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Slav-nsk [51]
2 years ago
12

1 . Alberto has 318 baseball cards and 273 basketball cards. Estimate how many sports cards Alberto has. Describe the strategy y

ou used to estimate. 2. Alberto has 92 stamps in one large album and 38 stamps in another small album. How can he use mental math to find how many more stamps are in the large album? Use drawings to show your answer. 3. Alberto has 62 pennies, 41 nickels, and 29 dimes. What strategy can Alberto use to find the total number of coins? Describe it and show . 4. Suppose Alberto collects another 343 coins. How many coins will he have in his collection now? Describe two strategies you can use. then choose one strategy and solve. 5. Of Alberto's total number of coins, 168 are quarters. Describe two strategies you can use to find how many coins are not quarters. Estimate the difference. Then choose one strategy and solve.
Mathematics
1 answer:
Galina-37 [17]2 years ago
6 0
For 1. To estimate how many sports cards Alberto had, you would round each number to the nearest ten, so 318 would become 320. 273 would then become 270. You would then add those two and would get 590. So, Alberto had 590 sports cards (estimated). If you were looking for the actual answer (not estimated) , you would get 591.
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18 3/4 cups are required to bake 15 dozen of cookies.

Step-by-step explanation:

x = 75/4

x = 18 3/4 cups

18 3/4 cups are required to bake 15 dozen of cookies.

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In a group of 40 people, 27 can speak English and 25 can speak Spanish. How many can speak
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\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Information \: provided \:  with  \: us }}}}}\: \bigstar}

➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{What \: we \:  have  \: to \: find ? }}}}}\: \bigstar}

➻ The required number of people who can speak both English and Spanish .

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Assumption}}}}}\: \bigstar}

<u>Consider</u> ,

➻ A → Set of people who speak English.

➻ B → Set of people who speak Spanish

➻ A∩B → Set of people who can speak both English and Spanish

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Given}}}}}\: \bigstar}

  • ➻ n (A) = 27

  • ➻ n (B) = 25

  • ➻ n (A∪B) = 40

  • ➻ n(A∩B) = ?

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Now}}}}}\: \bigstar}

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - n (A∩B)

➻ 40 = 52 - n (A∩B)

➻ n (A∩B) = 52 - 40

➻ ∴ n (A∩B) = 12

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Therefore}}}}}\: \bigstar}

∴ Required Number of persons who can speak both English and Spanish are <u>12 .</u>

━━━━━━━━━━━━━━━━━━━━━━

\qquad {\: \:\bigstar \:  {\underline{\overline{\boxed{\bf{Verification}}}}}\: \bigstar}

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - 12

➻ 40 = 52 - 12

➻ 40 = 40

➻ ∴ L.H.S = R.H.S

━━━━━━━━━━━━━━━━━━━━━━

6 0
2 years ago
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yanalaym [24]
The angle is arctan(3/4) => sin(2t) = sin(2arctan(3/4)) =
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<span>cos(2t) = cos^2(t) - sin^2(t) = cos^2(z) - sin^2(z) = (4/5)^2 - (3/5)^2 = (16 - 9)/25

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