Use logarithmic differentiation to find the derivative of the function. y = (cos(4x))* y'(x) = (cos(4x))*In(cos(4x))– 4x tan(4x).

Answer:

\(5h^2 + 7h + 7\)

Step-by-step explanation:

We can simplify this expression by combining like terms.

To combine like terms, we are looking for terms that share the same variable and exponent.

First, we can see that the terms \(7h^2\) and \(-2h^2\) share the same variable (h) and the same exponent (2).

\(7 - 2 = 5\)

This simplifies to \(5h^2\).

Next, we can see that \(5h\) and \(2h\) share the same variable (h) and the same exponent (1) so we can add these.

\(5+2=7\)

This simplifies to \(7h\).

Lastly, we can see that we just have 7, no more terms with the same variable (none). So this is 7.

Adding up all the terms in standard form (\(ax^2 + bx + c\)), we get \(5h^2 + 7h + 7\).

Hope this helped!

a) The passage is a piece of written text that provides information about Makayla's experience during an Easter egg hunt. (option c)

(b) It also highlights how knowledge gained in the classroom can be applied to everyday life.

At the beginning of the passage, Makayla is getting ready to go on an Easter egg hunt. This is evident from the line "Makayla was getting ready for the Easter egg hunt at the park." Easter egg hunts are a popular tradition in many parts of the world, where children search for hidden eggs that are often filled with candy or small toys.

Hence the correct option is (c).

Throughout the story, Makayla remembers information that Mrs. Narula taught in class. Mrs. Narula is Makayla's science teacher, and the information she taught in class is about the process of photosynthesis. Photosynthesis is the process by which plants convert sunlight, water, and carbon dioxide into oxygen and sugar.

Makayla remembers this information as she observes the trees and plants in the park during the Easter egg hunt. She notes that the plants are producing oxygen through photosynthesis and that this process is essential for the survival of all living beings.

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Answer:

Answer is A

Step-by-step explanation:

Ada Lovelace wrote the first algorithm intended to be carried out by a machine.

Answer:

36 3/4

Step-by-step explanation:

12 1/4 + 12 1/4 + 12 1/4 = 36 3/4 :)

Answer:

36 3/4

Step-by-step explanation:

12 1/4 + 12 1/4 + 12 1/4 = 36 3/4 :)

Answer:

\(28{cm}^{2} \)

Step-by-step explanation:

we know

area of rectangle=l*b=(7*4)sq cm=28sq cm

One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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The sum of expression \(1.723 \times 10^{2}\) and \(7.38 \times 10^{3}\) is \(7.5523 \times 10^{3}\). The numbers in scientific notation are added by summing the coefficients while keeping the exponent unchanged.

In scientific notation, numbers are expressed as a coefficient multiplied by a power of 10. To add numbers in scientific notation, we need to ensure that the powers of 10 are the same.

In this case, both numbers are already in scientific notation with powers of 10. We can directly add the coefficients while keeping the exponent the same.

Adding \(1.723 \times 10^2\) and \(7.38 \times 10^3\) gives us a sum of \(7.5523 \times 10^3\). The coefficient represents the numerical value, and the power of 10 indicates the magnitude.

Thus, the expression \(1.723 \times 10^2 + 7.38 \times 10^3\) evaluates to \(7.5523 \times 10^3\), indicating a significant increase in magnitude compared to the individual numbers.

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Answer:

Step-by-step explanation:

Given :

x = -6

-7x + 6y = -18 ... i)

Putting the value of x in equation ...i)

=> -7 (-6) + 6y = -18

=> 42 + 6y = -18

=> 6y = -18 -42

=> 6y = - 60

=> y = -60/6

=> y = -10

The value of y = -10 and x = -6

Answer:

x= 4, y=6

Step-by-step explanation:

9x-9y = -18

9x=-18+9y

x=-2+y

-6(-2+y) + 9y = 6

-12-6y+9y=6

3y=18

y=6

9x -9(6)=-18

9x-54=-16

9x=36

x=4

Answer:

A. Between 3.0 and 3.5 and between 4.0 and 4.5

Step-by-step explanation:

The zeroes of a function occur whenever a value of x returns zero. To predict where the zeroes lie, determine the interval(s) where the function crosses the x-axis. This occurs when either \(f(x)\) goes from a negative value to a positive value or vice versa.

