour.
The distance between Columbus Ohio and new York city is about 560 miles. We need to find how many hours would it take the train to travel between the cities.
268 miles = 1 hours
Divide both the sides by 268.
1 miles = 1/268 hours
Now multiply both sides by 560.
560 miles = 560/268 hours
560 miles = 2.0896 hours
Hence, it would take 2.0896 hours to travel between the cities.
lauren is building a tree house with her dad. the dimensions of the floor are 9 feet by 6 feet. what is the area of the floor, measured in the square yards?
A. 6 square yards
B. 15 square yards
C. 30 square yards
D. 54 square yards
Answer:
The answer is A) 6 square yards.
In a mixture of pretzels to corn chips the ratio of pretzels to corn chips is 3 to 7. How many pretzels will be in a mixture that has 100 total pieces in it?
rip walks a total of 12 miles to and from school each week. Lindsey rides her bike a total of 56 miles to and from school each week.
Use the greatest common factor and the distributive property to complete the equation, and find the total number of miles Trip and Lindsey travel to and from school each week.
A shop advertised a 23% off sale. If a coat originally sold for $258, find the decrease in price and sale price
what is 22.62 rounded to the nearest tenth
What kind of transformation is illustrated in this figure?
dilation
translation
rotation
reflection
Triangle D E F and another triangle D-prime E-prime F-prime is of the same size, shape but turned a different angle
cookies are sold singly or in packages of 12 or 36.With this packaging how many ways can you buy 72 cookies?
Suppose the length of a diagonal of a square increases from 16 cm to 16.1 cm. What would the change in the area of the square be
The change in area will be such that it will increase by 1.605 or 1.25%.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
Area of square = Side²
The perimeter of the square = 4× side
The area of a square with diagonal x is given as x²/2.
Area with diagonal 16 cm ⇒ 16²/2 = 128 cm²
Area with diagonal 16.1 cm ⇒ 16.1²/2 = 129.605 cm²
Change of area = 129.605 - 128 = 1.605 cm².
Percentage change = 1.605/128 x 100 = 1.25%.
Hence "The change in area will be such that it will increase by 1.605 or 1.25%".
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Size of U.S. States The total surface area (in square miles) for each of six selected eastern states is listed here.
28,995 PA
37,534 FL
31,361 NY
27,087 VA
20,966 ME
37,741 GA
The total surface area for each of six selected western states is listed (in square miles).
72,964 AZ
70,763 NV
101,510 CA
62,161 OR
66,625 CO
54,339 UT
Find the standard deviation for each data set. Which set is more variable?
Answer:
Second set.
Step-by-step explanation:
I put the formula of standart deviation in the image below.
x is each data of the list
μ is the data average
N is the amount of elements.
So, for the first list we have:
μ= [tex]\frac{28995+37534+31361+27087+20966+37741}{6}= \frac{183684}{6}=30614[/tex]
DE= [tex]\sqrt{\frac{|28995-30614|^{2}+|37534-30614|^{2}+|31361-30614|^{2}+|27087-30614|^{2}+|20966-30614|^{2}+|37741-30614|^{2}}{6} }[/tex]
= [tex]\sqrt{\frac{2621161+47886400+558009+12439729+93083904+50794129}{6} }[/tex]
= [tex]\sqrt{\frac{207383332}{6} }[/tex]
= [tex]\sqrt{ 34563888.6667 }[/tex]
= 5879.1061.
For the other list of elements:
μ= [tex]\frac{72964+70763+101510+62161+66625+54339}{6}= \frac{428362}{6}=71393.66[/tex]
DE=[tex]\sqrt{\frac{|72964-71393.66|^{2}+|70763-71393.66|^{2}+|101510-71393.66|^{2}+|62161-71393.66|^{2}+|66625-71393.66|^{2}+|54339-71393.66|^{2}}{6} }[/tex]
= [tex]\sqrt{\frac{2465967.71+397732.03+906993934.99+85242010.67+22740118.19+290861427.71}{6} }[/tex]
= [tex]\sqrt{\frac{1308701191.3}{6} }[/tex]
= [tex]\sqrt{218116865.21 }[/tex]
= 6029.32
Then, the second set is more variable.
what is the
equivalent to 3/6
Method for working out 5+-2--10
the distance from the earth to the Sun is approximately 9.3×10^7 miles. if light travels 1.2×10^7 miles in 1 minute, how many minutes does it take the light from the sun to reach the earth ?
It takes approximately 12.47 minutes for light from the Sun to reach the Earth.
Explanation:To find out how many minutes it takes for light from the Sun to reach the Earth, we can divide the distance from the Earth to the Sun by the distance light travels in 1 minute.
First, let's convert the distance from miles to kilometers. 1 mile is approximately 1.60934 kilometers, so the distance from the Earth to the Sun is approximately 1.496 × 108 kilometers.
Now, we divide this distance by the distance light travels in 1 minute: 1.496 × 108 kilometers / 1.2 × 107 kilometers per minute = 12.47 minutes.
Therefore, it takes approximately 12.47 minutes for light from the Sun to reach the Earth.
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The sum of two consecutive odd integers is −236. Find the two integers
two trains leave the station at the same time one heading west and the other East the westbound train travels at 55 miles per hour East bound train travels at 75 miles an hour how long will it take for the two trains to be 338 miles apart
Gina wants to ship 3 books that weigh 2 7/16 pounds 1 7/8 pounds and 1/2 pound the max weight she can ship is 6 pounds estimate to see if Gina can ship all 3 books.
Answer:
→Weight of First book
[tex]=2\frac{7}{16}\\\\=\frac{39}{16}[/tex]
→ Weight of Second book
[tex]=1\frac{7}{8}\\\\=\frac{15}{8}[/tex]
→Weight of Third book
[tex]=\frac{1}{2}[/tex]
→Total weight of three books
[tex]=\frac{39}{16}+\frac{15}{8}+\frac{1}{2}\\\\=\frac{39+30+8}{16}\\\\=\frac{77}{16}\\\\=4\frac{13}{16}[/tex]
→Maximum Weight of 3 books that Gina Can Ship =6 Pounds
[tex]\rightarrow 6 >4\frac{13}{16}[/tex]
Yes, Gina Can ship all 3 Books.
For a set of ordered pairs, the variable corresponding to the first coordinate is the
How could you represent the division as a fraction if 5 peopld shared 2 blocks if 6 people shared 5 blocks
The arcade has 3 pinball machines and 5 video games. If a person wants to play one pinball machine and one video game, how many different combinations of games could that person play?
The number of possible combinations of playing one pinball game and one video game, given there are 3 pinball machines and 5 video games available, is 15.
Explanation:The subject of this question is combinatorics, a part of Mathematics that deals with combination and arrangement of objects. The question in essence is asking about the number of combinations one can play on a pinball machine and a video game in an arcade.
In the given context, there are 3 pinball machines and 5 video games. If a person wants to play one of each (one pinball game and one video game), we can calculate the number of combinations by simply multiplying the number of options for each game. That is, 3 pinball machines multiplied by 5 video games equals 15 different combinations.
So, there are 15 different combinations of games a person can play when selecting one pinball and one video game from the given sets.
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please explain step by step for 0.67÷0.3=?
the village, 125 people were issued a parking ticket. this month only 83 people were issued one. What was the percent reduction from this month to last month in the number of people who were issued a parking ticket
Sam bought 11 pounds of rice for $7 . How many pounds of rice did he get per dollar?