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Final answer:

Matt's Ice Cream Shoppe can serve 56 sundaes with 7 cups of sprinkles, assuming each sundae uses 1/8 cup of sprinkles.

Explanation:

The question asks: How many sundaes can Matt's Ice Cream Shoppe serve with 7 cups of sprinkles if each sundae is served with 1/8 cup of sprinkles?

To find the answer, we divide the total amount of sprinkles by the amount used per sundae. Here's the calculation:

Therefore, Matt's Ice Cream Shoppe can serve a total of 56 sundaes with their current stock of sprinkles.

Matt's Ice Cream Shoppe can serve 56 sundaes with the 7 cups of sprinkles they have.

To find out how many sundaes Matt's Ice Cream Shoppe can serve with 7 cups of sprinkles, we need to divide the total amount of sprinkles by the amount of sprinkles used per sundae.

Given:

- Total amount of sprinkles: 7 cups

- Amount of sprinkles per sundae: [tex]\( \frac{1}{8} \)[/tex] cup

Let ( x ) be the number of sundaes that can be served.

We can set up the equation:

[tex]\[ \text{Total amount of sprinkles} = \text{Amount of sprinkles per sundae} \times \text{Number of sundaes} \][/tex]

[tex]\[ 7 = \frac{1}{8} \times x \][/tex]

Now, to solve for ( x ), we can multiply both sides of the equation by 8:

[tex]\[ 7 \times 8 = x \][/tex]

[tex]\[ x = 56 \][/tex]

Therefore, Matt's Ice Cream Shoppe can serve 56 sundaes with the 7 cups of sprinkles they have.

The error made was in the summation of the y^2 terms in each expression, leading to an incorrect final sum of the two expressions.

Kendall's error lies in incorrectly adding the terms that contain y^2. Specifically, Kendall summed 2y^2 from the first expression and -3y^2 from the second expression, but mistakenly calculated the result as -5y^2 instead of the correct -y^2. Remember, when performing operations with similar terms, you must carry the correct sign along with each term.

So, the correct sum of (6x^2+4xy+2y^2) and (4x^2-2xy-3y^2) is (10x^2+2xy-y^2).

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The total lease cost is the sum of the down payment, nonrefundable security deposit, acquisition fee, and the total payments over the lease term which amounts to $12,342.

The total lease cost can be calculated by adding all fees, the nonrefundable deposit, monthly payments, and any other additional costs. We start by adding the down payment, security deposit, and acquisition fee:

The monthly payment over the term of the lease is calculated by multiplying the monthly payment amount by the number of months in the lease term:

Multiplying the monthly payment by the lease term gives us the total amount paid over the course of the lease:

Adding all the costs together gives us the total lease cost:

Note that this calculation assumes that the security deposit is nonrefundable, which is often the case in a car lease. It's also important to note that additional costs may apply, such as excess mileage fees or wear and tear.

The side of cube is given as 3 1/2 inches.

converting 3 1/2 into mixed fraction we have 7/2 inches.

on dividing 7 by 2 we get 3.5 inches

Formula to find volume of cube is given by:

[tex] V = a^{3} [/tex]

where "a" is length of side.

Plugging the value of a in the formula we have,

[tex] V = (3.5)^{3} [/tex]

Volume of cube is 42.875 cubic inches.

Value of the car in 2018 after depreciation by 12% each year is equals to $13351.5

" Exponential decay is the decrease in the value of the product at a constant rate over a period of time interval."

Formula used

y = a (1 - r)ⁿ

a = Initial value

r =rate of depreciation

n = time

y = exponential function

According to the question,

Cost of new car 'a' = $28750

Rate of depreciation 'r' = 12%

2018 - 2012 = 6years

n = 6

Substitute the given values in the formula we get,

Exponential function

    y = 28750 [1 - (12 / 100)]⁶

⇒ y = 28750 ( 1 - 0.12)⁶

⇒ y = 28750 ( 0.88)⁶

⇒ y = 28750 (0.4644)   ( up to four decimals)

⇒ y = $13351.5

Hence, value of the car in 2018 after depreciation by 12% each year is equals to $13351.5

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A negative correlation means that high values of one variable are associated with low values of the other. This suggests that as one variable increases, the other decreases respectively and vice versa, which can be seen in various real-world scenarios such as the relationship between time spent studying and number of mistakes made on a test.

