What are inverse functions?

Answer:

\(4(x^4+7)\)

Step-by-step explanation:

Taking out the greatest common factor,\(16x^4+28=4(x^4+7)\).

The probability that Aakesh will select a blue marble from each bag is 4/45.

To find the probability that Aakesh will select a blue marble from each bag, we need to calculate the probability of selecting a blue marble from each bag and then multiply those probabilities together.

Let's start with the first bag, which contains 5 marbles: 2 red marbles, 2 blue marbles, and 1 green marble. The probability of selecting a blue marble from the first bag is:

P(Blue from first bag) = Number of blue marbles / Total number of marbles in the first bag

P(Blue from first bag) = 2 / 5

Now, let's move on to the second bag, which contains 9 marbles: 3 red marbles, 2 blue marbles, and 4 green marbles. The probability of selecting a blue marble from the second bag is:

P(Blue from second bag) = Number of blue marbles / Total number of marbles in the second bag

P(Blue from second bag) = 2 / 9

To find the probability of both events happening (selecting a blue marble from each bag), we multiply the individual probabilities together:

P(Blue from both bags) = P(Blue from first bag) * P(Blue from second bag)

P(Blue from both bags) = (2 / 5) * (2 / 9)

P(Blue from both bags) = 4 / 45.

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Answer:

\(W = 5h - 90 \\ 5h = W + 90 \\ h = \frac{W + 90}{5} \)

Answer:

h = w+90/ 5

Step-by-step explanation:

5h-90=w

5h/5= w+90/5

h= w+90/5

The probability that a defective component will be detected only by the first inspector is 0.19

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

The probability that all three defective components in a batch escape detection by both inspectors is 0.

It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.

Therefore P(A)=P(B)=81%=0.81

At least one inspector does not detect a defect on 38% of all defective components.

Therefore, bar P(A∩B)=0.38

As we know:

bar P(A∩B)=1-P(A∩B)=0.38

P(A∩B)=1-0.38=0.62

A defective component will be detected only by the first inspector.

P(A∩barB)=P(A)-P(A∩B)

=0.81-0.62

P(A∩barB)=0.19

The probability that a defective component will be detected only by the first inspector is 0.19

Part (B) A defective component will be detected by exactly one of the two inspectors.

This can be written as: P(A∩barB)+P(barA∩B)

As we know:

P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)

Substitute the respective values we get:

P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)

=0.81+0.81-2(0.62)

=1.62-1.24

P(A∩ barB)+P(bar A∩B)=0.38

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

Part (C) All three defective components in a batch escape detection by both inspectors

This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)

As we know bar P(A∩B)=P(bar A∪ bar B)=0.38

From part (B): P(bar A∩B)+P(A∩bar B)=0.38

This can be written as:

P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0

The probability that all three defective components in a batch escape detection by both inspectors is 0

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The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

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Using the given information, the cost of Max's electricity bill is R551.10

From the question, we are to calculate the cost of Max's monthly electricity bill

From the given information,

"Max's monthly electricity budget only allows him to use 250.50 kWh"

and

"The cost for 1 kWh is R2.20"

To determine the cost of Max's monthly electricity bill, we will multiply his monthly electricity budget by the cost for 1 KWh

That is,

Max's monthly electricity bill = 250.50 × R2.20

Max's monthly electricity bill = R551.10

Hence,

The cost of Max's monthly electricity bill is R551.10

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Answer:

A company produces electric insulators. The strength of the insulators is important since a broken insulator may cause a short circuit. Unfortunately, the strength varies significantly due to the material. Because of the expense, only a limited number of insulators could be tested. The engineers sampled 25 insulators (From a production run of 200), and conducted a destructive test to determine the force that was required to break the insulators. The mean value of this force was 1723 lbf with a sample standard deviation of 90 lbf. You may approximate the population standard deviation with the sample standard deviation for the following questions. a. Determine if the population is large enough or if a finite population correction (FPC) factor is needed. If so, what is the FPC factor? b. For 95% confidence, determine the margin of error (+ lbf) c. For these conditions, estimate the range of the probable population mean. Provide lower and upper values. For 95% confidence, determine the margin of error ( Assume the same mean and sample standard deviation. What is one advantage and one disadvantage of using 50 insulators instead of 25 insulators? d. lbf) if 50 insulators were tested.

Step-by-step explanation:

Answer:

4.

128

5.

40

hope this helps

Answer:

The numbers are 10 and -2.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

The first number is x

The second number is y.

A first number plus twice the second number is 8.

This means that:

\(x + 2y = 8\), that is, \(x = 8 - 2y\)

Twice the first number plus the second totals 19

So

\(2x + y = 19\)

Since \(x = 8 - 2y\)

\(2(8 - 2y) + y = 19\)

\(16 - 4y + y = 19\)

\(-3y = 3\)

\(y = -\frac{3}{3}\)

\(y = -1\)

\(x = 8 - 2y = 8 - 2(-1) = 8 + 2 = 10\)

The numbers are 10 and -2.

