The graph of the function f(x) = -(x + 3)(x - 1) is shown
below.
-6 -4-2
6
A
2
-2
-4
-6-
y
2
4
6
→
X
What is true about the domain and range of the function?
The domain is all real numbers less than or equal to
4, and the range is all real numbers such that -3 ≤x≤
1.
The domain is all real numbers such that -3 ≤ x ≤ 1,
and the range is all real numbers less than or equal to
4.
The domain is all real numbers, and the range is all
real numbers less than or equal to 4.
The domain is all real numbers less than or equal to
4, and the range is all real numbers.

The probability that the next two offspring will both be girls is 1/3.

To find P both children are girls

A: Event that both children are girls

A: {MM} and B: {MF, FM, MM} →→ P (A ∩∩ B) = {MM}

Probability that both are males, if we know one is a female =P(A/B)=P(A∩B)/P(B)

(P(A∩B)P(B))

Given S = {MM, MF, FM, FF}, we can see that: P (A) = 1414; P (B) = 3434; P (A ∩∩ B) = 1414

Therefore,

P(B/A)=P(A∩B)/P(A) = (1/4)/(3/4)=1/3.

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Answer:

12*10^4 lbs.

Step-by-step explanation:

This is the correct answer because you have to count using scientific notation by seeing the amount of times the decimal point has moved to the left which makes it positive.

The total weight of the two animals is 12x10⁴ lbs if the approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

The approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.

The total weight = 5.36 x 10⁴ + 6.2 x 10⁴

The total weight = (5.36+ 6.2)10⁴

The total weight = 11.56x10⁴

Or

The total weight = 12x10⁴ lbs

Thus, the total weight of the two animals is 12x10⁴ lbs if the approximate weights of the two animals are 5.36 x 10⁴ lbs. and 6.2 x 10⁴ lbs.

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Answer: Sym. Prop. of ≅

Step-by-step explanation:

no explanation

Answer: they have the same absolute value

Step-by-step explanation: -6 and positie 6 are both 6 units from zero

The value of the sales tax on the computer is 62 dollars and 93 cents.

Any number or a ratio which is expressed in terms of a fraction of 100 is known as a percentage.

Here, we are given that the price of a computer is 899 dollars.

The sales tax on the computer is 7%.

Thus, the value of the sales tax on the computer will be,

7% of 899

= 7/100 * 899

= 62.93

Thus, the sales tax on the computer comes out to be 62.93 dollars.

In 62.93 dollars, we can see that we have 62 complete dollars, plus 0.93 more dollars left.

0.93 dollars = 93 cents

Therefore, the sales tax on the computer is 62 dollars and 93 cents.

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Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The y coordinate tells us when we are going up for down.  So the rule would be (x, y + 5)  So, the x coordinate stays the same and the y goes up 5.

(1,2)  The 2 is the y coordinate. It will increase by 5 and become (1,7)

(3,2)  The 2 is the y coordinate.  It will increase by 5 and become (3,7)

(3,4)  The 4 is the y coordinate.  It will increase by 5 and become (3,9)

(1,4) The 4 is the y coordinate.  It will increase by 5 and become (1,9)

Answer:

3524442532 or 3.524442532 * 10 ^9

Step-by-step explanation:

The total change in the stock market from the beginning of the day to the end of the day is -49.75.

According to the statement

We have to find that the change in the stock market.

So, For this purpose, we know that the

The change is the difference between the current price and the last trade of the previous day.

From the given information:

At the beginning of the day the stock market goes up 30 1/2 points and At

The end of the day the stock market goes down 80 1/4 points.

Then

Stock market goes up through points = 30 1/2 = 61/2

Stock market goes down through points = 80 1/4 = 321/4

Then

Change = +61/2 - 321/4

Change  = +30.5 - 80.25

Change = -49.75

So, The total change in the stock market from the beginning of the day to the end of the day is -49.75.

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Answer: 22 degrees

Step-by-step explanation:

Since the angle 180° is in the third quadrant, subtract 180° from 202°.

Answer: 136, 625,532,413

Step-by-step explanation:

The simplified equation of the given Arithmetic  function (f- g)(x) is:

-x² + 3x + 7.

Arithmetic is a fundamental branch of mathematics that studies the properties of classical operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Addition, subtraction, multiplication, as well as division are the four basic arithmetic operations. There are additional arithmetic operators, such as exponentiation, modulus operations, increment, decrement, and so on. * - The operator for multiplication. As a result, the And operator is not an arithmetic operator.

