Let f(x)=3(12)x+1. Which is equal to f(1)?

A cafe makes ten 8-ounce fruit smoothies. Each smoothie is made with 4 ounces of soy milk and 1.3 ounces of banana flavoring. Th

Dvinal [7]

Answer:

27 ounces of blueberry juice. 40 ounces of soy milk. 13 ounces of banana flavoring.

Step by Step:

4 + 1.3 = 5.3, This is how much of the smoothie is made up of the soy milk and banana flavoring, 5.3 ounces.

So to find the amount of blueberry juice in the smoothie you have to subtract 8-5.3. This finds the remaining part of the smoothie, which is the blueberry juice. 8-5.3 = 2.7

2.7 ounces of blueberry juice in each smoothie.

Now you have to multiply every ingredient by 10, since there are 10 smoothies.

4 * 10 = 40

1.3 * 10 = 13

2.7 * 10 = 27

You need 40 ounces of soymilk, 13 ounces of banana flavoring, and 27 ounces of blueberry juice to make 10, 8-ounce smoothies.

7 0

2 years ago

Jeffrey is biking through the mountains. He bikes for six hours every day. When he started his ride one day the temperature was

Mashcka [7]

Answer:

47

Step-by-step explanation:

6 0

3 years ago

A florist can make a grand arrangement in 18 minutes or a simple arrangement in 10 minutes. The florist makes at least twice as

Colt1911 [192]

Answer:

See explanation

Step-by-step explanation:

Let x be the number of simple arrangements and y be the number of grand arrangements.

1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so

$x\ge 2y$

2. A florist can make a grand arrangement in 18 minutes $=\dfrac{3}{10}$ hour, then he can make y arrangements in $\dfrac{3}{10}y$ hours.

A florist can make a simple arrangement in 10 minutes $=\dfrac{1}{6}$ hour, so he can make x arrangements in $\dfrac{1}{6}x$ hours.

The florist can work only 40 hours per week, then

$\dfrac{3}{10}y+\dfrac{1}{6}x\le 40$

3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.

The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.

Total profit: $(10x+25y)

Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines $x=2y$ and $\dfrac{3}{10}y+\dfrac{1}{6}x=40$

But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is

$\$(10\cdot 126+25\cdot 63)=\$2,835$

8 0

3 years ago

Find all solutions of the equation: 2cos^2x-cosx=1

Art [367]

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Solve the trigonometric equation:

$\mathsf{2\,cos^2\,x-cos\,x=1}\\\\ \mathsf{2\,cos^2\,x-cos\,x-1=0}$

Make a substitution:

$\mathsf{cos\,x=t\qquad (-1\le t\le 1)}$

and the equation becomes

$\mathsf{2t^2-t-1=0}$

Rewrite conveniently – t as + t – 2t, and then factor the left-hand side by grouping:

$\mathsf{2t^2+t-2t-1=0}\\\\ \mathsf{t\cdot (2t+1)-1\cdot (2t+1)=0}$

Factor out 2t + 1:

$\mathsf{(2t+1)\cdot (t-1)=0}\\\\ \begin{array}{rcl} \mathsf{2t+1=0}&~\textsf{ or }~&\mathsf{t-1=0}\\\\ \mathsf{2t=1}&~\textsf{ or }~&\mathsf{t=1}\\\\ \mathsf{t=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{t=1} \end{array}$

Substitute back for t = cos x:

$\begin{array}{rcl}\mathsf{cos\,x=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{cos\,x=1}\\\\ \mathsf{cos\,x=cos\,60^\circ}&~\textsf{ or }~&\mathsf{cos\,x=cos\,0} \end{array}$

Therefore,

$\begin{array}{rcl} \mathsf{x=\pm\,60^\circ+k\cdot 360^\circ}&~\textsf{ or }~&\mathsf{cos\,x=0+k\cdot 360^\circ} \end{array}$

where k is an integer.

Solution set:

$\mathsf{S=\left\{x\in\mathbb{R}:~~x=-\,60^\circ+k\cdot 360^\circ~~or~~x=60^\circ+k\cdot 360^\circ~~or~~x=k\cdot 360^\circ,~~k\in\mathbb{Z}\right\}}$

I hope this helps. =)

3 0

3 years ago

Renae and her family are on vacation. During the drive from Denver to Rocky Mountain National Park, she saw 48 travel trailers a

Setler [38]

Answer:

27:48

Step-by-step explanation:

5 0

3 years ago

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