What are the prime factors of 48?
Answer:
48 = 2⁴ · 3
Step-by-step explanation:
You want the prime factorization of 48.
Prime factorsYou recognize that 48 is an even number, so you can divide by 2 and see what's left. You can keep doing that until you get a number divisible by another prime:
48/2 = 24
24/2 = 12
12/2 = 6
6/2 = 3
3 is prime.
The prime factorization of 48 is ...
48 = 2⁴ · 3
Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for the constant of integration.)
The integration by part is [tex]\frac{x^{3}In x }{3} -\frac{x^{3} }{9} +C[/tex] with indicated choices of u and dv.
What is integration by parts?
The method Integration by Parts is known to be a special method of integration that is often useful. In calculus, definite integrals are referred to as the integral with limits such as upper and lower limits. It is also possible to derive the formula of integration by parts with limits.
Given: ∫ [tex]x^{2} In x dx[/tex] ; [tex]u=In x[/tex] ; [tex]dv=x^{2} dx[/tex]
Consider [tex]u=In x[/tex] and [tex]dv=x^{2} dx[/tex]
⇒ [tex]u=In x[/tex] ⇒ [tex]dv=x^{2} dx[/tex]
⇒ [tex]du= \frac{1}{x} dx[/tex] ⇒ [tex]v=\frac{x^{3} }{3}[/tex]
Now, apply integration by parts to solve the integral
∫ u dv = uv - ∫ v du
the antiderivative of [tex]x^{n}[/tex][tex]=\frac{x^{n+1} }{n+1}[/tex] and the derivative of In x = [tex]\frac{1}{x}[/tex] .
⇒ ∫ [tex]x^{2} In x dx =[/tex][tex]\frac{x^{3} In x}{3} -\frac{x^{3} }{3} .\frac{1}{x} dx[/tex]
= [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{2} }{3} dx[/tex]
= [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{3} }{9} +C[/tex]
Hence, the final integration is [tex]\frac{x^{3}In x }{3}[/tex] [tex]-\frac{x^{3} }{9} +C[/tex]
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Im so confused with this question 21≥3(a-7)+9
Answer:
I got you!
a ≤ 11
For more info, look at the steps in the attached image!
Step-by-step explanation:
Answer:
a ≥11
Step-by-step explanation:
[tex]21 \geqslant 3a - 21 + 9 \\ 21 \geqslant 3a - 12 \\ 21 + 12 \geqslant 3a - 12 + 12 \\ 33 \geqslant 3a \\ 3a \leqslant 33 \\ a \geqslant 11[/tex]
Last year students planted 8 tomato plants and 16 pepper plants in a school garden
Answer:
whats the question
Answer:
What are you asking?
Peter opened up a savings account by making an initial deposit. After the initial deposit, Peter has been adding
$50 to his savings account each month. If after 8 months Peter has a total of $600 in his savings account, what
was the amount of his initial deposit?
Answer:
$200
Step-by-step explanation:
so if peter has been depositing 50 each month for 8 months then you would just do 50x8 which equals 400 and 600-400=200
alice and bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for alice. if they play 6 rounds, in how many ways can alice win or draw exactly three times? (answer: 300)
AS per the permutation concept, the number of ways can Alice win or draw exactly three times is 240
Permutation:
In probability, permutation refers the arrangement of objects in a definite order.
Given,
Alice and Bob are playing a game in which there are several rounds and each round can be a win, a loss, or a draw for Alice.
Here we need to find the number of ways can Alice win or draw exactly three times, if they play 6 rounds.
While we looking into the given question, we know that,
Total number of games = 6
Possible values = 3 ( win, loss, or draw)
Here we need to find the probability of winning 3 times, it can be calculated by using the permutation as,
=> 6! / (6 - 3)!
=> 6! / 3!
=> 120
Similarly, the the probability of draw 3 times, it can be calculated by using the permutation as,
=> 6!/ (6 - 3)!
=> 120
So, the number of ways can Alice win or draw exactly three times is
=> 120 + 120 = 240
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Please find out the slope and the y-intercept and put it in the y=mx+b
Answer:
y = [tex]\frac{3}{4}[/tex]x + 2
Step-by-step explanation:
To find the slope we will use the slope formula of y2-y1/x2-x1.
Our two y values are 2 and -1.
Our two x values are 0 and 4.
