Write the following polynomial in standard form:
\(7x^{3} + 5x^{2} - 2x^{6} +3x^{2} -4\)

Answer:

Those are the answers. hope it helps

Answer:

m=-32

Step-by-step explanation:

Answer:

M=(-32)

Step-by-step explanation:

-(9m+12)=6(14-m)

-(9m+12)=84-6m

-9m-12=84-6m

-9m+6m-12=84

-3m-12=84

-3m-12+12=84+12

-3m=96

-3m÷(-3)=96÷(-3)

m=(-32)

A comparison of multiple treatments and the use of the double-blind method are two fundamental components of all statistically designed experiments. (6) Compare various treatments; assign patients to treatments at random.

What is double-blind method?

A kind of clinical experiment in which neither the participants nor the researcher is aware of the treatment or intervention that each participant is receiving until the trial is complete.

                      This reduces the likelihood of skewed study outcomes.

What is a sample of a double-blind study?

Imagine, for instance, that researchers are looking into the effects of a novel medication.

                            The participants in a double-blind study would not be aware of who was receiving the real medication and who was receiving a placebo, and neither would the researchers who interact with them.

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The complete question is -

Two essential features of all statistically designed experiments are (2 Points) O use enough subjects; always have a control groups O always have a placebo group; use the double - blind method O use a block design; use chance to assign subjects to treatments O compare several treatments; use the double - blind method O compare several treatments; use chance to assign subjects to treatments.

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:

no you should. i literally bully my friends

Step-by-step explanation:

Answer:

Because its mean

Step-by-step explanation:

The interest rate on the savings deposit is 10%.

The initial principal amount with Sam in the savings account at the bank is $2000. The time period for which the interest is earned is 10 years. The final amount he received in total was $4000. Let the interest rate be "R".

The interest is the difference between the final and the initial amount. Simple interest is a quick and straightforward way to calculate the interest on a loan. Simple interest is calculated by multiplying the daily interest rate by the principle multiplied by the number of days between payments.

I = A - P

I = $4000-$2000

I = $2000

We will now use the formula for simple interest.

I = (P*R*T)/100

2000 = (2000*R*10)/100

R = 10

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Rounding off 9.4725 to the nearest cent will give 9.5

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths. When rounding money to the nearest cent, look at the number to the right of the full cents. In this case, that number is 9. If the number is five or more, increase the cents by 1. If the number is four or less, keep the cents the same. Because 9 is more than 5, $3.299 rounds to $3.30.

Applying same principle or concept here, we can round off 9.4725 to the nearest cent to give 9.5.

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Answer:

The answer is 1

Step-by-step explanation:

2(a+7)−7=9

Step 1: Simplify both sides of the equation.

2(a+7)−7=9

(2)(a)+(2)(7)+−7=9(Distribute)

2a+14+−7=9

(2a)+(14+−7)=9(Combine Like Terms)

2a+7=9

2a+7=9

Step 2: Subtract 7 from both sides.

2a+7−7=9−7

2a=2

Step 3: Divide both sides by 2.

2a

2

=

2

2

a=1

That's great! Observing and recording the phases of the moon over several months can be an interesting project.

Capture the moon's image: Using a camera or smartphone, take a picture of the moon on a daily basis. Aim for clear and focused shots that capture the moon's details.

Present the findings: The student can create a report or presentation summarizing their project, including the methodology, observations, and conclusions. They may also include a selection of the most representative pictures to showcase the changes in the moon's appearance.

Remember, this project requires patience and consistency in taking pictures each day. By documenting the moon's phases over three months, the student will gain a deeper understanding of this celestial phenomenon and its cyclical nature.

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Answer: The ball is dropped from a height of 10 ft, so it first travels down 10 ft until it hits the ground. The distance traveled in this first part is 10 ft.

On the first bounce, the ball rebounds to one-fifth of its previous height, which is 2 ft (since 10/5 = 2). The ball then travels up 2 ft and back down 2 ft to the ground, for a total distance traveled of 10 + 2 + 2 = 14 ft.

On the second bounce, the ball rebounds to one-fifth of its previous height, which is 2/5 ft (since 2/5 x 2 = 4/5). The ball then travels up 4/5 ft and back down 4/5 ft to the ground, for a total distance traveled of 2/5 + 4/5 + 4/5 = 2 ft.

On the third bounce, the ball rebounds to one-fifth of its previous height, which is 4/25 ft (since 4/25 x 2/5 = 8/125). The ball then travels up 8/125 ft and back down 8/125 ft to the ground, for a total distance traveled of 4/25 + 8/125 + 8/125 = 0.32 ft (rounded to two decimal places).

The ball will continue to bounce, getting closer and closer to the ground with each bounce. We can calculate the total distance traveled by summing the distances traveled on each bounce:

10 + 14 + 2 + 0.32 + ...

