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2 years ago

Does choosing a blue marble represent the complement event of choosing a red marble

2 answers:

7 0

Answer:The complementary event for choosing a red marble is choosing a blue or purple. The total number of marbles is 5. The probability of choosing a red marble is 1/5, and the complement would be 4/5. That is not the same as choosing a blue marble.

Step-by-step explanation:

Hatshy [7]2 years ago

3 0

No it is exactly the color.

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Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key

Irina-Kira [14]

Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

$\angle 9=180-59-59=62$ , by interior angles theorem.

$\angle 8 =62$ , by vertical angles theorem.

$\angle 10 = 180- \angle 9=180-62=118\°$ , by supplementary angles.

$\angle 7 = 118\°$ , by vertical angles theorem.

$\angle 5=90-59=31$ , by complementary angles.

$\angle 2 = \angle 5 = 31\°$ , by alternate interior angles.

$\angle 1 = 59\°$ , by complementary angles.

$m\angle BCD=90\°$ , because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

$m\angle ABD = 6\° = m\angle BDC$ , by alternate interior angles and by given. $m\angle CBE=90-6=84$ , by complementary angles.

$m\angle ADE=90-6=84$ , by complementary angles.

$m\angle AEB=180-6-6=168\°$ , by interior angles theorem.

$m\angle DEA=180-168=12$ , by supplementary angles.

$m\angle JMK=180-126=54$ , by supplementary angles.

$m\angle JKH=\frac{180-54}{2}=\frac{126}{2}=63$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle HLK=90\°$ , by definition of rectangle.

$m\angle HJL=\frac{180-126}{2}=27$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle LHK=90-27=63$ , by complementary angles.

$m\angle = JLK= m\angle HJL=27$ , by alternate interior angles.

The figure is a rectangle, which means its opposite sides are equal, so

$WZ=XY\\7x-6=3x+14\\7x-3x=14+6\\4x=20\\x=\frac{20}{4}\\ x=5$

Then, we replace this value in the expression of side WZ

$WZ=7x-6=7(5)-6=35-6=29$

Therefore, side WZ is 29 units long.

We know that the diagonals of a rectangle are congruent, so

$SQ=PR\\11x-26=5x+28\\11x-5x=28+26\\6x=54\\x=\frac{54}{6}\\ x=9$

Then,

$PR=5x+28=5(9)+28=45+28=73$

Therefore, side PR is 73 units long.

3 0

2 years ago

Simplify the radical expression

LenKa [72]

<span>To multiply two radicals together, we can simply multiply both the values inside the radicals together and put that in a radical.
So for 5*sqrt(45b) * 6*sqrt(48b), we get 30*sqrt(45b*48b) = 30*sqrt(2160b^2). This value can be simplified further by taking out b^2 and 12^2 from the radical giving us the answer 360b*sqrt(15).</span>

3 0

2 years ago

Read 2 more answers

the diameter of a football is five times the diameter of a cricket ball ratio of surface area of football and cricket ball is

LenKa [72]

Answer:

25 : 1

Step-by-step explanation:

The diameter of the football is 5 times the diameter of the cricket ball. This means that the radius of the football is also 5 times the radius of the cricket ball.

Let the radius of the football be R.

Let the radius of the cricket ball be r.

This implies that:

R = 5r

Both balls are spherical.

The surface area of the cricket ball is given as:

$a = 4\pi r^2$

The surface area of the football is given as:

$A = 4\pi R^2$

$=>A = 4\pi (5r)^2\\\\A = 100\pi r^2$

Therefore, the ratio of their surface areas is:

A : a

$100\pi r^2 : 4\pi r^2$

= 100 : 4

25 : 1

5 0

2 years ago

Ellie has a delivery van which she is going to deliver boxes each box is a cuboid brain.ly 45cm by 40cm by 35cm the space in the

jek_recluse [69]

Answer:

It will take Ellie 64 minutes to put as many boxes as possible.

Step-by-step explanation:

Let us work with meters.

The dimensions of Ellie's boxes in meters are: 0.45m by 0.40m by 0.35 ( <em>to convert from centimeters to meters we just divide by 100, because 1m =100cm).</em> therefore the volume of each box is: