expand each logarithm

Answer:  

Because of all the random factors beyond our control that enter the flipping process (force with which the coin is flipped, motion of the air in the room, position of our hand when we catch the coin...) we therefore expect a probability of 1/2 for heads, and 1/2 for tails. Each possible outcome is equally likely.

A coin has 2 possible outcomes because it only has two sides (heads or tails). This means that the probability of landing on heads is 1/2. So, the probability of landing on heads is (1/2) x 100, which is 50%.

What he and his fellow researchers discovered (here's a PDF of their paper) is that most games of chance involving coins aren't as even as you'd think. For example, even the 50/50 coin toss really isn't 50/50 — it's closer to 51/49, biased toward whatever side was up when the coin was thrown into the air.

Among any group of five integers, there are at least two with the same remainder when divided by 4.

To show that among any group of five integers, there are two with the same remainder when divided by 4, we'll use the Pigeonhole Principle. Here's a step-by-step explanation:

1. Consider the four possible remainders when dividing an integer by 4: 0, 1, 2, and 3.
2. Imagine these remainders as "boxes," where each integer will go into its respective remainder box.
3. We have five integers and four boxes. The Pigeonhole Principle states that if there are more "pigeons" (integers) than "holes" (boxes), at least one hole must contain two or more pigeons.
4. Since we have five integers and only four possible remainders, at least one of these remainder boxes must have two integers.

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The solution for the inequalities 5x – 10 > 20 or 5x – 10 ≤ –15 is:

x > 6 or x ≤ -1.

We have two inequalities to solve:

5x - 10 > 20

Adding 10 to both sides, we get:

5x > 30

Dividing both sides by 5, we get:

x > 6

And the second inequality is:

5x - 10 ≤ -15

Adding 10 to both sides, we get:

5x ≤ -5

Dividing both sides by 5 (and remembering to flip the inequality since we are dividing by a negative number), we get:

x ≤ -1.

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Answer:

T=15 S=5

Step-by-step explanation:

If you sold 3x more shirts(T) the other number must also apply. So the only one it can be is D. Also, 15x8+5x12=180

The step the student first made an error was step B

The given expression in simplest form is 8

From the question we are to determine the step the student first make an error and we are to simplify the given expression correctly.

The given expression is

5 - (-3)

The student steps are as follows:

Step A: 5+ (3)

Step B: 5+8

Step C: 13

The step the student first made an error was step B because

5 + (3) should evaluate to

5 + 3

and eventually 8

The correct simplification process is as follows:

5 - (-3)

Step A: 5+ (3)

Step B: 5 + 3

Step C: 8

Hence, the expression in simplest form is 8

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Thus, the value of f6 using a 3-day weighted moving average with w1 is 60.

To calculate the 3-day weighted moving average with w1 for the value of f6, we need to first calculate the weighted average for the past three days.

The formula for weighted moving average is:

WMAt = [(P1 * w1) + (P2 * w2) + (P3 * w3)] / (w1 + w2 + w3)

where:
- WMAt is the weighted moving average for time t
- P1, P2, P3 are the values of the variable for the three time periods being averaged
- w1, w2, w3 are the weights assigned to each period (in this case, w1 = 1 and w2 = w3 = 0)

For the past three days, we have:

- Day 4: 60 rolls sold
- Day 5: 53 rolls sold
- Day 6: 60 rolls sold

Using the formula above with w1 = 1 and w2 = w3 = 0, we get:

WMA6 = [(60 * 1) + (53 * 0) + (60 * 0)] / (1 + 0 + 0) = 60

Therefore, the value of f6 using a 3-day weighted moving average with w1 is 60.

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Answer:

(x-1)^2+(y+3)^2=25

Step-by-step explanation:

that's how iit'ss written in standard form.

The value of x that makes the triangle a right triangle is 25, the value of x that makes it acute is when x < 25 and angle X < 90° and for the triangle to be obtuse is when x > 25 and the angle X > 90°.

