Please answer this correctly without making mistakes

Answer:

[tex]\mathbf{P(X=5) =0.0888}[/tex]    

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

[tex]\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]

[tex]\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]

where;

n = 8 and π = 0.36

For x = 5

The probability [tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}[/tex]

[tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}[/tex]

[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}[/tex]

[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}[/tex]

[tex]\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}[/tex]

[tex]\mathtt{P(X=5) =0.0887645}[/tex]

[tex]\mathbf{P(X=5) =0.0888}[/tex]     to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5)[tex]\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})[/tex]

[tex]{P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +[/tex][tex]\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )[/tex]

P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888

P(x ≤ 5 ) = 0.9707

c. x ≥ 6

The probability of P ( x ≥ 6) = 1  - P( x  ≤ 5 )

P ( x ≥ 6) = 1  - 0.9707

P ( x ≥ 6) = 0.0293

Answer:

$270

Step-by-step explanation:

Price after markup was 1.20($250) = $300

Price after discounting:  (1.00 - 0.10)($300) = $270

Answer:

[tex] y = - 2 [/tex]

Step-by-step explanation:

Given that the 2 triangles are congruent based on the Hypotenuse-leg theorem, this implies that:

[tex] x - y = x + 2 [/tex] , and [tex] 2x - y = 4x + 2y [/tex]

Using the expression, [tex] x - y = x + 2 [/tex], solve for y:

[tex] x - y - x = x + 2 - x [/tex]

[tex] - y = 2 [/tex]

[tex] y = - 2 [/tex]

Answer:

1, 7

Step-by-step explanation:

Because the product is 0, either (x-1) or (x-7) is equal to 0. That means that x = 1, or 7

Answer:

y = 15°

Step-by-step explanation:

Since ∠QOR and ∠UOT are vertical, they are congruent so ∠UOT = 5y. Since POS is a straight line (which has a measure of 180°) and ∠POS = ∠POU + ∠UOT + ∠TOS, we can write:

5y + 5y + 2y = 180

12y = 180

y = 15°

Answer:

Means:

1.55

1.73

Standard Deviation:

0.1434

0.1338

Coefficient of variation:

9.2

7.7

the limited data listed here shows evidence of stealing by the security service​ company's employees.

Step-by-step explanation:

Given data:

security Service Company          Other Companies    

               x₁                                                 x₂

               1.5                                              1.8

               1.7                                               1.9

               1.6                                               1.6

               1.4                                                1.7

               1.7                                                 1.8

               1.5                                                 1.9

               1.8                                                 1.6

               1.4                                                  1.5

               1.4                                                  1.7

               1.5                                                  1.8

      n₁ = 10                                                 n₂ = 10

To find:

coefficient of variation for each of the two​ samples

Solution:

The formula for calculating coefficient of variation of sample is:

Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100%

Calculate Mean for Security Service Company data:

Mean =  (Σ x₁) / n₁

         = (1.5 + 1.7 + 1.6 + 1.4 + 1.7 + 1.5 + 1.8 + 1.4 + 1.4 + 1.5) / 10

         = 15.5 / 10

Mean = 1.55

Calculate Standard Deviation for Security Service Company data:

Standard Deviation = √∑(x₁ - Mean)²/n₁-1

                                = √∑(1.5-1.55)² + (1.7-1.55)² + (1.6-1.55)² + (1.4-1.55)² + (1.7-1.55)² + (1.5-1.55)² + (1.8-1.55)² + (1.4-1.55)² + (1.4-1.55)² + (1.5-1.55)² / 10-1

=√∑ (−0.05)² + (0.15)² + (0.05)² + (−0.15)² + (0.15)² + (−0.05)² + (0.25)² +  (−0.15)² +  (−0.15)² +  (−0.05)² / 10 - 1

= √∑0.0025 + 0.0225 + 0.0025 + 0.0225 + 0.0225 + 0.0025 + 0.0625 +        0.0225 + 0.0225 + 0.0025 / 9

= √0.185 / 9

= √0.020555555555556

= 0.14337208778404

= 0.143374

Standard Deviation = 0.143374

Coefficient of Variation for Security Service Company:

CV = (Standard Deviation / Mean) * 100%

     = (0.143374 /  1.55) * 100

     = 0.09249935 * 100

     = 9.249935

CV  = 9.2

CV  = 9.2%

Calculate Mean for Other Companies data:

