Use the properties of logarithms to evaluate each of the following expressions. (a) 2log 3 + log 4 = 0 5 12 Ine = In e (b) 0 - X Ś ?

The number of ways the ribbons can be awarded in a race with "x" runners is x * (x-1).

The number of ways the ribbons can be awarded depends on the total number of runners participating in the 100-meter dash.

If there are "x" runners participating, the winner can be any one of the x runners, and the second-place runner can be any one of the remaining (x-1) runners.

Therefore, the number of ways the ribbons can be awarded is equal to the number of possible choices for the winner multiplied by the number of possible choices for the second-place runner.

Mathematically, this can be expressed as:

Number of Ways = x * (x-1)

For example, if there are 5 runners in the race, there are 5 ways to choose the winner. After selecting the winner, there are 4 remaining runners from which we can choose the second-place runner. So, in this case, the number of ways the ribbons can be awarded is:

Number of Ways = 5 * 4 = 20

In general, the number of ways the ribbons can be awarded in a race with "x" runners is x * (x-1).

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Answer:

The one on the left

Step-by-step explanation:

i thought about it and its the dot on the left

The maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

To determine the maximum price Matthew can pay for the car, we need to consider his repayment capability and the terms of the loan.

Matthew can make annual repayments of $35,000. Since the loan term is six years, the total amount he can repay over the loan period is $35,000 multiplied by six, which equals $210,000.

To calculate the maximum price of the car, we need to account for the interest rate of 9.25%. The interest rate represents the cost of borrowing and is applied to the loan amount.

Let's assume the loan amount is denoted by P.

The formula to calculate the future value of a loan with interest is:

FV = P(1 + r)^n

Where:

FV = Future value (total amount repaid)

P = Principal amount (maximum price of the car)

r = Interest rate per period (9.25% or 0.0925)

n = Number of periods (six years)

Since Matthew can repay a total of $210,000 over the loan period, we can set up the equation:

$210,000 = P(1 + 0.0925)^6

Now we can solve for P:

P = $210,000 / (1 + 0.0925)^6

Evaluating this expression, we find:

P ≈ $126,318.29

Therefore, the maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.

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Answer:

3(n+5)≥17

Step-by-step explanation:

3(n+5)≥17 is the expression for three times the sum of a number n and 5 is at least 17.

The relationship between two expressions or values that are not equal to each other is called inequality.

Given that three times, the sum of a number n and 5 is at least 17.

According to the question, the expression will be = 3(n+5)≥17

Hence, 3(n+5)≥17 is the expression for three times the sum of a number n and 5 is at least 17.

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Answer:

Step-by-step explanation:

First we replace the original 'x' with 'x + 4,' which causes translation of the original parabolic graph 4 units to the left.  Next, reflect this translated graph about the x-axis (which is the effect of multiplying by -1/2 as shown).  Finally, shift the entire graph (the most recent one) down 5 units.

Answer: A

Step-by-step explanation:

Answer:

8/1

Step-by-step explanation:

because 800% is basically 800/100, when you divide both by 100 it would equal to 8/1 in simplest form

The equation of the perpendicular line that passes through the point (- 3, - 1) is y = 2 · x + 5.

In this question we must determine the equation of a line that is perpendicular to another line and pass through a given point. Mathematically speaking, lines are represented by the following equation:

y = m · x + b

Where:

And the slopes of two lines perpendicular to each other satisfy the following relationship:

m · m' = - 1

Where:

First, determine the slope of the perpendicular line by means of the slope relationship:

m = - 1 / 2

m' = - 1 / m

m' = - 1 / (- 1 / 2)

m' = 2

Second, find the intercept of the perpendicular line by the equation of the line:

b = y - m · x

b = - 1 - 2 · (- 3)

b = - 1 + 6

b = 5

Third, write the equation of resulting line:

y = 2 · x + 5

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Answer:

Step-by-step explanation:

118,000,000,000 +2,357,000,000=120,357,000,000

Answer:

3.14 million

Step-by-step explanation:

10.676 - 7.536 = 3.14

To check

7.536 + 3.14 = 10.676

Answer:

3.14 million is the correct answer

Answer:

1/3

Step-by-step explanation:

Does the spinner only have these 3 sections?

