Area is length x width:
4x^3y^2 x 3x^2y^3
Apply the exponent rule: a^b x a^c = a^(b+c)
4 x 3 = 12
x^3 x x^2 = x^5
y^2 x y^3 = y^5
Combine for final answer: 12x^5y^5
What is 1/10 of 1 3.027
Answer:
1.3027
Step-by-step explanation:
how to solve this equation x²=16
Step-by-step explanation:
Hey there!
To solve this type of question, you must take square of variable"X" to right side making it ±squareroot. As it is a quadratic equation it will have two values (±).
Given;
[tex] {x}^{2} = 16[/tex]
Taking (square) to right side. It becomes ± square root.
[tex]x = + - \sqrt{16} [/tex]
[tex]x = + - \sqrt{ {4}^{2} } [/tex]
Cancel square and square root.
[tex]x = + - 4[/tex]
Therefore, X = ±4
Hope it helps...
Answer:
There are two I results found which is x=4 and x=-4
Step-by-step explanation:
Step by Step Solution:
More Icon
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
x^2-(16)=0
Step by step solution :
STEP
1 :
Trying to factor as a Difference of Squares:
1.1 Factoring: x2-16
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 16 is the square of 4
Check : x2 is the square of x1
Factorization is : (x + 4) • (x - 4)
Equation at the end of step
1 :
(x + 4) • (x - 4) = 0
STEP
2 :
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Solving a Single Variable Equation:
2.3 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4 and/or x=-4
obtain the total salary?)
2. Xandria rides through a jeepney which charges P 8.00 for the first 4 kilometers
and additional P0.50 for each additional kilometer. Express the jeepney fare (F)
as function of the number of kilometers (d) that Xandria pays for the ride.
Answer
Answer:
F(d) = 30 + 0.50d
Step-by-step explanation:
Given
Charges = P8.00 ---- first 4 km
Additional = P0.50
Required
Write a function to address the scenario.
Represent the whole distance covered with d.
First,we need to determine the total charges for the first four hours.
Charges = 8.00 * 4
Charges = 32.00
Next, we determine the charges for additional distance.
Charges = 0.50 * (d - 4)
d - 4 is the remaining distance after the first 4.
Charges = 0.50d - 2
The function is then written as;
F(d) = 32 + 0.50d - 2
F(d) = 32 - 2 + 0.50d
F(d) = 30 + 0.50d
2. ABC is a right-angled triangle in which <A = 90° and AB=AC. Find
<B and <C.
(2 marks)
Answer:
<A=<C=45°
Step-by-step explanation:
you can see in the picture above
At one point the average price of regular unleaded gasoline was $3.39 per gallon. Assume that the standard deviation price per gallon is $ per gallon and use Chebyshev's inequality to answer the following. (a) What percentage of gasoline stations had prices within standard deviations of the mean? (b) What percentage of gasoline stations had prices within standard deviations of the mean? What are the gasoline prices that are within standard deviations of the mean? (c) What is the minimum percentage of gasoline stations that had prices between $ and $?
This question was not written completely
Complete Question
At one point the average price of regular unleaded gasoline was $3.39 per gallon. Assume that the standard deviation price per gallon is $0.07 per gallon and use Chebyshev's inequality to answer the following.
(a) What percentage of gasoline stations had prices within 3 standard deviations of the mean?
(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the mean? What are the gasoline prices that are within 2.5 standard deviations of the mean?
(c) What is the minimum percentage of gasoline stations that had prices between $3.11 and $3.67?
Answer:
a) 88.89% lies with 3 standard deviations of the mean
b) i) 84% lies within 2.5 standard deviations of the mean
ii) the gasoline prices that are within 2.5 standard deviations of the mean is $3.215 and $3.565
c) 93.75%
Step-by-step explanation:
Chebyshev's theorem is shown below.
1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.
As stated, the value of k must be greater than 1.
2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.
3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.
4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.
(a) What percentage of gasoline stations had prices within 3 standard deviations of the mean?
We solve using the first rule of the theorem
1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.
As stated, the value of k must be greater than 1.
Hence, k = 3
1 - 1/k²
= 1 - 1/3²
= 1 - 1/9
= 9 - 1/ 9
= 8/9
Therefore, the percentage of gasoline stations had prices within 3 standard deviations of the mean is 88.89%
(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the mean?
We solve using the first rule of the theorem
1) Chebyshev's theorem states for any k > 1, at least 1-1/k² of the data lies within k standard deviations of the mean.
As stated, the value of k must be greater than 1.
