Given f(x) = x^2 - 10x + 22, what is the range of f?

It takes 11 binary digits to represent the decimal number 2013. Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point.

Therefore, the correct option is C) 11

The complete question is:

How many binary digits does it take to represent the decimal number 2013?

a) 16

b) 8

c) 11

d) 2013

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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

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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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

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!

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]

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 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 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.

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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To evaluate the given line integral, you need to parameterize the curve composed of two segments. Then, you solve the integrals along the two separate segments and take the sum.

To evaluate the line integral where the curve c consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0) for the function (x + 9y) dx + x² dy, we need to parameterize the curve and solve the integral.

First, we parametrize the line segments. For the segment from (0, 0) to (9, 1), we have x = 9t and y = t for t in [0, 1]. For the segment from (9, 1) to (10, 0) let x = 9 + s and y = 1 - s for s in [0, 1].

Then, we integrate along the first and second segments separately with respect to t. For the first segment, the integral is ∫(9t + 9t) d(9t) + ∫(81t²) dt = ∫18t dt + ∫81t² dt. For the second segment, the integral is ∫(9 + s + 9(1 - s)) ds + ∫(81 + 2 * 9 * s + s²) d(1 - s) = ∫ds + ∫s² ds.

We then evaluate these integrals over the respective bounds, sum them up and that gives the line integral along the path described.

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The polynomial equation will be x³ +12x² +36x+32 =0

The roots of a polynomial equation is the value at which it will satisfy the quadratic equation , i.e. function (x) = 0 at the root .

It is given that x = -8 is a single root and

x = -2 is double root

x+8 = 0

(x+2 )(x+2)=0   (double root)

The polynomial equation will be

(x+8)(x+2 )(x+2 )=0

(x+8)( x² +4+4x) = 0

x³ +4x+4x²+8x²+32+32x = 0

x³ +12x² +36x+32 =0

Therefore the polynomial equation will be x³ +12x² +36x+32 =0

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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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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

The probability of selecting at random a score less than or equal to 370 is approximately 0.3821.

To find the probability of selecting at random a score less than or equal to 370 from a normal distribution with a mean [tex](\( \mu \))[/tex] of 400 and a standard deviation [tex](\( s \))[/tex] of 100, we can use the z-score formula and the standard normal distribution table.

The z-score formula is given by:

[tex]\[ z = \frac{x - \mu}{s} \][/tex]

Where:

- x is the value of the random variable (370 in this case)

- [tex]\( \mu \)[/tex] is the mean (400)

- s is the standard deviation (100)

Substituting the given values into the formula:

[tex]\[ z = \frac{370 - 400}{100} = -0.3 \][/tex]

Now, we look up the probability corresponding to z = -0.3 in the standard normal distribution table. The probability of selecting a score less than or equal to 370 is the cumulative probability up to z = -0.3.

From the standard normal distribution table, the cumulative probability corresponding to z = -0.3 is approximately 0.3821.

Therefore, the probability of selecting at random a score less than or equal to 370 is approximately 0.3821.

The probability that a proofreader who catches 70% of the word errors misses exactly 7 out of 10 will be 0.3504.

It should be noted that this is a binomial distribution.

From the information given, the human proofreaders catch 70% of word errors and a student was asked to proofread an essay in which you have deliberately made 10 word errors.

Here, n = 10

p = 0.3,

q = 1 - 0.3 = 0.7.

The probability will be:

= 1 - (10C0 × 0.3ⁿ × 0.7^10 + 10C1 × 0.3 × 0.7^9 + 10C2 × 0.3² × 0.7^8 + 10C3 × 0.3³ × 0.7^7)

= 1 - 0.6496

= 0.3504

In conclusion, the probability is 0.3504.

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