Suppose a jar contains 8 red marbles and 10 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer as a reduced fraction.

Answer:

Step-by-step explanation:

Lets substitute y in the second equation and find its minimum

Substitute

This expression gets minimum value at x = -b/2a as quadratic function's vertex:

Then finding the value of y:

The answer is (4.5, 1.5)

Answer:

\((9/2, 3/2)\)

Step-by-step explanation:

We have the equation:

\(3x+y=15\)

Which is equivalent to 15 among all pairs of (x, y).

We want to find the pair of solutions (x, y) such that:

\(x^2+y^2\)

Is minimum.

Note that our given equation is a line.

And the equation x²+y² is a circle centered on the origin.

In other words, we want to find the radius of the circle such that it is tangent to our line at 3x+y=15.

It must be tangent because this guarantees that it is the smallest value of  x²+y².

It's good if we have a visual of this. I've graphed the given linear equation. Please refer to it.

If you remember in geometry, in order for the radius to be tangent to a line, the radius must be perpendicular to our line.

So, let's find the perpendicular equation to our line. Our original equation is:

\(3x+y=15\)

Subtract 3x from both sides:

\(y=-3x+15\)

So, the slope of our original equation is -3.

This means that the slope of our perpendicular line must be the negative reciprocal of -3. Namely, it is 1/3.

And since our circle is centered on the origin, this line will go through the origin. Therefore, our perpendicular equation is:

\(y=\frac{1}{3}x\)

Graphing this will yield (please refer to the second graph):

Therefore, the intersection between our old and new line is at (4.5, 1.5).

Therefore, the (x, y) value that grants the minimum sum is 9/2 and 3/2.

We can check this by substituting them into our second equation. This yields:

\((9/2)^2+(5/2)^2\)

Square and add:

\(=81/4+9/4=22.5\)

Note that 22.5 is the radius squared.

Graphing this gives us (please refer to the third graph):

We can see that it is indeed tangent to our line. And it is the lowest value of P that does so.

So, our answer is x=9/2 and y=3/2.

The answer to the equation −0.22x + x − 0.33x is 0.11x.

The answer is 0.11x. To solve this, we can start by rearranging the terms of the equation. The equation can be written as:

−0.22x + x − 0.33x = −0.22 + 0.33x

We then subtract x from both sides of the equation, resulting in:

−0.22x − x = −0.22 + 0.33x − x

We then combine like terms on the left side of the equation, resulting in:

−1.22x = −0.55

Finally, we divide both sides of the equation by -1.22 to solve for x, resulting in:

x = 0.11

Therefore, the answer is 0.11x.

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Complete question

What is the value of -0.22+−0.33−0.22x+x−0.33x?

The fraction of cookie he needs to eat to consume more than 1/3 of his cookie is 2/3.

Fractions serve to symbolize more compact portions (or fragments) of a whole.

The given question is-

Mark wants to eat more than a 1/3 of his cookie.

The complete cookie will have the value 1.

So, to get ore than 1/3, subtract 1/3 from 1.

= 1 - 1/3

= (3 - 1)/3

= 2/3

Thus, the fraction of cookie he needs to eat to consume more than 1/3 of his cookie is 2/3.

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Well if Jorge's motion can be described by vectors then he first went +25 steps then -75 steps which means he did -50 steps in total. His position is thus 50 steps to the south of the original position.

Hope this helps.

Answer:

50

Step-by-step explanation:

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

I believe it is 7.5625 so 7.56

Answer:

440

Hope this helps! ;-)

The answer is 440!!!!

The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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Answer:

     y = 94

Step-by-step explanation:

Linear Pair:

The two adjacent angles whose non common arms form a straight line is called linear pair. They add up to 180

2x + 36 = 180 {linear pair}

       2x  = 180 - 36

       2x = 144

Sum of all angles of a n-sided polygon = (n-2)*180

                                                                 = ( 6-2)*180

                                                                 = 4 * 180

                                                                  = 720

y + 144 + 111 + 105 + 165 + 101 = 720

                                  y + 626  = 720

                                             y = 720 - 626

                                            \(\sf \boxed{y = 94^ \circ}\)

Answer:

94°

Step-by-step explanation:

2x + 36 = 180 (angles on a straight line)

