Find the perimeter and area of the composite figure.

Answer:

im pretty sure the ones that say "if not replaced" are independant, sorry if im wrong but im trying to help you out :)

Step-by-step explanation:

Step-by-step explanation:

Simplify.

Divide each side by -6, then flip the sign to accurately show the inequality:

\(z > - 4\)

the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.

A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.

Given the mean is 121 while the standard deviation of the women is 9. Therefore, Using the z-table, the probability can be found.

(a) The probability that a woman selected at random has blood pressures greater than 136.

\(P(x > 136) = 1 - P(x < 136)\\\\P(x > 136) = 1 - P(z < \dfrac{x-\mu}{\sigma})\)

                  \(=1 - P(z < \dfrac{136-121}{9})\\\\=1 - P(z < 1.667)\\\\=1-0.9515\\\\=0.0485\)

(b) The probability that a woman selected at random has a blood pressure less than 114.

\(P(x < 114)= P(z < \dfrac{114-121}{9})\\\\\)

                  \(= P(z < -0.77)\\\\= 0.2206\)

(c) The probability that a woman selected at random has a blood pressure between 114 and 128.

\(P(114 < x < 128)= P(\dfrac{114-121}{9} < z < \dfrac{128-121}{9})\\\\\)

                  \(= P(-0.77 < z < 0.77)\\\\= P(z < 0.77)-P(z < -0.77)\\\\= 0.7794 - 0.2206\\\\=0.5588\)

Hence, the probability that a woman selected at random has a blood pressure between 114 and 128 is 0.5588.

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Answer: x^6+6x^4+8x^2+2

Step-by-step explanation:

Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in

(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

Answer:

Earth to the Moon I think

Answer:

\(2+\dfrac{x}{5}\)

Step-by-step explanation:

Sign "+" is used for sum.

Sign either "÷" or "/"  is used for quotient or division.

We need to find the expression to represent the sum of two and the quotient of a number x and five.

Quotient of a number x and five is \(x\div 5=\dfrac{x}{5}\).

Sum of two and the quotient of a number x and five is

\(2+\dfrac{x}{5}\)

Therefore, the required expression is \(2+\dfrac{x}{5}\).

Answer:

It is skewed left because most of the points are to the left

Hope this helps :)

The number line highlighted such that  all the numbers that can be values of x so |x| < 7 is attached accordingly.

A number line is a graphic depiction of numbers on a straight line in mathematics. A number line has numbers that are consecutively set at identical distances throughout its span. It may be stretched in any direction indefinitely and is commonly depicted horizontally.

Number lines are significant because they show numbers in context. Primarily because they allowed negative numbers to be expressed in a meaningful fashion.

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The perimeter of a square field of area 800m² is 113.137

The area of the field is 800 m²

We need to determine the perimeter of the square field

The formula for area of a square is

area = side ² or a ²

a = √ area

a = √ 800

a = 20√2

a = 20 x 1. 414

a = 28.284

perimeter is the sum of all sides of a square

The formula to calculate the perimeter

p = 4 x side

p = 4a

p = 4 x 20√2 = 80√2

p = 80 x 1.414

p = 113.137

Therefore, the perimeter of a square field of area 800m² is 113.137

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The exact values of the remaining five trigonometric functions are as follows:

1. cosθ = -√(-1023)

2. tanθ = 32/(-√(-1023))

3. secθ = 1/(-√(-1023))

4. cscθ = 1/32

5. cotθ = (-√(-1023))/32

Given that sinθ = 32 and cosθ < 0, we can use the Pythagorean identity to find the value of cosθ:

\(cos^2\)θ = 1 - \(sin^2\)θ

\(cos^2\)θ = 1 - \((32/1)^2\)

\(cos^2\)θ = 1 - 1024

\(cos^2\)θ = -1023

Since cosθ < 0, we take the negative square root:

cosθ = -√(-1023)

Now, we can find the remaining trigonometric functions:

1. cosθ: We already found that cosθ = -√(-1023).

2. tanθ: tanθ = sinθ/cosθ

tanθ = 32/(-√(-1023))

3. secθ: secθ = 1/cosθ

secθ = 1/(-√(-1023))

4. cscθ: cscθ = 1/sinθ

cscθ = 1/32

5. cotθ: cotθ = 1/tanθ

cotθ = (-√(-1023))/32

Therefore, the exact values of the remaining five trigonometric functions are as follows:

1. cosθ = -√(-1023)

2. tanθ = 32/(-√(-1023))

3. secθ = 1/(-√(-1023))

4. cscθ = 1/32

5. cotθ = (-√(-1023))/32

Note: The value of √(-1023) is an imaginary number, so the exact values of the trigonometric functions involve complex numbers.

