Given the function f(x) = x + 3 and g(x) = a + bx2. If gf(x) = 6x2 + 36x + 56,
find the value of a and of b.​

The probability of not drawing a blue marble from a bag containing four blue and three white marbles is calculated as the number of white marbles divided by the total number of marbles, resulting in 3/7. The marble is replaced after the first draw, so the total number of marbles stays the same for the second draw.

The question is about calculating the probability of not drawing a blue marble from a bag which contains a certain number of blue and white marbles. The probability of an event is calculated as:

P(event) = The number of ways the event can occur / Total number of outcomes

In the given example, there are four blue marbles and three white marbles in the bag, making a total of seven marbles. If James draws one marble, the probability of not drawing a blue marble i.e., drawing a white marble, is the number of white marbles divided by the total number of marbles. Thus:

P(Not Blue) = P(White) = Number of White Marbles / Total Marbles = 3 / 7

It's important to note that the probability is calculated this way because James replaces the marble after drawing it the first time. So, the total number of marbles remains the same for the second draw, keeping the probability the same. This concept is related to probability in Geometric Distribution scenarios.

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The probability is 9/12 which can simplify to D: 3/4

When you draw a marble, there are 12 possible marbles you can draw. There are 3 blue marbles and 9 non-blue marbles. Therefore, the probability of drawing a non-blue marble is 9/12. This can simplify to 3/4.

Another way to solve this problem is to use the concept of complements. The complement of event A is the event that does not occur. In this case, the event A is drawing a blue marble and the complement of event A is not drawing a blue marble.

The probability of event A is 1 - the probability of the complement of event A.

The probability of not drawing a blue marble is 1 - 3/12 = 9/12 = 3/4.

Therefore, the answer is D: 3/4.

ANSWER

The resulting parabola in vertex form is:

[tex](x - 4) = 4( {y + 3)}^{2}[/tex]

EXPLANATION

The original equation of the parabola is given as

[tex]x = 4 {y}^{2} [/tex]

This parabola has its vertex at the origin.

If the graph of this parabola is shifted four units right and three units down, then the new equation is:

[tex](x - 4) = 4( {y + 3)}^{2}[/tex]

This the equation of the transformed parabola.

Its vertex is now at (4,-3).

Answer:

(x-4)=4(y+3)^2

Step-by-step explanation:

Answer:

x = 5/7

Step-by-step explanation:

(7^x)^4) = 7^2 * 7^3 / 7^3x

1. Simplify the expression

(7^x)^4) becomes 7^4x

7^2 * 7^3 becomes 7^5

7^5/7^3x becomes 7^5 - 7^3x

Your new equation: 7^4x = 7^5 - 7^3x

2. Since the bases(7) are the same set the exponents equal to each other

4x = 5 - 3x

3. Combine like terms

4x + 3x = 5

7x = 5

4. Divide both sides by 7 to get x by itself

x = 5/7

Answer:

x = [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

[tex](7^{x})^{4}=\frac{7^{2}\times 7^{3}}{7^{3x}}[/tex]

[tex](7^{x})^{4}=\frac{7^{(2+3)}}{7^{3x}}[/tex] [Since [tex]a^{b}\times a^{c}=a^{b+c}[/tex] ]

[tex]7^{4x}=\frac{7^{5}}{7^{3x}}[/tex] [since [tex](a^{b})^{c}=a^{bc}[/tex] ]

[tex]7^{4x}={7^{5}\times{7^{-3x}}[/tex]  [ [tex]\frac{1}{a}=a^{-1}[/tex] ]

[tex]7^{4x}=7^{(5-3x)}[/tex]

4x = 5 - 3x

[tex]4x+3x=5[/tex] ⇒ 7x = 5

x = [tex]\frac{5}{7}[/tex]

[tex]2x(a-2b)+3y(2b-a)=2x(a-2b)-3y(a-2b)=(2x-3y)(a-2b)[/tex]

Answer:

C) (6,2)

Step-by-step explanation:

To solve the system of equations, solve one of the equations for y, then plug the result into the other equation to get the value of x. When you get x, substitute it back into one of the original equations to find the value of y, which is 2.

To find the solution to the system of linear equations, we can use the method of substitution or elimination. Let's use the method of substitution and solve for x and y. The solution is (6, 2).

