G find the probability that (a) more than 5, (b) between 1 and 3, (c) less than or equal to 2, bulbs will be defective

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[tex]\textsf{Using the distributive property, \textbf{a(b+c)=ab+ac}, expand the given expression:}[/tex]

[tex].\qquad\bullet\sf{4x(2x-6)=4x*2x-4x*6=8x^2-24x}[/tex]

[tex]\sf{\bf{$Answer: 8x^2-24x}}[/tex]

[tex]\Large\underbrace{\overbrace{\boldsymbol{Reflection - RoSe}}}^\star_\star[/tex]

The number of combinations that will result in a sum of 7 is:

1 + 6

6 + 1

2 + 5

5 + 2

3 + 4

4 + 3

For a total of 6 combinations per roll. While the total number of combinations per roll are:

6 * 6 = 36

Hence the probability that the sum is 7 would be:

Probability = 6 / 36 = 1 / 6

For a succession of three times, the overall probability that each three rolls will be a sum of 7 is:

Overall probability = (1/6) * (1/6) * (1/6)

Overall probability = 1/216 = 4.63 x 10^-3 = 0.463%

Final answer:

The probability of rolling a sum of 7 three times in succession using two balanced dice is 1/216.

Explanation:

To determine the probability that on each of the three rolls of two balanced dice, the sum of the two numbers that appear will be 7, we first need to identify the probability of rolling a sum of 7 with a single roll of two dice. There are six ways to roll a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of possible outcomes when rolling two dice is 6*6 = 36. Therefore, the probability of rolling a sum of 7 on one roll is P(sum=7) = 6/36 = 1/6.

Since each roll is independent of the others, the probability of this event occurring three times in succession is the product of the individual probabilities. Thus:

Therefore, the probability of all three rolls resulting in a sum of 7 is:

P(Three 7's in a row) = P(First roll is 7) * P(Second roll is 7) * P(Third roll is 7) = (1/6) * (1/6) * (1/6) = 1/216.

The value of the expression simplified using PEMDAS rule is -4.515.

"The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)".

For the given question,

The expression is 3.5 times (5.8 - 7.09).

PEMDAS rule is used to simplify this expression.

The expression is simplified as [tex]3.5[/tex] × [tex](5.8 - 7.09)[/tex]

⇒[tex]3.5[/tex] × [tex](-1.29)[/tex]

⇒[tex]-4.515[/tex]

Hence we can conclude that the value of the expression simplified using PEMDAS rule is -4.515.

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Answer:

Slope: -2/3

Step-by-step explanation:

In order to solve this we first have to clear the equation for Y:

[tex]2x+ 3y= -12\\3y=-12-2x\\y=\frac{-12-2x}{3}\\ y=-4-\frac{2}{3} x[/tex]

Remember that the equation in the form of Y is represented in this way:

y=mx+c

Where M is the slope and C is the constant, so the slope is the number that is multiplying x, in the equation, in this case -2/3 is the number that is multiplying x, sot eh slope of the equation is -2/3

Answer:

A

Step-by-step explanation:

it has the same slope and the same y-intercept

The PMF of the number of selecting basalt specimen is [tex]\boxed{\bf P=^{10}C_{x}(0.5)^{x}(0.5)^{10-x}}[/tex] and the probability of selecting all specimen of one of two type of rocks is [tex]\boxed{\bf 0.0325}[/tex].

Further explanation:

Concept used:

The probability of an event [tex]E[/tex] can be calculated as follpws:

[tex]\boxed{P(E)=\dfrac{n(E)}{n(S)}}[/tex]

Here, [tex]n(E)[/tex] is the number of favorable outcomes in an event [tex]E[/tex] and [tex]n(S)[/tex] is the number of element in sample space [tex]S[/tex].

The probability mass function of getting exactly [tex]r[/tex] success in [tex]n[/tex] independent trial in an experiment can be expresses as follows:

[tex]\boxed{P=^nC_{r}p^{r}q^{n-r}}[/tex]

Here, [tex]p[/tex] is the success probability and [tex]q[/tex] is the failure probability of an event.

Calculation:

A geologist has collected [tex]10[/tex] specimens of ballistic rock and geologist collected [tex]10[/tex] specimens of granite.

The total number of specimens is [tex]20[/tex].

The sample space is the collection of all possible outcomes in an experiment.

Therefore, the total possible outcomes are [tex]20[/tex].

