Randomly pick 5 points from a sphere. Show that you can always find a closed semi-sphere (half a sphere and boundary) that contains 4 points.

Answer:

≈ 5.36

Step-by-step explanation:

If we have a triangle in which the angle measure of it being broken down are the same, that means that the legs in which the angle measures are the same will have the same length.

If we already know that DE ≈ 9.28, then we can subtract this from 20 and divide by two to get BD, which is equal to EC.

[tex]20-9.28=10.72\\10.72\div2=5.36[/tex]

However, I'm not 100% sure about this answer.

Hope this helped (and I hope I'm right)

Answer:

5.3589 or 5.36

Step-by-step explanation:

tan (15) = x / 20

x = 40 - 34.64

x = 5.36

Answer:

77 inches by 161 inches

Step-by-step explanation:

This is because you need to multiply 22 by 3.5(3 1/2) and the answer you get is 77 then you multiply 46 by 3 1/2 and the answer you get is 161.

So the dimensions of the new document is 77 inches by 161 inches.

Answer:

x=10  or x=-4

Step-by-step explanation:

|x-3|=7

There are two solutions, one positive and one negative

x-3 = 7   and x-3 = -7

Add 3 to all sides

x-3+3 = 7+3           x-3+3 = -7+3

x = 10                    x = -4

Well, if we are taking the absolute value, of |x - 3| = 7, then you have a total of two cases. 7 can be either positive or negitive.

Knowing this, we can write out our two cases as:

|x - 3| = 7, or

|x - 3| = -7

Using these two equations, we can solve the equations for our values of x:

First Case:

|x - 3| = 7

x - 3 = 7

x = 10

Second Case:

|x - 3| = -7

x - 3 = -7

x = -4

So, our two cases show us that x can equal -4, or 10.

Answer:

the slope is 5

Step-by-step explanation:

Solve for y

20x -4y = 40

Subtract 20x from each side

20x-20x -4y = -20x +40

-4y = -20x+40

Divide each side by -4

-4y/-4 = -20x/-4 +40/-4

y = 5x -10

This is in slope intercept form  y = mx+b where m is the slope and b is the y intercept

The slope is 5

Solve for y:

20x - 4y = 40

Subtract 20x to both sides

-4y = 40 - 20x

Divide -4 to everything

y = -10 + 5x

Therefore, the slope is 5

Best of Luck!

Answer:

Step-by-step explanation:

Enter data into the regression calculator.

Determine the regression equation.

Substitute the correct value for x or y into the equation.

Simplify to find the value of the other variable.

Answer:

the answer is c. One real number solution

Step-by-step explanation:

Hey There!!

I think the best answer will be is (D) 2.

Because, The discriminant is the expression b2 - 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. Based upon the sign of the expression, you can determine how many real number solutions the quadratic equation has. If you get a positive number, the quadratic will have two unique solutions. Im not a 100% sure this right... Hope This helps!! By ~♡Itsbrazts~♡

==============================================

Explanation:

Any regular hexagon is really the combination of six identical (aka congruent) equilateral triangles glued together. If we can find the area of one triangle, then we multiply by 6 to get our final answer.

The apothem is the height of the equilateral triangle with the triangular base being the side length of the hexagon.

area of triangle = (1/2)*base*height

area of triangle = 0.5*(hexagon side length)*(apothem)

area of triangle = 0.5*19*16.5

area of triangle = 156.75

This is the area of one equilateral triangle. Having 6 triangles leads to a total area of 6*156.75 = 940.5 square inches

The area of a regular hexagon with an apothem of 16.5 inches and a side of 19 inches is Area of hexagon = 1/2(length of apothem)(perimeter of the hexagon) = 940.5 inches. (Option-B)

Apothem is a perpendicular line from the center of the regular polygon to one of its sides.

Area = 1/2 x (length of apothem) x (perimeter of hexagon)

   • Given,  

     apothem = 16.5 inches and length of a side =19 inches

   • Perimeter = 6 x (side of a hexagon)

                       = 6 x (19)

                       = 114 inches

   • Hence,

      Area = 1/2 x (16.5) x (114) = 940.5 inches(rounded to the nearest tenth)

Know more about Regular hexagon :

https://brainly.com/question/10209400?referrer=searchResults

#SPJ2

Answer:

To justify a solution, students will need to be able to use appropriate mathematical language to give reasons for the particular approach used to solve a problem. Any time that a student produces a 'solution' in an attempt to solve a problem, that 'solution' needs to be justified.

