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Weekly wages ata certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $250 and $300.​

Answer:

a) mean = 24, standard deviation = 3.098386

b) the probability of exactly 27 ​successes is 0.08265

c) the probability of fewer than 30 ​successes is 0.96478

d) the probability of more than 20 ​successes is 0.8702

Step-by-step explanation:

Given the data in the question,

p = 0.60

n = 40

a) mean and standard deviation;

mean = np = 40 × 0.6

mean = 24

we know that Variance = np( 1 - p )

so standard deviation S.D = √( np( 1 - p ) )

S.D = √( 40 × 0.6( 1 - 0.6 ) )

S.D = √( 24( 0.4) )

S.D = √9.6

S.D = 3.098386

standard deviation = 3.098386

b) the probability of exactly 27 ​successes

P(  x=27 ) = ⁴⁰C₂₇ × ( 0.6 )²⁷ × ( 0.4 )⁽⁴⁰⁻²⁷⁾

= ⁴⁰C₂₇ × ( 0.6 )²⁷ × ( 0.4 )¹³

= [40! / ( 27!( 40 - 27 )! )] × ( 0.6 )²⁷ × ( 0.4 )¹³

= 0.08265

Hence, the probability of exactly 27 ​successes is 0.08265

c)  the probability of fewer than 30 ​successes.

P( x < 30 ) = 1 - P( x ≥ 30 )

= 1 - 0.3522248

= 0.96478

Hence, the probability of fewer than 30 ​successes is 0.96478

d) the probability of more than 20 ​successes.

p( x > 20 ) = 1 - P( x ≤ 20 )

= 1 - 0.1297657

= 0.8702

Hence, the probability of more than 20 ​successes is 0.8702

Answer:

Its 9.

Step-by-step explanation:

First you do the math inside the parenthesis (13), then your gonna multiply 7 by the numbers you got in the parenthesis (7*13), finally subtract 82 from 7*13 and you get your answer, 9.

( 10+3)-82= -69

13- 82 =69

Answer:

A: $100 + $70h = Cost

B: $590

Step-by-step explanation:

A: you can combine the use rate and the driver rate together since they both have the save variable.

B: $100 + $70 (7) = Cost

$100 + $490 = Cost

$590 = Cost

Answer:

0.333

Step-by-step explanation:

2^4-6(6)+3(6)÷2×3

=16-36+18÷6

=-2÷6=0.333

Answer:

d.

the plant is 7mm,then times 2 of itself by on week.

so in 4weeks, it will be .

7×2×2×2×2

Answer:

Step-by-step explanation:

Given,

Size of the lawn he mow's in 1/6 hour = 2/3

Therefore,

Size of the lawn which can be mowed in 1 hour

[tex] = \frac{2}{3} \times 6[/tex]

= 2 × 2

= 4 (Ans)

Answer:

[tex]x = \frac{205}{3}[/tex]

[tex]y =\frac{195}{4}[/tex]

Step-by-step explanation:

Given

[tex]p = 410[/tex] --- perimeter

See attachment for fence

Required

x and y

The perimeter of the fence is:

[tex]p = 2(x + y +5 + y) +x[/tex]

Open bracket

[tex]p = 2x + 2y +10 + 2y +x[/tex]

Collect like terms

[tex]p = 2x+x + 2y + 2y+10[/tex]

[tex]p = 3x + 4y+10[/tex]

Substitute: [tex]p = 410[/tex]

[tex]3x + 4y+10 =410[/tex]

Make 4y the subject

[tex]4y =410-10-3x[/tex]

[tex]4y =400-3x[/tex]

Make y the subject

[tex]y =\frac{400-3x}{4}[/tex]

The area (A) of the fence is:

[tex]A = (y + y + 5) * x[/tex]

[tex]A = (2y + 5) * x[/tex]

Substitute: [tex]y =\frac{400-3x}{4}[/tex]

[tex]A = (2*\frac{400-3x}{4} + 5) * x[/tex]

[tex]A = (\frac{400-3x}{2} + 5) * x[/tex]

Take LCM

[tex]A = (\frac{400-3x+10}{2}) * x[/tex]