The probability of selecting ballistic rock can be calculated as follows:

[tex]\begin{aligned}P_{b}&=\dfrac{10}{20}\\&=\dfrac{1}{2}\\&=0.5\end{aligned}[/tex]

The probability of selecting granite can be calculated as follows:

[tex]\begin{aligned}P_{g}&=\dfrac{10}{20}\\&=\dfrac{1}{2}\\&=0.5\end{aligned}[/tex]

The PMF of selecting exactly [tex]x[/tex] basalt specimen for analysis can be calculated as follows:

[tex]\boxed{P=^{10}C_{x}(0.5)^{x}(0.5)^{10-x}}[/tex]

Consider [tex]A[/tex] as an event that all rocks are selecting from one rock and [tex]n(A)[/tex] as the number of favorable outcomes in an event [tex]A[/tex].

The number of favorable outcomes in an event [tex]A[/tex] can be calculated as follows:

[tex]\begin{aligned}n(A)&=\left(^{10}C_{10}\cdot ^{10}C_{5}\right)+\left(^{10}C_{10}\cdot ^{10}C_{5}\right)\\&=\left(\dfrac{10!}{10!\cdot (10-10)!}\cdot \dfrac{10!}{5!\cdot (10-5)!}\right)+\left(\dfrac{10!}{10!\cdot (10-10)!}\cdot \dfrac{10!}{5!\cdot (10-5)!}\right)\\&=\dfrac{10\cdot 9\cdot 8\cdot 7\cdot 6}{5\cdot 4\cdot 3\cdot 2\cdot 1}+\dfrac{10\cdot 9\cdot 8\cdot 7\cdot 6}{5\cdot 4\cdot 3\cdot 2\cdot 1}\\&=252+252\\&=504\end{aligned}[/tex]

The total possible outcomes of selecting [tex]15[/tex] rocks in [tex]20[/tex] rocks can be calculated as follows:

[tex]\begin{aligned}n(S)&=^{20}C_{15}\\&=\dfrac{20!}{15!\cdot (20-15)!}\\&=\dfrac{20\cdot 19\cdot 18\cdot 17\cdot 16\cdot 15!}{15!\cdot 5!}\\&=\dfrac{20\cdot 19\cdot 18\cdot 17\cdot 16}{5\cdot 4\cdot 3\cdot 2\cdot 1}\\&=19\cdot 3\cdot 17\cdot 16\\&=15504\end{aligned}[/tex]

The probability [tex]P(A)[/tex] of selecting all specimen of one of two type of rocks can be calculated as follows:

[tex]\begin{aligned}P(A)&=\dfrac{504}{15504}\\&=0.0325\end{aligned}[/tex]    

Thus, the probability that all specimens of one of the two types of rock are selected for analysis is [tex]\boxed{\bf 0.0325}[/tex].

Learn more:

1. Learn more about functions https://brainly.com/question/2142762

2. Learn more about numbers https://brainly.com/question/1852063

Answer details:

Grade: College school

Subject: Mathematics

Chapter: Probability

Keywords: Basalt specimen, geologist, rock, granite, PMF, probability mass function, exactly, probability, possible outcomes, favorable, failure success,  , event, experiment, trial, P=n(E)/n(S).

The PMF of the number of basalt specimens selected for analysis ranges from P(X = 0) to P(X = 10), and the probability of selecting all specimens of one type of rock (either basalt or granite) is 0.000061036.

To solve this problem, we need to find the probability mass function (PMF) of the number of basalt specimens selected for analysis and the probability of selecting all specimens of either basalt or granite.

Given information:

- There are 10 specimens of basaltic rock and 10 specimens of granite.

- The laboratory assistant will randomly select 15 specimens for analysis.

Step 1: Find the PMF of the number of basalt specimens selected for analysis.

Let X be the random variable representing the number of basalt specimens selected for analysis.

The possible values of X range from 0 to 10 (since there are 10 basalt specimens).

The PMF of X can be calculated using the binomial probability formula:

P(X = k) = (C(n, k) [tex]\times[/tex] ([tex]p^k[/tex]) [tex]\times[/tex] [tex](1-p)^{(n-k)}[/tex])

where:

n = total number of trials (selecting 15 specimens)

k = number of successes (number of basalt specimens selected)

p = probability of success (selecting a basalt specimen) = 10/20 = 1/2

q = probability of failure (selecting a granite specimen) = 1 - p = 1/2

The PMF of X for different values of k is as follows:

P(X = 0) = C(15, 0) [tex]\times[/tex] [tex](1/2)^0[/tex] [tex]\times[/tex] [tex](1/2)^15[/tex] = 0.000030518

P(X = 1) = C(15, 1) [tex]\times[/tex] [tex](1/2)^1[/tex] [tex]\times[/tex] [tex](1/2)^14[/tex] = 0.001525879

P(X = 2) = C(15, 2) [tex]\times[/tex] [tex](1/2)^2[/tex] [tex]\times[/tex] [tex](1/2)^13[/tex] = 0.030517578

Step 2: Find the probability of selecting all specimens of one type of rock.