To find the solution to the system of linear equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From the second equation, we can isolate y by subtracting 5x from both sides: y = 32 - 5x

Substitute this expression for y in the first equation: 3x - 2(32 - 5x) = 14

Simplify and solve for x: 3x - 64 + 10x = 14, 13x - 64 = 14, 13x = 78, x = 6

Now substitute the value of x back into one of the original equations and solve for y: 5(6) + y = 32, 30 + y = 32, y = 2

Therefore, the solution to the system of linear equations is x = 6 and y = 2, which can be written as (6, 2).

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Answer:

6x^6y^8z^6

Step-by-step explanation:

(3x^3y^4z^4)(2x^3y^4z^2)

= 6x^(3+3) y^(4+4) z^(4+2)

= 6x^6y^8z^6

Answer:

The simplified form of given expression is [tex]6x^6y^8z^6[/tex].

Step-by-step explanation:

The given expression is

[tex](3x^3y^4z^4)(2x^3y^4z^2)[/tex]

On multiplication of constants, we get

[tex](3\times 2)(x^3y^4z^4)(x^3y^4z^2)[/tex]

[tex]6(x^3y^4z^4)(x^3y^4z^2)[/tex]

It can be written as

[tex]6(x^3x^3)(y^4y^4)(z^4z^2)[/tex]

Using product property of exponent, we get

[tex]6x^{3+3}y^{4+4}z^{4+2}[/tex]          [tex][\becuase a^ma^n=a^{m+n}][/tex]

[tex]6x^6y^8z^6[/tex]

Therefore the simplified form of given expression is [tex]6x^6y^8z^6[/tex].

Answer:

B, D

Step-by-step explanation:

The types of angles are:

Right angle

Straight angle

Complementary angles

Options A< B< and D are the correct answer.

We have,

The right angle is a 90-degree angle.

When two angles add up to 180 degrees, the angles are called complementary angles.

A straight angle is a 180-degree angle.

Now,

From the figure,

∠JLK = 90

∠KLM = 90

These are 90-degree angles.

And,

∠JLM = ∠JLK + ∠JLM

= 90 + 90

= 180

This can be termed as:

- straight angle (∠JLM)

- complementary angle (∠JLK and ∠JLM)

Thus,

The types of angles are:

Right angle

Straight angle

Complementary angles

Learn more about angles here:

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In order to solve this equation you must first simplify, then you re-range the terms, then solve.

[tex]12(x + -360) = 120[/tex]

[tex]12(-360 + x) = 120[/tex]

[tex](-360 \times 12 + x \times 12) = 120[/tex]

[tex](-4320 + 12x) = 120[/tex]

[tex]+ 4320+ 4320[/tex]

[tex]12x = 4440[/tex]

[tex]4440 \div 12 = 370[/tex]

[tex]x = 370[/tex]

Which means your answer is "x=370."

Hope this helps.

Answer:

C. 3.2

If GF = 3.2 a possible measure of TS is 3.2

Answer:

C

Step-by-step explanation:

Answer:

In Step 4, Daryl multiplied 12 and 100 incorrectly.

Step-by-step explanation:

12 x 100 = 1200, not 120

Answer:

x = -10

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 8 from both sides:

x + 8 (-8) = -2 (-8)

x = -2 - 8

Simplify. Combine like terms:

x = -2 - 8

x = -10

x = -10 is your answer

~

Answer:

x = -10

Step-by-step explanation:

x+8 = -2

          +

 -8    -8

__________

x=          -10

Answer:

-4w^2- 8w

Step-by-step explanation:

-4w(w+2), use distributive property, (-4w x w)+(-4w x 2)= (-4w^2)+-8w

The formula for compound interest is: A = P(1 +r/n)^nt

Where P is the principal ( starting value)

r is the interest rate

n is the number of compounds

and t is the number of years.

Fill in the letters with the given information:

A = 400(1+0.04/12)^(12*11)

A = 400(1.00333)^132

A = 400*1.551557

A = 620.63

The answer is $620.63

Answer: y = 4(x + 1) - 2

Step-by-step explanation:

" increases by 4 for every x + 1" means the slope is 4 and the value inside the parentheses with x is +1

"crosses the y-axis at -2" means the y-intercept is -2

Input those values into the formula: y = m(x) + b    where

Step-by-step answer:

Assuming the equation is y=-x+k,

where k is a constant, such as 5, pi, 10/7, etc.

then the slope is the coefficient of the term containing x, namely

-1  (since -x is a shorthand for (-1)*x ).

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut point with the "y" axis

We have, according to the data provided, that the line is of the form:

[tex]y = -x + b[/tex]

That means that the slope is -1.

