Answer:
1. 1, 9/4
2. 4^4
3. -0.0000000008723
4. -5100023*10^2, -6.6*10^(12)
Step-by-step explanation:
[tex]21^0 = 1;\ n^0\ always\ is\ 1.\\(\frac{2}{3})^{-2} = (\frac{3}{2})^2 = \frac{3^2}{2^2} = \frac{9}{4}; n^m\ is\ performed\ by\ doing\ n*n,\ m\ times.\\i.e.,\\ n^2=n*n;\\n^3=n*n*n;\\ n^4=n*n*n*n\\\\\frac{4^6}{4^2};\ original\\\\\frac{(4^2)^3}{4^2};\ (n^{mc}\ can\ be\ rewritten\ as\ (n^m)^c\\\\\frac{4^2}{4^2}*\frac{(4^2)^2}{1};\ split\ the\ fraction\ into\ two\ parts\ because\ of\ multiplication\ rules.\\\\1*4^4;\ \frac{n}{n}\ can\ be\ written\ as\ 1.\ \frac{n}{1}\ can\ be\ written\ as\ n.\\\\4^4[/tex]
Technically, [tex]4^4[/tex] is 256, but the answer is requested as a number with an exponent.
-8.723 * 10^-10 would be -0.0000000008723.
10^-10 = [tex]\frac{1}{10^{10}}[/tex], which would mean you must move your decimal left by the number of places indicated by the exponent.
[tex]-5.1*10^8-2.3*10^3 = x\\-51*10^7-23*10^2 = x\\10^7=10^{5+2}=10^5*10^2\\-5100000*10^2-23*10^2=x\\-5100023*10^2=x;\ combine\ like\ terms.\\-6*10^5 * 1.1*10^7 = x\\-6*1.1*10^5*10^7;\ rewrite\ for\ simplification.\\-6.6*10^{12}=x[/tex]
Alison is training for a marathon, Last week, she ran 26 miles in 208 minutes, If she runs at that speed a, How long would it take her to run 15 miles?b. How far could she run in 20 minutes?c. How fast is she running in miles per minute? In miles per hour?
Answer:
Answers below
Step-by-step explanation:
To find per 20 miles
= 26miles/ 208minutes / 26 (to simplify)
= 1mile / 8minutes / 2 (to simplify)
= 1/2mile / 4 minutes x 40 (to get miles per 20 min)
= 20 miles / 160 minutes
_____________________________________________
To find per 15 miles
= 26miles/ 208minutes / 26 (to simplify)
= 1mile / 8minutes / 2 (to simplify)
= 1/2mile / 4 minutes x 30 (to get miles per 15 minutes)
= 15 miles / 120 minutes
_____________________________________________
To find miles per minute
= 26miles/ 208minutes / 26 (to simplify)
= 1mile / 8minutes / 8 (to get miles per minute)
= 0.125 miles / 1 minute
_____________________________________________
To find miles per hour
= 26miles/ 208minutes / 26 (to simplify)
= 1mile / 8minutes / 2 (to simplify)
= 1/2mile / 4 minutes x 15 (to get miles per hour)
= 7.5 miles / 60 minutes
wich numbers are a distance of 2.2 units from -3 on a number line
So, The numbers on a distance of 2.2 units from −3 on a number line are
-3 - 2.2 and -3+2.2
= - (3+2.2) and - (3-2.2)
= -5.2 and - 0.8
solving systems by substitution (algebra 2)
7x + y = 12
y = 4x - 21
Answer:
x = 3, y = -9
Step-by-step explanation:
plug y=4x-21 into 7x+y=12 to get
7x + (4x-21) = 12 -> 11x -21 = 12 -> 11x = 33 -> x = 3
plug x=3 into y=4x-21 to get
y = 4(3) - 21 = 12 - 21 = -9
f=2+4/5f-3 solve for f
Answer:
f=-5
Step-by-step explanation:
12. Consider the following hypothetical basketball records for Spelman and Morehouse
Colleges.
Home games
Away games
a.
Spelman College
10 wins, 19 losses
12 wins, 4 losses
C.
