Find X and Y in the figure

Answer:

A.) 0.7647 b.) 13/ 16 C.) 0.9412 D.) 8.743 * 10^-10

Step-by-step explanation:

A)

Number of cards per suit = 13

Nunber of suits = 4

Probability = required outcome / Total possible outcomes

P(1) = probability of picking a card from a certain suit

P(1) = 13 / 52

Hence, probability that 2nd card will be from a suit different from the first :

Total possible outcomes = (52 - 1) = 51

Required outcomes = (13 * 3) = 39

= 39 / 51

= 0.7647

B.)

First toss being head :

Required outcome = H = 1

Total possible outcomes = T or H = 2

P(H) = 1/ 2

For 5 tosses

Total possible outcomes = 2^n = 2^5 = 32

Exactly 2 heads = 10

P(exactly 2 heads) = 10/32 = 5/16

1/2 + 5/16 = (8 + 5) / 16 = 13/16

c)

1 - P(both top and bottom are hearts)

Number of hearts = 13 ; number of cards = 52

P(both are hearts) = 13/52 * 12/51 = 0.05882

1 - 0.05882

= 0.94117

= 0.9412

d)

Either all marbles are red OR all marbles are green OR all marbles are blue

Total number of marbles = (20 + 20 + 20) = 60

Probability that all 15 marbles are of a certain color :

(20/60 * 19/59 * 18/58 * 17/57 * 16/56 * 15/55 * 14/54 * 13/53 * 12/52 * 11/51 * 10/50 * 9/49 * 8/48 * 7/47 * 6/46)

(2.9146E−10) + (2.9146E−10) + (2.9146E−10)

= 8.7438E−10

= 8.743 * 10^-10

Answer:

Step-by-step explanation:

25%

80%

60%

100%

25%

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

The mean of the data-set is given as follows:

E(X) = 1.8.

The standard deviation of the data-set is given as follows:

S(X) = 1.

The mean is given by the sum of all the outcomes multiplied by their respective probabilities, hence:

E(X) = 0 x 0.04 + 1 x 0.43 + 2 x 0.29 + 3 x 0.18 + 4 x 0.05 + 5 x 0.01

E(X) = 1.8.

The standard deviation is given by the square root of the sum of the difference squared between each outcome and the mean, multiplied by their respective probabilities, hence:

S(X) = sqrt[(0 - 1.8)² x 0.04 + (1 - 1.8)² x 0.43 + (2 - 1.8)² x 0.29 + (3 - 1.8)² x 0.18 + (4 - 1.8)² x 0.05 + (5 - 1.8)² x 0.01]

S(X) = 1.

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Answer:

30

Step-by-step explanation:

since the width is 20, there are 2 sides, so multiply by 2 and it's 40. Subtract 40 from 100 and you get 60. 60 is both lengths combined, so divide by 2 and you have 30 as your length. :)

Number of countries would west Virginia be expected to have is  18 countries

The number of campgrounds that North Dakota has = 465 campgrounds

The number of countries = 12 countries

The number of campgrounds that West Virginia has = 711 campgrounds

Given that the North Dakota was proportional to West Virginia in the number of campgrounds to counties.

The proportion will be

465 / 12 = 711 / x

Divide the terms

38.75 = 711 / x

x = 711 / 38.75

Divide the terms

x = 18.4

x ≈ 18 countries

Hence, number of countries would west Virginia be expected to have is  18 countries

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Answer:

12.5 %

Step-by-step explanation:

There are 8 total sections, and only one of them is yellow. So if we spun it eight times, the possibility of getting yellow is one time. As a result, 1/8 is 12.5%

Answer: C

Step-by-step explanation:

The answer is the third option, None

Because the fact that angle 2 is equal to angle 3 does not imply that AB is parallel to DC ot that AD is parallel to BC

Answer:

  see attached

Step-by-step explanation:

The attachment shows each of the rotated figures. In order, the original is red, the first 90° CW rotation is orange, the second is green, and the last one is blue.

__

Additional comment

You can achieve the same effect by rotating your grid paper 90° CCW and drawing the figure again in its original position to the left of point A.

The volume of the composite solid is 980.2 cm³.

A composite solid is a solid made of two or more well-defined solid objects.

To calculate the volume of the composite solid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

90%

Step-by-step explanation:

present students:40-4=36

36/40*100

=90%

Answer:

90% are present

Step-by-step explanation:

40-4=36

36 are present

36/40 = x/100

36x100=3600

3600/40=90

answer: 90/100 = 90%

The amount of dry ingredients used in the cake recipe is approximately 7 cups.

We have,

3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.

Now, first convert all quantity in same unit.

3 ½ cups of flour

= 3 cups + 0.5 cups

= 3 cups and 8 ounces.

and, 2 ⅔ cups of sugar

= 2 cups + 0.67 cups,

= 2 cups and 10.72 ounces.

and, 1 ¾ cups of cocoa

=1 cup + 0.75 cups

= 1 cup and 12 ounces.

So, the total amount

= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

= 7 cups

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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y=2/3x-4 is the equation of the line where 2/3 is the slope.

