Two urns contain blue and green balls. urn 1 contains 3 blue balls and 4 green balls. urn 2 contains 7 blue balls and 16 green balls.
1. if a blue ball is drawn, what is the probability that it came from urn 2?
2. if a green ball is drawn, what is the probability that it came from urn 1?

Step-by-step explanation:

Answer: B

[tex]f(x) = 7x-2[/tex] and        [tex]g(x) = \frac{x+2}{7}[/tex]

How to solve:

check if the composite functions of f(x) and g(x) are equal to x (this means they are inverses)

f[g(x)] = x

g[f(x)] = x

Step-by-step explanation:

Checking A.

[tex]f(x) = \frac{5}{x} -2[/tex]

[tex]g(x) = \frac{x+2}{5}[/tex]

[tex]f(g(x)) = f(\frac{x+2}{5} ) = \frac{5}{\frac{x+2}{5} } -2[/tex]

This does not equal x, so we know these are not inverses

Checking B.

[tex]f(x) = 7x-2[/tex]

[tex]g(x) = \frac{x+2}{7}[/tex]

[tex]f(g(x)) = f(\frac{x+2}{7} ) = 7(\frac{x+2}{7}) - 2 = x+2-2 = x[/tex]

[tex]g(f(x)) = g(7x-2) = \frac{7x-2 + 2}{7} = \frac{7x}{7} = x[/tex]

since both f(g(x)) = x and g(f(x)) = x, we can determine that they are inverses of each other.

The slope of the line is 745, the y-intercept of the line is 500 and the equation of the line is y = 745x + 500

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]

We have points on the graph:

(2, 1990) (5, 4225) (9, 7205)

The slope can be found using two points:

[tex]\rm m =\dfrac{4225-1990}{5-2}\\[/tex]

m = 745

The line can be written as:

y = mx + c

y = 745x + c

Plug point (2, 1990)

1990 = 745x + c

1990 = 745(2) + c

c = 500

y = 745x + 500

The pace of increase in money per month is represented by the slope.

Every month, the sum increases by $745.

The initial quantity of money when the business opened is represented by the y-intercept.

The company began with a $500 investment.

Thus, the slope of the line is 745, the y-intercept of the line is 500 and the equation of the line is y = 745x + 500

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Answer:

L=10y

Step-by-step explanation:

1cm=10mm

Hence, the length in millimeters will be 10 times the value in cm.

Answer:

5 units

Step-by-step explanation:

Use Pythagorean Theorem

x = 4 units     y = 3 units

4^2 + 3^2 = L^2

16 + 9 = L^2

L = 5

Answer:

5 units

Step-by-step explanation:

By the Pythagorean theorem:

c² = a² + b²

c = length of the line

a = 4

b = 3

Then:

c² = 4² + 3²

c² = 16 + 9

c² = 25

√c² = √25

c = 5

Answer:

b=204

Step-by-step explanation:

The law of sine states that: [tex]\frac{SinA}{a} =\frac{SinB}{b} =\frac{SinC}{c}[/tex]

We know that a triangle has 180° total, so we can subtract the two angle measures we know to find the third angle: [tex]180-90-41=49[/tex]°.

Using these two things, we can come up with the equality [tex]\frac{Sin90^{o} }{270} =\frac{Sin49^o}{b}[/tex], which we can use to solve for side b.

[tex]\frac{Sin90^o}{270} =\frac{1}{270}[/tex], so we know that [tex]\frac{1}{270} =\frac{Sin49^o}{b}[/tex].

Next, we would multiply both sides by b to get [tex]\frac{1}{270}b=Sin49^o[/tex].

Sin49°≈0.75471, so to find b we would multiply 0.75471×270=203.77

Since the problem asks us to round to the nearest whole number, b=204

Hope this helps! :)

Answer:

= x + 5

Step-by-step explanation:

(4x+1) - (3x-4)

= (4x+1) -3x + 4

= 4x - 3x + 1 + 4

= x + 5

Answer:

term to term rule. • a rule that defines the value of each term in a sequence. if the previous terms are known, e.g. the Fibonacci sequence. xn = xn-1 + xn-1.