A triangle with three acute angles (angles less than 90°) is called acute triangle while a triangle is called obtuse triangle if it has one obtuse angle (angle greater than 90°) and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle.

by Pythagoras rule, we can calculate for the value of x if the triangle is a right triangle as follows:

x² = 15² + 20²

x² = 225 + 400

x² = 625

x = √625

x = 25.

In conclusion, value of x that makes the triangle a right triangle is 25, the value of x that makes it acute is when x < 25 and angle X < 90° and for the triangle to be obtuse is when x > 25 and the angle X > 90°.

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Answer:

[tex] \sqrt{ {28}^{2} + {45}^{2} } = \sqrt{784 + 2025} = \sqrt{2809} = 53[/tex]

Answer:

A

Step-by-step explanation:

if we put x as equal to 2 that means x =2

substitute 2 in for x and then solve.

16*2 -16 = 16

4(4*2-4) = 16

Answer:

If the dimensions of the scaled painting are 8 times smaller than the actual painting, then the actual dimensions can be found by multiplying the scaled dimensions by 8.

So, the actual dimensions of the painting are:

12 inches x 8 = 96 inches (width)

16 inches x 8 = 128 inches (height)

The infusion rate for the given volume to be infused in the given time duration is given by 266.67 ml per hour (rounded to two decimal places).

Volume to be infused = 0.8liters

Time duration = 9 hours

Drop factor = 60 gtt/ml

Use the following formula to calculate the infusion rate,

Infusion rate = (Volume to be infused × Drop factor) / Time in minutes

Convert the units to liters and minutes, respectively,

1 liter = 1000 milliliters

⇒ 0.8 liters = 800 milliliters

1 hour = 60 minutes

⇒ 9 hours = 9 × 60

                 = 540 minutes

Substituting the given values, we get,

⇒ Infusion rate = (800 ml × 60 gtt/ml) / 540 min

⇒Infusion rate = 88.89 gtt/min (rounded to two decimal places)

The infusion rate is 88.89 drops per minute.

To convert this to milliliters per hour,

Use the following conversion,

since the drop factor is 60 gtt/ml

⇒ 1 ml = 20 drops

The infusion rate in ml/hour is,

= (88.89 gtt/min × 1 ml/20 gtt) × 60 min/hour

= 266.67 ml/hour

Therefore, the infusion rate is 266.67 ml per hour (rounded to two decimal places).

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The length of Rocky Mountain Juniper tree will be 1.5 feet.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that:

A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 6.8 inches.

Now,

Let the height of Rocky Mountain Juniper tree = x feet

And, A tour guide for Yellowstone National Park is 5.1 feet tall and casts a shadow of 6.8 inches.

So, The height of a Rocky Mountain Juniper tree be if at the same time of day it casts a shadow of 20.3 feet will be find as:

[tex]\rightarrow \dfrac{5.1}{6.8} =\dfrac{\text{x}}{20.3}[/tex]

Solve for x as:

[tex]\rightarrow \dfrac{51\times20.3}{6.8} = \text{x}[/tex]

[tex]\rightarrow \dfrac{103.53}{6.8} = \text{x}[/tex]

[tex]\rightarrow \text{x} = 1.5 \ \text{feet}[/tex]

Thus, The length of Rocky Mountain Juniper tree will be 1.5 feet.

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Answer:

Step-by-step explanation:

(a) Here is a tree diagram to model the situation:

                      P(red hair)=0.025

                      /            \

        P(brown eyed | red hair)=0.22    P(not brown eyed | red hair)=0.78

        /                                       \

P(brown eyed | not red hair)=0.65      P(not brown eyed | not red hair)=0.35

(b) The probability that a randomly selected person is brown eyed is equal to the sum of the probabilities of being brown eyed given red hair and being brown eyed given not red hair, weighted by the probabilities of having red hair and not having red hair:

P(brown eyed) = P(brown eyed | red hair) * P(red hair) + P(brown eyed | not red hair) * P(not red hair)

= 0.22 * 0.025 + 0.65 * (1 - 0.025)

= 0.6385

Therefore, the probability that a randomly selected person is brown eyed is approximately 0.6385, or 63.85%.

