Negative Exponent Rule: Which expressions are equivalent to 10−6? Select all that apply.
Answers
Answer:
[tex]\large\boxed{\textsf{See Below.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked which expressions are equivalent to 10}^{\tt -6}.[/tex]
[tex]\textsf{We are given that we need to use the \underline{Negative Exponent Rule}.}[/tex]
[tex]\large\underline{\textsf{What is the Negative Exponent Rule?}}[/tex]
[tex]\textsf{The Negative Exponent Rule is a rule that describe how to evaluate negative}[/tex]
[tex]\textsf{exponents.}[/tex]
[tex]\large\underline{\textsf{How do we use the Negative Exponent Rule?}}[/tex]
[tex]\textsf{We use the negative exponent rule to multiply the denominator of a number by}[/tex]
[tex]\textsf{itself how many times the value of the exponent is.}[/tex]
[tex]\underline{\textsf{Example of the Negative Exponent Rule;}}[/tex]
[tex]\tt 10^{-2}. \ \textsf{Start with 10}^{\tt 1}, \ \textsf{then continue.}[/tex]
[tex]\tt 10^{1} = \frac{10}{1} \rightarrow 10^{\tt 0} = \frac{10}{1 \times 10} = \frac{10}{10} \rightarrow 10^{\tt -1} = \frac{10}{10 \times 10} = \frac{10}{100} \rightarrow 10^{\tt -2} = \frac{10}{100 \times 10} = \boxed{ \frac{10}{1000} }[/tex]
[tex]\large\underline{\textsf{Use the Negative Exponent Rule for our given expressions;}}[/tex]
[tex]\tt \frac{1}{10 \times 10 \times 10 \times 10 \times 10 \times 10} \overset{\textsf{is the same as}} \rightarrow \frac{1}{10^{6}}[/tex]
[tex]\textsf{There is a fraction for this expression, meaning that the exponent is negative.}[/tex]
[tex]\tt \frac{1}{10^{6}} = 10^{\tt -6}[/tex]
[tex]\large\boxed{\tt \frac{1}{10 \times 10 \times 10 \times 10 \times 10 \times 10} = 10^{\tt -6}}[/tex]
-------------------------------------------------------------------------
[tex]\tt 10^{\tt -3} \times 10^{\tt 2}[/tex]
[tex]\textsf{Remember that when exponents multiply, they're going to add together due to}[/tex]
[tex]\textsf{this expression having at least 2 constants.}[/tex]
[tex]\tt 10^{\tt -3} \times 10^{\tt 2} \rightarrow 10^{\tt -3+2} \rightarrow 10^{\tt -1}[/tex]
[tex]\large\boxed{\tt 10^{\tt -3} \times 10^{\tt 2} \neq 10^{\tt -6}}[/tex]
-------------------------------------------------------------------------
[tex]\tt 10^{\tt -3} + 10^{\tt -3}[/tex]
[tex]\textsf{We should know that adding exponents is not like adding whole numbers/terms.}[/tex]
[tex]\textsf{We will need to evaluate 10}^{\tt -3} \ \textsf{using the Negative Exponent Rule.}[/tex]
[tex]\tt 10^{\tt 0} = \frac{10}{10} \rightarrow \tt 10^{\tt -1} = \frac{10}{10 \times 10} = \frac{10}{100} \rightarrow \tt 10^{\tt -2} = \frac{10}{100 \times 10} = \frac{10}{1000} \rightarrow \tt 10^{\tt -3} = \frac{10}{1000 \times 10} = \boxed{\frac{10}{10000}}[/tex]
[tex]\tt \frac{10}{10000} \ \textsf{can reduce to} \ \boxed{\tt \frac{1}{1000}}[/tex]
[tex]\underline{\textsf{We are now adding;}}[/tex]
[tex]\tt \frac{1}{1000} + \frac{1}{1000} = \frac{2}{1000} \rightarrow \boxed{\frac{1}{500} }[/tex]
[tex]\textsf{This does \underline{not} evaluate to 10}^{\tt -6}[/tex]
[tex]\large\boxed{\tt 10^{\tt -3} + 10^{\tt -3} \neq 10^{\tt -6}}[/tex]
-------------------------------------------------------------------------
[tex]\tt \frac{1}{10^{\tt 6}}[/tex]
[tex]\textsf{Because there's a fraction, the exponent is negative.}[/tex]
