Let w(s,t)=f(u(s,t),v(s,t)) where u(1,0)=−6,∂u∂s(1,0)=5,∂u∂1(1,0)=7 v(1,0)=−8,∂v∂s(1,0)=−8,∂v∂t(1,0)=6 ∂f∂u(−6,−8)=−1,∂f∂v(−6,−8)=2

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 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 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 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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Answer: It means the high temperature of Sunday is 3 degrees warmer than the high temperature of Tuesday.

Step-by-step explanation:

Let the temperature on Sunday be 'x'.

So, Temperature of Monday would be

[tex]x+5[/tex]

Temperature of Tuesday would be

[tex]x+5-8\\=x-3[/tex]

So, Comparing the  Sunday's high temperature to Tuesday's temperature.

[tex]x-3[/tex]

It means the high temperature of Sunday is 3 degrees warmer than the high temperature of Tuesday.

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

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)

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 answer is 5 because 15/3=5