Congruent sides???????????

Answer:

A 1/2

Step-by-step explanation:

Ratio of short length to hypotenuse

= cos60

= 1/2

9514 1404 393

Answer:

  ≈ 1000√10∠-129.04464° = -1992 -2456i

Step-by-step explanation:

  3 -i = √(3³+(-1)²)∠arctan(-1/3) ≈ √10∠-18.4349°

Then (3-i)^7 = 10^(7/2)∠(7×-18.4349°) = 1000√10∠-129.04464°

  = 1000√10(cos(-129.04464°) +i·sin(-129.04464°))

  = -1992 -2456i

Answer:

the operating characteristics have been solved below

Step-by-step explanation:

we have an average of 10 minutes per customers

μ = mean service rate = 60/10 = 6 customers in one hr

the average number of customers that are waiting in line

mean arrival λ = 2.5

μ = 6

[tex]Lq = \frac{2.5^{2} }{6(6-2.5)} \\[/tex]

= 6.25/21

= 0.2976

we calculate the average number of customers that are in the system

[tex]L=Lq+\frac{2.5}{6}[/tex]

= 0.2976+0.4167

= 0.7143

we find the average time that a customer spends in waiting

[tex]Wq=\frac{0.2976}{2.5}[/tex]

= 0.1190 hours

when converted to minutes = 0.1190*60 = 7.1424 minutes

[tex]0.1190+\frac{1}{6}[/tex]

=0.2857

probability that arriving customers would wait for the service

= 2.5÷6 = 0.4167

Answer:

15=2p+3

Step-by-step explanation:

Answer:

71 feet

Step-by-step explanation:

94×2=188

330-188=142

142÷2=71

Answer:

37.94

Step-by-step explanation:

the 9th percentile is equal to a zscore of -1.34

-1.34=(x-50)/9

x=37.94

Answer:

q=4

p=2

Step-by-step explanation:

3p+2q=14

10p+6q=44

10(3p+2q=14)

3(10p+6q=44)

30p+20q=140-

30p+18q=132

2q=8

2q/2=8/2

q=4

3p+2*4=14

3p+8=14

3p=14-8

3p/3=6/3

p=2

hope this helps

Answer:

[tex]p=2\\q=4[/tex]

Step-by-step explanation:

One is given the following system of equations,

[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]

The fastest method to solve a system of equations is the method of elimination. This process is manipulating one of the equations, by multiplying or diving it by a value, such that one of the coefficients variables in the equation is the additive inverse of the like term in the other equation. That way, when one adds the equations, one of the variables cancels out. Then one can solve for the other term. Finally, one can back sovle by substituting the value of the solved variable into one of the equations and simplifying to find the value of the other variable.

[tex]3p + 4q = 22\\\\10p + 12q = 68[/tex]

Manipulate the first equation so that the variable (q) cancels

[tex](3p + 4q = 22) *(-3)\\\\10p + 12q = 68[/tex]

[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]

Add the equations,

[tex]-9p + -12q = -66\\\\10p + 12q = 68[/tex]

[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]

Simplify,

[tex](10p-9p)+(-12q+12q)=(-66+68)[/tex]

[tex]p=2[/tex]

Backsovle for the variable (p). Substitute the values of (p) into one of the original equations. Then simplify and use inverse operations to solve for the variable (q).

[tex]3p+4q=22[/tex]

Substitute,

[tex]3(2)+4q=22[/tex]

Simplify,

[tex]3(2)+4q=22[/tex]

[tex]6+4q=22[/tex]

Inverse operations,

[tex]6+4q=22[/tex]

[tex]4q=16\\q=4[/tex]

Answer:

a) 0.0147 = 1.47% probability that none of them graduates from the local community college.

b) 0.9398 = 93.98% probability that at most four will graduate from the local community college.

c) The expected number that will graduate is 2.85.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they will graduate, or they will not. The probability of a student graduating is independent of any other student graduating, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

57% of students who enter the college as freshmen go on to graduate.

This means that [tex]p = 0.57[/tex]

Five freshmen are randomly selected.

This means that [tex]n = 5[/tex]

a. What is the probability that none of them graduates from the local community college?

