a) Kim rounds the numbers 554 and 16 to the nearest ten. Her estimated difference is 530. Is it Reasonable?____b) Kim uses compatible numbers 555 and 15. Her estimated difference is 540. Is it Reasonable?____

Answer: \(\frac{7}{10}\)

Step-by-step explanation:

The scale factor is the ratio of the side length of the image to the length of the corresponding side of the preimage.

So, the scale factor is \(\frac{28}{40}=\frac{7}{10}\).

Need 30,529.22 pounds to buy a Lexus that costs 5,000,000 yen

To buy a Lexus that costs 5,000,000 yen, you would first need to convert the yen to pounds. You can find the updated exchange rate online.

And based on March 2, 2023, here is the current exchange rate for 1 yen = 0.0061 pounds. Therefore, you would need to multiply the cost of the Lexus in yen by the exchange rate to get the cost in pounds:

5,000,000 yen * 0.0061 pounds = 30,529.22 pounds

So you would need 30,529.22 pounds to buy a Lexus that costs 5,000,000 yen.

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The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and y vary directly and y is 44 when x is 11.

Let, y ∝ x.

y = kx.

44 = 11k.

k = 44/11.

k = 4.

Now x = 9.

y = 4×9.

y = 36.

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The alternate hypothesis that indicates the mean of the x2 population is smaller than that of the x1 population is H1: μ2 < μ1, which can be tested using a two-sample t-test.

When conducting a test for the difference of means for two independent populations x1 and x2, the alternate hypothesis that would indicate that the mean of the x2 population is smaller than that of the x1 population is:

H1: μ2 < μ1

Where H1 represents the alternate hypothesis, μ1 represents the mean of population x1, and μ2 represents the mean of population x2. The symbol "<" indicates that the mean of population x2 is smaller than the mean of population x1.

In other words, this alternate hypothesis states that there is a significant difference between the means of the two populations, with the mean of population x2 being lower than the mean of population x1. This hypothesis can be tested using a two-sample t-test, where the null hypothesis assumes that there is no significant difference between the means of the two populations.

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Using the circumference formula, the radius of the smaller windmill is obtained as Option D: 60 feet.

What is circumference?

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.

For the larger windmill, the circumference is C = 660 feet.

Solving for the radius -

C = 2πr

660 = 2πr

r = 660/(2π)

r ≈ 105.1 feet

Also, the diameter is given as 210 feet.

So, the radius will be - diameter / 2.

This gives the radius value as -

Radius = 210/5

Radius = 105 feet

For the smaller windmill, the circumference is C = 376 feet.

Solving for the radius using the same formula -

C = 2πr

376 = 2πr

r = 376/(2π)

r ≈ 59.8 feet

Therefore, the radius of the smaller windmill is approximately 59.8 feet, or 60 feet.

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The scale of measurement used for the type of college, i.e., community colleges, 4-year colleges, and universities, is a nominal scale.

A nominal scale is used for variables that can be classified into distinct categories, but there is no inherent order or numerical value associated with them. In this case, the three types of colleges are discrete categories, and there is no inherent order or numerical value assigned to them.

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Answer:

43.09

Step-by-step explanation:

just round it. since someone reported my answer basically for no reason, it got deleted ;-;

Answer:

m<TQS=23

Step-by-step explanation:

(3x-5)+(x+1)

4x-4=180

   +      +

4x=184

---    ----

4       4

x= 46

46/2

=23

If a ray QT bisects <RQS, then \(m<TQS=23.5\) °

Given :

a ray QT bisects <RQS

<PQR and <RQS is a linear pair . It makes and angle 180 degree

\(m<PQR+m<RQS=180\)

From the diagram,

m<PQR=3x-5, and m<RQS=x+1

Substitute the expression and solve for x

\(m<PQR+m<RQS=180\\3x-5+x+1=180\\4x-4=180\\4x=180+4\\4x=184\\Divide \; by \; 4\\x=46\)

now ,  \(m<RQS = x+1 =46+1=47\)

Given  QT bisects <RQS. it means QT divides RQS equally

\(m<TQS= \frac{m<RQS}{2} \\m<TQS= \frac{47}{2} \\\\m<TQS=23.5\)

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Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

The value of ∫xf ''(x) dx is 12.

We can use integration by parts to find the value of the given integral. Let's assume F(x) is the antiderivative of f ''(x), which means F'(x) = f ''(x). Applying integration by parts, we have:

∫xf ''(x) dx = xF'(x) - ∫F(x) dx

Integrating F(x) with respect to x gives us ∫F(x) dx = ∫f ''(x) dx = f '(x) + C, where C is a constant of integration. Now, let's evaluate the integral:

∫xf ''(x) dx = xF'(x) - ∫F(x) dx = xF'(x) - f '(x) - C

To find the value of the integral, we need to evaluate the expression at the limits of integration. Given that f(1) = 4 and f '(1) = 3, we can substitute these values into the expression:

∫xf ''(x) dx = [xF'(x) - f '(x)] from 1 to 4

Evaluating this expression at x = 4 and x = 1, we get:

∫xf ''(x) dx = [4F'(4) - f '(4)] - [1F'(1) - f '(1)]

Substituting f '(1) = 3, f '(4) = 3, and simplifying the expression, we find:

∫xf ''(x) dx = [4F'(4) - 3] - [1F'(1) - 3] = 12

Therefore, the value of ∫xf ''(x) dx is 12.

