Find the inverse of each of the given functions.

f(x) = 4x − 12

f−1(x) = _x + _

Answer:

b

Step-by-step explanation:

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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[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]

- - - - - - - - - - - - - - - - - - -

[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]

18^3 = 5832 (volume of crate)

3^3 = 27 ( volume of small cubes)

5832/27 = 216 cubes ( divide volumes to get number of cubes)

To find the probabilities using the normal table and R's pnorm function, follow these steps: (a) p r(z ≤ 1.45) is 0.9265 or 92.65%. (b) p r(z > −1.28) is 0.8997 or 89.97%. (c) p r(−0.674 ≤ z < 1.036) is 0.6017 or 60.17%. (d) p r(z > 0.836) is 0.2013 or 20.13%.

To find the probabilities using the normal table and r's pnorm function, we can follow these steps:

For (a) p r(z ≤ 1.45), we can use the normal table or the pnorm function in R to find the area to the left of 1.45. The area is 0.9265 or 92.65%.

For (b) p r(z > -1.28), we can find the area to the left of -1.28 using the normal table or the pnorm function in R, which is 0.1003 or 10.03%. To find the area to the right of -1.28, we subtract this value from 1. The area is 0.8997 or 89.97%.

For (c) p r(-0.674 ≤ z < 1.036), we can find the area to the left of -0.674 using the normal table or the pnorm function in R, which is 0.2514 or 25.14%. To find the area to the left of 1.036, we can use the normal table or the pnorm function in R, which is 0.8531 or 85.31%. The difference between these two values gives us the area between the z-scores, which is 0.8531 - 0.2514 = 0.6017 or 60.17%.

For (d) p r(z > 0.836), we can find the area to the left of 0.836 using the normal table or the pnorm function in R, which is 0.7987 or 79.87%. To find the area to the right of 0.836, we subtract this value from 1. The area is 0.2013 or 20.13%.

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.

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.

Answer:

C.  

buying it at a 10% discount without sales tax

Step-by-step explanation:

The population standard deviation of the weights of the defensive tackles is approximately 3.96 pounds.

Here, we have to calculate the population standard deviation,

Calculate the mean:

Mean = (204 + 215 + 207 + 212 + 214 + 208) / 6

Mean = 1260 / 6

Mean = 210 pounds

Calculate the squared differences between each weight and the mean:

[tex](204 - 210)^2 = 36\\(215 - 210)^2 = 25\\(207 - 210)^2 = 9\\(212 - 210)^2 = 4\\(214 - 210)^2 = 16\\(208 - 210)^2 = 4[/tex]

Find the mean of the squared differences:

Mean of squared differences = (36 + 25 + 9 + 4 + 16 + 4) / 6

Mean of squared differences = 94 / 6

Mean of squared differences = 15.67

Take the square root of the mean of squared differences:

Population standard deviation = √(15.67)

Population standard deviation ≈ 3.96 pounds

So, the population standard deviation of the weights of the defensive tackles is approximately 3.96 pounds.

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Answer:

86

Step-by-step explanation:

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.

Answer:

A

Step-by-step explanation:

it has the same slope and the same y-intercept