If so, the probability of spinning an odd number is 1/3. There are a total of 3 possibilities (denominator), and only 1 is odd (numerator).

The P(odd) is the probability of spinning an odd number that would be equal to 1/3.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

You spin the spinner once.

6, 7, 8

There are a total of 3 possibilities (denominator), and only 1 is odd (numerator).

So, the probability of spinning an odd number = 1/3.

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Answer:

The answer is B because if you take the line of y=-x (which you can look up on desmos if you don't know what y=-x looks like) and reflect over that line you can see that when the dot reflects over the line y=-x it goes to points (0,2)

Step-by-step explanation:

There are 25 males in village 3

The given parameters are:

Total males = 75

                 Male     Female   Total

Village 1   20              25

Village 2  30                            50

Village 3                     30

Total         75

The number of male in village 3 is calculated using:

Male = Total Male - Male in villages 1 and 2

So, we have:

Male = 75- (20 + 30)

Evaluate

Male = 25

Hence, there are 25 males in village 3

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Complete question

An island has three villages and the total number of males is 75. The first village has 20 males and 25 females. The second village has 50 people of whom 30 are males. The third village has 30 females.

Calculate the number of male in third village

Answer:

he saves 3 dollars. its not worth it.

Step-by-step explanation:

you divide 12 by ten getting you 1.2 which you subtract from 1.50 that then multiply that by 10

The horizontal distance of the boat from the sailor will be 196.26 meters.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

From a coastal lookout P,100 m above sea level, a sailor sights a boat at an angle of depression of 27 degrees.

Then the horizontal distance of the boat from the sailor is given as,

tan 27° = 100 / d

d = 100 / tan 27°

d = 196.26 m

The horizontal distance of the boat from the sailor will be 196.26 meters.

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The angle ABD of the trapezoid ABCD measures 90 degrees where the sum of the diagonals is 180 degrees.

In a trapezoid, the sum of the diagonals is 180 degrees. For this:

m∠ABD + m∠BCD = 180°

We also know that m∠BCD is a right angle (90°) because it is the angle formed by the horizontal and vertical lines.

Substituting the resulting values in the above formed equation , we will obtain the following:

m∠ABD + 90° = 180°

Simplified, it looks like this:

m∠ABD = 90°

Therefore, the angle ABD of the trapezoid ABCD measures 90 degrees. So the answer is 90°. 

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Answer:

Step-by-step explanation:

Two different fractions where lowest common denominator is 20 are 1/4 and 1/5.

What are the lowest common denominator?

For two or more fractions, if the numbers at the bottom (or denominator) by which the lowest number can be divide into, is called the lowest common denominator. It is also known as the least common denominator.

Here, 20 is the given lowest common denominator. 

Therefore, we can write: 20 = 1 × 20, 20 = 2 × 10, 20 = 4×5

Hence, two fractions for which 20 can be a lowest common denominator are 1/4 and 1/5.

Hope it helps!

Answer: (2, -3)

Step-by-step explanation:

To get these points, you just need to multiply the coordinates by 1/4, or divide by 4

The probability that the first person to enter the room will be randomly seated at a walnut table is approximately 0.129, or 12.9%.

To calculate the probability that the first person to enter the room will be randomly seated at a walnut table, we need to determine the total number of tables and the number of walnut tables specifically.

The total number of tables in the room is the sum of the walnut, poplar, cedar, and cherry tables:

Total number of tables = 4 walnut tables + 9 poplar tables + 7 cedar tables + 11 cherry tables = 31 tables.

The probability of being seated at a walnut table can be calculated by dividing the number of walnut tables by the total number of tables:

Probability = Number of walnut tables / Total number of tables = 4 walnut tables / 31 tables ≈ 0.129.