Mean =  (Σ x₂) / n₂

          =  (1.8 + 1.9 + 1.6 + 1.7 + 1.8 + 1.9 + 1.6 + 1.5 + 1.7 + 1.8) / 10

          =   17.3 / 10

Mean  = 1.73

Calculate Standard Deviation for Other Companies data:

Standard Deviation = √∑(x₂-Mean)²/n₂-1

                                = √∑[(1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.7-1.73)² + (1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.5-1.73)² + (1.7-1.73)² + (1.8-1.73)²] / 10 - 1

                                = √∑ [(0.07)² + (0.17)² + (-0.13)² + (-0.03)² + (0.07)² + (0.17)² + (-0.13)² + (-0.23)² + (-0.03)² + (0.07)²] / 9

                                = √∑ (0.0049 + 0.0289 + 0.0169 + 0.0009 + 0.0049 + 0.0289 + 0.0169 + 0.0529 + 0.0009 + 0.0049) / 9

                                = √(0.161 / 9)

                                = √0.017888888888889                                

                                = 0.13374935098493

                                =  0.13375

Standard Deviation = 0.13375

Coefficient of Variation for Other Companies:

CV = (Standard Deviation / Mean) * 100%

     = (0.13375 / 1.73) * 100

     = 0.077312 * 100

     = 7.7312

CV = 7.7

CV = 7.7%

Yes, the limited data listed here shows evidence of stealing by the security service​ company's employees because there is a significant difference in the variation.

Answer:

  $74,748.11

Step-by-step explanation:

In order to make use of the amortization formula, we need to find the equivalent monthly interest rate.

When 12% interest is compounded continuously, the annual multiplier is ...

  e^0.12 ≈ 1.127497

The equivalent multiplier when the interest is compounded monthly is the 12th root of this,

  (e^0.12)^(1/12) = e^0.01 ≈ 1.0100502 = 1 + r

___

The amortization formula tells us that monthly payment amount A will pay off principal P in n months:

  P = A(1 -(1 +r)^-n)/r = $900(1 -1.0100502^-180)/0.0100502

  P = $74,748.11

The customer can pay off a 12% loan of $74,748.11 at the rate of $900 per month for 15 years.

Answer:

H0:  u = 185      against     Ha: u > 185

or

H0:  u ≤ 185      against     Ha: u > 185

Step-by-step explanation:

The null and alternative hypotheses for this experiment would be

H0:  u = 185      against     Ha: u > 185

or

H0:  u ≤ 185      against     Ha: u > 185

This is a one tailed test .

If the results are such that we reject the null hypothesis and accept the alternative hypothesis it means that the Americans are getting fatter as the mean weight is increasing day by day.

The null hypothesis deals with all the values equal to or less than 185 pounds and the alternative with all the values greater than 185  pounds.

Answer:

[tex]x > -1[/tex] or

[tex]x > 2[/tex] or

[tex]x > 3[/tex]

Step-by-step explanation:

Given

[tex](x + 1)(x - 2) (x - 3) > 0[/tex]

Required

Solve; with steps

[tex](x + 1)(x - 2) (x - 3) > 0[/tex]

Start by splitting the inequality as follows

[tex]x + 1 > 0[/tex] or [tex]x - 2 > 0[/tex] or  [tex]x - 3 > 0[/tex]

Solve the inequalities one after the other

Solving: [tex]x + 1 > 0[/tex]

Subtract 1 from both sides

[tex]x + 1 - 1 > 0 - 1[/tex]

[tex]x > -1[/tex]

Solving: [tex]x - 2 > 0[/tex]

Add 2 to both sides

[tex]x - 2 +2 > 0 +2[/tex]

[tex]x > 2[/tex]

Solving: [tex]x - 3 > 0[/tex]

Add 3 to both sides

[tex]x - 3 +3> 0+3[/tex]

[tex]x > 3[/tex]

Hence, the solution to the inequality is

[tex]x > -1[/tex] or

[tex]x > 2[/tex] or

[tex]x > 3[/tex]

Answer:

139 cards

Step-by-step explanation:

This is basically just a division statement - we have 417 cards and want to split it with 3 people (two friends + himself = 3 people).

We can divide these using a calculator or long division, but either way you will get:

[tex]417\div3=139[/tex]

Hope this helped!

Answer: 139

Step-by-step explanation:

417 divided by 3 gives you 139.

Answer:

Quantitative

Step-by-step explanation: Quantitative or numerical variable are statistical or measured variables which involves numbers. Numerical variables allows for mathematical operations such as addition, subtraction and so on to be performed in them. Quantitative variables include height, age, weight, population and other measured variable with have numerical attributes. They can be measured on either ordinal, ratio or interval scales. Hence, since Julien is trying to determine height, the variable is a quantitative or numeric variable.

