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3 years ago

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Mario has 3 1/6 lbs of trail mix. He puts equal amounts of trail mix into 5 bags for his friends. If he uses all of the trail mi

x, how many lbs will be in each bag?
A) 19/30
B) 95/6
C) 15 1/6
D) 8 1/6

1 answer:

Angelina_Jolie [31]3 years ago

7 0

I think it’s C.

Hope this helps :)

Have a great day

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Given the set points K+1:(-1,8),(1,0) and (2,5), find the quadratic polynomial interpolate

Sauron [17]

Answer:

The interpolating polynomial is $p(x) = 1-4x+3x^2$ .

Step-by-step explanation:

We want to find a quadratic polynomial $p(x)$ such that $p(-1)=8$ , $p(1)=0$ and $p(2)=5$ . In order to do this let us write $p(x) = a_0+a_1x+a_3x^2$ .

Now, evaluating the polynomial in the points -1, 1 and 2 we get

$\begin{cases} 8 = p(-1) &= a_0-a_1+a_2\\ 0 = p(1) &= a_0+a_1+a_2\\ 5 = p(2) &= a_0+2a_1+4a_2\end{cases}$

This relations give us a linear system of equations:

$\begin{cases} 8 &= a_0-a_1+a_2\\ 0 &= a_0+a_1+a_2\\ 5&= a_0+2a_1+4a_2\end{cases}$

where the $a_0$ , $a_1$ and $a_2$ are the unknowns.

The augmented matrix of the system is

$\begin{pmatrix}1 & -1 & 1 & 8\\ 1 & 1 & 1 & 0\\ 1 & 2 & 4 & 5\end{pmatrix}$

In this matrix it is easy to eliminate the 1's of the first column and get

$\begin{pmatrix} 1 & -1 & 1 & 8\\ 0 & 2 & 0 & -8\\ 0 & 3 & 3 & -3\end{pmatrix}$

From this matrix we can find the values of each unknown. Notice that the second row gives us $2a_2=-8$ that yields $a_1=-4$ .

Then, the third row means $3a_1+3a_2=-3$ that gives $-12+3a_2=-3$ . So, $a_2=3$ .

Finally, the first row is $a_0-a_1+a_2=8$ and substituting is $a_0+7=8$ that yields $a_0=1$ .

Therefore, the interpolating polynomial is

$p(x) = 1-4x+3x^2$ .

8 0

3 years ago

Applying properties of Exponents In Exercise, use the properties of exponents to simplify the expression.

eimsori [14]

Answer:

(a) $5^{8}$

(b) 3

(c) 27

(d) $\dfrac{1}{6}$

Step-by-step explanation:

We need simplify the given expressions.

(a)

Consider the given expression is

$(5^4)(25^2)$

$(5^4)((5^2)^2)$

Using the properties of exponents we get

$(5^4)(5^4)$ $[\because (a^m)^n=a^{mn}]$

$5^{4+4}$ $[\because a^ma^n=a^{m+n}]$

$5^{8}$

(b)

Consider the given expression is

$(9^{\frac{1}{3}})(3^{\frac{1}{3}})$

$((3^2)^{\frac{1}{3}})(3^{\frac{1}{3}})$

Using the properties of exponents we get

$(3^{\frac{2}{3}})(3^{\frac{1}{3}})$ $[\because (a^m)^n=a^{mn}]$

$3^{\frac{2}{3}+\frac{1}{3}}$ $[\because a^ma^n=a^{m+n}]$

$3^{1}$

$3$

(c)

Consider the given expression is

$(\dfrac{1}{3})^{-3}$

Using the properties of exponents we get

$(\dfrac{3}{1})^{3}$ $[\because a^{-n}=\dfrac{1}{a^n}]$

$3^{3}$

$27$

(d)

Consider the given expression is

$(6^4)(6^{-5})$

Using the properties of exponents we get

$6^{4+(-5)}$ $[\because a^ma^n=a^{m+n}]$

$6^{-1}$

$\dfrac{1}{6^{1}}$ $[\because a^{-n}=\dfrac{1}{a^n}]$

$\dfrac{1}{6}$

6 0

3 years ago

1^2 + 2^2 + 3^2 +.... + 28^2 + 29^2 + 30^2 = ......<br> Find the value <br> Thank you!

liberstina [14]

Step-by-step explanation:

The sum of consecutive squares is

$1^2+2^2+\dots+n^2=\frac16n(n+1)(2n+1)$

Therefore

$1^2+2^2+\dots+30^2=\frac16(30)(31+1)(2\cdot30+1) = 9455$

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3 years ago

Fourteen less than three fourths of a number is negative eight. Find the number

Lapatulllka [165]

The word "is" in this kind of problem typically means "=", so we know that something =-8. Since we're finding the number, we should start with the closest thing in the phrase given to that number. In this case, it's 3/4x. Finally, since we have the "14 less than", we need to add that in. Your answer is:

3/4x-14=-8. Now we can just solve!
+14 +14

3/4x=6.
*4/3 *4/3

x=8.
<em>
</em>
<em><u>Don't forget to rate this answer the </u><u>Brainliest</u><u>!</u></em>

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3 years ago

Which best describes the shape of this distribution?

Eddi Din [679]

I believe it would be uniform

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3 years ago

Read 2 more answers