Morehouse College
9 wins, 19 losses
56 wins, 20 losses
Give numerical evidence to support the claim that Spelman College has a better team
than Morehouse College.
b. Give numerical evidence to support the claim that Morehouse College has a better team
than Spelman College.
Which claim makes more sense and why?
The claim made by Morehouse college make more sense as their ratio of winning a game than losing it is higher.
a) In home games, the Spelman college won 10 wins whereas Morehouse College won only 9 games.
So, Spelman College has a better team than Morehouse College in home games.
b ) In Away games, Morehouse College won 56 games whereas Spelman College only won 12 games. So, Morehouse College has a better team than Spelman College in Away games.
c ) In total, Spelman College has won 22 games and lost 23 games. The ratio of win is to lose is 22 : 23 that is it won 0.96 games against it lost 1 game. In total, Morehouse College won 65 games and lost 39 games. The ratio of win it to lose is 65 : 39 that is it won 1.67 games against the 1 game it lost.
So, the claim of Morehouse College makes more sense.
Therefore, we get that the claim made by Morehouse college make more sense as their ratio of winning a game than losing it is higher.
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Solve the system using the substitution method.
x - 7y = 23
8x - y = 74
Answer:
y = -2
x = 9
Step-by-step explanation:
x - 7y = 23
8x - y = 74
-----------------
Extra:
(x - 7y = 23) -8
-8x + 56y = -184
-----------------------
-8x + 56y = -184
8x - y = 74
--------------------------
55y = -110
÷55 ÷55
-------------------
y = -2
x - 7y = 23
x - 7(-2) = 23
x + 14 = 23
-14 -14
-------------------
x = 9
I hope this helps!
38 Points pls help Evaluate the expression (2 + 2) (3) × 5 - 3.
Answer:
4/9
Step-by-step explanation:
3 meters of cloth is the ratio of 3:7
When given 3 meters of cloth and it is to be divided in a ratio of 3:7 then one part will have 0.9 meters and the other will have 2.1 meters.
How to divide cloth by ratio?The first thing to do is to find the denominator of the ratio by summing the two numbers in the ratio:
= 3 + 7
= 10
The first part of the cloth would be:
= 3 / 10 x 3 meters
= 0.3 x 3 meters
= 0.9 meters
The second part of the cloth would be:
= 7 / 10 x 3 meters
= 0.7 x 3
= 2.1 meters
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'DesTunes is a new music streaming service.
Write an equation to represent each scenario, where x represents the number of months and y represents the total charge.
Scenario 1: DesTunes charges adults $15 per month.
The equation that represent scenario 1 is y = 15x while the equation that represent scenario 2 is y = 5x + 20
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represents the number of months and y represents the total charge.
Scenario 1: DesTunes charges adults $15 per month.
Hence:
y = 15x
Scenario 2: DesTunes charges students a $20 sign-up fee and $5 per month, hence;
y = 5x + 20
The equation that represent scenario 1 is y = 15x while the equation that represent scenario 2 is y = 5x + 20
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write a polynomial function of least degree with integral coefficients that has the given zeros. -1, 3+3i
The least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².
What do we mean by polynomial function?A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 2x+5 is a polynomial with an exponent of one.So, given zeroes are -1, 3+3i.
We got: x = -1Then, x + 1 = 0.Hence, one factor of the polynomial function is (x+1).Similarly,
We have: 3+3iRewrite as: x = 3 + √-9Square both the sides: x² = 9 - 9So, the other factor is x².So, the polynomial has the function: (x+1)x²
(x+1)x²x³ + x²f(x) = x³ + x²Therefore, the least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².
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A water molecule has a mass
of 3 x 10-29 kg. A bottle
contains 1.7x 1028 molecules of water. Calculate the mass
of water in the bottle.
Answer: 5.1 x 10⁻¹ kg
To find the mass of water in the bottle, we can multiply the mass of one molecule by the number of molecules.
Dimensional AnalysisBy using dimensional analysis, or by cancelling out units, we can figure out what to multiply or divide. Dimensional analysis uses fractions written with units. Dividing the same unit cancels out units we don't need.
To solve:
Figure out what units we need in the answer.Write the fractions using given information from the question.Put the fractions in an equation.Cancel out units to solve.Units we need in the answerWe are looking for the mass of H₂O in the bottle.
The units we need in the answer are: [tex]\displaystyle{ \frac{kg}{bottle} }[/tex]
Write fractions with given informationThe question tells us:
the mass of one H₂O molecule is 3 x 10⁻²⁹ kg: [tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O}}[/tex]the bottle has 1.7 x 10²⁸ molecules of H₂O: [tex]\displaystyle{ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}[/tex]Write an equationOur equation puts the fractions in an equation, making them multiply to get the units we need.
[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}\ =\ \frac{kg}{bottle}[/tex]
Why is this equation correct?
Remember that dividing the same unit will cancel them out. In the equation, we have H₂O in a numerator and H₂O in a denominator. So, H₂O will cancel out. In the end, we will only have kg in the numerator and bottle in the denominator.
Cancel out units to solveTake the equation we wrote. Now that we know our equation gives us the right units, we only need the front part.
[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}[/tex]
Cancel out H₂O:
[tex]=\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1} \ *\ \frac{(1.7*10^{28})}{1\ bottle}}[/tex]
Simplify the equation:
[tex]=\displaystyle{ \frac{(3 * 10^{-29})*(1.7*10^{28})\ kg}{1\ bottle}[/tex]
[tex]=\displaystyle{ \frac{3 * 10^{-29}*1.7*10^{28}\ kg}{1\ bottle}[/tex]
Use exponent rules to multiply 10⁻²⁹ with 10²⁸:
[tex]=\displaystyle{ \frac{3 *1.7*10^{28-29}\ kg}{1\ bottle}[/tex]
[tex]=\displaystyle{ \frac{3*1.7*10^{-1}\ kg}{1\ bottle}[/tex]
Multiply within the numerator to simplify:
[tex]=\displaystyle{ \frac{5.1*10^{-1}\ kg}{1\ bottle}[/tex]
∴ The mass of water in the bottle is 5.1 x 10⁻¹ kg.
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HELP PLEASE!! I WILL GIVE BRAINLYEST
Diego made the shape on the left, and Elena made the shape on the right. Each shape uses 5 circles.
Answer:
Options 2-5
Step-by-step explanation:
1. False, since the designs aren't identical.
2. True, both circles have a radius of 1.
3. True, you can translate the circles in Diego's design up to that they are all tangent to each other to make Elena's design.
4. True, both circles have diameter 10.
5. True, simlar logic to 2 and 4
Shureka Washburn has scores of 82, 72, 81, and 79 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with
an average of 78 or higher, given that the final exam counts as two tests.
b. Explain the meaning of the answer to part (a).
An architectural company is trying to test the effectiveness of its promotional activity by looking at how many designs for
new buildings it sells each year.
Year Sales
2012 23
2013 18
The company assumes its promotional activity is less effective, which is why sales decreased. However, there could be many
confounding factors. Which of the following is not a possible confounding factor?
The factor that is not a possible confounding factor is B. the expected sales for the year 2014.
What is a confounding factor?A confounding factor is a third variable that influences or explains both the independent and dependent variables.
The independent variable here is the year while sales are the dependent variable.
However, confounding factors could include the number of new buildings constructed in 2013, which was not factored in by the architectural company and the state of the economy in 2013.
Thus, the expected sales for the year 2014 cannot be a confounding variable for the decreased sales in 2013 because it cannot explain the 2013 performance.
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Question Completion:A. the number of new buildings constructed
B. the expected sales for the year 2014
C the state of the economy
No
5) Determine if the list of numbers is an arithmetic sequence by choosing Yes or No. If Yes
then choose the option with the correct common difference "d."
18, 16, 14, 12, 10,...
Yes, d= -2
Yes, d = -3
Yes, d = 2
Helppp!!
The option yes, d = -2 is correct
The arithmetic sequence or progression is a sequence of numbers such that the difference between the consecutive terms is constant.
The formula of an arithmetic sequence is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n-1)d
Here the sequence is 18, 16, 14, 12, 10...... which is in arithmetic sequence as there is a common difference between them.
Now we have to find the common difference between the two consecutive terms of the series,
common difference (d) = 16- 18 = 14 - 16 = -2
Therefore the series is an arithmetic sequence and the common difference between them is -2.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Write the least common multiple of 7 and 14.
Answer:
14
Step-by-step explanation:
To work out the lowest common multiple, we first:
List multiples of both numbersFind the first similarity7, 14, 21, 28...
14, 28...
The common multiples of 7 and 14 are 14, 28 etc, but the LEAST (or lowest) common multiple is 14.
Hope this helps.
PLS COULD YALL HELP !!?!??
Answer:
x = 11
m<H = 39°
Step-by-step explanation:
m<G = 6x - 15
m<H = 3x + 6
complementary angles = angles that add up to 90
6x - 15 + 3x + 6 = 90
9x = 99
x = 11
m<H = 3x + 6, plug in 11 as x
3 * 11 + 6
= 33 + 6
m<H = 39°
How much it’s 27+ 0.185
Answer: 27.185
Step-by-step explanation:
Hi there!
If you just want to add 27+0.185, the answer is 27.185.
You just have to add 27+0.185 (what I think of for this question is just adding the 27 to it).
Hope this helps! Have a great day!
How are ratios, rates, and unit rates used to solve problems?
Answer:
The Ratios, Rate and unit rate are used to solve many real-world problems.
Step-by-step explanation:
As a ratio is a comparison of two numbers or measurements.
A rate is also a ratio in which the two terms are in different units.
A unit rate means a rate for one of something
Jane is 3 years older than Mary. Mary is twice as old as Kay. If Kay is x years how old is jane
Jane is 2x+3 years old. (answer)
In this case, we can use Kay as the base/foundation in this problem. Kay is x years old. Mary is twice as old as Kay, making Mary 2 times x or 2x. We are solving for Jane. Jane is 3 years older than Mary, who we know is 2x. We can add on 3 years making the final expression for Jane's age: 2x+3. Since we do not know Kay's age, or x, we cannot solve this problem any further.
Explain how negative powers of 10 can be
helpful when writing and comparing small
numbers.
Negative powers of 10 helpful when writing and comparing small numbers.
Small numbers (numbers between 0 and 1) are written with a negative power of ten. The specific power of 10 indicates just how big or how small the number is. You can compare two numbers written in scientific notation by looking at their powers of 10. The number with the greater power of 10 will be the greater number.
When comparing small numbers, write these numbers in scientific notation (only one non-xero digit must be before point) and then
if the powers of 10 are the same in compared numbers are the same, just compare the numbers which are multiplied by these powers of 10. For example, 3.6× 10∧-6 is greater than 2.6× 10∧-6 because powers are the same (-6) and 3.6 is greater than 2.6if the powers are different, then the smaller is power, the smaller is number (number with the smaller negative power has more places after decimal point). For example,3.6× 10∧-6 is greater than 2.6× 10∧-7 because -6 > -7.10 to the power of negative 7 is equal to 0.0000001.For example- 0.00003450000
3.45 x 10 -5
3.450000 x 10 -5
0.345 x 10 -4
0.3450000 x 10 -4
Hence it is prooved that negative powers of 10 helpful when writing and comparing small numbers.
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probability from a two way table
Answer:
82% or 23/28
Step-by-step explanation:
2+3+18=23
2+3+18+6=28
23/28=
Carton has a length of 2 2/3, a weight of one and 1/8, and a height of 1 1/5. What is the volume of the carton
Rawr!~ Allow me to help you today!
Answer:
[tex]V=\frac{2}{5}[/tex] cubic units!
