find derivative of y= sin x sin 3x​

12x² + 102x² + 114x - 84

Answer:

Solution Given:

1st term: 6x²+39x-21

Taking common

3(2x²+13x-7)

doing middle term factorization

3(2x²+14x-x-7)

3(2x(x+7)-1(x+7))

3(x+7)(2x-1)

2nd term: 6x²+54x+84

taking common

6(x²+9x+14)

doing middle term factorization

6(x²+7x+2x+14)

6(x(x+7)+2(x+7))

2*3(x+7)(x+2)

Now

Least common multiple = 2*3(x+7)(2x-1)(x+2)

2(x+2)(6x²+39x-21)

(2x+4)(6x²+39x-21)

2x(6x²+39x-21)+4(6x² + 39x-21)

12x³+78x² - 42x+4(6x² + 39x-21)

12x³+78x² - 42x + 24x² + 156x-84

12x³ + 102x²-42x + 156x - 84

12x² + 102x² + 114x - 84

Answer:

[tex]12x^3+102x^2+114x-84[/tex]

Step-by-step explanation:

Given polynomials:

[tex]\begin{cases} 6x^2+39x-21\\6x^2+54x+84 \end{cases}[/tex]

Factor the polynomials:

Polynomial 1

[tex]\implies 6x^2+39x-21[/tex]

[tex]\implies 3(2x^2+13x-7)[/tex]

[tex]\implies 3(2x^2+14x-x-7)[/tex]

[tex]\implies 3[2x(x+7)-1(x+7)][/tex]

[tex]\implies 3(2x-1)(x+7)[/tex]

Polynomial 2

[tex]\implies 6x^2+54x+84[/tex]

[tex]\implies 6(x^2+9x+14)[/tex]

[tex]\implies 6(x^2+7x+2x+14)[/tex]

[tex]\implies 6[x(x+7)+2(x+7)][/tex]

[tex]\implies 6(x+2)(x+7)[/tex]

[tex]\implies 2 \cdot 3(x+2)(x+7)[/tex]

The lowest common multiplier (LCM) of two polynomials a and b is the smallest multiplier that is divisible by both a and b.

Therefore, the LCM of the two polynomials is:

[tex]\implies 2 \cdot 3(x+7)(x+2)(2x-1)[/tex]

[tex]\implies (6x^2+54x+84)(2x-1)[/tex]

[tex]\implies 12x^3+108x^2+168x-6x^2-54x-84[/tex]

[tex]\implies 12x^3+102x^2+114x-84[/tex]

Step-by-step explanation:

I assume this means exactly one wrong number in the 10 attempts.

the probability to get a wrong number is 0.15 (15%).

therefore, the probability to get a correct number is

1 - 0.15 = 0.85

in 10 tries to get 1 wrong number (and 9 correct numbers) looks like this :

0.15×0.85⁹ = 0.034742542...

this would be the probability to e.g. get a wrong number at the first attempt, and all other attempts are correct.

how many different constellations can we have that way ?

10.

because the wrong number could be given at any of the 10 attempts.

so, the probability to get exactly 1 wrong answer is

10×0.15×0.85⁹ = 0.34742542... ≈ 35%

now, if the question is about the probability to get at least one number wrong, then we can say this is the opposite of the probability to get all 10 numbers correctly.

the probability to get all 10 numbers correctly is

0.85¹⁰ = 0.196874404... ≈ 20%

and therefore, the probability to get at least 1 number wrong is

1 - 0.196874404... = 0.803125596... ≈ 80%

FYI :

this would be, of course, also the result of we did it the complex way :

the sum of the probabilities of

exactly 1 number wrong

exactly 2 numbers wrong

...

exactly 9 numbers wrong

all 10 numbers wrong

and for each of the cases of n wrong numbers the probability is

(10! / (n! × (10-n)!)) × 0.15^n × 0.85^(10-n)

this represents the constellation of n numbers wrong (and 10-n numbers right) multiplied by the number of possible combinations of picking n numbers out of 10.

and again, all this summed up (1 <= n <= 10) is the same as

0.803125596...

The probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Now, Let q = probability of giving out wrong number = 15 % = 0.15

And, p = probability of not giving out wrong number = 1 - q

= 1 - 0.15 = 0.75

Hence, For a binomial probability,

P(x) = ⁿCₓ qˣ pⁿ⁻ˣ.

With n = 10 and x = 1, the probability of getting a number wrong

P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹

          = 10(0.15)(0.75)⁹

           = 1.5(0.0751)

           = 0.1126

           = 11.26 %

b. At most one wrong is P(x ≤ 1) = P(0) + P(1)

= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹

= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹

= 0.0563 + 0.01126

= 0.06756

= 6.756 %

≅ 6.76 %

Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.

