4-76. The fill volume of an automated filling machine used for filling cans of carbonated beverage is normally distributed with a mean of 12.4 fluid ounces and a standard deviation of 0.1 fluid ounce.

Answer: See explanation

Step-by-step explanation:

From the question, we are informed that the weight of 90 books is 50kg. We need to get the weight of a book first and this will be:

= 50/90

= 5/9

Therefore, the weight of 180 such books will be 5/9 multiplied by 180. This will be:

= 5/9 × 180

= 100kg

The probability that at least two of the 14 bits are 1 is approximately 0.9658 if a sequence of 14 bits is randomly generated.

Sequence number = 14

favourable outcome = 1

we can use the complement rule to calculate the probability that at least two of the 14 bits are 1.

The probability of a single bit 1 = 1/2

The probability of a single bit 0 = 1/2.

The probability that a single bit is not 1 =  \((\frac{1}{2}) ^{14}\)

The probability that exactly one bit is 1 =  \(14*(\frac{1}{2} ^{14} )\)

Therefore, the probability that at least two of the 14 bits are 1 is:

probability  = 1 - \((\frac{1}{2} ^{14} ) - 14*(\frac{1}{2} ^{14} )\)

probability  = 1 - \(15*( \frac{1}{2} ^{14} )\)

probability  = 0.9658

Therefore we can conclude that the probability that at least two of the 14 bits are 1 is approximately 0.9658.

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Answer:

If we square both sides then we get

x2-8x+16 = (x-4)2

Now if we expand the right side of the equation we get

x2-8x+16 = (x-4)(x-4)

x2-8x+16 = x2-8x+16

So no matter what x is, the right side will be equal to the left side.

However, if we look at the original equation on the left side, √(x2-8x+16) , the value under the square root symbol has to be greater than or equal to zero (otherwise we get an imaginary number and you might not be working with those yet)

Step-by-step explanation:

So in order for √(x2-8x+16) to be greater than or equal to zero, x has to be greater than or equal to 4. If x is less than 4 you get a negative number. If x is greater than 4, you'll get the same answer on both sides no matter what x is

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's solve ~

\(\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 8x + 16} \)

\(\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 4x - 4x + 16} \)

\(\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{} (x - 4) - 4(x - 4)} \)

\(\qquad \sf  \dashrightarrow \: \sqrt{ (x - 4)(x - 4)} \)

\(\qquad \sf  \dashrightarrow \: \sqrt{ (x - 4) {}^{2} } \)

\(\qquad \sf  \dashrightarrow \: x - 4\)

Now, it's given that ~

\(\qquad \sf  \dashrightarrow \:x \geqslant 4\)

plug the value of x as 4 :

\(\qquad \sf  \dashrightarrow \:4 - 4\)

\(\qquad \sf  \dashrightarrow \:0\)

So, we can infer that :

Value of the required expression lies in :

\(\qquad \sf  \dashrightarrow \: \sqrt{ {x}^{2} - 8x + 16} \geqslant 0\)

it's value is always greater than pr equal to 0, satisfying the given condition ~

Step-by-step explanation: A square root function has a range of y greater-than-or-equal-to 0.

For example, the function f(x) = √x has a domain of x greater-than-or-equal-to 0 and a range of y greater-than-or-equal-to 0. This is because the square root of a positive number is always positive, and the square root of 0 is equal to 0. So, for any value of x greater-than-or-equal-to 0, the corresponding value of y will always be greater-than-or-equal-to 0.

Other functions that have a range of y greater-than-or-equal-to 0 include:

the absolute value function: f(x) = |x|

exponential functions with positive bases: f(x) = e^x, f(x) = 2^x, etc.

any linear function with a positive slope: f(x) = mx + b, where m > 0.

These are just a few examples of functions that have a range of y greater-than-or-equal-to 0.

The value of cos θ is equal to 1/3 when sec θ= √6/2.

Since we are given the value of secant of theta, we can use the relationship between secant and cosine to find the value of cosine of theta.

Let's start by recalling the definitions of secant and cosine functions. The secant of an angle is defined as the reciprocal of the cosine of that angle.

In other words, secθ = 1/cosθ

Conversely, the cosine of an angle is defined as the reciprocal of the secant of that angle.

cosθ = 1/secθ

We are given that secθ= √6/2

We can use this value to find cosθ= 1/secθ

cosθ = 1 / (√6/2)

To simplify this expression, we can multiply both the numerator and denominator by 2/sqrt(6).

cosθ = ((2/√6) / (√6/2) * (2/√6))

cosθ = (2/√6) / 1

cosθ = (2/√6 * √6/√6)

cosθ = 2/6 = 1/3

Therefore, the value of cosθ is equal to 1/3 when secθ = sqrt(6)/2.

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Answer:

\(a_n=112\left(-\frac{1}{4}\right)^{n-1}\)

Step-by-step explanation:

Geometric Sequences

There are two basic types of sequences: arithmetic and geometric. The arithmetic sequences can be recognized because each term is found as the previous term plus a fixed number called the common difference.

In the geometric sequences, each term is found by multiplying (or dividing) the previous term by a fixed number, called the common ratio.

We are given the sequence:

112, -28, 7, ...

It's easy to find out this is a geometric sequence because the signs of the terms are alternating. If it was an arithmetic sequence, the third term should be negative like the second term.

Let's find the common ratio by dividing each term by the previous term:

\(\displaystyle r=\frac{-28}{112}=-\frac{1}{4}\)

Testing with the third term:

\(\displaystyle -28*-\frac{1}{4}=7\)

Now we're sure it's a geometric sequence with r=-1/4, we use the general equation for the nth term:

\(a_n=a_1*r^{n-1}\)

\(a_n=112\left(-\frac{1}{4}\right)^{n-1}\)

The answer is option (b) The measured values agree with one another, but neither agrees with the expected value.

Given three values, we need to check if they agree with one another or not. According to the given, a measured value agrees with an established/expected value if the established value is within the 95% confidence interval, which is a range of ±2Δx around the measured mean. The Δx is the standard uncertainty.

If we have two measured values, we can roughly say that two values agree if their 95% confidence intervals overlap.

According to the question, the three values are 1.65, 1.64 and 1.63. The expected value is 1.67.

The standard deviation of the three values can be calculated by:

\($\frac{(1.65 - 1.64)^2 + (1.64 - 1.67)^2 + (1.63 - 1.67)^2}{3-1} = \frac{0.0006 + 0.0009 + 0.0016}{2} = 0.0015$\)

The standard error of the mean is

\($\frac{0.0015}{\sqrt{3}} = 0.0009$\)

Now, the 95% confidence interval of the expected value is

\($\pm 2(0.0009)$\), i.e. 1.67±0.0018 = [1.68, 1.66].

The 95% confidence intervals of the measured values are:

1.65±0.0018 = [1.65, 1.63], 1.64±0.0018 = [1.64, 1.62], 1.63±0.0018 = [1.63, 1.61].

The 95% confidence intervals of the measured values overlap each other, so they agree with one another. However, none of the measured values agree with the expected value. Therefore, the answer is an option (b) The measured values agree with one another, but neither agrees with the expected value.

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Answer:

A≈380.13 m²

Step-by-step explanation:

looked it up

Answer:

A= 380.13 m²

Step-by-step explanation:

A=\(\pi r^{2}\)

A= \(\pi\)x\(11^{2}\)

A= 380.13

Answer:

a=q+f

Step-by-step explanation:

1. a-f=q

2. you need to do the opposite of -f which is +f to cancel it out

after that you need to do the +f to the q

Hope this helps

Using the literal equation a-f = q, the solution for a = p + q

A literal equation are  type of equations which have two or more unknown variables . A literal equation can be solved by adding or subtracting or multiplying or divide by same numbers to the both sides of the equation in order to solve the expression for the required variable.

For example if an given equation is x+ y =2 and we want to solve it for y

Then we will try to keep y on one side and take remaining terms to other side.⇒ y = x-2  is solution for y.

Given equation :

a- f = q

To solve for a, add f to both sides

⇒ a- f +  f = q+ f

⇒ a = q + f

Solution for a is q +f.

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Answer: 3/4

Step-by-step explanation:

Answer: 5.

Step-by-step explanation:

the distance from zero in either the positive or negative direction. 3/4 and -3/4 is written as |3/4| in absolute terms and is true for any value |5|.

Answer:

4.8

Step-by-step explanation:

24/5 = 4.8

A rational number is any whole number, fraction, finite decimal or repeating decimal. Therefore 4.8 = rational number.

A rational expression to represent the amount of juice in each cup is 24/5.

A fraction is a part of the whole represented by a/b, where a and b are any integers.

Given, Kim divided 24 ounces of orange juice into 5 cups.

Therefore, the amount of juice in each cup is:

24/5

Hence, a rational expression to represent the amount of juice in each cup is 24/5.

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Answer:

my biggest tip would be use a percentage calculator

The transformation represented by the rule (x, y) → (-x, -y) is a reflection across the origin.

The rule (-x, -y) reflects each point (x, y) across both the x-axis and the y-axis simultaneously. When a point is reflected across the x-axis, its y-coordinate changes sign, and when a point is reflected across the y-axis, its x-coordinate changes sign. Therefore, the rule (-x, -y) reflects a point (x, y) across both axes, resulting in the point (-x, -y).

A reflection across the origin involves reversing the sign of both the x-coordinate and the y-coordinate. This means that the transformation takes each point (x, y) and maps it to the point (-x, -y), effectively reflecting it across the origin (0, 0).

Thus, the given rule represents a reflection across the origin, and it can also be described as a rotation of 180° about the origin.

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Step-by-step explanation:

Given,

Side of a square = 4xy

Therefore, area of the square = side × side

= 4xy × 4xy

\(16 {x}^{2} {y}^{2} (ans)\)

Answer:

it will help you

Answer:

The countertop is  8.37 square meters

Step-by-step explanation:

Let

L ----> the length of the countertop

W ----> the width of the countertop

we know that

The area of rectangle (countertop) is equal to

we have

Remember that

To convert feet to meters multiply by 0.305

so

Find the area in square meters

Answer:

8.37

Step-by-step explanation:

hope this helps!

have a good day :)

Answer:

It must be less than 180º.

Step-by-step explanation:

A triangle always adds up to 180º which then means that since two angles have already been stated that means the total of those two angles is 74º which you subtract from 180º to get 106º which is the measure of the third angle.

Answer:

d'(n) = d

Step-by-step explanation:

Answer:

96

Step-by-step explanation:

25% can be written as 0.25

so:

24= .25*x

Divide both sides by 0.25

24 - .25x

.25 - .25

x=96

The measured signal could have a dynamic error of approximately 21.6% of the true value due to the limitations of the 1st order system with a time constant of 0.7 seconds.

The dynamic error that could result from measuring a 2 Hz periodic waveform using a 1st order system with a time constant of 0.7 seconds can be estimated using the following formula:

Dynamic error = 100% x (1 - exp(-T/τ)),

where T is the period of the input signal, τ is the time constant of the system, and exp(-T/τ) is the system's gain at the input frequency.

Substituting T = 0.5 s (since the period of a 2 Hz waveform is 0.5 seconds) and τ = 0.7 s, we get:

Dynamic error = 100% x (1 - exp(-0.5/0.7)) ≈ 21.6%

This means that the measured signal could have a dynamic error of approximately 21.6% of the true value due to the limitations of the 1st order system with a time constant of 0.7 seconds. This error is due to the fact that the system cannot respond fast enough to the rapid changes in the input signal, leading to an output that lags behind the input. The larger the time constant of the system relative to the period of the input signal, the larger the dynamic error will be.

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Answer:

Just put each factor = 0 and get the answer

2x-7 = 0

x = 7/2

7x + 2 = 0

x = -2/7

Thus answer is first option

Answer:

x = 7/2  This is a zero of the polynomial

x = -2/7  This is the other zero

Step-by-step explanation:

This quadratic function is the product of two linear factors.  Set each of these factors = to zero and solve each resulting equation for x:

2x - 7 = 0 => 2x = 7  =>  x = 7/2  This is a zero of the polynomial.

7x + 2 = 0 =>  7x = -2  =>  x = -2/7  This is the other zero.

Answer:

A

Step-by-step explanation:

Given: functions f(x) and g(x)

To choose: the correct option

Solution:

A function is a relation in which each element of the domain has a unique image in the co-domain.

Composition of functions refers to the combining of two or more functions such that the output of one function becomes the input for the next function.

Two functions f(x) and g(x) are inverse functions if (ƒ ∘ g)(x) = (g ∘ ƒ)(x) = x.

Answer:

A) (ƒ ∘ g)(x) = (g ∘ ƒ)(x) = x

Step-by-step explanation:

Answer:

p = 0.42n.