2 - (-1) = 3
0 - 4 = -4
3/4 = [tex]\frac{3}{4}[/tex]
y = [tex]\frac{3}{4}[/tex]x + 2
calculate the expected return for stocks a and b. (do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)b.calculate the standard deviation for stocks a and b.
a) The expected return for stocks a and b is 13.56% and 20.02% respectively.
b) The standard deviation for stocks a and b are 8.32% and 32.60%.
a) Expected return = Probability of recession × Return during recession + Probability of normal × Return during normal + Probability of boom × Return during boom
Expected return for stock A = 0.21 × 0.04 + 0.61 × 0.12 + 0.18 × 0.30
The expected return for stock A = 0.1356
The expected return for stock A = 13.56%
Expected return for stock B = 0.21 × (-0.41) + 0.61 × 0.31 + 0.18 × 0.54
The expected return for stock B = 0.2002
The expected return for stock B = 20.02%
b) Standard deviation of stock = √{Probability(Recession) × (Rate during recession - expected rate )² + Probability(Normal)(Rate during normal - expected return)² + Probability(Boom) × (Rate in boom - Expected return)²}
Standard deviation of stock A = √[(0.21 × (0.04-0.1356)² + 0.61 × (0.12 - 0.1356)² + 0.18 × (0.30-0.1356)²)]
The standard deviation of stock A = 0.0832
The standard deviation of stock A = 8.32
Standard deviation of stock B = √(0.21 × (-0.41-0.2002)² + 0.61(0.31 - 0.2002)² + 0.18 × (0.54-0.2002)²)]
The standard deviation of stock B = 0.3260
The standard deviation of stock B = 32.60%
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the given pattern continues. write down the nth term of the sequence suggested by the pattern 1/18, 2/19, 3/20, 4/21
The nth term of the pattern is (1+n)/(18+n)
What is a sequence?
succession is the act of doing something after another. successional order: a list of books organized by title. a running or interconnected sequence: a series of sonnets. something that happens after; a following event; a result; or a repercussion. In contrast to a set, the order of the components in a sequence does important, and the same elements may occur more than once at various positions. A series can officially be described as a function from natural numbers.
We are given a sequence
1/18, 2/19, 3/20, 4/21
As we can see the second term is (1+1)/(18+1)
Third term is (1+2)/(18+2)
Hence the n th term of the sequence can be given as (1+n)/(18+n)
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suppose that based on a random sample, a 95% confidence interval for the mean hours slept (per day) among graduate students was found to be (6.5, 6.9). what is the margin of error of this confidence interval? responses
The margin of error for the confidence interval (6.5, 6.9) is 0.2 , the correct option is (c) .
In the question ,
it is given that ,
the 95% confidence interval for mean hours slept in the graduate students is (6.5, 6.9) ,
we have to find the margin of error ,
we know that the formula for the margin of error is
= (upper limit of confidence interval - lower limit )/2
From the given interval ,
we see that ,
upper limit of confidence interval = 6.9
lower limit of confidence interval = 6.5
Substituting the above value in margin of error formula ,
we get ,
margin of error = (6.9 - 6.5)/2
= 0.4/2
= 0.2
Therefore , the margin of error is 0.2 .
The given question is incomplete , the complete question is
Suppose that based on a random sample, a 95% confidence interval for the mean hours slept (per day) among graduate students was found to be (6.5, 6.9). What is the margin of error of this confidence interval? responses
(a) 6.7
(b) 0.4
(c) 0.2
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A flagpole casts a 20-foot shadow at the
same time Lexi casts a 5-foot shadow. If
Lexi is 5'9", find the height of the flagpole.
Answer:
20-foot shadow
Step-by-step explanation:
What value does each equation need to be multiplied by in order to eliminate the x-terms?
Equation 1: 6x − 5y = -4
Equation 2: 4x + 2y = 28
Please help
You need to find what x is equal to for each equation, so you can sub why x is equal to in the place I'd x to eliminate the variable
1. 6x-5y=-4
6x=5y-4
X=5/6y-2/3
2. 4x+2y=28
4x=-2y+28
X=-1/2y+7
Hope this helps!
g please find out how many numbers must be selected from the set 1, 2, 3, 4, 5, 6, 7, 8 to guarantee that at least one pair of those numbers add up to 9 ?
To guarantee that at least on pair o the numbers adds up to 9, you must select at least 3 numbers from the set by combination
1. First, select any two numbers from the set.
2. Now, calculate their sum.
3. If the sum of the two numbers is not equal to 9, select a third number from the set.
4. Determine the three numbers' sum.
5. If the sum of the three numbers is still not equal to 9, select a fourth number from the set and calculate the sum.
6. Repeat this process until the sum of the selected numbers is equal to 9 by combination
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Your team has contracted to design and build a 500 ft, square-based, open-top, rectangular steal holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible.
For dimensions of x =10 and y=5 for the base and height that will make the tank weight as little as possible.