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Answer:

I think its complementary

Answer:

X=1/2. X=4/3

Step-by-step explanation:

6x2+5X-4=0

6X2+8X-3X-4=0

2x(3x+4) - 1(3x+4)=0

2x-1) (3X-4)

X=1/2. X=4/3

The Solution of Equation is x = -4/3 or x= 2.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have the Equation:

6x² + 5x - 4 = 0

Solving the Quadratic equation

6x² + 5x - 4 = 0

6x² -3x + 8x - 4 = 0

3x( x- 2) +4 (x-2)= 0

(3x + 4) (x-2) = 0

3x +4 = 0 or x-2 = 0

x = -4/3 or x= 2

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Answer:

\( \frac{168}{120} = \frac{21}{15} = \frac{7}{5} = 1.4\)

So the percent increase is 40%.

The percentage increase from 120 to 168 is 40%. This is calculated by finding the increase (48), dividing it by the original number (120), and multiplying the result by 100.

The question asks for the percentage increase from 120 to 168. To find this, we first determine the increase in the number, which is 168 - 120 = 48. The percentage increase is then calculated by dividing this increase by the original number (120 in this case), and then multiplying the result by 100 to get the percentage. So, the calculation would be (48/120) * 100 = 40. Therefore, the percentage increase from 120 to 168 is 40%.

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Answer: 21 water stations

Step-by-step explanation:

From the question, we are informed that a marathon is 26.2 miles long and that there is a water station every 1 1/4miles along the race route and at the finish line.

To get the number of water stations that are needed for this marathon, we divide 26.2 miles by 1 1/4miles. This will be:

= 26.2miles/1 1/4 miles

= 26.2 miles/1.25 miles

= 20.96

= 21 water stations

The company's revenue at the break-even point is:

Total Revenue = Price per Table x Number of Tables Sold Total Revenue = 166 x 50 = $8,300

1a. In order to earn revenue of $7,104, the number of tables that the company must sell is 216.

We can find the solution through the following steps:

Let x be the number of tables that the company must sell to earn the revenue of $7,104.

Total Revenue = Total Cost + Total Profit64x = 49x + 2700 + 710464x - 49x = 9814x = 216

1b. In order to earn a profit of $6,000, the number of tables that the company must produce and sell is 60.

We can find the solution through the following steps:

Let x be the number of tables that the company must produce and sell to earn a profit of $6,000.

Total Profit = Total Revenue - Total Cost6,000 = (182x - 32x) - 1500(182 - 32)x = 7,500x = 60

The company must produce and sell 60 tables to earn a profit of $6,000.

1c. To find the company's revenue at the break-even point, we need to first find the number of tables at the break-even point using the formula:

Total Revenue = Total Cost64x = 34x + 150064x - 34x = 150030x = 1500x = 50 tables

The company's revenue at the break-even point is:

Total Revenue = Price per Table x Number of Tables Sold Total Revenue = 166 x 50 = $8,300

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Answer: If your simplifying it's: 2x (power of 3) + x (power of 2) + 3x + 12x +2. Dividing would be 2x (power of 2) − 3x + 9 − 6/x+2. Have a nice day ;)

2 gallons will he have to buy

In both imperial and US customary units, the gallon is a unit of volume. The imperial gallon (imp gal), which is or was used in the UK, Ireland, Canada, Australia, New Zealand, and some Caribbean countries, is defined as 4.54609 liters; the US gallon (US gal), which is used in the US and some Latin American and Caribbean countries, is defined as 3.785411784 L; and the US dry gallon (usdrygal), which is defined as 18 US bushel.

A gallon contains four quarts and two pints respectively. The differences between imperial and US gallons are explained by variations in pint sizes.

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The approximate standard deviation of returns of U.S. common stocks during the period between 1900 and 2017 is 20%.

Standard deviation is a measure of how much the returns of a particular asset, in this case U.S. common stocks, vary from the average return. It is a measure of the risk associated with investing in the asset.

According to data from the NYU Stern School of Business, the average annual return of U.S. common stocks between 1900 and 2017 was 11.44%, with a standard deviation of 20.00%. This means that the returns of U.S. common stocks during this period varied, on average, by 20% from the average return of 11.44%.

It is important to note that this is an approximate value, as the exact standard deviation may vary slightly depending on the data source and calculation method used.

However, it provides a good estimate of the risk associated with investing in U.S. common stocks during this time period.

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Translate circle A (blue), so that its center is the same with circle B (black)

A dilation is needed to increase the size of circle A to coincide with circle B. Let x be the value when multiply by r will create s.

The scale factor , x, to increase circle A is

He must work the rest of the 7 weeks to earn at least $270 for the week. 8

So we know that he's already earned $80 because he earned $8 per hour 9 for the first 10 hours.

