For the given function sin−1(9x + 1), the "inside" function is 9x + 1 and the "outside" function is

Answer with Step-by-step explanation:

The average marks of Shahid first four papers is 88.

Let a,b,c and d be the marks in first four papers

⇒  [tex]\dfrac{a+b+c+d}{4}=88[/tex]

⇒  a+b+c+d=88×4

                  =352

Let marks in fifth paper be x

The average of five papers become 90

⇒ [tex]\dfrac{a+b+c+d+x}{5}=90[/tex]

⇒ a+b+c+d+x=90×5

⇒  352+x=450   (since a+b+c+d=352)

⇒ x=450-352

⇒ x=98

Hence, Correct option is:

d.98

The Complex Conjugate Root Theorem dictates that if -4 is a root of f(x), then 4 must also be a root. This theorem applies to polynomials with real coefficients, ensuring non-real complex roots appear in conjugate pairs.

If a polynomial function f(x) has roots 3 and -4, then by the Complex Conjugate Root Theorem (also known as the Conjugate Pairs Theorem), if the polynomial has real coefficients, which is the usual assumption unless stated otherwise, the complex roots must come in conjugate pairs. Therefore, if -4 is a root, its complex conjugate 4 must also be a root of f(x). This applies to all non-real complex roots of a polynomial with real coefficients.

The Complex Conjugate Root Theorem is essential for understanding the behavior of polynomial functions with complex roots. In general, if a polynomial has a complex root a + bi, where a and b are real numbers and i is the imaginary unit (the square root of -1), its conjugate a - bi is also a root. This is true because polynomial equations with real coefficients have the property that their roots are either real or occur in complex conjugate pairs.

Answer:

A: -5 - √3i

This should be correct on edge

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]\frac{y}{x}=k[/tex] or [tex]y=kx[/tex]

where

k is the constant of proportionality

In this problem we have

[tex]y=2.5x[/tex]

so

the constant of proportionality k is equal to

[tex]k=2.5[/tex]

therefore

the answer is

[tex]k=2.5[/tex]

The constant of proportionality in the equation [tex]y = 2.5x[/tex] is [tex]\boxed{2.5}.[/tex]

Further explanation:

The relation is defined as the relationship between the input values and output values.

The x coordinates are the domain of the function and the y coordinates are the range of the function.

Given:

The equation is [tex]y = 2.5x.[/tex]

Explanation:

The proportionality equation can be expressed as follows,

[tex]y \propto x[/tex]

The value of [tex]y[/tex] changes as [tex]x[/tex] changes. If the value of [tex]x[/tex] increases then the value of y is also increasing.

The equation can be expressed as follows,

[tex]y = kx[/tex]

The inversely proportional relationship can be expressed as,

[tex]y \propto \dfrac{1}{x}[/tex]

Here, [tex]k[/tex] is the proportionality constant.

The given equation is [tex]y = 2.5x.[/tex]

The y is the independent variable and [tex]x[/tex] is the dependent variable.

The proportionality constant is 2.5.

The constant of proportionality in the equation [tex]y = 2.5x[/tex] is [tex]\boxed{2.5}.[/tex]

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Ratio and proportion

Keywords: proportional, directly proportional, constant, proportionality equation, y=0.41x, constant of proportionality.

perimeter of a square is 4 times side length (4s)

to find the length of a side divide the perimeter by 4

53.2 / 4 = 13.3

 so each side is 13.3 inches

The correct index form for the product of prime factors of 60, which is 2x2x3x5, is 2^2 x 3 x 5.

The product of prime factors for 60 is indeed 2x2x3x5. To write this in index form, we group the same numbers together and count how many there are. Then we use the base and exponent form to write it. Here, 2 is repeated twice. So, 2x2 can be written as 2^2. The primes 3 and 5 are each given once, so, we do not write powers for them. Therefore, the correct index form is 2^2 x 3 x 5.

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The water output rate for the Sanders family's sprinkler was 25 liters per hour, and for the Wright family's sprinkler was 15 liters per hour.

Let the water output rate as "x" liters per hour and the water output rate for the Wright family's sprinkler as "y" liters per hour.

Given that the combined total output of water from both sprinklers was 1025L, we can set up the following equation:

20x + 35y = 1025

We also know that the sum of the two rates is 40L per hour:

x + y = 40

x = 40 - y

Substituting this value of x into the first equation:

20(40 - y) + 35y = 1025

800 - 20y + 35y = 1025

15y = 225

y = 15

Substituting this value of y back into the second equation:

x + 15 = 40

x = 25

Therefore, the water output rate for the Sanders family's sprinkler was 25 liters per hour, and for the Wright family's sprinkler was 15 liters per hour.

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The required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.

Given that,
To translate “the perimeter of a rectangle is equal to 2 times the length plus twice the width."

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Perimeter is the measure of the figure on its circumference.

Here, the given string,  “the perimeter of a rectangle is equal to 2 times the length plus twice the width" can be translated in the mathematical form is,
Perimeter = 2 * length + 2 * width.

Thus, the required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.