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.57)^{0}.(0.43)^{5} = 0.0147[/tex]

0.0147 = 1.47% probability that none of them graduates from the local community college.

b. What is the probability that at most four will graduate from the local community college?

This is:

[tex]P(X \leq 4) = 1 - P(X = 5)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{5,5}.(0.57)^{5}.(0.43)^{0} = 0.0602[/tex]

So

[tex]P(X \leq 4) = 1 - P(X = 5) = 1 - 0.0602 = 0.9398[/tex]

0.9398 = 93.98% probability that at most four will graduate from the local community college.

c. What is the expected number that will graduate?

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

In this question:

[tex]E(X) = 5*0.57 = 2.85[/tex]

The expected number that will graduate is 2.85.

it is 2000 ml after she drank it on Tuesday

Answer:

2000 mL

Step-by-step explanation:

1. The amount of milk left after 1/5 is drank is 4 litres, which is 4000 mL.

2. She drinks half of that, so divide 4000 mL by two.

2000 mL are left after tuesday

Answer:

A and F

Step-by-step explanation:

A and F both represent instances of division of 14/5

B represent multiplication

C represent the reciprocal of the problem, 5/14

D represent addition

......hope it helps......

Answer:

yes,.to obtain sinx as 1 the angle must be 90degrees

so the answer is correct

but there are more solutions like when the cosine angle is 45 the answer is 1

and when x is 450 still sinx = 1..that is to say sin450= 1

Answer:

[tex]E(x)=\$9.118[/tex]

Step-by-step explanation:

From the question we are told that:

Available bills

 [tex]\$5=N0 9\\\\\$10=N0 5[/tex]

 [tex]\$20=N0 3[/tex]

Therefore

Total Bills

 [tex]n=5+9+3[/tex]

 [tex]n=17[/tex]

Probability of selecting each bill

 [tex]For\$5[/tex]

 [tex]P(\$5)=\frac{9}{17}[/tex]

 [tex]For\$10[/tex]

 [tex]P(\$10)=\frac{5}{17}[/tex]

 [tex]For\$20[/tex]

 [tex]P(\$20)=\frac{3}{17}[/tex]

Generally the equation for Expected winning is mathematically given by

 [tex]E(x)=\sum(X)*P(X)[/tex]

 [tex]E(x)=5*\frac{9}{17}+10*\frac{5}{17}+20*\frac{3}{17}[/tex]

 [tex]E(x)=\$9.118[/tex]

Answer:

Step-by-step explanation:

Part A.....let P be the number of people that will show up.....so....

The total amount of broccoli needed (in ounces)  =    8P  ounces

Part B

32  =  8P       divide both sides by 8

4 = P            so.....4 people can be fed.....!!!

Step-by-step explanation:

Answer:

0.18431525 = 18.4%

Step-by-step explanation:

General Formula :

total trials Cn⋅p(success)^n⋅p(fail)^total−n

1198144* (.0218)^3 * (1-.0218)^191

Answer:

A a vertex

Step-by-step explanation:

When rays meet they form a point is formed known as the vertex.

Answer:

[tex](a)\ P(White) = \frac{1}{2}[/tex]

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

[tex]White = 5[/tex]

[tex]Black =3[/tex]

[tex]Red = 2[/tex]

Solving (a): P(White)

This is calculated as:

[tex]P(White) = \frac{White}{Total}[/tex]

[tex]P(White) = \frac{5}{5+3+2}[/tex]

[tex]P(White) = \frac{5}{10}[/tex]

[tex]P(White) = \frac{1}{2}[/tex]

Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]

Let the additional white balls be x

So:

[tex]P(White) = \frac{White+x}{Total+x}[/tex]

This gives:

[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]

Cross multiply

[tex]30+3x = 20 + 4x[/tex]

Collect like terms

[tex]4x - 3x = 30 - 20[/tex]

[tex]x = 10[/tex]

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]

Let the additional black balls be x

So:

[tex]P(White) = \frac{White}{Total+x}[/tex]

So, we have:

[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]

Cross multiply

[tex]10+x = 5 * 4[/tex]

[tex]10+x = 20[/tex]

Collect like terms

[tex]x = 20 -10[/tex]

[tex]x = 10[/tex]

Hence, 10 additional black balls must be added

40

Step-by-step explanation:

Each number is followed by a number that is half its value, so the sequence goes like

320, 160, 80, 40, 20, 10.

