lisa had 1,750 stamps. Minah had 480 stamps fewer stamps than lisa. Lisa gave some stamps to Minah. Now, Minah has 3 times as many stamps as lisa. How many stamps did minah have at first?

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

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

bar is 10 1/4" so center would be  10 1/4 / 2 = 5 1/8"

door is 26 1/3" so center would be 26 1/3 / 2 =13 1/6

13 1/6 - 5 1/8 = 8 1/24 inches from the edge

1/3 + 1/2  = 2/6 + 3/6 = 5/6

5/6 - 1/5 = 25/30 - 6/30 = 19/30 pounds left

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.

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

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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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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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

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 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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The two numbers whose difference is 4 will be +2 and -2. The two have the minimum product is -4.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that, there are two numbers whose difference is 4​ and it must have a minimum product.

We have to apply arithmetic operation operations in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Suppose one number is x and the other x−4.

The minimum product is,

=x(x−4)

=x²−4x

Differentiate both sides to obtain minimum value,

=2x-4

2x=4

x=2

The other number is,

=x−4

=2-4

=-2

Thus, the two numbers whose difference is 4 will be +2 and -2. The two have the minimum product is -4.

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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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Answer: (3,2)

Step-by-step explanation:

From the given picture , it is given that the point R = (-3,2)

We know that the rule of reflection across y axis is :

[tex](x,y)\rightarrow\ (-x,y)[/tex] i.e.the polarity of x coorinate changes.

Therefore, the reflection image of R across the y-axis will be :-

[tex](-3,2)\rightarrow\ (3,2)[/tex]

Hence, the reflection image of R across the y-axis =(3,2)