Use the P (A + B) = P (A) x P (B) rule to find the probability of system failure. Let A and B be the events that the first alarm and second alarm, respectively, fail. Do you get the same answer you did in the earlier question?

Answer:

Base area=5*12=60

Height is 4

Perimeter or the base is 2*(12+5)=34

Surface area is 2B+Ph=120+136=256

Answer:

18m squared

Step-by-step explanation:

4m x 4.5m = ?

The approximate area of the shaded region is 2794 m². The correct option is the first option 2794 square meters

From the question, we are to determine the approximate area of the shaded region

The area of the shaded region = Area of the triangle - Area of the circle

Area of triangle = 1/2 × base × height

Area of the triangle = 1/2 × 90 × 90

Area of the triangle = 4050 m²

Area of a circle = πr²

Where r is the radius

In the diagram,

Diameter = 40 m

∴ Radius = 40/2 = 20 m

Thus,

Area of the circle = π × 20²

Area of the circle = 3.14 × 400

Area of the circle = 1256 m²

Therefore,

The area of the shaded region = 4050 m² - 1256 m²

The area of the shaded region = 2794 m²

Hence,

The darkened area covers about 2794 m²  

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Answer:

27/2 =x

Step-by-step explanation:

We can write a ratio to solve

3             2

-----  = ---------

3+x          11

Using cross products

3*11 = 2(3+x)

33 = 6+2x

Subtract 6 from each side

33-6 = 6+2x-6

27 = 2x

27/2 = 2x/2

27/2 =x

Answer:

[tex]\frac{9}{5}[/tex]

Step-by-step explanation:

[tex]\frac{4}{9}[/tex] × [tex]\frac{45}{36}[/tex]

= [tex]\frac{4}{9}[/tex] × [tex]\frac{5}{4}[/tex] ( cancel 4 on numerator/ denominator )

[tex]\frac{5}{9}[/tex]

Given a number n then its reciprocal is [tex]\frac{1}{n}[/tex]

Then the reciprocal of [tex]\frac{5}{9}[/tex] is

[tex]\frac{1}{\frac{5}{9} }[/tex] = [tex]\frac{9}{5}[/tex]

Step-by-step explanation:

[tex]v = \frac{\pi r {}^{2}h }{3} [/tex]

[tex]3v = \pi {r}^{2} h[/tex]

[tex] \frac{3v}{\pi h} = {r}^{2} [/tex]

[tex] \sqrt{ \frac{3v}{\pi h} } = r[/tex]

Answer:

y=3x-2

Step-by-step explanation:

The slope of the equation is (-2-(-5))/(0-(-1))=3. The y intercept is - 2. So y=3x-2

Answer:

Step-by-step explanation:

A(1) is the amount after 1 decade.

A(0.1) is the amount after 1  year.

Every year, the amount of CO₂ increases by a factor of 1.06^(0.1) ≅ 1.0058

Answer:

Rate of Return is 14.8%

Step-by-step explanation:

We know that 20 shares of Stock are purchased for $30 per share.

This gives us a total value of: 20 × 30 = $600.

Now, the shares are sold for $710 with a commission sale of $6. This means the final money going to the seller is; 710 – 6 = $704.

Thus, the rate of return percentage is = (704 – 600)/704) × 100% = 14.7727%

To the nearest tenth gives us 14.8%

Answer:

17ft

Step-by-step explanation:

5*2 + 3.5*2=17

Answer:

150 Newtons

Step-by-step explanation:

Given

[tex]t = \sqrt{\frac{4\pi^2mr}{F}}[/tex]

[tex]t = 12[/tex]

[tex]r =6.5[/tex]

[tex]\pi = 3.14[/tex]

[tex]m = 84.4[/tex]

See attachment

Required

Find F

We have:

[tex]t = \sqrt{\frac{4\pi^2mr}{F}}[/tex]

Square both sides

[tex]t^2 = \frac{4\pi^2mr}{F}[/tex]

Multiply both sides by F

[tex]Ft^2 = 4\pi^2mr[/tex]

Divide both sides by [tex]t^2[/tex]

[tex]F = \frac{4\pi^2mr}{t^2}[/tex]

Substitute known values

[tex]F = \frac{4*3.14^2*84.4*6.5}{12^2}[/tex]

[tex]F = \frac{21635.90624}{144}[/tex]

[tex]F = 150.249348889[/tex]

[tex]F = 150N[/tex]

Answer:

Step-by-step explanation:

a) 0.5*0.365=18.25%

b) (100%-20,7%-50%)=29.3

Answer:

A. 24

Step-by-step explanation:

Five and above rounds up

so 25,26,27,28,29 rounds up to 30

We leave it alone when 4 or less

34,33,32,31,30 remains at 30

24 would not round to 30

Answer:

I would rather use:

(b) 10,000 batches of 10 observations each.

Step-by-step explanation:

It is easier to have 10,000 batches of 10 observations each than to have 50 batches of 2,000 observations.  Human errors are reduced with fewer observations. For example, Hadoop, a framework used for storing and processing big data, relies on batch processing.  Using batch processing that divides the 100,000 stationary waiting times into 10 observations with 10,000 batches each is more efficient than having 2,000 observations with 50 batches each.

