What is the least number of colors you need to correctly color in the sections of the pictures so that no two touching sections are the same color?

Answer:

50 meters

Step-by-step explanation:

The area of a circle is [tex]\pi r^2[/tex], so assuming that [tex]\pi[/tex] is 3.14, we can make the equation [tex]3.14 \cdot r^2[/tex].

Assuming the radius is r, which is 4, we can substitute the values into the equation.

[tex]3.14 \cdot 4^2\\3.14\cdot16\\50.24[/tex]

This question is asking for the area to the nearest square meter so rounding 50.24 to the nearest square meter results in 50.

Hope this helped!

Stokes' theorem equates the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation

[tex]x^2+z^2=16[/tex]

Parameterize this circle by

[tex]\mathbf r(t)=4\cos t\,\mathbf i+4\sin t\,\mathbf k[/tex]

with [tex]0\le t\le2\pi[/tex].

The surface is oriented such that its normal vector points in the positive y direction, which corresponds to the curve having counterclockwise orientation. The parameterization we're using here already takes this into account.

Now compute the line integral of F along C :

[tex]\displaystyle\iint_S\mathrm{curl}\mathbf F(x,y,z)\cdot\mathrm d\mathbf S=\int_C\mathbf F(x,y,z)\cdot\mathrm d\mathbf r[/tex]

[tex]=\displaystyle\int_0^{2\pi}\mathbf F(4\cos t,0,4\sin t)\cdot\frac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}(4\sin t\,\mathbf i+4\cos t\,\mathbf j)\cdot(-4\sin t\,\mathbf i+4\cos t\,\mathbf k)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}-16\sin^2t\,\mathrm dt[/tex]

[tex]=-8\displaystyle\int_0^{2\pi}(1-\cos(2t))\,\mathrm dt=\boxed{-16\pi}[/tex]

Line integral of F along C is,

[tex]\rm \int \int_S curl F(x,y,z) dS = -16\pi[/tex]

Step-by-step explanation:

Given :

Hemisphere -   [tex]x^2 +y^2+z^2=16[/tex]

Calculation :

Accordind to Stoke's theorem the surface integral of the curl of F to the line integral of F along the boundary of the hemisphere. The boundary itself is a circle C (the intersection of the hemisphere with the plane y = 0) with equation

[tex]x^2+z^2=16[/tex]

then parameterize the circle,

[tex]\rm r(t) = 4 cos(t) \;\hat{i} + 4 sin(t)\;(\hat{k})[/tex]

with , [tex]0\leq t\leq 2\pi[/tex]

Line integral of F along C is,

[tex]\rm \int \int_S curl F(x,y,z) dS = \int_{C}^{} F(x,y,z) \;dr[/tex]

[tex]= \int_{0}^{2\pi} F(4cos(t),0,4sin(t)) \;\dfrac{dr}{dt}.dt[/tex]

[tex]= \int_{0}^{2\pi}(4sin(t)i+4cos(t) j).(-4sin(t)i+4cos(t)k) \;dt[/tex]

[tex]= \int_{0}^{2\pi} -16sin^2tdt[/tex]

[tex]=-8 \int_{0}^{2\pi} (1-cos(2t))dt[/tex]

[tex]= -16\pi[/tex]

For more information, refer the link given below

https://brainly.com/question/8130922?referrer=searchResults

Answer:

x^2 + 2x - 20 = 0

x^2 + 2x - 20 + 20 = 0 + 20  ( add 20 to both sides)

x^2 + 2x = 20

x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)

( x + 1 )^2 = 21

x = [tex]\sqrt{21}-1[/tex]

x = [tex]-\sqrt{21}-1[/tex]

Answer:

A)  x = –1 ± square root 21

is the answer:)

Answer:

35.25

Step-by-step explanation:

Give the data set:

23 37 49 34 35 41 40 26 32 22 38 42

We are expected to calculate the midquartile of the given data set.

