Answer:
$8.1
Step-by-step explanation:
Convert 45 yards of ribbon to feet through proper conversion factor.
(45 yards)(3 ft / 1 yard) = 135 feet
Divide this number by 5 to determine the number of 5-ft ribbon that customers can purchased.
n = 135 ft / 5 ft = 27
Then, multiply by $0.80.
R = (27)($0.80) = $21.6
The profit is equal to $21.6 and $13.50,
P = $21.6 - $13.50 = $8.1
Answer: $8.1
Hey there!
Tom's age to Mary's is 3:4; an equivalent ratio is 15:x (x symbolizes Mary's age).
To solve for this, we need to divide our proportions. By that, I mean divide Tom's older age by his younger age. If we do so, we should get a scale factor that we can multiply Mary's younger age by.
15 / 3 = 5
This means that the scale factor of the ages is 5.
x / 4 = 5 (Solving for Mary's unknown age.)
To solve for x, multiply both sides by 4.
x/4 * 4 = x
5 * 4 = 20
x = 20
Mary's age is 20.
I hope this helps!
Answer:
1) The solution of the system is

2) The solution of the system is

Step-by-step explanation:
1) To solve the system of equations

using the row reduction method you must:
Step 1: Write the augmented matrix of the system
![\left[ \begin{array}{ccc|c} 0 & 3 & -5 & 89 \\\\ 6 & 0 & 1 & 17 \\\\ 1 & -1 & 8 & -107 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%200%20%26%203%20%26%20-5%20%26%2089%20%5C%5C%5C%5C%206%20%26%200%20%26%201%20%26%2017%20%5C%5C%5C%5C%201%20%26%20-1%20%26%208%20%26%20-107%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 2: Swap rows 1 and 2
![\left[ \begin{array}{ccc|c} 6 & 0 & 1 & 17 \\\\ 0 & 3 & -5 & 89 \\\\ 1 & -1 & 8 & -107 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%206%20%26%200%20%26%201%20%26%2017%20%5C%5C%5C%5C%200%20%26%203%20%26%20-5%20%26%2089%20%5C%5C%5C%5C%201%20%26%20-1%20%26%208%20%26%20-107%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 3: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 3 & -5 & 89 \\\\ 1 & -1 & 8 & -107 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%203%20%26%20-5%20%26%2089%20%5C%5C%5C%5C%201%20%26%20-1%20%26%208%20%26%20-107%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 4: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 3 & -5 & 89 \\\\ 0 & -1 & \frac{47}{6} & - \frac{659}{6} \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%203%20%26%20-5%20%26%2089%20%5C%5C%5C%5C%200%20%26%20-1%20%26%20%5Cfrac%7B47%7D%7B6%7D%20%26%20-%20%5Cfrac%7B659%7D%7B6%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 5: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & -1 & \frac{47}{6} & - \frac{659}{6} \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%20-%20%5Cfrac%7B5%7D%7B3%7D%20%26%20%5Cfrac%7B89%7D%7B3%7D%20%5C%5C%5C%5C%200%20%26%20-1%20%26%20%5Cfrac%7B47%7D%7B6%7D%20%26%20-%20%5Cfrac%7B659%7D%7B6%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 6: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & 0 & \frac{37}{6} & - \frac{481}{6} \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%20-%20%5Cfrac%7B5%7D%7B3%7D%20%26%20%5Cfrac%7B89%7D%7B3%7D%20%5C%5C%5C%5C%200%20%26%200%20%26%20%5Cfrac%7B37%7D%7B6%7D%20%26%20-%20%5Cfrac%7B481%7D%7B6%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 7: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{1}{6} & \frac{17}{6} \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & 0 & 1 & -13 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B1%7D%7B6%7D%20%26%20%5Cfrac%7B17%7D%7B6%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%20-%20%5Cfrac%7B5%7D%7B3%7D%20%26%20%5Cfrac%7B89%7D%7B3%7D%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-13%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 8: 
![\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 5 \\\\ 0 & 1 & - \frac{5}{3} & \frac{89}{3} \\\\ 0 & 0 & 1 & -13 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%200%20%26%205%20%5C%5C%5C%5C%200%20%26%201%20%26%20-%20%5Cfrac%7B5%7D%7B3%7D%20%26%20%5Cfrac%7B89%7D%7B3%7D%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-13%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 9: 
![\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 5 \\\\ 0 & 1 & 0 & 8 \\\\ 0 & 0 & 1 & -13 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%200%20%26%205%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%208%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-13%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 10: Rewrite the system using the row reduced matrix:
![\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 5 \\\\ 0 & 1 & 0 & 8 \\\\ 0 & 0 & 1 & -13 \end{array} \right] \rightarrow \left\begin{array}{ccc}x_1&=&5\\x_2&=&8\\x_3&=&-13\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%200%20%26%205%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%208%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-13%20%5Cend%7Barray%7D%20%5Cright%5D%20%5Crightarrow%20%5Cleft%5Cbegin%7Barray%7D%7Bccc%7Dx_1%26%3D%265%5C%5Cx_2%26%3D%268%5C%5Cx_3%26%3D%26-13%5Cend%7Barray%7D%5Cright)
2) To solve the system of equations

