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After 6 years, the difference between owning the house and renting is $12,000.

The first step is to determine the total cost of renting the house for six years.

Total cost of renting the house = rent per month x number of years x number of months in a year

1500 x 12 x 6 = $108,000

Difference = cost of owning - cost of renting

$120,000 - $108,000  = $12,000

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The largest integer less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13. is 1440

Given, a number less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13.

On using the Chinese remainder theorem. As, the numbers 7, 11, 13 are pairwise coprime.

Firstly, an integer  m  such that  m−5  is divisible by 7 and  m−10  is divisible by 11 .

The Chinese remainder theorem says that all integers that work will be of the form  54+7⋅11⋅k=54+77k  for any integer  k .

Next an integer  n  such that  n−10  is divisible by 13 and  n−54  is divisible by 77.

Then, by the Chinese remainder theorem, all the integers that also work are of the form  439+13⋅77⋅k=439+1001k .

Hence, the positive integers satisfying the condition are: 439, 439 + 1001 = 1440, 1440 + 1001 = 2441, and so on.

The largest integer less than 2010 is 1440.

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Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

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Answer:

5^3+4^2-8

Step-by-step explanation:

Answer:

5^3+4^2-8

Step-by-step explanation:

Answer:

The Correct answer is

57°

The displacement of the particle during the time interval [-3, 9] is 48 mysec in the positive direction. The distance traveled by the particle during this time interval is 72 mysec.

To find the displacement of the particle, we need to integrate the velocity function with respect to time over the given time interval. Integrating the function v(t) = -2t - 9t^2 - t + 8, we get the displacement function as d(t) = -t^2 - 3t^3/3 - t^2/2 + 8t + C, where C is the constant of integration. To find C, we evaluate the displacement at t = -3, which gives us d(-3) = 9 + 27/3 + 9/2 - 24 + C = 0. Solving for C, we find C = -12. The displacement at t = 9 is then calculated as d(9) = -81 - 729/3 - 81/2 + 72 - 12 = 48 mysec in the positive direction.

To find the distance traveled by the particle, we consider the absolute value of the velocity function and integrate it over the time interval [-3, 9]. Taking the absolute value of v(t) = -2t - 9t^2 - t + 8, we have |v(t)| = 2t + 9t^2 + t - 8. Integrating this function over [-3, 9], we find the distance traveled as |d(t)| = 2t^2/2 + 9t^3/3 + t^2/2 - 8t + D, where D is the constant of integration. Evaluating |d(t)| at t = -3, we get |d(-3)| = 18/2 + 27/3 + 9/2 + 24 + D = 72 + D. Therefore, the distance traveled by the particle during the time interval [-3, 9] is 72 mysec.

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Answer:

A

Step-by-step explanation:

positive leading coefficient means increasing

Answer:

0 and 3, I think those are the answers cause they make the most sense

Step-by-step explanation:

Answer:

The solution to the inequality is:

\(-1\le \:x\le \:3\)

The line graph of the solution is also attached.

Step-by-step explanation:

Given the expression

\(4x-1\:\le \:5x\:\le \:3\left(x+2\right)\)

solving the expression

\(4x-1\:\le \:5x\:\le \:3\left(x+2\right)\)

\(4x-1\le \:5x\quad \mathrm{and}\quad \:5x\le \:3\left(x+2\right)\)

solving

\(4x-1\le \:5x\)

Add 1 to both sides

\(4x-1+1\le \:5x+1\)

Simplify

\(4x\le \:5x+1\)

Subtract 5x from both sides

\(4x-5x\le \:5x+1-5x\)

simplify

\(-x\le \:1\)

Multiply both sides by -1 (reverse inequality)

\(\left(-x\right)\left(-1\right)\ge \:1\cdot \left(-1\right)\)

Simplify

\(x\ge \:-1\)

Similarly solving

\(5x\le \:3\left(x+2\right)\)

Subtract 3x from both sides

\(5x-3x\le \:3x+6-3x\)

Simplify

\(2x\le \:6\)

Divide both sides by 2

\(\frac{2x}{2}\le \frac{6}{2}\)

Simplify

\(x\le \:3\)

So combine the interval

\(x\ge \:-1\quad \mathrm{and}\quad \:x\le \:3\)

Merge overlapping intervals

\(-1\le \:x\le \:3\)

Therefore, the solution to the inequality is:

\(-1\le \:x\le \:3\)

The line graph of the solution is also attached.

