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3 years ago

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There are 15 marbles in a bag: 7 are blue, 6 are white, and 2 are green. If one marble is drawn, what is the probability that it

is either white or green?

1 answer:

DIA [1.3K]3 years ago

6 0

40% white
13.33% green

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In the adjoining equilateral triangle PQR , X , Y and Z are the middle points of the sides PQ , QR and RP respectively. Prove th

olasank [31]

Answer:

See Below

Step-by-step explanation:

<u>Statements:</u> <u>Reasons:</u>

<u /> $1)\text{ } \Delta PQR\text{ is equilateral}$ Given

$2)\text{ }PQ=QR=RP$ Definition of Equilateral

$3)\text{ } X, Y, Z\text{ are the midpoints of } PQ, QR, RP$ Given

$4)\text{ } PX=XQ$ Definition of Midpoint

$5)PQ=PX+XQ$ Segment Addition

$6)\text{ } PQ=2XQ$ Substitution

$7)\text{ } QY=YR$ Definition of Midpoint

$8)\text{ }QR=QY+YR$ Segment Addition

$9)\text{ } QR=2QY$ Substitution

$10)\text{ } 2XQ=2QY$ Substitution

$11)\text{ } XQ=QY$ Division Property of Equality

$12)\text{ } XQ=PX=QY=YR$ Transitive Property

$13)\text{ } RZ=ZP$ Definition of Midpoint

$14)\text{ } RP=RZ+ZP$ Segment Addition

$15)\text{ } RP=2RZ$ Substitution

$16)\text{ } 2XQ=2RZ$ Substitution

$17)\text{ } XQ=RZ$ Substitution

$18)\text{ } XQ=PX=QY=YR=RZ=ZP$ Transitive Property

$19)\text{ } \angle Q\cong \angle R\cong \angle P$ Definition of Equilateral

$20)\text{ } \Delta XQY\cong \Delta YRQ \cong \Delta ZPX$ SAS Congruence

$21)\text{ } XY\cong YZ\cong ZX$ CPCTC

$22)\text{ } \Delta XYZ\text{ is equilateral}$ Equilateral Triangle Theorem

5 0

3 years ago

Read 2 more answers

*Urgent*<br><br> Please help!!

satela [25.4K]

Answer:

5, 0

Step-by-step explanation:

3 0

2 years ago

I need help with all of this

Drupady [299]

1. 7x + 9 = 48
7x = 58 - 9
7x = 49
X = 7

4 0

2 years ago

sprinter can run 10 yards in 5⁄3 seconds. How long will it take the same sprinter at the same speed to run 30 yards?

Novosadov [1.4K]

Answer:

5 seconds

Step-by-step explanation:

All you have to do is make a ratio.

10 yards = 5/3 seconds

10 * 3 = 30 yards

5/3 * 3 = 15/3 = 5 seconds

3 0

3 years ago

The LB Company has long manufactured a light bulb with an average life of 5400 hours. Company researchers have recently develope

elena55 [62]

<h2><u>Answer with explanation</u>:</h2>

Let $\mu$ be the average life of light bulbs.

As per given , we have

Null hypothesis : $H_0 : \mu =5400$

Alternative hypothesis : $H_a : \mu >5400$

Since $H_a$ is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.

Formula for Test statistic : $z=\dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

where, n= sample size

$\overline{x}$ = sample mean

$\mu$ = Population mean

$\sigma$ =population standard deviation

For $n=95,\ \overline{x}=5483\ \&\ \sigma=500$ , we have

$z=\dfrac{5483-5400}{\dfrac{500}{\sqrt{95}}}=1.61796786124\approx1.6180$

Using z-value table , Critical one-tailed test value for 0.06 significance level :

$z_{0.06}=1.5548$

Decision : Since critical z value (1.5548) < test statistic (1.6180), so we reject the null hypothesis .

[We reject the null hypothesis when critical value is less than the test statistic value .]

Conclusion : We have enough evidence at 0.06 significance level to support the claim that the new filament yields a longer bulb life

8 0

3 years ago