From \(x=3.0\) and \(x=3.5\), the y-values go from 4.0 (positive) to -0.2 (negative), respectively. Therefore, there must be a zero in this interval.

From \(x=4.0\) and \(x=4.5\), the y-values go from -0.8 (negative) to 0.1 (positive), respectively. Therefore, there must also be a zero in this interval.

Thus, the zeros of this function occur between 3.0 and 3.5 and between 4.0 and 4.5, leading to answer choice A.

Answer:

between 3.0 and 3.5 and between 4.0 and 4.5

Step-by-step explanation:

Plato/Edmentum

Simple mathematics.

2+3 1/10==5 1/10-4==1 1/10 -9 == -8 1/10 == -8.1

-10-4 1/2== -14 1/2 +2 +9 == -3 1/2 == -3.5

Answer:

2+1=3, 3-3=0

Step-by-step explanation:

Answer:

25pi-24 cm²

Step-by-step explanation:

pi(5)²-2(1/2)*6*4

25pi-24 cm²

The area of the shaded region is (25π - 24) sq.cm.

"\(A = \pi \times r^2\), where 'r' is the radius of the circle."

"\(A=\frac{1}{2}\times b\times h\), where b is the base and h is the height."

For given question,

area of the shaded region = area of circle - area of 2 isosceles triangles

First we find the area of the circle:

Here, radius r = 5 cm

So, the area of the circle would be,

\(A=\pi\times r^2\\\\A=\pi \times 5^2\\\\A=25\pi~cm^2\)

Now, for isosceles triangle,

base b = 6 cm

And height h = 5 - 1

                   h = 4 cm

Using the formula for area of the triangle,

\(A=\frac{1}{2}\times b\times h\\\\ A=\frac{1}{2}\times 6\times 4\\\\ A=12~cm^2\)

So, the area of the shaded region would be,

the area of the shaded region

\(= 25\pi - (2 \times 12)\\\\= 25\pi - 24 ~sq.cm.\)

Therefore, the area of the shaded region is (25π - 24) sq.cm.

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Answer:

\(100.00 \div 6 \)

The probability that the youngest member of the group sits in the seat closest to the door 1 / 6

Given that, a group of 6 friends of varying ages meets at a coffee shop and sits in a circle, we need to find the probability that the youngest member of the group sits in the seat closest to the door,

So, the probability = favorable outcomes / total outcomes

Here, the favorable outcome = 1

The total outcomes = 1, 2, 3, 4, 5, 6 = 6

So, the probability = 1/6 = 1/2

Hence, the probability that the youngest member of the group sits in the seat closest to the door 1 / 6

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Exponential of 1 is equal to the number itself which means 1.

Exponent is usually described as the method of demonstrating large numbers in terms of powers. It means, exponent refers to the count, that how many times a number is multiplied to itself to calculate that exponent.

In accordance with the exponent rule, any number raised to power of 1 would always be equal to 1 that is because it doesn't matter how many times we multiply 1 to itself. It is going to yield 1. For example, multiplying 1 hundred times i.e. 1^100 also results in 1.

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The correlation coefficient between history and math exam scores is of -0.1321, which means that there is a weak negative correlation between history grades and math grades.

Using a calculator, inserting the history and math scores, the coefficient is of -0.1321, which means that there is a weak negative correlation between history grades and math grades.

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The difference between r and p.  is that r represents the sample correlation coefficient while p represents the p-value

Generally, r represents the sample correlation coefficient, which is a measure of the strength and direction of the linear relationship between two variables in a sample of data. It ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.

p represents the p-value, which is a measure of the statistical significance of the sample correlation coefficient. It represents the probability that the observed correlation occurred by chance, assuming that there is no true correlation in the population.