22 23 26 32 34 35 37 38 40 41 42 49

First step is to find the lower quartile which comprises of

22 23 26 32 34 35

Here the Q1 is (26+32)/2 = 58/2= 29

Second step to find the upper quartile which comprises of

37 38 40 41 42 49

Here the Q3 is (40+41) /2 = 81/2 = 41.5

Then to find the midquartile which is (Q1+Q3) /2 where Q1 is 29 and Q3 is 41.5

= (29+41.5)/2

= (70.5) /2 = 35.25

Answer:

Option C

Step-by-step explanation:

The whole numbers a,b and c such that [tex]a^2+b^2 = c^2[/tex] are Pythagorean triples satisfying the Pythagorean theorem.

Answer:

C

Step-by-step explanation:

a, b, and c are side lengths of the triangle.

The three side lengths that make up a right triangle are most commonly known as Pythagorean triples.

Answer:

5050

Step-by-step explanation:

Place value of a digit is the value of digit based on its position the given number.

to determine the place value of a digit

we multiply the digit by number of 10's which is equal to number of digits in its right.

example

for a number 1234687

the place value of 3 is

we take 3 and

multiply it by number of 10' in its right

number of 10's in the right is 4

thus place value of 3 = 3*10*10*10*10 = 30000

________________________________________________

15954

place value of 5 at thousandth position = 5*10*10*10 = 5000

place value of 5 at tens position = 5*10 = 50

Thus, sum of place value of 5 in 15954 = 5000+50 = 5050

Answer:

  $0.50

Step-by-step explanation:

Let's remove common factors from the equations.

Subtracting the first equation from the second, we find the cost of an apple:

  (2x +y) -(x +y) = 1.75 -1.25

  x = 0.50

The cost of one apple is $0.50.

Answer:

The sample size is  [tex]n = 600[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample proportion is  [tex]\r p = 0.48[/tex]

     The  margin of error is  [tex]MOE = 0.04[/tex]

Given that the confidence level is 95%  the level of significance is mathematically represented as

        [tex]\alpha = 100 - 95[/tex]

        [tex]\alpha = 5 \%[/tex]

        [tex]\alpha = 0.05[/tex]

Next  we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is

                   [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The reason we are obtaining critical value of    [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because  

[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval (  [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error

Generally the margin of error is mathematically represented as

      [tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p(1- \r p )}{n} }[/tex]

substituting values

          [tex]0.04= 1.96* \sqrt{ \frac{0.48(1- 0.48 )}{n} }[/tex]

         [tex]0.02041 = \sqrt{ \frac{0.48(52 )}{n} }[/tex]

         [tex]0.02041 = \sqrt{ \frac{ 0.2496}{n} }[/tex]

          [tex]0.02041^2 = \frac{ 0.2496}{n}[/tex]

           [tex]0.0004166 = \frac{ 0.2496}{n}[/tex]

=>       [tex]n = 600[/tex]

Answer:

43 mountain climbers have not climbed either mountain.

Step-by-step explanation:

Total number of mountain climbers, i.e. n(U) = 60

Number of mountain climbers who have climbed Mt. Everest, n(E) = 10

Number of mountain climbers who have climbed Mt. Rainier, n(R) = 15

Number of mountain climbers who have climbed both, n(E [tex]\cap[/tex] R) = 15

Using the formula to find number of climbers who have climbed either of the mountains:

[tex]n(A \cup B) = n(A)+n(B)-n(A\cup B )[/tex]

[tex]\therefore n(E \cup R) = n(E)+n(R)-n(E\cup R )\\\Rightarrow n(E \cup R) = 10+15-8 = 17[/tex]

To find, who have not climbed either mountain:

[tex]n(E\cup B)'=n(U) - n(E\cap B)\\\Rightarrow n(E\cup B)'=60 - 17 = \bold{43}[/tex]

So, the answer is:

43 mountain climbers have not climbed either mountain.

