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3 years ago

Grayson baked 24 sugar cookies. His family ate 1/3 of the cookies. How many cookies did they eat? How many cookies are left?

Mathematics

1 answer:

horrorfan [7]3 years ago

4 0

Answer:

His family ate 8 sugar cookies.

16 sugar cookies are left.

Step-by-step explanation:

His family ate 1/3 of the 24 sugar cookies: 1/3 x 24= 8

How many are left: 24-8=16

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Barbara drives between Miami, Florida and West Palm Beach, Florida. she drives 45 miles in clear weather and then encounters a t

WINSTONCH [101]

Answer:

Barbara's speed in clear weather is $60mph$ and in the thunderstorm is $38mph$ .

Step-by-step explanation:

Let $v_1$ be the speed and $t_1$ be the time Barbara drives in clear weather, and let $v_2$ be the speed and $t_2$ be the time she drives in the thunderstorm.

Barbara drives 22 mph lower in the thunderstorm than in the clear weather; therefore,

(1). $v_2 = v_1 -22$

Also,

(2). $v_1t_1 = 45miles$

(3). $v_2 t_2 = 57$ ,

and

(4). $t_1+t_2 = 2.25hr$

From equations (2) and (3) we get:

$t_1 = \dfrac{45}{v_1}$

$t_2 =\dfrac{57}{v_2}$

putting these in equation (4) we get:

$\dfrac{45}{v_1}+\dfrac{57}{v_2}=2.25$

and substituting for $v_2$ from equation (1) we get:

$\dfrac{45}{v_1}+\dfrac{57}{v_1-22}=2.25$

This equation can be rewritten as

$2.25v_1^2-151.5v_1+990=0$

which has solutions

$v_1 = 60$

$v_1 = 7.33$

We take the first solution $v_1 =60$ because it gives a positive value for $v_2:$

$v_2 = v_1 -22$

$v_2 = 60 -22\\$

$v_2 = 38$ .

Thus, Barbara's speed in clear weather is $60mph$ and in the thunderstorm is $38mph$ .

4 0

3 years ago

Rewrite the equation in Ax+By=C form. use intergers for A,B,C y=1/5-1

schepotkina [342]

Answer:

$5y=-4$

Sure hope this helps you :D

6 0

2 years ago

Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 13 people, while each carton of c

lutik1710 [3]

Answer:

233 cartons of food; 467 cartons of clothing

Step-by-step explanation:

This linear programming problem can be formulated as two inequalities (in addition to the usual constraints that the variables be non-negative). One of these expresses the constraint on weight. Let f and c represent numbers of food and clothing containers, respectively.

40f +25c ≤ 21000

The other expresses the limit on volume.

20f + 5c ≤ 7000

_____

Feasible Region vertex

We can subtract the boundary line equation of the first inequality from that of 5 times the second to find f:

5(20f +5c) -(40f +25c) = 5(7000) -21000

60f = 14000

f = 233 1/3

The second boundary line equation can be rearranged to find c:

c = 1400 -4f = 466 2/3

The nearest integer numbers to these values are ...

(f, c) = (233, 467)

The other vertices of the feasible region are associated with one or the other variable being zero: (f, c) = (0, 840) or (350, 0).

Check of Integer Solution

Trying these in the constraint inequalities gives ...

40·233 +25·467 = 20,995 < 21000
20·233 +5·467 = 6995 < 7000

Selection of the Answer

The answer to the question will be the feasible region vertex that maximizes the number of people helped. That is, we want to maximize ...

p = 13f + 6c

The values of p at the vertices are ...

p = 13·233 + 6·467 = 5831

p = 13·0 + 6·840 = 5040

p = 13·350 + 6·0 = 2100

The most people are helped when the plane is filled with 233 food cartons and 467 clothing cartons.

7 0

3 years ago

What is 3/4÷1/8 3/4÷1/8 explain or show your reasoning

Vikki [24]

Answer:

52.5

Step-by-step explanation:

it is simple. very simple

6 0

3 years ago

Read 2 more answers

Need help with the last three asap

Sunny_sXe [5.5K]

13) Angle 1= 54 Angle 2=36
14) Angle 1=122 Angle 2=58
15) Angle 1=51 Angle 2=39
Attached is the work
Hope this helps!

7 0

3 years ago