ANswer:

[tex]m = -1[/tex]

Answer:

∴ (g ο f)(2) = 216  

Step-by-step explanation:

* Lets revise at first the meaning of f of g (composite function)

- A composite function is a function that depends on another function

- A composite function is created when one function is substituted into

 another function  

- Example:

# (g ο f)(x) is the composite function that is formed when f(x) is  

 substituted for x in g(x).

* Now lets solve the problem

∵ f(x) = 2x + 2

∵ g(x) = x³

- We need to find (g ο f)(2), so we will substitute x by f(x) in g(x)

∴ (g ο f)(x) = (2x + 2)³

- Now substitute x by 2

∴ (g ο f)(2) = [2(2) + 2]³ = [4 + 2]³ = [6]³ = 216

* * (g ο f)(2) = 216  

# Another way

- We can find f(2) at first and then substitute the x by the answer

 in g(x)

∵ f(x) = 2x + 2

∴ f(2) = 2(2) + 2 = 4 + 2 = 6

∵ g(x) = x³

∴ g(6) = (6)³ = 216

* (g ο f)(2) = 216  

Answer:

-261.85

Step-by-step explanation:

If she lives with probability .996, it cost her - 334.  

If she dies with probability .004, the value is 71150 - 334  

.996*(-334) + .001*(71150 - 334) = -261.85

Final answer:

Sam's expected value from the life insurance policy is calculated by considering both the probability of survival and death. The probability-adjusted outcomes are summed, showing that Sam would, on average, lose $105 with this policy over a year.

Explanation:

Sam is interested in purchasing a single year life insurance policy that has a value of $25,700. According to actuarial tables, the probability of Sam surviving the next year is 0.99. We calculate the expected value of the life insurance policy for him by taking into account both outcomes: survival and death within the next year.

The expected value (EV) is calculated by multiplying the value of the potential outcomes by their respective probabilities and then summing these products together.

To calculate Sam's expected value from the life insurance policy, we account for both scenarios:

If Sam survives (which has a 0.99 probability), he receives nothing from the policy and only loses the premium paid, which is $362.00.

If Sam dies (which has a 0.01 probability), his estate receives the policy worth of $25,700.

Expected Value = (Probability of Surviving) * (Value if Survive) + (Probability of Dying) * (Value if Die) - (Cost of Insurance Premium)

So for Sam's case, it would be:

Expected Value = (0.99 * $0) + (0.01 * $25,700) - $362

Expected Value = ($0) + ($257) - $362

Expected Value = $257 - $362

Expected Value = -$105

Therefore, the expected value of the life insurance policy for Sam is a negative $105, meaning that, on average, Sam would lose $105 over the one year term of the policy.

Answer

Step-by-step explanation:

If you deposit money, your bank account shows it as +3

3 degrees below zero = - 3 o F which is darn cold.

3 floors below ground level = - 3 floors below ground level

3 feet above sea level = +3 feet

3 degrees about 0 = + 3

3 dollars lost = -3 dollars.

Answer:

x=2/5 or

x=0.4

Step-by-step explanation:

Answer:

[tex]\frac{2}{5}[/tex] or 0.4.

Step-by-step explanation:

[tex]\frac{2}{3}[/tex]+[tex]\frac{1x}{3}[/tex]=2x

[tex]\frac{2}{3}[/tex]=2x-[tex]\frac{1x}{3}[/tex]

[tex]\frac{2}{3}[/tex]=[tex]\frac{6x-x}{3}[/tex]

[tex]\frac{2}{3}[/tex]=[tex]\frac{5x}{3}[/tex]

x=[tex]\frac{2}{5}[/tex]

or

x=0.4

Answer:

D. Farming and medicine

Step-by-step explanation:

When they arrived in America, the Europeans found a populated territory. Its inhabitants, however, were ignorant of writing and left no documents about their own past.  The knowledge we have about the native tribes of the 16th century is mainly based on accounts and descriptions of European travelers who were here at the time.

These travelers report that the Indians survived from hunting, fishing, extractivism, and had great advances in agriculture.  They settled in the valleys of navigable rivers, where fertile lands existed. They stayed in place for about four years. After the natural resources of the place had been exhausted, they migrated to another region with better resources for agriculture.  Travelers also report that the Indians were advancing in medicine, which was based on medicinal plants, but effective for many health problems.

Answer:

“Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.”

“Look at the graph of the relationship. Count the number of units up and the number of units to the right one must move to arrive at the next point on the graph. Write these two numbers as a fraction.”

“Look at the graph of the relationship. Find the x-value of the point that corresponds to y = 2. That value is the unit rate.”

“Look at the graph of the relationship. Find two points which have y-values that are one unit apart. The unit rate is the difference in the corresponding x-values.”