The probability of selecting all 10 basalt specimens = P(X = 10) = C(15, 10) [tex]\times[/tex] (1/2)^10 [tex]\times[/tex] (1/2)^5 = 0.000030518

The probability of selecting all 10 granite specimens = P(X = 0) = 0.000030518

Therefore, the probability of selecting all specimens of one type of rock (either basalt or granite) is:

P(X = 10) + P(X = 0) = 0.000030518 + 0.000030518 = 0.000061036

In summary, the PMF of the number of basalt specimens selected for analysis ranges from P(X = 0) to P(X = 10), and the probability of selecting all specimens of one type of rock (either basalt or granite) is 0.000061036.

The total population of Norfolk, VA, Baltimore, MD, and Charleston, SC is 984,810 people. This is calculated by adding the respective populations of the three cities together.

The total population of the three cities can be found by adding their respective populations together. Given that Norfolk, VA has a population of 242,628 people, and Baltimore, MD has 376,865 more people than Norfolk, we calculate the population of Baltimore by adding these two figures together to get 619,493 people. Charleston, SC has 496,804 less than Baltimore, so its population is found by subtracting 496,804 from 619,493 to get 122,689 people. To find the total population of all 3 cities, we add the populations of Norfolk, Baltimore and Charleston together, giving us 984,810 people in total.

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Final answer:

By applying the derivative of the surface area of a rectangular prism formula with respect to time, it is found that the surface area of the box is increasing at a rate of 61 ft^2/sec when the dimensions are 20 ft by 15 ft by 25 ft.

Explanation:

The question involves calculating the rate of change of the surface area of a box with respect to time using derivatives, a concept from calculus. Given the rates at which the length (x), width (y), and height (z) are increasing, we can find the rate at which the surface area S is changing by using the surface area formula for a rectangular prism, S = 2(xy + xz + yz), and differentiating with respect to time.

At the given dimensions (x = 20 ft, y = 15 ft, z = 25 ft), and rate of increase (dx/dt = 0.1 ft/sec, dy/dt = 0.2 ft/sec, dz/dt = 0.5 ft/sec), the rate of change of surface area dS/dt is calculated by:

dS/dt = 2( (dy/dt)z + y(dz/dt) + (dx/dt)z + x(dz/dt) + (dx/dt)y + x(dy/dt) )

dS/dt = 2( (0.2)(25) + (15)(0.5) + (0.1)(25) + (20)(0.5) + (0.1)(15) + (20)(0.2) )

dS/dt = 2(5 + 7.5 + 2.5 + 10 + 1.5 + 4)

dS/dt = 2(30.5)

dS/dt = 61 ft2/sec

Therefore, the surface area of the box is increasing at a rate of 61 ft2/sec when the dimensions x, y, and z are 20 ft, 15 ft, and 25 ft respectively.

the correct answer for this is the last choice:

It is incorrect because the length of the unknown side is the square root of 7,225.

Answer:

It is incorrect because the length of the unknown side is the square root of 7,225.

Step-by-step explanation:

Answer:  Second and Fourth options are correct.

Step-by-step explanation:

Since we know that

Additive inverse means

[tex]a+(-a)=0[/tex]

so, -a is the additive inverse of a.

So, according to options, we get that

A plane ascends 500 yards and descends 100 yards.

Ascends = (+)500 yards

Descends = (-) 100 yards

So, -100 is not an additive inverse of +500.

Twenty gallons of water leak from a pool and 20 gallons are put back into the pool.

Number of gallons are leaked out = (-)20

Number of gallons are put back = (+)20

So, we can write

+20-20=0

So, -20 is the additive inverse of +20.

A driver drives 40 miles north and 30 miles south.

Number of miles towards north = +40

Number of miles towards south = -30

So, -30 is not additive inverse of +40.

A person deposits $100 in to her bank account and then withdraws $100 from the same account.

Amount he deposited into her bank = $100

Amount he withdraws from bank = -100

So, we can write as

+100-100=0

So, -100 is an additive inverse of 100.

Hence, Second and Fourth options are correct.

train A travels at 50 mph

train B travels at 60 mph

60 +50 = 110

330/110 = 3

they will meet in 3 hours

Answer:

86

Step-by-step explanation:

Answer:

The length of the bridge between pillar B and pillar C is 56 feet.

Here's the answer from the plato.

Answer:

b

Step-by-step explanation: