Which statement best explains why Ben uses the same width to draw arcs from A and B which intersect at S?

Answer:

The probability is 0.357

Step-by-step explanation:

Given that,

The system has at least one type of defect,

Suppose, A certain system can experience three different types of defects.

Let [tex]A_{i}[/tex] (i = 1,2,3) denote the event that the system has a defect of type i.

Suppose that the following probabilities are,

[tex]P(A_{1})=0.11[/tex]

[tex]P(A_{2})=0.08[/tex]

[tex]P(A_{3})=0.05[/tex]

[tex]P(A_{1}\cup A_{2})=0.13[/tex]

[tex]P(A_{1}\cup A_{3})=0.13[/tex]

[tex]P(A_{2}\cup A_{3})=0.11[/tex]

[tex]P(A_{1}\cap A_{2}\cap A_{3})=0.01[/tex]

[tex]P(A_{1}\cap A_{2})=0.06[/tex]

[tex]P(A_{1}\cap A_{3})=0.03[/tex]

[tex]P(A_{2}\cap A_{3})=0.02[/tex]

[tex]P(A_{1}\cup A_{2}\cup A_{3})=0.14[/tex]

We need to calculate the probability that it has exactly one type of defect

Using given data

[tex]P=\dfrac{P(A_{1}\cap A_{2}'\cap A_{3}')}{P(A_{1}\cup A_{2}\cup A_{3})}+\dfrac{P(A_{1}'\cap A_{2}\cap A_{3}')}{P(A_{1}\cup A_{2}\cup A_{3})}+\dfrac{P(A_{1}'\cap A_{2}'\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]

[tex]P=\dfrac{P(A_{1})-P(A_{1}\cap A_{2})-P(A_{1}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex] + [tex]\dfrac{P(A_{2})-P(A_{1}\cap A_{2})-P(A_{2}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]+ [tex]\dfrac{P(A_{3})-P(A_{1}\cap A_{3})-P(A_{2}\cap A_{3})+P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]

P = [tex]\dfrac{P(A_{1})+P(A_{2})+P(A_{3})-2P(A_{1}\cap A_{2})-2P(A_{1}\cap A_{3})-2P(A_{2}\cap A_{3})+3P(A_{1}\cap A_{2}\cap A_{3})}{P(A_{1}\cup A_{2}\cup A_{3})}[/tex]

Put the value into the formula

[tex]P=\dfrac{0.11+0.08+0.05-2(0.06)-2(0.03)-2(0.02)+3(0.01)}{0.14}[/tex]

[tex]P=0.357[/tex]

Hence, The probability is 0.357

Answer:

[tex]R(x,y) = (\frac{7}{4},\frac{1}{4})[/tex]

Step-by-step explanation:

Given

[tex]A = (1,-1)[/tex]

[tex]B = (4,4)[/tex]

[tex]AR:AB = 1:4[/tex]

Required

Determine R

This question will be solved using line ratio formula

[tex]R(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2+ny_1}{m + n})[/tex]

Where

[tex]A = (1,-1)[/tex]

[tex]B = (4,4)[/tex]

[tex]m:n = AR : RB[/tex]

Since R is on A and B;

[tex]AB = AR + RB[/tex]

[tex]4 = 1 + RB[/tex]

[tex]RB = 3[/tex]

Hence;

[tex]m:n = 1 : 3[/tex]

[tex]A = (1,-1)[/tex]

[tex]B = (4,4)[/tex]

[tex]R(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2+ny_1}{m + n})[/tex] becomes

[tex]R(x,y) = (\frac{1 * 4 + 3 * 1}{1+3},\frac{1 * 4 + 3 * -1}{1 + 3})[/tex]

[tex]R(x,y) = (\frac{4 + 3}{4},\frac{4 - 3}{4})[/tex]

[tex]R(x,y) = (\frac{7}{4},\frac{1}{4})[/tex]

Answer:

Ava = 1.12 m tall

Olivia =  0.89 m tall

Step-by-step explanation:

given;

Ava is 23cm taller then Olivia,

Olivia is half the height of Lucas.

