Using laws of logarithms, write the given expressions usingsums and/or differences of logarithmic expressions which donot contain the logarithms of products, quotients, or powers.a. log(45x) = log(45)+log(x). Previewb. log (x⁵⁵) = 55log(x). Previewc. 10 log(⁵√x) = 1/5log(x)^10. Preview2/5 log(x)¹⁰ syntax ok

Hence, the correct match of probabilities with their corresponding situations is given by option 4.

To match the probabilities with their corresponding situations, we can utilize the formulas given below:

[tex]P(A ∩ B) = P(A) x P(B|A)P[/tex](2 aces) =[tex](4/52) x (3/51) = 1/221[/tex]

P(heart and club) =[tex](13/52) x (13/51) = 169/2652[/tex]P(spade and ace of hearts) = 0P(2 of the same card) = (1/52) + (3/51) + (2/50) + (1/49) + (4/48) + (3/47) + (2/46) + (1/45) = 20/663P(red card and four of spades) = (16/52) x (1/51) = 4/663

Therefore, the probabilities with their corresponding situations are:3: P(spade and ace of hearts) = 0 (Not possible as Ace of hearts is not spade)

4: P(2 aces) = 1/2211: P(heart and club) = 169/26521: P(heart and club) = 169/26522: P(red card and four of spades) = 4/663

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Step-by-step explanation:

Since the three horizontal lines are parallel, you can set up a simple ratio:

71 is to 79    as   x is to 81

71/79 = x/81

x = 71/79 * 81 = 73 units   ( rounded to two S.D.)

After 6 weeks, the size of the bacteria is 1600, and after 15 weeks, the size of the bacteria is 12800

Let N₀ be the initial number of bacteria in a population and r be the growth rate of the bacteria.

The doubling time t doubles the population after each time interval t, hence:

Nt = N₀ × 2^(t/t) Nₜ

= N₀ × 2^(t/d)Nt/N₀

= 2^(t/d)ln(Nₜ/N₀)

= (t/d)ln2ln(Nₜ) - ln(N₀)

= (t/d)ln2ln(Nₜ/N₀)

= (t/d)ln2t/d

= ln(Nt/N₀) / ln2

Now, we can calculate the time required for the population to double in size as

t = d × ln2/ln(Nₜ/N₀)

Now, let's substitute the values given and solve:

a) After 6 weeks, t = 3 weeks (since doubling time is 3 weeks)

So, Nₜ/N₀ = 2^(t/d)

= 2^(6/3)

= 2^2 = 4

Nt = N₀ × 4

= 100 × 4

= 400.

After 6 weeks, the size of the bacteria is 400.

b) After 15 weeks,

t = d × ln2/ln(Nₜ/N₀)ₜ

= 3 × ln2/ln(128)

= 3 × 0.9983/7.1554

= 0.4186 weeks

So, Nₜ/N₀ = 2^(t/d)

= 2^(15/3)

= 2^5

= 32Nₜ

= N₀ × 32 = 100 × 32

= 3200

After 15 weeks, the size of the bacteria is 3200.

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Solving a linear equation we can see that the answer is 40 months.

We know that company A only charges $70 per month, so the cost in dollars after x months is given by the linear equation:

A(x) = 70*x

For company B you need to pay $50 per month plus the $500 phone, so here the cost is:

B(x) =500 + 50*x

We want to find for what value of x we have B(x) = A(x), then we needto solve:

70x = 500 + 50x

70x - 50x = 500

20x = 500

x = 500/20

x = 40

After 40 months the cost will be the same one than in company A.

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The 0.05(x+4)+0.10(x) = $1.25 equation could be used to determine the number of dimes, x, in his pocket.

An equation is a mathematical expression containing an equal sign that states the equality of two expressions. It is essentially a statement of balance, showing that two expressions are equal in value. Equations are used to solve a wide variety of problems in mathematics, science, and engineering. For example, the equation x+2=4 expresses the fact that when 2 is added to any number x, the result is 4.

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Since the sequence is always decreasing and cannot go below the lower bound, it becomes increasingly closer to the lower bound, and thus converges to a limit.

A sequence is said to be decreasing if each term is smaller than the previous one, and bounded below if there exists a lower bound such that no term in the sequence is smaller than this bound. In this case, the sequence is decreasing and bounded below by 0.

When a sequence is both decreasing and bounded below, it must have a limit because the terms cannot continue to decrease indefinitely, as they cannot go below the lower bound (in this case, 0). This means that as we progress through the terms of the sequence, the difference between consecutive terms will decrease and eventually approach a constant value.

The limit of a sequence is a value that the terms of the sequence approach as they get closer and closer to the end. In this situation, the limit is the smallest possible value that the sequence can approach, without going below the lower bound.

