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Brrunno [24]
3 years ago
14

Factor using ac-method,  15y+6y²-21= ________

Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
3 0
15y+6y^2-21=\\
6y^2+15y-21=\\
3(2y^2+5y-7)=\\
3(2y^2-2y+7y-7)=\\
3(2y(y-1)+7(y-1))=\\
3(2y+7)(y-1)

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Twenty percent of drivers driving between 10 pm and 3 am are drunken drivers. In a random sample of 12 drivers driving between 1
Lesechka [4]

Answer:

(a) 0.28347

(b) 0.36909

(c) 0.0039

(d) 0.9806

Step-by-step explanation:

Given information:

n=12

p = 20% = 0.2

q = 1-p = 1-0.2 = 0.8

Binomial formula:

P(x=r)=^nC_rp^rq^{n-r}

(a) Exactly two will be drunken drivers.

P(x=2)=^{12}C_{2}(0.2)^{2}(0.8)^{12-2}

P(x=2)=66(0.2)^{2}(0.8)^{10}

P(x=2)=\approx 0.28347

Therefore, the probability that exactly two will be drunken drivers is 0.28347.

(b)Three or four will be drunken drivers.

P(x=3\text{ or }x=4)=P(x=3)\cup P(x=4)

P(x=3\text{ or }x=4)=P(x=3)+P(x=4)

Using binomial we get

P(x=3\text{ or }x=4)=^{12}C_{3}(0.2)^{3}(0.8)^{12-3}+^{12}C_{4}(0.2)^{4}(0.8)^{12-4}

P(x=3\text{ or }x=4)=0.236223+0.132876

P(x=3\text{ or }x=4)\approx 0.369099

Therefore, the probability that three or four will be drunken drivers is 0.3691.

(c)

At least 7 will be drunken drivers.

P(x\geq 7)=1-P(x

P(x\leq 7)=1-[P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)]

P(x\leq 7)=1-[0.06872+0.20616+0.28347+0.23622+0.13288+0.05315+0.0155]

P(x\leq 7)=1-[0.9961]

P(x\leq 7)=0.0039

Therefore, the probability of at least 7 will be drunken drivers is 0.0039.

(d) At most 5 will be drunken drivers.

P(x\leq 5)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)

P(x\leq 5)=0.06872+0.20616+0.28347+0.23622+0.13288+0.05315

P(x\leq 5)=0.9806

Therefore, the probability of at most 5 will be drunken drivers is 0.9806.

5 0
3 years ago
PLS HELP ME 6, 7, and 8 (SHOW WORK!!) + LOTS OF POINTS + THANKS! + BRAINLIEST IF POSSIBLE!
julsineya [31]
6. 1 \frac{1}{2} = \frac{6}{4} since \frac{1}{4} = 4 feet. Then 6*4=24 So the answer is C

7. 1200 m/8 cm = C. 1 cm = 150 m 

8. A. Since 1 in = 3 feet then 6 inches = 18 feet (6*3=18) and 4 inches = 12 feet (4*3=12) so the dimensions of her room are 16'x12'.

B. A=lxw so 16*12= 216 m^{2}

Hope that helps
6 0
3 years ago
Read 2 more answers
The vertices of quadrilateral PQRS are P(4, 5), Q(6, 6), R(9, 4), and S(7, 2). Write a paragraph proof to determine whether quad
Svetlanka [38]
The vector PQ is Q-P = (2, 1). The vector SR is R-S = (2, 2). One is not a multiple of the others, so the vectors are not parallel. In a parallelogram, these vectors would be identical. PQRS is not a parallelogram.

5 0
3 years ago
X+y=5 <br> 3x-4y=8 <br> please i need the steps
grandymaker [24]

Answer:

x + y = 5

<u>3x - 4y = 8</u><u> </u><u> </u><u> </u>

3x + 3y = 15

<u>3x - 4y = 8 </u>-

7y = 7

y = 1

x + y = 5

x + 1 = 5

x = 4

x = 4

y = 1

Hope it helps!

6 0
2 years ago
Can someone help me with this? I am a little confused
arsen [322]
28 .to explain they want to know the missing side and the triangles are equal to each-other just one is projected smaller than the other . So the one with 16 16 and 24 is the smaller one . The difference between 24-16 is 8 . And In the bigger one the sides 20 and 20 where given so since the smaller one is equal to the bigger one you just do 20+8=28
4 0
2 years ago
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