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allochka39001 [22]

2 years ago

13

E saca una bola de billar al azar de una caja que contiene 15 bolas de billar numeradas del 1 al 15 y se registra el número obte

nido con la letra "n". Encuentra la probabilidad de que el número obtenido "n" de la bola de billar sacada de la caja sea mayor a 10 y "n" sea par.

1 answer:

Julli [10]2 years ago

5 0

Answer:

P = 2/7 = 0.2857 or 28.57%

Step-by-step explanation:

First, we know that we have 15 balls, and we need to know which one of them is pair, and higher than 10.

So, we first need to calculate the probability that the obtained number is pair.

The pair numbers are 2,4,6,8,10,12,14

We have 7 numbers out of 15 ---> P(B) = 7/15

From those numbers, only two of them are higher than 10, which are 12 and 14, so: P(A|B) = 2/15

To get the probability to get a number higher than 10 and pair:

P(A/B) = P(A|B) / P(B)

P(A/B) = 2/15 / 7/15 = 2/7 = 0.2857

To get the percentage: 0.2857 * 100 = 28.57%.

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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.

<h3>1.</h3>

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

<h3>2.</h3>

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

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

<h3>3.</h3>

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.

<h3>4.</h3>

$m\angle BCD=90\°$ , 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.

<h3>5.</h3>

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

<h3>6.</h3>

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.

<h3>7.</h3>

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

Lisa invests $4,000 in two types of bonds, bond A and bond B. Bond A offers a 10% return, and bond B offers a 6% return. Lisa in

ss7ja [257]

X+y=4000....(1)
10x+6y=340*100⇒5x+3y=17000......(2)

(2)- 3*(1)⇒ 2x=5000⇒x=2500,y=4000-2500=1500

7 0

2 years ago

Read 2 more answers

Let's find 1/2 - 1/6. First, write the subtraction so the fractions have denominator . Then subtract. 1/2 - 1/6 = blank/6 - 1/6

SOVA2 [1]

Step-by-step explanation:

1/2 - 1/6 = 3/6 - 1/6 = 2/6

Hope this helps!!!

7 0

2 years ago

Which ordered pairs are solutions to the inequality 2y−x≤−6 ?

Vinil7 [7]

Given inequality: 2y−x ≤ −6

Option-1 : (-3,0)
2×0 - (-3) = 0 + 3 = 3 > -6
Not satisfied

Option-2 : (6,1)
2×1 - 6 = 2 - 6 = -4 > -6
Not satisfied

Option-3 : (1, -4)
2×(-4) - 1 = -8 - 1 = -9 < -6
Satisfied.
Thus, (1, -4) is a solution.

Option-4 : (0, -3)
2×(-3) - 0 = -6 - 0 = -6 = -6
Satisfied.
Thus, (0, -3) is a solution.

Option-5 : (2, -2)
2×(-2) - 2 = -4 - 2 = -6 = -6
Satisfied.
Thus, (2, -2) is a solution.

Solutions are: (1, -4), (0, -3) , (2, -2)

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2 years ago

What is the following quotient 3 sqrt 8/ 4 sqrt 6

adell [148]

We have that
(3√8)/(4√6)

we know that
√8---------> √(2³)-----> 2√2
so
(3√8)/(4√6)=(3*[2√2])/(4√6)---> 6√2/(4√6)
√6=√(2*3)---> √2*√3
6√2/(4√6)=6√2/(4√2*√3)----> 6/(4√3)----> 6/(4√3)*(√3/√3)-----> 6√3/(4*3)----> √3/2

the answer is
√3/2

7 0

2 years ago

Read 2 more answers