\((\frac{8a^{-5}b^{4} }{12a^{-6}b^{-2} })\)

Answer:

39

Step-by-step explanation:

Lets solve for x:

We know the ratio is 1:3

1x+3x = 52

4x = 52

x = 13

Since the ratio is 1:3:

13(3) = 39

13:39

Which makes 39 the larger number

As the equation of tangent line is y = -3x, the value of slope, m is -3 and value of b is 0.

To find the equation of the tangent line at the point (π, -3π), we need to find the derivative of the function y = 3xcos(x), which is

y' = 3cos(x) - 3xsin(x)

and then evaluate the derivative at x = π to find the slope of the tangent line.

The slope at x = π is

m = 3cos(π) - 3πsin(π) = -3

So, the equation of the tangent line is y = -3x + b.

To find the value of b, we use the point (π, -3π) and the slope -3:

-3π = -3 * π + b

b = 0

So, the equation of the line tangent to the curve y = 3xcos(x) at the point (π, -3π) is y = -3x + 0 or simply y = -3x.

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Answer:

i have made it in pic above

The expression equivalent to\(-4x^2 + 2x - 5(1 + x)\)  is \(4x^2 + 8x + 5.\)

This expression matches the form \(x^2 + x + c,\) where c = 5.

To simplify the given expression \(-4x^2 + 2x - 5(1 + x)\) and make it equivalent to the expression \(x^2 + x + c,\) where c is a constant term, we need to perform some algebraic operations.

First, let's distribute the -5 to the terms inside the parentheses:

\(-4x^2 + 2x - 5 - 5x\)

Next, we can combine like terms:

\(-4x^2 + (2x - 5x) - 5 - 5x\)

Simplifying further:

\(-4x^2 - 3x - 5 - 5x\)

Now, let's rearrange the terms to match the form \(x^2 + x + c:\)

\(-4x^2 - 3x - 5x - 5\)

To make the leading coefficient positive, we can multiply the entire expression by -1:

\(4x^2 + 3x + 5x + 5\)

Now, we can combine the x-terms:

\(4x^2 + 8x + 5\)

So, the expression equivalent to \(-4x^2 + 2x - 5(1 + x)\) is \(4x^2 + 8x + 5.\)This expression matches the form \(x^2 + x + c,\) where c = 5.

It's important to note that the original expression and the equivalent expression have different coefficients and constants, but they represent the same mathematical relationship.

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Answer:

RISE/RUN

Step-by-step explanation:

Answer:

60π

Step-by-step explanation:

Formula for surface area of a cylinder is 2πrh + 2r²π

2πrh: this is the formula to find the area of the cylinder itself (circumference of the base times the height of the cylinder)

2r²π: this is the formula to find the area of the 2 circles at the end of the cylinder (area of a circle times 2)

We can substitute h with 7 and r with 3 to solve:

2πrh + 2r²π

2(3)(7)π + 2π(3²)

42π + 18π

60π

That is your answer

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46,536 is the possible number of codes if repeats are not allowed and the second letter must be 'g' and the first digit must be '3'.

If repeats are not allowed, and the second letter must be 'g', and the first digit must be '3', then we have to find the number of codes that can be possible.

Solution: Here we have to calculate the total number of possible codes if repeats are not allowed and the second letter must be 'g' and the first digit must be '3'.

The given conditions:

First digit = 3

Second letter = g

We know that a code is usually formed by combining letters, numbers or both.

Thus, for the formation of the code, the remaining 4 digits are free to choose any digit or alphabet, except the two already selected ones.

We know that the number of codes that can be formed by n objects taken k at a time, without repetition is given by:P(n, k) =n!/(n−k)!

Here, n = 25, as we have to select 25 letters, starting from A to Y.

We exclude G from these, as it has already been selected as the second letter.

k = 4 as we need to select 4 remaining characters.

We have to find the number of possible codes that can be formed without repetition, and with the conditions specified.

Here, we have 1 fixed number (3) and one fixed alphabet (g) and four spaces for the remaining digits:

Thus, the number of ways of selecting the remaining four characters = 24 × 23 × 22 × 21

Total number of codes possible = 1 × 1 × 24 × 23 × 22 × 21 = 46,536, which is our answer.

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When added correctly, you will come to the answer of 959,959.

hope this helped, dont forget to mark this answer as the brainliest!!!!

Step-by-step explanation:

Not sure if I'm right or not but I think your question is

6/4 + 8/4

so I'll solve now

6/4 + 8/4 .........look for the common denominator (4)

6+8/ 4

14/ 4

In decimals = 3.5

In fractions =7/2

To calculate the probability that two people chosen at random were born during the same month of the year, we need to consider the total number of possible outcomes and the favorable outcomes.

There are 12 months in a year, so the total number of possible outcomes is 12 (one for each month).

Now, let's consider the favorable outcomes. To have two people born in the same month, we need to choose any one of the 12 months for the first person, and then the second person should also be born in the same month.