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To write an explicit formula for the number of tulips Marko has, use the formula n = a + (x-1)d, where n represents the number of tulips, a is the initial number of tulips, x is the number of years, and d is the change in number of tulips each year. The explicit formula for Marko's tulips is n = 20 + 5(x-1). To predict the number of tulips Marko will have in 7 years, substitute x = 7 into the formula and solve for n, giving Marko will have 50 tulips in 7 years.

To write an explicit formula for the number of tulips Marko has, we can use the formula: n = a + (x-1)d. Here, n represents the number of tulips, a is the initial number of tulips (20), x is the number of years, and d is the change in number of tulips each year (5). So, the explicit formula is n = 20 + 5(x-1).

To predict the number of tulips Marko will have in 7 years, we can substitute x = 7 into our formula: n = 20 + 5(7-1). Solving this equation, we get n = 20 + 5(6) = 20 + 30 = 50. Therefore, Marko will have 50 tulips in 7 years.

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Answer:

1. 76,000

2. 8050

3. 240000

Step-by-step explanation:

We know that

1 tens = 10 ones

1 hundreds = 100 ones

1 thousand = 1000 ones

10 thousands = 10000 ones

Using these conversions we get,

1 : [tex]760\text{ hundreds}=760\times 100=76,000[/tex]

2 : [tex]805\text{ tens}=805\times 10=8050[/tex]

3 : [tex]24\text{ ten thousands}=24\times 10000=240000[/tex]

Table can be filled as shown below:

                 Thousands                                           Ones

Q. no. Hundreds    Tens     Ones    Hundreds    Tens      Ones

1.                                  7             6             0              0              0

2.                                                8             0              5              0

3.                2              4              0             0              0               0

You should get your answer of 306 :)

[tex]\sqrt[7]{2142}[/tex]

^online division .-.

To calculate the total number of doses in 3 1/3 bottles of medicine, multiply the fraction of bottles (10/3) by the number of doses per bottle (40). The result is 133 1/3 doses.

The student is asking how many doses are in 3 1/3 bottles of medicine if one bottle contains 40 doses. To find the answer, we need to multiply the number of bottles by the number of doses per bottle.

Here is the step-by-step calculation:

So, there are 133 1/3 doses in 3 1/3 bottles of medicine.

Answer:  B. [tex]48.5\%[/tex]

Step-by-step explanation:

Given : A number cube is rolled with these results:

64 ones, 67 twos, 73 threes, 59 fours, 72 fives, and 71 sixes.

Even numbers : 2,4,6

The number of times of rolling even number = [tex]67+59+71=197[/tex]

Total outcomes = [tex]64+67+73+59+72+71=406[/tex]

Now, the  experimental probability of rolling an even number :-

[tex]\dfrac{197}{406}[/tex]

In percent,  [tex]\dfrac{197}{406}\times100=48.52216748\approx48.5\%[/tex]

Hence, the experimental probability of rolling an even number = [tex]48.5\%[/tex]

The rate at which sand is leaking out when the altitude is 10 inches is

600π inches³ / min.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is (1/3)πr²h.

We have,

A conical pile formed due to a leak out of a hole whose radius is equal to its height.

dh/dt = 6 in/min

The rate at which the sand is leaking when height is 10 inches.

We have,

Volume = (1/3)πr²h and h = 10 inches

V = 1/3 πh²h

V = 1/3 πh³

Differentiating both sides.

dV/dt = 1/3 x π x 3 x h² (dh/dt)

dV/dt = π x h² x 6

dV/dt = π x 10² x 6

dV/dt = 600π inches³ / min

Thus,

The rate at which sand is leaking out when the altitude is 10 inches is

600π inches³ / min.

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Answer:

35*n+100=650

Step-by-step explanation:

I got the question right on TTM

Associate of science

Answer:

Assosiate in science

Step-by-step explanation:

An Associate of Science (AS) is a 2-year degree offered by most community colleges. Most AS degrees are transfer degrees and provide an academic foundation, but not specific career training. The A.S. degree is intended for students planning to pursue a bachelor’s degree in the areas of math or science.  

I hope you find this information useful and interesting! Good luck!

To find the probability the Jets will win, we use the Law of Total Probability. The probability that it snows on game day and the Jets win is found using the definition of conditional probability. Lastly, to find the probability that it snows on game day given that the Jets win, Bayes' theorem is used.

To solve this problem, we can use the concept of conditional probability. Let's define the following events:

A = it snows on game day

B = the Jets win

We are given:

P(B|A) = 0.32 (the probability of the Jets winning if it snows)

P(B|A') = 0.41 (the probability of the Jets winning if it doesn't snow)

P(A) = 0.29 (the probability of it snowing on game day)

To find the probability of the Jets winning, we can use the Law of Total Probability:

P(B) = P(B|A)P(A) + P(B|A')P(A')

P(B) = 0.32 * 0.29 + 0.41 * (1 - 0.29)

P(B) = 0.0928 + 0.1059

P(B) ≈ 0.1987

To find the probability that it snows on game day and the Jets win, we can use the definition of conditional probability:

P(A and B) = P(A) * P(B|A)

P(A and B) = 0.29 * 0.32

P(A and B) ≈ 0.0928

To find the probability that it snows on game day given that the Jets win, we can use Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(A|B) = (0.32 * 0.29) / 0.1987

P(A|B) ≈ 0.4643