2x = 180 - 36

2x = 144

2x = 144°

Sum of all angles of a n-sided polygon = (n-2)×180 = ( 6-2)×180

= 4 × 180

= 720

y + 144 + 111 + 105 + 165 + 101 = 720

y + 626 = 720

y = 720 - 626

y=94 °

The calculated scale factor from ABC to A'B'C is 1/3

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

The triangles

From the triangles, we have the following parameters

A = (0, 3)

A' = (0, 1)

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

Scale factor of the dilation = A'/A

So, we have

Scale factor of the dilation = (0, 1)/(0, 3)

Evaluate

Scale factor of the dilation = 1/3

Hence, the scale factor of the dilation is 1/3

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Answer:

1/12 gallons

Step-by-step explanation:

We can determine how much more hot chocolate than apple cider die Joe serve by subtracting 1/12 from 1/6.

Step 1:  Since 1/12 has the bigger denominator and 6 * 2 = 12, let's give 1/6 the same denominator as 1/12 by multiplying the entire fraction by 2/2

(1/6) * (2/2) = 2/12

Step 2:  Now we can subtract 1/12 from 2/12:

2/12 - 1/12 = 1/12

Thus, Joel served 1/12 more gallons of hot chocolate than apple cider.

Answer:

Step-by-step explanation:

1) f(-4) --> if x < or equal to 3

2) 1/(-4)-4

3) The answer is - 1/8

The area of the kite is A = 48 units²

Given data ,

Let the area of the kite be represented as A

Now , the value of A is

Let the first diagonal of the kite be d₁ = 12 units

Let the second diagonal of the kite be d₂ = 8 units

Now , Area of kite = ( 1/2 ) d₁ x d₂

On simplifying , we get

A = ( 1/2 ) ( 12 ) ( 8 )

A = 48 units²

Therefore , the value of A is A = 48 units²

Hence , the area of the kite is A = 48 units²

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Answer:

Yes.

Step-by-step explanation:

-5 3/11 is equal to -5.27 repeating therefore, it is greater than -5.2. Hope this helps. :)

Applying exponent rules, the factored expression is given as follows:

125^6 - 27^15 = 5^18 - 3^45.

The expression is factored according to the like terms of the expression, which are placed into evidence.

For this problem, the expression is:

125^6 - 27^15

First, we have to factor 125 and 27, finding it's prime factors, hence:

Thus the expression can be written as:

125^6 - 27^15 = (5³)^6 - (3³)^15

There will be no like terms on the expression, as the bases are different,  of 3 and 5, hence we just apply the exponent rules, as follows:

a^b^c = a^(b x c), which is the power of power rule.

Hence:

Hence the simplified expression is given as follows:

(5³)^6 - (3³)^15 = 5^18 - 3^45.

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The sum of the scores is equal to 160.

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of scores (data set), we have;

∑x = 20 + 60 + 30 + 50

∑x = 160.

Mean = [F(x)]/n = 160/4 = 40.

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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\( log(550) = log(2 \times 5 \times 5 \times 11) = \\ \)

\( log(2) + log( {5}^{2} ) + log(11) = \)

\(1 - log(5) + 2 log(5 ) + log(11) = \\ \)

\(1 + log(5) + log(11) = \)

\(1 + a + b\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

log(a x b) = Log(550)

Step-by-step explanation:

Depends what question is asking

Log rule (So long as they have the same base)

Log(m) + Log(n) = Log(m x n)

Log(a) + Log(b) = Log(a x b)

Log(5) + Log(11) = Log(5 x 11)

=Log (550)

Answer:

B, C, G

Step-by-step explanation:

If we look at the graph, it shows that if an employee works for 5 hours, then they will earn $36.25.

We can take 36.25 and divide that by 5 to get the hourly wage.

36.25 ÷ 5 = 7.25

We now know that employees get $7.25 every hour.

Using this we can look back to the graph.

'A' says that if an employee does not work, they will earn $7.25.

We know that this is wrong because if you do not work, then you do not earn money.

Let's look at 'B'.

If employees work for one hour, they will earn $7.25

We know this is correct because we now know the hourly wage.

Let's look at 'C'

If employees work for 4 hours, then they will get a revenue of $29.

We can figure this out by using this equation.

number of hours × hourly wage = total payment

4 × 7.25 = 29

Then this means that this is correct.

Let's look at 'D'

It says that if employees work for 10 hours, they will earn $73

Let's use that same equation again.

10 × 7.25 = 72.5

Employees earn $72.5 for working 10 hours, not $73.

So, this is obviously incorrect.

