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marishachu [46]

3 years ago

9

A random generated list of numbers from 0 to 4 is being used to simulate an event, with the numbers 3 and 4 representing a succe

ss. what is the estimated probability of a success?
A. 60%
B. 40%
C. 25%
D. 75%

1 answer:

Sloan [31]3 years ago

6 0

Since there are 5 numbers 0-4 and there are 2 numbers that is a success. The probability is 2/5 or 40% or B.

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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

3 years ago

A set has 62 proper subsets how many elements has it for?<br>

MrRissso [65]

Answer:

6

Step-by-step explanation:

Total number of subsets is given as

${2}^{n}$

But the subset of a set consists of the proper subsets, an empty set and the set itself.

Total number of subsets are 64

Therefore,

${2}^{n} = 64$

${2}^{n} = {2}^{6}$

Comparing both sides

$n = 6$

5 0

2 years ago

Last spring, the drama department at Greenwood High School had 10 student audition for the musical. This spring, there were 8 st

Brilliant_brown [7]

20% cuz 2/10 students dropout then 2/10=20%

5 0

2 years ago

What would be the correlation between the ages of husbands and wives if men always married woman who were(a) 3 years younger tha

Allushta [10]

Answer:

the correct answer is a

8 0

2 years ago

Antoine Purchase 1.8 kg of apples and 315 dekagrams of oranges This was 1350 g more than the weight of bananas bridges what was

victus00 [196]

Answer: 3600 grams

Step-by-step explanation:

A dekagram means 10 grams.

1 kilogram = 1000 grams

Therefore the total number of grams when Antoine Purchase 1.8 kg of apples and 315 dekagrams of oranges will be:

= (1.8 × 1000) + (315 × 10)

= 1800 + 3150

= 4950 grams

Since this was 1350g more than the weight of bananas, the weight of the bananas Antonio purchased in grams will be:

= 4950 - 1350

= 3600 grams

6 0

2 years ago