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Using the hypergeometric distribution, there is a 0.2486 = 24.86% probability that the entire batch will be rejected.

The formula to find the hypergeometric distribution formula is

P(X=x)=P(x, N, n, K)[tex]=\frac{C_{k, x} C_{N-k, n-x} }{C_{N, n} }[/tex]

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

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

For this problem, the values of the parameters are given as follows:

N = 8000, n = 7, k = 0.04 x 8000 = 320

The probability that the entire batch will be rejected is P(x≥1), given as follows: P(x≥1)=1-P(X=0)

In which,

P(X=0)=P(0, 8000, 7, 320)[tex]=\frac{C_{320, 0} C_{7680, 7} }{C_{8000, 320} }=0.7514[/tex]

Now, P(x≥1)=1-0.7514=0.2486

Therefore, 0.2486 = 24.86% probability that the entire batch will be rejected.

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Step-by-step explanation:

a square has the same perimeter as a 5cm by 7cm rectangle. which of the following area of the square

Answer:

At sea level, the altimeter would read 0 feet. Any positive readings on the altimeter would indicate she is above sea level. Any negative readings on the altimeter would indicate she is below sea level.

Step-by-step explanation: PLATO

Answer:

-2x-8

Step-by-step explanation:

-5x + (3x-8)

-5x +3x -8

-2x - 8

Answer:

-2x-8

Step-by-step explanation:

-5x+(3x-8)

-5x+3x-8

-2x-8

Try this

The conversion of (6, pi/2) from polar into rectangular coordinates is (0, 6)

An equation is an expression that shows the relationship between two or more numbers and variables.

The conversion from polar to rectangular coordinates is:

x = rcosФ and y = rsinФ

Hence:

x = 6cos(π/2) = 0, y = 6sin(π/2) = 6

The conversion of (6, pi/2) from polar into rectangular coordinates is (0, 6)

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Bricklayer Ben placed a total of 462 bricks.

Bricklayer Ben places 42 bricks per hour.

Bricklayer Bob places 36 bricks per hour.

Let

x = number of hours worked by Bricklayer Bob

y = number of hours worked  by Bricklayer Ben

Therefore,

x = 2y

42y + 36x = 1254

42y + 36(2y) = 1254

42y + 72y = 1254

114y = 1254

y = 1254 / 114

y = 11

Hence,  Bricklayer Ben placed a total of 42 × 11 = 462 bricks.

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Answer:

y=7x

Step-by-step explanation:

The equation of the with a slope of m and a y-intercept of b is y=mx+b.

Answer: 13 questions

Step-by-step explanation:

52% of 25 is 13

25/x=100%/52%

x=13

Answer:

B

Step-by-step explanation:

The only x,y pair in the table is  4,2

Options A,B and D. The correction about the area of the triangle are

Firstly this is an equilateral triangle

3 of the sides have the length of 8.7cm

b = half of 8.7

= 4.35cm

To get A we have

a² + b² = c²

a² + 4.35² = 5²

When we solve this out we would have

a² = 25 - 18.9225

a ≈ 2.5 cm.

Hence we have proved that the first option is correct.

For B,

In an equilateral triangles, each of the angles = 60 degrees

60/2 = 30 is the angle that is made from the base

a / 4.35 = tan 30

then a = 4.35 tan 30

This would also give us an approximate of 2.5

For D

The calculations we have done based on the statements in A and B shows that D is correct as 2.5.

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Answer:

by sss

Step-by-step explanation:

The property of congruence:

ΔABC ≅ ΔDCB by the SSS criterion.

The correct option is the SSS postulate.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given information:

AB ≅ DC and AC ≅ DB.

The proof is given described as:

In triangle ABC and triangle DCB,

The two sides are congruent,

AB ≅ DC and AC ≅ DB ( As per the information provided).

And as per the diagram and reflexive property of congruence,

BC ≅ BC.

Therefore, ΔABC ≅ ΔDCB by the SSS criterion.

