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padilas [110]
2 years ago
12

O A box contains 40 oranges, 12 of which are

Mathematics
1 answer:
konstantin123 [22]2 years ago
5 0

Step-by-step explanation:

Nø of sample space, n(s) = 40

nø of unripe oranges, n (u) = 12

no of ripe oranges, n (r) = 40 - 12 = 28

Now

The probability that it is ripe is, P(E)

= n(r) / n(s)

= 28 / 40

= 7 / 10

Also the probability that it is unripe is, P(E)

= n(u) / n(s)

= 12 / 40

= 3 / 10

Hope it will help :)❤

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There are approximately 15 milliliters (mL) in 1 tablespoon (tbsp). Which expression can be used to find the approximate number
Greeley [361]
We develop the ratio between the number of milliliters present in 1 tablespoon and that is,
                               15 mL: 1 tablespoon
We let x be the number of millileter in 3 tbsp and it can be determined through the equation below.
                                x = 3 tbsp x (15 mL/ 1 tbsp) = 45 mL
Therefore, there are 45 mL in 3 tbsp.
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3 years ago
The Johnson twins were born five years after their older sister. This​ year, the product of the three​ siblings' ages is exactly
Mamont248 [21]

Answer:

13 years.

Step-by-step explanation:

Suppose, today, the Johnson twins' age is x years. Then the age of their elder sister will be (x + 5) years old. It is given that product of the three​ siblings' ages is exactly 2998 more than the sum of their ages. Therefore:

x + x + x + 5 + 2998 = (x)(x)(x + 5).

3x + 3003 = x^3 + 5x^2.

x^3 + 5x^2 - 3x - 3003 = 0.

To solve the question, factor theorem will be used. It states if any number c satisfies the equation f(c) = 0, then c is the factor of f(x). By observation, it can be seen that x = 13 can be a possible candidate for the factor of f(x). To verify, check f(13).

f(13) = 13^3 + 5(13^2) - 3(13) - 3003 = 2197 + 845 - 39 - 3003 = 0.

Since f(13) = 0, therefore x = 13 is the factor of f(x).

Now applying synthetic division:

Column 1       2       3       4            5

     13    |         1       5      -3        -3003  (Row 1)

______|______<u>  _13__234___3003</u>   (Row 2)

            |         1       18      231          0    (Row 3)

The method requires to write the coefficients of all the powers in the Row 1 on the right hand side of the table. Put the factor x = 13 on the left hand side of the table (Row 1 Column 1). The first step involves the second column elements to be added. Since there is only 1, thus there will be 1 below the line. Next step involves multiplying 1 with the factor (which is 13) and this will be the element for row 2 column 3. The add the elements of the column 3. The answer comes out to be -3. Repeat the above steps for the columns 4 and 5. The sum of the column 5 (the last column) should be 0, which is the case. The elements of the last row are actually the coefficients of the quadratic equation which is resultant from dividing f(x) by (x - 13). Thus:

x^2 + 18x + 231 = 0.

Using completing the square:

x^2 + 18 = -231.

(x)^2 + 2*(x)*(9) + (9)^2 = -231 + (9)^2.

(x + 9)^2 = -231 + 81.

(x + 9)^2 = -150.

Taking square root on both sides shows that rest of the 2 answers of this polynomial will be complex roots since square root of -150 does not exist in real numbers. Therefore, since the age is a real quantity and not a complex quantity, the age of the twins is 13 years!!!

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