Answer:

1 71years

Step-by-step explanation:

x+10=81

x=71

2. x+8=49

x=41

3. x+11=100

x=99

Answer:

Angle formed by the sector measuring x% will be 126°.

Step-by-step explanation:

Since, sum of all sectors formed in a circle is 100%.

By adding the measures of all the sectors,

x + x + 21 + 9 = 100

2x + 30 = 100

2x = 70

x = 35%

Now we know sum of all the central angles formed at the center of a circle = 360°

Therefore, angle formed by x% = 360° × 35%

                                                    = [tex]\frac{360\times 35}{100}[/tex]

                                                    = 126°

[tex] \frac{ - 15}{23} + \frac{30}{ - 46} \\ = \frac{ - 15}{23} + \frac{(2) \times (15)}{(2) \times ( - 23)} \\ = \frac{ - 15}{23} + \frac{15}{ - 23} \\ = \frac{ - 15}{23} - \frac{15}{23} \\ = \frac{ -3 0}{23} \\ = - 1.3[/tex]

Answer:

[tex]Pr= 0.00725[/tex]

Step-by-step explanation:

Given

[tex]p = 0.05[/tex] ---- probability that each component fails

[tex]n = 3[/tex]

Required

[tex]P(System\ Overheats)[/tex]

We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z

The events that the system will overheat are: xyz', xy'z, x'yz and xyz

Where ' means that the component did not fail, and the probability is 1 - p (i.e. complement rule)

So, we have:

[tex]xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375[/tex]

[tex]xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375[/tex]

[tex]x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375[/tex]

[tex]xyz \to 0.05 * 0.05 * 0.05 =0.000125[/tex]

So, the required probability is:

[tex]Pr= 0.002375 +0.002375 +0.002375 + 0.000125[/tex]

[tex]Pr= 0.00725[/tex]

Answer:

the answer of r is 8 i hope it will help

Answer:

19.3 miles per gallon

Step-by-step explanation:

First, subtract 54,042.8-53,737.7. The answer is 305.1

Then, find the unit rate. 305.1/15.8

You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.

That's your answer!

Answer: 9 feet

Step-by-step explanation:

From the information given, we have already been given the equation which is x(x-3)=54. Therefore we will find the value of x which will be:

x(x-3)=54

x² - 3x - 54

x² - 9x + 6x - 54

x(x - 9) + 6(x - 9)

Therefore,

(x - 9) = 0

x = 0 + 9

x = 9

The length is 9 feet

The width will be:

x - 3 = 9 - 3 = 6 feet

Answer:

The sales tax on a 320 dollars purchase is of $29.6.

Step-by-step explanation:

State sales tax y is directly proportional to retail price x.

This means that:

[tex]y = cx[/tex]

In which c is the constant of proportionality.

An item that sells for 156 dollars has a sales tax of 14.42 dollars.

This means that [tex]x = 156, y = 14.42[/tex]. We use this to find c. So

[tex]y = cx[/tex]

[tex]14.42 = 156c[/tex]

[tex]c = \frac{14.42}{156}[/tex]

[tex]c = 0.0924[/tex]

Then

[tex]y = 0.0924x[/tex]

What is the sales tax on a 320 dollars purchase?

y when [tex]x = 320[/tex]. So

[tex]y = 0.0924(320) = 29.6[/tex]

The sales tax on a 320 dollars purchase is of $29.6.

Answer:

3+ 0 = 3

( 4+7) + 3.0 × 1 = 4 + (7+3)

9 + 8 = 8 + 9

Answer:

2/15

Step-by-step explanation:

(-3/5) (-2/9)

Rewriting

-3/9 * -2/5

-1/3 * -2/5

A negative times a negative is a positive.

2/15

Answer:

1326

Step-by-step explanation:

[tex]{52\choose2}=\frac{52!}{(52-2)!2!}=\frac{52!}{50!*2!}=1326[/tex]