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Answer:

- x + 1

Step-by-step explanation:

(x² + 2x + 3) - (x² + 3x + 2) ← multiply terms inside parenthesis by - 1

= x² + 2x + 3 - x² - 3x - 2 ← collect like terms

= - x + 1

Answer:

x = - 5 , x = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

the values of x that make f(x) zero are the zeros

to find the zeros let f(x) = 0 , that is

3x² + 13x - 10 = 0

consider the factors of the product of  the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = + 13

the factors are + 15 and - 2

use these factors to split the x- term

3x² + 15x - 2x - 10 = 0 ( factor the first/second and third/fourth terms )

3x(x + 5) - 2(x + 5) = 0 ← factor out (x + 5) from each term

(x + 5)(3x - 2) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]

Using the normal distribution, it is found that there is a 0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion and the sample size are given, respectively, by:

p = 0.4, n = 743

Hence the mean and the standard error are given, respectively, by:

The probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3% is the p-value of Z when X = 0.43 subtracted by the p-value of Z when X = 0.37, hence:

X = 0.43:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.43 - 0.4}{0.018}[/tex]

Z = 1.67

Z = 1.67 has a p-value of 0.9525.

X = 0.37:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.37 - 0.4}{0.018}[/tex]

Z = -1.67

Z = -1.67 has a p-value of 0.0475.

0.9525 - 0.0475 = 0.905.

0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.

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Answer:

23.20

Step-by-step explanation:

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Answer:

α ≈ 23.20°

Step-by-step explanation:

given all 3 sides of the triangle , then any of the trig ratios may be used, that is sine, cosine or tangent to find α

tanα = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{7}[/tex] , then

α = [tex]tan^{-1}[/tex] ( [tex]\frac{3}{7}[/tex] ) ≈ 23.20° ( to the nearest hundredth )

or

sinα = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{\sqrt{58} }[/tex] , then

α = [tex]sin^{-1}[/tex] ( [tex]\frac{3}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )

or

cosα = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{7}{\sqrt{58} }[/tex] , then

α = [tex]cos^{-1}[/tex] ( [tex]\frac{7}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )

The Answer Is:

4z

Hope this helped!

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\large\textbf{Identify the equivalent expression z + z + z + z}\downarrow[/tex]

[tex]\huge\textbf{Let's find out which one is equal to}\\\\\huge\textbf{the following expressions:}[/tex]

[tex]\large\textbf{z + z + z + z}[/tex]

[tex]\large\textbf{= 1z + 1z + 1z + 1z}[/tex]

[tex]\large\textbf{= 2z + 1z + 1z}[/tex]

[tex]\large\textbf{= 3z + 1z}[/tex]

[tex]\large\textbf{= 4z}[/tex]

[tex]\huge\textbf{Anwer:}[/tex]

[tex]\huge\boxed{\textsf{Option A. 4z}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

15556913140

Step-by-step explanation:

Answer:

[tex] \frac{2 ln(5) }{3 ln(2) } [/tex]

Step-by-step explanation:

[tex] log_{8}(25) = \frac{ ln(25) }{ ln(8) } = \frac{ ln( {5}^{2} ) }{ ln( {2}^{3} ) } = \frac{2 ln(5) }{3 ln(2) } [/tex]

Answer:

200+500

Step-by-step explanation:

its wrong i answered the wrong question

Using a system of equations, the correct statement is given as follows:

B. The equation that represents this situation is 10 + x = -18. The second number is -28.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The numbers are x and y, and their sum is -18, hence:

x + y = -18.

The number y is 10, hence:

x + 10 = -18.

x = -18 - 10 = -28.

Which means that option B is correct.

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Answer:

[tex](x+5)^{3}[/tex]

Step-by-step explanation:

Hope this helps

The expression for the word problem is ( x + 5 )².

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given word problem is the cube of the sum of a number and 5. The expression will be formed as below:-

Let the unknown number be x.

