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mihalych1998 [28]
3 years ago
15

Mac hine A pops 12,75 ounces of popcorn in 3 minutes. Machine B pops 18 ounces of popcorn in 4minutes. If each machine pops popc

orn for 10 minutes, will there be enough popcorn for eight 9-ounce bags?
Mathematics
1 answer:
Nataly [62]3 years ago
8 0

yes. Machine A pops 42.5 ounces of popcorn in 10 minutes. Machine B pops 45 ounces of popcorn in 10 minutes. Add the two to get 87.5 ounces. 8 times 9 is 72 which is less than 87.5 ounces


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PLEASEEE HELPPPP IM BEGGIN U
Anna71 [15]

Answer:

  a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)

  b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.

  c, d) See attached

Step-by-step explanation:

Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.

Synthetic division is essentially polynomial long division with some modifications:

  • the variables are omitted ("place value" is used instead)
  • the constant in the divisor is <em>negated</em> so its product with the partial quotient can be <em>added</em> to obtain the new dividend
  • the divisor binomial is assumed to have a leading coefficient of 1.

__

<h3>a) </h3>

The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.

When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.

Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.

The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.

__

<h3>b)</h3>

The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.

Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.

__

<h3>c)</h3>

The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)

Maybe this is the table you want:

  \begin{array}{|c|c|c|}\cline{1-3}x&-4&3\\\cline{1-3}y&0&-210\\\cline{1-3}\end{array}

__

<h3>d)</h3>

The second attachment shows synthetic division by the factor (x+4).

_____

<em>Additional comment</em>

The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.

The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.

6 0
2 years ago
Calculate the mean,median,and mode of the following set of data. Round to the nearest tenth 10,1,10,15,1,7,10,1,6,13
lions [1.4K]
Let's start with the mean. 

To find the mean of a data set, add all the numbers, then divide by the number of numbers there are. 

10 + 1 + 10 + 15 + 1 + 7 + 10 + 1 + 6 + 13 = 74
74/10 = 7.4

The mean is 7.4

Now for the median.

To find the median put all the numbers in order, then find the middle number.

1, 1, 1, 6, 7, 10, 10, 10, 13, 15

The number in between 7 and 10 is 8.5
The median is 8.5

And finally, the mode.

To find the mode, find the number that appears the most. 

1, 1, 1, 6, 7, 10, 10, 10, 13, 15

In this case, there are two modes. 1, and 10.

Hopefully this helps! If you have any more questions or don't understand, feel free to DM me, and I'll get back to you ASAP! :)
8 0
3 years ago
Read 2 more answers
This is the whole picture can someone help??
Maksim231197 [3]

Step-by-step explanation:

I can't see good the picture

3 0
3 years ago
Which expression is equivalent to (5x^3)(2x)^3
Taya2010 [7]
Hello:
(5x^3)(2x)^3 = (5x^3)(2)^3(x)^3 = <span>(5x^3)8x^3=40x^6  ... (answer C)</span>
3 0
3 years ago
Read 2 more answers
Jasmyn uses 42% of a gift card to buy groceries if she spent $67.20 on groceries, how much was on the gift card to begin with
lapo4ka [179]

Answer:

The card was worth $160.

Step-by-step explanation:

It is given that:

Percent of gift card used = 42%

Cost of groceries = $67.20

Let,

x be the total amount on gift card.

42% of x = 67.20

\frac{42}{100}x=67.20

0.42x = 67.20

\frac{0.42x}{0.42}=\frac{67.20}{0.42}\\x=160

Therefore,

The card was worth $160.

4 0
3 years ago
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