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The new coordinates of point s after the dilation are (12x, 12y)

A dilation is a type of transformation that changes the size of an object. It can be thought of as a resizing or stretching of the object. In this case, we are dilating a point with a center at the origin (0,0) and a scale factor of 12.

The center of dilation is the point around which the dilation occurs. In this case, the center of dilation is the origin. This means that the point will be resized relative to the origin.

The scale factor is a number that determines the amount by which the object is resized. In this case, the scale factor is 12. This means that the point will be enlarged 12 times its original size.

To find the new coordinates of the point after the dilation, we multiply the original coordinates by the scale factor. Let the original coordinates of the point be (x, y). Then, the new coordinates of the point after the dilation are:

New x-coordinate = 12 × x

New y-coordinate = 12 × y

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Just ignore this answer, its incorrect

*edited*

Answer:

Step-by-step explanation:

144/25=x/5

times both sides by 5

144/5=x

simplify

x=144/5 or 28.8

Answer: x= 144/5

Step-by-step explanation:

Cross-Multiply

144/25 = 25x

Swap the sides so you can solve

720 =25x

Divide both sides

25x=720

x=144/5

Answer:

Step-by-step explanation:

Since the value of a is less than 0, the graph of the parabola would be opening downwards. Because of this we can rule out option C. In a quadratic equation, c represents the y-intercept, and, in this case c is negative, meaning the y-intercept is less than 0. Only option B has a downward-opening curve and a y-intercept less than 0, so it is the answer.

Answer: p= 2+c

Step-by-step explanation:

The answer of the given question based on the number line is the difference between 8 and -16 is not 14, it is 24. and 8 and -16 are 24 units apart on the number line.

A number line is a visual representation of the real number system, where numbers are placed in order from left to right, with zero in the center. The number line is an important mathematical tool used in a variety of ways, including:

Understanding and comparing numbers: By plotting numbers on a number line, we can visually see the relative size and position of numbers in relation to each other.

Performing arithmetic operations: The number line can be used to add, subtract, multiply, and divide numbers.

Graphing functions: The number line can be used as the horizontal axis of a graph to plot functions and other mathematical relationships.

Actually, the difference between 8 and -16 is not 14, it is 24.

To find the difference between two numbers on a number line, you need to subtract the smaller number from the larger number. In this case, 8 is larger than -16, so we subtract -16 from 8:

8 - (-16) = 8 + 16 = 24

Therefore, 8 and -16 are 24 units apart on the number line.

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P (-1, -2/5) is the point of segment of line .

What is the name of a line segment?

When both end points of a line segment are vertices of a polygon or polyhedron, the line segment is either a diagonal or an edge (of that polygon or polyhedron) if the vertices are close to one another.

                                A line segment is known as a chord when both of its end points are on a curve (such as a circle) (of that curve).

A = (-3,2)

B = (7,-10)

 1: 4

P (x,y) partition A (x₁ , y₁) B (x₂ , y₂) into ratio

 = (4 * -3 + 1 * 7) / (1 + 4)

 = -5/5

 = -1

y = (by₁ + ay₂) / (a+b)

 = (4 * 2 + 1 * -10) / (1 + 4)

 = -2/5

P (-1, -2/5)

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Evaluating the (2.7)³ - (1.6)³ - (1.1)³ using the suitable identity is given by the term 26.19.

The sum of cubes (of two integers) formula is what is known as the a3 + b3 formula. Without computing the two cubes, the total may be calculated using the a cube + b cube formula. The binomials of cubes are factorised using it as well.

Let a = 2.7, b = 1.6, c = 1.1

We see that,

a + b + c = 2.7 + 1.6 + 1.1 = 5.4

Now as we know that,

If a+b+c =  5.4

then using the identity:

a³ - b³ - c³ = ( a+ b+ c ) (a² + b² + c² - ab - bc - ca) + 3 abc

so,

a³ - b³ - c³ = 5.4(2.7² + 1.6² + 1.1² - 4.32 - 1.76 - 2.97) + 14.256

= 5.4(7.29 + 2.56 + 1.41 - 4.32 - 1.76 - 2.97) + 14.256

a³ - b³ - c³ = 26.19

Therefore,  (2.7)³ - (1.6)³ - (1.1)³ is  26.19

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The function that could not be true is , f(-1) = 4.option b, f(3) = 30 is not correct.

To find f(2), we simply substitute 2 for x in the function f(x):

[tex]f(2) = (2 + 1)^2 = 9[/tex]

Therefore,

[tex]f(2) = 9.[/tex]

Now, to determine which of the following statements could not be true if f(x) is a function and f(1) = 5, we need to check whether they violate any properties of functions. Here are the statements:

f(1) = 5

means that y = 5x

so when y = 1

x = 5

Therefore, option b, f(3) = 30 is not correct.