The required answer for the given mathematical operation is 182.5

What are arithmetic operations?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given, 67.4 + 43 + 30 + 42.10

        = 110.4 + 30 + 42.1

        = 140.4 + 42.1

        = 182.5

Hence, the required answer for the given mathematical operation is 182.5

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The equation that represents a line that passes through (-9, -3) with a slope of -6 is D. y+3=-6(x+9). I made a mistake when I was solving it to double-check.

The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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The answer is 166

First solve for the main rectangle.

7x5=35

Now double that because the opposite side is the same. 35+35=70

Next, do the rectangle that is 7 meters by 4 meters. 7x4=28. Double it again. 28+28=56

Finally we do the rectangle on the top and bottom. 5x4= 20. Double it to get 40.

Finally add all the numbers together to get  166

The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.

We have,

Cylinder and prism.

Here we have to find the equivalent ratio to 8/2.

First simplifying the given ratio as

8/2

= (4 x 2)/2

= 4 /1

Now, some more ratios equivalent to 8/2.

1. 8/2 x 3/3 = 24/ 6

2. 8/2 x 4/4 = 32/8

3. 8/2 x 6/6= 48/12

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\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

The required equation is :

\(\qquad \rm \dashrightarrow \:y =a \cos(bx) + k\)

Now, let's find the required values :

period (p) = 6

[distance between any successive Crest or trough]

a = - 4 (flipped)

b = 2π/p = 2π/6 = π/3

k = -2

Distance of starting position from origin = k

Now, plug in the values ~

\(\qquad \rm  \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2\)

Answer:

Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose 57 dollars on each policy sold.

Explanation:

If a person lives to the age of 70, they will earn $765. So, there is a 97% chance to earn $765. On the other hand, if a person dies before age of 70, they will lose $26635 because

$27,400 - $765 = 26,635

Then, there is a 3% chance to lose $26635.

Now, we can find the expected value, multiplyion each option by its probability, so:

E = $765(0.97) - (26635)(0.03)

E = $742.05 - $799.05

E = - $57

Since the sign is negative they can expect to lose money, so the answer is:

Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose 57 dollars on each policy sold.

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

The probability of 3 or more deaf people in a sample of 100 is given as follows:

0.3633 = 36.33%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of the parameters for this problem are given as follows:

p = 0.02, n = 100.

The probability of 3 or more deaf people are given as follows:

P(X >= 3) = 1 - P(X < 3).

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Hence:

Thus:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X < 3) = 0.1326 + 0.2707 + 0.2334

P(X < 3) = 0.6367.

P(X >= 3) = 1 - P(X < 3).

P(X >= 3) = 1 - 0.6367.

P(X >= 3) = 0.3633.

We suppose that 2% of the population is deaf, and want to find the probability of 3 or more deaf people in a sample of 100.

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The rate of interest is given by the equation R = 2.4 %

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the rate of interest be represented as R

Now , the equation will be

The amount with interest is A = $ 65,783.91

The principal amount P = $ 65,000

The time period b = 6 months = 0.5 years

The number of times interest is applied n = 12

So , A = P ( 1 + r/n )ⁿᵇ

And , the rate of interest R = n [ ( A/P )^1/nt - 1 ]

Substituting the values in the equation , we get

The rate of interest R = 12 [ ( 65,783/65,000 )^1/6 - 1 ]

On simplifying the equation , we get

The rate of interest R = 0.024

So , the percentage of interest = 0.024 x 100

The rate of interest R = 2.4 %

Hence , the rate of interest is 2.4 %

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Answer:

10.8

Step-by-step explanation:

24 * .45 = 10.8

Answer:

it would be 100 rounded because 14x8=112 and 112 is rounded to 100 to the nearest hundreth. Please subscribe to Amiredagoat Yt

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

[ ( 7 - 3 ) * 2 + 6 ] * 3

= [ 4 * 2 + 6 ] * 3

= [ 8 + 6 ] * 3

= 14 * 3

= 42

Answer:

-0.38

Step-by-step explanation:

0.6-(0.7)(1.4)

0.6-0.98

-0.38

Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

Answer:

-2x-8

2x= -8

x = -4

or

( x - 2 )(x + 2 )

x=2

x= -2

Answer:

13ft a second it's just a an average it the feet divided by the time by 2

The box plot for the data given is shown below

Box Plot for MY Data

Answer:

\(77, 385\)

Step-by-step explanation:

Start by writing the equations in symbolic form. I will represent one number with an x and the other with a y.

One number is one-fifth of the other number:

\(x=\frac{1}{5}y\)

The difference between the two numbers is 308:

\(y-x=308\)

This difference is positive, therefore I am assuming that y is the larger number. In the first equation, I made x a part of y, so this should check out.

Now we have a system of equations:

\(\left \{ {{x=\frac{1}{5}y } \atop {y-x=308}} \right.\)

I will rewrite the first equation for simplicity:

\(5x=y\)

Now, I will substitute y from the first equation for y in the second equation:

\(5x-x=308\)

Simplify:

\(4x=308\\x=77\)

Now, use x to find y using the second equation:

\(y-77=308\\y=385\)

Now, I can check the solutions by plugging them into the first equation!

\(x=\frac{1}{5}y\\ 77=\frac{1}{5}(385)\\77=77\)

The solution is correct!