Angela ordered 2 glass paperweights. The volume of each paperweight is 5 cubic inches, and the density of the glass is 1.5 ounces per cubic inch. Angela can use the calculation below to find the total weight of her order.

2×(5×1.5)

How can Angela simplify the calculation using only the associative property of multiplication?

Drag and drop the appropriate number or expression into each box.

The differential equation for the amount of salt a(t) in the tank at time t > 0 is dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t).

To find the differential equation for the amount of salt a(t) in the tank at time t > 0, we need to consider the rate of change of the salt concentration in the tank.

Let A(t) represent the amount of salt in the tank at time t. The salt entering the tank each minute is given by the concentration (4 lb/gal) multiplied by the rate of inflow (3 gal/min), which is 12 lb/min.

The salt leaving the tank each minute is given by the concentration in the tank (A(t)/V(t)) multiplied by the rate of outflow (2 gal/min), which is 2A(t)/(35 + (3 - 2)t).

Therefore, the rate of change of the salt in the tank is given by the difference between the rate of inflow and the rate of outflow: dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t). This is our differential equation for the amount of salt in the tank.

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To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2. The two points are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2.

First, we find the derivative of the function:

dy/dx = 3x^2 - 12x - 34

Next, we set the derivative equal to 2 and solve for x:

3x^2 - 12x - 34 = 2

3x^2 - 12x - 36 = 0

Using the quadratic formula, we find the solutions for x:

x = (-b ± √(b^2 - 4ac))/(2a)

Substituting the values a = 3, b = -12, and c = -36 into the quadratic formula, we get:

x = (-(-12) ± √((-12)^2 - 4(3)(-36)))/(2(3))

x = (12 ± √(144 + 432))/6

x = (12 ± √(576))/6

x = (12 ± 24)/6

x = 12/6 ± 24/6

x = 2 ± 4

So the two points where the slope of the tangent line is 2 on the curve are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

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To find the year two states would theoretically have equal median house values, one could use provided growth rates and starting house values to set up an equation and solve for time. However, assuming a linear trend can lead to inaccurate results as real estate markets are affected by many fluctuating factors.

To calculate the year in which two states would have theoretically had equal median house values, we first need to know the starting house values for each state and the annual growth rate trends. We've learned from the FRED® Economic Data that median sales price for a home in the U.S. was $122,900 in 1990 and rose to $232,000 by the end of 2016, an average growth rate of 3.1% annually. In other periods, such as the 1970s, 1980s, and 1990s, housing prices increased about 6% per year on average. During the 'housing bubble' years (2003-2005), they experienced a sharp rise and then a fall with the 2007-2008 recession.

Assuming linear trend (constant growth), we would set up an equation with these variables and solve for the year (time) where the values are equal. However, do kindly note that assuming the same trend can often lead to absurd results as housing markets are affected by a variety of economic, political, and demographic factors and do not always follow a linear trend.

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a) Home values have increased at a higher rate in New York.

b) The median home value in Arkansas in 2010 would be $82,400.

c) The two states' median house values were equal in year = 190

Let’s break down each question:

a) To determine which state’s home values have increased at a higher rate, we need to calculate the rate of change for each state. The rate of change is calculated as the difference in home values divided by the difference in years.

For Arkansas, the rate of change is (72,800 - 24,800) / (2000 - 1950) = $960 per year.

For New York, the rate of change is (148,700 - 61,500) / (2000 - 1950) = $1,744 per year.

So, home values have increased at a higher rate in New York.

b) If these trends were to continue, the median home value in Arkansas in 2010 would be the 2000 home value plus the rate of change times the number of years since 2000.

So, the median home value in Arkansas in 2010 would be 72,800 + $960 * (2010 - 2000) = $82,400.

c) If we assume the linear trend existed before 1950 and continues after 2000, the two states’ median house values will be equal when the equation for Arkansas’s home values equals the equation for New York’s home values.

We are given that the median home value in Arkansas in 1950 was $24,800 and in 2000 it was $72,800. This gives us a rate of increase of $960 per year. So, the value of a home in Arkansas in year ‘x’ can be represented by the equation:

[tex]V_{Arkansas}(x) = 24800 + 960 * (x - 1950)[/tex]

Similarly, the median home value in New York in 1950 was $61,500 and in 2000 it was $148,700. This gives us a rate of increase of $1,744 per year. So, the value of a home in New York in year ‘x’ can be represented by the equation:

[tex]V_{NewYork}(x) = 61500 + 1744 * (x - 1950)[/tex]

The two states’ median house values will be equal when

[tex]V_{Arkansas}(x) = V_{NewYork}(x)[/tex]

Setting the two equations equal to each other and solving for ‘x’ gives us:

[tex]24800 + 960 * (x - 1950) = 61500 + 1744 * (x - 1950)[/tex]

[tex]24800+960x-1872000=61500+1744x-3400800\\784x=149100\\x=190.17[/tex]

We round it to the nearest whole number because it represents a year.

So, the two states' median house values were equal in year = 190

Complete Question:

The median home value in Arkansas and New York (adjusted for inflation) are shown below:

Year Arkansas  New York

1950 24,800 61,500

2000 72,800 148,700

If we assume that the house values are changing linearly,

a) In which state have home values increased at a higher rate?

b) If these trends were to continue, what would be the median home value in Arkansas in 2010?