The probability that the second person is born in the same month as the first person is 1/12 since there is only one favorable outcome out of 12 possible outcomes.

Therefore, the probability that two people chosen at random were born during the same month of the year is 1/12 or approximately 0.0833 (rounded to four decimal places).

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Answer:

y = 44

Step-by-step explanation:

y = 300

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Steps are in the attached picture!

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Joke: What runs around a farm but doesn’t move?

Answer: A fence.

Have a great day and God bless! :D

Answer:

623

Step-by-step explanation:

5^3 x 5 = 625

625 - 2 = 623

Answer:

Step-by-step explanation:

to ez its =12

A conformal map from the sector {z=reiθ:r>0,−π/4<θ<π/4} to the horizontal strip {z:−π

To find a conformal map between the given sector and the horizontal strip, we can use the exponential function. Let's consider the transformation w = e^z, where z is in the sector and w is in the strip.

In the sector, we can represent z as z = r * e^(iθ), where r > 0 and -π/4 < θ < π/4. Now, applying the transformation, we get w = e^(r * e^(iθ)).

To simplify further, we can use Euler's formula, e^(iθ) = cosθ + i*sinθ, to rewrite the expression as w = e^(r * (cosθ + i*sinθ)).

Now, using the properties of the exponential function, we can write w = e^(r*cosθ) * e^(i*r*sinθ).

The first factor, e^(r*cosθ), represents the magnitude of w, which is positive for all r and θ. The second factor, e^(i*r*sinθ), represents the angle of w, which varies from -π/4 to π/4 as θ varies from -π/4 to π/4.

Therefore, the transformation w = e^z maps the given sector onto the horizontal strip {z:−π

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Answer:

12

Step-by-step explanation:

20 + 50 = 70

70 - 58 = 12

so yea 12

Answer:

12

Step-by-step explanation:

58-20=38

38+12=50

The measure of central tendency is the most appropriate for this data is median.

There are a few different measures of central tendency to choose from, but the most common ones are the mean, median, and mode.

The mean is the arithmetic average of the data. To find the mean, you would add up all the values and divide by the total number of values. However, the mean can be sensitive to outliers or extreme values, which could skew the results. In this case, there are no extreme values, but the data is not evenly distributed across the three groups, so the mean may not be the best measure of central tendency to use.

The median is the middle value of the data when it is arranged in order from smallest to largest.

This can be a better measure of central tendency when the data is not evenly distributed. In this case, we can find the median by arranging the data in order: 25, 125, 250. The middle value is 125, which means that half of the pet owners surveyed own fewer than 125 pets, and half own more than 125 pets.

So, the median might be a good choice of measure of central tendency in this case.

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Answer;

50% increase

Step-by-step explanation:

It would be 50% because 50% of 60 is 30 and 90 is 150% of 60, and so you're adding on 50%, or increasing 50%.

Factor when dividing the function the remainder is zero. The factorized form of the polynomial 64-x¹⁵ is (4-x⁵)(16+4x⁵+x¹⁰).

A factor of a function is a factor which when multiplied by another the result is the function itself.

In order to find the factors of the given polynomial, we will rewrite the equation,

\(64-x^{15}\\\\4^3-(x^5)^3\)

Now, we will use the algebraic property to solve the problem,

\(4^3-(x^5)^3\\\\=(4-x^5)(4^2 + 4x^5+ x^{10})\\\\=(4-x^5)(16 + 4x^5+ x^{10})\)

Hence, the factorized form of the polynomial 64-x¹⁵ is (4-x⁵)(16+4x⁵+x¹⁰).

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The predicted number of adults in Oak City whose main source of news is newspapers or the radio is 85

To predict the number of adults in Oak City whose main source of news is newspapers or the radio, we need to add the number of adults who answered "Newspapers" to the number of adults who answered "Radio".

According to the sample data

Number of adults who answered "Newspapers": 64

Number of adults who answered "Radio": 21

Therefore, the predicted number of adults in Oak City whose main source of news is newspapers or the radio we have to use the addition

64 + 21 = 85

Rounding this answer to the nearest whole number, we get

85 ≈ 85

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The given question is incomplete, the complete question is:

There are 44,000 adults living in Oak City. In examining attitudes toward the news, a research group asked a random sample of Oak City adults "What is your main source of news?" The results are shown below. Main Source of News Newspapers Number of Adults 64 Internet 80 Television 126 Radio 21 Other 40 Based on the sample, predict the number of adults in Oak City whose main source of news is newspapers or the radio. Round your answer to the nearest whole number.

Point B is (-6,8)

To get from 1,6 to 8,4____7,-2

To get from 1,6 to B_____-7,2

Answer:

Proper Fractions, Improper Fractions, Mixed Fractions:

Step-by-step explanation:

Answer:  -21

Step-by-step explanation:

11-32

Answer:

  $9,039.81

Step-by-step explanation:

Given the exponentially decaying price history of a vehicle as $21,000; $18,900; $17,010; $15,309; $13,778.10; $12,400.29; you want to know the value after 8 years of depreciation at the same rate.

