Answer please will give brainlest answer!

Answer:

1.5 feet long

Step-by-step explanation:

you have to do 12 ÷ 8 then...

12.0 ÷ 8 = 1.5

a) The probability that an employee does not know C/C++ = 0.4

(b) The probability that an employee knows either C/C++ or R = 0.8

(c) The probability that an employee knows R and does not know C/C++ =  0.2

(d) The probability that an employee knows at least one of the languages = 0.8

Let us assume that an event A:  employee knows C/C++ languages

here, 60% know C/C++

So, P(A) = 0.6

event B:  employee knows R

here, 50% know R

This means, P(B) = 0.5

30% know both languages

This means, P(A ∩ B) = 0.3

Also, 20% know neither language.

⇒  P(A ∪ B)c = 0.2

a.  the probability that an employee does not know C/C++ would be,

1 - P(A)

= 1 - 0.6

= 0.4

b. the probability that an employee knows either C/C++ or R

We know that the formula, P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 0.6 + 0.5 - 0.3

P(A∪B) = 0.8

c.  the probability that an employee knows R and does not know C/C++

P(B) - P(A∩B)

= 0.5 - 0.3

= 0.2

d.  the probability that an employee knows at least one of the languages

1 - P(A ∪ B)c

= 1 - 0.2

= 0.8

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Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

Answer:

11.6 lbs

Step-by-step explanation:

Answer:

0.06

Step-by-step explanation:

The surface area of the given sphere is 764.15 square inches.

Given that, the sphere has diameter = 15.6 inches.

Here, radius = 15.6/2 = 7.8 inches

We know that, surface area of a sphere is 4πr².

Now, surface area = 4×3.14×7.8²

= 764.15 square inches

Therefore, the surface area of the given sphere is 764.15 square inches.

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Answer:

  3·ln(x) -ln(1+x)

Step-by-step explanation:

You want to "solve" the expression ln(x³/(1+x)).

The relevant rules of logarithms are ...

  ln(a^b) = b·ln(a)

  ln(a/b) = ln(a) -ln(b)

The given log expression can be expanded as ...

  \(\ln{\left(\dfrac{x^3}{1+x}\right)}=\ln(x^3)-\ln(1+x)=\boxed{3\ln(x)-\ln(1+x)}\)

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

(x - 2)(x - 5)(x - k) >= 0

Let's set each term equal to 0

x - 2= 0

Add 2 to both sides

x = 2.

x - 5 = 0

Add 5 to both sides

x = 5

x - k = 0

Add k to both sides

x = k

Since x = 2 and 5, k = 2, 5

Let's plug our numbers into the inequality.

(2 - 2)(2 - 5)(2 - 2) >= 0

(0)(-3)(0) >= 0

0>=0

(5 - 2)(5 - 5)(5 - 5) >= 0

(3)(0)(0) >= 0

0 >= 0

This proves that 2 and 5 are equal to k

Answer:

52

length = 12+2=14 feet

P = 2l+2w = (2 x 14) + (2 x 12) = 52

Step-by-step explanation:

Hope that helps! Have a wonderful day :)

As per the given variables, Victor jumped a total of 4 yards.

Total yards jumped = 6 feet high

Additional yards = 2

A yard is one linear yard. "Yd" is the yard symbol. The standard of measurement has always been derived from either a natural item or a portion of the human body, such as a foot, an arm's length, or the width of a hand.

Converting the initial jump of 6 feet to yards, as the additional distance given is also in yards.

There are 3 feet in a yard, therefore -

6 feet = 6/3  

= 2

Thus, Victor jumped 2 yards initially, and then 2 more yards as given in the problem.

Calculating, the total distance Victor jumped in yards -

= 2 + 2

= 4

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The width of the laptop screen is equal to 16 inches.

In order to determine the width of the laptop screen, we would have to apply Pythagorean's theorem.

Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

Substituting the parameters, we have:

c² = a² + b²

20² = 8² + b²

400 = 64 + b²

b² = 400 - 64

b²  = 256

b = √256

b = 16 inches.

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Step-by-step explanation:

again ?

out of the total of 70°, 30° are taken by the first angle.

so, that leaves 70 - 30 = 40° for the second angle.

q = 40°

is there still something unclear about this ? please let me know.

