Events A and B are mutually exclusive with P(C) = 0.3 and P(B) = 0.2. Then P(Bc) =

The first battery voltage is 12.

The second battery voltage is 6.

The third battery voltage is 36.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

First battery voltage = M

Second battery voltage = N

Third battery voltage = O

Now,

We can make an expression as,

M + N + 0 = 54 _____(A)

And,

M = 2N  ____(1)

M = (1/3)O ____(2)

Now,

From (1) and (2)

N = M/2

O= 3M

Substituting in (A)

M + N + O = 54

M + M/2 + 3M = 54

4M + M/2 = 54

8M + M = 108

9M = 108

M = 12

Now,

N = M/2 = 12/2 = 6

O= 3M = 3 x 12 = 36

Thus,

First battery voltage = 12

Second battery voltage = 6

Third battery voltage = 36

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When a variable is eliminated from the equation during the equation solving process, the two possible solutions are:

A single unique solution and No solution:

When a variable is eliminated from an equation during the solving process, it results in an equation with only one variable. The two possible solutions are:

A single unique solution: This means that there is one specific value for the remaining variable that satisfies the equation.

No solution: This means that there is no value for the remaining variable that satisfies the equation, resulting in an inconsistent or contradictory statement.

Let's consider an example equation to illustrate these possibilities:

3x + 2y = 10

6x + 4y = 20

To solve this system of equations, eliminate the variable "x" by multiplying the first equation by 2 and subtracting it from the second equation:

[tex](6x + 4y) - 2(3x + 2y) = 20 - 2(10)\\6x + 4y - 6x - 4y = 20 - 20[/tex]

0 = 0

In this case, the variable "x" has been eliminated, and we are left with the equation 0 = 0. This equation is true for all values of "y".

Therefore, the system of equations has infinitely many solutions, and any value of "y" would satisfy the equations.

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Volume = pi * r^2 * h 
h = 3r
pi * r^2 * (3r) = 24 pi
3r^3 = 24
r^3 = 8
r = 2

 Height = 3*2 = 6 units

Answer:

8 Hours!!

Step-by-step explanation:

[tex]3x^3y ( 6xy + 7x^2 - 2y )[/tex] is the factored form of [tex]18x^4y^2+21x^5y-6x^3y^2[/tex] .

Given, expression [tex]18x^4y^2+21x^5y-6x^3y^2[/tex] .

To factorize the expression take the common terms present in each part of an expression.

Expression : [tex]18x^4y^2+21x^5y-6x^3y^2[/tex]

Highest power of x which is present in each part = x³

Highest power of y which is present in each part = y

HCF of 18, 21 , 6 = 3

Factorizing the expression:

Take 3x³y as common,

Factored form : [tex]3x^3y ( 6xy + 7x^2 - 2y )[/tex] .

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There are 22,100 possible hands of 3 cards from a 52-card deck using combinations. The probability of dealing three eights in a row from the deck is approximately 0.000181.

This question involves calculating probabilities and combinations related to card hands from a deck of 52 cards.

Possible Hands of 3 Cards:

To determine the number of possible hands of 3 cards from a 52-card deck, we use the combination formula: C(n, k) = n! / [k! * (n - k)!], where n is the total number of cards and k is the number of cards to choose.

C(52, 3) = 52! / [3! * (52 - 3)!] = 52! / (3! * 49!) = (52 × 51 × 50) / (3 × 2 × 1) = 22100. Therefore, there are 22,100 possible hands of 3 cards.

Probability of Dealing Three Eights:

The probability of dealing three eights in a row can be determined as follows:

Therefore, the probability of dealing three eights is: (4/52) × (3/51) × (2/50) = 24 / 132600 = 1 / 5525 ≈ 0.000181.

This detailed explanation helps in understanding how combinations and probabilities in card games are calculated.

Answer:c

Step-by-step explanation:

(4,-6), because this point makes both the equations true.

The slope m of the straight line through the points (6, 5) and (7, 2) is -3.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

The slope of the line is defined as the ratio of the rise to the run.

To find the slope, we can use the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (6, 5) and (x₂, y₂) = (7, 2).

Substituting these values, we get:

m = (2 - 5) / (7 - 6) = -3 / 1 = -3

Therefore, the slope of the straight line through the given pair of points is -3.

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Using number sets, it is found that a whole number cannot be irrational, hence option a is correct.

In this problem, any whole number can be represented by a fraction, hence it cannot be irrational and option a is correct.

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Answer:

A. An Irrational Number

Step-by-step explanation:

Irrational numbers are numbers like pi or angles with degrees, while whole numbers are numbers from 0+

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Answer

Find out the what is the approximate length of the side adjacent to angle C .