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Complete question:

Find f(2) if f(x) = (x + 1)2.

If f(x) is a function and f(1) = 5, then which of the following could not be true?

f(10) = 50

f(3) = 30

f(2) = 10

f(7) = 35

By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.

To construct a 95% CI for the population mean of a normal distribution, we can use the formula:

CI = sample mean ± z* (standard error)

Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:

standard error = population standard deviation / √sample size

In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:

standard error = 5.48 / √20 = 1.226

Now, we can use the formula for the CI:

CI = 10 ± 1.96 x 1.22

Simplifying this expression gives us:

CI = (7.59, 12.41)

This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.

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Answer:

there

Step-by-step explanation:

the right option is B.) a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 22

A linear function is a polynomial function whose degree is utmost zero or one. It is represented as a straight line in the graph.

The corresponding graph for the given data is a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (1,25), (3,19), (4,16) and (7,7)

Time(in days)    -    Number of boxes

1                                  25

3                                  19

4                                   16

7                                    7

This forms a straight line.

By critically observing the graph and relationship between the time and number of boxes, we determine a function for the graph.

That is y=--3x+28

Putting x=0, we get

y=-3(0)+28=28

Putting x=2, we get

y=-3(2)+28

y=22

hence,. a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 22

The diagram is attached below.

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Opioids are a class of drugs that include both prescription painkillers, such as oxycodone, hydrocodone, and fentanyl, and illegal drugs, such as heroin.

Opioids are highly addictive and can lead to physical dependence and addiction with prolonged use. They can also cause a range of negative side effects, including drowsiness, confusion, constipation, nausea, and respiratory depression, which can be life-threatening in high doses.

Opioid addiction has become a major public health crisis in many countries, including the United States, where it has been linked to a dramatic increase in overdose deaths.

The numbers that match the phrases are;

1 - j

2 - c

3 - b

4 - a

5 - i

6 - d

7 - e

8 - f

9 - j

10 - h

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Answer:

Step-by-step explanation:

To make this Cuboid you need to workout how many cubes are missing from this cuboid.

To get the cubes numbers you have to get the volume of this cuboid which is 3x4x3=36

So there is 36 cubes in this cuboid.

And then workout how many cubes are missing from this plan, front and side elevation.

Front Elevation 3x3=9

Side Elevation 4x3=12 then deduct 3 blocks from the left. Then deduct 4 blocks from right top corner which is 4 blocks.

3+4=7 missing blocks, then do this 12-7=5 Side has 5 added blocks fron the front.

Front 9 blocks Side 5 blocks. 9+5=14

So 36-14=22 ANSWER is 22 BLOCKS has been added.

The domain of a function f(x) = 2√(-x² + 10x) in interval notation is given by (-∞, 0] ∪ [10, ∞).

Function f(x) = 2√(-x² + 10x).

Domain of a function is the set of all possible input values of x for which the function is defined.

Values of x for which the expression inside the square root is non-negative.

As the square root of a negative number is not a real number.

Take out the common factor -x we have,

-x² + 10x ≥ 0

⇒ -x(x - 10) ≥ 0

⇒ -x ≥ 0 or ( x - 10 ) ≥ 0

The inequality is satisfied when x ≤ 0 or x ≥ 10.

This implies,

The domain of the function f(x) = 2√(-x² + 10x) is the set of all real numbers such that x ≤ 0 or x ≥ 10.

In interval notation form,

The domain is represented as,

(-∞, 0] ∪ [10, ∞).

Therefore, the domain of the given function is equal to (-∞, 0] ∪ [10, ∞).

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The above question is incomplete , the complete question is:

What is the domain of a function f(x) = 2√-x²+ 10x

Answer:

Fraction form:

[tex]\text{h} = \dfrac{4}{1.5} \ \text{in}[/tex]

Decimal form:

[tex]2.667 \ \text{in}[/tex]

Step-by-step explanation:

I've attached the work below

The formula use is usually use to find the area of a triangle but allowed us to work backward after inputting given values

Hope it helps, Let me know if you have any more questions/concerns.

Arabella drive 17. 8 miles a day, Yaya drives 1. 6 times as far for each day. Therefore, 598.08 miles Yaya drive in three weeks.

Miles:

The mile, sometimes the international mile or the regulation mile, to distinguish it from other miles, is an imperial unit of the United Kingdom and a customary unit of distance in the United States; both are based on the old imperial unit of length, 5,280 imperial feet or 1,760 meters. The statute mile was standardized by an international agreement between the Commonwealth of Nations and the United States in 1959, when it was officially redefined as 1,609,344 meters in terms of SI units.