Janet has 630 options to customize a car based on the given features.

How to solve the question?

To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:

10 car models x 7 exterior colors x 9 interior colors = 630

Thus, Janet has 630 options to customize a car based on the given features.

It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.

Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.

In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.

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The volume of the composite figure is 228 ft³.

To calculate the volume of a composite figure, we need to break it down into its individual components and then sum up the volumes of each component.

From the given dimensions, it seems that the composite figure consists of multiple rectangular prisms. Let's calculate the volume of each prism and then add them together.

First prism:

Length = 8 ft, Width = 4 ft, Height = 6 ft

Volume = Length * Width * Height = 8 ft * 4 ft * 6 ft = 192 ft³

Second prism:

Length = 3 ft, Width = 2 ft, Height = 6 ft

Volume = Length * Width * Height = 3 ft * 2 ft * 6 ft = 36 ft³

Now, let's add the volumes of both prisms:

192 ft³ + 36 ft³ = 228 ft³

Therefore, the volume of the composite figure is 228 ft³.

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What is the volume of the composite figure? 8 ft 4 ft 6 ft 3 ft 2 ft

Answers 96 ft³3 76 ft³ 228 ft³ 192 ft³ ​

Answer:

Number of items sold, discrete; time spent at desk, continuous

Step-by-step explanation:

The random variables from the survey is number of items sold, discrete; time spent at desk, continuous

A selection that is chosen randomly (purely by chance, with no predictability). Every member of the population being studied should have an equal chance of being selected.

According to the question

The supervisor at an office randomly selected 45 employees and observed their work habits.

She recorded

i > number of items sold  

ii > total time the employees spent at their desk  

As per observation

Number of items sold = discrete

as it is not possible to sell items in a continuous manner

But

time spent at desk = continuous

as every employee spend time at there desk

Hence, the random variables from the survey is number of items sold, discrete; time spent at desk, continuous

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The relationship in the figure is a function because each input has only one output to which they are linked

A function is a definition or rule that maps each element in a set of input values to exactly one element in a set output values.

The data in the sets can be presented as follows;

x  \({}\)               f(x)

-1 \({}\)      →         2

0\({}\)        →        2

1\({}\)         →        -3

2\({}\)         →       -2

8\({}\)         →        3

The above table indicates that each x-value has only one f(x) value, which indicates that the relationship s a function. The relationship is still a function with the presence of an f(x) value, 2, having two x values, -1 and 0, as the condition satisfies the definition of a function.

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Answer:

Option e: 2/3 is the correct answer.

Step-by-step explanation:

The slope of a line is given by:

\(m = \frac{y_2-y_1}{x_2-x_1}\)

Two-points on line are needed to calculate slope of a line. In the attached diagram, two points are highlighted which are located on line C.

The two points are:

(x1,y1) = (9,4)

(x2,y2) = (3,0)

Putting the values in the formula

\(m = \frac{0-4}{3-9}\\=\frac{-4}{-6}\\=\frac{2}{3}\)

The slope of line C is: 2/3

Hence,

Option e: 2/3 is the correct answer.

Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

\(\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}\)

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

\(\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}\)

\(\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4\)

\(\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}\)

\(\textsf{Step 4:} \quad y+2=-4x+24\)

\(\textsf{Step 5:} \quad y+2-2=-4x+24-2\)

\(\textsf{Step 6:} \quad y=-4x+22\)

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

a. The transfer function h(z) for the given difference equation is H(z) = (1/√2) (1 + \(z^{-1\)).

The zeros and poles are: Zero at z = -1 and pole at z = 0.

b. The transfer function h(z) for the given difference equation is H(z) = (1/√2) (1 -\(z^{-1\)).

The zeros and poles are: Zero at z = 1 and pole at z = 0.

c. The transfer function h(z) for the given difference equation is H(z) = (8.23z² - 5.4z + 23.45) / (1 - 6.2z + 5.75z²).

The zeros and poles can be found by factoring the denominator of the transfer function. The two poles are at z = 1.7 and z = 4.0, and there are no zeros.