To prove

As given

In a right triangle, angle C measures 40°.

The hypotenuse of the triangle is 10 inches long.

Than by using the trignometric identity

[tex]cos\angle C= \frac{Base}{Hypotenuse}\\cos\angle C= \frac{BC}{AC}[/tex]

As shown the diagram is given below

AC= 10 inches , ∠C = 40 °

cos 40 = 0.766 (approx)

Put in the above formula

0.766 × 10 = BC

7.66 = BC

7.7 inches (approx) = BC

Option (b) is correct .

The correct option is Option C [tex]\boxed{{\mathbf{7}}{\mathbf{.66 inches}}}[/tex] .

Further explanation:

The cosine ratio can be represented as,

  [tex]\cos \theta  = \frac{{{\text{base}}}}{{{\text{hypotenuse}}}}[/tex]

Here, base is the length of the side adjacent to angle [tex]\theta[/tex]  and hypotenuse is the longest side of the right angle triangle.

The length of side opposite to angle [tex]\theta[/tex]  is perpendicular that is used for the sine ratio.

Step by step explanation:

Step 1:

From the given information, the observed right angle is attached.

First find the hypotenuse and the base of the right angle triangle.

It can be seen from the attached figure that the side [tex]BC[/tex]  is adjacent to angle [tex]C[/tex]  and the side [tex]AC[/tex]  is the hypotenuse of triangle.

Thus, the [tex]{\text{base}}=BC[/tex]  and [tex]{\text{hypotenuse}}=10[/tex] .

Step 2:

We know that the cosine ratio is [tex]\cos \theta =\frac{{{\text{base}}}}{{{\text{hypotenuse}}}}[/tex] .

Therefore, it can be written as,

 [tex]\cos \theta=\frac{{BC}}{{AC}}[/tex]

Now substitute the value [tex]BC=x[/tex]  and [tex]{\text{AC}}=10[/tex]  in the cosine ratio.

[tex]\begin{aligned}\cos C&=\frac{x}{{10}}\\{\text{co}}s40&=\frac{x}{{10}}\\0.766&=\frac{x}{{10}}\\x&=7.66\\\end{aligned}[/tex]

Therefore, the approximate length of the side adjacent to angle [tex]C[/tex]  is [tex]7.7{\text{ inches}}[/tex]  .

Thus, option C is correct.

Learn more:  

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Trigonometry

Keywords: Distance, Pythagoras theorem, base, perpendicular, hypotenuse, right angle triangle, units, squares, sum, cosine ratio, adjacent side to angle, opposite side to angle.

The sum of the first 10 terms of the series is 23.

An arithmetic progression(AP) is a sequence or series of numbers such that the difference of any two successive members is a constant. The first term is a, the common difference is d, n is number of terms.

For the given situation,

The series is 0.5,0.9,1.3,1.7.....

Here the first term, a = 0.5,

The common difference, d = [tex]0.9-0.5[/tex]

⇒ [tex]d=0.4[/tex]

Number of terms, n = 10

The formula of sum of n terms is

[tex]S_{n}=\frac{n}{2} [2a+(n-1)d][/tex]

On substituting the above values,

⇒ [tex]S_{10}=\frac{10}{2} [2(0.5)+(10-1)(0.4)][/tex]

⇒ [tex]S_{10}=5 [1+9(0.4)][/tex]

⇒ [tex]S_{10}=5 [1+3.6][/tex]

⇒ [tex]S_{10}=5 [4.6][/tex]

⇒ [tex]S_{10}=23[/tex]

Hence we can conclude that the sum of the first 10 terms of the series is 23.

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It will take you 15 minutes to walk one mile at a speed of 4 miles per hour.

To determine how long it will take you to walk one mile, we can use the formula:

Time = Distance / Speed

Let's plug in the values:

Distance = 1 mile

Speed = 4 miles per hour

Time = 1 mile / 4 miles per hour

Time = 0.25 hours

Since there are 60 minutes in an hour, we can convert the time to minutes:

Time = 0.25 hours × 60 minutes per hour

Time = 15 minutes

Therefore, it will take you 15 minutes to walk one mile at a speed of 4 miles per hour.

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To find the amount of salt when the tank contains exactly 40 gallons, create and solve differential equations for salt concentration and tank size over time. We find the tank size is 40 at 10 minutes, at which point there is approximately 14.2 lbs of salt.

To solve this, you need to understand that the total amount of salt at any time t is equal to the amount of salt coming in minus the amount of salt going out.

To begin with, the tank has 80 gal x 1/8 lb/gal = 10 lbs of salt.

The amount of salt coming in is 4 gal/min * 1 lb/gal = 4 lbs/min

The amount of salt going out depends on the concentration of the salt in the tank at that time. This is (4-8)(total salt/liters in tank at time t).