Here we are given the information of a square-based, open-top, rectangular steel holding tank, so here the tank is in the shape of a cuboid and we know the formula for :
volume = x*y*z, as here it is a square base, so the volume will be
volume = x²*y, where x and y are the dimension of the base and height
So for the given reason,
=>x²*y = 500
=> y = 500/x²
Again, the surface area formula will be
S=x²+4xy, substituting the value of y in this question
=>S=x²+4x(500/x²)
=>S=x²+2000/x
Differentiating the above formula with respect to x, we get
=>2x-2000/x²=0
=>2x³= 2000
=>x³= 1000
=>x =10
so the substituting the x values of x in the equation y , we get
y = 500/x²
=>y = 5
so the dimensions are x= 10 and y=5
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PLEASE HELP ME ASAP !!!!!!!!!!!!!!!!!!!
The triangles in the diagram indicates that ΔABD is an isosceles triangle, therefore;∠2 ≅ ∠1
The two-column method can be used to prove that the angle m∠BAC > m∠C as follows;
Statement [tex]{}[/tex] Reasons
1. BC > BA [tex]{}[/tex] 1. Given
2. BA ≅ BD [tex]{}[/tex] 2. Given
3. ΔABD is an isosceles Δ[tex]{}[/tex] 3. Definition of isosceles triangle
4. ∠1 ≅ ∠2 [tex]{}[/tex] 4. Base ∠s of isosceles triangle ΔABD
5. ∠1 = ∠2 [tex]{}[/tex] 5. Definition of congruency
6. ∠1 = ∠3 + ∠C [tex]{}[/tex] 6. Exterior angle theorem
7. ∠2 = ∠3 + ∠C [tex]{}[/tex] 7. Substitution property
8. ∠2 - ∠3 = ∠C [tex]{}[/tex] 8. Subtraction property
9. ∠2 > ∠C [tex]{}[/tex] 9. Definition
What is an isosceles triangle?An isosceles triangle is a triangle that have a pair of congruent sides and one pair of congruent angles.
The reasons in the above two-columns used to prove m∠BAC > m∠C are as follows;
Isosceles triangle ΔABD
The triangle ΔABD that have side AB congruent to side BD is an isosceles triangle by definition of an isosceles triangle.
The base angles of an isosceles triangle that are angles opposite congruent sides in a triangle are also congruent.
Definition of congruency
A geometric figure is congruent to another figure if their measurements are the same.
Exterior angle theorem
The exterior angle of a triangle theorem states that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Substitution property
The substitution property of equality states that if a quantity a is equal to another quantity b then a can be substituted by b in expressions and equations without changing their value.
Subtraction property
The subtraction property of equality states that if the same quantity is subtracted from both sides of an equation, then the new amount obtained are also equal
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guillermo bought textbooks and notebooks at the bookstore . the number of textbooks was three more than twice the number of notebook .he hought seven textbooks . how many notebooks did he buy?
2 notebooks
Step-by-step explanation:
the variables I'm gonna use are t for textbooks and n for notebooks
t = (n•2)+3 (two times the notebooks then add 3)
now we'll plug in the amount of notebooks we have so t=7
7=(n•2)+3
we can subtract 3 from each side that leaves us with
4=n•2
then divide by 2
2=n
Guillermo bought 2 notebooks
find the open intervals on which the function f(x)axbxc, a0, is increasing and decreasing. describe the reasoning behind your answer.
The intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a
Given that,
We have to find the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing.
We know that,
Take the function equation,
f(x)=ax² + bx + c
The derivative of the function of x is
f'(x)=ax+b
So, f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
Then we can say
f'(x) > 0 , when b > 0 and a < 0
2ax + b < 0
2ax < - b
x<-b/2a
Now,
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
x>-b/2a
Therefore, the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a.
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Find an equation in point-slope form for the line having the slope m=2 and containing the point (8,2)
Write code using the range function to add up the series 15, 20, 25, 30,. 50 and print the resulting sum each step along the way.
The range function to add up the series is 15 ,35 ,60 ,90, 125,165,210 ,260
What is a python function?
A unit of code with a name is referred to as a function in Python. We utilize functions anytime we need to repeat a process repeatedly without writing the same code.
Given: Series 15, 20, 25, 30,.. 50
Program (Pascal ABC) and Result:
Program:
Var i, Summ : integer;
begin
i : = 15;
Summ : = 15;
While i <= 50 do
begin
WriteIn ( ' ' , Summ) ;
i : = i + 5 ;
Summ : = Summ + i ;
end ;
end.