The z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

The z-scores will not change if you convert the height measurements from inches to centimetres or vice versa. The z-score is a standard score representing the number of standard deviations, a value above or below the mean of a normal distribution.

The z-score is calculated using the formula z = (x - mean)/standard deviation, where x is the value being compared to the mean and standard deviation of the distribution.

Converting the height from inches to centimetres or vice versa will only change the units of measurement, but the relative position of a value within the distribution will remain unchanged.

Therefore, the z-scores will remain the same regardless of whether you use inches or centimetres for the height measurements.

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Assuming that a randomly selected subject is given a bone density test, the test scores are normally distributed with a mean score of 85 and a standard deviation of 12.

This means that 68% of subjects have bone density test scores within one standard deviation of the mean, which is between 73 and 97.

The probability of randomly selecting a subject with a bone density test score less than 60 is 0.0062 or 0.62%.

Given: Mean = 85

Standard Deviation = 12

Using the standard normal distribution table, we find that the probability of z being less than -2.08 is 0.0188.

Therefore, the probability of a randomly selected subject being given a bone density test, with a score less than 60 is 0.0188 or 1.88%.

Summary: The given problem is related to the probability of a randomly selected subject being given a bone density test with a score less than 60. Here, we have used the standard normal distribution table to calculate the probability. The calculated probability is 0.0188 or 1.88%.

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Answer: $9.45

Step-by-step explanation:

Set up a proportion of 2.70/1 = x/3.5. To solve, multiply 2.70 by 3.5 and divide by 1. 2.70*3.5 = 9.45/1 = 9.45.

The appropriate measure of variability for the given data is the IQR, and its value is 16.

Based on the given stem-and-leaf plot, which represents the scores earned in a flower-growing competition, we can determine the appropriate measure of variability for the data.

The stem-and-leaf plot shows the individual scores, and to measure the spread or variability of the data, we have two commonly used measures: the range and the interquartile range (IQR).

The range is calculated by subtracting the smallest value from the largest value in the dataset. In this case, the smallest value is 20, and the largest value is 65. Therefore, the range is 65 - 20 = 45.

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). Looking at the stem-and-leaf plot, we can identify the quartiles. The first quartile (Q1) is 25, and the third quartile (Q3) is 41. Therefore, the IQR is 41 - 25 = 16.

In this case, both the range and the IQR are measures of variability, but the IQR is generally preferred when there are potential outliers in the data. It focuses on the central portion of the dataset and is less affected by extreme values. Therefore, the appropriate measure of variability for the given data is the IQR, and its value is 16.

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Given the curve, y = 6 sin x, y = 0, x = 27, and r = 37,which bound the region to be rotated about the y-axis.

We have to find the volume generated by rotating the region about the y-axis.

Therefore, the formula for the volume of the solid of revolution is given by:

V = π∫[a, b] f²(y) dy

Here, a = 0 and b = 27, and f (y) is the inverse of the function x = 6 sin x.

So, y = 6 sin x is equivalent to

x = sin⁻¹(y/6),

which is the inverse function of y = 6 sin x.

Therefore, we have:

f(y) = sin⁻¹(y/6)

The radius of revolution is given by the distance between the y-axis and the curve.