Given:

f(x) = 3x+1

g(x)=x²-6

(f- g)(x) =

Substituting the value we get:

(f - g)(x) = (3x + 1) - (x² - 6)

= 3x + 1 - x² + 6

= -x² + 3x + 7

The simplified equation of the given Arithmetic  function (f- g)(x) is = -x² + 3x + 7.

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First of all let me tell you UPSC is the body which conducts the civil services examination in our country. To prepare for the civil services you must know it is the highest offered post by the government to an citizen of India.

You have many subjects in order to complete the syllabus of civil services.

The examination takes place in two parts. In the first part there are multiple choice questions and in the second part there are subjective questions which must be answered in a descriptive format.

The candidate also has to face interview after clearing both the examinations.

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Using translation concepts, the first graph is the correct one.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the function y = |x - 1| is a shift right of 1 unit of the function y = |x|. For the inequality, all the values above the line, including the line, are marked.

The graph of |x - 1| is triangular positive, with vertex at x = 1, hence the first graph is the correct one.

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hi

a ( b +c) =  a*b +a*c

here a = -3  

        b = -4x

        c = +5

so :  

-3 ( -4x +5)  =  -3*-4x + -3* 5  

                   =  -12x + (-15)

                  = -12x -15

as I cannot add  -12x and  -15   ( they are two differents sort of figures )

so it's done

Answer:

12x - 15

Step-by-step explanation:

What you need to do for this is -3 · -4x + -3 · 5 = 12x+(-15). Which simplifies to 12x - 15.

Answer:

5.462 is the answer because if 1.088 ounces is pineapple juice then 6.55-1.088 is the rest.

Step-by-step explanation:

-ln ( 1 - x/y - x) = c is a bernoulli equation. xdy/dx-(1 x)y=xy^2.

What is a differential equations explain?

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f(x) (x)

[tex]\frac{-1}{y} = u[/tex]

[tex]\frac{y'}{y^{2} } = u'[/tex]

[tex]xy' - ( 1 + x )y = xy^{2}[/tex]

[tex]x\frac{y'}{y^{2} } - ( 1 + x ) \frac{1}{y} = x[/tex]

xu' + ( 1 + x )u = x

xu' + u + ux = x

 xu = s

u + xu' = s'

s' + s = x

s - x  =t

s' - 1 = t'

t' + 1 + t = 0

dt/dx = - ( 1 + t)

-∫ [tex]\frac{dt}{1 + t} =[/tex]  ∫dx

-ln ( 1+ t ) = x + c

-in ( 1 + s - x ) = x + c

-ln ( 1 + xu - x ) = x + c

-ln ( 1 - x/y - x) = c

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a) The times that the projectile will reach a height of 20.8 ft are 3.643 seconds and 0.357 seconds, respectively.

b) The projectile will hit the ground 4 seconds later of its launch.

Herein we find a physical model known as projectile motion, which considers that the motion of the object is created solely by gravity and effects from Earth's rotation and air viscosity are neglected. The height of the projectile is represented by the following quadratic equation:

s = - 16 · t² + 64 · t

In the first part, we need to determine when the projectile will reach a height of 20.8 feet:

20.8 = - 16 · t² + 64 · t

16 · t² - 64 · t + 20.8 = 0

(t - 3.643) · (t - 0.357) = 0

The times that the projectile will reach a height of 20.8 ft are 3.643 seconds and 0.357 seconds, respectively.

And the time when the projectile hits the ground is found by solving on t in the following quadratic equation:

- 16 · t² + 64 · t = 0

- 16 · t · (t + 4) = 0

The projectile will hit the ground 4 seconds later of its launch.

In the part (a) a dot symbol was omitted, correct part is: Find the time(s) that the projectile will (a) reach a height of 20.8 ft.

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The domain of the graph in set builder notation is; x ≤ -2 or x ≥ 1

The range of the graph in set builder notation is; y ≥ -2 or y ≥ 1

Domain refers to the set of all possible input values and Range refers to the set of all possible output values generated by the function.