(c) The probability that a randomly selected person has red hair given the person selected isn't brown eyed can be calculated using Bayes' theorem:

P(red hair | not brown eyed) = P(not brown eyed | red hair) * P(red hair) / P(not brown eyed)

To calculate the denominator, we need to use the law of total probability, which states that the probability of an event is equal to the sum of the probabilities of that event given each possible condition:

P(not brown eyed) = P(not brown eyed | red hair) * P(red hair) + P(not brown eyed | not red hair) * P(not red hair)

= 0.78 * 0.025 + 0.35 * (1 - 0.025)

= 0.3685

Substituting this and the other given probabilities into Bayes' theorem, we get:

P(red hair | not brown eyed) = 0.78 * 0.025 / 0.3685

≈ 0.0529

Therefore, the probability that a randomly selected person has red hair given the person selected isn't brown eyed is approximately 0.0529, or 5.29%.

(d) The probability that a sample of 20 people will have at least 1 person with red hair can be calculated using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event of interest is that none of the 20 people have red hair, so the probability of this event happening is:

P(none have red hair) = (1 - 0.025)^20

≈ 0.3585

Therefore, the probability that at least 1 person in the sample has red hair is:

P(at least 1 has red hair) = 1 - P(none have red hair)

≈ 0.6415

So, the probability that a sample of 20 people will have at least 1 person with red hair is approximately 0.6415, or 64.15%.

The call would cost $11 and the duration would be 2 minutes under both plans.

To solve the problem, assume the required time with a variable and set up equations for the cost of the call under Abbey's plan and Wendell's plan. We then set these expressions equal to each other and solved for the duration that variable that made the costs equal.

Here we have

On her plan, Abbey pays $5 just to place a call and $3 for each minute.

Wendell makes an international call he pays $1 to place the call and $5 for each minute.

Let's assume that the call duration is x  minutes.

Under Abbey's plan, the cost of the call would be:

$5 (for placing the call) + $3 per minute (for t minutes) = 5 + 3x

Under Wendell's plan, the cost of the call would be:

$1 (for placing the call) + $5 per minute (for t minutes) = 1 + 5x

To find the duration x that makes the cost of the call exactly the same under both plans set the two equations equal to each other and solve

=>  5 + 3x = 1 + 5x

=>  5x - 3x = 5 - 1

=>  2x = 4

=>  x = 2

So the call duration is 2 minutes, and the cost of the call under both plans would be:

$5 (for placing the call) + $3 per minute (for 2 minutes) = $11

$1 (for placing the call) + $5 per minute (for 2 minutes) = $11

Therefore,

The call would cost $11 and the duration would be 2 minutes under both plans.

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The value of the variable x is -6

Algebraic expressions are described as those mathematical expressions that are known to consist of terms, coefficients, variables, constants and factors.

These expressions also consist of arithmetic operations, such as;

From the information given, we have the equation;

x + 12/2 = 3(x + 7)

expand the bracket

x +12/2 = 3x + 21

cross multiply the values

x + 12 = 6x + 42

collect like terms

-5x = 30

x = -6

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The outcomes that are part of the sample space are 3,5; 2,2; and 4,3, options A, C, & E are correct.

For the first spin, there are 5 possible outcomes: 1, 2, 3, 4, and 5.

Similarly, for the second spin, there are also 5 possible outcomes: 1, 2, 3, 4, and 5.

To calculate the total number of outcomes for both spins, we multiply the number of outcomes for each spin together:

5 * 5 = 25.

Now let's consider each option provided and determine if they are part of the sample space:

A) 3,5 - Both outcomes (3 and 5) are part of the sample space since they fall within the possible outcomes for each spin.

