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3 years ago

Calculate the sizes of the unknown angles in each diagram. Please, answer with explanation.

Mathematics

1 answer:

denis23 [38]3 years ago

5 0

Step-by-step explanation:

a) 2z+3z+4z=180

9z=180

z=20

So,three angles are 40,60 and 80

b) (y+30)+(2y+80)+(y+10)=180

y+30+2y+80+y+10=180

4y+120=180

4y=60

y=15

Three angles are 45,110,25

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36-3•4 15-9 Divided by three

matrenka [14]

Answer:

Step-by-step explanation:

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3 years ago

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The average distance between the Earth and the Moon is 384 400 km. Express it in standard form.

ycow [4]

Answer:

$3.84\times10^8\ m$

Step-by-step explanation:

It is given that,

The average distance between the Earth and the Moon is 384 400 km.

We need to express in in standard form.

1 km = 1000 m

It means,

384400 km = 384400000 km

= $3.84\times10^8\ m$

Hence, the average distance between the Earth and the Moon is $3.84\times10^8\ m$ .

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3 years ago

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling

lara31 [8.8K]

Answer:

Maureen's null hypothesis is, H₀: p₁ ≥ p₂.

Step-by-step explanation:

Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies wants test whether her goal of shipping 100% orders within 24 hours is achieved or not.

After reviewing the order filling operations at her warehouses she determines that neither the East coast nor the West coast warehouse has achieved the goal. But the East Coast warehouse has consistently out-performed the West Coast warehouse.

To check whether this determination is correct or not Maureen's staff randomly selected 200 orders from the West Coast warehouse (population 1) and 400 orders from the East Coast warehouse (population 2).

Of the 200 orders from the West Coast warehouse, 190 were shipped within 24 hours. And of the 400 orders from the East Coast warehouse, 372 were shipped within 24 hours.

The hypothesis can be defined as follows:

H₀: The proportion of orders that were shipped within 24 hours is not more for East Coast warehouse than for West Coast warehouse, i.e. p₁ ≥ p₂.

Hₐ: The proportion of orders that were shipped within 24 hours is more for East Coast warehouse than for West Coast warehouse, i.e. p₁ < p₂.

Thus, Maureen's null hypothesis is, H₀: p₁ ≥ p₂.

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3 years ago

Six hundred paving stones were examined for cracks, and 15 were found to be cracked. The same 600 stones were then examined for

9966 [12]

Answer: 0.01

Step-by-step explanation:

Let the events are :

C = paving stones found to be cracked.

D = paving stones found to be discolored.

Given : Total stones : T = 600 (i)

C = 15

D= 27

C'∩D'= 564 (ii)

Since C'∩D' = (C∪D)' = T- C∪D (iii)

From (i) , (ii)and (ii) , we have

564 = 600- C∪D

⇒ C∪D=600- 564= 36

Formula : C∩D= C+D- C∪D

Put values , we get

C∩D= 15+27-36=6

Now ,

$P(C\cap D)=\dfrac{C\cap D}{T}=\dfrac{6}{600}=0.01$

The probability that it is both cracked and distorted is 0.01.

4 0

3 years ago

find the equation of a straight line passing through the point (3,3) which is perpendicular to the line y=-1/2x-4

Mars2501 [29]

Answer:

y = 2x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - $\frac{1}{2}$ x - 4 ← is in slope- intercept form

with slope m = - $\frac{1}{2}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{1}{2} }$ = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (3, 3) into the partial equation

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 2x - 3 ← equation of perpendicular line

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3 years ago