Solve like terms

[tex]A = (\frac{410-3x}{2}) * x[/tex]

Open bracket

[tex]A = \frac{410x-3x^2}{2}[/tex]

Remove fraction

[tex]A = 205x-1.5x^2[/tex]

Differentiate both sides

[tex]A' = 205 - 3x[/tex]

To maximize; set [tex]A' =0[/tex]

[tex]205 - 3x =0[/tex]

Solve for 3x

[tex]3x = 205[/tex]

Solve for x

[tex]x = \frac{205}{3}[/tex]

Recall that: [tex]y =\frac{400-3x}{4}[/tex]

So, we have:

[tex]y =\frac{400-3*205/3}{4}[/tex]

[tex]y =\frac{400-205}{4}[/tex]

[tex]y =\frac{195}{4}[/tex]

It Is My Work From My Laptop

Answer

72is the multiple of 9

Answer:

1.5

Step-by-step explanation:

.25*0+1*.25+2*.25+3*.25=1.5

Answer:

Time, t = 5 seconds.

Step-by-step explanation:

Given the following data;

Initial velocity = 16 ft/s

Height = 480 ft

Acceleration due to gravity = 32 ft/s²

To find how much time it will take the ball to reach the ground, we would use the kinematic equation given by the formula;

[tex] d = V_{i}t + \frac {1}{2}at^{2} [/tex]

Where;

Substituting into the equation, we have;

[tex] 480 = 16t + \frac {1}{2}*32t^{2} [/tex]

[tex] 480 = 16t + 16t^{2} [/tex]

Dividing all through by 16, we have;

[tex] 30 = t + t^{2} [/tex]

Re-arranging the quadratic equation, we have;

[tex] t^{2} + t - 30 = 0 [/tex]

We would solve the quadratic equation by factorization;

[tex] t^{2} + 6t - 5t - 30 = 0 [/tex]

[tex] t(t + 6) - 5(t + 6) = 0[/tex]

[tex] (t + 6)(t - 5) = 0 [/tex]

t = -6 or 5

Since we know time can't be negative, we would ignore the value of -6.

Therefore, time = 5 seconds

9514 1404 393

Answer:

  4. 8 yds

  5. 30 mi

Step-by-step explanation:

The relation according to the Pythagorean theorem is ...

  c² = a² + b²

This can be solved for 'a' or 'b' to get ...

  a = √(c² -b²)

  b = √(c² -a²)

__

4. b = √(17² -15²) = √(289 -225) = √64 = 8

The length of leg b is 8 yards.

__

5. a = √(50² -40²) = √(2500 -1500) = √900 = 30

The length of leg 'a' is 30 mi.

_____

Additional comment

You may recognize the relevant Pythagorean triples as (3, 4, 5) and (8, 15, 17). A few others that are often seen are (5, 12, 13), (7, 24, 25) and (9, 40, 41). Any of these can be multiplied by some factor, as the (3, 4, 5) triple is in problem 5.

Answer:

- 3x = 21

Step-by-step explanation:

- 3x - 5 = 16

- 3x - 5 + 5 = 16 + 5

- 3x = 21

- 3x ÷ - 3 = 21 ÷ - 3

x = - 7

Answer:

It’s either D or C

Step-by-step explanation:

Answer:

0.7 , 0.251 , 0.18 , 0.171

Step-by-step explanation:

0.7 is highest 0.251 is 2nd highest 0.18 is lower and 0.171 is lowest as it is simplified to 0.17 to which is lower than 0.18. I am only 8 years old and you should thank me so yeah.

Answer:

x=3

Step-by-step explanation:

2 triangles are proportional so we have

4/6=x/4,5

--> x=(4.4,5)/6=3

You can also use sin cos but this way is faster

Answer:

- 10

Step-by-step explanation:

-6+8×5÷-10

-6+40÷-10

-6-4

-10

Answer and Step-by-step explanation:

According to PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction),

First we multiply, then divide, then finally add/subtract.

-8 times 5 is -40.

-40 divided by -10 is 4.

-6 - 4 = -10

The answer to the expression is -10.