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The scouts eat 51 bags of chips on their trip

The given parameters are:

Boxes = 9

Bag = 10 chips

2 full boxes of potato chips and 3 bags left over.

This represents:

Potato chips = 2 * 10 + 3

Potato chips = 23 i.e. 23 bags potato chips are left over

1 fewer box of nacho chips than potato chips, with no bags left over

This represents

Nacho chips = (2 - 1) * 10

Nacho chips = 10 i.e. 10 bags of nacho chips are left over

The loose bags of potato chips is 3.

So, we have:

Barbecue chips = 2 * 3 bags

Barbecue chips = 6 bags

At this point, we have:

The total number of bags left over is

Total = 23 + 10 + 6

Total = 39

The number of bags eaten is:

Eaten = 9 * 10 - 39

Evaluate

Eaten = 51

Hence, the scouts eat 51 bags of chips on their trip

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The best sampling strategy would be a stratified sample.

Samples may be classified as:

For this problem, the 4 different brands of the recorders must be considered, hence the buyers should be divided into groups, and a proportion of each group should be sampled, hence a stratified sample should be used.

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Answer:

.00476

Step-by-step explanation:

Answer:

15u+15x-20

Step-by-step explanation:

* = multiply or times

We have to multiply everything in the parenthesis by -5, meaning:

-5*-3u = 15u

-5*-3x = 15x

-5*4 = -20

Put it all together: 15u+15x-20

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the distributive formula?}[/tex]

[tex]\mathsf{a(b + c)}\\\\\mathsf{= a(b) + a(c)}\\\\\mathsf{= ab + ac}[/tex]

[tex]\large\textbf{Extended distributive property formula:}[/tex]

[tex]\mathsf{a(b + c + d)}\\\\\mathsf{= a(b) + a(c) + a(d)}\\\\\mathsf{= ab + ac + ad}[/tex]

[tex]\huge\textbf{What are we solving for?}[/tex]

[tex]\large\textbf{It seems like you have the extended distributive property}[/tex]

[tex]\mathsf{-5(-3u - 3x + 4)}[/tex]

[tex]\huge\textbf{What are the steps to solving for the}\\\\\huge\textbf{given equation?}[/tex]

[tex]\mathsf{-5(-3u - 3x + 4)}\\\\\mathsf{= -5(-3u) - 5(-3x) - 5(4)}\\\\\mathsf{= 15u + 15x - 20}[/tex]

[tex]\huge\textbf{What is the answer to the equation?}[/tex]

[tex]\huge\boxed{\frak{{= 15\mathsf{u} + 15\mathsf{x} - 20}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: 470.4 N

Step-by-step explanation:

Concept:

1 kg on Earth = 9.8 N

Given information:

Mass = 48 kg

Find the weight on Earth

1 kg = 9.8 N

48 kg = 48 * 9.8 = [tex]\Large\boxed{470.4N\\}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The solution for the given expression is 16.

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

First, you apply the Power Rules - Power for  [tex](\frac{2^2x^2y}{xy^3} )^2}[/tex]. For this rule, you should repeat the base and multiply the exponents. Thus, the result will be:[tex]\frac{16x^4y^2}{x^2y^6}[/tex].

After that, you should apply the  Power Rules - Division . For this rule, you should repeat the base and  subctract the exponents. Thus, the result will be:[tex]\frac{16x^2}{y^4}[/tex].

Now, you should replace the variable x by 4 and the variable y by 2. Thus, the result will be:[tex]\frac{16*4^2}{2^4}=\frac{16*16}{16} =16*1=16[/tex]

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Step-by-step explanation:

that question is fundamentally wrong.

"appropriate" completely depends on the situation and circumstances.

if we are dealing with a weight that a human can feel, lift and distinguish from other weights without any special tool, then we are usually using kg. because then we humans can "connect" with the case, and deal with every day numbers.

if we are dealing with tiny little quantities like dosages of substances in a pill or other medication, then milligram is more than "appropriate".

because then, as humans, we are still dealing with numbers we can understand. like tens or hundreds.

if we kept kg in such situations, we would have to deal with numbers like 0.000008 kg vs. 0.000021 kg, where we could not see the magnitude of difference right away.

Answer:

[tex]\displaystyle{1.) \ \ f(x) = \dfrac{2}{3}x-8}\\\\\displaystyle{2.) \ \ f(x) = -4x+11}[/tex]

Step-by-step explanation:

- Range is a set of all y-values in a set of coordinate points.

