MATHEMATICS
MIDDLE SCHOOL

2. 1/12 < 1/4 < 2/3 < 5/8

3. 1/4 < 1/12 < 5/8 < 2/3

Answer: The last choice is right

COLLEGE

David's class is on a tour if the local chocolate factory. In one section, it is known that 40% of the chocolates are caramel. David chooses 5 caramels at random and tried them. (i) Find the probability that the first chocolate is not a caramel.

I know the answer is .6. I just need to know how to get there.

We do not need to use the fact that he chooses 5 chocolates and random, since we are only concerned about the first one. If there is a 40% chance that a random chosen first chocolate is a caramel, then there is a 60% chance that it is NOT a caramel. Therefore the probability is 0.6.

MIDDLE SCHOOL

Right triangle has legs measuring 20 inches and 28 inches what is the length of the hypotenuse

I think its 34.4 inches

MIDDLE SCHOOL

How to write 19/5 as a mixed number

Answer: 3 and 4/5

Step-by-step explanation: To write an improper fraction as a mixed number, we divide the denominator into the numerator.

So in this problem, we divide 5 into 17.

5 divides into 19 three times.

3 x 5 is 15 and 19 - 15 is 14.

So 5 divides into 3 times with a remainder of 4.

In other words, we have 3 wholes and 4 out of 5.

We keep the same denominator.

So our mixed number is 3 and 4/5.

Answer:

19/5

3 (4/5)

3 (4/5) is the answer

MIDDLE SCHOOL

2 parter part 1: 1: Describe two ways to find the product of two binomials.

2: Explain how the letters of the words "FOIL" can help you remember how to multiply two binomials

Use the distributive to find the products of 3-11

3: (x+1) (x+3)

4: (y+6) (y+4)

5: (z-5) (z+3)

6: (a+8) (a-3)

7: (g-7) (g-2)

8: (n-6) (n-4)

9: (3m+1) (m+9)

10: (2p-4) (3p+2)

11: (6-5s) (2-s)

Use the FOIL method to find the products of 13-14

13: (b+3) (b+7)

14: (w+9) (w+6)

There are actually three ways to multiply binomials. I am not sure which ones you covered, so I will just mention the three:

A. Vertical method: Similar to multiplying whole numbers, you line up the given and multiply each term. The partial products should line up with similar terms before you add them together.

B. Distributive: This method uses the distributive property of multiplication. Each term of each binomial will be distributed to the terms of the other.

C. FOIL: Similar to the distributive method. FOIL is a mnemonic which means:

F = First term (Multiply the first terms of each binomial)

O = Outer terms (Multiply the terms that are on the outside)

I = Inner terms (Multiply the terms that are on the inside)

L = Last terms (Multiply the last terms of each binomial)

It is also important to note that the FOIL method works only on binomials. As for distributive and vertical, it can be used on polynomials.

2. Using mnemonics are useful for memorizing. FOIL helps you remember the order in which you will multiply the terms. It is also less confusing than the distributive because it is a shorter process.

3.

Combine like terms

4.

Combine like terms

5.

Remember to carry the sign

Combine like terms

6.

Combine like terms

7.

Remember to carry the sign

Combine like terms

8.

Remember to carry the sign

Combine like terms

9.

Combine like terms

10.

Combine like terms

11:

Combine like terms

Arrange the terms in descending order and carry the signs.

13: (b+3) (b+7)

F = (b)(b) = b²

O= (b)(7) = 7b

I = (3)(b) =3b

L = (3)(7) =21

b²+7b+3b+21

b²+10b+21

14: (w+9) (w+6)

F = (w)(w) = w²

O= (w)(6) = 6w

I = (9)(w) =9w

L = (9)(6) =54

w²+6w+9w+54

w²+15w+54

A. Vertical method: Similar to multiplying whole numbers, you line up the given and multiply each term. The partial products should line up with similar terms before you add them together.

B. Distributive: This method uses the distributive property of multiplication. Each term of each binomial will be distributed to the terms of the other.

C. FOIL: Similar to the distributive method. FOIL is a mnemonic which means:

F = First term (Multiply the first terms of each binomial)

O = Outer terms (Multiply the terms that are on the outside)

I = Inner terms (Multiply the terms that are on the inside)

L = Last terms (Multiply the last terms of each binomial)

It is also important to note that the FOIL method works only on binomials. As for distributive and vertical, it can be used on polynomials.

2. Using mnemonics are useful for memorizing. FOIL helps you remember the order in which you will multiply the terms. It is also less confusing than the distributive because it is a shorter process.