So eight times 10 is 80.

Saving money helps you overcome difficult situations, meet your financial obligations, and build wealth. Saving money is essential. Provides financial security and freedom and covers financial emergencies. Saving money helps you avoid debt and reduces stress.

Saving is important because it helps cushion financial emergencies and unexpected expenses. In addition, savings can help you pay for big purchases, avoid debt, reduce financial stress, and increase your sense of financial freedom.

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The assumptions necessary for confidence interval 90% with population mean salary  μ turns out to be (1000, 2100) this interval is based on sample size 25 is given by option C) The population must have an approximately normal distribution.

For a confidence interval to be valid, it is necessary to make certain assumptions about the population and the sample.

Here, the assumptions necessary for a valid 90% confidence interval based on a sample of size n = 25 are,

Random sampling,

The sample should be a random sample from the population.

That every member of the population has an equal chance of being selected.

Independence,

The sample observations should be independent of each other.

The value of one observation does not affect the value of another observation.

Normality,

The population of salaries must have an approximately normal distribution.

This assumption is necessary because the confidence interval is based on the Central Limit Theorem.

Which states that the sampling distribution of the sample mean is approximately normal.

Provided that the sample size is large enough and the population distribution is approximately normal.

Sample size,

The sample size should be large enough to ensure that the sampling distribution of the sample mean is approximately normal.

In general, a sample size of 25 is considered sufficient to meet this requirement.

Option A is incorrect because it describes an assumption necessary for the validity of a confidence interval based on the Central Limit Theorem.

Option B is incorrect because the population is assumed to have a normal distribution, not an approximate t-distribution.

Option D is incorrect because it describes a biased sample distribution.

Which would invalidate the results of any statistical analysis based on the sample.

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Answer:

1/64+2*1/8*2a+4a^2= 1/64+a/2+4a^2

Step-by-step explanation:

The sample space for rolling a number cube with faces labeled from 1 to 6 consists of all the possible outcomes or numbers that could be rolled. The sample space can be represented as {1, 2, 3, 4, 5, 6}.

In this case, rolling the number cube once gives us six equally likely outcomes, which are represented by the numbers 1, 2, 3, 4, 5, and 6. Each number represents the face that lands on top when the cube is rolled.

The sample space represents all the possible results that can occur when rolling the number cube, and it includes all the distinct elements or numbers in the set {1, 2, 3, 4, 5, 6}. Each number in the sample space has an equal probability of occurring since the number cube is fair and unbiased.Therefore, the sample space for rolling the number cube once is {1, 2, 3, 4, 5, 6}.

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Answer:

c x 6 or 6c

Step-by-step explanation:

The y-axis is 4π/3 cubic ,To find the volume of the solid obtained by rotating the region bounded by the curves y = 1/x^5, y = 0,

x = 1, and x = 9 about the y-axis, we can use the method of cylindrical shells.

The volume of each cylindrical shell can be calculated as the product of the circumference of the shell, the height of the shell, and the thickness of the shell. In this case, the circumference of each shell is given by 2πx, the height is given by y = 1/x^5, and the thickness is dx.

The integral to find the volume is:

V = ∫[1, 9] 2πx * (1/x^5) dx

Let's solve this integral step by step:

V = 2π ∫[1, 9] (1/x^4) dx

Using the power rule for integration, we can simplify the integral:

V = 2π [(-1/3) * x^(-3)] |[1, 9]

V = 2π * [(-1/3) * (1/9^3 - 1/1^3)]

V = 2π * (1/3 - 1)

V = 2π * (-2/3)

V = -4π/3

Since we're dealing with volume, the negative sign doesn't have any physical significance.

Therefore, the volume of the solid obtained by rotating the region bounded by the given curves about the y-axis is 4π/3 cubic units.

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Answer:

1 = 19.     3 = 21.     7 = 25

Step-by-step explanation:

w = t + 18

19 = 1 + 18

21 = 3 + 18

25 = 7 + 18

The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.

To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.

The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).

Rationalizing the denominator

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)

Note that multiplying the conjugate of the denominator is like squaring a binomial:

This simplifies to:

(-6√(5y))/(√(5y) * √(5y))

The denominator simplifies to:

√(5y) * √(5y) = √(5y)^2 = 5y

So, the expression becomes:

(-6√(5y))/(5y)

Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).

\($(a-b)(a+b)=a^2-b^2$\)

This is what we will do to rationalize the denominator in this problem.

We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).

Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)

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Answer: yes

Step-by-step explanation:

The velocity vector points in the direction of the tangent line to the curve at t=1, and the acceleration vector points in the direction of the curvature of the curve at that point.

We can find the velocity vector by taking the derivative of r(t):

v(t) = r'(t) = i + 2t j

At t = 1, the velocity vector is v(1) = i + 2j.

To find the acceleration vector, we take the second derivative of r(t):

a(t) = r''(t) = 2j

At t = 1, the acceleration vector is a(1) = 2j.

To sketch these vectors on the curve, we first plot the point r(1) = i + 8. Then, we draw the velocity vector i + 2j starting from this point, and the acceleration vector 2j starting from the same point.

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