The multiplier of value each year is 18900/21000 = 0.9. This means the value of the vehicle can be represented by the price function ...

   price = (initial price) · 0.9^t

where t is the number of years the vehicle has depreciated.

After 8 years, the value will be ...

  price = $21000·0.9^8 ≈ $9,039.81

After 8 years, the value of the car will be $9,039.81.

Answer:

height = 2.5 units

Step-by-step explanation:

The volume of a rectangular prism is given by the product of its base area and its height. If the area of the base is 28 square units and the volume is 70 cubic units, we can find the height as follows:

Volume = base area * height

70 = 28 * height

height = 70 / 28

height = 2.5 units

The height of the rectangular prism is 2.5 units.

From the information given,

BA is congruent to AC

AD is common to triangle ABD and ACD

Since the two sides of triangle ABC are congruent, it means that the triangle is an isosceles triangle. Thus,

angle ABD = angle ACD

Triangle ABD and ACD are congruent. Thus, the corresponding sides are congruent

If BD = 3, then

CD = 3

\((2x^2+5)(2x^2+5)\\\\=(2x^2+5)^2\\\\=(2x^2)^2 +2(2x^2)(5) + 5^2\\\\=4x^4 + 20x^2 +25\)

Answer:

7/75

Step-by-step explanation:

8 Batman cards, 12 Superman cards, and 5 captain America =25 cards

P( batman) = 8/25

no replacement since he hands them out

7 Batman cards, 12 Superman cards, and 5 captain America =24 cards

P( batman) = 7/24

P(batman, no replacement, batman) = 8/25 * 7/24 = 7/75

In symbolizing truth-functional claims, the word "if" is used to introduce the consequent of a condition, while the phrase "only if" represents the antecedent.

Symbolizing truth-functional claims involves representing statements or propositions using logical symbols. When using the word "if" in a truth-functional claim, it typically introduces the consequent of a conditional statement. A conditional statement is a type of proposition that states that if one thing (the antecedent) is true, then another thing (the consequent) is also true. For example, the statement "If it is raining, then the ground is wet" can be symbolized as "p → q," where p represents "it is raining" and q represents "the ground is wet."

On the other hand, the phrase "only if" is used to represent the antecedent in a truth-functional claim. In a conditional statement using "only if," it states that if the consequent is true, then the antecedent must also be true. For example, the statement "The ground is wet only if it is raining" can be symbolized as "q → p," where p represents "it is raining" and q represents "the ground is wet."

In summary, when symbolizing truth-functional claims, the word "if" introduces the consequent of a condition, while the phrase "only if" represents the antecedent. These terms help express the relationships between propositions in logical statements.

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The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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The area of the surface generated by revolving the curve about the x-axis is 9664π  / 3 square units.

Given: The equation of the curve is y = 4√x on [21,77]

The formula for finding the surface area of a curve rotated about the x-axis on some interval [a, b] is given by:

\(S = \int\limits^b_a {2\pi f(x)\sqrt{1 +(f'(x))^{2} } } \, dx\)

where S is the surface area,

f(x) is y

a and b is the given interval such that a ≤ x ≤ b or [a, b]

Now in this question,

f(x) = 4√x

a = 21, b = 77

f'(x) = 4 * 1 / 2√x = 2 / √x

f'(x) = 2 /√x

Placing the respective values in the equation we get,

\(S = \int\limits^{77}_{21} {2\pi. 4\sqrt{x} \sqrt{1+(\frac{2}{\sqrt{x} } )^{2} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x} \sqrt{1+\frac{4}{x} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x} * \frac{\sqrt{x + 4} }{\sqrt{x} } } \, dx\)

\(S = 8\pi\int\limits^{77}_{21} {\sqrt{x+4} } } \, dx\)

we know the formula for the integral

\(\int\limits^b_a {\sqrt{ax + b} } \, dx = \frac{2}{3a}(ax+b)^{\frac{3}{2} } | { {{b} \atop {{a}}} \right.\)

Therefore, by applying the formula, we get:

\(S = 8\pi *\frac{2}{3}(x+4)^{\frac{3}{2} } | { {{77} \atop {{21}}} \right.\)

\(S = \frac{16\pi }{3} \{ (77+4)^{\frac{3}{2}} - (21+4)^{\frac{3}{2} }\}\)

\(S = \frac{16\pi }{3} \{ (81)^{\frac{3}{2}} - (25)^{\frac{3}{2} }\}\)

\(S = \frac{16\pi }{3} \{729 - 125\}\)

\(S = \frac{16\pi }{3} * 604\)

\(S = \frac{9664\pi }{3}\)

Hence, The area of the surface generated by revolving the curve about the x-axis is 9664π  / 3 square units

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Disclaimer: The given question is incomplete. The complete question is mentioned below:

Find the area of the surface generated when the given curve is rotated about the x-axis y= 4sqrt(x) on [21,77]

The area of the surface generated by revolving the curve about the x-axis is ___ square units (type an exact answer, using pi as needed)