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oee [108]
3 years ago
14

Christopher buys 120 hot dog buns for a picnic. He buys two different brands of hot dog buns. Brand X has 12 hot dog buns in a p

ackage that costs $4.50. Brand Y has 8 hot dog buns in a package that costs $3.50. Christopher spends $49.50 on hot dog buns. a. Write a system of equations that can be used to find the number of packages of Brand X hot dog buns, x, and Brand Y hot dog buns, y, that Christopher buys. b. Solve the system of equations to find the values of x and y. Show your work or explain how you know.
Mathematics
1 answer:
Mariana [72]3 years ago
4 0
Brand X cost: $4.50
Brand Y cost: $3.50

Christopher spends total: $49.50

Equation: 4.50x + 3.50y = 49.50

Idk how to solve the equation but this should be the correct equation
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3 years ago
From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th
wel

Answer:

\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}

Step-by-step explanation:

The <u>width</u> of a square is its <u>side length</u>.

The <u>width</u> of a circle is its <u>diameter</u>.

Therefore, the largest possible circle that can be cut out from a square is a circle whose <u>diameter</u> is <u>equal in length</u> to the <u>side length</u> of the square.

<u>Formulas</u>

\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}

\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}

\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}

If the diameter is equal to the side length of the square, then:
\implies \sf r=\dfrac{1}{2}s

Therefore:

\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}

So the ratio of the area of the circle to the original square is:

\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}

Given:

  • side length (s) = 6 in
  • radius (r) = 6 ÷ 2 = 3 in

\implies \sf \textsf{Area of square}=6^2=36\:in^2

\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)

Ratio of circle to square:

\implies \dfrac{28}{36}=\dfrac{7}{9}

5 0
2 years ago
Help please math thank you
bija089 [108]

Answer:

5

Step-by-step explanation:

4 0
2 years ago
Consider two x distributions corresponding to the same x distribution. The first x distribution is based on samples of size n =
Tanya [424]

Answer:

The distribution with n = 225 will give a smaller standard error.

Since sigma x = sigma/√n, dividing by the square root of 225 will result in a small standard error regardless of the value of sigma.

Step-by-step explanation:

Standard error is given by standard deviation (sigma) divided by square root of sample size (√n).

The distribution with n = 225 would give a smaller standard error because the square root of 225 is 15. The inverse of 15 multiplied by sigma is approximately 0.07sigma which is smaller compared to the distribution n = 100. Square of 100 is 10, inverse of 10 multiplied by sigma is 0.1sigma.

0.07sigma is smaller than 0.1sigma

8 0
3 years ago
Each person attending a two-day conference receives 4 meal vouchers to use.
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Part A: Let x and y be the number of persons attending the two-day conference and y be the number of vouchers released. The equation that would best express the given is,
                                             y = 4x

Part B: The number of people attending the conference is determined by dividing the given number of vouchers by 4. The answer is 956. 
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3 years ago
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