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3 years ago

3. Martin's car had 86,456 miles on it. Of that distance, Martin's wife drove 24,901

Mathematics

1 answer:

Jet001 [13]3 years ago

8 0

Answer:

Martin Drove about 60,000

Martin Drove exactly 53,558

Step-by-step explanation:

90,000 - (20,000 +10,000) = x

60,000 = x

86,456 - (24,901 - 7,997) = x

53,558 = x

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A soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while

bija089 [108]

Answer:

The probability that the assembly line will be shut down is 0.00617.

Step-by-step explanation:

We are given that a soda bottling company’s manufacturing process is calibrated so that 99% of bottles are filled to within specifications, while 1% is not within specification.

Every hour, 12 random bottles are taken from the assembly line and tested. If 2 or more bottles in the sample are not within specification, the assembly line is shut down for recalibration.

Let X = <u><em>Number of bottles in the sample that are not within specification</em></u>.

The above situation can be represented through binomial distribution;

$P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.....$

where, n = number of trials (samples) taken = 12 bottles

x = number of success = 2 or more bottles

p = probabilitiy of success which in our question is probability that

bottles are not within specification, i.e. p = 0.01

So, X ~ Binom (n = 12, p = 0.01)

Now, the probability that the assembly line will be shut down is given by = P(X $\geq$ 2)

P(X $\geq$ 2) = 1 - P(X = 0) - P(X = 1)

= $1-\binom{12}{0} \times 0.01^{0}\times (1-0.01)^{12-0}-\binom{12}{1} \times 0.01^{1}\times (1-0.01)^{12-1}$

= $1-(1 \times 1\times 0.99^{12})-(12 \times 0.01^{1}\times 0.99^{11})$

= <u>0.00617</u>

8 0

3 years ago

Freddy wants an average grade of 93 from his four algebra exams. The scores for his first three exams are 94, 89, and 96. What g

White raven [17]

He would need a 93% on his fourth exam.

94+89+96+93= 372, 372 divided by 4= 93

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2 years ago

The parent function f(x)=x^2 is translated such that the function g(x)=-x^2+6x-5 represented the new function. What is true abou

Alla [95]

<h3>Answer:</h3>

g(x) has an axis of symmetry at x = 3
g(x) is shifted right 3 units from the graph of f(x)
g(x) is shifted up 4 units from the graph of f(x)

<h3>Step-by-step explanation:</h3>

The vertex form of g(x) is ...

... g(x) = -(x -3)² +4

This is offset to the right by 3 and up by 4 from the parent function. (It is also first reflected across the x-axis.)

_____

<em>Vertex form</em>

You know the leading coefficient is -1 because that's what it is for x² in the given form. When you factor -1 from the first two terms, of the given form, you have ...

... g(x) = -1(x² -6x) -5

Half the x coefficient inside parentheses will be the constant in the squared binomial term, so that term is (x -3)². The constant in that square is +9, so adding that value inside and outside parentheses in g(x) gives ...

... g(x) = -1(x² -6x +9) -5 +9

... g(x) = -(x -3)² +4 . . . . . vertex form

_____

<em>About transformations</em>

g(x) = f(x -a) causes the graph of f(x) to be shifted "a" units to the right. For a function f(x) with an axis of symmetry at x=0, it moves the axis of symmetry to x=a.

g(x) = f(x) +a causes the graph of f(x) to be shifted "a" units up.

g(x) = -f(x) causes the graph of f(x) to be reflected across the x-axis.

Here, we have all three of these transformations. First is the reflection:

... f₁(x) = -f(x) = -x²

Then we have shifting to the right 3 units. (also moves the axis of symmetry)

... f₂(x) = f₁(x-3) = -(x -3)²

Finally, we have shifting up 4 units.

... g(x) = f₂(x) +4 = -(x -3)² +4

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3 years ago

Read 2 more answers

Please help. ASAP. This is so confusing.

Anni [7]

1. right triangle?

-> c²= g²+b²

c²= 20²+21²

c²= 841

c=V841

c=29

-> triangle BCG is right

cos B= 20/29

tan B= 21/20

sin B= 21/29

sin G= 20/29

cos G= 21/29

tan G= 20/21

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