Setting up a differential equation and solving gives us an equation for salt concentration and volume at time t:

The equation for the tank size(in gallons) at time t (in minutes) is: tank size = 80 - 4t

The equation for the salt in tank at time t (in minutes) is: salt = 10 - 4t + 80e^-2t

When the tank size is exactly 40 gallons, tank size = 40 = 80 - 4t so t = 10 minutes

Plugging t = 10 into our equation for salt gives us: salt = 10 - 4*10 + 80e^-20 = approximately 14.2 lbs.

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Answer:

Pool needed to be filled = 7623.62 gallons

Step-by-step explanation:

Length of rectangular pool = 24.5 feet

Width of rectangular pool = 13 feet

Depth of rectangular pool = 4 feet

Now, Volume of the pool = Length × Width × Depth

                                          = 24.5 × 13 × 4

                                          = 1274 cubic feet

Now, 1 cubic feet = 7.48 gallons

⇒ 1274 cubic feet = 7.48 × 1274

                              = 9529.52 gallons

So, Volume of the pool = 9529.52 gallons

Now, the pool is to be filled 80%

So, Pool needed to be filled = 9529.52 × 0.80

                                                 = 7623.62 gallons

The number of gallons of water to the nearest tenth, that are needed to fill the pool to 80% capacity is 7623.6 gallons.

First step:

Volume of the pool=Length × Width × Depth

Volume of the pool= 24.5 ft × 13ft × 4ft

Volume of the pool=1274 cubic feet

Second step:

Number of gallons=(7.48 × 1274)×80%

Number of gallons=9529.5 gallons×80%

Number of gallons=7623.6 gallons

Inconclusion the number of gallons of water to the nearest tenth, that are needed to fill the pool to 80% capacity is 7623.6 gallons.

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The Inequality that has the graph shown below is [tex]y \ge -\frac{1}{4}x + 1.[/tex] correct choice is [tex]y \ge -\frac{1}{4}x + 1.[/tex]

This can be seen by noting that the line is solid and shaded above the line, which indicates that all points above the line satisfy the inequality.

Graphs are often used to visually represent inequalities in mathematics. Inequalities compare the relative sizes of two expressions, and their graphs help illustrate the solutions to these inequalities on a number line or in a coordinate plane

The other inequalities in the image are not correct because:

[tex]y > -\frac{1}{4}x + 1[/tex]would have the line shaded below the line.

[tex]y < = -\frac{1}{4}x + 1[/tex] would have the line dashed, not solid.

[tex]y < -\frac{1}{4}x + 1[/tex]would have no points above the line satisfying the inequality.

Therefore, the correct inequality is [tex]y \ge -\frac{1}{4}x + 1.[/tex]

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Since a pelidisi below ( 100 ) is considered undernourished and a pelidisi greater than ( 100 ) indicates overfeeding, with a pelidisi of ( 114 ), this individual is considered to be overfed.

Let's denote the pelidisi as ( P ), the weight in grams as ( W ), and the sitting height in centimeters as ( H). According to the given information, the pelidisi varies directly as the cube root of the person's weight and inversely as the person's sitting height. This relationship can be expressed mathematically as:

[tex]\[ P = k \times \frac{\sqrt[3]{W}}{H} \][/tex]

where ( k ) is the constant of variation.

We are given that a person with a weight of ( 48,820 ) g and a sitting height of ( 78.7 ) cm has a pelidisi of ( 100 ). We can use this information to find the value of ( k ):

[tex]\[ 100 = k \times \frac{\sqrt[3]{48820}}{78.7} \][/tex]

Solving for \( k \):

[tex]\[ k = \frac{100 \times 78.7}{\sqrt[3]{48820}} \]\[ k \approx \frac{7870}{36} \approx 218.611 \][/tex]

Now that we have the value of \( k \), we can find the pelidisi for a person with a weight of \( 54,688 \) g and a sitting height of \( 72.6 \) cm:

[tex]\[ P = 218.611 \times \frac{\sqrt[3]{54688}}{72.6} \][/tex]

Calculating \( P \):

[tex]\[ P \approx 218.611 \times \frac{38}{72.6} \]\[ P \approx 218.611 \times 0.522 \]\[ P \approx 114.14 \][/tex]

Rounded to the nearest whole number, the pelidisi of a person with a weight of ( 54,688 ) g and a sitting height of ( 72.6 ) cm is ( 114 ).

Since a pelidisi below ( 100 ) is considered undernourished and a pelidisi greater than ( 100 ) indicates overfeeding, with a pelidisi of ( 114 ), this individual is considered to be overfed.