Now, from the given graph, we can see that there are two lines. Thus;

Domain of left graph line is; x ≤ -2

Domain of right graph line is; x ≥ 1

Thus, the domain of the graph in set builder notation is;

x ≤ -2 or x ≥ 1

Similarly, the range is as follows;

Range of the left graph line is; y ≥ 1

Range of the right graph line is; y ≥ -2

Thus, the range of the graph in set builder notation is;

y ≥ -2 or y ≥ 1

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The y values from:

1. ₋6

2. ₋3

3. 0

4. 3

Given the x values and y value as y = 3x

1. when x = ₋2 then y = 3x

y = 3(₋2)

y = ₋6

2. when x = ₋1 then y = 3x

y = 3(₋1)

y = ₋3

3. when x = 0 then y = 3x

y = 3(0)

y = 0

4. when x = 1 then y = 3x

y = 3(1)

y = 3

therefore we get the points as (₋2 , ₋6) (₋1 , ₋3) (0,0) (1 , 3).The graph is pltted and attached.

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Hello, the answer is 194.04.

First, you would convert 140% to a decimal which is 1.4. Next, you would multiply 1.4 x 138.6 = 194.04.

So the steps to a percentage multiplied to a number are:

1. Convert the percentage to a decimal.

2. Multiply the decimal by the number.

3. You get the answer.

For the functions in this problem, we have that:

a) The function is exponential, and the table is completed as follows.

b) The function is linear, and the table is completed as follows.

c) The function is exponential and given by:

[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

A function with initial value 1 and where the y-value is computed by multiplied the previous y-value by 5, as in item a, is an exponential function with parameters a = 1 and b = 5, hence the rule is:

[tex]y = 5^x[/tex]

Then:

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

A proportional relationship is also classified as linear with a intercept of 0. For item b, since each y-value is the x-value multiplied by 5, the rule is:

y = 5x.

Hence the table is:

For item c, when x changes by 1, y is always multiplied by 1/2, and due to the multiplication, the function is exponential and given by:

[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]

The -16 is because when x = 0, y = -16.

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Answer:  C, I think is correct

The function which represents how much money Janet makes each day according to the task content is; (8j/2) - 150.

Given;

According to the given parameters; the total amount of money made from honey sale is; $8 × j = $8j.

Hence, since she splits the money with her mom, it follows that her personal income is; $8j/2.

Ultimately, after paying $150 a day for the booth rental, the amount made by Janet is; $8j/2 - $150.

The required function, f(j) is therefore;

f(j) = (8j/2) - 150.

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(a) The third term of the sequence is 19.

(b) The term-to-term rule of the new sequence is "subtract 13 and then divide by 6".

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Answer: we have to divide a

This should be done by using a long division method.

multiply x+1 by

Therefore the quotient is

The remainder is 0

Step-by-step explanation: hope this helps

Answer:

2x^3-7x/2 -1

Step-by-step explanation

Let me know if this is an option. I was unsure if the x was the letter x or the multiplication symbol. Thanks, let me know

The general solution for the given equation is 40°+120°n.

The period of g(x) is π.

The range of f(x) is [-1, 1].

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Answer:

w = [tex]\frac{p -2l}{2}[/tex]

Step-by-step explanation:

p = 2l + 2w  Subtract 2l from both sides of the equation

p - 2l = 2p  Divide both sides by 2

[tex]\frac{p -2l}{2}[/tex] = w

y = \frac{-x}{2 } + \frac{1}{4}  + ce^-{2x} is  the general solution to the differential equation put the problem in standard form.

What is meant by integrating factor?

x² + 2xy + x . dy/dx = 0

x dy/dx  + 2xy = [tex]- x^{v}[/tex]

[tex]\frac{dy}{dx} =+ 2y = -x[/tex]

[tex]left u(x) = e^{\int\limits^_ {} } 2dx = e^{2x}[/tex]

integration  factor p(x) = u(x) = [tex]e^{2x}[/tex]

Now ,multiply  [tex]e^{2x}[/tex] both sides

[tex]e^{2x} ( \frac{dy}{dx} + 2y ) = -x . e^{2x}[/tex]

[tex]e^{2x} \frac{dy}{dx} + 2e^{2x} . y = -x e^{2x}[/tex]

[tex]\frac{d}{dx} (e^{2x} .y) = -x e^{2x}[/tex]

integrate both sides

∫ [tex]d .( e^{2x} .y )[/tex]     = ∫[tex]-xe^{2x} .dx[/tex]

[tex]e^{2x} .y = -\frac{e^{2x}}{2} . x + \frac{e^{2x}}{4} + c[/tex]

[tex]y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x}[/tex]

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The complete question is -

Find the general solution to the differential equation 2 dy X+ + 2xy + x dx = 0 Put the problem in standard form. Find the integrating factor, p(x) = 2x - Find y(x) Use C as the unknown constant.