3.

Combine like terms

4.

Combine like terms

5.

Remember to carry the sign

Combine like terms

6.

Combine like terms

7.

Remember to carry the sign

Combine like terms

8.

Remember to carry the sign

Combine like terms

9.

Combine like terms

10.

Combine like terms

11:

Combine like terms

Arrange the terms in descending order and carry the signs.

13: (b+3) (b+7)

F = (b)(b) = b²

O= (b)(7) = 7b

I = (3)(b) =3b

L = (3)(7) =21

b²+7b+3b+21

b²+10b+21

14: (w+9) (w+6)

F = (w)(w) = w²

O= (w)(6) = 6w

I = (9)(w) =9w

L = (9)(6) =54

w²+6w+9w+54

w²+15w+54

MIDDLE SCHOOL

What is the sum of 2 1/5 +1 3/4?

✦ - - Let's solve:

✦ - - Start by solving:

✦ - - Now

=

=

✦ Final answer:

✦Hope this helps✦

✦ - - Start by solving:

✦ - - Now

=

=

✦ Final answer:

✦Hope this helps✦

HIGH SCHOOL

What is a quartic function with only the two real zeros given? x = -4 and x = -1

A.

y = x4 + 5x3 + 5x2 + 5x + 4

B.

y = x4 - 5x3 - 5x2 - 5x - 4

C.

y = -x4 + 5x3 + 5x2 + 5x + 4

D.

y = x4 + 5x3 + 5x2 + 5x - 5

Given that the two real solutions are x = -1 and x = -4 you now that (x+1) and (x+4) are factors of the quartic function.

So, you need to factor the polynomials given or divide them by (x+1)(x+4).

(x+1)(x+4) = x^2 + 5x + 4

Using the first function you get:

(x^4 + 5x^3 + 5x^2 + 5x + 4) / ( x^2 + 5x + 4) = x^2 + 1

And you know that x^2 + 1 does not have a real solution, so the function

x^4 + 5x^3 + x^2 + x + 4 has the two real solutions given, x = -1 and x = -4, and two not real solutions.

Now you know that the answer is the first option.

If you want to check the other functions you just must divide and analyze the quotient obtained.

Answer: option A. x^4 + 5x^3 + 5x^2 + 5x + 4.

So, you need to factor the polynomials given or divide them by (x+1)(x+4).

(x+1)(x+4) = x^2 + 5x + 4

Using the first function you get:

(x^4 + 5x^3 + 5x^2 + 5x + 4) / ( x^2 + 5x + 4) = x^2 + 1

And you know that x^2 + 1 does not have a real solution, so the function

x^4 + 5x^3 + x^2 + x + 4 has the two real solutions given, x = -1 and x = -4, and two not real solutions.

Now you know that the answer is the first option.

If you want to check the other functions you just must divide and analyze the quotient obtained.

Answer: option A. x^4 + 5x^3 + 5x^2 + 5x + 4.

HIGH SCHOOL

What type of triangle has two congruent sides of two angles measuring 45 degrees?

The isosceles right triangle. Two congruent sides mean an isosceles triangle. Total of interior angles of any triangle is 180º. Since two of the angles measure 45º, the remaining angle is 180º - 2*45º = 90º so it is also a right triangle.

Hope I helped :)

Hope I helped :)

The answer is B. right isosceles

COLLEGE

A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 15 wood and 14 graphite are defective and one racket is randomly selected from the sample, find the probability that the racket is wood or defective.

Answer:

The probability that the racket is wood or defective is 0.57.

Step-by-step explanation:

Let W represents wood racket, G represents the graphite racket and D represents the defective racket,

Given,

n(W) = 100,

n(G) = 100,

⇒ Total rackets = 100 + 100 = 200

n(W∩D) = 15,

n(G∩D) = 14,

⇒ n(D) = n(W∩D) + n(G∩D) = 15 + 14 = 29,

We know that,

n(W∪D) = n(W) + n(D) - n(W∩D)

= 100 + 29 - 15

= 100 + 14

= 114,

Hence, the probability that the racket is wood or defective,

MIDDLE SCHOOL

What is the solution to the inequality? - 9x – 15<3

x > 2

x <-2

x < 2

x >-2

Answer:

x > -2

Step-by-step explanation:

First: - 9x – 15 < 3, you would want to take the 15 and add from each side.

Now it looks like: - 9x < 18

Second: You want to take the -9 and divide it from 18

Now it looks like: x < -2

Third: Chnage the less than sign into a greather than sign because we are dealing with a negative #

Now it looks like: x > -2