B) 1,6 - Outcome 6 is not part of the sample space since the spinner is only labeled 1–5.

C) 2,2 - Both outcomes (2 and 2) are part of the sample space since they fall within the possible outcomes for each spin.

D) 5,0 - The outcome 0 is not part of the sample space since the spinner is labeled 1–5, not 0–5.

E) 4,3 - Both outcomes (4 and 3) are part of the sample space since they fall within the possible outcomes for each spin.

Hence, option A, C, & E are correct.

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Answer:

Since ∠CAB = 90°, we know that AC is the hypotenuse of the right triangle ABC. Let's use the sine function to find the length of AC:

sin(∠ABC) = BC/AB

sin(46°) = BC/9.4

BC = 9.4 * sin(46°)

Now, using the Pythagorean theorem, we can find the length of AC:

AC = sqrt(AB^2 + BC^2)

AC = sqrt(9.4^2 + (9.4*sin(46°))^2)

AC ≈ 12.632

Rounding this to 3 significant figures, we get:

AC ≈ 12.6

Therefore, the length of AC rounded to 3 significant figures is approximately 12.6 units.

The total pies purchased if total cost is $19, $28.50 and $47.50 is 38,57, and 95, under the condition that each pie costs $0.50.

Here we have to implement the principles of algebra to evaluate this problem,
Let us consider p to be the number of pies purchased
c  to be the cost of each pie which = $0.50.
Therefore, the total cost of pies is equal to 9:50 times p
c × p = 9.50 × p
Applying simplification to the given equation by implementing subtracting 0.50p from the both sides
c × p - 0.50p = 9.50 × p - 0.50p
c × p - 0.50p = 9p
c × p = 9p + 0.50p
c × p = 9.50p

Then, we can evaluate for p by dividing both sides by c
p = total cost / c

The total pies purchased if total cost is $19, $28.50 and $47.50 is 38,57, and 95.

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The complete question is
Each pie at a bakery costs $0.50 The total cost of pies is equal to 9:50 times p.  Find the number of pies purchased if the total cost is $19.00, $28.50, or $47.50

Answer:

Step-by-step explanation:

The relation is not a function. A function is a relation in which each input value leads to exactly one output value. In this case, the input value of 1 leads to two different output values, -2 and 3. Therefore, the relation is not a function.

The correct answer is No, because for each input there is not exactly one output.

The inequality for the possible values of w are;  w >  2l.

We know that the sum of length of the sides used to made the given figure.

We are given that perimeter of the rectangle > perimeter of the triangle

Let the dimension of the rectangle be w as width and L as length

Then perimeter of the rectangle = 2(L + w)

Now let the side of triangle be w then;

The perimeter of the triangle = 3w

The inequality becomes as;

2(L + w) > 3w

2w + 2L > 3w

w + 2l> 0

w >  2l

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The measure of CD in triangle is 18.

We are given that;

CE=7, HB=13, HF=3

Now, In triangle GDH

GD=1/2 * BD

=24/2=12

BC= 2* EC

=2* 7= 14

By pythagoras theorem;

EH^2 + EB^2 = BH^2

EH^2 + 49 = 169

EH^2 = 120

EH= rt120

FD= 16

CD= 18

Therefore, by the given triangle answer will be 18.

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Answer:

27/2197 chance of picking 3 white marbles

Step-by-step explanation:

The probability of picking 3 white marbles when each marble is returned to the bag before the next marble is picked is 27/2197.

The probability of picking one white marble from the bag is 3/13. Since each marble is returned to the bag before the next one is picked, the probability of picking a white marble on the second draw is also 3/13. The same applies to the third draw. Therefore, the probability of picking 3 white marbles in a row is (3/13) x (3/13) x (3/13) = 27/2197, or approximately 0.0123.