C) If we assume the linear trend existed before 1950 and continues after 2000, the two states' median house values will be (or were) equal in what year? (The answer might be absurd)

Answer:

CHEATING

Step-by-step explanation:

becaus eI got it right on egde

The information given that the skier covered 2.6509 miles is wrong because the decimal was wrongly put.

Since the cross-country skier skied at a rate of 10.82 miles per hour, it should be noted that in 2.45 hours, we've to multiply 10.82 miles by 2.45 hours and this will be:

= 10.82 × 2.45

= 26.509 miles

From the information given, we are told that in 2.45 hours, the skier covered 2.6509 miles, this is incorrect as the miles covered is 26.509 miles.

Therefore, information given that the skier covered 2.6509 miles is wrong because the decimal was wrongly put.

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Final answer:

To make the lengths the same, she would have to cut 0.3 feet from the longer piece.

Explanation:

To find the amount she would have to cut to make the two lengths the same, we need to subtract the smaller length from the larger length.

The first length is 3 4/5 feet, which can also be written as 3 + 4/5 = 3 + 0.8 = 3.8 feet.

The second length is 3 1/2 feet, which can also be written as 3 + 1/2 = 3 + 0.5 = 3.5 feet.

Subtracting the smaller length (3.5 feet) from the larger length (3.8 feet), we get:

3.8 feet - 3.5 feet = 0.3 feet.

So she would have to cut 0.3 feet from the longer piece to make the lengths the same.

A) unknown information is how much she spent on the taxi ride

B) 31 = x +16+6

C ) 31= x +22

     x =31-22 = 9

   She spent $9 on the taxi

(A) How much money Hera spent on the taxi ride.

(B) 31 = x + 16 +6

(C) 16 + 6 = 22 31 - 22 = 9

(D) She spent $9 on the taxi.

(also sorry im uh 4 years late aldksjfladfoajsdflkj)

Answer:

A. always

Step-by-step explanation:

parallel lines are always going to be coplanar

Answer:  The required simplified fraction is [tex]\dfrac{2}{1}.[/tex]

Step-by-step explanation:  We are given that in a grocery store there are 4 self-checkout lines and 8 lines with cashiers.

We are to find the ratio of the number of lines with cashiers to the number of self-checkout lines.

Let n represents the number of lines with cashier and m represents the number of self-checkout lines.

Then, we have

n = 8 and  m = 4.

Therefore, the required ratio of the number of lines with cashiers to the number of self-checkout lines is given by

[tex]\dfrac{n}{m}=\dfrac{8}{4}=\dfrac{2}{1}.[/tex]

Thus, the required simplified fraction is [tex]\dfrac{2}{1}.[/tex]

since the refrigerator is 15% off

it is selling at 100%-15% = 85% of the original value

85% = 0.85

 so 0.85Pis one price

other store is selling at p-150

 so 0.85p = p-150

To calculate the property taxes on a townhouse valued at $73,000, divide the value by $100 to find the number of $100 increments, and then multiply this by the tax rate of $1.15.

To find the property taxes on a townhouse valued at $73,000, we need to calculate the tax amount based on the given tax rate. The tax rate is $1.15 for every $100 of home value.

First, we need to find how many $100 increments are there in the home value.

Divide $73,000 by $100:

$73,000 ÷ $100 = $730

Now, multiply the number of $100 increments by the tax rate:

$730 × $1.15 = $839.50

Therefore, the property taxes on a townhouse valued at $73,000 would be $839.50.

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use order of operations

8^2 = 64

4(64+4*4*8)

4(64+128)

4(192)

768

First calculate the total amount of liters consumed:

Volume gas consumed = (6 L / 100 km) * 2000 km = 120 L

Then calculate the total cost:

Cost = ($1.20 / L) * 120 L = $144

Since there are three of them, so each must pay:

Payment of each = $144 / 3 = $48 per person

Answer:

$48 per person

Carrier A is 2104 feet long and carrier B is 2094 feet.

This problem can be solved using simple algebra. Let's denote the length of carrier A as 'a' and the length of carrier B as 'b'. We know two things about these lengths from the question:

Now, you can add these two equations together to eliminate 'b'. This will give: 2a=4208. Hence, by dividing by 2, you will find that a=2104. Now, substitute a=2104 back into the first equation: a+b=4198. This will give: 2104+b=4198, which simplifies to b=2094. So, the length of carrier A is 2104 feet and the length of carrier B is 2094 feet.

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The probability of drawing an ace and rolling a "2" is 0.012859.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that the probability of drawing an ace from a deck of cards is 0.077 and the probability of rolling a "2" using a fair die is 0.167.

The probability of drawing an ace and rolling a "2" is calculated as,

Probability = 0.077 × 0.167

Probability = 0.012959

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Writing 3.441 in expanded form shows that each digit represents a different value depending on its place in the decimal number. This is determined by the power (exponent) of 10 corresponding to the decimal shift from the right side of the digit. This understanding is essential for scientific notation and handling large and small numbers.

Writing the number 3.441 in expanded form helps to clarify why the same digit can possess different values based on its position in the decimal number. To write 3.441 in expanded form we break it down into the addition of its respective place values, like this:

3.441 = 3 x 1 + 0.4 x 1/10 + 0.04 x 1/100 + 0.001 x 1/1000.

As we can see, each digit represents a different value based on its placement. This is determined by the power (exponent) of 10 which is equal to the number of places the decimal is shifted from the right side of the digit. This method is also applicable to scientific notation, transforming both very large and very small numbers into more manageable expressions for calculations.

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