You are trying to memorize a speech for your public
speaking class. After 1 day, you memorized 200 words. Each
of the following days, you memorized an additional 30
words.
Use the given information to write a linear equation in point-
ten
slope form. Then use the equation to find the number of
words will you have memorized after 8 days.
words

Given:

The value of x = 2.

Solution:

F ( x ) = 2x⁴ - x³ + 5x - 9

=> 2 ( 2 )⁴ - ( 2 )³ + 5 × 2 - 9

=> 2 × 16 - 8 + 10 - 9

=> 32 - 8 + 10 - 9

=> 24 + 1

=> 25

A. 25

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

The volume of the solid formed by rotating the region inside the first quadrant enclosed by the curves y = x and y = 5x about the x-axis is (250π/7) cubic units. When finding the volume of a solid of revolution, we use the method of cylindrical shells.

To calculate the volume, we integrate the area of each cylindrical shell formed by rotating an infinitesimally small strip about the x-axis. The height of each shell is the difference between the y-values of the two curves, which is (5x - x²). The circumference of each shell is given by 2πx, and the thickness is dx. Therefore, the volume of each shell is 2πx(5x - x²)dx.

To find the total volume, we integrate this expression over the interval where the two curves intersect. Setting\(y = x^2\)and y = 5x equal to each other, we get x² = 5x. Solving this equation, we find two intersection points: x = 0 and x = 5. Thus, the limits of integration are from 0 to 5.

Integrating the expression \(2\pi x(5x - x^2)dx\) from 0 to 5 gives us the volume of the solid formed by rotating the region inside the first quadrant. Evaluating this integral, we find the volume to be (250π/7) cubic units.

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Around 68% of values are within 1 standard deviation from the mean with the probability that an exponentially distributed random variable takes on a value within one standard deviation of its mean.

As the empirical rule says, or also know as the 68-95-99.7 rule, tells where most of the values lie in a normal distribution, with this we know that:

Around 68% of values are within 1 standard deviation from the mean.

And around 95% of values are within 2 standard deviations from the mean.

And around 99.7% of values are within 3 standard deviations from the mean.

The empirical rule is a quick way to get an overview of the data and check for any outliers or extreme values that don’t follow the pattern.

If data from small examples do not follow the pattern closely, then other distributions like the t-distribution must be more appropriate. Once the identification of the distribution of the variable is done, then appropriate statistical tests can be applied.

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a. It will take Nicholas approximately 9.69 years to save enough to buy a $27,000 car. b. Lauren needs to earn an annual interest rate of 5.02% in order to have $251,000 left after 27 years.

To calculate the time it will take for Nicholas to save enough for a $27,000 car, we can use the formula for compound interest. The formula is given by:

Future Value = \(Present Value * (1 + interest rate)^{(number of periods)}\)

In this case, Nicholas is saving $232 per month, so the future value (FV) is $27,000 and the interest rate (r) is 3.7% per year. We need to find the number of periods (t) in years. Rearranging the formula, we get:

t = log(FV / PV) / log(1 + r)

Plugging in the values, we have:

t = log(27000 / (232 * 12)) / log(1 + 0.037)

≈ 9.69 years

Therefore, it will take Nicholas approximately 9.69 years to save enough to buy a $27,000 car.

To calculate the required annual interest rate for Lauren, we can use the formula for future value with regular withdrawals. The formula is given by:

\(Future Value = Withdrawal Amount * ((1 + interest rate)^{t - 1} / interest rate\)

In this case, the future value (FV) is $251,000, the withdrawal amount is $7,000 per month, and the time (t) is 27 years. We need to find the interest rate (r). Rearranging the formula, we have:

\(r = ((FV * interest rate) / Withdrawal Amount + 1)^{(1 / t) - 1}\)

Plugging in the values, we get:

\(r = ((251000 * r) / 7000 + 1)^{1 / 2}\)7) - 1

Solving this equation, we find that Lauren needs to earn an annual interest rate of approximately 5.02% to have $251,000 left after 27 years.

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Answer:

  (a)  (3, -1)

Step-by-step explanation:

You want the graphical solution to the system ...

A graphing calculator plots these equations easily, and will give you the coordinates of the point where the lines intersect. That point is the solution to the system of equations:

  (x, y) = (3, -1)

__

Additional comment

Here, the offered choices are the y-intercepts (clearly wrong), and points in the first and fourth quadrants. You can choose the correct point by thinking about the x-intercepts.

