If g(x) + x cos(g(x)) = x3, find g ′(0).

Answer:

x-7

Step-by-step explanation:

Whatever her current age is, she was 7 years younger 7 years ago. Because her current age is undefined, it must remain an equation.

a) The probability of exactly 21 particles arrive in a particular one minute period is 0.0426

b) The probability of exactly one particle arrives in a particular one second period is 0.2042

Probability is the ratio of the total number of conceivable outcomes to the number of outcomes in an exhaustive set of equally likely alternatives that result in a particular occurrence.

The probability is given by:

P(X=x) = (e⁻ⁿ nˣ)/x!

a)  The probability of exactly 21 particles arrive in a particular one minute period is given by :

P(X=21) = (e⁻16 × 16²¹)/21!

P(X=21) = (2.176746853×10¹⁸)/51090942171709440000

P(X=21) = 0.0426

b) The probability of exactly one particle arrives in a particular one second period is :

1 min = 16 particles

1 sec = 16/60 particles

1 sec = 0.2667 particles

P(X=1) = (e⁻⁽¹⁶/⁶⁰⁾ × (16/60)¹)/1!

P(X=1) = 0.2042

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Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.

Answer:

y = 3x² + 30x + 27

Step-by-step explanation:

Formula: Ax + By = C

y = 3 (x + 9) (x + 1)

y = 3x + 27x + 3x + 7

y = 3x² + 30x + 27

Answer:

look at the photo..............

Answer:

It's 6552

Step-by-step explanation:

We'll beat 1 x 13 × 8 x 9 x 7

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

In the equation, we will need to calculate the maximum amount of money Marian can spend on the house.

We can calculate the maximum amount of money Marian can spend on a house by multiplying her monthly income by the number of months she would want to save.

Marian earns $4,100.00 per month

Suppose Marian wants  to save for  x months,  then the maximum amount that she can spend on the house is:

4100  *   x    +  21390

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

Hope this helps!

Answer: 4x3=12 5x3=15 6x3=18 7x3=21 This is multiplied by 3

Step-by-step explanation:

If the value of a in the quadratic function f f(x) = ax² + bx + c is 1/2, the function will; open up and have a minimum

We are told that the value of a in the quadratic function f(x) = ax² + bx + c is 1/2. Thus, the quadratic function is expressed as;

f(x) = ¹/₂x² + bx + c

If the signs of the coefficients of x² and x are equal, then the graph axis of symmetry will be on the left hand side of the y-axis. This is because the axis of symmetry is expressed as; x = -b/2a

Now, if the sign of the constant term is positive, then it means that the y-intercept is positive. This is because the y-intercept is the value at which x = 0 which is f(0)

Now, if the discriminant is negative, then it means that the quadratic graph will not touch the x-axis. This is because the graph touches x-axis when f(x) = 0, but the solution will be imaginary and as such it doesn't touch on the graph.

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Complete question is;

If the value of a in the quadratic function f(x) = ax² + bx + c is 1/2 the function will:

open down and have a minimum

open up and have a maximum

open down and have a maximum

open up and have a minimum

Answer:

59

Step-by-step explanation:

6 plus 4 equals 8 plus 9

Answer:

12 - x= 3

x + 3y = 27

4y + 10 = 34

1/3xy = 18

Step-by-step explanation:

evaluating where x = 9 and y = 6

12 - x

12 - 9 = 3

x + 3y

9 + 3(6) = 9 + 18 = 27

4y + 10

4(6) + 10 = 24 + 10 = 34

1/3xy

1/3(9* 6 ) = 54 / 3 = 18

The values of the expressions are given below:-

12 - x= 3

x + 3y = 27

4y + 10 = 34

1/3xy = 18

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Evaluating where x = 9 and y = 6

1) 12 - x

12 - 9 = 3

2) x + 3y

9 + 3(6) = 9 + 18 = 27

3) 4y + 10

4(6) + 10 = 24 + 10 = 34

4) 1/3xy

1/3(9* 6 ) = 54 / 3 = 18

Therefore, the values of the different expressions are solved above.

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to get the y-intercept of any equation we can simply set x = 0 and solve for "y", so let's do so

\(y=6\left( x-\cfrac{1}{2} \right)(x+3)\implies \stackrel{\textit{setting x = 0}}{y=6\left( 0-\cfrac{1}{2} \right)(0+3)}\implies y=6\left( -\cfrac{1}{2} \right)(3) \\\\\\ y=(-3)(3)\implies y=-9\hspace{12em} {\Large \begin{array}{llll} \stackrel{y-intercept}{(0~~,~~-9)} \end{array}}\)

Answer:

2.221992

Step-by-step explanation:

can i have the crown pls ૮ ♡ﻌ♡ა

Answer:

2.221

Step-by-step explanation:

The probability of randomly forming the word "woord logic" is:Probability = 1 / (10! / (2!))

To calculate the probability of forming the word "woord logic" by randomly arranging the letters l, o, g, i, c, we need to consider the total number of possible arrangements and the number of arrangements that result in the desired word.

The word "woord logic" has 10 letters in total. Among these letters, there are 2 o's and the remaining letters appear only once.

The total number of possible arrangements is given by the factorial of the total number of letters:

Total arrangements = 10!

However, since the letter "o" appears twice, we need to divide by the factorial of the number of repeated letters:

Total arrangements = 10! / (2!)

To calculate the number of arrangements that result in "woord logic," we consider that the arrangement of "woord logic" is unique and distinct. Thus, there is only one arrangement that matches the desired word.Simplifying this expression would yield the exact probability.

