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Tanya [424]
3 years ago
6

If Juan purchased three 24-ounce cans of motor oil for $10.80, how much did he pay per ounce? A. $.45 B. $3.60 C. $2.59 D. $.15

Mathematics
2 answers:
34kurt3 years ago
5 0

    The answer would be D, you have THREE 24 oz. cans which is the equivalent to 72 oz.  and $10.80 divided by 72 is 15 cents.

Keith_Richards [23]3 years ago
4 0

Answer:

D. $.15

Step-by-step explanation:

well you do 3 times 24, which iis 72 and then you do $10.80 divide by 72

and that would be $.15

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4 friends went to the movies and each ordered a container of popcorn.They spent $24 on popcorn.How much did each container of po
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Answer: $6

Step-by-step explanation:

24/4 = 6

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A particular fruit's weights are normally distributed, with a mean of 774 grams and a standard deviation of 31 grams.
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3 years ago
Please help!!<br> Write a matrix representing the system of equations
frozen [14]

Answer:

(4, -1, 3)

Step-by-step explanation:

We have the system of equations:

\left\{        \begin{array}{ll}            x+2y+z =5 \\    2x-y+2z=15\\3x+y-z=8        \end{array}    \right.

We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:

\begin{bmatrix}x_1& y_1& z_1&c_1\\x_2 & y_2 & z_2&c_2\\x_3&y_2&z_3&c_3 \end{bmatrix}

Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.

In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:

\begin{bmatrix}1 & 0& 0&x\\0 & 1 & 0&y\\0&0&1&z \end{bmatrix}

Where the (x, y, z) is our solution set.

Reducing:

With our system, we will have the following matrix:

\begin{bmatrix}1 & 2& 1&5\\2 & -1 & 2&15\\3&1&-1&8 \end{bmatrix}

What we should begin by doing is too see how we can change each row to the reduced-form.

Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:

\begin{bmatrix}1 & 2& 1&5\\2+(-2) & -1+(-4) & 2+(-2)&15+(-10) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\0 & -5 & 0&5 \\3&1&-1&8 \end{bmatrix}

Now, we can multiply R₂ by -1/5. This yields:

\begin{bmatrix}1 & 2& 1&5\\ -\frac{1}{5}(0) & -\frac{1}{5}(-5) & -\frac{1}{5}(0)& -\frac{1}{5}(5) \\3&1&-1&8 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3&1&-1&8 \end{bmatrix}

From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:

\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\3+(-3)&1+(-6)&-1+(-3)&8+(-15) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&-5&-4&-7 \end{bmatrix}

We can eliminate the -5 in R₃ by adding 5(R₂). This yields:

\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0+(0)&-5+(5)&-4+(0)&-7+(-5) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&-4&-12 \end{bmatrix}

We can now reduce R₃ by multiply it by -1/4:

\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\ -\frac{1}{4}(0)&-\frac{1}{4}(0)&-\frac{1}{4}(-4)&-\frac{1}{4}(-12) \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 2& 1&5\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}

Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:

\begin{bmatrix}1+(0) & 2+(-2)& 1+(0)&5+(-(-2))\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 1&7\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}

And finally, we can eliminate the second 1 by adding -(R₃):

\begin{bmatrix}1 +(0)& 0+(0)& 1+(-1)&7+(-3)\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}\\\Rightarrow\begin{bmatrix}1 & 0& 0&4\\ 0 & 1 & 0& -1 \\0&0&1&3 \end{bmatrix}

Therefore, our solution set is (4, -1, 3)

And we're done!

3 0
3 years ago
Question shown in images
Mars2501 [29]
Answer is 2 (answer choice a)
5 0
3 years ago
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Chocolate chip and peanut butter cookies are randomly chosen from a cookie jar and placed onto a plate. The first plate had four
soldier1979 [14.2K]

Answer:

3 peanut cookies

Step-by-step explanation:

Given that :

Plate 1:

Number of chocolate chip = 4

Number of peanut butter cookies = 1

Probability of drawing chocolate chip cookies from plate 1 :

Probability =( number of required outcome / Total possible outcomes)

P(chocolate chip) = 4 / 5

Plate 2:

Number of chocolate chip = 2

Number of peanut butter cookies = p

P(chocolate chip) = 2 / (2 + p)

Probability of drawing chocolate chip from plate 1 and then plate 2 = 8/ 25

(4/5) * 2/(2+p) = 8/ 25

8 / (10 + 5p) = 8/ 25

8(10 + 5p) = 8 * 25

80 + 40p = 200

40p = 200 - 80

40p = 120

p = 3

7 0
2 years ago
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