Answer:

growth is usually reffered to as physical growth happening in size while development happens more gradually and happens mentally.

Step-by-step explanation:

idk if u meant pyscologically or not but that is my understanding.

Answer:

Top left: no

Top middle: one

Top right: no

Bottom left: infinite

Bottom middle: one

Bottom right: one

Step-by-step explanation:

Top left: no

Top middle: one

Top right: no

Bottom left: infinite

Bottom middle: one

Bottom right: one

Answer:

65.8

Step-by-step explanation:

Use the sin formula

100/sin (28) = x/ sin (18)

(sin (18) (100))/ sin (28) = x

x = 65.8223

x = 65.8

Answer:

65.8

Step-by-step explanation:

Accellus Correct

Answer:

96

Step-by-step explanation:

From the given information:

At 95% Confidence interval level,Level of significance [tex]\alpha[/tex] 0.05, the value of Z from the standard normal tables = 1.96

Margin of Error = 0.10

Let assume that the estimated proportion = 0.5

therefore; the sample size n can be determined by using the formula: [tex]n =(\dfrac{Z}{E})^2 \times p\times (1-p)[/tex]

[tex]n =(\dfrac{1.96}{0.1})^2 \times 0.5\times (1-0.5)[/tex]

[tex]n =(19.6)^2 \times 0.5\times (0.5)[/tex]

n = 96.04

n [tex]\approx[/tex] 96

Answer:

Perimeter= 29.12 unit

Step-by-step explanation:

Perimeter of the triangle is the length of the three sides if the triangle summef up together

Let's calculate the length of each side.

For (-4,-6),(3,3)

Length= √((3+4)²+(3+6)²)

Length= √((7)²+(9)²)

Length= √(49+81)

Length= √130

Length= 11.40

For (-4,-6),(7,2)

Length= √((7+4)²+(2+6)²)

Length= √((11)²+(8)²)

Length= √(121+64)

Length= √185

Length= 13.60

For (3,3),(7,2)

Length=√( (7-3)²+(2-3)²)

Length= √((4)²+(-1)²)

Length= √(16+1)

Length= √17

Length= 4.12

Perimeter= 4.12+13.60+11.40

Perimeter= 29.12 unit

Answer:

y-k

x-h

Step-by-step explanation:

Given E &D, F would be at (x, k).

That means E to F would be y-k.

And F to D would be x-h.

I assume you don’t need to find E to D, since that’s just r. (You could use the Distance Formula or Pythagoreans theorem to come up with and equation, but it wouldn‘t be one of those listed.)

Answer:

The answer is A.

Step-by-step explanation:

Local maximums are whenever the graph reaches it's highest y value.

Local minimums are whenever the graph reaches it's lowest y value.

From the graph, we can see that the maximum y-value the graph reaches is y=1. And this happens when x=0.

This only happens once (from the graph shown). Thus, the local maximum would be:

[tex](0,1)[/tex]

The minimum values we can see from the graph is at y=-1. This happens twice from the graph, once at -π and again at 3π/2.

Thus, the local minimums are:

[tex](-\pi,-1), (3\pi/2,-1)[/tex]

Answer:

The sequence is 14, 19, 24, 29, 34, 39.

Step-by-step explanation:

Let's call the common difference (the difference between two consecutive terms) as d. We see that the second term is 19 and the 5th term is 34 and since 5 - 2 = 3, we add d 3 times to 19 to get 34 so therefore:

19 + 3d = 34

3d = 15

d = 5 so the first term is 19 - 5 = 14, the third would be 19 + 5 = 24, the fourth would be 24 + 5 = 29 and the sixth would be 34 + 5 = 39.

