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solong [7]
3 years ago
14

A mysterious box is delivered to the dinner party you are attending. The label on the box says that the volume of a box is the f

unction f(x) = x3 + 3x2 – 10x – 24. To open the box, you need to identify the correct factors of f(x). Partygoers offer up solutions, and it is your job to find the right ones.
Their suggestions are:
•(x – 1)
•(x + 2)
•(x – 3)
•(x + 4)
•(x + 6)
•(x – 12)


List the correct factors. Then justify your selections with complete sentences.
Mathematics
1 answer:
Lapatulllka [165]3 years ago
6 0
F(x) = x³ + 3x² - 10x - 24

The root factors must be the factors of 24.
1 x 24 ; 2 x 12 ; 3 x 8 ; 4 x 6.

The most probable roots would be -4, -3, -2, -1, 1, 2, 3, or 4.

Using synthetic division, one can find that the smallest root is -3.
(x - 3)(x² - 6x - 8). The quadratic can now be factored as (x + 2)(x - 4) and further factored as (x - 3)(x + 2)(x - 4). 

The correct factors are: (x - 3) (x + 2) (x - 4)
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If $396 is invested at an interest rate of 13% per year and is compounded continuously, how much will the investment be worth in
Vilka [71]

Answer:  First option is correct.

Step-by-step explanation:

Since we have given that

Amount invested = $396

Interest rate = 13% per year

Time = 3 years

We will use the "Exponential growth formula" i.e.

A=Pe^{rt}

Here,

P denotes Principle amount

r denoted rate of growth

t  denotes number of years,

So, it becomes

A=396e^{0.13\times 3}\\\\A=396e^{0.69}\\\\A=\$584.88

Hence, First option is correct.

3 0
3 years ago
Read 2 more answers
What is the volume of a box that measures 13 inches by 6 inches by 6 inches
finlep [7]

Answer: 234!!!

Step-by-step explanation: Cube or box's volume = length x width x height

4 0
3 years ago
2. An article in the Journal of the American Medical Association reports the results of a
Scrat [10]

Answer:

a.  113/338

b. The relative frequency distribution is presented as follows;

{}                                      St. John's wort              Zoloft                 Placebo

Full response {}               27/91                             27/91                  37/91

Partial response {}           16/55                             26/55                13/55

No response {}                35/96                            7/24                    11/32

c. 29.67%

Step-by-step explanation:

a. The proportion of subjects assigned to take St. John wort is found as follows;

The total number of subjects = 27 + 27 + 37 + 16 + 26 + 13 + 70 + 56 + 66 = 338 subjects

The number of subjects assigned to take St. John wort = 27 + 16 + 70 =  113

The proportion of subjects assigned to take St. John wort = 113/338

b. The distribution of change in depression response using relative frequency is found as follows;

Total full response = 27 + 27 + 37 = 91

Total partial response = 16 + 26 + 13 = 55

No response = 70 + 56 + 66 = 192

{}                                      St. John's wort              Zoloft                 Placebo

Full response {}               27/91                             27/91                  37/91

Partial response {}           16/55                             26/55                13/55

No response {}                35/96                            7/24                    11/32

c. The percentage of subjects that took Zoloft and showed full response is given as follows;

The percentage of subjects that took Zoloft and showed full response = 27/91 × 100 = 29.67%

5 0
3 years ago
1. Find the 9th term of this sequence: a(n) = 5n - 8
erik [133]

Answer:

Step-by-step explanation:

substitute n with the numbers

btw, follow bodmas/pemdas

e.g., 5*1(n)-8= -3

so (5*9)-8=37

and the sum of the first 4 is

-3+2+7+12=18

5 0
4 years ago
Ryan purchase five packs of them are 3 to 6 in each pack. How many sticks of gum does he have?
dezoksy [38]
Between 15-30 pieces
5 0
3 years ago
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