The line with positive slope has an x-intercept of 7/2 = 3.5. For positive x-values less than this, the line is in the 4th quadrant.

The line with negative slope has an x-intercept of -8/-3 ≈ 2.7. For positive x-values greater than this, the line will be in the 4th quadrant.

The point of intersection must be in the 4th quadrant with an x-value between 2.7 and 3.5. Only one answer choice is like this: (3, -1).

Answer:

1. 6

2. 8

3. 10

4. 12

5. 14

Step-by-step explanation:

just solve

Answer:

76% of the student body are not seniors

Step-by-step explanation:

450-108=342 (to find how many students are not seniors)

342/450=0.76 (to find the percentage of non seniors against the whole student body)

0.76x100= 76

Therefore, 76% of the student body are not seniors.

Mine is not heating up I don't know about others

It is reasonable for Stacy to use a normal model for the sampling distribution of the sample proportion. This is because, according to the Central Limit Theorem,

when the sample size is large enough (typically considered to be at least 30), the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution.

In Stacy's case, she plans on surveying a random sample of students, which implies that she will have a sufficiently large sample size. Therefore, the conditions for using a normal model are satisfied.

In conclusion, Stacy can use a normal model for the sampling distribution of the sample proportion in her survey for the final project.

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Answer: Ok to solve this question you would have to do $7.50 divided by  

3 and your answer should come out to be $2.5 or $2.50 per each pound.

Step-by-step explanation:

$7.50 divided by 3 = 2.5

and with money if you get a $2.5 it would be $2.50 because you have to add the zero to the end of it.

Answer:

x=60

Step-by-step explanation:

125=2x+5

125-5=120

120÷2=60

x=60

Answer:

is finding the square root

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number.

When a number is squared, it is multiplied by itself. For example, squaring the number 4 gives 4^2 = 16.

The inverse operation undoes the effect of squaring and returns you to the original number. In this case, finding the square root of a number is the inverse operation of squaring.

The square root of a number "x" is a value that, when squared, gives the original number. It is denoted by the symbol √x.

For example, if you have the number 25 and you want to find its square root, you calculate:

√25 = 5

5 is the square root of 25 because when you square 5 (5^2), you get 25.

The inverse operation of squaring a number is finding the square root of that number. The square root of a number "x" is the value that, when squared, gives the original number. The concept of square root and squaring are inverse operations that are used in various mathematical calculations and problem-solving.

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a) the inverse function is:

f-1(y) = (y-b)/a

b) f(x) is not one-to-one, it does not have a unique inverse function. Therefore, (F-1)(a) = DNE.

First, let's answer the first part of the question:

To determine whether the function f(x) = ar+b is one-to-one, we need to check if different inputs produce different outputs. Let's suppose that f(x1) = f(x2), where x1 and x2 are distinct inputs. Then, we have:

ar+b = f(x1) = f(x2) = ar+b

Subtracting ar+b from both sides, we get:

ar-ar+b-b = 0

Simplifying, we get:

a(x1 - x2) = 0

Since a is nonzero, this equation implies that x1 = x2, which contradicts our assumption that x1 and x2 are distinct. Therefore, the function f(x) = ar+b is one-to-one.

To find the inverse function of f(x) = ar+b, we can solve for x in terms of y:

y = ar+b

y-b = ar

r = (y-b)/a

x = (y-b)/a

Therefore, the inverse function is:

f-1(y) = (y-b)/a

Now, let's answer the second part of the question:

To find (F-1)(a) for f(x) = x2 + 2x - 1 and a = -4, we set y = -4 and solve for x:

y = x2 + 2x - 1

-4 = x2 + 2x - 1

x2 + 2x - 3 = 0

(x + 3)(x - 1) = 0

x = -3 or x = 1

Since f(x) is not one-to-one, it does not have a unique inverse function. Therefore, (F-1)(a) = DNE.

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Answer: Option B.

Step-by-step explanation: I got it right.

Given data:

The given number of names are n=5.

TEhe expression for the probability that Ross doesn't drew his

name is,

P(R')=4/5

Thus, the option (D) is correct.

To determine the minimum number of people with names beginning with the same letter of the alphabet in a group of 200 people, we can use the Pigeonhole Principle.

Since there are 26 letters in the alphabet, there are 26 "pigeonholes" or categories for the first letter of a name. If we assume that each person in the group has a different first letter of their name, then we can put one person in each pigeonhole. However, if we add just one more person, there will be at least one pigeonhole with two people in it (since there are only 26 pigeonholes). Therefore, the minimum number of people with names beginning with the same letter of the alphabet in a group of 200 people is 2.

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Answer:

D, E

Step-by-step explanation:

D. all angles do not have to be congruent

E. diagonals do not have to be congruent

Option D is incorrect 100%

Option E should be incorrect aswell.

Work Shown:

y = 15.6 - 3.8x

y = 15.6 - 3.8*3

y = 4.2

The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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the possible whole number measures of the third side are 5, 6, and 7, listed in ascending order.

what is ascending order?

Ascending order refers to a sorting arrangement in which items are arranged from smallest to largest or from lowest to highest. For example, if you have a list of numbers such as 2, 7, 1, 9, 5, arranging them in ascending order would give you the sequence

In the given question,

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, in this case, we have:

6 + 2 > x

Where x is the length of the third side. Simplifying this inequality, we get:

8 > x

So, the third side must be less than 8.

Now, we also know that the third side must be greater than the difference between the first two sides:

6 - 2 < x

4 < x

So, the third side must be greater than 4.

Therefore, the possible whole number measures of the third side are 5, 6, and 7, listed in ascending order.

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Answer:  \(\dfrac{8}{15}\)

Step-by-step explanation:

Slope line AB equal

\(slope =tgA=\dfrac{d}{b} =\dfrac{8}{15}\)

To show that the given differential form is exact, we need to find a function f(x,y) such that its partial derivatives with respect to x and y are equal to the coefficients of dx and dy, respectively.

Let's consider the differential form:

M(x,y)dx + N(x,y)dy = (y^2-2xy)dx + (x^2-2xy)dy

Taking the partial derivative of M(x,y) with respect to y and the partial derivative of N(x,y) with respect to x, we have:

dM/dy = 2y - 2x = dN/dx

Since the partial derivatives are equal, the differential form is exact.

Now we need to find the potential function f(x,y) such that:

df/dx = M(x,y) and df/dy = N(x,y)

Integrating the first equation with respect to x, we obtain:

f(x,y) = y^2x - x^2y + g(y)

where g(y) is a constant of integration that depends only on y.

Now we differentiate f(x,y) with respect to y and compare it with N(x,y):

df/dy = 2xy - x^2 + g'(y) = x^2 - 2xy

Equating the coefficients of x^2 and xy, we get:

g'(y) = 0, and -2x = 0

Solving these equations, we obtain:

g(y) = C, and x = 0

where C is an arbitrary constant.

Substituting these results back into the expression for f(x,y), we get:

f(x,y) = y^2x - x^2y + C

Therefore, the potential function of the given differential form is f(x,y) = y^2x - x^2y, and we can evaluate the integral as follows:

∫ C dx + ∫ (-x^2 + y^2) dy

where C is a constant of integration.

Evaluating the first integral with respect to x, we get:

C x + g(y)

where g(y) is another constant of integration.

Evaluating the second integral with respect to y, we get:

C x + (1/3) y^3 - (1/3) x^3 + h(x)

where h(x) is another constant of integration.

Therefore, the general solution is:

C x + (1/3) y^3 - (1/3) x^3 + g(y) + h(x)

Since the initial point is (0,0), we have:

C (0) + (1/3) (0)^3 - (1/3) (0)^3 + g(0) + h(0) = 0

Simplifying, we get:

g(0) + h(0) = 0

Therefore, the value of the integral at the point (0,0) is:

∫ (y^2-2xy)dx + (x^2-2xy)dy = 0 + 0 + g(0) + h(0) = 0

Hence, the value of the integral at the point (0,0) is 0.

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Answer:

C has a slope of zero

B has slope 1/2

Answer:

\(c=\sqrt{a}^{2}+b^{2}\)

Step-by-step explanation:

Answer:

The formula is a^2+b^2=c^2

Answer:

D. 45°

Step-by-step explanation:

Since the lines are parallel, 2y°=90° If you divide both sides by 2, y°=45°

Answer:

414

Step-by-step explanation:

87+41=128

542-128=414

Answer:

Jim's Jeans had the better buy

You would pay $12

Step-by-step explanation:

Hope This Helps!

Plz Mark Brainliest!

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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Answer: 42

Step-by-step explanation

Switch x out with 3

using Pemdas do the exponent first

3^2 is 9

then multiply

5*9= 45

then subtract

45-3=42