[tex]\large\boxed{\tt \frac{1}{10^{\tt 6}} = 10^{\tt -6}}[/tex]
-------------------------------------------------------------------------
[tex]\tt \frac{10^{\tt 3}}{10^{\tt 9}}[/tex]
[tex]\textsf{Remember that when dividing exponents, they are going to subtract due to both}[/tex]
[tex]\textsf{of these numbers are constants.}[/tex]
[tex]\tt \frac{10^{\tt 3}}{10^{\tt 9}} \rightarrow \tt 10^{\tt 3-9} = 10^{\tt -6}[/tex]
[tex]\large\boxed{\frac{10^{\tt 3}}{10^{\tt 9}} = 10^{\tt -6}}[/tex]
[tex]\large\underline{\textsf{Hence;}}[/tex]
[tex]\large\boxed{\tt \frac{1}{10 \times 10 \times 10 \times 10 \times 10 \times 10} = 10^{\tt -6}}[/tex]
[tex]\large\boxed{\tt 10^{\tt -3} \times 10^{\tt 2} \neq 10^{\tt -6}}[/tex]
[tex]\large\boxed{\tt 10^{\tt -3} + 10^{\tt -3} \neq 10^{\tt -6}}[/tex]
[tex]\large\boxed{\tt \frac{1}{10^{\tt 6}} = 10^{\tt -6}}[/tex]
[tex]\large\boxed{\frac{10^{\tt 3}}{10^{\tt 9}} = 10^{\tt -6}}[/tex]
Related Questions
Could someone please help me?
Answers
Small = 6.25 kilograms
Answer:
Small = 6.25 kilograms
Large = 15.25 kilograms
Step-by-step explanation:
The shirts available in a clothing store are sizes S, M, and L. A total of 240 shirts are sold in a day. 20% of the shirts are of size S and 45% are size M. Find the number of shirts sold for each of the sizes.
Answers
Answer: L 38
Step-by-step explanation:
total 84
Answer: 48 small shirts
108 medium shirts
84 Large shirts
Step-by-step explanation:
20% of 240 = 48
45% pf 240 = 108
45 + 20 = 65, 100 - 65 = 35
35% of 240 = 84
And 48 + 108 + 84 = 240
The question is on the picture
Answers
A circular circus tent has a diameter of 5 meters. What is the approximate area of the floor of the circus tent? Use 3.14 for pi.
Answers
Answer:
[tex]\text{A}=19.6 \ \text{m}^2[/tex]
Explanation:
We are given a circular circus tent
diameter = 5m
we know that
[tex]\text{radius}=\dfrac{\text{diameter}}{2}[/tex]
[tex]\text{radius}=\dfrac{\text{5}}{2}[/tex]
[tex]\text{radius}=2.5[/tex]
so, [tex]\text{r}=2.5[/tex]
now, we can use area formula
[tex]\text{A}=3.14(\text{r})^2[/tex]
now, we can plug values
[tex]\text{A}=3.14(\text{2.5})^2[/tex]
[tex]\text{A}=19.625[/tex]
so,
[tex]\text{A}=19.6 \ \text{m}^2[/tex]
Answer:
Step-by-step explanation:
The approximate area of the floor of the circus tent is 19.625 square metres.
The area to be found is that of a circle. The data given in the question is
the diameter of the circle. To calculate the area of the circle, we need to first find the radius. The radius is half of the diameter. By calculation, d/2, we get 5/2= 2.5m. The formula for finding the area of the circle is πR². By substituting the values, we get A(Area) = 3.14 (given) * 2.5 * 2.5 square metres. The area comes out to be 19.625 square metres.
To know more about area,
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500
Answers
Answer:
Answer is B)
Step-by-step explanation:
Josiah's mistake is (b) He did not multiply the numerator and denominator by the correct number to equal 1,500
The proportion is given as:
Multiply both sides by 1500
Evaluate the expression on the right-hand side
Multiply 10 by 1500 on the left-hand side
Divide 15000 by 20 on the left-hand side
Rewrite the equation as:
From the question, we can see that the products are not well carried out.
