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Answer:

The mean is 24.205

Step-by-step explanation:

Firstly, we need to get the z-score

From the question, the probability we have is the probability that commuters take more than 22 minutes to commute one-way

So the probability we had was;

P( x > 22)

So we need the z-score corresponding to 63.70% or simply 0.637

We can use the standard normal distribution table to get this

Mathematically, from the standard normal distribution table this is -0.35

z-score = (x- mean)/SD

-0.35 = (22-mean)/6.3

22-mean = -2.205

mean = 22 + 2.205 = 24.205

Answer:

The probability is 31/35

Step-by-step explanation:

Answer:

The probability is  [tex]P( 0.2 < p < 0.3) = 0.89751[/tex]

Step-by-step explanation:

From the question  we are told that

   The population proportion is  p =  0.25

   The sample size is  n  =  200  

Generally given that the sample size is large the mean of this sampling distribution is mathematically represented as [tex]\mu_{x} = p = 0.25[/tex]

 Generally the standard deviation is mathematically represented as

        [tex]\sigma = \sqrt{ \frac{ p (1- p ) }{n} }[/tex]

=>     [tex]\sigma = \sqrt{ \frac{ 0.25(1- 0.25 ) }{200} }[/tex]

=>     [tex]\sigma = 0.03062[/tex]

Generally the probability that between 20% (0.2) to 30% (0.3) of the households in the sample have a burglar alarm is mathematically represented as  

      [tex]P( 0.2 < p < 0.3) = P(\frac{ 0.2 - 0.25}{ 0.03062 } < \frac{p- \mu_{x}}{\sigma } < \frac{ 0.2 - 0.25}{ 0.03062 } )[/tex]

[tex]\frac{p -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \  p )[/tex]

=>   [tex]P( 0.2 < p < 0.3) = P(-1.6329 < Z <1.6329 )[/tex]

=>   [tex]P( 0.2 < p < 0.3) = P( Z< 1.6329) - P( Z <- 1.6329 )[/tex]

From the z table  the area under the normal curve to the left corresponding to  1.6329 and  -1.6329  is

    [tex]P( Z< 1.6329) = 0.94875[/tex]

and

    [tex]P( Z <- 1.6329 ) = 0.051245[/tex]

So

   [tex]P( 0.2 < p < 0.3) = 0.94875 - 0.051245[/tex]

=> [tex]P( 0.2 < p < 0.3) = 0.89751[/tex]

Answer:

m∠1 = 140°

m∠2 = 40°

m∠3 = 65°

m∠4 = 75°

m∠5 = 115°

Step-by-step explanation:

We will use a few different methods to find the angles:

A triangle's angles will always add up to 180°. With this information, we can find the last angle of the triangle on the left:

∠1+∠2+∠3=180°

60+80+∠3=180°

Let x represent the value of ∠3. Simplify addition:

[tex]140+x=180[/tex]

Subtract 140 from both sides:

[tex]140-140+x=180-140\\\\x=40[/tex]

The unknown angle is 40°. With this information, we can find the

m∠1:

m∠1 and the 40° we just found are supplementary angles, which means that their measures will add up to a total of 180°.

∠1+∠2=180°

Insert the value we know:

40°+∠2=180

Let x represent the value of ∠2. Subtract 40 from both sides:

[tex]40-40+x=180-40\\\\x=140[/tex]

There fore:

m∠1=140°

We can use this same rule to find the m∠2:

∠1+∠2=180°

or, we can use the vertical angles rule. The first angle we found (Which is 40°) is a vertical angle to m∠2, so they have the same value. Therefore:

m∠2=40°

To find m∠3, we need to find the other missing angle in the middle triangle. Use the supplementary angle rule, since the missing angle is supplementary to the angle that is 105°:

∠1+∠2=180°

Insert the known values, substituting x for the unknown angle:

[tex]x+105=180[/tex]

Subtract 105 from both sides:

[tex]x+105-105=180-105\\\\x=75[/tex]

The unknown angle is 75°. Now find m∠3, knowing that triangles add up to 180°:

m∠2+m∠3+75=180

Insert the m∠2, make m∠3 be x:

[tex]40+x+75=180[/tex]

Simplify addition:

[tex]115+x=180[/tex]

Subtract 115 from both sides:

[tex]115-115+x=180-115\\\\x=65[/tex]

Therefore:

m∠3=65°

To find m∠4, use the vertical angle rule.

Therefore:

m∠4=75°

To find m∠5, we could find all triangle measures of the least triangle, or we can use the following:

An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees.

The m∠5 is the exterior angle, and the opposite interior angles are 75° and 40°:

[tex]75+40=115[/tex]

Therefore:

m∠5=115°

:Done

Answer:

Mr. Pharm will earn $108.50 in two years, having deposited $1,500 into an account earning 3.5% simple interest.

Step-by-step explanation:

1550 * 3.5% * 2 = $108.50

Answer:

y= -5x + -7 is your answer

Answer:

Hence, option 'd' is correct.

Step-by-step explanation:

Unlike the expected frequency which is obtained based on prediction, the observed frequency is the actual frequency that is determined from the experiment.

