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lana66690 [7]
2 years ago
10

1.

Mathematics
1 answer:
Ivenika [448]2 years ago
4 0
Here’s the full solution:

(Please mark as BRAINLIEST that would mean a lot to me)

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In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A
vredina [299]

Answer:

c) P(270≤x≤280)=0.572

d) P(x=280)=0.091

Step-by-step explanation:

The population of bearings have a proportion p=0.90 of satisfactory thickness.

The shipments will be treated as random samples, of size n=500, taken out of the population of bearings.

As the sample size is big, we will model the amount of satisfactory bearings per shipment as a normally distributed variable (if the sample was small, a binomial distirbution would be more precise and appropiate).

The mean of this distribution will be:

\mu_s=np=500*0.90=450

The standard deviation will be:

\sigma_s=\sqrt{np(1-p)}=\sqrt{500*0.90*0.10}=\sqrt{45}=6.7

We can calculate the probability that a shipment is acceptable (at least 440 bearings meet the specification) calculating the z-score for X=440 and then the probability of this z-score:

z=(x-\mu_s)/\sigma_s=(440-450)/6.7=-10/6.7=-1.49\\\\P(z>-1.49)=0.932

Now, we have to create a new sampling distribution for the shipments. The size is n=300 and p=0.932.

The mean of this sampling distribution is:

\mu=np=300*0.932=279.6

The standard deviation will be:

\sigma=\sqrt{np(1-p)}=\sqrt{300*0.932*0.068}=\sqrt{19}=4.36

c) The probability that between 270 and 280 out of 300 shipments are acceptable can be calculated with the z-score and using the continuity factor, as this is modeled as a continuos variable:

P(270\leq x\leq280)=P(269.5

d) The probability that 280 out of 300 shipments are acceptable can be calculated using again the continuity factor correction:

P(X=280)=P(279.5

8 0
3 years ago
Please help solve this question​
Rasek [7]

95141 1404 393

Answer:

  • arc BC: 8.55 cm
  • chord BC: 8.03 cm

Step-by-step explanation:

The length of an arc that subtends central angle α will be ...

  s = rα . . . . where α is in radians

The central angle BOC is twice the measure of angle QBC, so is 70°, or 7π/18 radians. So, the length of arc BC is ...

  s = (7 cm)(7π/18) ≈ 8.55 cm . . . arc BC

__

For central angle α and radius r, the chord subtending the arc is ...

  c = 2r·sin(α/2)

  c = 2(7 cm)sin(35°) ≈ 8.03 cm . . . . chord AB

5 0
3 years ago
Find AB, given that line AD is the perpendicular bisector of BC
astraxan [27]

Answer:

AB = 9

Step-by-step explanation:

The perpendicular bisector divides Δ ABC into 2 congruent triangles, that is

Δ ABD ≅ Δ ACD , then

AB = AC = 9

5 0
3 years ago
Ajar contains 4 red marbles numbered 1 to 4 and 10 blue marbles numbered 1 to 10. A marble is
Reptile [31]

Answer:

a)2/7

b)1/2

c)9/14

d)6/7

Step-by-step explanation:

The jar contains 4 red marbles, numbered 1 to 4 which means

Red marbles = (R1) , (R2) , (R3) , (R4)

It also contains 10 blue marbles numbered 1 to 10 which means

Blue marbles = (B1) , (B2) , (B3) , (B4) , (B5) , (B6) , (B7) , (B8) , (B9) , (B10) .

We can calculate total marbles = 4red +10 blues

=14marbled

Therefore, total marbles= 14

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10) =7

Total number of Blue marbles = 10

Blue and even marbles = 5

(a) The marble is red

P(The marble is red)=total number of red marbles/Total number of marbles

=4/14

=2/7

(b) The marble is odd-numbered

Blue marbles with odd number= (B1) , (B3) , (B5) , (B7) , (B9) ,

Red marbles with odd number = (R1) , (R3)

Number of odd numbered =(5+2)=7

P(marble is odd-numbered )= Number of odd numbered/ Total number of marbles

P(marble is odd-numbered )=7/14

=1/2

(C) The marble is red or odd-numbered?

Total number of red marbles = 14

Number of red and odd marbles = 2

The marbles that has odd number = (R1) , (R3) ,(B1) , (B3) , (B5) , (B7) , (B9) =7

n(red or even )= n(red) + n(odd)- n(red and odd)

=4+7-2

=9

P(red or odd numbered)= (number of red or odd)/(total number of the marble)

= 9/14

(d) The marble is blue or even-numbered?

Number of Blue and even marbles = 5

Total number of Blue marbles = 10

Number of blue that are even= 5

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10)

=7

n(Blue or even )= n(Blue) + n(even)- n(Blue and even)

= 10+7-5 =12

Now , the probability the marble is blue or even numbered can be calculated as

P(blue or even numbered)= (number of Blue or even)/(total number of the marble)

= 12/14

= 6/7

6 0
3 years ago
5/7^3 = 5(7^x)<br> Thank you for helping!!
SIZIF [17.4K]

When solving this equation you get x = -3.

To solve this, simply follow the order of operations for solving.

\frac{5}{7^{3}}  = 5(7^{x} ) ----> start by dividing both sides by 5

\frac{1}{7^{3}}  = (7^{x} ) -----> Now you can transform the front side of the equation to use negative exponents.

7^{-3} = 7^{x}

Since both x and -3 are the powers of x, we can eliminate the 7 and just make the exponents equal.

-3 = x

8 0
3 years ago
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