We have to find the equation of line which is passing through points (0, -4) and (3, -2).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁.

Slope = -2+4/3-0

=2/3

Now let us find the y intercept.

-4=2/3(0)+b

b=-4

The equation of line is y=2/3x-4.

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Answer:

3/-2

Step-by-step explanation:

bc the other ones don't make sense  To get an equivalent fraction all we have do to is multiply it by 2...

The number of hours that Marisol will be 113 miles from home is 5.5 hours.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Since Marisol is 415.5 miles from home. She drives an average of 55 miles per hour on her trip home.

Let the number ot hours be h.

The number of hours that Marisol will be 113 miles from home will be:

415.5 - 55h = 113

55h = 415.5 - 113

55h = 302.5

Divide

h = 5.5 hours

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Step-by-step explanation:

154 is my answer thank you

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

\(\cfrac{a}{18}=\cfrac{32}{a}\implies a^2=(32)(18)\implies a=\sqrt{(32)(18)}\implies a=24 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{b}{50}=\cfrac{32}{b}\implies b^2=(32)(50)\implies b=\sqrt{(32)(50)}\implies b=40\)

Answer:

1st option (top left)

Step-by-step explanation:

1st option represents a linear function

y = x/2

Answered by GAUTHMATH

Answer:

answer is sister's.

Step-by-step explanation:

sisters mean more than one sister.

sisterses isn't a word.

sisters' also isn't a word.

sister's is a word and it means that she has possession of something or that she owns something.

The answer as a simplified fraction in the box is -1/6

Given the expression

[3-|-5/6 -2(-1/3)|] ÷ (-17)

Using PEDMAS

P is for parenthesis

[3-|-5/6+2/3)|] ÷ (-17)

[3-|2/3 - 5/6)|] ÷ (-17)

[3-|(4-5)/6)|] ÷ (-17)

[3-|-1/6)|] ÷ (-17)

Since the modulus of a negative number is equal to a positive number, the result will give:

[3 - 1/6] ÷ (-17)

[(18-1)/6] ÷ (-17)

17/6  ÷ (-17)

Next is to carry out the division operation

17/6  × (-1/17)

= -1/6

Hence, The answer as a simplified fraction in the box is -1/6

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Answer:

    \(\textsf{Choice A } \quad y = \dfrac{5}{3}x + 1\)

Step-by-step explanation:

Slope intercept form of a line equation is

y = mx + b

where

m = slope

b = y-intercept

A perpendicular line to y = mx + b will have a slope of -1/m

Let's first find the equation for line z in slope-intercept form
Slope m for a line  = (y2- y1)/(x2 - x1) where x1, y1 and x2, y2 are two points on the line

Slope of line z is
\(m = \dfrac { 2 - (-1) }{-2 - 3} = \dfrac{3}{-5} = - \dfrac{3}{5}\)

So line z will have an equation of the form
\(y = -\dfrac{3}{5}x + b\)

We know that a line perpendicular to this line will have a slope of
\(- \dfrac{1}{-\dfrac{3}{5}} = \dfrac{5}{3}\)

So the equation of the perpendicular line is
\(y = \dfrac{5}{3}x + b\)

Only one of the 4 choices, name choice A has this slope of 5/3

Therefore the correct answer choice is A

There is no need to compute b, the y intercept but if you wanted to, this is how you would do it:

The perpendicular line passes through (3, 6). This means when x = 3, y =6

Substitute these values of x, y into the equation for the perpendicular line and solve for b

\(y = \dfrac{5}{3}x + b\\\\\text{When x = 3, y = 6}:\\\\6 = \dfrac{5}{3} \cdot 3 + b\\\\6 = 5 + b\\\\b = 6 - 5 = 1\\\\\text{So, the equation of the perpendicular line is }\\y = \dfrac{5}{3}x + 1\)

This corresponds to Choice A

Answer:

216 degrees

Step-by-step explanation:

2016/360= 5.6   drop the 5

  .6 x 360 = 216 °

Answer:

2 sqrt(13)

Step-by-step explanation:

We can use the Pythagorean theorem

The x value between A and B is  4 units and the y value is  6 units

The distance is

d = sqrt( x^2 + y^2)

   = sqrt( 4^2 + 6^2)

   = sqrt( 16+36)

  = sqrt(52)

  = sqrt(4*13)

 = 2 sqrt(13)

Answer:

146 degrees

Step-by-step explanation:

The sum of internal angles of any quadrilateral is always 360 degrees. This means x is 360 - (107 + 49 + 58), which is 360 - 214, which equals 146.

The expression is factored to give 2x²y²(3y - 2xy). Option C

We need to know that index forms are described as mathematical forms that are used for the representation of numbers or figures too large or small.

Some rules of index forms are;

From the information given, we have that;

6x²y⁵ - 4x³y³

Factorize the index forms by determining the common factor and exponents, then, we have;

2x²y²(3y - 2xy)

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Answer:

a. \(3^{7}\)

b. \(2^{-8}\)

c. \(3^{-8}\)

Step-by-step explanation:

It's pretty simple. Just keep dividing till you get your answer (which is above)