A p-value of less than 0.05 is often used as a threshold for determining statistical significance, meaning that the observed correlation is unlikely to have occurred by chance and is likely to reflect a true correlation in the population.

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Answer:

Option (4)

Step-by-step explanation:

Option (1)

f(x) = 4x⁴- 7x²+ x + 25

Possible rational roots will be,

\(\frac{\pm \text{Factors of constant term '25'}}{{\pm \text{Factors of leading coefficient '4'}}}\)

For the given function,

Possible rational roots = \(\frac{\pm 1, 5, 25}{\pm 1,2}\)

                                      = \(\pm 1, \pm 5, \pm 25, \pm \frac{1}{2},\pm\frac{5}{2},\pm\frac{25}{2}\)

Therefore, \(-\frac{2}{5}\) is not the possible root.

Option (2)

f(x) = 9x⁴- 7x²+ x + 10

Possible rational roots = \(\frac{\pm 1,\pm 2,\pm 5,\pm10}{\pm 1,\pm3,\pm9}\)

Therefore, \(-\frac{2}{5}\) is not the possible root.

Option (3)

f(x) = 10x⁴- 7x²+ x + 9

Possible rational roots = \(\frac{\pm1, \pm3, \pm9}{\pm 1,\pm2,\pm5,\pm10}\)

Therefore, \(-\frac{2}{5}\) is not the possible root.

Option (4)

f(x) = 25x⁴- 7x²+ x + 4

Possible rational roots = \(\frac{\pm 1,\pm2,\pm5}{\pm1,\pm5,\pm 25}\)

                                      = \(\pm1,\pm2,\pm5,\pm\frac{1}{5},\pm\frac{1}{25},\pm\frac{2}{5},\pm\frac{2}{25}\)

Therefore, \(-\frac{2}{5}\) is the possible rational root.

Option (4) will be the answer.

Area under the standard normal distribution curve is as follows:

to the right of z = 0.77 = 0.2206

Between z = −1.31 and z = −2.73 = 0.0921

to the right of z = −2.22 = 0.9861

The area under the standard normal distribution curve: To the right of z = 0.77, using the standard normal distribution table: According to the standard normal distribution table, the area to the left of z = 0.77 is 0.7794.

The total area under the curve is 1. Therefore, the area to the right of z = 0.77 can be found by subtracting 0.7794 from 1, which equals 0.2206.

Therefore, the area under the standard normal distribution curve to the right of z = 0.77 is 0.2206.

To the right of z = −2.22, using the standard normal distribution table:

According to the standard normal distribution table, the area to the left of z = −2.22 is 0.0139.

The total area under the curve is 1.

Therefore, the area to the right of z = −2.22 can be found by subtracting 0.0139 from 1, which equals 0.9861.

Therefore, the area under the standard normal distribution curve to the right of z = −2.22 is 0.9861.

Between z = −1.31 and z = −2.73, using the standard normal distribution table:

According to the standard normal distribution table, the area to the left of z = −1.31 is 0.0951, and the area to the left of z = −2.73 is 0.0030.

The area between these two z values can be found by subtracting the smaller area from the larger area, which equals 0.0921.

Therefore, the area under the standard normal distribution curve between z = −1.31 and z = −2.73 is 0.0921.

Area under the standard normal distribution curve:

To the right of z = 0.77 = 0.2206

Between z = −1.31 and z = −2.73 = 0.0921

To the right of z = −2.22 = 0.9861

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Answer:

Erin will pay a total of $21.196 in shipping and handling fees.

Step-by-step explanation:

To calculate the shipping and handling fees, we first need to find 20% of the price of the trampoline. Since 20% is the same as 0.20, we can multiply the price of the trampoline by 0.20 to find the shipping and handling fees. If the trampoline costs $105.98, then the shipping and handling fees would be $105.98 * 0.20 = $<<105.98*0.20=21.196>>21.196.

Answer:

∠ 1 = 36° , ∠ 2 = 144°

Step-by-step explanation:

∠ 1 and ∠ 2 are adjacent angles on a straight line and sum to 180° , that is

x + 12 + 6x = 180

7x + 12 = 180 ( subtract 12 from both sides )

7x = 168 ( divide both sides by 7 )

x = 24

Then

∠ 1 = x + 12 = 24 + 12 = 36°

∠ 2 = 6x = 6 × 24 = 144°

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

1

3

gives the next term. In other words,

a

n

=

a

1

r

n

−

1

.

Geometric Sequence:

r

=

1

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of

a

1

=

486

and

r

=

1

3

.

a

n

=

486

(

1

3

)

n

−

1

Apply the product rule to

1

3

.

a

n

=

486

1

n

−

1

3

n

−

1

One to any power is one.

a

n

=

486

1

3

n

−

1

Combine

486

and

1

3

n

−

1

.

a

n

=

486

3

n

−

1

Substitute in the value of

n

to find the

n

th term.

a

5

=

486

3

(

5

)

−

1

Simplify the denominator.

Tap for more steps...

a

5

=

486

81

Divide

486

by

81

.

a

5

=

6

Step-by-step explanation:

\( \frac{3}{4} x + \frac{7}{8} = 4 \frac{1}{4} \)

\( \frac{3}{4} x = \frac{17}{4} - \frac{7}{8} \)

\( \frac{3}{4} x = \frac{34}{8} - \frac{7}{8} \)

\( \frac{3}{4} x = \frac{27}{8} \)

\(3x \times 8 = 27 \times 4\)

\(24x = 108\)

\(x = \frac{108}{24} \)

\(x = \frac{9}{2} \)

The value of x in the expression (3/4)x+7/8 = 17/4 is 9/2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given,  (3/4)x+7/8 = 17/4.

Now to get rid of the denominator LCM of 4 and 8 is 8 so we'll multiply each term by 8.

6x + 7 = 34.

6x = 27.

2x = 9.

x = 9/2.

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The lateral area of the pentagonal prism is   = 850

A prism with two pentagonal bases and five rectangular sides is called a pentagonal prism. It is a hexagon.

the pentagonal prism has a base that is pentagonal. With seven faces, fifteen edges, and ten vertices, it is a particular kind of heptahedron.

All of an object's sides, excluding its base and top, are referred to as its lateral surface (when they exist). The size of the lateral surface is referred to as the lateral surface area. The total surface area, which consists of the lateral surface area along with the areas of the base and top, should be distinguished from this.

base of a pentagonal right prism is  = 17

lateral edge of the prism measures  = 10

the prism's lateral area = ?

According to the formula :

Area = 5 x base x height

       = 5 x 17 x 10

       =  850

The lateral area of the pentagonal prism is   = 850

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Answer:

Step-by-step explanation:

Using Trigonometry: SOH CAH TOA,

Cross multiplying:

x = tan (47°) × 35

  =  37.5329

  = 37.53 to two decimal places

Answer:

A, C, D

Step-by-step explanation:

I took the test lol :)

(A) The amount of change is different for the percent increase and the percent decrease.

(C) The ratio for the percent increase has a smaller denominator than the percent decrease.

(D) The ratio for the percent increase has a different numerator than the percent decrease.

Therefore, the correct options are as follows -

(A) The amount of change is different for the percent increase and the percent decrease.

(C) The ratio for the percent increase has a smaller denominator than the percent decrease.

(D) The ratio for the percent increase has a different numerator than the percent decrease.

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If the two sides of the triangle are equal then these two triangles are similar. The sides EF and GF are congruent to each other. Then the correct option is D.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

In ΔEDF and ΔGDF

DF = DF = radius (common side)

ED = GD = radius

If the two sides of the triangle are equal then these two triangles are similar.

Thus, EF and GF are congruent to each other.

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Answer:

the answer is D

Step-by-step explanation:

EF and GF

Answer:hours

Step-by-step explanation: