1.32 Factory defective rate. A factory quality control manager decides to investigate the percentage of defective items produced each day. Within a given work week (Monday through Friday) the percentage of defective items produced was 2%, 1.4%, 4%, 3%, 2.2%. (a) Calculate the mean for these data. (b) Calculate the standard deviation for these data, showing each step in detail.

Answer:

multiply both by 2

Step-by-step explanation:

2 x 2 = 4

10 x 2 = 20

Answer:

3 more students

Step-by-step explanation:

6-3=3

How did you get that?

6 students live 2 miles away, while only 3 students live 3 miles away. To find the difference, subtract the two numbers.

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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Answer:

Step-by-step explanation:

divide by R

This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.

The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:

∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))

The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.

The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.

The statement can be interpreted as follows:

"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."

In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.

It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.

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And , the Y's variance is \(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)To find the mode of Y, we need to find the value of y that maximizes the joint probability density function\(f_X, Y(x,y).\)

To do this, we can fix x to be a particular value and then find the value of y that maximizes \(f_X, Y(x,y).\)

For any fixed x between 0 and 2, the function\(f_X, Y(x,y)\) is maximized at y = 1, since this is the only value of y that depends on x and maximizes the function\(cx^2y.\) Therefore, the mode of Y is 1.

To find the value of c that makes this a valid probability density function, we need to ensure that the integral of \(f_X, Y(x,y)\)over the entire sky-plane is equal to 1. We can set up the integral as follows:

integral from 0 to 2 of (integral from 0 to 2 of cx^2y dy) dx

= integral from 0 to \(2 of [c*x^2/2 * y^2]\)evaluated from 0 to 2 dx

= integral from 0 to 2 of \(c*x^2 x2d\)

= [2c/3 * x^3] evaluated from 0 to 2

= (16c/3)

For this to equal 1, we must have c = 3/16. Therefore, the valid probability density function is:

f_X,Y(x,y) = { (3/16)x^2y, 0 <= x <= 2, 0 <= y <= 2; 0, otherwise }

To find the expected value of Y, we need to integrate Y times the joint probability density function f_X, Y(x,y) over the entire xy-plane:

E[Y] = integral from 0 to 2 of (integral from 0 to 2 of y*f_X, Y(x,y) dy) dx

= integral from 0 to 2 of \([(3/16)*x^2/2 * y^2]\) evaluated from 0 to 2 dx

= integral from 0 to 2 of (3/16)*x^2 dx

= [3/16 * x^3/3] evaluated from 0 to 2

= 1

Therefore, the expected value of Y is 1.

To find the variance of Y, we first need to find the second moment of Y by integrating Y^2 times the joint probability density function f_X, Y(x,y) over the entire xy-plane:

E[Y^2] = integral from 0 to 2 of (integral from 0 to 2 of y^2*f_X, Y(x, y) dy) dx

= integral from \(0 to 2 of [(3/16)*x^2/3 * y^3]\) evaluated from 0 to 2 dx

= integral from \(0 to 2 of (3/8)*x^2 dx\)

= \([3/8 * x^3/3]\) evaluated from 0 to 2

= 2

And , the Y's variance is

\(V[Y] = E[Y^2] - (E[Y])^2 = 2 - 1^2 = 1.\)

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At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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Step-by-step explanation:

the area of a parallelogram is

baseline × height = 5 × 3.2 = 16 m²

Answer:

28 biscuits

18 packages of pemmicans

4 packages of butter and cocoa

Step-by-step explanation:

We are given percentage of total daily calories for each item.

Since total number of calories per person each day is 5600,then;

Number of calories from biscuit daily = 40% × 5600 = 2240 calories

Since there are 80 calories per biscuits, then number of biscuits = 2240/80 = 28 biscuits

Number of calories from pemmican daily = 45% × 5600 = 2520 calories

Since there are 140 calories per package, then number of packages of pemmican = 2520/140 = 18 packages of pemmicans

Number of calories from butter and cocoa daily = 15% × 5600 = 840

Since there are 210 calories per package, then number of packages = 840/210 = 4 packages of butter and cocoa

Answer:

That's literally all there is to it! 12/100 as a decimal is 0.12. I wish I had more to tell you about converting a fraction into a decimal but it really is that simple and there's nothing more to say about it. If you want to practice, grab yourself a pen and a pad and try to calculate some fractions to decimal format yourself.

Step-by-step explanation:

Happy 2 help :)

Answer:

Step-by-step explanation:

1) 12/10 as a decimal is?

→ 12/10

→ 6/5 = 1.2

2) 132/100 as a decimal is?

→ 132/100

→ 1.32

3) 546/100 as a decimal is?

→ 546/100

→ 5.46

4) 123/10 as a decimal is?

→ 123/10

→ 12.3

5) 872/100 as a decimal is?

→ 872/100

→ 8.72

Hence, these are the answers.

Answer:

- 1800 ; 4284.8579 ;

Step-by-step explanation:

Given the table :

Outcome _____ probability

-12000 ________ 0.15

__ 0 __________ 0.85

Expected loss, m: Σx*p(x)

(-12000 * 0.15) + (0 * 0.85)

-1800 + 0 = - 1800

Standard deviation = sqrt(Var(x))

Var(x) = Σx²*p(x) - m²

(-12000^2 * 0.15) + (0^2 * 0.85)] - 1800^2

21,600,000 - 3240000

= 18360000

Standard deviation = sqrt(18360000)

Standard deviation = 4284.8579

Answer:

m + m1 ≥ +m

m2 - m1 ≤ -m

Step-by-step explanation:

Let's assume in the inequality m + m1 ≥ +m;

Which results in a value greater than and equal to m (meaning it is a positive value)

While in the inequality m2 - m1 ≤ -m2;

Which results in a value lesser than and equal to m2 (meaning it is a negative value)

Step-by-step explanation: I hope this helps.

Answer:

Answer:

AC ≅ AE

Step-by-step explanation:

According to the SAS Congruence Theorem, for two triangles to be considered equal or congruent, they both must have 2 corresponding sides that are of equal length, and 1 included corresponding angle that is of the same measure in both triangles.

Given that in ∆ABC and ∆ADE, AB ≅ AD, and <BAC ≅ DAE, the additional information we need to prove that ∆ABC ≅ ADE is AC ≅ AE. This will satisfy the SAS Congruence Theorem. As there would be 2 corresponding sides that are congruent, and 1 corresponding angle in both triangles that are congruent to each other.

Answer:

A).   AC ≅ AE

Step-by-step explanation: took test on edge

Using cosine law in the triangle given, the length of BC is 32 units

The law of cosines (also known as the cosine formula) is an equation that relates the lengths of the sides of a triangle to the cosine of one of its angles. It states that:

a² = b² + c² - 2(b)(c) Cos(A)

In the given problem, the data;

Substituting the values into the formula and solve for BC;

BC² = 29² + 23² - 2(29)(23) Cos 75

BC² = 1024.735393

BC = √1024.735393

BC = 32.01

BC ≈ 32

The length of side BC in the triangle is 32 units

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Mathematical induction is a method used to prove statements for all positive integers.

To prove the formula 1 + 2 + 3 + ... + (n-1) + n = n(n+1)/2 using induction,

we first show it holds for the base case n = 1.

When n = 1, the formula becomes 1 = 1(1+1)/2, which is true.

Then, we assume the formula holds for some integer k, and prove it holds for k+1.

Inductive step: Assume that the formula holds for some integer k, i.e., 1 + 2 + ... + (k-1) + k = k(k+1)/2. We need to prove that the formula also holds for k+1.

So, 1 + 2 + ... + (k-1) + k + (k+1) = k(k+1)/2 + (k+1) = (k+1)(k+2)/2, which shows that the formula holds for k+1 as well.

By repeating this process, we conclude the formula holds for all positive integers.

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The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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Answer:

pretty sure it's h(12)

the first choice

To find the probability of x successes in n trials when the trials are dependent, we use the hypergeometric probability function.

The hypergeometric probability function is given by

Where N is the number of elements in the population and r is the number of trials labeled as success.

n is the number of trials, x is the number of successes.

Therefore, the correct answer is the hypergeometric probability function.

Answer:

Square root of

65

lies between

8.0

and

8.1

.

.

Step-by-step explanation:

Explanation:

Squares of natural numbers are

{

1

,

4

,

9

,

16

,

25

,

36

,

49

,

64

,

81

,

...

}

, which are squares of

{

1

,

2

,

3

,

4

,

5

,

6

,

7

,

8

,

9

,

...

.

}

As

65

lies between

64

and

81

, square root of

65

lies between

8

and

9

Further,

8.1

2

=

65.61

and as

8.0

2

=

64

, square root of

65

lies between

8.0

and

8.1

Answer:

between what 2 consecutive number, √65 lies?

D. 8 and 9

Answer:

35^67

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

Look at two points whose coordinates are easy to read.

I see (0, 2) and (5, 3).

slope = rise/run

You need to go from one point to the other using only vertical and horizontal segments. The rise is the vertical displacement. The run is the horizontal displacement.

Start at (0, 2). To go to (5, 3), first go up 1 unit. 1 unit up is a rise of 1. Now go right 5 units. 5 units to the right is a run of 5 units.

slope = rise/run = 1/5

Answer: 1/5

Answer:

D) 56

Step-by-step explanation:

\(\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56\)

In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

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Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

Answer:   \(= ( x^2) + 1\)

Step-by-step explanation:

NOTE: Any restrictions on the domains of f or g must be taken into account when performing these operations.

Composition is another operation that may be performed among functions. Simply stated, it is evaluating one function in terms of another. The format for composition is: (f ○g)(x) = f(g(x)).

Step 1. Find (f ○ g)(x)

\(Since (fo g)(x) = f( g(x) ), then\)

                      \(= f( x + 1 )\\ = ( x + 1 )^2\)

Step 2. Find (g ○ f)(x)

\(Since (g of)(x) = g( f(x) ), then\)

\(= g ( x^2 )\\ = ( x^2) + 1\)

Answer:

what grade r u in

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

is not a polynomial because it has a negative exponent.

Answer:

2/8 are seniors

Step-by-step explanation:

one half = 4/8

4/8 + 1/8 + 1/8 = 6/8.

What's left is 2/8

\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)