Answer:

Step-by-step explanation:

f(x) = 4x⁴ + 4x³ - 8x² - 13x - 5

g(x) = x + 1

To find (f/g)(2) first find (f/g)(x)

To find (f/g)(x) factorize f(x) first

That's

f(x) = 4x⁴ + 4x³ - 8x² - 13x - 5

f(x) = ( x + 1)( 4x³ - 8x - 5)

So we have

[tex] (f/g)(x) = \frac{( x + 1)( 4x³ - 8x - 5)}{x + 1} [/tex]

Simplify

We have

To find (f/g)(2) substitute 2 into (f/g)(x)

That's

(f/g)(2) = 4(2)³ - 8(2) - 5

= 4(8) - 16 - 5

= 32 - 16 - 5

= 11

Hope this helps you

Answer:

$3,000

Step-by-step explanation:

Given that the shares are $50 per share and that Kyle buys $30,000 worth of shares,

Number of shares bought = total price of shares ÷ price per share

= $30,000 ÷ $50

= 600 shares

We are also give that a year later, the shares are worth $55

Total value of shares 1 year later = Price per share one year later x number of shares

= $55 x 600

= $33,000

Hence the investment gained $33,000 - $30,000 = $3,000

Answer:

10%

Step-by-step explanation:

x - amount of shares bought

x * 50[$] = 30000[$]

x = 30000/50 = 600

if he bought 600 shares then he sold earning in total:

600 * 55[$] = 33000[$]

that means investmant gain can be calculate as:

return on investment =  (gain from investment – cost of investment) / cost of investment

return on investment = (33000 - 30000) / 30000 = 3000/30000 =0.1 = 10%

Answer:

(3x+11)/ (5x-9)

Step-by-step explanation:

The numerator is what is on the top of the bar in the middle

(3x+11)/ (5x-9)

Answer:

[tex]\large \boxed{\mathrm{Option \ B}}[/tex]

Step-by-step explanation:

The numerator of a fraction is the top section of the fraction.

Answer:

New length of component y' = 7.2 m (Approx)

Step-by-step explanation:

Given:

Length of component x = 4 m

Length of component y = 10 m

New length of component x' = 8 m

Find:

New length of component y' = ?

Computation:

Length vector of rotation = √x² + y²

Length vector of rotation = √4² + 10²

Length vector of rotation = √16 + 100

Length vector of rotation = √116

Length vector of rotation = √x'² + y'²

√116 = √x'² + y'²

116 = x'² + y'²

116 = 8² + y'²

New length of component y' = 7.2 m (Approx)

Answer:

-11

Step-by-step explanation:

Answer:

(3,-2)

Step-by-step explanation:

Given equations of line

3x-2y=13

2y+x+1=0​

=> x = -1 -2y

Point of intersection will coordinates where both equation have same value of (x,y)

top get that we have to solve the both equations by using method of substitution of simultaneous equation.

using this value of x in 3x-2y=13, we have

3(-1-2y) -2y = 13

=> -3 -6y-2y = 13

=> -8y = 13+3 = 16

=> y = 16/-8 = -2

x = -1 - 2y = -1 -2(-2) = -1+4= 3

Thus, point of intersection of line is (3,-2)

Answer:

A. Congruent and D. Discs

Step-by-step explanation:

You won't see a cylinder that doesn't have congruent bases

Look at the shape of the bases and look at a disc compare their shape

We can describe the bases of a cylinder as congruent.

The volume of cylinder is given by -

V = πR²h

Given is to describe the bases of a cylinder.

The cylinders are uniform in cross - section. Therefore, the bases of the cylinder will have the same area. So, we can conclude that the given bases are congruent.

Therefore, we can describe the bases of a cylinder as congruent.

To solve more questions on cylinders, visit the link below-

https://brainly.com/question/16134180

#SPJ7

Answer:

Step-by-step explanation:

[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]

To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F

Let's solve

First expression = x - 2

Second expression = x + x - 6

Here, we have to find the two numbers which subtracts to 1 and multiplies to 6

= x + ( 3 - 2 ) x + 6

Distribute x through the parentheses

= x + 3x - 2x + 6

Factor out x from the expression

= x ( x + 3 ) - 2x + 6

Factor out -2 from the expression

= x ( x + 3 ) - 2 ( x + 3 )

Factor out x+3 from the expression

= ( x + 3 ) ( x - 2 )

Here, x - 2 is common in both expression.

Thus, H.C.F = x - 2

Hope I helped!

Best regards!!!

Answer:

x - 2

Step-by-step explanation:

by factorization method

1) x - 2

2) x^2 + x - 6

by splitting method

x^2 + 3x - 2x - 6

taking separate common from the first two terms and last two terms

x(x + 3) - 2(x + 3)

now writing x+3 once and the other term to get the right answer

(x + 3)(x - 2)

in both parts just see the similar term and write it as HCF

HCF= x - 2

and the second method by which you can get this answer is division method

Answer:

Step-by-step explanation:

Using the given formula, we put n = 5

[tex]h = 8* {(\frac{1}{2}) ^{n-1}[/tex]

h = 8 / 16

h = 1 / 2 inches