Result : 15 ,35 ,60 ,90, 125,165,210 ,260
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In VWX, X ≈ W, WX = 17 and VW = 16. Find XV. HELPPPPP
Answer:
XV = 16
Step-by-step explanation:
Triangle VWX is an isosceles triangle. Since the base angles are the same, the sides opposite the angle are also the same. See image. They gave VW so XV is the same as VW.
There are 4 tomato plants, 8 lettuce plants, and 2 cucumber plants in Jill's garden.
a. What is the ratio of tomato plants to lettuce plants?
b. What is the ratio of lettuce plants to cucumber plants?
a) The ratio of tomato plants to lettuce plants:
4 ÷ 8 ⇒ 1 ÷ 2b) The ratio of lettuce plants to cucumber plants:
8 ÷ 2 ⇒ 4 ÷ 1For daniel's lemonade recipe, 4 lemons are required to make 16 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade?.
Using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."
The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
So, we know that:
Lemons required to make 16 cups of lemonade: 4 lemons
Then, the rate of lemons being used in lemonade per cup:
4/16
1/4
Therefore, using mathematical operations we can conclude that the rate of lemons being used in a cup of lemonade is 1/4.
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Find the value of the product (4a2 + 3b) (4a2+36) at a = 1, b = 2.
The final value of the product = 292
According to the given equation -
= (4a2+3b)x(4a2+36)
multiply the whole equation-
= 16a4+144+12a2b+108
as we can see that the values of a and b are given 1 and 2 respectively,
so putting the values of a and b in the equation we get -
= 16(1)4+144+12(1)2(2)+108
= 292
The product of the following equation will be = 292
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Solve negative 5 times y plus seven thirds times y equals negative 5 minus eight thirds times y minus 4 for y.
Infinite solutions
No solution
y = −14
y = 0
NEED A ANSWER ASAP!!!!!!!
Answer:
None of the Above?
Step-by-step explanation:
1.) If we put this into words, we would get -5y+7/3y=-5-8/3y-4
2.) By moving all y terms to one side, we get -5y + 7/3y + 8/3y = -5 - 4
3.) By simplifying, you would get -4 2/3y = -9.
4.) If you divide both sides by -4 2/3, you would get that y = -9 * - 3/14 = 27/14
Enter the equivalent decimal.
9/9/25
Answer:
Step-by-step explanation:
.36
What fraction is a hour in 20 mins
20 minutes is [tex]1/3^{rd}[/tex] of an hour
mr. eaton is ordering sandwiches for a school picnic. the best deal is the 6-foot-long sandwich, which is cut into 4-inch-long pieces. mr. eaton expects 90 people to attend the picnic. he thinks each person will eat 2 pieces. how many 6-foot-long sandwiches should he order?
He should order 10 sandwiches of 6 foot long so, as to make sure that everyone will eat 2 pieces.
What is Conversion ?We need to convert between the units in order to ensure the accuracy and to prevent measurement misinterpretation. For example, we do not measure the pencil's length in kilometres. In this situation, one must convert from kilometres (km) to centimetres (cm) (cm). In most cases, multiplicative conversion factors are used to convert one unit to another of the same quantity. Let's see how to change the length and mass units.
1 Feet = 12 Inches
So, 6 Foot = 72 inches
The Length of sandwich- piece is 4 inch
So, when we convert 6 foot long sandwich into 4 inch,
Then we get number of piece is = 72/4 = 18
From 6 foot long sandwich we get 18 pieces of 4 inch long sub.
Now, Total people who will attend picnic is 40
and each people will eat 2 pieces.
It means total number of piece required = 2 (90) = 180
Mr. eaton required 180 pieces of sandwiches.
Number of sandwiches = 180 / 1.8 = 10
He should order 10 sandwiches of 6 foot long.
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what is the product of 5/6 x 4 2/3
Answer:
35/9
Step-by-step explanation:
Carlos wants to buy some new video games. Each game he buys costs him $36. Is the relationship between the number of games Carlos buys and the total price proportional?
The relationship between the number of games Carlos buys and the total price is proportional.
What is a proportional relationship?
A proportional relationship exists between two or more variables if they move in the same direction. If one of the variables increases, the other variable increases.
As the number of games that are bought increases, the total price paid also increases. This means that the relationship is proportional.
The formula that is used to represent proportional relationship is:
T = kg
Where:
T = total price k = constant g = number of games boughtT = $36g
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how can i tell if an equation is linear/non linear without using a graph?
Answer:
Using an Equation
Simplify the equation as closely as possible to the form of y = mx + b. Check to see if your equation has exponents. If it has exponents, it is nonlinear. If your equation has no exponents, it is linear.
Answer:
Step-by-step explanation:
To be linear it must have the form y=mx+b.IN a linear equation the variables are shown in first degree and terms with products of variables are absent .