E = ( x + 5 )²

Therefore, the expression for the word problem is ( x + 5 )².

The complete question is given below:-

The cube of the sum of a number and 5. Write the mathematical expression.

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Answer:

The answer is 6 and -6

Step-by-step explanation:

The given equation is
[tex]x^2 - kx + 9 = 0 ... (1)[/tex]

where a = 1. b = -k, c = a

since the equation (1) has equal roots

[tex]\Rightarrow b^2 - 4ac = 0 \newline\\\Rightarrow (-k)^2 - 4(1)(9) = 0\\ \newline\\\Rightarrow (k)^2 - 36 = 0 \newline\\\Rightarrow k^2 = 36 \newline\\\Rightarrow k = \pm 6[/tex]

Hence volume of k = 6, -6

Step-by-step explanation:

IR = 9√3

E = 60°

I = 30°

R = 90°

• Find ER.

ER/sin(I) = IR/sin(E)

ER/sin(30°) = 9√3/sin(60°)

ER/(1/2) = 9√3/(1/2 √3)

ER/(1/2) = (9√3 . 2)/√3

ER/(1/2) = 18√3/√3

ER/(1/2) = 18 → IR/sin(E)

ER = 18 . 1/2

ER = 9 is the answer

• Find IE (There are 2 ways).

First, using a Sinus Rule.

IE/sin(R) = IR/sin(E)

IE/sin(90°) = 9√3/sin(60°)

IE/1 = 9√3/(1/2 √3)

IE = (9√3 . 2)/√3

IE = (18√3)/√3

IE = 18 is the answer

Second, using a Pythagoras Theorem.

IE = √(IR² + ER²)

IE = √((9√3)² + 9²)

IE = √(81.3 + 81)

IE = √(243 + 81)

IE = √324

IE = 18 is the answer

Answer:

31,41,51,71

Step-by-step explanation:

Answer:

The answer is: 31,41,51,71

The quantity of wheat to be transported by the company in metric tonnes is; 1.224 metric tonnes.

Since it follows that 1 metric tonne is equivalent to 2205 lb. It therefore follows that the quantity which is equivalent to 2700lb to be transported is;

= 2700/2205 = 1.224

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The true statements among the given options are written below

bc || ad

ba ≅ cd  

∠cba ≅ ∠bcd

In an isosceles trapezoid, there is one pair of legs of equal length and a pair of parallel lines.

Given that quadrilateral abcd is a isosceles trapezoid.

In the given trapezoid abcd

bc || ad ( pair of parallel sides )

So this is correct.

ba ≅ cd  ( For an isosceles trapezoid legs are equal)

So this is correct

∠cba ≅ ∠bcd (According to  the property of isosceles  trapezoid )

So this is correct.

Hence, bc || ad, ba ≅ cd, ∠cba ≅ ∠bcd are correct

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Answer:

BAC=BDC(BDX)=30°

Step-by-step explanation:

We know that BD=OD.

But OD=OB= Radius of the circle.

Therefore

BD=OD=OB

BDO is equilateral triangle.

Angle DBO= 60°

Now let us take the intersecting point of CD and AB as X.

In triangle BDX,

BXD= 90°(BXD+BXC=180°, BXD+90°=180°, BXD=90°)

BXD+DBX+BDX=180°{Angle Sum Property}

90°+60°+BDX= 180°

BDX= 30°

We also know that,

BDC(BDX)= BAC (Angles lie on the same arc{BC} are equal in measure.

Therefore,

BAC=BDC(BDX)=30°

Answer:

There are 6 possible outcomes for die A and 6 possible outcomes for die B.

Each of the 6 outcomes of die A can be combined with each of the 6 outcomes of die B. Therefore the total number of possible outcomes for each roll is given by:

6*6=36

Plug the second equation (the one already solved for y) into the first equation

2x - (2x + 3) = 7

2x - 2x - 3 = 7

-3 = 7

Since the 2x's canceled out and left a false statement, this system of equations has no solution.

Hope this helps!