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Answers:

a = -6/37

b = -1/37

============================================================

Explanation:

Let's start things off by computing the derivatives we'll need

\(y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\\)

Apply substitution to get

\(y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right) + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x) + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x) + \left(a - 6b\right)\cos(x) = \sin(x)\\\\\)

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a  -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

(a) The probability that a customer does not shop downtown is 70%

(b) The probability that a customer shops in the downtown area or in a local mall is 75%

(c) The probability that he will shop downtown is 25%

(d) The probability that a customer shopped at the local mall, given that he shopped downtown is 50%

1. Probability that a customer does not shop downtown:
Since 30% of people shopped downtown, the probability that a customer does not shop downtown is :

100% - 30% = 70%.

2. Probability that a customer shops in the downtown area or in a local mall:
Since 15% of people shopped both in the downtown area and at the local mall, we can use the formula for the probability of the union of two events:

P(A∪B) = P(A) + P(B) - P(A∩B).
P(A∪B) = 60% (local mall) + 30% (downtown) - 15% (both)
P(A∪B) = 75%
3. Given that a customer shopped in a local mall, the probability that he will shop downtown:
This is asking for the conditional probability P(B|A), where A is shopping in the local mall and B is shopping downtown.
P(B|A) = P(A∩B) / P(A) = 15% (both) / 60% (local mall) = 0.25 or 25%.
4. Probability that a customer shopped at the local mall, given that he shopped downtown:
This is asking for the conditional probability P(A|B),

where A is shopping in the local mall and B is shopping downtown.
P(A|B) = P(A∩B) / P(B) = 15% (both) / 30% (downtown) = 0.5 or 50%.

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Answer:

Vertex = (-1, 2)  

Maximum

Step-by-step explanation:  

The middle point of the graph is at x coordinate -1 and the point is at the top while the graph slopes down so it is a maximum point and not a minimum point.

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Answer: 203, 204, 205

Step-by-step explanation:

Let's say the number is x.

So the three consecutive numbers are: x, x + 1, and x+ 2

3x + 3 = 612

3x = 609

x = 203

Plug in x.

203, 204, and 205

Answer: 203, 204, 205

Step-by-step explanation:

Consecutive numbers are numbers that are right next to each other. An example would be 1,2,3 or 67,68,69. Since this problem is asking for three consecutive numbers where the sum is equal to 612, we need to find the numbers that will be greater than 200.

Since we know that the sum is 612, we know that the numbers will be in the 2 hundreds. All we need to do is find 3 numbers that equal to 12.

3+4+5=12

Now that we have the three numbers, let's add 200.

203+204+205=612

Therefore, the three numbers are 203, 204, 205.

If he gives ninety-three centimeters of the rope to his brother, Ravi has 132 centimeters of rope left.

Two and one-fourth meters of rope can be written as 2.25 meters. Since 1 meter is equal to 100 centimeters, we can convert 2.25 meters to centimeters by multiplying it by 100, giving us 225 centimeters.

If Ravi gives 93 centimeters of the rope to his brother, we can subtract it from the original length to find how much rope he has left.

225 cm - 93 cm = 132 cm

In general, to convert between meters and centimeters, you can multiply the number of meters by 100 to get the length in centimeters. To convert between centimeters and meters, you can divide the number of centimeters by 100 to get the length in meters.

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Answer:

-1 because you would go over down because it’s negative then move back up to negitave 3 and then right 2 would give you -1

Step-by-step explanation:

System of equations

• Equation 1

• Equation 2

Procedure

Solving the system by substitution.

0. Isolating ,x ,from equation 2:

2. Replacing the expression of x obtained in equation 1:

3. Simplifying:

4. Finally, we replace this value in the isolated expression of x and solve it:

Answer: (3, 2)

1. The difference in the distance of Jupiter from the sun than Mercury will be 4.816.

2. The difference in the distance of Neptune from the sun than Mars will be

3. The greatest distance between Earth and Uranus is Uranus.

4. The greatest distance between Venus and Saturn is Saturn

From the information, the average distance from the sun to each planets have been given. The difference in the distance of Jupiter from the sun than Mercury will be:

= 5.203 - 0.387

= 4.816

The difference in the distance of Jupiter from the sun than Mars will be:

= 30.07 - 1.524

= 28.546

The greatest distance between Earth and Uranus is Uranus and the greatest distance between Venus and Saturn is that of Saturn.

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\(m\angle ABC=24^{\circ}\) by the inscribed angle theorem.

Answer:= 24

Step-by-step explanation:

by the inscribed angle theorem.

Answer:

b,c

Step-by-step explanation:

b is written  in the written form properly and  is is extended using the right place values

Answer:

x=10,y=120

Step-by-step explanation:

3x-30=60 CDA

3x=30

x=10

again,

y+60=180 straight line

y = 120

Answer:

Below

Step-by-step explanation:

Secant is defined as  1/cos

   so sec = 1 / (sqrt (3) /2 )  = 2/\(\sqrt{3}\) = 2 \(\sqrt{3}\) / 3

Answer:

2/root3

Step-by-step explanation:

the function is a reciprocal

The solution is x^3+15x^2+75x+109

From the question, we have

(x+5)^3-16-0

=(x^3+3x^2⋅5+3x⋅5^2+5^3 )-16

=(x^3+3⋅5x^2+3x⋅25+125)-16

=(x^3+15x^2+3⋅25x+125)-16

=(x^3+15x^2+75x+125)-16

=x^3+15x^2+75x+125-16

=x^3+15x^2+75x+109

The solution is x^3+15x^2+75x+109

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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