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ycow [4]
3 years ago
15

Aluminum usage in automobiles has been climbing steadily. As recently as 1990, there were no aluminum-structured passenger cars

in production anywhere in the world, but by 1997, there were seven of them, including the Audi A8. With weight savings of up to 47% over steel vehicles, such cars use less fuel, create less pollution, and are recyclable. Aluminum pistons are also used in automotive internal combustion engines. Aluminum pistons are manufactured through casting because of its capability to produce near-net shaped parts at the required production rates. However, with poorly designed molds, under-fills or excess porosity can cause parts to be rejected. In a process that manufactures certain aluminum pistons, the probability that a piston has an under-fill defect is 0.05, the probability that a piston has a porosity defect is 0.04, and the probability that a piston has both defects is 0.01. What is the probability that a randomly chosen piston has a defect?
Mathematics
1 answer:
lara [203]3 years ago
8 0

Answer:

P(A U B)= 0.08

Step-by-step explanation:

1.Let:

P(A) as the probability that a psiton has an under-fill defect

P(B) as the probability that a pistón has a porosity defect

P(A ∩ B) the probability of having both defectos

Then:

P(A)=0.05

P(B)=0.04

P(A ∩ B)=0.01

2. The probability that a randomly chosen piston has a defect could be calcularse as the union of the probability of choosing a piston with am under-fill defect and one with porosity defect.

That Is P(A U B)

Aplying the probability properties we have:

P(A U B)= P(A) + P(B) -P(A ∩ B)

Replacing the probabilities:

P(A U B)= 0.05+0.04-0.01

P(A U B)= 0.08

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Find the volume of the cylinder
AleksandrR [38]

The volume of the cylinder in terms of π is 18,095.5736 square yards,

the volume of the cylinder by using π equals 3.14 is 18.086.4 square yards.

Step-by-step explanation:

Step 1; The volume of any cylinder is given by π times the product of the square of the radius (r²) and the height (h). The given cylinder has a radius of 12 yards and a height of 40 yards.

The volume of any cylinder = π × r² × h.

Step 2; The value of π equals 3.14159263588. So substituting this value in the equation to calculate the volume we get

The volume of the given cylinder = 3.14159263588 × 12² × 40 = 18,095.5736 square yards.

Step 3; If we substitute the value of π as 3.14 in the equation to calculate the volume, we get

The volume of the given cylinder = 3.14 × 12² × 40 = 18.086.4 square yards.

6 0
3 years ago
Help me with this plzzzzz I need to finish it rn so PLZZ help asp
garri49 [273]

Answer:

1. 16π

2. 112π

3. 351.68

Step-by-step explanation:

Area of a circle = πr^2

Substitute...

=4^2π

=16π

To find the how much fluid it can hold, just basically find its volume. To do that, you mutiply the area of the base by the height. So...

16π*7=122π

You then just subsitute π by 3.14 so...

122(3.14)=351.68

4 0
3 years ago
Dr yang buys a violin for £13200 plus vat at 20% dr yang pays a deposit for the violin he then pays the rest of the cost in 12 e
Andre45 [30]

Answer:

8/3

Step-by-step explanation:

Given that:

Cost of violin = 13200 plus VAT at 20%

Cost of violin = (100 + 20)% * 13200

Cost of violin = 1.20 * 13200 = £15,840

Instalment pay = (360 * 12) = 4320

Therefore, deposit made equals ;

Total cost - Instalment pay

£(15,840 - 4320) = £11,520

Hence, ratio of deposit made to the total Instalment payment made ;

£11520 / £4320 = 8 / 3

5 0
2 years ago
An article reports the following data on yield (y), mean temperature over the period between date of coming into hops and date o
skelet666 [1.2K]

Answer:

x1=c(16.7,17.4,18.4,16.8,18.9,17.1,17.3,18.2,21.3,21.2,20.7,18.5)

x2=c(30,42,47,47,43,41,48,44,43,50,56,60)

y=c(210,110,103,103,91,76,73,70,68,53,45,31)

mod=lm(y~x1+x2)

summary(mod)

R output: Call:

lm(formula = y ~ x1 + x2)

Residuals:  

   Min      1Q Median      3Q     Max

-41.730 -12.174   0.791 12.374 40.093

Coefficients:

        Estimate Std. Error t value Pr(>|t|)    

(Intercept) 415.113     82.517   5.031 0.000709 ***  

x1            -6.593      4.859 -1.357 0.207913    

x2            -4.504      1.071 -4.204 0.002292 **  

---  

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  

Residual standard error: 24.45 on 9 degrees of freedom  

Multiple R-squared: 0.768,     Adjusted R-squared: 0.7164  

F-statistic: 14.9 on 2 and 9 DF, p-value: 0.001395

a).  y=415.113 +(-6.593)x1 +(-4.504)x2

b). s=24.45

c).  y =415.113 +(-6.593)*21.3 +(-4.504)*43 =81.0101

residual =68-81.0101 = -13.0101

d). F=14.9

P=0.0014

There is convincing evidence at least one of the explanatory variables is significant predictor of the response.

e).  newdata=data.frame(x1=21.3, x2=43)

# confidence interval

predict(mod, newdata, interval="confidence")

#prediction interval

predict(mod, newdata, interval="predict")

confidence interval

> predict(mod, newdata, interval="confidence",level=.95)

      fit      lwr      upr

1 81.03364 43.52379 118.5435

95% CI = (43.52, 118.54)

f).  #prediction interval

> predict(mod, newdata, interval="predict",level=.95)

      fit      lwr      upr

1 81.03364 14.19586 147.8714

95% PI=(14.20, 147.87)

g).  No, there is not evidence this factor is significant. It should be dropped from the model.

4 0
2 years ago
The table below represents an exponential function. What is the missing value? 0,8 1,16 2,32 3,64 4,_
dezoksy [38]

Answer:

128

Step-by-step explanation:

16 + 16 = 32

32 + 32 = 64

64 + 64 = 128

Hope this helps!!

5 0
2 years ago
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