Therefore, we conclude that

Hence, option 'd' is correct.

b = 0

To solve make b the subject so:

4b + 6 = 2 - b + 4

5b + 6 = 6

5b = 0

5 = 0/5

= 0

Answer:

i know a nice song it's called hi guy. you are cool and smart

Step-by-step explanation:

you should take a bath everyday

Step-by-step explanation:

When x=-3

7-2(-3)=7-(-6)

=7+6

=13

Answer:

27/4

Step-by-step explanation:

To find the answer, all you would need to do is multiply the denominator by the whole number and add the numerator. And so if you multiply the denominator (4) by the whole number (6) , and add the numerator (3) , you will get the answer: 27/4

Answer:

27/4

Step-by-step explanation:

6*4=24

24+3=27

Answer:

115% of 75

Step-by-step explanation:

Answer:

This cannot be simplified any further. That is the simplest you'll get.

Answer:

50.50$

Step-by-step explanation:

8.5x+25

x is the hours

8.5(3)+25= 50.50

He will use as much paper that will work

C. <3

pls give brainlyist

[tex]56(cos(33^{\circ}) + i sin(33^{\circ})) \div 7(cos(11^{\circ}) + i sin(11^{\circ}))\\\\=8(cos(22^{\circ}) + i~ sin(22^{\circ}))[/tex]

"The number of the form a + ib, where a, b are real numbers and [tex]i=\sqrt{-1}[/tex]"

"This theorem gives a formula for computing powers of complex numbers.

[tex](r(cos\theta+i~sin\theta))^n=r^n~(cos(n\theta)+i~sin(n\theta))[/tex] "

For given question,

We need to divide two complex numbers.

[tex]56(cos(33^{\circ}) + i sin(33^{\circ})) \div 7(cos(11^{\circ}) + i sin(11^{\circ}))[/tex]

Consider,

[tex]56(cos(33^{\circ}) + i~ sin(33^{\circ})) \div 7(cos(11^{\circ}) + i ~sin(11^{\circ}))\\\\=8[(cos(33^{\circ}) + i~ sin(33^{\circ})) \div (cos(11^{\circ}) + i ~sin(11^{\circ}))][/tex]                 ...........(i)

Consider the first complex number.

[tex](cos(33^{\circ}) + i sin(33^{\circ}))[/tex]

We can write this complex number as,

[tex]cos(3(11^{\circ}) )+ i sin(3(11^{\circ}))[/tex]

By De Moivre's theorem,

[tex]cos(3(11^{\circ}) )+ i~ sin(3(11^{\circ}))\\\\=(cos(11^{\circ})+ i~ sin(11^{\circ}))^3[/tex]

Substitute this value in (i),

[tex]56(cos(33^{\circ}) + i~ sin(33^{\circ})) \div 7(cos(11^{\circ}) + i ~sin(11^{\circ}))\\\\=8[(cos(33^{\circ}) + i~ sin(33^{\circ})) \div (cos(11^{\circ}) + i ~sin(11^{\circ}))]\\\\=8[(cos(11^{\circ}) + i~ sin(11^{\circ}))^3 \div 7(cos(11^{\circ}) + i~ sin(11^{\circ}))]\\\\=8[(cos(11^{\circ}) + i~ sin(11^{\circ}))^2]\\\\=8[(cos(2\times 11^{\circ}) + i~ sin(2\times 11^{\circ}))]~~~~~~~~~.............(De~Moivre's~theorem )\\\\=8(cos(22^{\circ}) + i~ sin(22^{\circ}))[/tex]

Therefore, [tex]56(cos(33^{\circ}) + i sin(33^{\circ})) \div 7(cos(11^{\circ}) + i sin(11^{\circ}))[/tex] is [tex]8(cos(22^{\circ}) + i~ sin(22^{\circ}))[/tex]

Learn more about the De Moivre's theorem here:

brainly.com/question/17211848

#SPJ3

Answer:

25

Step-by-step explanation:

40%x = 10

40/100 x=10

x=10* 100/40

x = 25

Answer:- 8

Step-by-step explanation:

-4 + 4(3)/ -4+3

-4 +12 / -1

8/-1

Answer:

680 oranges

15 levels

Step-by-step explanation:

Add 2, add 3, add 4, add 5.....

1+3+6+10+15+21+28+36+45+55+66+78+91+105+120=680

15 levels

He can’t add a 16th level, because it would have 136 oranges, which would put him over 800.

Answer:

15 levels, 680 oranges.

Step-by-step explanation:

Guess an check. The first 15 add to 680. The 16th is 136. 680+136=810, which is over 800.

Answer:

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

Let x be number

Multiply by 2 = x * 2

Now, divide by 3 = 2x ÷ 3 = [tex]\frac{2x}{3}[/tex]

So, this is same as multiplying 'x' by [tex]\frac{2}{3}[/tex]

Answer:

m=-1/6

Step-by-step explanation:

m=1-3/4+8=-2/12=-1/6

Answer:

39 R 10

Step-by-step explanation:

18 goes into 586 evenly 32 times, but there is 10 left over, making that the remainder.

Answer:

Step-by-step explanation:

A.

Given parameter:

  Side length  = 9cm

Unknown;

Area of the square  = ?

Solution:

The shape given is a square.

 Area of a square  = L²

 L is the side length

  Insert the parameters and solve;

     Area of the square  = 9²  = 81cm²

B.

Given parameters:

Area of the square = 9cm²

Unknown:

Side length  = ?

Solution:

The shape is a square;

  Area of a square  = L²

         9  = L²

          L = √9 = 3cm