Hence, Josiah's mistake is (b)
He got the rock songs part right. He did not multiply the numerator and denominator by the correct number until 1500.
What is Fraction ?What is fraction and example?
A fraction is numerical value that is a part of a whole. It is evaluated by dividing a whole into number of parts
Types of Fractions Proper fraction,Improper fraction,Mixed fraction,Like fractions,Unlike fractions,Equivalent fractions.
The statements that are true about Josiah's solution are:
He correctly found the proportion of rock songs by setting the ratio (number of rock songs in the sample) / (total number of songs in the sample) = (number of rock songs in the MP3 player) / (total number of songs in the sample). sample MP3 player) and solving for x:
Start Fraction 10 over 20 EndFraction = Start Fraction x over 1500 End Fraction.
Initial fraction 10 times 30 over 20 times 30 final fraction = initial fraction x over 1500 final fraction.
300 = x.
He didn't hit the average of the rock songs right because the average of 4 and 6 is 5, not 300.
He did not multiply the numerator and denominator by the correct number to 1500 because he should have multiplied both by 75 instead of 30 to get:
Initial fraction 10 times 75 over 20 times 75 final fraction = initial fraction x over 1500 final fraction. He did not have to divide 10 by 2 when he determined the ratio, because the ratio is already in its simplest form. So the real arguments are:
He got the rock songs part right. He did not multiply the numerator and denominator by the correct number until 1500. He did not have to divide 10 by 2 to determine the ratio.
Learn more about Proper fraction here
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❗⚠️PLEASE HELP ASAP!!!!!!!!! ⚠️❗
A histogram shows the number of magazines read last month by the students in a class. What percent of the students read less than six magazines?
can you find the mean and median of the data? Explain.
Answers
This is because there are 20 students (all frequency numbers added 15+3+2=20) and 17 if those 20 read less than 6 so
17/20=0.85
0.85(100)=85%
You can not find the mean number of magazines read because it is the middle number but the numbers are given in ranges.
You can not find the median because it is the total total number magazines read divided by number of students and you once again can't find the exact number of magazines because they are in ranges.
74% percent of the students read less than six magazines
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
A histogram shows the number of magazines read last month by the students in a class
The total number of students are 2+15+3
Number of students=23
Number of students read less than six magazines is 17
Now let us find 17 is what percent of 23
x/100×23=17
23x=1700
Divide both sides by 23
x=1700/23
x=73.9
x=74%
Hence, 74% percent of the students read less than six magazines
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Can someone help me with questions 8,9 and 10 I will make you the brainliest
Answers
Answer:
8 - 75%
9 - 25%
10 - 50%
Step-by-step explanation:
Look at the figure attached which illustrates the Percentages at different regions which we will use it to solve the required questions.
8 - The Percentage of Data below the Upper Quartile = 25% + 25% + 25% = 75%
9 - The Percentage of Data located between the Lower Quartile and the Median = 25%
10 - The Percentage of the Data above the Median = 25% + 25% = 50%
9 is 25%
10 is 50%
Need help in this
Sam has a deck that is shaped like a triangle with a base of 15 feet and a height of 6 feet. He plans to build a 4:5 scaled version of the deck next to his horse's water trough.
Part A: What are the dimensions of the new deck, in feet? Show every step of your work. (4 points)
Part B: What is the area of the original deck and the new deck, in square feet? Show every step of your work. (4 points)
Part C: Compare the ratio of the areas to the scale factor. Show every step of your work. (4 points)
Answers
Answer:
Part A: 42 Part B: 90
Step-by-step explanation:
Part A: 6x2=12 15x2=30
12+30= 42
Part B: LxW=A
6x15= 90
I NEED HELP PLSS. I CANT DO IT
Answers
Answer:
A= 8/200
B) 81/200
Please answer the question
Answers
Answer:
X=10
Step-by-step explanation:
subtract 30 from 68= 38
add two to 38 = 40
what times 4 gives you forty?= 10
How many terms are in this expression?
