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2 years ago

Is x-10 a factor of f(x)=5x^3+60x^2+109x+90

Mathematics

1 answer:

RUDIKE [14]2 years ago

4 0

Answer:

Step-by-step explanation:

Given values are

f(x) = 5x^3+60x^2+109x+90

x = -10.

Given Polynomial is 5x^3+60x^2+109x+90 .

= (90)+(5.x^3)+(60.x^2)+(109.x)

By putting x = (-10) we can rewrite it as

= (90)+(5.(-10)^3)+(60.(-10)^2)+(109.(-10))

= (90)+(-5000)+(6000)+(-1090)

= 0

The remainder of given polynomial is 0.

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An elementary school is offering 3 language classes: one in Spanish, one inFrench, and one in German. The classes are open to an

Elis [28]

Answer:

0.5 = 50% probability that he or she is not in any of the language classes.

Step-by-step explanation:

We treat the number of students in each class as Venn sets.

I am going to say that:

Set A: Spanish class

Set B: French class

Set C: German class

We start building these sets from the intersection of the three.

In addition, there are 2 students taking all 3 classes.

This means that:

$(A \cap B \cap C) = 2$

6 that are in both French and German

This means that:

$(B \cap C) + (A \cap B \cap C) = 6$

$(B \cap C) = 4$

4 French and German, but not Spanish.

4 that are in both Spanish and German

This means that:

$(A \cap C) + (A \cap B \cap C) = 4$

$(A \cap C) = 2$

2 Spanish and German, but not French

12 students that are in both Spanish and French

This means that:

$(A \cap B) + (A \cap B \cap C) = 12$

$(A \cap B) = 10$

10 Spanish and French, but not German

16 in the German class.

This means that:

$(C - B - A) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 16$

$(C - B - A) + 2 + 4 + 2 = 16$

$(C - B - A) = 8$

8 in only German.

26 in the French class

$(B - C - A) + (A \cap B) + (B \cap C) + (A \cap B \cap C) = 26$

$(B - C - A) + 10 + 4 + 2 = 26$

$(B - C - A) = 10$

10 only French

28 students in the Spanish class

$(A - B - C) + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 16$

$(A - B - C) + 10 + 2 + 2 = 28$

$(A - B - C) = 14$

14 only Spanish

At least one of them:

The sum of all the above values. So

$(A \cup B \cup B) = 14 + 10 + 8 + 10 + 2 + 4 + 2 = 50$

None of them:

100 total students, so:

$100 - (A \cup B \cup B) = 100 - 50 = 50$

(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?

50 out of 100. So

50/100 = 0.5 = 50% probability that he or she is not in any of the language classes.

4 0

2 years ago

A lumber company is making boards that are 2638.0 millimeters tall. If the boards are too long they must be trimmed, and if the

Anna [14]

Answer:

The answer is "Fail to reject $H_o$ , because $w_o$ is sufficient evidence for claim".

Step-by-step explanation:

$H_0 \mu=2638.0 \ \ / \ \ H_a \mu \neq 2638.0 \\\\\mu < 2638.0 \ \ or \ \ \mu > 2638.0 \\\\\alpha =0.05 \ \ level \ \ at \ \ sufficient \\\\$

Test Statistic:

$t =\frac{\bar{x}- \mu}{\frac{S}{\sqrt{n}}}\\\\=\frac{2636.5- 2638.0}{\frac{12.0}{\sqrt{18}}}\\\\= -0.5303\\\\$

$dt=17\\\\$

p-value $=0.6028$

3 0

2 years ago

Can someone help me please

vlada-n [284]

Answer:

y=(x+4)^2 is shifted four units to the left.

Step-by-step explanation:

When you think of this transformation you have to know that the parabola isn't changed and only the units do in this situation.

8 0

2 years ago

HELP PLEASE!!!!!!!!!!!!!!!!!!!

baherus [9]

The answer is the first 1, 3,929. Because you would have to multiply 0.86 to the 11th power, then multiply that by 20646.

8 0

2 years ago

Hey can you please help me posted picture of question

mote1985 [20]

Two events are occurring:

1) Rolling a die
Sample Space = {1,2,3,4,5,6}
Total number of outcomes in sample space = 6
Favorable outcomes = Odd number
Number of Favorable outcomes = 3

Probability of getting an odd number = 3/6

2) Tossing a coin
Sample Space = {H, T}
Probability of getting a head= 1/2

The probability of getting odd number and head will be the product of two probabilities, which will be = 3/6 x 1/2 = 3/12

Thus there is 3/12 = 1/4 (0.25 or 25%) probability of getting an odd number and a head in given scenario.

So correct answer is option C

4 0

3 years ago

Read 2 more answers