The quotient of (x4 â€"" 3x2 4x â€"" 3) and a polynomial is (x2 x â€"" 3). What is the polynomial? x4 â€"" 2x2 5x â€"" 6 x2 â€"" x 1 x6 x5 â€"" 6x4 x3 10x2 â€"" 15x 9 x4 â€"" 4x2 3x.

The function y(t) = 1/cos(t) is a solution to the differential equation d2y/dt2 = 2y3 - y if it satisfies the equation when substituted into it. To verify this, we can substitute the function into the equation and simplify.

First, let's find the first and second derivatives of the function:
dy/dt = (sin(t))/(cos^2(t))
d2y/dt2 = (2sin^2(t))/(cos^3(t)) - (1/cos^3(t))

Now, let's substitute these derivatives and the original function into the differential equation:
(2sin^2(t))/(cos^3(t)) - (1/cos^3(t)) = 2(1/cos(t))^3 - (1/cos(t))

Simplifying the right side of the equation gives us:
(2sin^2(t))/(cos^3(t)) - (1/cos^3(t)) = (2/cos^3(t)) - (1/cos(t))

Combining like terms on the right side gives us:
(2sin^2(t))/(cos^3(t)) - (1/cos^3(t)) = (2 - cos^2(t))/(cos^3(t))

Since sin^2(t) + cos^2(t) = 1, we can substitute 1 - cos^2(t) for sin^2(t) to get:
(2(1 - cos^2(t)))/(cos^3(t)) - (1/cos^3(t)) = (2 - cos^2(t))/(cos^3(t))

Simplifying the left side gives us:
(2 - 2cos^2(t))/(cos^3(t)) - (1/cos^3(t)) = (2 - cos^2(t))/(cos^3(t))

Combining like terms on the left side gives us:
(1 - cos^2(t))/(cos^3(t)) = (2 - cos^2(t))/(cos^3(t))

Since both sides of the equation are equal, we can conclude that the function y(t) = 1/cos(t) is a solution to the differential equation d2y/dt2 = 2y3 - y.

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Answer:

5x + 4y = - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

4x - 5y = 20 ( subtract 4x from both sides )

- 5y = - 4x + 20 ( divide all terms by - 5 )

y = \(\frac{4}{5}\) x - 4 ← in slope- intercept form

with slope m = \(\frac{4}{5}\)

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{\frac{4}{5} }\) = - \(\frac{5}{4}\) , thus

y = - \(\frac{5}{4}\) x + c ← is the partial equation

To find c substitute (- 4, 3) into the partial equation

3 = 5 + c ⇒ c = 3 - 5 = - 2

y = - \(\frac{5}{4}\) x - 2 ← in slope- intercept form

Multiply through by 4

4y = - 5x - 8 ( add 5x to both sides )

5x + 4y = - 8 ← equation in standard form

Answer:315

Step-by-step explanation:

The matching for different kinds of telescopes is shown. (Refer to the matching shown below.)

A telescope is a tool used to view distant objects through the electromagnetic radiation that they emit, absorb, or reflect.

The term "telescope" now refers to a broad range of instruments capable of detecting different regions of the electromagnetic spectrum, and in some cases, other types of detectors, in addition to the original meaning of the word, which was only an optical instrument using lenses, curved mirrors, or a combination of both, to observe distant objects.

Refracting telescopes with glass lenses were the first practical telescopes ever made, and they were developed in the Netherlands at the start of the 17th century.

The matching according to the question:

Reflecting Telescopes: The Hubble Space Telescope, the largest telescope in the world, is currently the one most frequently used by professional astronomers.

Refracting Telescopes: In Galileo's telescopes, very large telescopes become "top-heavy," incoming light travels through glass, and the largest reflecting telescope in the world has a diameter of one meter.

Therefore, the matching for different kinds of telescopes is shown.

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The harmonic mean would give equal weight to both of these trails, despite their different distances.

The harmonic mean would make the most sense when calculating the average one-way mileages for trails to different lakes. When it comes to calculating the average of one-way mileages for trails to different lakes, it's important to choose the appropriate type of average based on the nature of the data.

In this case, since we're dealing with mileages, one-way distances, and travel times, the best option would be the harmonic mean. The harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocals of a set of numbers. In other words, it's a weighted average of the reciprocals of the numbers.

This type of average is useful in situations where rates, speeds, or frequencies are involved.  In this case, the harmonic mean would be the most appropriate choice for calculating the average one-way mileage for trails to different lakes because it takes into account the fact that distances and travel times are inversely related.

For example, if one trail has a distance of 10 miles and a speed of 2 miles per hour, it will take 5 hours to travel that distance. On the other hand, if another trail has a distance of 20 miles and a speed of 4 miles per hour, it will also take 5 hours to travel that distance.