Therefore,r = x = sin⁻¹(y/6) + 37

Thus, the formula for the volume is given by:

V = π∫[0, 6] (sin⁻¹(y/6) + 37)² dy

Here, we use u-substitution,

let u = sin⁻¹(y/6) + 37,

therefore du/dy

= 1/√[1 - (y/6)²]6(du)

= (1/√[1 - (y/6)²]) dy

Therefore, the integral becomes:

V = π ∫[37, 37.1] u² sin⁻¹(u - 37)

du = 5.068 π cubic units

The value of V is expressed in terms of π, which is the exact form of the volume generated by rotating the region about the y-axis.

Therefore, the volume of the solid of revolution is 5.068 π cubic units.

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Answer:

-30% or 30% decrease

Step-by-step explanation:

What's percentage decrease?

How do we solve this problem?

Therefore, the answer is 30% decrease.

To solve this problem, we can use the Chinese Remainder Theorem. We need to find the remainder when 2202 202 is divided by both 2101 and 251.

First, note that 2101 and 251 are relatively prime. Therefore, by the Chinese Remainder Theorem, there exists a unique remainder between 0 and 2101 * 251 - 1 (inclusive) that satisfies the two conditions.

To find this remainder, we can use the remainders when 2202 202 is divided by 2101 and 251.

Note that 2202 is congruent to 101 (mod 2101) and 0 (mod 251). Therefore, we can use the Chinese Remainder Theorem to find that the remainder when 2202 202 is divided by 2101 * 251 is congruent to:

101 * (251^2) * (251^(-1)) + 0 * (2101^2) * (2101^(-1)) (mod 2101 * 251)

Using the fact that 251^(-1) is congruent to 201 (mod 2101) and 2101^(-1) is congruent to 1922 (mod 251), we can simplify this expression to:

101 * (251^2) * (201) + 0 * (2101^2) * (1922) (mod 2101 * 251)

Simplifying further, we get:

101 * 251 * 201 (mod 2101 * 251)

This is congruent to 101 * 201 (mod 251), which is congruent to 101 (mod 251).

Therefore, the remainder when 2202 202 is divided by 2101 251 1 is 101, which is option (b).

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The critical region(s) on a normal curve distribution would be located in the tail(s) of the curve. In hypothesis testing, the critical region(s) refers to the area(s) of the distribution that corresponds to rejecting the null hypothesis. This region(s) is based on the significance level of the test, which is typically set at 0.05 or 0.01.

In this case, the null hypothesis would be that listening to Vance Joy does not have a significant effect on happiness levels. The alternative hypothesis, which is what the researcher is testing for, would be that there is a significant difference in happiness levels between those who listen to Vance Joy and those who do not.
Assuming a two-tailed test, where the researcher is interested in whether the effect could be positive or negative, the critical region(s) would be located in both tails of the normal curve distribution. The exact location of the critical region(s) would depend on the sample size and the significance level of the test.
If the sample size is large, the critical region(s) would be located farther from the mean, indicating a higher level of confidence in rejecting the null hypothesis. Conversely, if the sample size is small, the critical region(s) would be located closer to the mean, indicating a lower level of confidence in rejecting the null hypothesis.
Overall, the critical region(s) on a normal curve distribution represents the area(s) of the distribution that corresponds to rejecting the null hypothesis, and its location depends on the sample size and the significance level of the test.

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Step-by-step explanation:

they are different because the first equation only ax is in absolute but in the second equation both ax and b are in absolute, so we could solve them differently.

Answer:

Step-by-step explanation:

Add like terms. 3x & 7x are like terms

3x +7x - 2 = 10x - 2

Answer:

0.2

Step-by-step explanation:

3x+7x-2

3x+7x-2=0

3x+7x=2

10x=2

x=2/10

x=\(\frac{1}{5}\)

Answer: -3.11111112

Step-by-step explanation:

1 and 5/9 as a decimal is 1.555555556

-1/2 as a decimal is -0.5

1.555555556 divided by -0.5 is -3.11111112

Answer:

5x^3 + 5x+ 2x^2 + 2

Step-by-step explanation:

(5x+2)(x^2+1)

5x^3 + 5x+ 2x^2 + 2

Given the function f(x)=sin(2πx), with x = 0.3, f(x) = 0.951057. The objective is to approximate the value of f(0.2) using the first two terms in the Taylor series and Vx=0.1.

We know that the Taylor series for a function f(x) can be written as:f(x)=f(a)+f′(a)(x−a)+f′′(a)2(x−a)2+…+f(n)(a)n!(x−a)n+…The first two terms of the Taylor series are given by:f(x)=f(a)+f′(a)(x−a)The first derivative of f(x) is given by:f′(x)=2πcos(2πx)On substituting x = a = 0.1, we get:f′(0.1) = 2πcos(2π * 0.1) = 5.03118603447The value of f(x) at a=0.1 is given by:f(0.1) = sin(2π * 0.1) = 0.587785252292With a=0.1, the first two terms of the Taylor series become:f(x)=0.587785252292+5.03118603447(x−0.1) = 0.587785252292+0.503118603447x−0.503118603447×0.1Using x=0.2 and substituting the values of a and f(a) in the equation above, we get:f(0.2)=0.587785252292+0.503118603447*0.2−0.503118603447×0.1=0.712261After approximating the value of f(0.2) using the first two terms in the Taylor series,

we can conclude that the value of f(0.2) = 0.712261 with a = 0.1, with an error of approximately 0.012796.

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Answer:

its cos 50

Step-by-step explanation:

amen

Answer:

70feet

Step-by-step explanation:

during the

1st sec it travels 28 ft

2nd sec =28-7=21ft

3rd sec= 21-7=14ft

4th sec= 14-7= 7ft

last sec=7-7=0ft, at this point the car stops.

so altogether it travels 28+21+14+7+0= 70 feet

DNA contains the instructions needed for an organism to develop, survive and reproduce. To carry out these functions, DNA sequences must be converted into messages that can be used to produce proteins, which are the complex molecules that do most of the work in our bodies. Hope this helps!

Answer:

C. The scale factor is less than one.

Step-by-step explanation:

By definition, similar triangles have equal angles and proportional corresponding side lengths. Thus, A, B, and D are all mutually exclusive, leaving C the only possible answer. Upon further inspection, the scale factor is indeed greater than one (each side length is scaled by a factor of two, which is large than one)

In a grouped data,

it is not possible to find the median for the given observation by looking at the cumulative frequencies.

The middle value of the given data will be in some class interval. So, it is necessary to find the value inside the class interval that divides the whole distribution into two halves.

In this scenario, we have to find the median class.

To find the median class, we have to find the cumulative frequencies of all the classes and n/2.

After that, locate the class whose cumulative frequency is greater than (nearest to) n/2. The class is called the median class.

After finding the median class, use the below formula to find the median value.

\(Median = l +(\frac{\frac{n}{2}- cf}{f} )*h\)

Where

l is the lower limit of the median class

n is the number of observations

f is the frequency of median class

h is the class size

cf is the cumulative frequency of class preceding the median class.

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The fraction of time in the long run that the poker player has good luck is 0.8 or 80%.

Let's use the law of total probability to calculate the fraction of time in the long run that the poker player has good luck.

Let G denote the event that the poker player has good luck, and B denote the event that she has bad luck. Then we have:

P(G) = P(G|G)P(G) + P(G|B)P(B)

From the problem statement, we know that if the poker player has good luck one time, then she has good luck the next time with probability 0.5, which means P(G|G) = 0.5. Similarly, if she has bad luck one time, then she has good luck the next time with probability 0.4, which means P(G|B) = 0.4.

We don't know the value of P(G) yet, but we can use the fact that P(G) + P(B) = 1. So we can write:

P(G) = P(G|G)P(G) + P(G|B)(1 - P(G))

Substituting the values we know, we get:

P(G) = 0.5P(G) + 0.4(1 - P(G))

Simplifying and solving for P(G), we get:

P(G) = 0.8

Therefore, the fraction of time in the long run that the poker player has good luck is 0.8 or 80%.

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