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3 years ago

Question 1 Part A: If (2^6)^x = 1, what is the value of x? Explain your answer. (5 points)

1 answer:

3 0

Part À: x=0 because anything to the zeroth power is one, so the only answer would be 0.
Part B: x=1 OR 0 because we know 5^0 is one, and one to the first power is just one too. One to the zeroth power is also one.

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Бр - 5 =13 need help !

malfutka [58]

Answer:

$p=3$

Step-by-step explanation:

$6p-5=13$

$+5$ $+5$

$6p=18$

$/6$ $/6$

$p=3$

4 0

3 years ago

5. Miguel took 32 comic books to his friend's house. This is 40% of his total

AfilCa [17]

The correct answer is A) 80

8 0

3 years ago

A company produces a certain product, and each unit of this product may have 3 different types of defects. Let Di, D2,Ds represe

Stella [2.4K]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a) 0.88

b) 0.02

c) 0.01

d) 0.99

Step-by-step explanation:

Step one: State the given parameters

$P(D_{1} ) = 0.12$ $P(D_{2} ) = 0.07$

$P(D_{3} ) = 0.05$ $P (D_{1} U D_{2} ) = 0.13$

$P(D_{1}n D_{2}n D_{3}) = 0.01$ $P(D_{1} U D_{3}) = 0.14$

Step 2 : Obtain the probability that a unit does not have a type 1 defect

$P(\frac{}{D_{1} })$ = $1 -P(D_{1} )$

= $1 - 0.12$

= 0.88

Step 3 : Obtain the probability that a unit has both type 2 and 3 defect?

The probability of the unit having both type 2 and type 3 defect is denoted as $P(D_{2} n D_{3} )$

This is calculated as

$P(D_{2}n D_{3}) =P(D_{2} ) + P(D_{3}) - P(D_{2} U D_{3})\\\\ = 0.07 + 0,05 - 0.13$

= 0.02

Therefore P(D_{2} n D_{3} ) = 0.02

Step 4 : Obtain the probability that the unit has both a type 2 and type 3 ,but not a type 1 defect

Let $P(\frac{}{D_{1}} n D_{2} n D_{3} )$ denote the probability that the unit has both a type 2 and type 3 ,but not a type 1 defect.

This can be calculated as follows :

$P(\frac{}{D_{1}} n D_{2} n D_{3} ) = P(D_{2} n D_{3}) - P(D_{1} n D_{2}nD_{3})$

= 0.02 - 0.01

= 0.01

Step 4 : Obtain the probability that a unit has at most two defects

P(at most 2 defects) = 1 - P(all three defects)

= $1- P(D_{1} n D_{2}nD_{3})$

= 1 - 0.01

= 0.99

7 0

3 years ago

The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi √in, given in in

Grace [21]

Answer:

A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Step-by-step explanation:

We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;

68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2, 76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.

Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;

P.Q. = $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ ~ $\chi^{2} __n_-_1$

where, s = sample standard deviation = $\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }$ = 5.063

$\sigma$ = population standard deviation

n = sample of observations = 22

Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.

So, 90% confidence interval for the population standard deviation, $\sigma$ is ;

P(11.59 < $\chi^{2}__2_1$ < 32.67) = 0.90 {As the critical value of chi at 21 degrees

of freedom are 11.59 & 32.67}

P(11.59 < $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ < 32.67) = 0.90

P( $\frac{ 11.59}{(n-1) \times s^{2}}$ < $\frac{1}{\sigma^{2} }$ < $\frac{ 32.67}{(n-1) \times s^{2}}$ ) = 0.90

P( $\frac{(n-1) \times s^{2} }{32.67 }$ < $\sigma^{2}$ < $\frac{(n-1) \times s^{2} }{11.59 }$ ) = 0.90

90% confidence interval for $\sigma^{2}$ = [ $\frac{(n-1) \times s^{2} }{32.67 }$ , $\frac{(n-1) \times s^{2} }{11.59 }$ ]

= [ $\frac{21 \times 5.063^{2} }{32.67 }$ , $\frac{21 \times 5.063^{2} }{11.59 }$ ]

= [16.48 , 46.45]

90% confidence interval for $\sigma$ = [ $\sqrt{16.48}$ , $\sqrt{46.45}$ ]

= [4.06 , 6.82]

Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

5 0

3 years ago

can someone please help me?!

stealth61 [152]

Answer:

z = 92

x = 11

Step-by-step explanation:

From the figure,

13x - 55 = 88 (Opposite angles made by two straight lines are equal)

13x = 88 + 55

13x = 143

x = 143/13

x = 11

Again,

88 + z = 180 (Sum of angles of a straight line)

z = 180 - 88

z = 92

5 0

3 years ago

Read 2 more answers