#teamtrees #PAW (Plant And Water)

Answer:

None

Step-by-step explanation:

Given

[tex]m = (4,-2)[/tex]

Required

Point 2 units from m

There are 4 possible points 2 units from m and they are:

[tex]m' = (4+2,-2) = (6,-2)[/tex]

[tex]m" = (4,-2+2) = (4,0)[/tex]

[tex]m'''= (4-2,-2) = (2,-2)[/tex]

[tex]m'''' = (4,-2-2) = (4,-4)[/tex]

From the graph, we have:

[tex]A = (4,2)[/tex]

[tex]B = (-4,2)[/tex]

[tex]C = (2,-3)[/tex]

None of the points is 2 units from m

Point m is located at (4,-2), then point C is located approximately 2 units from point m.

A point in a graph is its location denoted using x and y axis.

Given the following information:

Coordinates of point m=(4,-2)

Coordinates of point A=(4,2)

Coordinates of point B=(-4,2)

Coordinates of point C=(2,-3)

Formula used to find distance between two points say (x1,y1) and (x2,y2) is

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

D1 distance between m and A is

[tex]D_1=\sqrt{(4-4)^2+(2+2)^2}\\D_1=4[/tex]

D2 distance between m and B is

[tex]D_2=\sqrt{(-4-4)^2+(2+2)^2}\\D_2=4\sqrt5[/tex]

D3 distance between m and C is

[tex]D_3=\sqrt{(2-4)^2+(-3+2)^2}\\D_3=\sqrt5\\D_3=2.2\\[/tex]

D3 is approximately equivalent to 2 not exactly 2.

Thus, point C is approximately at 2 units from m.

Learn more about coordinates, here:

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17 and 4, the two y values, are in the wrong place and should be swapped

Answer:

12/13

Step-by-step explanation:

The cosine of O

= QO / PO

= 12 / 13

Step-by-step explanation:

2 to the 5th power =2⁵=2×2×2×2×2=32

The value of 2 to the 5th power (2⁵) is equal to 32.

To calculate 2 to the power of 5 (2⁵).

We have to multiply the base number (2) by itself for the number of times specified by the exponent (5).

So, 2⁵ can be calculated as:

2 × 2 × 2 × 2 × 2

= 32

Therefore, 2 to the 5th power (2⁵) is equal to 32.

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Answer:

2ap + aq - bq -2bp = (a - b)(2p + q)

Step-by-step explanation:

(2ap + aq) - (bq -2bp)

a(2p +q) -b(q + 2p)    [ taking a common from the first, and b from the second]

(2p + q) [a - b]           [takin (2p + q)]

(2p + q)(a - b)

The completely factored form of the expression 2ap + aq - bq - 2bp is

(a - b)(2p + q).

In order to completely factorize the given expression, we need to look for common factors and apply factorization techniques.

Given expression: 2ap + aq - bq - 2bp

Step 1: Look for common factors.

Notice that 'a' is common in the first two terms, and '-b' is common in the last two terms.

Step 2: Factor out the common terms.

We can factor 'a' from the first two terms: a(2p + q)

And factor '-b' from the last two terms: -b(q + 2p)

Step 3: Rearrange the expression.

Now we have: a(2p + q) - b(q + 2p)

Step 4: Factor by grouping.

We can see that (2p + q) is common in both terms, so we can factor it out: (2p + q)(a - b)

Step 5: Final result.

Thus, the completely factored form of the given expression is

(a - b)(2p + q).

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Answer:

97.68 %

z(lower) = .0227

z(upper) = .999

Step-by-step explanation:

Answer:

Step-by-step explanation:

#1

#2

#1

Equation in point slope form

That's also slope intercept form

#2

Slope

Equation in point slope

9514 1404 393

Answer:

  -4

Step-by-step explanation:

The points at the ends of the interval are ...

  (3, f(3)) = (3, 8)

  (6, f(6)) = (6, -4)

The slope is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-4 -8)/(6 -3) = -12/3 = -4

The average rate of change is -4.

Answer:

[tex]ax \: \: \: \: \: \: \: \:xb[/tex]