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Answer:

2/1

Step-by-step explanation:

8/4 which is also 2/1

Answer:

B. n ≥ 12

Step-by-step explanation:

As you can see, the number is represented by n. So when n is no less than 12, it means that n is greater than 12 but can also be equal to it.

Therefore, the answer is n ≥ 12

Answer:

AAA

Step-by-step explanation:

Answer:

Combination.

167960

58344

Step-by-step explanation:

A.)

Choosing 11 players from 20 ; here the order in which the players are chosen does not matter, hence it is a combination problem.

2.)

Using nCr

n = 20 ; selection, r = 11

nCr = n! / (n-r)!r!

20C11 = 20! / 9!11!

20C11 = 167960

3.)

1 goalie 10 players

3C1 * 17C10

3 * 19448

= 58,344 ways

The value of x is; x = 17.48.

Here, we have,

from the given diagram, we get,

there is a right angle triangle.

we have to find the value of x.

we know that,

Let the angle be θ , such that

sin θ = opposite / hypotenuse

here, we get,

sin 39 = 11/x

so, we have,

0.6293 = 11/x

so, x = 17.48

Hence, The value of x is; x = 17.48.

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The relation "r" on the set of integers is a mathematical concept that describes a certain relationship between pairs of integers.

A relation on the set of integers, denoted as "r," is a mathematical construct that defines a connection or association between pairs of integers. It is represented by a set of ordered pairs (a, b), where "a" and "b" are integers. In this context, we will evaluate the given statements and determine their correctness.

Reflexive: A relation "r" is reflexive if every integer is related to itself. This means that for all integers "a," the pair (a, a) must be in the relation "r." If this condition holds true for the given relation, we can mark it as correct.

Symmetric: A relation "r" is symmetric if for every pair (a, b) in "r," the pair (b, a) is also in "r." To determine the correctness of this statement, we need to check if for every (a, b) in "r," (b, a) is also present. If this condition is satisfied, we can mark it as correct.

Transitive: A relation "r" is transitive if for any three integers a, b, and c, if (a, b) and (b, c) are in "r," then (a, c) must also be in "r." To validate this statement, we need to verify if for every pair (a, b) and (b, c) in "r," (a, c) is present. If this condition is met, we can mark it as correct.

By carefully evaluating these properties of the given relation "r" on the set of integers, we can determine which statements are correct and which are not, based on the definitions of reflexivity, symmetry, and transitivity.

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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The type of set that allows you to position rollers diagonally and set from multiple points of origin is an oblong set.

An oblong set is a type of parallel set consisting of two parallel rectangular bars or blocks, with rollers positioned diagonally between them. The oblong shape of the set allows for the rollers to be positioned at a diagonal angle, which can be useful when setting up workpieces that need to be adjusted at an angle or from multiple points of origin.

In contrast, a half oval set and a half circle set are both types of circular sets that consist of rollers positioned in a semi-circular shape. These types of sets are useful for supporting workpieces that have a curved or circular shape, but they do not provide the flexibility to position rollers at a diagonal angle or from multiple points of origin.

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Answer:

the answer is 1 whole and 1/2

Step-by-step explanation:

1 and 1/2

Step-by-step explanation:

1)y=17-2=15

2)y=17-6=11

3)y=17-8=9

4y=17-10=7

Answer:

Step-by-step explanation:

Just exchange (x) with the numbers and do the equations :)

Answer:

2.478 million at the end of 2015

Step-by-step explanation:

Multiply the amount of population at the end of 2012 times 6%

2.1 times 0.06 = 0.126 million

So, at a constant rate, yearly, the population of Dubai increases 0.126 million

2015-2012 = 3

0.126 times 3 = 0.378 million

2.1 + 0.378 = 2.478 million

hope this helps:)

Answer:

39.6

Step-by-step explanation:

The percent of change from 5.3 to 7.4 is 39.6%