A linear equation or function always have range equal to set of real number because you can substitute f(x) as any numbers and you'll still be able to solve for x-variable.

An quadratic equation or function may have range equal to set of positive real number or negative real number depending whether if the coefficient of x² is in positive or negative but consider this:

Suppose we have f(x) = x², f(x) cannot be negative number because that'd make the equation not real. Therefore, a quadratic function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range.

For an exponential function, it's same as quadratic equation. It depends whether if a base is in negative or positive. You can consider like this:

Suppose we have [tex]\displaystyle{f(x)=2^x}[/tex], f(x) cannot be negative number because there are no x-values that make the equation true. Therefore, an exponential function does not have [tex]\displaystyle{\mathbb{R}}[/tex] range as well.

Answer:

D

Step-by-step explanation:

When f(x) is equal to 0, x=4.

Step-by-step explanation:

x = number of heavy equipment operators

y = number of general laborers

x + y = 37 (37 people were hired)

out if this we get e.g.

x = 37 - y

124x + 82y = 3916 (daily rate for each role, in total 3916)

now we use the first equation in the second :

124(37 - y) + 82y = 3916

4588 - 124y + 82y = 3916

672 - 42y = 0

672 = 42y

y = 16

x = 37 - y = 37 - 16 = 21

21 heavy equipment operators were hired.

16 general laborers were hired.

Answer:

  (b)  (x -10)(x +10)

Step-by-step explanation:

The factorization of the difference of squares is a special form:

  a² -b² = (a -b)(a +b)

Your expression is recognizable as the difference of squares:

  x² -100 = x -10²

Using the above form, the factorization is ...

  = (x -10)(x +10) . . . . . . . . matches the second choice

Answer:

BED =57°

Step-by-step explanation:

angle at circumference standing on the same arc

Answer:

$140

Step-by-step explanation:

interest = 8x5 = 40

total = time + interest

total = 100 + 40 = $140

The two integers are are mathematically given as

x=3.70

y=13.7

Generally, the equation for the two integers is mathematically given as

x + 10 = y

1/x + 2/y = 2/3

Substitute

1/x + 2/x+10 = 2/3

Multiply by 3

3/x + 6/x + 10 = 2

Multiply by x

2 + 6x/x + 10 = 2x

Multiply by x + 3

2(x + 10) + 6x = 2x(x + 3)

2x+20+6x=2x^2+6x

-2x^2+2x+20=0

x=3.70

hence y

x + 10 = y

3.70+ 10 = y

y=13.7

In conclusion,  the two integers are

x=3.70

y=13.7

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Answer: Ans. Option c As the price of basket in England is $15, which is less than the world

The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

The function is given as:

f(x)=−2x3+x2−4x+1 is divided by x+3.

Set the divisor to 0

x + 3 = 0

Solve for x

x = -3

Calculate f(-3)

f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1

Evaluate the expression

f(-3)= 76

Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76

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Answer:

x ≤ 4

Step-by-step explanation:

the solid dot at 4 indicates that x can equal 4

the arrow points to the left indicating values less than 4 , then

x ≤ 4

Answer:

23370 students live with in 500 miles of the university.

Step-by-step explanation:

large university students =24000

selected students = 750

surveyed students =120 lives far away from university.

students live with in 500mile=?

750-120=630

24000-630=23370

(730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15. This can be obtained by using formula for confidence interval and using statistical table for values.

The formula for finding the confidence interval for population variance is:

[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]

where n is the size of the sample, (n - 1) is the degrees of freedom, s is the standard deviation, α is the significance level.

Here it is given that,

α/2 = 0.02/2 = 0.01

1 - α/2 = 1 - 0.01 = 0.99

For (n - 1) degrees of freedom,

[tex]\chi^{2}_{\frac{\alpha}{2} }[/tex] = 29.141 , and  [tex]\chi^{2}_{1-\frac{\alpha}{2} }[/tex] = 4.660 (Using statistical table)

Using the formula we get,

[tex]\frac{(n-1)s^{2} }{\chi^{2} _{\frac{\alpha }{2} } } < \sigma^{2} < \frac{(n-1)s^{2} }{\chi^{2} _{1-\frac{\alpha }{2} } }[/tex]

[tex]\frac{(14)39^{2} }{29.141} < \sigma^{2} < \frac{(14)39^{2} }{4.660}[/tex]

[tex]730.72 < \sigma^{2} < 4569.53[/tex]

The confidence interval for the population variance is (730.72, 4569.53)

Hence (730.72, 4569.53) is the confidence interval for the population variance σ² given that c = 0.98, s = 39 and n = 15.

