Simplify the expression.(4 - 1)[(1 + 6) + 2]



23

27

42

45

Answers

Answer 1
Answer: Always simplify expressions in the order of PMDAS
(Parenthesis, Multiplication, Division, Addition, Subtraction)
(4-1) = (3)
[(1+6) + 2] = [7 + 2] = (9)
(3)x(9) = 27
The answer is 27

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A car travels 32 km due north andthen 46 km in a direction 40° west of
north. Find the magnitude of the
car's resultant vector.

Answers

Answer:

73.2km

Step-by-step explanation:

first you have to decompose 46 km into y and x components.

x=sin40°*46km

x=0.64*46km

x=29.44km

y=cos40°*46km

y=0.76*46km

y=34.96

now you add the y components together

32+34.96=66.98

finally use Pythagorean thereom to find the resultant vector.

a*a+ b*b=c*c

66.98*66.98+29.44*29.44=c*c

c*c= 4486.3+866.7

c=√5353

c=73.2 km this is the approximate value

I can type 800 words in 12 minutes. How many words can I type in 1 minute?​

Answers

the answer would be 67 words per minute because 800 divided by 12 would be 66.66 but if you round it; it would be 67 words per minute

Answer:

66 2/3 words per minute

Step-by-step explanation:

To convert 800 words in 12 minutes to a unit rate, you need to divide 800 and 12 by 12. Since 80012=2003=6623  

12

800

​  

=  

3

200

​  

=66  

3

2

​  

, then 800 words in 12 minutes = 6623words per minute  

66  

3

2

​  

words per minute

​  

.

Subtract.
(3x - 8) - (x2 - 5x - 2)

Answers

Answer:

  -x^2 +8x -6

Step-by-step explanation:

Distribute the minus sign and collect terms.

  (3x -8) -(x^2 -5x -2)

  = 3x -8 -x^2 +5x +2

  = -x^2 +8x -6

Zhao Xue wants to buy milk and yogurt. She wants to buy a total of at least 6.5 gallons of dairy products (condition A), and she has a budget of $20 (condition B). The graph represents the constraints on the number of gallons of milk M and yogurt Y Zhao Xue buys. Zhao Xue buys 4 gallons of milk. how many gallons of yogurt can she buy to meet both her constraints? A.) Exactly 2.5 gallons
B.) At least 4 gallons and at most 6.5 gallons
C.) At least 2.5 gallons and at most 4 gallons
D.) Zhao Xue doesn’t have enough money left to buy any yofurt

Answers

Answer: The answer is (D). Zhao Xue doesn’t have enough money left to buy any yofurt


Step-by-step explanation:  Given that Zhao Xue is buying buy milk and yogurt, a total of at least 6.5 gallons of dairy products and she has a budget of $20. The given graph represents the constraints on the number of gallons of milk 'M' and yogurt 'Y' Zhao Xue buys. Zhao Xue buys 4 gallons of milk. We need to calculate the number of gallons of yogurt she can buy to meet both her constraints.

From the graph, we can write

Condition A :

M+Y\geq 6.5.

Condition B :

8M+5Y\leq40.

Now, if she buys 4 gallons of milk, the the conditions become

4+Y\geq 6.5~~\Rightarrow Y\geq 2.5,\n\n8* 4+5Y\leq 40~~\Rightarrow Y\leq 1.6.

Here, there will be no solution to these constraints.

Therefore, she does not have enough money left to buy any yogurt.

Thus, the correct option is (D).

Answer: exactly 2.5 gallons

This is for khan academy.

123 grams is rounded to nearest whole. Write down the minimum possible mass it could have been.

Answers

Since we want the minimum value we are going to be rounding up from a smaller number. So we know the whole number will be 122. Now we find the smallest number that will round up which is .5. Answer is 122.5

122.4 would've rounded down.

Answer: 122.5



Step-by-step explanation: when it becomes 0.5 when rounding to the nearest whole number ot

8. The base of a circular cone has a diameter of 10 cm and an altitude of 10 cm. The cone is filled with water. A sphere is lowered into the cone until it just fits. Exactly one-half of the sphere remains out of the water. Once the sphere is removed, how much water remains in the cone?

Answers

Answer:

The volume of water that remains on the cone is 523.6 cm³

Step-by-step explanation:

To solve this problem you have to keep in mind the formules that describes the volume of a cone and the volume of a sphere.

Volume of a cone = (πr²h)/3

Volume of a sphere = (4/3)πr³

So, if the base of the cone has a diameter of 10 cm, its radius is 5 cm. Its altitude is 10 cm. ⇒Volume = (πr²h)/3 ⇒ Volume = [π(5²)10) ⇒

          Volume = 785.4 cm³. This is the initial volume of water.

Now if the sphere fits in the cone and half of it remains out of the water, the other half is inside the cone. Estimating the volume of the sphere and dividing it by two, you find the volume of water that was displaced.

Volume of a sphere = (4/3)πr³, here the radius is the same of the base of the cone (5 cm).

⇒ Volume = (4/3)π(5³)  ⇒ Volume = 523.6 cm³ ⇒ The half of this volume is 261.8 cm³. This is the volume of water displaced.

⇒ The volume of water that remains on the cone is 523.6 cm³ (785.4 cm³- 261.8 cm³)