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mestny [16]
3 years ago
11

A recipe for granola bars calls for 2/3 cup of oats. How much of the pats would you use to make 1/2 of the amount in the origina

l recipe?
Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
5 0

Answer:

1/3 cups

Step-by-step explanation:

If you want to make half of the recipe that requires 2/3 cup oats, then you would use half the oats. Half of 2/3 cup of oats is 1/3 cup of oats.

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How can caregivers give children self confidence safely?
Ann [662]
Telling them that no mater what they should love them for who they are love your self no matter what
8 0
3 years ago
Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60
TEA [102]

Answer: the rate at which the distance between the boats is​ increasing is 68 mph

Step-by-step explanation:

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(south) of the right angle triangle.

Let y represent the length the longer leg(east) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

z = √1156

z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

68dz/dt = 1024 + 3600

68dz/dt = 4624

dz/dt = 4624/68

dz/dt = 68 mph

6 0
3 years ago
The graph relates the distance traveled by Train A, in miles, and the time taken, in hours. The table shows the distance travele
melomori [17]

Answer:A)

Yes, the relationship is proportional.

B)

66,000 miles.

Step-by-step explanation:

A)

Yes, the graph represents a proportional relationship.

Since, A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y=kx

for some constant k , called the constant of proportionality .

As y=12000x hence the relationship is proportional.

B)

We calculate the equation of the graph with the help of two points on the graph namely (2,24000) and (4,48000) with the help of slope-intercept form of the line.

y=mx+c where m denotes the slope of the line and c denotes the y-intercept of the line.

Here when x=2 y=24000 and when x=4 y=48000

Hence, 24000=2x+c

and 48000=4x+c

on subtracting the above two equations we have:

m=12000 and c=0

Hence, the equation of line is y=12000x

Now the value at x=5.5 is:

y=12000×5.5=66,000

Hence, the number of miles the probe travels in 5.5. hours is 66,000 miles.

Step-by-step explanation:

4 0
2 years ago
A 234 inch board is cut into two pieces. One piece is five times the length of the order. Find the length of the shorter piece.
hammer [34]

Answer:

39 inches

Step-by-step explanation:

5x+x=234

6x=234

234/6=39

x=39 inches

7 0
2 years ago
What is the average rate of change for the table and graph below over the interval [0,3]?
Leokris [45]

Answer:

-2

Step-by-step explanation:

The average rate of change is the slope using the points (0, 10) and (3, 4).  The slope is found using the formula \frac{y2-y1}{x2-x1}

\frac{4-10}{3-0}= \frac{-6}{3}=-2

6 0
3 years ago
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