According to the Question:

We know that:

In a week there are 07 days

Therefore,

In 03 weeks there are = 7×3

                                     = 21 days

Given that :

Arabella drive 17.8 miles daily

and Yaya drives 1.6 times far from 17.8 miles daily.

Therefore,

Yaya drives = 17.8 × 1.6 miles

                    = 28.48 miles

Now,

for three weeks = 28.48 × 21

                           = 598.08 miles.

Therefore, 598.08 miles Yaya drive in three weeks.

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Your longitude in DMS is 135 degree. So the option D is correct.

This is because there are 12 hours left in the local time ( i.e. 12 hours noontime or mid-day).

As UT (or GMT) time is 9 p.m., there are 9 hours between GMT time and local time.

9 hours = 9 × 60 minutes = 540 minutes

Now, we know that:

Every four minutes, the Earth turns one degree.

Thus, 1-degree longitude difference = 4 minutes

Or, 4 minutes of time difference = 1 degree of longitude

Or, 1 minute of time difference = 1/4 degree of longitude

Or, 540 minutes of time difference = (1/4) × 540 degrees of longitude

540 minutes of time difference = 135 degrees of longitude

Also, we can infer that the current location is in the Western hemisphere because we know that it is 9 hours behind GMT (or UT) time.

Hence, the longitude of the current location = 135⁰

So the option 4 is correct.

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The complete question is:

Your chronometer is set for Greenwich Mean Time (GMT or Universal Tim, UT). High noon at your present location is 9 pm UT. What is your longitude in DMS (not decimal degrees)?

1. 30° 18'W

2. 30° 16'W

3. 30° 17'W

4. none of the above

Answer:

x=2.4

y=2.5

z=3.3

Step-by-step explanation:

6/5=1.2

1.2 = scale factor

x=2x1.2=2.4

y=3/1.2=2.5

z=4/1.2=3.3

Answer:

Step-by-step explanation: This week, I had a question in math class about the different types of angles, such as alternate interior angles theorem, alternate exterior angles, same-side interior angles, same-side exterior angles, corresponding angles, concurrent lines, perpendicular lines, and a few more types of angles about lines and knowing what matches to what type of angle. Yes, I did ask a few questions when I was confused about certain lines and how they have this angle, such as a concurrent line. Yes, my question was answered. I actually enjoy asking questions because if I don't learn what I'm confused about, how will I know how to improve and avoid making the same mistakes? Yes, I had someone else ask the same question I had before, whether it was something new learned in class or something confusing or difficult to learn. It made me feel relieved and grateful because I'm glad I wasn't the only one who was confused, and it makes it easier when someone else doesn't understand the same step, and challenges when learning new things. The questions we ask lead to new discoveries. Questions lead us to answers we never considered before we asked the question. Of course, one cannot simply ask question after question without considering possible answers. Many people, on the other hand, are afraid that by asking questions, they will appear weak, ignorant, or unsure. They are afraid that asking questions will place them in a negative light. Lastly, some people are so eager to get things done that they don't stop to ask questions because it might slow them down.

Therefore , the solution of the given problem of surface area comes out to be  240 tiles will cover the floor.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.

Here,

Let's first determine how many 6 inch squares are required to span the floor:

=> 80 square feet is the size of the floor (8 feet by 10 feet).

We require the following because each 6-inch square spans an area of => (1/2) ft x (1/2) ft = 1/4 square feet:

=>  80 square feet 1/4 square foot = 320 tiles in a row of 6 inch tiles.

Since a 12 inch square encompasses a space that is 1 foot by 1 foot, we require:

=>  80 square feet /  12 inch square tile,

which equals 80 tiles.

Using 12 inch squares rather than 6 inch squares allows us to save the following amount of tiles:

=> Number of 6 inch tiles - Number of 12 inch tiles = 320 - 80 = 240 tiles

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The arithmetic mean return is 3.6%, and the standard deviation is 2.14%.

To find the arithmetic mean, we add up the five returns and divide by the number of returns (in this case, 5):

(3% + 6% + 0% + 6% + 3%) / 5 = 3.6%

To find the standard deviation, we first need to find the variance. We can do this by taking each return, subtracting the mean return (3.6%), squaring the result, summing these values, and dividing by the number of returns minus 1 (4 in this case):

((3% - 3.6%)^2 + (6% - 3.6%)^2 + (0% - 3.6%)^2 + (6% - 3.6%)^2 + (3% - 3.6%)^2) / 4 = 0.046

The standard deviation is the square root of the variance:

√0.046 = 0.214 or 2.14%

Therefore, the arithmetic mean return for security y is 3.6%, and the standard deviation (sample) is 2.14%.


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