Step-by-step explanation:

To work out the term to term rule, give the first term and then the pattern. The first term is 17, and the pattern is to subtract 3 each time, so the term to term rule is 'start at 17 and subtract 3'. The next two terms of the sequence are 5 and 2, giving the sequence as: Question.

The value of a is 1/4 and the value of h and k is (2,-7/4)

A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.

(x-h)² = 4a(y-k)

It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).

Therefore
(x -2)² = 4a(y +2)

The parabola passes through the point (3,-1)

(3-2)² = 4*a(-1+2)

1 = 4 a

a = 1/4

Now to determine the value of focus point , (h,k)

(h = 2)

k = - 2 +1/4 = -7/4

Therefore The value of a is 1/4 and the value of h and k is (2,-7/4)

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The number of months when the gyms cost the same is 5 months.

Total cost of joining the gym = registration fee + (cost per month x number of months)

When the gyms costs are the same, the two above equations would be equal to each other:

50 + 20m = 70 + 10m

20m - 10m = 70 - 20

10m = 50

m = 50 / 10

m = 5

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Answer:

A   x+2 would move the coordinate 2 units to the right while (x)+2 would move the coordinate 2 up and 2 to the right

Step-by-step explanation:

sorry i couldnt do the second part i ran out of time

x = 6(√2)

Step 1:

Say, 6 is perpendicular and x is the hypotenuse.

Step 2:

As we know sine is the ratio of perpendicular and hypotenuse.

∴ [tex]sin 45 = \frac{perpendicular}{hypotenuse}=\frac{6}{x}[/tex] ......................................(1)

Step 3:

As we know, sin45 = 1/√2

∴ put the value in equation 1

⇒ [tex]\frac{1}{\sqrt{2}} = \frac{6}{x}[/tex]

By solving the above equation, we get,

x = 6(√2)

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when receiving this kind of questions, you just need to find a figure that you can calculate the area of or split the figure in multiple figures that you can calculate.

Answer: 95 cm³

Step-by-step explanation: To find the volume of any prism, you have to multiply the base × width × height.

In this case, this 3D shape is split into 2 parts.

The first part's dimensions are 8×5×2. So the volume is 80 cm³.

The second part's dimensions are 1×3×5. So the volume is 15 cm³.

Finally, you add both volumes together, and the final answer is 95 cm³.

Answer:

Step-by-step explanation:

equation of The line L : y = -(1/2)x + 6

A(8 , b) ∈ L  then b = -(1/2)(8) +6 then b = -4 + 6 = 2

Therefore ,

A(8 , 2)

AB = 2

CD = 6

BC = 8

…………………………………………

Area of the trapezoid ABCD

= (CB÷2)×(AB + CD)

= (8÷2)×(6+2)

= 32

Answer:

x=−2

Step-by-step explanation:

hope it helps yaa

Answer:

make it more clear its not clear enough to understand the question

Answer:

tan A = 5/12

Step-by-step explanation:

The tangent ratio is equal to the length of the side opposite of the angle over the length of the side adjacent to the angle. If we are finding tangent in respect to angle A, the opposite side would be line CB with a length of 5. The adjacent side is line AC with a length of 12. Therefore, the tan A ratio is 5/12.

The t-coordinate of the solution to this system represents C. the time at which the ball and the dog's mouth are at the same height.

A coordinate time scale is a time standard designed for use as the time coordinate in the calculation.

When Laurie throws a tennis ball toward her dog from a height, the t-coordinate of the solution to this system represents the time at which the ball and the dog's mouth are at the same height

The complete question is:

Laurie throws a tennis ball toward her dog from a height of 4.5 ft. The initial vertical velocity of the ball is 18 ft/s. At the same time as Laurie throws the ball, her dog jumps with an initial vertical velocity of 21 ft/s. When the dog jumps, its mouth is 1.5 ft above the ground. What does the t-coordinate of the solution to this system represent?

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Answer:

C

Step-by-step explanation:

I got it right

The correct answer is option D which is No because one x-value corresponds to two different y-values.

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

We can see from the table that the value of x at 5 is giving two different values of y that is 2 and 3. For a function, it is not possible to have two different outputs for the same input.

Therefore the correct answer is option D which is No because one x-value corresponds to two different y-values.