Therefore, the harmonic mean would give equal weight to both of these trails, despite their different distances.

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The standard deviation of the mean birth weights for samples of 100 babies is 50 grams.

The standard deviation of the mean birth weights for samples of 100 babies can be calculated using the formula:

Standard deviation of the mean = Standard deviation of the population / sqrt(sample size)

Given that the standard deviation of birth weights for individual babies in the population is 500 grams, and the sample size is 100, we can plug in these values into the formula:

Standard deviation of the mean = 500 / sqrt(100) = 50 grams

Therefore, the standard deviation of the mean birth weights for samples of 100 babies is 50 grams.

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The write answer of your question is C

According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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A researcher wants to determine the effect of a new drug on mental alertness. The researcher's hypothesis test will be conducted using the significance level of .05 (two-tailed test), based on a sample of n = 16 college students.

The null hypothesis states that the drug has no effect on mental alertness (μ = 7) while the alternative hypothesis claims that the drug has a significant effect on mental alertness (μ ≠ 7).H0: μ = 7HA: μ ≠ 7The test statistic for the sample data is computed as follows:
t = (M - μ) / (s / √n)
t = (9 - 7) / (2.5 / √16)
t = 4The corresponding p-value is p < .01. The test statistic has a critical value of ±2.13 with degrees of freedom of n - 1 = 15 at the .05 level of significance.The sample provides enough evidence to conclude that the new drug has a significant effect on mental alertness. The researcher must reject the null hypothesis and accept the alternative hypothesis because the test statistic (t = 4) is greater than the critical value of ±2.13.The conclusion should be written in APA format as follows:

The sample of 16 college students who took the new drug showed significantly improved mental alertness (M = 9, s = 2.5, t(15) = 4, p < .01) compared to the population mean of 7. Therefore, the null hypothesis was rejected, and the alternative hypothesis was accepted. The drug has a significant effect on mental alertness.

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Answer:

$0.30

Step-by-step explanation:

Divide 4.50 by 15.

Answer:

32 is rational number.

Step-by-step explanation:

Because it can be expressed as the quotient of two integers : 32/1

Answer:

Answer: 2000

Step-by-step explanation:

They started counting the population after the year 2000 meaning that in 2000 they had an initial count .

Answer:

P

Step-by-step explanation:

The least absolute value is what number is closest to zero.

The angle between vectors a and b is 71.79° for using the Dot Product property of vectors.

The given two vectors are a = ⟨2,2,−1⟩ and b = ⟨5,−3,2⟩. We need to find the angle between vectors a and b.

Using the Dot Product property of vectors we can find the angle between vectors. The formula for the dot product of vectors is given as follows.

a . b = |a| |b| cos(θ)

where |a| and |b| are the magnitudes of vectors a and b respectively and θ is the angle between vectors a and b.

Rearranging the above equation gives,

cos(θ) = (a . b) / (|a| |b|)

Taking the dot product of vectors a and b, we get,

a . b = (2 × 5) + (2 × −3) + (−1 × 2)

= 10 − 6 − 2

= 2

Now, we need to calculate the magnitudes of vectors a and b.

The magnitude of a is,

|a| = √(2² + 2² + (-1)²)

= √9

= 3

The magnitude of b is,

|b| = √(5² + (-3)² + 2²)

= √38

cos(θ) = (a . b) / (|a| |b|)

cos(θ) = 2 / (3 × √38)

cos(θ) = 0.3271

θ = cos⁻¹(0.3271)

θ = 71.79°

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Answer:

below

Step-by-step explanation:

Standard form

ax + gy = c       re-arrange to slope -int form   subtract ax from both sides of the equation

gy = - ax + c       divide thru by 'g'

y = -a/g x + c/g      - a/g would be the slope , m   and c/g would be the y-axis

  intercept , b    for   slope intercept form    y - mx +b  

Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

According to our question-

automobile is priced at $3,500.

Tom needs more collateral, so P

=P + 3500 Total Collateral Value

His bank is able to lend up to 80% of the value of the collateral.

=> loan = (80/100)(P + 3500)

=> loan = 0.8P + 2800

Loan amount needed: 4,750.

0.8P + 2800 = 4,750.

=> 0.8P = 1950

=> P = 2,437.5

Tom has to put up an additional $2,437.5 in collateral in order to borrow enough money to take his vacation as planned.

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Answer:

480 minutes would be the answer

Step-by-step explanation:

Answer:

480 minutes

Step-by-step explanation:

We can write this relationship as \(y=0.11x+18\) and then solve for x when y=70.80:

\(y=0.11x+18\\\\70.80=0.11x+18\\\\52.80=0.11x\\\\480=x\)

Therefore, you spent 480 minutes talking.

