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3 years ago

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The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a ye

ar is 193 . The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 15 . Thirty more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.

1 answer:

padilas [110]3 years ago

7 0

9514 1404 393

Answer:

89 in a restaurant
45 in a car
59 at home

Step-by-step explanation:

Let r, c, h represent the numbers of meals eaten in a restaurant, car, and at home, respectively. The problem statement tells us of the relations ...

r + c + h = 193

-r + c + h = 15

r + 0c -h = 30

Add the last two equations:

(-r +c +h) +(r -h) = (15) +(30)

c = 45

Add the first two equations:

(r + c + h) +(-r + c + h) = (193) +(15)

2c +2h = 208

h = 104 -c = 59 . . . . solve for h, substitute for c

The last equation can be used to find r.

r = 30 +h = 30 +59 = 89

89 meals are eaten in a restaurant; 45 meals in a car; and 59 at home.

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babunello [35]

Answer:

Step-by-step explanation:

In all of these problems, the key is to remember that you can undo a trig function by taking the inverse of that function. Watch and see.

a. $sin2\theta =-\frac{\sqrt{3} }{2}$

Take the inverse sin of both sides. When you do that, you are left with just 2theta on the left. That's why you do this.

$sin^{-1}(sin2\theta)=sin^{-1}(-\frac{\sqrt{3} }{2} )$

This simplifies to

$2\theta=sin^{-1}(-\frac{\sqrt{3} }{2} )$

We look to the unit circle to see which values of theta give us a sin of -square root of 3 over 2. Those are:

$2\theta =\frac{5\pi }{6}$ and

$2\theta=\frac{7\pi }{6}$

Divide both sides by 2 in both of those equations to get that values of theta are:

$\theta=\frac{5\pi }{12},\frac{7\pi }{12}$

b. $tan(7a)=1$

Take the inverse tangent of both sides:

$tan^{-1}(tan(7a))=tan^{-1}(1)$

Taking the inverse tangent of the tangent on the left leaves us with just 7a. This simplifies to

$7a=tan^{-1}(1)$

We look to the unit circle to find which values of <em>a</em> give us a tangent of 1. They are:

$7\alpha =\frac{5\pi }{4},7\alpha =\frac{\pi }{4}$

Dibide each of those equations by 7 to find that the values of alpha are:

$\alpha =\frac{5\pi}{28},\frac{\pi}{28}$

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Take the inverse cosine of each side. The inverse cosine and cosine undo each other, leaving us with just 3beta on the left, just like in the previous problems. That simplifies to:

$3\beta=cos^{-1}(\frac{1}{2})$

We look to the unit circle to find the values of beta that give us the cosine of 1/2 and those are:

$3\beta =\frac{\pi}{6},3\beta =\frac{5\pi}{6}$

Divide each of those by 3 to find the values of beta are:

$\beta =\frac{\pi }{18} ,\frac{5\pi}{18}$

d. $sec3\alpha =-2$

Let's rewrite this in terms of a trig ratio that we are a bit more familiar with:

$\frac{1}{cos(3\alpha) } =\frac{-2}{1}$

We are going to simplify this even further by flipping both fraction upside down to make it easier to solve:

$cos(3\alpha)=-\frac{1}{2}$

Now we will take the inverse cos of each side (same as above):

$3\alpha =cos^{-1}(-\frac{1}{2} )$

We look to the unit circle one last time to find the values of alpha that give us a cosine of -1/2:

$3\alpha =\frac{7\pi}{6},3\alpha =\frac{11\pi}{6}$

Dividing both of those equations by 3 gives us

$\alpha =\frac{7\pi}{18},\frac{11\pi}{18}$

And we're done!!!

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3 years ago

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Answer:

The correct option is;

False

Step-by-step explanation:

Here, we note that the proportion of the test statistic which is used in the test is 5% and the P-value for the test is 0.03

The hypothesis test is meant to check if people will still drive to work when the gas prices are above $10.00 and the suggestion was that we can conclude that when the fuel price is above $5.00 everyone would still drive to work without a P-value for the test, hence we can not come to the stated conclusion.

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Nata [24]

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3 years ago

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GaryK [48]

Answer:

1. A number decreased by seven.

2. A number increased by nine.

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4. The product of three and a number increased by five is equal to twenty.

5. The product of two and a number increased by eight is equal to twenty-three.

Step-by-step explanation:

1. x-7

A number decreased by seven.

2. y+9

A number increased by nine.

3. 6m/8

The product of six and a number, divided by eight.

4. 3y+5 =20

The product of three and a number increased by five is equal to twenty.

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Anestetic [448]

Answer:

Graph (C)

Step-by-step explanation:

To find whether the graph\table represents a relationship or a function we have to analyze the input-output values given.

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So the graph doesn't represent a function.

Graph B.

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So the graph doesn't represent a function.

Graph C.

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Therefore, graph represents a function.

Graph D.

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Therefore, graph doesn't show the relationship.

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3 years ago