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The midpoint between \(-3,5 and 1,6 is (-1,5.5)\)

The midpoint between two points can be found by averaging the coordinates of the points separately for each dimension (x-axis and y-axis). Let's calculate the midpoint between \(-3,5 and 1,6\).

The coordinates of the two points are:

Point 1: (\(-3,5\))

Point 2: (\(1,6\))

To find the midpoint, we can average the x-coordinates and y-coordinates separately.

Midpoint's x-coordinate = (x-coordinate of Point \(1\) + x-coordinate of Point \(2\)) / \(2\)

Midpoint's y-coordinate = (y-coordinate of Point \(1\) + y-coordinate of Point \(2\)) / \(2\)

According to the problem

Midpoint's x-coordinate = \((-3+1)/2= -2/2= -1\)

Midpoint's y-coordinate = \((5+6)/2= 11/2 = 5.5\)

So, the midpoint between \(-3,5\) and \(1,6\) is \((-1,5.5)\).

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Answer:

$78,000

Step-by-step explanation:

75,000 * 4% is 3000

3000+ 75000

78000

Verified Answer!

Answer:

75,000 times 0.04 which equals 3000 abd then add the 3000 to the original amount

Answer:

A.  (5,-9) and (5,9) are reflections over the y-axis

Step-by-step explanation:

To find the probability of either event occurring, we can use the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Given that P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.25, we can substitute these values into the formula.

\(P(A or B) = P(A) + P(B) - P(A and B)\)
\(P(A or B) = 0.6 + 0.5 - 0.25\)
\(P(A or B) = 0.85 - 0.25\)
\(P(A or B) = 0.60\)
The probability of either event occurring is 0.60 or 60%.

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The probability of either event occurring can be found by adding the probabilities of the individual events and subtracting the probability of both events happening together. In this case, the probability of either event A or event B occurring is 0.6.

The probability of either event occurring can be calculated using the principle of addition. To find the probability of either event happening, we need to sum the individual probabilities of the events and subtract the probability of both events happening together.

Given:

p(a) = 0.6 (probability of event A occurring)
p(b) = 0.5 (probability of event B occurring)
p(a and b) = 0.25 (probability of both events happening together)

To calculate the probability of either event occurring, we can use the formula:

p(a or b) = p(a) + p(b) - p(a and b)

Substituting the given values into the formula:

p(a or b) = 0.6 + 0.5 - 0.25

p(a or b) = 0.85 - 0.25

p(a or b) = 0.6

Therefore, the probability of either event A or event B occurring is 0.6.

To understand this concept better, let's consider an example. Suppose event A represents rolling a fair six-sided die and getting an even number (2, 4, or 6). The probability of event A occurring would be 0.5. Now, let event B represent flipping a fair coin and getting heads. The probability of event B occurring would be 0.5.

If we want to find the probability of either rolling an even number or flipping heads, we can use the formula mentioned earlier. The probability of rolling an even number is 0.5, the probability of flipping heads is 0.5, and the probability of both happening together is 0.25. Plugging these values into the formula, we get:

p(A or B) = 0.5 + 0.5 - 0.25

              = 0.75

Therefore, the probability of either rolling an even number or flipping heads is 0.75.

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Answer:

A. System C simplifies to 2x - 3y = 4 and 4x - y = 54 by dividing the second equation by three (3).

B. Systems A and C have the same solutions.

C. Systems A and B have different solutions.

Step-by-step explanation:

Given the following system of equations;

System A

2x - 3y = 4  .....equation 1

4x - y = 18  .......equation 2

We would solve the above equations using the elimination method;

Multiplying eqn 1 by 2;

2*(2x) - 2*(3y) = 4*2

4x - 6y = 8  ...... equation 3

Subtracting eqn 2 from eqn 3;

(4x - 4x) + (-6y - (-y)) = 8 - 18

0 + (-6y + y) = -10

-5y = -10

5y = 10

\( y = \frac {10}{5} \)

y = 2

To find the value of x;

2x - 3y = 4

2x - 3(2) = 4

2x - 6 = 4

2x = 4 + 6

2x = 10

\( x = \frac {10}{2} \)

x = 5

Solutions (x, y) = (5, 2)

System B

3x - 4y = 5  ..... equation 1

y = 5x + 3  ..... equation 2

We would solve the equations using substitution method;

Substituting eqn 2 into eqn 1, we have;

3x - 4(5x + 3) = 5

3x - 20x - 12 = 5

-17x - 12 = 5

-17x = 12 + 5

-17x = 17

\( x = \frac {-17}{17} \)

x = -1

To find the value of y;

y = 5x + 3

y = 5(-1) + 3

y = -5 + 3

y = -2

Solutions (x, y) = (-1, -2)

System C

2x - 3y = 4  ..... equation 1

12x - 3y = 54  ...... equation 2

We would solve the above equations using the elimination method;

Subtracting eqn 2 from eqn 1;

(2x - 12x) + (-3y -(-3y)) = 4 - 54

-10x + (-3y + 3y) = -50

-10x + 0 = -50

-10x = -50

10x = 50

\( x = \frac {50}{10} \)

x = 5

To find the value of y;

2x - 3y = 4

2(5) - 3y = 4

10 - 3y = 4

3y = 10 - 4

3y = 6

\( y = \frac {6}{3} \)

y = 2

Solutions (x, y) = (5, 2)

Using the normal distribution, it is found that 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem, the mean and the standard deviation are given, respectively, by \(\mu = 15.1, \sigma = 2.2\).

The proportion of penguins from the population have a weight between 13.0 kg and 16.5 kg is the p-value of Z when X = 16.5 subtracted by the p-value of Z when X = 13.

X = 16.5:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{16.5 - 15.1}{2.2}\)

Z = 0.64

Z = 0.64 has a p-value of 0.7389.

X = 13:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{13 - 15.1}{2.2}\)

Z = -0.95

Z = -0.95 has a p-value of 0.1711.

0.7389 - 0.1711 = 0.5678.

0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

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Step-by-step explanation:

Calculating your loan-to-value ratio

Current loan balance ÷ Current appraised value = LTV.

Example: You currently have a loan balance of $140,000 (you can find your loan balance on your monthly loan statement or online account). ...

$140,000 ÷ $200,000 = .70.

Current combined loan balance ÷ Current appraised value = CLTV.

n((A-B)U C) = 0

C. A={1,2,3), B = {1,3} Since B is a subset of A, (A-B) U C = C, which is the set of all natural numbers less than 5. Therefore, n((A-B)U C) = 0.

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The value of the missing angles are:

a) x = 71°

b) y = 48°

c) g = 48°

f = 132°

h = 48°

k = 132°

d = 80° = c

b = 100° = a

e = 52°

We know that alternate angles are defined as two angles that are formed when a line crosses two other lines, that lie on opposite sides of the transversal line and on opposite relative sides of the other lines. If the two lines crossed are parallel, the alternate angles are equal.

a) Angle x is an alternate angle to 71°

Thus: x = 71°

b) Angle x is a corresponding angle to 132°.

Angle at a point is 180 degrees and as so:

y = 180 - 132

y = 48°

c) Angle g is an opposite angle to 48 degrees and as such:

g = 48°

Sum of angles on a straight angle is 180 degrees and as such:

f = 180 - 48

f = 132°

angle h is an alternate angle to 48 degrees and such:

h = 48°

k is a corresponding angle to f and as such k = 132°

d is an alternate angle to 80 degrees and as such:

d = 80° = c

Sum of angles in a straight line is 180 degrees and as such:

b = 180 - 80

b = 100° = a

e = 180 - (48 + 80)

e = 52°

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0.3814 is the probability that the sample contains two white balls and two red ones .

What is probability in math?

Total number of balls = 8 + 12 = 20

Total number of elementary cases

           = ( 20 4 )

Total number of favourable cases

           = ( 8 2 ) * ( 12 2 )

Required probability

   = ( 8 2 )  *  ( 12 2 )/( 20  4 )

 = 0.3814

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The statement "The probability of success and failure does not remain constant during attempts" is NOT a property of the binomial distribution. The correct option is (b).

The binomial distribution has the following properties:

a. There are n identical attempts: In a binomial distribution, there are a fixed number of independent trials or attempts, denoted by n. Each attempt has two possible outcomes, usually referred to as success and failure.

b. The probability of success remains constant during attempts: One of the key assumptions of the binomial distribution is that the probability of success, denoted by p, remains constant across all trials. This means that the probability of success or failure does not change from one trial to another.

c. Events are collectively exhaustive: In a binomial distribution, the outcomes of the trials are mutually exclusive and collectively exhaustive. This means that the events of success and failure cover all possible outcomes of each trial, and no other outcomes are possible.

d. Events are mutually exclusive: In a binomial distribution, the events of success and failure are mutually exclusive. This means that only one of the two outcomes can occur in each trial. A trial cannot simultaneously be a success and a failure.

Therefore, the statement "The probability of success and failure does not remain constant during attempts" is not a property of the binomial distribution because the binomial distribution assumes a constant probability of success throughout the trials.

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To determine the next step, we need to slove the expression.

divide both sides by -1:

Square both sides of the equation:

Answer:

s = -11

Step-by-step explanation:

14 = -2s - 8

22 = -2s

2s = -22

s = -11

14= -2s -8

+8 +8 Add 8 to both sides to isolate -2s

22= -2s

--- ----

-2 -2 Divide -2 by both sides

-11=s This is the answer.

The value of x is 6 when the equation is √x+2= x-4.

Given that,

The equation is

√x+2= x-4

The value of x must be determined.

Equations are mathematical expressions with two algebraic expressions on either side of the equals (=) sign. It shows that the expressions written on the left and right sides have an equal relationship. A mathematical statement known as an equation is one that uses the word "equal to" between two expressions with the same value.

Take the equation,

√x+2= x-4

√x=x-4-2

√x=x-6

√x-x=-6

x=6

Therefore, The value of x is 6 when the equation is √x+2= x-4.

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Answer:

6v^2 - 35v + 6wv - 42w - 49

Step-by-step explanation:

Use distributive property

First multiply 6v to each term within the second set of parentheses

6v^2 - 42v

Now multiply 6w to each term within the second set of parentheses

6wv - 42w

Next multiply 7 to each term within the second set of parentheses

7v - 49

Add all of these numbers together

6v^2 - 42v + 6wv - 42w + 7v - 49

Combine like terms

6v^2 - 35v + 6wv - 42w - 49

No more like terms so the expression is simplified

Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold.

Isaac has a 1/40 chance of winning the raffle, or a 2.5% chance. This indicates that he has a 2.5% probability of having his ticket chosen out of the 40 tickets that were sold. This is because there is only one raffle winner and it is impossible to predict which ticket will be picked.

It's also crucial to remember that his odds of winning are entirely independent of those of any other ticket holder; nobody else's ticket will affect the outcome of the raffle. As a result, Isaac has the same chance of winning as any other ticket holder. It's also vital to remember that regardless of how many tickets are sold, the likelihood of winning stays the same. Therefore, regardless of how many raffle tickets are sold, there is a 2.5% chance of winning.

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Using probabilities P(A₁) = 0.40 , P(A₂) = 0.60, P(B|A₁) = 0.20, P(B|A₂) = 0.05,

a) No, A₁ , A₂ are not mutually exclusive because , their intersection probability is not a zero.

b) P(A₁∩ B) is 0.08 , P(A₂ ∩ B) is 0.03

c) P(B) = 0.09

d) Using Bayes' theorem P(A₁|B) is 0.89 , P(A₂|B) is 0.33 .

a. A₁ and A₂ are not mutually exclusive, as their intersection probability is non-zero (given as 0 in the problem statement).

b. We can compute P(A₁∩ B) and P(A₂∩ B) using the formula for conditional probability:

P(A₁∩ B) = P(B|A₁) * P(A₁) = 0.20 * 0.40 = 0.08

P(A₂ ∩ B) = P(B|A₂) * P(A₂) = 0.05 * 0.60 = 0.03

c. To compute P(B), we can use the law of total probability, which states that the probability of an event B can be calculated as the sum of the probabilities of B given each possible event in the sample space:

P(B) = P(B|A₁) * P(A₁) + P(B|A₂) * P(A₂) = 0.20 * 0.40 + 0.05 * 0.60 = 0.09

d. To compute P(A₁|B) and P(A₂|B), we can use Bayes' theorem:

P(A₁|B) = P(B|A₁) * P(A₁) / P(B) = 0.20 * 0.40 / 0.09 ≈ 0.89

P(A₂|B) = P(B|A₂) * P(A₂) / P(B) = 0.05 * 0.60 / 0.09 ≈ 0.33

Therefore, the probability that event A₁ occurred given that event B occurred is approximately 0.89, and the probability that event A₂ occurred given that event B occurred is approximately 0.33.

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Answer:

209.23

Step-by-step explanation:

Answer:

425 pesos

Step-by-step explanation:

Just divide both $250 and 4,250 pesos by 10 to get your answer! :)