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Answer:

1 and 4

Step-by-step explanation:

x-1 = 0

x = 1

x^2 - 5x + 4

(x-4)(x-1) = 0

x can't be 1 or 4

Answer:  1 and 4

Step-by-step explanation:

1. To find excluded values, we need to make the denominator equal to zero.

x² - 5x + 4 = 0

2. Then we need to find the x the product of them was 4, but they add up to -5, which are -4 and -1. We get:

(x - 4)(x - 1) = 0

x - 4 = 0          x - 1 = 0

    x = 4               x = 1

These two numbers will make the denominator equal to 0, the denominator cannot be equal to 0, so they are excluded numbers.

Step-by-step explanation:

An acute angle is an angle less or equal to 90 degrees.

let the other angle be x.

x + 36 = 90

grouping like terms

X = 90 - 36

X = 54 degrees

Answer:

54

Step-by-step explanation:

= ∠A + ∠B + ∠C = 180o … [∵sum of the angles of a triangle is 180]

or 180 = 36 + 90 + ∠C

C=54

Answer:

The ratio is 3 : 2.

Step-by-step explanation:

42 cm : 28 cm

= 21 : 14 (Divide both sides by 2)

= 3 : 2 (Divide both sides by 7)

The ratio between the length and width of the rectangle is 3:2.

We have,

The concept used here is the concept of ratio.

In mathematics, a ratio is a comparison of two quantities.

It expresses how many times one quantity contains another or how many times it is greater or smaller than the other quantity.

The ratio between the length and width of the rectangle can be found by dividing the length by the width:

Ratio = Length / Width

= 42 cm / 28 cm

= 7 x 6 / 7 x 4

Cancel out the common factor.

= 6/4

= 2 x 3 / 2 x 2

Cancel out the common factor.

= 3/2

Thus,

The ratio between the length and width of the rectangle is 3:2.

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Answer:

Perimeter = 72 meters

Step-by-step explanation:

Let L be the length and W the width of the rectangle

We have the following relationship

L = 2W + 6

Area of the rectangle = LW = (2W+6)W   by substituting for L

Area =

2W² + 6W =260 ==> 2W² + 6W -260 = 0

Dividing both sides by 2 yields

W² + 3W -130 = 0

This is a quadratic equation which can be solved using the formula for the roots of the equation ie the values of W which satisfy the above equation

However in this case it is easier to solve by factorization

W² + 3W -130  

= W² + 13W - 10W - 130
= W(W + 13) -10(W + 13)

= (W+13)(W-10) = 0

This means W is either -13 or W = 10

Since W cannot be negative, we get W = 10 and

L = 2(10) + 6 = 26

Perimeter of a rectangle is given by

2(L + W) = 2(26 + 10) = 2(36) = 72  Answer

Answer:

R=i

Step-by-step explanation:

R=i×100÷p×t

r=30105×100÷6570×12

r=3010500÷78840

r=38.18

Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6

Probability is the likelihood or chance that an event will occur. Mathematically, the formula for calculating probability is expressed as:

Probability = expected outcome/Total outcome

Sample space is the total number of element in a given set of probability. The subsets if this sets are called event

Let the six children the couple plan to have ne 1, 2, 3, 4, 5,6 such that the sample space will be:

S = {1, 2, 3, 4, 5, 6}

Since there are 6 elements in the given set, hence the possible outcome in the sample space is 6

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Answer:

Step-by-step explanation:

To find the value of t, isolate it on one side of the equation.

[tex]\sf{\dfrac{3}{2}+t=\dfrac{1}{2}}[/tex]

First, you subtract by 3/2 from both sides.

[tex]\Longrightarrow: \sf{\dfrac{3}{2}+t-\dfrac{3}{2}=\dfrac{1}{2}-\dfrac{3}{2}}[/tex]

Solve.

1/2-3/2

1-3/2

1-3=-2

-2/2

Divide.

-2/2=-1

[tex]\Longrightarrow: \boxed{\sf{t=-1}}[/tex]

Therefore, the solution is t=-1, which is our answer.

I hope this helps, let me know if you have any questions.

STEP BY STEP EXPLANATION;

1.To solve the equation,the least common multiple of the denominators must be found.

LCM=2

Therefore,

3/2 +t =1/2

2.Each term must be multiplied by the LCM.

i.e

2(3/2)+2(t)=2(1/2)

3+2t=1

2t=1-3  ( subtracting 3 from each side of the equation)

2t=1-3

2t/2=-2/2 (dividing both sides of the equation by the co-efficient of t)

t=-1