For the given difference equations, the transfer functions and corresponding zeros and poles have been determined. For part a, the transfer function is H(z) = (1/√2) (1 + \(z^{-1\)), with a zero at z = -1 and a pole at z = 0. For part b, the transfer function is H(z) = (1/√2) (1 - \(z^{-1\)), with a zero at z = 1 and a pole at z = 0. For part c, the transfer function is H(z) = (8.23z²  - 5.4z + 23.45) / (1 - 6.2z + 5.75z² ), with poles at z = 1.7 and z = 4.0 and no zeros.

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The speed of the second pedestrian is 5 kilometers per hour.

Let's say that the speed of the second pedestrian is S.

We know that the other pedestrian walks at a speed of 4km/h, and they (together) travel a distance of 27km in 3 hours, then we can write the linear equation:

(4km/h + S)*3h = 27km

It says that both pedestrians work, together, a total of 27km in 3 hours.

Now we can solve that linear equation for S, to do this, we need to isolate S in the left side of the equation.

4km/h + S = 27km/3h = 9 km/h

S = 9km/h - 4km/h = 5km/h

The speed of the second pedestrian is 5 kilometers per hour.

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Given:

Total Population = 500  millions

Population Under 16 Years of Age or Institutionalized = 120 millions

Not in Labor Force = 150  millions

Unemployed = 23 millions

Now,

A) Labor force

= Total population – Population under 16 years of age – Not in labor force

= 500 – 120 – 150

= 230 millions

B) Unemployment rate \($=\frac{\text { Unemployment }}{\text { Labor force }} \times 100 \%$\)

or

Unemployment rate \($=\frac{23 \text { million }}{230 \text { million }} \times 100 \%$\)

or

Unemployment rate \($=10 \%$\)

The complete question is,

Assume the following data for a country:

Category Number of People (in Millions)

Total Population 500

Population Under 16 Years of Age or Institutionalized 120

Not in Labor Force 150

Unemployed 23

Part-Time Workers Looking for Full-Time Jobs 10

A) What is the size of the labor force (in millions)?

B) What is the official unemployment rate (in percentage)?

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Answer:

Mode

Step-by-step explanation:

I believe mode because 8 is the number that appears most often in this set of numbers.

note: Mode is the number that appears most often in any set of numbers.

Answer:

The total no. of purple marbles will be:

\( \boxed{ \underline{ \rm{28}}}\)

Step-by-step explanation:

It is given that for every 5 blue marbles, we have 4 purple marbles. And similarly we have to find for the no. of purple marbles for 35 blue marbles.

First, Let's divide these 35 blue marbles in groups of 5. We will get:

➝ 35 ÷ 5 = 7 groups

For each group of 5 marbles, there are 4 purple marbles. So for 7 groups, No. of purple marbles will be:

➝ 4 × 7 = 28 purple marbles.

And we are done! :D

Answer:

24th term

Step-by-step explanation:

Given

\(S_n = 600\)

\(Sequence:2,4,6,8..\)

Required

Find n

First, calculate common difference d

\(d = 4 -2 = 2\)

Calculate n using:

\(S_n = \frac{n}{2}[2a + (n - 1)d]\)

So:

\(600 = \frac{n}{2}[2*2 + (n - 1)*2]\)

\(600 = \frac{n}{2}[4 + 2n - 2]\)

Multiply by 2

\(120 = n[2 + 2n]\)

\(1200 = 2n^2 + 2n\)

Rewrite as:

\(2n^2 + 2n - 1200 = 0\)

Divide by 2

\(n^2 + n - 600 = 0\)

Solve quadratic equation.

It gives:

\(n = -25\ n = 24\)

Since n can't be negative;

Then

\(n = 24\)

Answer:

B(6, 5), C(1, -7)

Step-by-step explanation:

A(2, 5)

From A to B, there is translation x, (4, 0).

Add 4 to A's x-coordinate, and add 0 to A's y-coordinate.

B(2 + 4, 5 + 0) = B(6, 5)

From C to B there is the translation y, (5, 12).

Since we are going from B to C, we undo translation y.

The translation from B to C is (-5, -12).

C(6 - 5, 5 - 12) = C(1, -7)