6s+7u+4
Answers
6s, 7u, and 4
Answer:5
Step-by-step explanation:O its 5 the answer is 5
1/5 divided by 4 help!
Answers
Answer: 0.05 or 1/20
Explanation: 1/5 divided by 4 in fraction form is 1/20, and in decimal form it is 0.05.
4 3/40 simplest form.
HELP THIS DUE TOOODAAAY!!!
Answers
Answer:
163/40
Step-by-step explanation:
multiply 4x40
then add 3
= 163
then put it over 40
163/40
Answer:
To simplify 4 3/40, we need to convert the mixed number to an improper fraction and then simplify:
4 3/40 = (4 × 40 + 3) / 40 (convert to improper fraction)
= 163 / 40
Now, we can simplify this fraction by finding the greatest common factor (GCF) of the numerator and denominator, which is 1:
163 / 40 = (163 ÷ 1) / (40 ÷ 1)
= 163 / 40
Therefore, 4 3/40 in simplest form is 163/40.
(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)
Algae cannot survive at depths greater than 300 meters below sea level. The inequality that represents depths at which algae cannot survive is x < –300. Graph the solution on the number line provided
Answers
Answer:
b is the correct graph
Step-by-step explanation:
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Answers
Answer:
By answering the presented question, we may conclude that Therefore rectangle 855 square yards is the closest response choice.
What is rectangle?
In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
The rectangle has a 20-yard base and a 10-yard height, hence its area is:
200 square yards = 20 yards x 10 yards
The triangle on the left has a 20-yard base and a 45-yard height (since the top side of the polygon is indicated as 45 yards), hence its area is:
450 square yards = 1/2 x 20 yards x 45 yards
210 square yards = 1/2 x 12 yards x 35 yards
As a result, the total playground area is:
860 square yards = 200 square yards plus 450 square yards plus 210 square yards
Therefore 855 square yards is the closest response choice.
Can someone help! Thank you!
Answers
Reason:
The numerator is [tex](2.1)^5[/tex]
Raising that to the third power gives
[tex]((2.1)^5)^3 = (2.1)^{5*3} = (2.1)^{15}[/tex]
We multiply the exponents. The general rule is
[tex](a^b)^c = a^{b*c}[/tex]
Use that same rule to cube the denominator.
[tex]((0.9)^4)^3 = (0.9)^{4*3} = (0.9)^{12}[/tex]
Therefore,
[tex]\left(\frac{(2.1)^5}{(0.9)^4}\right)^3=\frac{((2.1)^5)^3}{((0.9)^4)^3}\\\\=\frac{(2.1)^{5*3}}{(0.9)^{4*3}}\\\\=\frac{(2.1)^{15}}{(0.9)^{12}}\\\\[/tex]
In short
[tex]\left(\frac{(2.1)^5}{(0.9)^4}\right)^3=\frac{(2.1)^{15}}{(0.9)^{12}}\\\\[/tex]
Aziz's guess must have been ____ gumballs or ____ gumballs since his guess had a percent error of 5%.
Answers
Answer: 722 or 798
Step-by-step explanation: Therefore, Aziz's guess must have been 722 gumballs or 798 gumballs since his guess had a percent error of 5%.
Answer:
The percent error Chelsea's guess is 2.3% and Aziz's guess must have been 722 gumballs or 798 gumballs.
Step-by-step explanation:
Find the value of x.
A) 27
B) 34
C) 21
D) 31
Answers
Step-by-step explanation:
From the given figure, we can see that angles and are vertically opposite angles.
Since, vertically opposite angles are equal, therefore we have
Hence, the value of x = 21.
Answer:
C
Step-by-step explanation:
since both angles would be the same (z-angle shape), the angle would also be the same
3x+1
3(21)+1
63+1
64
therefore, the answer would be C
12 plus the quotient of 8 and 4
Answers
Quotient means divide
12+(8/4)
12+2
14
Answer:
[tex]14[/tex]
Step-by-step explanation:
[tex]12+(8/4)\\12+2\\14[/tex]
1. A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect to prefer comic books?
A. 10
B. 20
C. 70
D. 80
E. 100
2. About how many students do not prefer non-fiction?
A. 60
B. 75
C. 100
D. 150
E. 180
3. Overall, about how many students prefer literature (poems, plays, or novels)?
A. 45
B. 90
C. 100
D. 130
E. 180
Graph #2: Membership in School Clubs
4. At Rory’s school, students must join one after-school club. Based on the data in Graph #2, which club attracted about 30% of students?