Hence, k = 3
1 - 1/k²
= 1 - 1/2.5²
= 1 - 1/6.25
= 6.25 - 1/ 6.25
= 5.25/6.25
We convert to percentage
= 5.25/6.25 × 100%
= 0.84 × 100%
= 84 %
Therefore, the percentage of gasoline stations had prices within 2.5 standard deviations of the mean is 84%
What are the gasoline prices that are within 2.5 standard deviations of the mean?
We have from the question, the mean =$3.39
Standard deviation = 0.07
μ - 2.5σ
$3.39 - 2.5 × 0.07
= $3.215
μ + 2.5σ
$3.39 + 2.5 × 0.07
= $3.565
Therefore, the gasoline prices that are within 2.5 standard deviations of the mean is $3.215 and $3.565
(c) What is the minimum percentage of gasoline stations that had prices between $3.11 and $3.67?
the mean =$3.39
Standard deviation = 0.07
Applying the 2nd rule
2) At least 75% or 3/4 of the data for a set of numbers lies within 2 standard deviations of the mean. The number could be greater.μ - 2σ and μ + 2σ.
the mean =$3.39
Standard deviation = 0.07
μ - 2σ and μ + 2σ.
$3.39 - 2 × 0.07 = $3.25
$3.39 + 2× 0.07 = $3.53
Applying the third rule
3) At least 88.89% or 8/9 of a data set lies within 3 standard deviations of the mean.μ - 3σ and μ + 3σ.
$3.39 - 3 × 0.07 = $3.18
$3.39 + 3 × 0.07 = $3.6
Applying the 4th rule
4) At least 93.75% of a data set lies within 4 standard deviations of the mean.μ - 4σ and μ + 4σ.
$3.39 - 4 × 0.07 = $3.11
$3.39 + 4 × 0.07 = $3.67
Therefore, from the above calculation we can see that the minimum percentage of gasoline stations that had prices between $3.11 and $3.67 corresponds to at least 93.75% of a data set because it lies within 4 standard deviations of the mean.
2. Timmy and Anita decide to organize a dodgeball tournament at lunch recess and they ask
that any student from grade 6-8 who is interested to come to a meeting. At recess 24 grade
6 students arrive along with 48 grade 7 students and 36 grade 8 students. Timmy and Anita
decide to create EQUAL teams but to keep the grades separate. What is the greatest number
of students on each team making sure that all of the teams are equal? How many teams are
then formed in each grade?
Answer :pink i think
Step-by-step explanation:
The point slope form of a line that has a slope of 1/4 and passes through the point (3,0 ) is shown .
Y-0= 1/4 (x-3)
What is the equation in slope intercept form?
Answer:
Y=1/4x-3/4
Step-by-step explanation:
I got this answer right on my questions
Simplify the expression: 3(1 - 2x) + 7
10 - 6x
7-6x
10-X
6x + 7
Solve.
X-9 = 12
.....
Answer:
x=21
Step-by-step explanation:
x=9+12 x=21
Answer:
Step-by-step explanation:
X-9=12
Reverse the operation into
9+12=x
9+12=21
Now check
21-9=12
Which of the following equals 5.96?
A. 2.98 + 2.89
B. 0.6 + 5.9
C. 6.03 + 0.07
D. 1.061 + 4.899
Answer:
D. 1.061 + 4.899
Step-by-step explanation:
1061 + 4899 149 149
——————————— = ———
1000 25 25
149
——— = 5.96000
25
If this helps please mark brainliest. Have a great day!
Given the following formula, solve for a
I WILL GIVE BRAINLIST!!
Answer:
a=2s-b-c
Step-by-step explanation:
2s=a+b+c
a=2s-b-c
Answer:
2s-c-b =a
Step-by-step explanation:
s = ( a+b+c)/2
Multiply each side by 2
2s = ( a+b+c)/2 *2
2s = a+b+c
Subtract c from each side
2s -c = a+b+c-c
2s -c = a+b
Subtract b from each side
2s-c-b = a+b-b
2s-c-b =a
Is this answer right?
Answer:
Step-by-step explanation:
yes!
simplify picture down Below
Answer:
[tex]x^{2}[/tex]
I hope this helps!
A parking lot is 100 yards long. What is the length of 3/4 of the parking lot, in feet? (Not in words)
1 yard = 3 feet.
100 yards x 3 = 300 feet.
300 feet x 3/4 = 225 feet.
The answer is 225 feet.