*see attachment for clearer diagram

Answer:

16.5

Step-by-step explanation:

BC = 11

AB = 3

Area of the shaded region = area of ∆AEB + area of ∆CED

Area of a triangle is given as,

A = ½*base*height

Find the area of each triangle and add together

✔️Area of ∆AEB = ½*bh

Where,

base (b) = 3

height (h) = ½(BC) = ½(11) = 5.5

Area of ∆AEB = ½*3*5.5 = 8.25

✔️Area of ∆CED = ½*bh

Where,

b = 3

h = ½(BC) = ½(11) = 5.5

Area of ∆CED = ½*3*5.5 = 8.25

✅Area of the shaded region = area of ∆AEB + area of ∆CED

= 8.25 + 8.25

= 16.5

Answer:

y = [tex]\frac{20}{9}[/tex]

Step-by-step explanation:

Since the figures are similar then the corresponding sides are in proportion, that is

[tex]\frac{JH}{PQ}[/tex] = [tex]\frac{FM}{ST}[/tex] , substitute values

[tex]\frac{6}{4}[/tex] = [tex]\frac{7}{3y-2}[/tex] ( cross- multiply )

6(3y - 2) = 28

18y - 12 = 28 ( add 12 to both sides )

18y = 40 ( divide both sides by 18 )

y = [tex]\frac{40}{18}[/tex] = [tex]\frac{20}{9}[/tex]

Answer:

20/9

Step-by-step explanation:

since the 2 are similar,

JH/PQ = FM/ST

6/4 = 7/(3y-2)

6(3y-2) = 7*4

18y-12=28

18y = 40

y = 40/18 = 20/9 = 2 2/9

Answer:  

STEP 1  

M_{4,2} is set of 4x2 matrices hence each matrix has 4*2=8 entries. Each entry can be filled independently.  

Hence its basis has 8 linearly independent vectors.  

STEP 2  

Dimension= cardinality of basis = 8.

Answer:

44.8

Step-by-step explanation:

Using the Cosine formula, we first have Cos 48 = 30/x. So then we just solve for x and get 44.8342965, which rounds to 44.8

I hope this helped! :D

I'll be referring to each of these numbers as x and y.

x + y = 4

(x^2) + (y^2) - 3(x)(y) = 76

x = 4 - y

(4 - y)^2 + (y^2) - 3(4 - y)(y) = 76

(4 - y)(4 - y) + y^2 - (3y)(4 - y) = 76

16 - 4y - 4y + y^2 + y^2 - 12y + 3y^2 = 76

16 - 20y + 5y^2 = 76

5y^2 - 20y - 60 = 0

y^2 - 4y - 12y = 0

(y - 6)(y + 2) = 0

y = 6 or -2

x = 4 - 6 = -2

x = 4 - - 2 = 6

As you can see, we got the same numbers for both x and y, -2 and 6. Therefore, the two numbers are -2 and 6. But, we can check our work to ensure that the answer is correct.

x = -2

y = 6

6 - 2 = 4

4 = 4

(-2)^2 + (6^2) - 3(-2)(6) = 76

4 + 36 - 3(-12) = 76

40 + 36 = 76

76 = 76

Hope this helps!

Answer:

X and y = -2 or 6

Step-by-step explanation:

Answer:

----------------------------

quartile first = 73

----------------------------

Answer:

53,800,013

need brainliest!!!

Answer:

Step-by-step explanation:

It is convenient to let a graphing calculator show the answers to these questions.

The exponential equation modelling the growth will be of the form ...

  f(x) = (initial value) × (1 +growth rate)^x

Richland's GDP/person can be modeled by r(x) = 10·1.01^x

Poorland's GCP/person can be modeled by p(x) = 5·1.03^x

The attached graph shows values for x=5, 10 and r(x)=p(x).

It will take about 35.3 years for Poorland to catch up.

Answer:

n(A)+n(B)-49/400=n(AUB)

n(B)=1-7/20+49/400

n(B)=(400+49-140)/400

n(B)=309/400

Answer:

-4

Step-by-step explanation:

The remainder when P(x) is divided by (x + 2) is P(-2) which is - 4

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the amount invested at 13%. Then (3x+199) is the amount invested at 12%. The total interest earned in 1 year is ...

  (13%)(x) +(12%)(3x+199) = 1561.50

  0.49x +23.88 = 1561.50 . . . . simplify

  0.49x = 1537.62 . . . . . . . . . . subtract 23.88

  x = 3138 . . . . . . . . . . . . . . . . divide by 0.49

  3x+199 = 9613

$3138 was invested at 13%; $9613 was invested at 12%.

Answer:

[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]

updated response , given that you confirmed the question....

if the percent is the variable a% then ....

[tex]x*(\frac{a+100}{100}) = 2000[/tex]

[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]

I think that there is missing information here ....

you can make any number work here the result of the number being increased by the percent has to be 2000...

so if if the number is 1000 then the percent would be 100%

if you make the number  1500 then the percent would be 33 1/3 %

Step-by-step explanation:

The number is [tex]\frac{2000}{(1+\frac{a}{100})}[/tex]

Let us assume that the number be x.

When the number x is increased by  a% the new number will be,

[tex]x(1+\frac{a}{100})[/tex]

Now, this number is decreased by 80%. So, the new number will be,

[tex]x(1+\frac{a}{100})*(1-\frac{80}{100} )\\=x(1+\frac{a}{100})*(1-0.8 )\\=x(1+\frac{a}{100})*0.20[/tex]

By the given condition,

When x increased by a% and decreased by 80% it becomes 400

Therefore, we can write

[tex]x(1+\frac{a}{100})*0.20=400[/tex]

[tex]x(1+\frac{a}{100})=\frac{400}{0.20}[/tex]

[tex]x(1+\frac{a}{100})=2000[/tex]

[tex]x=\frac{2000}{(1+\frac{a}{100})}[/tex]

So, the number will be [tex]\frac{2000}{(1+\frac{a}{100})}[/tex].

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