Step-by-step explanation:

Answer:

[tex] \boxed{\sf d = -1 \ \ \ or \ \ \ d = -7} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: d \: over \: the \: real \: numbers: \\ \sf \implies {(d + 4)}^{2} = 9 \\ \\ \sf Take \: the \: square \: root \: of \: both \: sides: \\ \sf \implies \sqrt{ {(d + 4)}^{2} } = \sqrt{9} \\ \\ \sf 9 = {3}^{2} : \\ \sf \implies \sqrt{ {(d + 4)}^{2} } = \sqrt{ {(3)}^{2} } \\ \\ \sf \implies d + 4 = \pm 3 \\ \\ \sf \implies d + 4 = 3 \: \: \: \: \: or \: \: \: \: \: d + 4 = - 3 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies d + (4 - 4)= 3 - 4 \: \: \: \: \: or \: \: \: \: \: d + (4 - 4) = - 3 - 4 \\ \\ \sf \implies d = - 1 \: \: \: \: \: or \: \: \: \: \: d = - 7[/tex]

Answer:

[tex]\huge\boxed{Perimeter = 34\ units}[/tex]

Step-by-step explanation:

DE = 10 units

GF = 10 units

DG = 7 units

EF = 7 units

Perimeter of rectangle = Sum of all sides

P = DE + GF + DG + EF

P = 10 + 10 + 7 + 7

Perimeter = 34 units

Answer:

D) 34 units

Step-by-step explanation:

Coordinates:

D: (-5,4)

E: (5,4)

F: (5, -3)

G: (-5,-3)

Distance between points D and E = Distance between points F and G = 10

Distance between points E and F = Distance between points G and D = 7

Formula for perimeter of your rectangle:

2(x) + 2(y) =

2(10) + 2(7) =

20 + 14 = 34 units

That's your answer!

Hope that helps and maybe earns a brainliest!

Have a terrific day! >   <

                                   U

BAE + HEG = 180°

124 + 2x+6 = 180°

2x+6 = 56

x = 50/2

x = 25°

Reason:

Given

HEG = EAD since they are corresponding angles

EAD + EAB = 180° since they are supplementary angles.

xx

Answer:

32 miles/4 hours.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The first one is not. Think money. Would you rather be 1 dollar in the hole or 6 dollars in the hole? b = - 1. It is larger than - 6.

The third one is not correct either. -c = - 5

- b = 1

1 is larger than -5

The answer is the middle one

-b becomes 1 which is greater than 0.

Answer:

(7, -5.5)

Step-by-step explanation:

is seen below on this graph (7, -5.5) shows x = 7 and y = -5.5

Answer:

The car would be worth 1200.

Step-by-step explanation:

  Okay, the way to solve this type of question is quite simple,

you would start with the amount is lost per year being $325 a year, then multiply that by the 4 years grandpa waited and then subtract the overall amount lost in worth of the car from the original price and you got your answer.

The math: 2500-(325*4)=1200

16.7%

There are 6 ways we can roll doubles out of a possible 36 rolls (6 x 6), for a probability of 6/36, or 1/6, on any roll of two fair dice. So you have a 16.7% probability of rolling doubles with 2 fair six-sided dice.

Answer:

The answer is 16.7%

Step-by-step explanation:

There are 6 ways we can roll doubles out of a possible 36 rolls (6 x 6), for a probability of 6/36, or 1/6, on any roll of two fair dice. So you have a 16.7% probability of rolling doubles with 2 fair six-sided dice. hope this helped

Answer:

100 times

Step-by-step explanation:

5•1000000 has 2 more zeros than 5•10000 so that means the first number is 100 times larger than the second number! hope this helps and please mark as brainiest

Answer:

Option (A),

    _____________

-2 |      5     9     -6

Step-by-step explanation:

Division is an algorithm that is used to find the factors of a number. One method of dividing polynomials is through a process of Synthetic division. Synthetic division for polynomials requires that the divisor (an expression that one uses to divide the polynomial) is linear. One will then set the divisor equal to zero and solve for the unknown such as the following,

x + 2 = 0

x = -2

Under the division sign, one will put all of the coefficients of the divided (the number that will be divided) in order of degree. The coefficient of the term with the highest degree is on the leftmost side, the lowest degree is the rightmost. Therefore the problem would appear as the following,

[tex]\frac{5x^2+9x-6}{x+2}[/tex]

= ([tex]5x^2+9x-6[/tex]) ÷ ([tex]x+2[/tex])

    _____________

-2 |      5     9     -6

Therefore, the correct choice is option (A).

*the table being referred to is attached below

Answer:

The table does not show a proportional relationship between variable g and h.

Step-by-step explanation:

For a proportional relationship to exist between two variables, there must be a constant, of which serves like a unit rate, when comparing two variables.

Thus, in the table attached below, there is no obvious constant of proportionality between variable g and variable h.

Thus, [tex] \frac{9}{3} [/tex] ≠ [tex] \frac{36}{6} [/tex] ≠ [tex] \frac{81}{9} [/tex]

Answer:

x = 180 - [(180 - 3x) + (180 - 2x)]

Step-by-step explanation:

Start off by finding the angles of the triangle

Angle F = 180 - 3x

The angle across from I (which I will call I) = 180 - 2x

Angle G = 180 - (F + I)

Now that we know what G is, we know what x is because the Alternate Exterior Angles Theorem states that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent. So pretty much X = G

Therefore x =  180 - (F + I) or otherwise said as:

x = 180 - [(180 - 3x) + (180 - 2x)]

I hope this is helpful :)

Answer:

B. 13.8

Step-by-step explanation:

The five-number summary consists of five items which is usually displayed on a box plot, and can be represented in ascending order.

The five-number summary given: 3.5, 12, 19.1, 25.8, 31.8, represents the following in ascending order:

1. The minimum value = 3.5

2. First quartile (Q1) = 12

3. The median = 19.1

4. Third quartile (Q3) = 25.8

5. The maximum value = 31.8

The interquartile range = Q3 - Q1

Therefore, the interquartile range of the data = 25.8 - 12 = 13.8

Answer:

Part A:

The ratios in the table are equivalent.

The two quantities in this table represent a proportional relationship.

The graph of the relationship would be straight line through origin

Step-by-step explanation:

Part A

The ratios in the table are equivalent.

Length: Cost

6 : 42   = 1 : 7

15: 105 = 1: 7

24 : 168 = 1:7

30 : 210 = 1 : 7

The two quantities in this table represent a proportional relationship.

If we take length = x, then cost =7x

When length = 6 ,  Cost = 7 *6 = 42

When length = 15 ,  Cost = 7 * 15 =  105

When length = 24 ,  Cost = 7 *24 = 168

The graph of the relationship would be straight line through origin

y = 7x

y -> cost and x -> length

When x = 0 , y= 0. so, this graph go through the origin

Part B:

$ 7 per foot

Step-by-step explanation:

x = -2 is a zero, so x + 2 is a factor of P(x).

Use grouping to factor.

P(x) = 2x³ + x² − 11x − 10

P(x) = 2x³ + 4x² − 3x² − 11x − 10

P(x) = 2x² (x + 2) − (3x² + 11x + 10)

P(x) = 2x² (x + 2) − (x + 2) (3x + 5)

P(x) = (x + 2) (2x² − (3x + 5))

P(x) = (x + 2) (2x² − 3x − 5)

P(x) = (x + 2) (x + 1) (2x − 5)

The other zeros are x = -1 and x = 5/2.

Hey there! I'm happy to help!

Let's look at our diameters.

[tex]1*10^2^1\\5*10^2^2[/tex]

We want to see how many times greater the diameter of the IC 1101 is than the Milky Way. So, we will divide it's diameter by the diameter of the Milky Way.

[tex]\frac{5*10^2^2}{1*10^2^1} \\[/tex]

We divide the numbers without exponents, giving us 5. Then, we divide the 10s with exponents. When dividing exponents, you subtract the numbers in the exponent to get your result. For example, x³÷x²=x

[tex]\frac{5*10^2^2}{1*10^2^1} = 5*10=50[/tex]

Therefore, your answer is 50.

Have a wonderful day! :D

use [tex] a^2-b^2=(a+b)(a-b)[/tex]

to get [tex] (\cos^3A-\sin^3A)(\cos^3A+\sin^3A)[/tex]

then use [tex] a^3+b^3=(a+b)(a^2+b^2-ab)[/tex]

and [tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex]

also, [tex] \sin^2\theta+\cos^2\theta=1[/tex]

to get [tex](\cos A-\sin A)(1+\sin A\cos A)(\cos A+ \sin A)(1-\sin A\cos A)[/tex]

then again use the first identity In both pairs, i.e.

[tex](\cos A-\sin A)(\cos A+ \sin A) \cdot (1+\sin A\cos A)(1-\sin A\cos A)[/tex]

to get [tex] \cos 2A (1-\sin^2A\cos^2A)[/tex]

multiply and divide by 4 to get the RHS.

because, [tex] \sin(2A)= 2\sin A \cos A[/tex]

squaring both sides, [tex] \sin^2 (2A)=4\sin^2A\cos^2A[/tex]

Answer:

they take the same form

Step-by-step explanation:

factor (1 - 1/4 sin ^2 (2A) )  (cos ^ 2 (A) -sin ^2(A))

= ( -sin 2A/ 2)  + 1 ) (sin (2A)/ 2) -1

= - (-1 + )  (sin 2A/2)  (1 +) (sin 2A/2) ( cos (A) + sin (A) (cos (A)- sin (A))

= (sin (2A) +sin 2) (sin (2A) -2)/4 = cos ^2(A) = (sin ^2(A)+cos (A) sin (A)) cos ^2(A) +s)

Answer:

A. 1010 FT^3

Step-by-step explanation:

19 x 14.5 x 5 = 1377.5

you need to subtract now, so the only option would be A

Answer:

[tex]1,010 ft^{3}[/tex]

Step-by-step explanation:

You can break the figure into 2 sections; one with the dimensions of 4, 5 and 7; the other with dimensions of 14.5, 5, and 12.

Multiply the first three dimensions (4, 5 and 7) to get 140 ft cubed.

Multiply the last three dimensions (14.5, 5, and 12) to get 870 ft cubed.

Now, just add both volumes together to get 1,010 ft cubed!

Hope that helps and maybe earns a brainliest!

Have a great day! :)