Answer:

8 and 9

Step-by-step explanation:

If x is the smaller integer, and x + 1 is the larger integer, then:

(x + 1)² + 3x = 105

x² + 2x + 1 + 3x = 105

x² + 5x − 104 = 0

(x + 13) (x − 8) = 0

x = -13 or 8

Since x is positive, x = 8.  So the two integers are 8 and 9.

Answer:

In order for a sample to be considered biased, some members of the total population must have either a larger or lower chance of being included in the sample. In this case, your sample contained 17 reviews. It is biased because it was completely voluntary and customers who have a bad experience with a product or service generally tend to express more their dissatisfaction than satisfied customers show their satisfaction.

In marketing, there is a saying that unsatisfied clients talk bad about our product or service 4 times more than satisfied clients. I'm not sure if this saying is exact or not, but all marketing research point in the same direction.

This means that clients that did not get a good service or got no service at all, are more likely to post a review about the company than clients who got a good service. This is what makes the sample biased.

Answer:

Increase

Step-by-step explanation:

Precision describes the closeness of estimates from different samples, it refers to the width of the confidence interval and can aso be described as the margin of error. While the confidence level describes the accuracy.

Going for a higher confidence level will bring about a wider confidence interval, and thus lead to a less precise estimate.

Answer:$207.48

Step-by-step explanation:You need to find how much gallons he would need so you divide 2,093 by 23 and you get 91. After that you multiply it by $2.28, The price per gallon and you get 207.48.

Answer:

Excluded value = -7

Solution = [tex] x = \frac{5}{9} [/tex]

Step-by-step Explanation:

The excluded value is the value that will make the denominator 0.

Thus,

[tex] x + 7 = 0 [/tex]

Subtract 7 from both sides

[tex] x + 7- 7 = 0 - 7 [/tex]

[tex] x = -7 [/tex]

The excluded value is -7

Solution=>

[tex] \frac{2x}{x + 7} + \frac{3x + 1}{x + 7} = \frac{1}{2} [/tex]

[tex] \frac{2x + (3x + 1)}{x + 7} = \frac{1}{2} [/tex]

[tex] \frac{5x + 1}{x + 7} = \frac{1}{2} [/tex]

Cross multiply

[tex] 2(5x + 1) = 1(x + 7) [/tex]

[tex] 10x + 2 = x + 7 [/tex]

[tex] 10x - x = -2 + 7 [/tex]

[tex] 9x = 5 [/tex]

[tex] x = \frac{5}{9} [/tex]

Answer:

1 3/8

Step-by-step explanation:

Well to find the average or the mean we need to add all the numbers,

3/8 + 2/4 + 5/8 + 7/8 + 1 1/8 + 1 5/8 + 1 7/8 + 4

= 11

Then we divide t by the number of numbers in the set.

11 ÷ 8 = 1 3/8

Thus,

the average in the set is 1 3/8.

Hope this helps :)

Answer:

486 feet

Step-by-step explanation:

h = -16t² + 550

h = -16(2)² + 550

h = 486

Answer:

The standard Deviation would increase

Step-by-step explanation:

Is this advantages?

Answer:

-5+5i

Step-by-step explanation:

(2-i)(-3+i)=-6+3i+2i-i²   (i²=-1)

-6+3i+2i-(-1)

-6+3i+2i+1=-5+5i

-5+5i

Answer:

a=6, b=5.5

Step-by-step explanation:

By looking at the sides of the triangles it can easily be seen that some of the sides match up. Side b is similar to the side of 11 and same with side a and the side of 3. Since one side is 16 and the other side on the smaller triangle is 8, the bigger triangle is twice as large than the smaller one. So 3 x 2 = 6 and 11 / 2 = 5.5

Answer:

b. [tex]g(x)=f(x)-5[/tex]

Step-by-step explanation:

You have that the function f(x) has its y-intercept for y=3.

Furthermore, you have that g(x) is a transformation of f(x) with y-intercept for y=-2.

In this case you have that f(x) has been translated vertically downward.

The general way to translate a function vertically in the coordinate system is:

[tex]g(x)=f(x)+a[/tex]      (1)

being a positive or negative.

if g(x) has its y-intercept for y=-2, and the y-intercept of f(x) is for y=3, then the value of a in the equation (1) must be a = -5, which is the difference between both y-intercepts, in fact:

a = -2 -3 = -5

Then, the answer is:

b. [tex]g(x)=f(x)-5[/tex]

Answer: g(x) = f(x) - 5

Step-by-step explanation:

just took this

Answer:

8

Step-by-step explanation:

Answer: x = 1

Step-by-step explanation:

x = 1 provides one solution for any linear equation, as it is a straight vertical line.

Hope it helps <3

Answer:

x=2

Step-by-step explanation:

Our equation is y=2x+4

the line goes through (2,0) and (0,4)

This equation has one solution for y=0

there are millions of similar equations that has one solution like:

x = 2

Answer:

1/30

Step-by-step explanation:

The probability of getting ”E” is 1/6.

There is only 1 “E” out of 6 letters.

There is no replacement.

There are now 5 letters without “E”.

”A”, “B”, “C”, “D”, “F”

The probability of getting ”B” is 1/5.

There is only 1 “B” out of 5 letters.

⇒ 1/6 × 1/5

⇒ 1/30

It's adding 3 and subtracting 2 every time.

This means the next two terms would be +3 and -2 since the last one was -2.

The next term = 4+3=7

The next next term = 7-2=5

Answer:

Please see the attached picture.

Hope it helps...

Best regards!!

Answer:

The answer is

Step-by-step explanation:

From the above question the prism in the picture is a cube since all it's sides are equal

So the formula for finding the volume of a cube is

V = l³

where l is the length of one side

From the question l = 12″

Volume of the prism = 12³

= 1728″

Hope this helps you

Answer:

B = (A - 6) / 10

Step-by-step explanation:

This problem has 2 variables and 1 equation so it is not trivial to solve with confidence the value of B; however, we can solve for B in terms of A.  With that being said, let's start.

If A divided by B = 10:

A/B = 10

10 remainder of 6

Could also be written as 10 & 6/B since B is the divisor.  Rewrite this, you can get the equation:

A/B = (10B + 6) / B

A = 10B + 6

A - 6 = 10B

B = (A - 6) / 10

Thus, you have solve B in terms of A.

Cheers.

Answer:

Step-by-step explanation:

Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.

Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7

Mean = 76.2/7

Mean = 10.9

The mean score is 10.9 to 1 decimal place.

Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.

b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;

9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7

After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.

The median represents the center

c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.

The mode(s) does (do) not represent the center because it (one) is the largest data value.

Answer:

The variables that can be used in the analysis are:

Dependent variable: person's height (Height)

Independent variable: person's dad's height (DadsHt)

Step-by-step explanation:

A linear regression model is used to predict the value of the dependent variable based upon the value of the independent variable.

The general form of a linear regression model is:

[tex]y=a+bx[/tex]

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variables in the model are changed.

The dependent variables are also known as response variables.

Independent variables are the variables that are being altered to see a proportionate change in the dependent variable. In a regression model there can be one or more than one independent variables.

The independent variables are also known as the predictor variables.

In this vase we need to form a regression model such that, a person's dad's height can be used to predict how short or tall the person will be.

That is, the dependent variable is the person's height and the independent variable is the person's dad's height.

The variables that can be used in the analysis are:

Dependent variable: person's height (Height)

Independent variable: person's dad's height (DadsHt)

Answer:

$60,000

Step-by-step explanation:

$2500*6=15000

45000+15000=60000

Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9

Remember, we flip the sign of the inequality by multiplying / dividing by a negative number.

Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9