In this scenario, we have a bag containing 6 red, 3 white, and 4 blue marbles. Since each marble is returned to the bag before the next marble is picked, the probability remains constant for each draw.

To find the probability of picking 3 white marbles, we can use the formula:

P(white) = (Number of white marbles) / (Total number of marbles)

There are 3 white marbles and a total of 13 marbles (6 red + 3 white + 4 blue). So the probability of picking one white marble is:

P(white) = 3/13

Since the marbles are replaced, we can simply multiply the probability for each pick:

P(3 white marbles) = P(white) * P(white) * P(white) = (3/13) * (3/13) * (3/13)

P(3 white marbles) = 27/2197

Thus, the probability of picking 3 white marbles when each marble is returned to the bag before the next marble is picked is 27/2197.

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The value of the product of the "complex-numbers" (2i)(5+3i) is "-6+10i", Option(a) is correct.

The Complex numbers are defined as the numbers that can be expressed in the form "a + bi", where a and b are real numbers and "i" is the imaginary unit, which is defined as the square root of -1.

To multiply the two complex numbers (2i)(5+3i), we use the distributive property of multiplication:

⇒ (2i)×(5+3i) = (2i)×(5) + (2i)×(3i),

Simplifying this expression,

We get,

⇒ (2i)×(5+3i) = 10i + 6i²,

Since i² = -1, we substitute this value into the expression:

⇒ (2i)×(5+3i) = 10i + 6(-1) = -6 + 10i,

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

What is the value of the product (2i)×(5+3i)?

(a) -6 + 10i

(b) 10 + 6i

(c) -10 + 6i

(d) 10 - 6i

The value of n in the given equation is determined as 5.

option C.

The value of n in the given equation is calculated by applying the following method of simplification.

2n / (n - 5) + (4n - 30) / (n - 5) = n

Since the common denominator is n - 5, multiply through by n - 5;

2n + (4n - 30) = n(n - 5)

6n - 30 = n² - 5n

n² - 11n + 30 = 0

Factorize the expression as follows;

n² - 5n - 6n + 30 = 0

n(n - 5) - 6(n - 5) = 0

(n - 6)(n - 5) = 0

n = 5 or 6

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The approximate probability of drawing one orange marble and one green marble from a bag containing five red marbles, four orange marbles, one yellow marble, and three green marbles is approximately 0.154.

To find the approximate probability of drawing marbles, we can use the following formula

probability = (number of favorable outcomes) / (total number of outcomes)

We need to find the number of favorable outcomes where one marble is orange and the other is green. We can choose one orange marble from four orange marbles in the bag in 4 ways, and one green marble from three green marbles in 3 ways. So, the number of favorable outcomes is 4 x 3 = 12.

The total number of ways of choosing two marbles from the bag is 13C2, which is the number of combinations of 2 marbles that can be drawn from the 13 marbles in the bag. Therefore, the total number of outcomes is

13C2 = (13 x 12) / (2 x 1) = 78

Thus, the approximate probability of drawing one orange marble and one green marble is

probability = number of favorable outcomes / total number of outcomes = 12/78 ≈ 0.154

Therefore, the approximate probability of drawing one orange marble and one green marble from the bag is approximately 0.154.

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The value of x is 8 if the lines a is parallel to b and c is parallel to d

a is parallel to b and c is parallel to d

We have to find the value of x

3x+36+15x=180

18x+36=180

Subtract 36 from both sides

18x=180-36

18x=144

Divide both sides by 18

x=144/18

value x=8

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The evaluation of the expression as per the PEMDAS rule is 1.095 x 10⁴.

The provided expression is,

3.45 × 10³ + 7.5 × 10³.

To evaluate the expression, first, simplify the expression,

which is,

(3.45 x 1000) + (7.5 x 1000).

Now, the expression can be solved using PEMDAS,

The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

3450 + 7500.

Now add the expression to get the final value,

10950.

Now, simplify as the required term,

1.095 x 10⁴.

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