In the context of statistics and data analysis, a negative correlation means that high values of one variable are associated with low values of the other. This implies that as one variable increases, the other decreases correspondingly and vice versa. For instance, if we were examining the relationship between time spent studying and number of mistakes made on a test, a negative correlation might indicate that the more time a student spends studying, the fewer mistakes they make on the test. This is indicative of a negative correlation because as the value of one variable (study time) increases, the value of the other variable (mistakes) decreases.

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Final Answer:

The result of dividing [tex](5x^3y^3z - 6x^4y^2z^2 + 4xy^3z)[/tex] by xyz is [tex](5x^2y^2 - 6x^3yz + 4y^2z).[/tex]

Explanation:

To divide [tex](5x^3y^3z - 6x^4y^2z^2 + 4xy^3z)[/tex] by xyz, we'll divide each term in the polynomial by xyz separately.

First, let's divide [tex]5x^3y^3z by xyz: (5x^3y^3z) / (xyz) = 5x^2y^2.[/tex]

Then, divide [tex]-6x^4y^2z^2 by xyz: (-6x^4y^2z^2) / (xyz) = -6x^3yz.[/tex]

Lastly, divide [tex]4xy^3z by xyz: (4xy^3z) / (xyz) = 4y^2z.[/tex]

Thus, the resulting polynomial after division is [tex]5x^2y^2 - 6x^3yz + 4y^2z.[/tex]This is derived from individually dividing each term in the polynomial by xyz, simplifying each term, and collecting like terms together to obtain the final result.

In this process, division by xyz means dividing each term of the polynomial by the factors x, y, and z, and simplifying the expression. By doing so, we obtain a simplified form of the polynomial where each term is reduced by the common factors x, y, and z, resulting in the expression [tex](5x^2y^2 - 6x^3yz + 4y^2z)[/tex] as the quotient.

Complete question:

Divide [tex](5x^3y^3z - 6x^4y^2z^2 + 4xy^3z)[/tex] by xyz.

Solution:

Wyatt's dog is tethered to a post in his yard.

The rope tied to the dog is 12 feet long.

we have been asked to find

How many square yards does the dog have access to?

when Wyatt's dog is tethered to a post in his yard, then that dog can move along that post only and the area covered will be a circle with radius 12ft.

So Area access to dog in ft^2 [tex] = \pi r^2=\pi 12^2=144 \pi [/tex]

But it ask for area in yards, so we will have to use conversion formula

[tex] 1ft=0.33333yard [/tex]

Area access to dog in yards[tex] =144*3.14*(0.33333)^2=50.24 \ Yards [/tex]

Answer:

Wyatt's dog is tethered to a post in his yard.

The rope tied to the dog is 12 feet long.

we have been asked to find

How many square yards does the dog have access to?

when Wyatt's dog is tethered to a post in his yard, then that dog can move along that post only and the area covered will be a circle with radius 12ft.

So Area access to dog in ft^2  

But it ask for area in yards, so we will have to use conversion formula

Area access to dog in yards

Step-by-step explanation:

The distance of Aldo's house from the mountains when calculated using the parameters is; 280 miles

We know that distance is given by;

Distance = speed * time

Distance with traffic = 8x

Distance without Traffic plus average rate = 5(x + 21)

Thus;

8x = 5(x + 21)

8x = 5x + 105

3x = 105

x = 105/3

x = 35

Thus;

Distance from his house = 5(35 + 21) = 280 miles

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Answer:area is 140

Step-by-step explanation:

Answer:

Area= 140 square units

Step-by-step explanation:

q(-9, 5). r(6,10). s(2,-10).

find the area of the triangle QRS.

Area=140 square units