If Lucas is 1.78m tall

find:

how tall are Ava and Olivia

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

Ava = Olivia + 0.23

Olivia = Lucas / 2

Lucas = 1.78

plugin values into the equation above

Olivia = 1.78 / 2

Olivia =  0.89 m tall

Ava = 0.89 + 0.23

Ava = 1.12 m tall

Drama, English, French, Math, History, Physics, Psychology

Answer:

= 7-2x. is the answer :p

Answer: 178 4/5 or as an improper fraction 894/5

Hope this helps!

Please mark Brainliest!

Hey there!

[tex]-9\frac{1}{6}+7[/tex]

After that, multiply the whole number by the denominator and then add the numerator after you multiply.

[tex]-\frac{55}{6}+1[/tex]

[tex]9*6=54+1=55[/tex]

Now add the negative sign to 55.

[tex]\frac{-55}{6}+7[/tex]

[tex]\frac{-13}{6}[/tex]

Now simplify.

[tex]\frac{-13}{6}=-2\frac{1}{6}[/tex]

Hope this helps!

[tex]\text {-TestedHyperr}[/tex]

Answer:

I think 2nd option is correct

Answer:

56.44%

Step-by-step explanation:

From the question, we have the following values

% Discount = 3%

Full allowed payment days = 30 days

Discount days = 10 days

1 year = 365 days

The formula for Effective Annual rate or Annual rate in effect =

Discount %/(1-Discount %) x (365 days/(Full allowed payment days - Discount days))

= 3%/(1 - 3%) × (365 days/30 days - 10 days)

= 0.03/(1 - 0.03) × (365/20)

= 0.03/0.97 × (365/20)

= 0.5644329897

Converting to percentage

0.5644329897 × 100

= 56.44329897%

Approximately = 56.44%

Therefore, the annual rate Heidi, in effect, is paying the supplier if she fails to pay the invoice at the end of the discount period is 56.44%

Answer:

24

Step-by-step explanation:

If you put 12 in for x, you would get y=2*12 and 2 times 12 is 24. I hope this helps :)

Answer:

45, 90/2 equals 45. everytime you need to find it you do miles/hours

Answer:

[tex] \frac{27}{35} \\ [/tex]

Step-by-step explanation:

If you are going to multiply fractions, you just going to multiply their numerators and denominators and simplify when needed.

[tex] \frac{3}{5} \times \frac{9}{7} \\ \frac{3 \times 9}{5 \times 7} \\ \frac{27}{35} [/tex]

Answer:

3

Step-by-step explanation:

513 = 500 + 10 + 3

The 5 is worth 500.

The 1 is worth 10.

And the 3 is worth 3 !

Answer:

The value of 3 in 513 is the ones place.

Step-by-step explanation:

Answer:

$640

Step-by-step explanation:

Let [tex]x[/tex] equal the original price of the machine.

We know that $64 is 10% of [tex]x[/tex] because $64 is left of [tex]x[/tex] after the 90% reduction.

Set up an equation:

[tex].10x=64[/tex]

Divide by the coefficient of [tex]x[/tex], which in this case is [tex].10[/tex]

[tex]x=640[/tex]

Answer: it’s B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

Probability of heads is 1/2, and the probability of tails is 1/2.  The probability of getting no heads (3 tails) is:

P = (1/2)³

P = 1/8

P = 0.1250

Answer:

$1500

Step-by-step explanation:

Total interest:

Additional money is $1500

Answer:

The answer to this question can be defined as follows:

In option a "0.0067".

In option b "0.1755".

In option c "0.5595".