Answer:

5/6 is the simplest form

Hope that helps

The solutions are

a. 10000 = 9359.08e(0.05)

e⁰⁰⁵ = 10000/9359.08

= 0.05 = ln(10000/9359.08)

= 1.325 years

convert to months = 15.9 months

Hence it is going to take 15.9 months to raise 10000 dollars

b. 9359.08 x e^(0.05 x1.25)

= 9962.69

10000 - 9962.69

= $37.31

You will have $37.31 after you have bought the car

c. The money loss and the deficit would be same as above $37.31

d. ln(e^a) = a

We can clearly see that the money cannot be raised in the 15 months from $ 9359.08. there is a deficit amount of $37.31

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The investment strategy that Zhang should adopt depends on his personal financial situation, investment goals, and risk tolerance. he be a  aggressive investor.

It's important for Zhang to conduct thorough research and consult with a financial advisor before making any investment decisions.it is possible that Zhang may be comfortable with an aggressive investment strategy. Aggressive investors typically prioritize growth and are willing to take on more risk in their investments. Since Zhang is young and has a long time horizon, he may be able to tolerate more risk in his investments to potentially achieve higher returns in the long run. However, it is important to note that aggressive investing involves a higher level of risk, and it is crucial to do thorough research and consult with a financial professional before making any investment decisions. It is also important for Zhang to have a well-diversified portfolio that can help spread out risk and minimize potential losses.

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The area or the common pasture will be 12 acres.

Based on the information given, the formula to use will be:

ab/ac = 2/4

b/c = 1/2 .... i

Also, ab/bd = 2/6

a/d = 1/3 .... ii

Multiply both equation

1/2 × 1/3 = 1/6

Therefore, the area will be

= 6 × 2

= 12 acres

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Answer:

35%

Step-by-step explanation:

The required percentage of the mocha cupcakes that were sold that day is 85%.

Given that,
A bakery sells mocha cupcakes and chocolate cupcakes. One day it sold 238 mochas and 42 chocolate. What percent of the cupcakes sold that day were mocha is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Number of mocha cupcakes = 238
Number of chocolate cupcakes = 42
Total cupcakes = 238 + 42 = 280
Percentage of mocha sold = 238/280 = 0.85 or 85%

Thus,  the required percentage of the mocha cupcakes that were sold that day is 85%.

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(d) The equation for the situation is n * (1/8) = 3/4, where n represents the number of items Jane can find. (e) By solving the equation, we find that n = 6. (f) Jane can find 6 items before the store closes.

(d) To create a model or write an equation for the situation, we can use the information provided. Let's represent the number of items Jane can find before the store closes as "n". We know that it takes about 1/8 hour (or 1/8 * 60 minutes = 7.5 minutes) for Jane to find 1 item on her shopping list. Since she has 3/4 hour before closing time, we can set up the equation:

n * (1/8) = 3/4

(e) To find the solution, we can solve the equation. By multiplying both sides of the equation by 8, we can eliminate the fraction:

8 * (n * (1/8)) = 8 * (3/4)

n = 6

So the solution is n = 6.

(f) The full sentence stating the solution is: Jane can find 6 items before the store closes.

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Answer:

13.5

Step-by-step explanation:

Answer:

(2, 4).

Step-by-step explanation:

For y = -x  the transform is:

( x, y )  reflects to (-y, - x)

So (-4, -2) reflects to (2, 4)

Question 1

\(\angle 1\) and \(\angle 2\) are supplementary.

\(3x+20+x=180 \\ \\ 4x+20=180 \\ \\ 4x=160 \\ \\ x=40\)

\(\angle 1\) and \(\angle 4\) are vertical angles. Thus, \(m\angle 4=3(40)+20=140^{\circ}\).

Question 4

\(105+3x=180 \\ \\ 3x=75 \\ \\ x=25\)

As the sales price is 65% off you find the 65% of the original cost and then substract it from the original cost:

Answer:

2.85 x 10⁷

Step-by-step explanation:

Answer:

The value of x is 7.

Step-by-step explanation:

Answer:

D and E

Step-by-step explanation:

remote interior angles are not adjacent to a given angle. or basically 1 is our exterior angle, so the opposites of 1 and the remote interior angle.

The remote interior angles of Z1 are ∠4 and ∠3. The correct options are D and E.

A triangle's remote interior angles are the two angles that are not adjacent to a given exterior angle. An exterior angle of a triangle is formed by extending one of the triangle's sides.

The following theorem can be used to calculate the remote interior angles of a triangle:

A triangle's remote interior angles are equal in size to the exterior angle that is not adjacent to them.

In other words, if we know the measure of one of a triangle's exterior angles, we can find the measure of the distant interior angles by subtracting that measure from 180 degrees.

Thus, the correct options are D and E.

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