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lidiya [134]
3 years ago
11

Consider the polynomial equation x(x -3)(x +6)(x -7)=0. Which of the following are zeros of the equation? Select all that apply.

Mathematics
1 answer:
grigory [225]3 years ago
4 0
(0,0), (3,0), (-6,0), and (7,0)
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1.A bag has 4 green blocks, 3 red blocks, 2 blue blocks, and 1 yellow block. Find the probability of randomly selecting a block
maks197457 [2]

Answer: 1) 7/10  2) 15  3) 240  4) 1/4  5) 4/9  6) 1/20  7) No, not independent

Step-by-step explanation:

1. 4 green+3red+2blue+1yellow = 10 total

if 3/10 are red, then 7/10 are not red. So the second option, 7/10

2. 3 cartons in every 40

40*5 = 200

so do 3*5 = 15

so 15 or the third option

3. 40 out of 110

110*6 = 660

so do 40*6 = 240

so 240 or the fourth option

4.

Flipping heads: 1/2

rolling even: well, there is 2, 4, and 6, or 3 even numbers so 3/6 or 1/2

do 1/2*1/2 = 1/4

so 1/4 or the third option

5. Numbers more than 2: 3, 4, 5, 6 (4 numbers)

4/6 or 2/3 chance the first time, 2/3 chance the second time

do 2/3*2/3 = 4/9

so 4/9 or the second option

6. 5 dishes and 4 desserts

1/5 chance of picking the dish

1/4 chance of picking the dessert

do 1/5*1/4 = 1/20

so 1/20 or the fourth option

7. Since you don’t replace the marble after picking it, it affects the outcome of the second draw. Therefore the events are dependent, or not independent. So the second option.

7 0
3 years ago
One plus one over 2 y equal x
iris [78.8K]

Answer:

one plus one over 2 y equals x

is

1 + 1/2y = x

Step-by-step explanation:

8 0
4 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!!!

8 0
3 years ago
The value of a painting recently sold at an auction is expected to increase in value over time. The function v(t)=12,000(1.15)^t
tensa zangetsu [6.8K]
This is an exponential equation with a starting value of 12000 and an increase of 15% each years.

The following are true:

C. Each year, it increases by 15%

E. The painting's value was 12,000 at the time is was sold.
8 0
3 years ago
There are 4,000 undergraduates registered at a certain college. Of them, 364 are taking one course, 496 are taking two courses,
kykrilka [37]

Answer:

X=1, P = 0.091

X=2, P = 0.124

X=3, P = 0.115

X=4, P = 0.378

X=5, P = 0.264

X=6, P = 0.028

Step-by-step explanation:

To calculate the probability distribution of X, first we have to define the sample space.

In this case X=1,2,3,4,5,6. This are the values that X can take.

The probability is calculated as equal to the relative frequency of each of the values.

For X=1, P = 364/4000 = 0.091

For X=2, P = 496/4000 = 0.124

For X=3, P = 460/4000 = 0.115

For X=4, P = 1512/4000 = 0.378

For X=5, P = 1056/4000 = 0.264

For X=6, P = 112/4000 = 0.028

4 0
3 years ago
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