To calculate the sum of this infinite series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where S is the sum, a is the first term, and r is the common ratio.

In this case, a = 10 (the distance traveled on the first drop), and r = 1/5 (the fraction by which the height decreases on each bounce). Plugging in these values, we get:

S = 10 / (1 - 1/5)

= 12.5

So the total distance traveled by the ball is 12.5 ft.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

The perimeter of triangle is equal to the sum of all sides of triangle

then:

5y + (x+8) + (x+3) = 60

5y + 2x +11 = 60

5y +2x = 49  ..............................................................(1)

the hypotenuse - shorter leg = 10

hint (  shorter leg ) = x+3

then

5y - (x + 3 ) = 10

5y - x - 3 = 10

5y - x = 13               .................................................... (2)

from 1 and 2

5y +2x = 49  .................................................................. (3)

5y - x = 13 (multiply both sides by 2 )

10y - 2x = 26 ..................................................................(4)

by sum 3 and 4

15y = 75

then y = 75/15 = 5

then hypotenuse = 5y = 5 x 5 = 25

Answer:

5

Step-by-step explanation:

Answer:

you do this in your own

Step-by-step explanation:

solve this problem

Answer:

\( Slope (m) = -\frac{3}{4} \)

Step-by-step explanation:

Using any two pairs from the table of values given, (-2, 5) and (2, 2):

\( Slope (m) = \frac{y_2 - y_1}{x_2 - x_1} \)

Where,

\( (-2, 5) = (x_1, y_1) \)

\( (2, 2) = (x_2, y_2) \)

Plug in the value into the slope formula:

\( Slope (m) = \frac{2 - 5}{2 -(-2)} \)

\( Slope (m) = -\frac{3}{4} \)

From the given frequency table,

Frequency represents the number of people who made the calls.

Total number of people who made the calls = 16 + 11 + 5 + 3 + 1

                                                                          = 36

Number of people who made less than 13 calls = 16 + 11 + 5

                                                                                 = 32

Number of people who made at least 9 calls = 5 + 3 + 1

                                                                            = 9

Percentage of people who made at least 9 calls = \(\frac{\text{Number of people who made at least 9 calls}}{\text{Number of people who made the calls}}\times 100\)

= \(\frac{9}{36}\times 100\)

= 25%

Difference in the number of people who made the calls between 5-8 calls than 13-16 calls = 11 - 3 = 8

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Answer:

0.25 or 1/4

Step-by-step explanation:

easy - 3250 pounds divided by 13000 students

everyone will get 0.25 or 1/4 of a pound of chicken

hope this helps!!

Have a nice day!

Answer:

Step-by-step explanation:

Answer:

The equation of the line is;

3y = 2x-8

Step-by-step explanation:

Firstly, we need the to get the slope of the given line

To do this, we will write the equation of the line in the standard form

the standard form

is;

y = mx + b

where m is the slope and b is the y-intercept

y -4 = 2/3(x-3)

y -4 = 2x/3 - 2

y = 2x/3 -2 + 4

y = 2x/3 + 2

with respect to the given equation, the slope of the line is 2/3

Mathematically, when two lines are parallel, the slopes of the line are equal

So now, we want to find the equation of the line that has a slope of 2/3 and passes through the point (1,-2)

so;

y = 2x/3 + b

So substitute the values of (1,-2)

1 for x and -2 for y

-2 = 2/3(1) + b

-2 = 2/3 + b

b = -2 - 2/3

b = (-6-2)/3 = -8/3

So the equation of that line is;

y = 2/3x - 8/3

Multiply through by 3

3y = 2x - 8

Answer:

easy y/x is the answer for you answer

Answer:

Factoring a polynomial is the process of decomposing a polynomial into a product of two or more polynomials.

Hope this helps!!

When the problem is solved using fraction addition, the answer is 3601/2520 in common fraction.

Subset S has the following values: 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, and 1/10.

The element in subset S product is 3601/2520.

Therefore, we can calculate the product of the elements in S by solving the numbers using fractional addition.

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Answer:

Step-by-step explanation:

The answer should be 8/3.

Answer:

P(t) = A * (1 + r)^t ;

14,922 ;

Year 2013

Step-by-step explanation:

Given the following :

Continuous growth rate(r) = 5% = 0.05

Population in year 2000 = Initial population (A) = 10,100

Time(t) = period (years since year 2000)

A)

Find a function that models the population,P(t) , after (t) years since year 2000 (i.e. t= 0 for the year 2000).

P(t) = A * (1 + r)^t

Trying out our function for t = year 2000, t =0

P(0) = 10,100 * (1 + 0.05)^0

P(0) = 10,100 * 1.05^0 = 10,100

B.)

Use your function from part (a) to estimate the fox population in the year 2008.