Step-by-step explanation:

To derive an equation, the price per orange will need to be found. Since 6 oranges costed $2.52, simply divide to find the price:

2.52/ 6 = $0.42 per orange.

Therefore, an equation representing the total price for 'n' amount of oranges would be:

p = 0.42n.

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The Surface area of the triangular prism is :

From the total of 300 workers in the factory :

a. Number of men = 200 and Women = 100

b. Number of workers works in the morning = 225

c. Number of workers unionized are 150.

d. Number of workers trustworthy are 50.

Total number of workers in the factory are 300.

a. Fraction of men in the factory are ( 2/3)

= 2/3 of 300

= 200

Women

= 300 -200

= 100

b. Number of workers in the morning shift are

= 3/4 of 300

= 225

c. Total number of workers unionized

= 1/ 2 of 300

= 150

d. Number of trustworthy workers

= 1/6 of 300

= 50

Therefore, out of 300 workers in the factory answer of the following questions are:

a. Number of men and women work in the factory are 200 and 100 respectively.

b. Number of workers works in the morning is 225.

c. Unionized workers = 150

d. Trustworthy workers = 50.

The above question is incomplete , the complete question is :

The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.

a. How many men work in the factory and how many women?

b. How many workers work in the morning?

c. How many are unionized?

d. How many are trustworthy?

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Answer:

Step-by-step explanation:

3

Answer:

6435 ways

Step-by-step explanation:

Since the order does not matter, it is a combination, also because they do not indicate how many men and how many women should be in the group of 8, which means that it would be the ways of putting together a group of 8 with 15 people (10 men + 5 women)

That is to say:

nCr = n! / (r! * (n-r)!)

n = 15, r = 8, replacing:

15C8 = 15! / (8! * (15-8)!)

15C8 = 6435

which means that there are 6435 ways to arm the group

Answer: 129 Feet

Step-by-step explanation:

You can make an equation where Height=h, and Base=b. So going backwards with the first question, the base will equal 4 times the height: b=4h, and 11 less. b=4h-11. The the other equation will be just that the base plus the height is 49. b+h=49. Then you put that into y=mx+b form. The first equation already is, and the second equation would be b=49-h. So, since the equations equal the same things, you throw away the b. Then you make a new equation by having 4h-11 equal 49-h. Since this is true seeing as they are the same triangle. Then you just use propreties of equality for the equation. You end up with 5h=60. The. You divide 60 by 5 to make 5h just equal h. So you get h=6. Then, like the qeuation said, the base (unknown) plus the height (6) is 49. So to get from 6 to 49, the answer is 43. The formula for that area of a triangle is (base x height) /2 = area. So 43 times 6 is 258. Then divided by 2 is 129. So the area of the triangle is 129.

The area of the triangle is 222 square feet.

The formula for calculating the area of the triangle is expressed as:

A = 0.5bh

The base of a triangle is eleven feet less than  four times its height,

b = 4h - 11

Also, if the sum of the lengths of  the base and height of the triangle is 49 is expressed as:

b + h = 49

4h-11+h = 49

5h = 49 + 11

5h = 60

h = 12

Since 4h = b + 11

4(12) = b + 11

b = 48 - 11

b = 37

A = 0.5(12)(37)

A = 222ft^2

Hence the area of the triangle is 222 square feet.

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Bob is 2 years older than Carol and the reverse of Carol's age is 3 times Bob's age, which makes Bob's to be 17 years.

Let 1B represent Bob's age and let 1C represent Carol's age, we can write the following equations;

Reversing Carol's age gives;

The multiples of 3 that have the form X1 have 7 as the rightmost number.

Given that 1B is a teenager, we have;

When;

The reverse of Carol's age is therefore;

Therefore, from the given description, Bob's age 1B = 17 years

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When a postal worker counts the number of complaint letters received by the united states postal service in a given day, the type of data collected is quantitative.

Quantitative data is data that can be measured and expressed in numbers. In this case, the number of complaint letters received by the United States Postal Service in a given day can be measured and expressed as a number.

Qualitative data, on the other hand, is data that cannot be measured or expressed in numbers. For example, the contents of the complaint letters would be qualitative data.

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The exponential equation is \(y=ab^x\). Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = \(ab^{x}\) . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = \(ab^{x}\) . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = \(ab^{x}\)

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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