A. yearbook
B. art
C. drama
D. hiking
E. running
F. science
5. Approximately What percent of students chose not to join the yearbook club?
A. 15%
B. 30%
C. 75%
D. 85%
E. 90%
6. About what percent of students joined the art club?
A. 30%
B. 25%
C. 20%
D. 15%
E. 5%
Answers
Answer:
1. A
2.150
3.c
4. d
5.im not sure
6. B
Step-by-step explanation:
Find which statement is wrong.
Answers
Answer:
The incorrect statement is number #2
Step-by-step explanation:
i gest said it lol
can someone pls help me with this i-ready question!!
Answers
Answer: from what I saw on the internet yes and no meant he same thing because 2+2=microwave so on a complete hypothetical metaphorical basis the answer is wiggle your doggies. I also saw on the hub that excusing the behavior of little children is indeed acceptable, so that concludes my answer in finding the ratio of unborn fried air.
Answer:
the mean is 9 because it is the middle number when they are in order
evaluate the expression when m=5. m^2-16
Answers
6. As part of a science project, Juaquim
built the figure shown.
6a. How much space does the figure take up?
6b. What are the dimensions of the three
rectangular prisms you used to find the
volume of the figure?
14 in.
5 in.
6c. Draw lines on the figure to show how you could have divided it into
prisms differently.
14 in.
16 in.
6
-16 in.
5 in.
Answers
Answer:
Volume (V) = Area of base × height of the prism
Can't do this because of numbers including e in it.
Answers
Answer:
Step-by-step explanation:
Answer:
A) 756522
B) 5687649.7
C) 14561856000000000000
Step-by-step explanation:
please help and if you answer both I will give Brainliest
Answers
Answer:
For the first one it's B. 339.12 square units
and for the last one it's D. 235.5 squad units
Step-by-step explanation:
I'm 99.9% that this is right!
I'm really sorry if it's not!
hope this helps!
Answer:
1.B
2. D
Step-by-step explanation:
I use this website too often but please HELP ME
3 of the 11 oz, 3 of the 8oz, and 4 of the 6 oz
Platter Prices
6-ounce $9.95
8-ounce $12.95
11-ounce $15.95
If a gratuity of 16% was added to the bill, which of the following is closest to the total of the steak platters and gratuity, ignoring sales tax?
A. $170
B. $134
C. $20
D. $147
Answers
Answer:
D, because yes.
20 - [(8 + 6) divide by 2]
Answers
Answer:
13
Step-by-step explanation:
As per the BODMAS, 8+6=14
14/2=7
20-7=13
Answer: The answer is 13!
Step-by-step explanation:
The first thing that you have to do is use PEMDAS, and do the things in parentheses first. This is 8+6. This equals 14. Divide 14 by 2 to get 7. The final thing to do is 20-7, and this is 13. Thus the answer is 13.
I hope this helped you! A brainilist is appreciated and helpful! <3
WILL MARK BRAINLIEST IF YOU ANSWER THIS!!!! (not joking)
There are approximately 7.48 liquid gallons in a cubic foot. If a cylindrical tank holds 1,600 liquid gallons and has a radius of 2.2 feet, what is the approximate height of the water tank? Approximate using pi = 3.14 and round to the nearest tenth.
213.9 feet
44.2 feet
14.1 feet
4.8 feet
Answers
Answer: 14.1
................................
Event A: Spinning blue on the spinner shown Event B: Rolling a 5 on a number cube What is P(A and B)?
Answers
Event A: The probability of spinning and landing on blue is 1/5
Event B: The probability of rolling a 5 on a number cube is 1/6
The probability of both A and B happening is:
[tex]\frac{1}{5}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{30}[/tex]
Hope it helps!