using the row reduction method you must:
Step 1:
![\left[ \begin{array}{ccc|c} 4 & -1 & 3 & 12 \\\\ 2 & 0 & 9 & -5 \\\\ 1 & 4 & 6 & -32 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%204%20%26%20-1%20%26%203%20%26%2012%20%5C%5C%5C%5C%202%20%26%200%20%26%209%20%26%20-5%20%5C%5C%5C%5C%201%20%26%204%20%26%206%20%26%20-32%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 2: 
![\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 2 & 0 & 9 & -5 \\\\ 1 & 4 & 6 & -32 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%20-%20%5Cfrac%7B1%7D%7B4%7D%20%26%20%5Cfrac%7B3%7D%7B4%7D%20%26%203%20%5C%5C%5C%5C%202%20%26%200%20%26%209%20%26%20-5%20%5C%5C%5C%5C%201%20%26%204%20%26%206%20%26%20-32%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 3: 
![\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 0 & \frac{1}{2} & \frac{15}{2} & -11 \\\\ 1 & 4 & 6 & -32 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%20-%20%5Cfrac%7B1%7D%7B4%7D%20%26%20%5Cfrac%7B3%7D%7B4%7D%20%26%203%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B15%7D%7B2%7D%20%26%20-11%20%5C%5C%5C%5C%201%20%26%204%20%26%206%20%26%20-32%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 4: 
![\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 0 & \frac{1}{2} & \frac{15}{2} & -11 \\\\ 0 & \frac{17}{4} & \frac{21}{4} & -35 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%20-%20%5Cfrac%7B1%7D%7B4%7D%20%26%20%5Cfrac%7B3%7D%7B4%7D%20%26%203%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B1%7D%7B2%7D%20%26%20%5Cfrac%7B15%7D%7B2%7D%20%26%20-11%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B17%7D%7B4%7D%20%26%20%5Cfrac%7B21%7D%7B4%7D%20%26%20-35%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 5: 
![\left[ \begin{array}{ccc|c} 1 & - \frac{1}{4} & \frac{3}{4} & 3 \\\\ 0 & 1 & 15 & -22 \\\\ 0 & \frac{17}{4} & \frac{21}{4} & -35 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%20-%20%5Cfrac%7B1%7D%7B4%7D%20%26%20%5Cfrac%7B3%7D%7B4%7D%20%26%203%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B17%7D%7B4%7D%20%26%20%5Cfrac%7B21%7D%7B4%7D%20%26%20-35%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 6: 
![\left[ \begin{array}{cccc} 1 & 0 & \frac{9}{2} & - \frac{5}{2} \\\\ 0 & 1 & 15 & -22 \\\\ 0 & \frac{17}{4} & \frac{21}{4} & -35 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcccc%7D%201%20%26%200%20%26%20%5Cfrac%7B9%7D%7B2%7D%20%26%20-%20%5Cfrac%7B5%7D%7B2%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%20%5Cfrac%7B17%7D%7B4%7D%20%26%20%5Cfrac%7B21%7D%7B4%7D%20%26%20-35%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 7: 
![\left[ \begin{array}{ccc|c} 1 & 0 & \frac{9}{2} & - \frac{5}{2} \\\\ 0 & 1 & 15 & -22 \\\\ 0 & 0 & - \frac{117}{2} & \frac{117}{2} \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%20%5Cfrac%7B9%7D%7B2%7D%20%26%20-%20%5Cfrac%7B5%7D%7B2%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%200%20%26%20-%20%5Cfrac%7B117%7D%7B2%7D%20%26%20%5Cfrac%7B117%7D%7B2%7D%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 8: 
![\left[ \begin{array}{cccc} 1 & 0 & \frac{9}{2} & - \frac{5}{2} \\\\ 0 & 1 & 15 & -22 \\\\ 0 & 0 & 1 & -1 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcccc%7D%201%20%26%200%20%26%20%5Cfrac%7B9%7D%7B2%7D%20%26%20-%20%5Cfrac%7B5%7D%7B2%7D%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-1%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 9: 
![\left[ \begin{array}{cccc} 1 & 0 & 0 & 2 \\\\ 0 & 1 & 15 & -22 \\\\ 0 & 0 & 1 & -1 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcccc%7D%201%20%26%200%20%26%200%20%26%202%20%5C%5C%5C%5C%200%20%26%201%20%26%2015%20%26%20-22%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-1%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 10: 
![\left[ \begin{array}{cccc} 1 & 0 & 0 & 2 \\\\ 0 & 1 & 0 & -7 \\\\ 0 & 0 & 1 & -1 \end{array} \right]](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bcccc%7D%201%20%26%200%20%26%200%20%26%202%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%20-7%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-1%20%5Cend%7Barray%7D%20%5Cright%5D)
Step 11:
![\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 2 \\\\ 0 & 1 & 0 & -7 \\\\ 0 & 0 & 1 & -1 \end{array} \right]\rightarrow \left\begin{array}{ccc}x_1&=&2\\x_2&=&-7\\x_3&=&-1\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbegin%7Barray%7D%7Bccc%7Cc%7D%201%20%26%200%20%26%200%20%26%202%20%5C%5C%5C%5C%200%20%26%201%20%26%200%20%26%20-7%20%5C%5C%5C%5C%200%20%26%200%20%26%201%20%26%20-1%20%5Cend%7Barray%7D%20%5Cright%5D%5Crightarrow%20%5Cleft%5Cbegin%7Barray%7D%7Bccc%7Dx_1%26%3D%262%5C%5Cx_2%26%3D%26-7%5C%5Cx_3%26%3D%26-1%5Cend%7Barray%7D%5Cright)
Answer:
the answer would be x= 8/3 happy to help ya:) and pls mark me as brainliest!!!!!!!!!
Step-by-step explanation:
Answer:
0.0425
Step-by-step explanation:
probability of basket player = 0.25
probability of being a soccer player = 0.17
chances that a sixth grader plays basketball AND soccer = 0.25×0.17 = 0.0425