Year 2008, t = 8

P(8) = 10,100 * (1 + 0.05)^8

P(8) = 10,100 * 1. 05^8

P(8) = 10,100 * 1.4774554437890625

= 14922.29

= 14,922

c) Use your function to estimate the year when the fox population will reach over 18,400 foxes. Round t to the nearest whole year, then state the year.

P(t) = A * (1 + r)^t

18400 = 10,100 * (1.05)^t

18400/10100 = 1.05^t

1.8217821 = 1.05^t

1.05^t = 1.8217821

In(1.05^t) = ln(1.8217821)

0.0487901 * t = 0.5998151

t = 0.5998151 / 0.0487901

t = 12.293787

Therefore eit will take 13 years

2000 + 13 = 2013

To create a tangent line, 1st we need to know the points at which the tangent is to be located, then calculate the slope and finally with the help of these points and slope we can construct the equation of tangent line.

We need to  take the following steps in order to build a tangent line:

Hence, the above three steps are crucial to create a  tangent line.

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Answer:  E, A, D, C, B

Step-by-step explanation:

First, we need to get y alone. So we will add 7 to the side of the equation that has the 4y in it.

So the first one will be.

Add 7 to both sides of the equation.

Now the second one is

4y = 25 + 7  Because what you do to one side of the equation, you do to the other. So we add 7 to 25.

Then the 3rd one will be 4y = 32  because 25+7 is equal to 32. But we still have that 4y on the other side of the equation. So the next equation is 4y = 32.

The second to last step is Divide both sides by 4  because thats

how you isolate y. So once you divide both sides by 4. You will get 8. Leading you into the next and final step.

Y = 8

And thats how you do it!

The given statement "Zeros are also called roots, x-intercepts, and solutions" is true.

Zeros, roots, x-intercepts and solutions are all the same and interchangeable terms. These terms are used to describe the value of x for which a function's value is 0. Zeros of a function are called roots because they are solutions to the equation f(x) = 0.

They are called x-intercepts because the x-axis is the line where the value of y is 0, and so the zeros occur at the points where the graph intersects the x-axis. Finally, they are called solutions because finding the zeros of a function is equivalent to solving the equation f(x) = 0. In conclusion, all these terms are synonymous with each other, meaning that they refer to the same thing, the value(s) of x for which the function's value is zero.

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Answer:

\( \: answer \: c = x < - 4\)

Answer:

For the given function f(x)= -|x| + 2

the domain of the function is: All real numbers

the range of the function is: all numbers greater than or equal to 2

Step-by-step explanation:

We need to find the domain and range of the function f(x)= -|x| + 2.

Domain: Domain is defined as all the possible x values of x for which the function is true.

Range: Range is defined as all the possible y values.

So, For the given function f(x)= -|x| + 2

the domain of the function is: All real numbers (the function is true for all real numbers)

the range of the function is: all numbers greater than or equal to 2

(When solving the equation we will have value of f(x) equal or greater than 2)

To find the height of the pyramid, we need to use the formula for the volume of a square-based oblique pyramid, which is given by:

\(Volume = (1/3) * Base Area * Height\)
Given that the volume of the pyramid is 125 m^3 and the base area is unknown, we can rearrange the formula to solve for the height:
\(Height = Volume / ( (1/3) * Base Area )\)
Since the base of the pyramid is square-based, the base area can be found by taking the square of one of the sides. Let's call this side length "s". The base area is s^2.

Now, substitute the given values into the equation:
\(125 = (1/3) * s^2 * Height\)
To find the height, we need to isolate it on one side of the equation. Multiply both sides by 3:
\(375 = s^2 * Height\)

Next, divide both sides by \(s^2\):
\(Height = 375 / s^2\)
Since we don't know the value of s, we cannot determine the exact height of the pyramid. Without additional information, we can only express the height of the pyramid in terms of the side length "s" as\(Height = 375 / s^2.\)

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The height of the pyramid can be determined by evaluating the expression (3 * 125) / (√B).

The volume of a square-based oblique pyramid is given by the formula V = (1/3) * B * h, where V represents the volume, B represents the area of the base, and h represents the height of the pyramid.

In this case, the volume of the pyramid is given as 125 m³. We need to find the height of the pyramid.

We know that the base of the pyramid is a square, so the area of the base can be calculated using the formula A = s², where s represents the length of one side of the square base.

To find the height, we can rearrange the formula for the volume: h = (3V) / (B).

First, let's find the area of the base. Since the base is square-based, the area of the square can be found by taking the square root of the base area.

Let's assume the side length of the square base is s meters. Thus, the area of the base is A = s² = √B.

Now, substitute the values into the formula to find the height: h = (3 * 125) / (√B).

This is how to find the height of the given square-based oblique pyramid with a volume of 125 m³.

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