Answer:
225 ft hope it helps
A team has won 51 out of 68 games explain how to use the bar diagram to find the percent of games the team has won
you would divide -> 51/68 and you would get .75. move the 2 first numbers after the dot to the front and you get 75%
Answer:
I the diagram, 17 represents 25% of the total games. Since 17 times 3 equals 51, you use the first 3 columns to find the answer of 75%.
Just took test that was the answer they gave.
Step-by-step explanation:
a kilogram of dalandan in pure gold costs P55. if jessica bought k kilograms, represent the amount paid A as a function
Answer:
[tex]A(k) = 55k[/tex]
Step-by-step explanation:
Given
[tex]1kg = P55[/tex]
Required
Determine the cost of k kilogram
[tex]1kg = P55[/tex]
Multiply both sides by k
[tex]k * 1kg = P55 * k[/tex]
[tex]k\ kg = 55 k[/tex]
Representing this as a function:
[tex]A(k) = 55k[/tex]
or numbers 8a–8c, choose Yes or No to indicate whether the statement is correct.
15 points
Yes No
8a. 1,289 ÷ 22 is 58 r13.
8b. 189 ÷ 17 is 11 r2.
8c. 1,427 ÷ 13 is 190 r1.
8a. 1,289 ÷ 22 is 58 r13.
8b. 189 ÷ 17 is 11 r2.
8c. 1,427 ÷ 13 is 190 r1.
Answer:
1,289 divided by 22 is 58 r13
Step-by-step explanation:
I just need to know what's Nine sixty-eight thousand one hundred twenty-three
is in numbers bc
idk my brain is kind of jumbled rn
Elijah's father is 47. He is 17 years older than twice Elijah's age. How old is Elijah?
Answer:
let Elijah age be a
Then
2*a + 17 =47
2a=47-17
2a=30
a=15
Step-by-step explanation:
The table below shows four problems using decimals.
Problem
Problem
Number
1
2
3
How many grams are in 2.3 kilograms? Recall that there are 1000
grams in a kilogram.
How many 85-cent nutrition bars can Mary buy for $20.00?
How many quarts does Mike have to buy for a recipe that calls for
13.7 cups? Recall that there are 4 cups in a quart.
How many days will a trip take if it takes 152.45 hours? Recall that
there are 24 hours in a day.
4.
Which problem would be solved using multiplication, and what is the solution to the problem?
Problem 1 requires multiplication. There are 2300 grams in 2.3 kilograms.
Problem 2 requires multiplication. Mary can buy 23 nutrition bars.
Problem 3 requires multiplication. Mike has to buy 54.8 quarts for the recipe.
Problem 4 requires multiplication. The trip will take 3658.8 days.
Nark this and retum
Answer
The answer is A
Answer:
It is A. my friend
Step-by-step explanation:
HELPPPPPPP MEEEEEEEEEEEE
Answer:
your answer is b 32/4=8
Step-by-step explanation:
if you take the groups of 4 and count them up it is 32 and then you divide them in to equal groups and it is 8 groups of 4
hope this helped
:)
2.Brian is heading out for a steady early morning jog as one of his training runs for a marathon. He plans to jog
18 miles. He covered the first 4 miles in 39 minutes. Keeping the same steady pace, which of the following
is closest to the time that it will take Brian to finish his jog from the 4-mile point?
(1) 2.3 hours
(3) 2.9 hours
(2) 2.5 hours
(4) 3.3 hours
If the quotient of a number and 16 is added to 1/4 the result is 5/16
Answer:
if youre trying to find the number then the number is 1
Step-by-step explanation:
the equation would be x/16+1/4=5/16
well we want to make everything have the same denominator and 16 is the LCD ( least common denominator ) so you would multiply 1/4 by 4/4 to get 4/16.
this means x/16+4/16=5/16 and and 4+1=5 so 1 is the answer
Find the extreme values of f on the region described by the inequality.
f(x, y) = e−xy; x2 + 4y2 ≤ 1
Answer:f(x, y) = e
−xy. For the interior of the region, we find the critical points:
fx = −ye−xy
, fy = −xe−xy, so the only critical point is (0, 0), and f(0, 0) = 1.
For the boundary, we use Lagrange multipliers.
g(x, y) = x
2 + 4y
2 = 1 ⇒ λ∇g = h2λx, 8λyi, so setting ∇f = λ∇g we get
−ye−xy = 2λx and −xe−xy = 8λy. The first of these gives e
−xy = −2λx/y,
and then the second gives −x(−2λx/y) = 8λy ⇒ x
2 = 4y
2
. Solving this
last equation with the constraint x
2 + 4y
2 = 1 gives x = ± √
1
2
and y = ±
1
2
√
2
.
Now f
± √
1
2
, ∓
1
2
√
2
= e
1/4 ≈ 1.284 and f
± √
1
2
, ±
1
2
√
2
= e
−1/4 ≈ 0.779.
The former are the maxima on the region and the latter are the minima.
Step-by-step explanation:
Solve the following and explain your steps. Leave your answer in base-exponent form. (3^-2*4^-5*5^0)^-3*(4^-4/3^3)*3^3 please step by step!!!!
Answer:
[tex]\boxed{2^{\frac{802}{27}} \cdot 3^9}[/tex]
Step-by-step explanation:
I will try to give as many details as possible.
First of all, I just would like to say:
[tex]\text{Use } \LaTeX ![/tex]
Texting in Latex is much more clear and depending on the question, just writing down without it may be confusing or ambiguous. Be together with Latex! （＊＾Ｕ＾）人（≧Ｖ≦＊）/
[tex]$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$[/tex]
Note that
[tex]\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }[/tex]
The denominator can't be 0 because it would be undefined.
So, we can solve the expression inside both parentheses.
[tex]\left(\dfrac{1}{3^2} \cdot \dfrac{1}{4^5} \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3[/tex]
Also,
[tex]\boxed{a^{0} = 1, a\neq 0 }[/tex]
[tex]\left(\dfrac{1}{9} \cdot \dfrac{1}{1024} \cdot 1 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]
Note
[tex]\boxed{\dfrac{1}{a} \cdot \dfrac{1}{b}= \frac{1}{ab} , a, b \neq 0}[/tex]
[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27[/tex]
[tex]\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]
[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]
[tex]\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)[/tex]
Note
[tex]\boxed{\dfrac{1}{\dfrac{1}{a} } = a}[/tex]
[tex]9216^3\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)[/tex]
[tex]\left(\dfrac{ 9216^3\cdot 27}{4^{\frac{4}{27} } }\right)[/tex]
Once
[tex]9216=2^{10}\cdot 3^2 \implies 9216^3=2^{30}\cdot 3^6[/tex]
[tex]\boxed{(a \cdot b)^n=a^n \cdot b^n}[/tex]
And
[tex]$4^{\frac{4}{27}} = 2^{\frac{8}{27} $[/tex]
We have
[tex]\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)[/tex]
Also, once
[tex]\boxed{\dfrac{c^a}{c^b}=c^{a-b}}[/tex]
[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27[/tex]
As
[tex]30-\dfrac{8}{27} = \dfrac{30 \cdot 27}{27}-\dfrac{8}{27} =\dfrac{802}{27}[/tex]
[tex]2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3[/tex]
[tex]2^{\frac{802}{27}} \cdot 3^9[/tex]
express 7.84684846 as a rational number in the form p/q were p and q have no common factors
It's not clear what the pattern is supposed to be for the digits in the givne number. It looks like the repeating block should be 846, but it could just as easily be 84684.
Assume the first case, and let x = 7.846846846... . Then
1000x = 7846.846846846...
Subtract x from this to cancel the repeating decimal part, then solve for x :
999x = 7846 - 7 = 7839
x = 7839/999 = 871/111
If instead you meant the second case, let x = 7.846848468484684... . Then
10⁵ x = 784,684.846848468484684...
Solve for x :
99,999 x = 784,684 - 7 = 784,677
x = 784,677/99,999 = 261,559/33,333
Maybe you meant something else altogether?
what is the third power of 3
Answer:
27
Step-by-step explanation:
How is 41/1,000 written as a decimal? Enter your answer in the box.
Answer:
0.041
I know this because 1,000 has 3 zeros, so you would move 41 three places to the right.
The decimal equivalent of the fraction 41/1000 is 0.041.
What is a decimal?A decimal is represented by a dot that separates the whole part and the fractional part of a number. Decimals can also be converted into fractions and vice versa.
Given, a fraction 41/1000, here the numerator is less than the denominator so it is a proper fraction.
Now, As in the denominator we have three zeroes we'll put a decimal three places before the numerator value which is,
= 0.041/1.
= 0.041.
So, 41/1000 is equal to 0.041.
learn more about decimal numbers here :
https://brainly.com/question/4708407
#SPJ2
what is the ratio of white cirlces to blue cirlces?
Im guessing the ratio for a cirlce could be 1/2 or more
uplod the pic so i can solve the problem
How do you do this question?
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.