Let's look at 'E'

It says that if employees work for 3.5 hours, they will get a revenue of $21.75.

3.5 × 7.25 = 25.375

Therefore, this is incorrect.

Now let's take a look at 'F'.

It says that if employees work for 7.25 hours, then they earn $1.

This is incorrect.

And lastly, 'G'.

We know that if you do not work, then you do not earn money.

Therefore, A, B and G are the correct answers.

Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.

The units-of-activity method is one of the depreciation methods in use.

Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.

The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.

Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)

Expected total miles for Bus #3 = 125,000

Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)

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Bus    Acquired    Cost    Salvage    Useful Life     Depreciation
                                          Value         in Years          Method

1          1/1/12      $99,100   $7,900           4             Straight-line

2         1/1/12      128,000     11,000          4             Declining- balance

3         1/1/13       66,350      8,800          5             Unit-of-activity

Answer:

201.6

i think

Answer: I am pretty sure its A

Step-by-step explanation:

Answer:

5 × (x + 27) ≥ 6 × (x + 26).

Step-by-step explanation:

The solution set of " Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26" is (-∞, -21]

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

For this case, let the number in consideration be 'x', then according to the condition specified, we get:

Also, we get:

Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26 as:

\(5(x+27) \geq 6(x+26)\)

Expanding and taking x on one side:

\(5x+135 \geq 6x+156\\135-156 \geq x \\\\x \leq -21\)

Thus, the considered statement is true for all the numbers which is smaller or equal to -21. Symbolically, the solution set is: (-∞, -21]

The square bracket shows that the -21 is included in the interval. And the interval  (-∞, -21] is  set of all real numbers smaller or equal to -21.

Thus, the solution set of " Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26" is (-∞, -21]

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The probability that a viewer will turn to channel 8 during Jimmy's performance is 2.67%.

The show is 30 minutes long, which is equivalent to 1800 seconds. Jimmy's performance starts at 6:06 pm, which is 366 seconds into the show, and ends at 6:14 pm, which is 414 seconds into the show. Therefore, Jimmy's performance lasts for 48 seconds.

The probability of a viewer turning to channel 8 during Jimmy's performance can be calculated by dividing the length of Jimmy's performance by the length of the entire show:

P = (length of Jimmy's performance) / (length of entire show) = 48 / 1800 = 0.0267

Multiplying by 100 gives the probability as a percentage: 2.67%

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Answer:

1.11

Step-by-step explanation:

100 x 1.11

becuase 1.11 is the multiplier

In a rectangle, there are 2 pairs of congruent sides. Therefore, the area of a rectangle can be found using:

\(\text{A}=\text{l} \times \text{w}\)

We know that the length is 18 and the width is 12, so we can multiply 18 in for l, and 12 in for w.

\(\text{A}=\text{18} \times \text{12}\)

Multiply the numbers together

\(\text{A}=216\)

So, the area is 216 inches.

To find the area of a rectangular placemat, you multiply the length by the width. In this case, the length is 18 inches and the width is 12 inches. Therefore, the area of the tablecloth is:

Area = Length × Width

Area = 18 inches × 12 inches

Area = 216 square inches

So, the correct answer is option a. 216.

Answer:

No your rectangles would not be scaled copies

Answer:

Step-by-step explanation:

The graph of y=[x]-2 is the graph of the floor function shifted downward 2 units. The floor function takes any real number x and returns the greatest integer less than or equal to x. So, the graph of y=[x] is a series of horizontal steps with each step starting at an integer value of x and ending at the next integer value of x.

When we subtract 2 from the floor function, the entire graph shifts downward 2 units. So, each horizontal step of the graph of y=[x] is now 2 units lower than before.

Answer:

b = 5

Step-by-step explanation:

All quadratic equations are formed in the format of \(a^{2}\) + bx + c = 0

Using this formula, we can re-arrange the equation to fit the given format.

\(3x^{2}\) - 2 = -5x
\(3x^{2}\) + 5x - 2 = 0

5 is plugged in for "b" in this equation, therefore b = 5.

Answer:

The answer is 2/5.

Step-by-step explanation:

First, use the stay-switch-flip method. Keep 1/5 the same, switch the division sign into a multiplication sign, and flip the numerator and the denominator of 1/2 to get 1/5 x 2/1. Multiply the numerators. 1 x 2 = 2. Now, multiply the denominators. 5 x 1 = 5. Therefore, you're answer is 2/5.

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Answer

Polygon D is double of Polygon A