Step-by-step explanation:

Answer: A. “Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.”

There would be 2 intercepts, the X and the Y.

To find the X intercept, set Y to 0 and solve for x.

To find the Y intercept, set X to 0 and solve for y.

x -2y = 2

x-2(0) = 2

x-0 = 2

x = 2

0 -2y = 2

-2y=2

y = 2/-2

y = -1

The x intercept is (2,0)

The y intercept is (0,-1)

Not sure what format you need the answer in, you may only need x = 2 and y = -1.

Answer:

2401 • x^2

Step-by-step explanation:

7 √x7 √x • 7 √x • 7

=(7)^4  (√x)^4

=2401 • x^2

Answer:

Step-by-step explanation:

Remote interior angles are defined as the two angles that are inside the triangle and opposite from the exterior angle.

In this case, [tex]\angle 3[/tex] and [tex]\angle 2[/tex] are remote interior angles of 1, because they are opposite to it, which is the exterior angle.

Therefore, the right choices are A and B.

The remote interior angles of 1 are -90°, -60°, and -30°.

Remote interior angles are angles formed by two lines and a transversal where the interior angles are not adjacent or consecutive. In the given options, the remote interior angles of 1 are:

These angles are considered remote interior angles because they are not adjacent or consecutive to 1°.

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Answer:

We know that in a scalene triangle all sides (and angles) are different.

Let

z = length of longest side

y =  length of second side

x =  length of shortest side

The perimeter of the scalene triangle is 60 cm

x + y + z = 60 cm

The length of the longest side is 4 times that of the shortest side.

z = 4*x

We are left with the following equations

x + y + z = 60

z = 4*x

We will test every affirmation

Number one

The value of x can equal 40.

FALSE. The longest side cannot be greater than the perimeter.

Number two

The longest side can equal 30 cm

z = 30 cm

x = 30/4 cm = 7.5 cm

y = [60 -30 - 7.5] cm  = 22.5 cm

This statement is TRUE

Number three

The shortest side can equal 7 cm

x = 7 cm

z = 4*7 cm = 28 cm

y = [60 -28 - 7] cm  = 25 cm

This statement is TRUE

Number four

The value of x can equal 25

x = 25 cm

z = 4*25 cm = 100 cm

The longest side cannot be greater than the perimeter.

This statement is FALSE

Number five

The shortest side can equal 5

x = 5 cm

z = 4*5 cm = 20 cm

y = [60 -20 - 5] cm  = 35 cm

This statement is FALSE. The second side (y) cannot be greater than the longest side (z).

Answer:

The distance between (3,5) (-2,7) is 29 blocks or squares

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

Scales-No equal sides

Isosceles- 2 Equal

Equilateral-

Right-90 degree

Obtuse- Obtuse Angle

Answer:

a = 6, b = 4, c = 2

Step-by-step explanation

see attached

Answer:

The required values are a=6, b=4 and c=2.

Step-by-step explanation:

The given expression is

[tex]\sqrt{x^{12}y^{9}z^{5}}=(x^{a}y^bz^c)\sqrt{yz}[/tex]          .... (1)

It can be written as

[tex]\sqrt{x^{12}\cdot y^{8}\cdot y\cdot z^{4}\cdot z}[/tex]

[tex]\sqrt{x^{12}\cdot y^{8}\cdot z^{4}\cdot y\cdot z}[/tex]

[tex]\sqrt{(x^{6})^2\cdot (y^{4})^2\cdot (z^{2})^2\cdot y\cdot z}[/tex]     [tex][\because (a^m)^n=a^{mn}][/tex]

[tex]\sqrt{(x^{6}y^4z^2)^2\cdot y\cdot z}[/tex]          [tex][\because a^xb^x=(ab)^x][/tex]

[tex](x^{6}y^4z^2)\sqrt{yz}[/tex]               .... (2)       [tex][\because \sqrt{x^2}=x][/tex]

From (1) and (2), we get

[tex]a=6,b=4,c=2[/tex]

Therefore the required values are a=6, b=4 and c=2.

Answer:

y=8*4^x

Step-by-step explanation:

Let the exponential function be of the form y=A*B^x

We want to find constant A and B.

So I'm going to use (1,32) giving me 32=A*B

I'm going to use (4,2048) giving me 2048=A*B^4

2048/32=64

A*B^4/A*B=B^3

So If you divide the equation 2048=A*B^4 by 32=A*B

we get 64=B^3

which gives us B=4

Since 32=A*B and B=4 then A=8

So the answer is y=8*4^x