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lidiya [134]
2 years ago
10

You have 4 pounds of peanuts. You want to put it in the bags so that there is 2/3 pounds in each bag. How many bags can you fill

?
Mathematics
1 answer:
topjm [15]2 years ago
7 0

Answer:

6 bags

Step-by-step explanation:

This problem is essentially asking how many (\frac{2}{3}) peanut bags can one fill with (4) pounds of peanuts. This problem can be solved by divided (4) by (\frac{2}{3}). Set up the problem,

4 ÷ \frac{2}{3}

In order to divide by a fraction, one must change the multiplication sign to a division sign, then take the reciprocal of the second number, the fraction. In order to take the reciprocal of a fraction, switch the numerator (number on top) and the denominator (number on the bottom).

4 * \frac{3}{2}

Multiply,

\frac{12}{2}

Simplify,

6

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The stopping distance d of an automobile is directly proportional to the square of its speed s. On one road, a car requires 75 f
Anton [14]

Answer:

The car requires 192 feet to stop from a speed of 48 miles per hour on the same road

Step-by-step explanation:

  • Direct proportion means that two quantities increase or decrease in the same ratio
  • If y is directly proportional to x (y ∝ x) , then \frac{y_{1}}{y_{2}}=\frac{x_{1}}{x_{2}}  <em>OR</em>  y = k x, where k is the constant of proportionality

∵ The stopping distance d of an automobile is directly

   proportional to the square of its speed s

- That means d ∝ s²

∴  \frac{d_{1}}{d_{2}}=\frac{(s_{1})^{2}}{(s_{2})^{2}}

∵ A car requires 75 feet to stop from a speed of 30 miles per hour

∴ d = 75 feet

∴ s = 30 miles/hour

- Change the mile to feet

∵ 1 mile = 5280 feet

∴ 30 miles/hour = 30 × 5280 = 158400 feet/hour

∵  The car require to stop from a speed of 48 miles per hour

    on the same road

- Change the mile to feet

∴ 48 miles/hour = 48 × 5280 = 253440 feet/hour

∵  \frac{d_{1}}{d_{2}}=\frac{(s_{1})^{2}}{(s_{2})^{2}}

- Substitute the values of d_{1} by 75 feet, s_{1} by 158400 feet/hour

   and s_{2} by 253440 feet/hour

∴ \frac{75}{d_{2}}=\frac{(158400)^{2}}{(253440)^{2}}

∴  \frac{75}{d_{2}}=\frac{25}{64}

- By using cross multiplication

∴ 25 × d_{2} = 75 × 64

- Divide both sides by 25

∴ d_{2}  = 192 feet

The car requires 192 feet to stop from a speed of 48 miles per hour on the same road

4 0
2 years ago
A resting heart rate for men on a chart say 62-65 beats per minute puts men in the good category of scott counted 238 heart beat
olganol [36]
No, his bpm is too high, the average heart will go about 217-227.5 in a span of 3 1/2 min, and his is about 15.75 to high, (his bpm is 68 while it should be 62-65)
7 0
3 years ago
AB, CD, and EF intersect at O. If CD is perpendicular to EF and m
REY [17]

Answer:

m(∠AOF) = 148°

Step-by-step explanation:

From the figure attached,

CD intersects line EF at a point O.

Line CD is perpendicular to the line EF.

m(∠AOE) = 32°

m(∠COE) = 90°

Since m(∠COE) = m(∠AOE) + m(∠AOC) = 90°

32° + m(∠AOC) = 90°

m(∠AOC) = 90° - 32° = 58°

m(∠AOF) = m(∠AOC) + m(∠COF)

               = 58° + 90°

               = 148°

Therefore, m(∠AOF) = 148° will be the answer.

4 0
3 years ago
Use quadratic regression to find
Rashid [163]

The quadratic equation is given by:

y = 3x² + 10x - 8

The standard equation of a parabola is given by:

y = ax² + bx + c

Where a, b, c are constants

At point (4, 80):

80 = a(4)² + b(4) + c

16a + 4b + c = 80     (1)

At point (-3, -11):

-11 = a(-3)² + b(-3) + c

9a - 3b + c = -11     (2)

At point (-1, -15):

-15 = a(-1)² + b(-1) + c

a - b + c = -15     (3)

Solving equations 1, 2 and 3 simultaneously gives:

a = 3, b = 10, c = -8

Therefore the quadratic equation becomes:

y = 3x² + 10x - 8

Find out more on quadratic equation at: brainly.com/question/1214333

8 0
2 years ago
Tony runs a pizza parlor. His daily cost for operating the restaurant consists of a constant cost of $75 for rent, employee wage
Annette [7]
So in conclusion, 52 pizzas made costs $52 from 52*1=52. The total cost he makes adds up to $75 which is $75+$52=$127.
6 0
3 years ago
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