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Answer:

QR = 3

Step-by-step explanation:

given that Q is on the segment PR , then

PQ + QR = PR ( substitute values )

16 + QR = 19 ( subtract 16 from both sides )

QR = 3

The calculated length of the segment QR is 3 units

From the question, we have the following parameters that can be used in our computation:

Point Q is on line segment PR

PQ = 16 and PR = 19

using the above as a guide, we have the following:

PQ + QR = PR

substitute the known values in the above equation, so, we have the following representation

16 + QR = 19

So, we have

QR = 19 - 16

Evaluate

QR = 3

Hence. the length of the segment QR is 3

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A. Distance between A and B is: 5 units.

B. Triangle ABC is not an equilateral triangle because only two of its sides are equal.

An equilateral triangle has three sides that have the same length.

Given the vertices with their coordinate points as:

A (-3, 2)

B (-6, -2)

C (0, -2)

Use the distance formula, [tex]d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find AB, BC, and AC:

AB = √[(−6−(−3))² + (−2−2)²]

AB = √25

AB = 5 units

BC = √[(−6−0)² + (−2−(−2))²]

BC = √36

BC = 6 units

AC = √[(−3−0)² + (2−(−2))²]

AC = 25

AC = 5 units

Only two of the sides of the triangle, AB and AC, are equal. Therefore, it is not an equilateral triangle.

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Answer:

547.40

Step-by-step explanation:

476*15%

15 percent *476

= (15/100)*476

= (15*476)/100

= 7140/100 = 71.40

71.40 + 476 = 547.40 as original price

[tex]\dfrac{2x^3+4x^2 -x+8}{x^2 +3x+2}\\\\\\=\dfrac{2x^3+6x^2+4x-2x^2-6x-4+x+12}{}\\\\=\dfrac{2x(x^2 +3x+2)-2(x^2 +3x+2)+x+12}{x^2 +3x+2}\\\\\\=\dfrac{2x(x^2+3x+2)}{x^2 +3x +2 }- \dfrac{2(x^2 +3x +2)}{x^2 +3x +2 } + \dfrac{x+12}{x^2 +3x+2}\\\\\\=2x-2 + \dfrac{x+2}{x^2 +3x +2}\\\\\\=2x-2 + \dfrac{x+12}{x^2 +2x +x +2}\\\\\\=2x-2 + \dfrac{x+12}{x(x+2) + x+2}\\\\\\=2x-2 + \dfrac{x+12}{(x+1)(x+2)}\\[/tex]

Answer:

  D.  20 m

Step-by-step explanation:

The potential energy at Point B will be the sum of the potential and kinetic energies at point A.

__

For mass M, the potential energy at h meters above a rest height is ...

  PE = Mgh

The kinetic energy of mass M with velocity v is ...

  KE = 1/2Mv²

A pendulum with mass M launched downward at v = 14 m/s will have a total energy of ...

  PE +KE = M(9.8 m/s²)(10 m) +1/2(M)(14 m/s)² = M(98 +98) = 196M J/kg

When the pendulum comes to rest at point B, its energy will all have been converted to potential energy. Then the height at point B is given by ...

  PE = Mgh

  196M J/kg = M(9.8 m/s²)h

  h = (196M)/(9.8M) m = 20 m

The height of the mass at point B will be 20 meters.

..:

[tex]12 {x}^{3} y - 18x {y}^{2} \\ [/tex]

Factor out 6xy:

[tex]\boxed{(6xy)(2 {x}^{2} - 3y)} [/tex]

(which is the maximum you could get(atleast in this problem))

Answer:

$ 375 / month

Step-by-step explanation:

$ 18 000 / 48 months = 375 /month

The minimum amount he should save per month to achieve his goal is $375.00. Thus, option 2 is correct.

Given that:

Number of months = 48

Monthly savings = $18,000

The minimum amount to save per month can be calculated by dividing the total amount by the number of months:

Minimum monthly savings goal = Total amount to save / Number of months

Minimum monthly savings goal = $18,000 / 48

Minimum monthly savings goal ≈ $375.00

Therefore, the minimum amount he should save per month to achieve his goal is $375.00. Thus, option 2 is correct.

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Answer:

Step-by-step explanation

2 * [3 * (16 + 1)] - 8 =

2 * [3 * 17] - 8 =

2 * 51 - 8

102 - 8 =

94