The sum of two numbers is 23. Twice one number increased by 6 is the same as 4 times the other number decreased by 2. What is the largest of the two numbers?

Answer:

A) P(X ≥ 3 ) = 0.7648

B) P(X ≥ 6) = 0.7515

C) P(X < 5) = 0.0949

D) P(X < 6) = 0.00031113

Yes. This is likely to happen if the true value of p is 0.65

E) P(X ≥ 17) = 0.012118

No. This is unlikely to happen if the true value of p is 0.65

Step-by-step explanation:

Solving this question means we have to deal with binomial probability distribution which follows a formula;

P(X = x) = C(n, x) * p^(x) * (1 - p)^(n - x)

We are given p = 65% = 0.65

A) probability of getting At least 3 out of the 5 business days, we have;

P(X ≥ 3 ) = P(X = 3) + P(X = 4) + P(X = 5)

And n = 5

Thus;

P(X = 3) = C(5, 3) × 0.65³ × (1 - 0.65)^(5 - 3)

P(X = 3) = 0.3364

P(X = 4) = C(5, 4) × 0.65⁴ × (1 - 0.65)^(5 - 4)

P(X = 4) = 0.3124

P(X = 5) = C(5, 5) × 0.65^(5) × (1 - 0.65)^(5 - 5)

P(X = 5) = 0.116

Thus;

P(X ≥ 3 ) = 0.3364 + 0.3124 + 0.116

P(X ≥ 3 ) = 0.7648

B) Probability of getting at least 6 out of the 10 business days.

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

From online binomial calculator, we have;

P(X = 6) = 0.2377

P(X = 7) = 0.2522

P(X = 8) = 0.1757

P(X = 9) = 0.0725

P(X = 10) = 0.0134

P(X ≥ 6) = 0.2377 + 0.2522 + 0.1757 + 0.0725 + 0.0134

P(X ≥ 6) = 0.7515

C) probability of getting fewer than 5 out of the 10 business days.

P(X < 5) = P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1)

From online binomial calculator, we have;

P(X = 4) = 0.0689

P(X = 3) = 0.0212

P(X = 2) = 0.0043

P(X = 1) = 0.0005

P(X < 5) = 0.0689 + 0.0212 + 0.0043 + 0.0005

P(X < 5) = 0.0949

D)probability of getting fewer than 6 out of the next 20 business days;

P(X < 6) = P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1)

From online binomial calculator, we have;

P(X = 5) = 0.000261

P(X = 4) = 0.000044

P(X = 3) = 0.0000056

P(X = 2) = 0.0000005

P(X = 1) = 0.00000003

P(X < 6) = 0.000261 + 0.000044 + 0.0000056 + 0.0000005 + 0.00000003

P(X < 6) = 0.00031113

Yes, in this scenario, It is likely to happen and I would think p is less than 0.65 because probability is less than 1 out of 1000.

E) probability of getting more than 17 out of the next 20 business days.

P(X ≥ 17) = P(X = 18) + P(X = 19) + P(X = 20)

From online binomial calculator, we have;

P(X = 18) = 0.0099846

P(X = 19) = 0.00195187

P(X = 20) = 0.00018125

P(X ≥ 17) = 0.0099846 + 0.00195187 + 0.00018125

P(X ≥ 17) = 0.012118

Probability is around 12 in 100 and not up to 50%. Thus, This is unlikely to happen if the true value of p is 0.65

Answer:

C

Step-by-step explanation:

Answer: C: 204 ft

Step-by-step explanation: plz mark me brainliest. 12x17=204

Answer:

y = -4x + 3

Step-by-step explanation:

(0, 3) and (2, -5)

m= (y2-y1)/(x2-x1)

m= (-5-3)/(2-0)

m= (-8)/2

m = -4

y - y1 = m(x - x1)

y - 3 = -4(x - 0)

y - 3 = -4x + 0

y = -4x + 3

Answer:

I think the 1st one would be 10...

Step-by-step explanation:

Because 12-2=10 and 18-8=10.

If I'm wrong, im super sorry

Answer:

Standard line equation:

y=ax+b

The point (5,1) is on the line. so :

1=a(5)+b → 1=5a+b

The point (1,-5) is also on the line. Then :

-5=a(1)+b → -5=a+b

Subtract the two equations in terms of a and b. we have:

6=4a → a=3/2 , b=-6.5

y=1.5x-6.5

Answer:

a. 15

b. 27

c. 4

d. 72

e. 2

Step-by-step explanation:

If you need an explanation lmk! happy to help.

Answer:

[tex] \frac{2}{5} [/tex]

Answer:

The answer to this equations would be 1.3 repeated i included a image with how to go about working the problem out

i believe the area is 48 if it's not correct sorry

Answer:

X = 4

y = 15

Step-by-step explanation:

I hope that is useful for you :)

Answer:

The answer is D.

Step:

6*5*12=360

Answer:

This is NOT a solution

Step-by-step explanation:

If we plug in the coordinates (-4,3) into 4x-y our new equation is 4×-4-3 and if we solve this equation.... 4×-4=-16 and -16-3=-19 which does NOT equal to -13

Answer:x=4/3y+8

Step-by-step explanation:

Step 1: Add 4 to both sides.

Step 2: Divide both sides by 1/2.

Answer:

3x-4y =24

Step-by-step explanation:

hope this helped xoxo

Answer:

297.84 miles

Step-by-step explanation:

176 miles in 13 hours is 13.5 miles per hour

13.5 * 22 = 297.84

Answer:

I believe the answer is $52.46

Hope this helps :)

Answer:

make a story!

Step-by-step explanation:

I think what they want you to do is add a story Line to the problem! For example : John is selling cards for $4. After selling 3 cards etc, Sorry if this isn't much of a help! They want you to make a story to the answer (I think)

Answer:

160/196

Step-by-step explanation:

it would be easier if you converted all fractions to improper fractions

so 3 1/5 would equal 16/5 and 2 4/5 would equal to 14/5

[tex]\frac{14}{5} - \frac{2}{3}[/tex] : to solve this you would need the same common denomenator,

to do this you can multiply 5 and 3 by something to make the lowest common denominator, which would be 15

thus

multiplying first fraction by 3 and the second by 5

42/15 - 10/15 = 32/15

now 32/15 divided by 14/5

the rule for dividing fractions, is flipping the fraction which you will be using to divide, and then multiplying it to the first fraction:

[tex]\frac{32}{14}[/tex] multiplied by [tex]\frac{5}{14}[/tex]

thus, answer is 160/196

Answer:

Step-by-step explanation:

Answer:

The surface area of the square pyramid is 34.63cm².

Step-by-step explanation:

[tex]A=a^{2} +2a\sqrt{\frac{a^{2} }{4} +h^{2} } =3^{2} +2[/tex]×3×[tex]\sqrt{\frac{3^{2} }{4} +4^{2} }[/tex]≈34.63cm^2

Answer:

Step-by-step explanation:

Answer:

35.7 I believe

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Answer:

Well it's the same because it's the same problem just worded different it's like saying "May I?" and your sister says "Can I?" It's the same question just different wording.

Answer:

The answer will be 41/14

Step-by-step explanation:

2.928571429

Step-by-step explanation:

Spinner 2

Probability helps us to know the chances of an event occurring. Sam should use the second spinner.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given that Sam plans to use a spinner to choose which friend to invite to the movies, he wants each friend to have a fair chance of being selected.

The term fair means that everyone or everything that is in the list should have equal opportunity.

Now, since Sam wants each friend to have a fair chance of being selected, therefore, the area on the spinner for each friend should be equal.

Hence, Sam should use the second spinner.

Learn more about Probability here:

https://brainly.com/question/795909

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