Step-by-step explanation:
Step 1: Draw the carton (Carton is in the image)
Step 2: Calculate the volume V
[tex]V=LWH[/tex]
[tex]V=\frac{8}{3}[/tex] × [tex]\frac{1}{8}[/tex] ×[tex]\frac{6}{5}[/tex]
[tex]V=\frac{2}{5}[/tex] cubic units
I hope this helps you! <3
Answered by:AshTheNeko
Distribute and simplify these radicals.
2√3 (√2+√3)
O 2√5 +6
O2√15
O 30
O6√2+6
Determine whether the sequence converges or diverges. How do you know if it converges or diverges? If it converges, give the limit. (7)
The sequence converges as the degree of the numerator and denominator are the same.
How to find the limit of a rational equation
In this question we have the case of a rational equation representing a sequence, of which we must determine if the sequences converges and diverges. An useful form to prove the convergence of rational equations is using limit and algebra properties:
(5 · n - 1) / (n + 1)
[(5 · n - 1) / (n + 1)] · 1
[(5 · n - 1) / (n + 1)] · (n / n)
[(5 · n - 1) · n] / [(n + 1) · n]
[(5 · n - 1) / n] / [(n + 1) / n]
(5 - 1 / n) / (1 + 1 / n)
As n → + ∞, then 1 / n → 0 and the limit of (5 · n - 1) / (n + 1) is 5. Thus, the sequence converges as the degree of the numerator and denominator are the same.
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The difference of the squares of two positive consecutive even integers is 84. Find the integers. Use the fact that, if x represents an even integer, then x + 2 represents the next consecutive even integer.
Answer:
The integers are 20 and 22
Step-by-step explanation:
Let the first even integer be x . Then the next consecutive even integer
= x + 2
The relationship between these two integers is the difference of the squares = 84
This means
(x + 2)² - x² = 84
Use the relationship a² - b² = (a + b) (a -b)
Here a = x + 2 and b = x
So
a + b = (x + 2 ) + x = x + 2 + x = x + x + 2 = 2x + 2
a - b = (x + 2) - x = x + 2 - x = x -x + 2 = 2
Therefore
(a + b)(a - b) in terms of x is
(2x + 2) x 2 = 4x + 4
We know this is 84
So 4x + 4 = 84
Subtract 4 on both sides:
4x = 84 -4
4x = 80
x = 20
So the next consecutive even integer = 22
The integers are 20 and 22
the base is of this pyramid is a square. how do you find the area of a square.
Answer:
If you're just looking for the area of the square, then it's 49m. If you want the surface area of the whole pyramid, it's 189.
Step-by-step explanation:
For just the square, it's easy: Multiply the side lengths. 7x7 is 49.
For the surface area, find the area of the square (49) and the four triangles. To find the areas of the triangles, multiply the base (bottom, here it's the side length of the square) by the height (in this case 10m) and divide by 2. 7x10=70 and 70/2=35. Now since there are 4 triangles, multiply that by 4. 35x4=140, and now add the area of the square; 140+49=189. I don't think you wanted the surface area though, but I hope this helps!
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Circle all rational numbers from the list below.
EXPLAIN how you know if they are rational or irrational.
2.0
1 7/8
π
√16
6.39
√5
3.45_
Answer:√16 and 6.39 are rational numbers because they can be expressed as a ratio and a fraction.
The container that holds the water for the football team is 2/5 full. After pouring in 6 gallons of water, it’s 7/10 full. How many gallons can the container hold
Answer:
20
Step-by-step explanation:
We need to determine what fraction of the container 6 gallons is. We know the difference between 2/5 and 7/10 is 6 gallons, so all we have to do is solve for 7/10 - 2/5. The common denominator is 10, as both 5 and 10 are factors of 10. 10/5 is 2, so we multiply the numerator of 2/5 by 2.
7/10 - 4/10 = 3/10
We now know that 6 gallons is 3/10 of the container. Now we solve.
10/3 = 3 1/3
So:
6 x 3 1/3 = 20
Answer:
20 gallons.-
Step-by-step explanation:
Let x be the number of gallons that the container holds.
The we have the equation
2/5 x + 6 = 7/10 x
Multiply through be 10
4x + 60 = 7x
3x = 60
x = 20.