Step-by-step explanation:

It is about the distribution of Poisson:

[tex]\lambda = 5 (rate)[/tex]

t = 1

The formula for calculating Mean:  

[tex]\to \mu = \lambda \times t[/tex]

[tex]\to P(X=x) = \frac{e^{-\mu} \mu^{x}}{x!}[/tex]

calculate the value of Mean:

[tex]\to \mu =5 \times 1\\\\ \to \mu= 5[/tex]

In point a:

When the value of x is equal to 0:

[tex]\to P(X = 0) = \frac{e^{-5} 5^{0}}{0!}[/tex]

                    [tex]= \frac{e^{-5} \times 1 }{0}\\\\ = 0.0067 \times 1 \\\\ = 0.0067[/tex]

In point b:

When the value of x is equal to 5:

[tex]\to P(X = 0) = \frac{e^{-5} 5^{5}}{5!}[/tex]

                    [tex]= \frac{e^{-5} \times 3125 }{120}\\\\ = \frac{0.0067 \times 3125}{120} \\\\ = \frac{21.0560}{120}\\\\ =0.1754 \\\\[/tex]

In point c:

When the value of x is equal to 5:

[tex]\to P(X \ge 5) = 1 - P(X < 5) \\\\ \to P(X \ge 5) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4) \\\\ \to P(X \ge 5) = 0.5595[/tex]

Answer: 9 - [tex]\sqrt{x}[/tex]

Step-by-step explanation:

Let say the number is x.

So the square root of x will  be [tex]\sqrt{x}[/tex]  and is less than 9  so we will subtract that from 9.

[tex]9-\sqrt{x}[/tex]

Given :

∠m1 = ( 7x - 19 )° .

∠m2 = ( x + 5 )° .

To Find :

The value of x .

Solution :

Since , relation between angle ∠m1 and ∠m2 is not given .

Let , us assume that sum of ∠m1 and ∠m2 is 180° .

So ,

[tex](7x-19)+(x+5)=180^{\circ}\\\\8x-14=180\\\\8x=194\\\\x=24.25^{o}[/tex]

Angle ∠m2 = (24.25  + 5 )° = 29.25° .

Therefore , ∠m2 = 29.25° .

Hence , this is the required solution .

Answer:

Given :

∠m1 = ( 7x - 19 )° .

∠m2 = ( x + 5 )° .

To Find :

The value of x .

Solution :

Since , relation between angle ∠m1 and ∠m2 is not given .

Let , us assume that sum of ∠m1 and ∠m2 is 180° .

So ,

Angle ∠m2 = (24.25  + 5 )° = 29.25° .

Therefore , ∠m2 = 29.25° .

Hence , this is the required solution .

Step-by-step explanation:

Answer:

X=70

Step-by-step explanation:

Interior angles of parallel line sum up to be 180° so:

45+(2x-5)=180

45+2x=185

2x=140

x=70

Steps to solve:

-32 + (2 - 6)(10)

~Simplify

-32 + (-4)(10)

~Multiply

-32 - 40

~Subtract

-72

Best of Luck!

Answer:

Step-by-step explanation:

The equation is: –32 + (2 – 6)(10).

Then u have to do PEMDAS

P=Parentheses

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

you follow the steps to get -49

Answer:

58%

Step-by-step explanation:

50/86 is approximately equal to 0.58, and when you convert that into percentage you get 58%

Answer:

Step-by-step explanation:

quadratic trinomial, because the highest degree of x is 2 and the expression has 3 terms.

Answer:

40/4 shaded in squares

Step-by-step explanation:

for 0.4, since 100 is a whole, multiply by 100.

0.4*100=40

shade in 40 squares

for 0.04, multiply by 100

0.04*100=4

shade in 4 squares

Answer:

a) 118

b) 55

Step-by-step explanation:

a) Originally, there are 2 red balls and a total of 17 balls.

8/9 = (2 + x) / (17 + x)

8 (17 + x) = 9 (2 + x)

136 + 8x = 18 + 9x

x = 118

b) Originally, there are 8 white balls and a total of 17 balls.

1/9 = 8 / (17 + x)

17 + x = 72

x = 55

Answer:

you just math you know pretty easy when you know what to do

Step-by-step explanation:

just practice