Find the domain and range of f(x)=2x+cos x

Ms. Nash, an executive with a television company, is trying to decide on the subject matter for a new television series for adults. She chooses to conduct a survey to help her make an informed decision. Which of the following sampling techniques should Ms. Nash use in order to obtain the most representative sample of the viewing audience?

Ms. Nash should ask a randomly–chosen, equal number of men and women shopping at a department store.

Ms. Nash should ask the first two hundred men she encounters on the busy street in front of her office.

Ms. Nash should ask five men and five women shopping at a local grocery store.

Ms. Nash should ask men and women from a variety of age ranges who are attending a science fiction movie festival.

It’s the first one

Final answer:

Ms. Nash should use a stratified random sampling method to ensure a representative sample of the viewing audience for a new TV series. The best option available is to query men and women from a variety of age ranges at a science fiction movie festival, despite potential genre bias.

Explanation:

Ms. Nash, an executive with a television company, should employ a sampling technique that ensures a representative sample of the adult viewing audience for a new television series. The most effective approach would be to use random sampling with a stratified design, which takes into account various characteristics such as age, gender, and possibly other demographics or interests relevant to the content of the television series. Although none of the options provided perfectly align with this methodology, the most appropriate among them is the fourth option, which suggests asking men and women from a variety of age ranges who are attending a science fiction movie festival. This method attempts to achieve some level of stratification by including a variety of age ranges, which is a crucial aspect when trying to extrapolate the preferences of a larger population. Moreover, by selecting from men and women, there is an acknowledgment of the need to balance gender representation. However, the choice of a science fiction movie festival may introduce a selection bias toward viewers who prefer that genre, so it's not entirely ideal for a general audience survey.

Answer:

PS=5.4

Step-by-step explanation:

The centroid divides each median in the ratio 2:1

If U is the centroid, then

[tex]3.6:x+0.8=2:1[/tex]

We use ratio to obtain;

[tex]\frac{3.6}{x+0.8}=\frac{2}{1}[/tex]

Cross multiply;

[tex]3.6=2(x+0.8)[/tex]

Expand;

[tex]3.6=2x+1.6[/tex]

Group similar terms;

[tex]3.6-1.6=2x[/tex]

[tex]2=2x[/tex]

x=1

PS=PU+US

PS=3.6+1+0.8

PS=3.6+1+0.8

PS=5.4

Answer:

tons

Step-by-step explanation:

Answer:

The Answer is 5 (3/4) more miles.

Step-by-step explanation:

For this we just need to add and subtract fractions.

We we want  to get to 13 (1/2) miles...however we have already ran

3 (1/2) + 4 (1/4) ... this is the same as 3.5 plus 4.25. When we add those up we get...

3.5+4.25 = 7.75 then we subtract ... 13.5 - 7.75 = 5.75 = 5 (3/4) our answer.

Final answer:

Lorenz needs to run 5 3/4 more miles to meet his goal for his training plan this week.

Explanation:

To find out how many more miles Lorenz needs to run this week to meet his goal, we need to add up the miles he has already run and subtract that from his goal. Lorenz has already run 3 1/2 miles on Monday and 4 1/4 miles on Tuesday, so we can add these two amounts to get 3 1/2 + 4 1/4 = 7 3/4 miles. Next, we subtract this amount from his goal of 13 1/2 miles: 13 1/2 - 7 3/4 = 5 3/4 miles. Therefore, Lorenz needs to run 5 3/4 more miles to meet his goal for his training plan this week.

Answer:

60 mph

Step-by-step explanation:

time = distance/speed

If s represents the return speed, then the relationships of the travel times is ...

300/(s-10)-1 = 300/s

300s -s(s-10) = 300(s-10) . . . . . multiply by s(s-10)

-s^2 +310s = 300s -3000 . . . . eliminate parentheses

s^2 -10s -3000 = 0 . . . . . . . . . . write in standard form

(s -60)(s +50) = 0 . . . . . . . . . . . . factor

This has solutions s=60, s=-50. The negative solution is extraneous.

The return speed was 60 mph.

We want to find the speed in your return given that increasing the speed by 10 mph would saved you an hour of trip.

The speed was 72.62 mi/h

We know the relationship:

distance = speed*time

Let's assume the speed is represented with the variable S, and the time it took you to return is represented with T.

We know that the distance of the roundtrip was 600 miles.

then we can write:

600mi = S*T

Now we know that if we increase the speed by 10mi/h, the time decreases by one hour, so we can also write:

600mi = (S + 10mi/h)*(T - 1h)

So we have a system of equations:

To solve this, we can isolate one of the variables in one of the equations and then replace that on the other equation.

I will isolate T in the first one:

T =  600mi/S

Now we replace this in the other equation to get:

600mi = (S + 10mi/h)*(600mi/S - 1h)

Now we can solve this for S, the speed.

600mi = 600mi - 1h*S + (6,000 mi^2/h)/S - 10mi

0 = -1h*S + (6,000 mi^2/h)/S - 10mi

Now we multiply both sides by S to get:

0 = -1h*S^2 + (6,000 mi^2/h) - 10mi*S

This is a quadratic equation, we can solve this byt using the Bhaskara's formula:

[tex]S = \frac{10mi \pm \sqrt{(10mi)^2 - 4*(6,000 mi^2/h)*(-1h)} }{2*(-1h)} \\\\S = \frac{ 10mi \pm 155.24mi}{-2h}[/tex]

We need to take the positive solution, so we get:

S = (10mi - 155.24 mi)/(-2h) = 72.62 mi/h

The speed was 72.62 mi/h

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Answer:

x = -7

Step-by-step explanation:

Since the equation for a directrix of a parabola that opens horizontally is x = h-p, we can plug it in. So h = -3 and p = 4. So x = -3-4 or x = -7.

Answer:

x=-7

Step-by-step explanation:

Answer:

The measure of the fourth angle is 81°

Step-by-step explanation:

we know that

The sum of the internal angles of a quadrilateral must be equal to 360 degrees

Let

x----> the measure of the fourth angle

we have

90°+90°+99°+x=360°

Solve for x

279°+x=360°

x=360°-279°=81°

Answer:

The sum of polynomials [tex](6x^{3} +8x^{2} +2x+4)[/tex] and [tex](10x^{3} +x^{2} +11x+9)[/tex] is [tex]16x^{3} +9x^{2} +13x+13[/tex].

Adding [tex](3x-2)[/tex] to the sum above gives a sum of [tex]6x^{3} +9x^{2} +16x+11[/tex]

Step-by-step explanation:

To add two polynomials, the coefficients of the terms of the same degree must be added together. The result of adding two terms of the same degree is another term of the same degree. If any term is missing from any of the grades, it can be completed with 0.

[tex](6x^{3} +8x^{2} +2x+4)+(10x^{3} +x^{2} +11x+9)= 16x^{3} +9x^{2} +13x+13[/tex]

If we adding [tex](3x-2)[/tex] to the sum above, we get:

[tex](16x^{3} +9x^{2} +13x+13)+(0x^{3} +0x^{2} +3x-2)= 16x^{3} +9x^{2} +16x+11[/tex]

Simplify √8 to 2√2

2√2 + √98 + √72

Simplify √98 to 7√2

2√2 + 7√2 + √72

Simplify √72 to 6√2

Simplify

= 15√2

Answer:

C

Step-by-step explanation:

√8 + √98 + √72

√(4×2) + √(49×2) + √(36×2)

2√2 + 7√2 + 6√2

15√2

Answer C.

Answer:

C) about 113

Step-by-step explanation:

"How many people are there per square mile?" means that we want a ratio with miles as denominator. In other words, to find the population density, we just need to divide the population by the land area (miles squared):

[tex]population-density=\frac{people}{land-area}[/tex]

We know that the population of Alabama is 90,000 people and its land area is 800 miles squared, so [tex]people=90000[/tex] and [tex]land-area=800mi^{2}[/tex].

Replacing values:

[tex]population-density=\frac{people}{land-area}[/tex]

[tex]population-density=\frac{90000}{800mi^{2}}[/tex]

[tex]population-density=112.5[/tex]

Which rounds to:

[tex]population-density=113[/tex]

We can conclude that there are approximately 113 people per square mile in Alabama.

Answer:

About 113

Step-by-step explanation:

Hope this help

5xbxh hope it helps

Answer:

242.4 ft

Step-by-step explanation:

The angle immediately adjacent to the 29° angle is (90° - 29°) , or 61°.

The cosine function relates this 61° angle to the 500 ft hypotenuse and the unknown adjacent side y:

                    y

cos 61° = -----------

                500 ft

so that y = (500 ft)(cos 61°) =  (500 ft)(cos 61°) =  (500 ft)(0.485) = 242.4 ft

By the confront theorem we know that the limit only exists if both lateral limits are equal

In this case they aren't so we don't have limit for x approaching 2, but we can find their laterals.

Approaching 2 by the left we have it on the 5 line so this limit is 5

Approaching 2 by the right we have it on the -3 line so this limit is -3

Think: it's approaching x = 2 BUT IT'S NOT 2, and we only have a different value for x = 2 which is 1, but when it's approach by the left we have the values in the 5 line and by the right in the -3 line.

ANSWER

The limit does not exist.

EXPLANATION

From the graph the left hand limit is the value the graph is approaching as x-values approaches 2.

[tex] \lim_{x \to {2}^{ - } }(f(x)) = 5[/tex]

Also the right hand limit is the value that the graph approaches, as x-values approach 2 from the right.

[tex]\lim_{x \to {2}^{ + } }(f(x)) = - 3[/tex]

Since the left hand limit is not equal to the right hand limit, the limit as x approaches 2 does not exist

Answer:

b= 7 times the square root of 2

Step-by-step explanation: In a 45-45-90 degree triangle the base and the height both equal x and the hypotenuse is equal to x times the square root of 2.

Hope this helps

Answer:

a = 7

b = 7√2

Step-by-step explanation:

45 45 90 right triangle and it's also isosceles right triangle

a = 7

Ratio of leg : hypotenuse = x : x√2

leg a = 7

hypotenuse b = 7√2

Answer:

I think the answer is B Plz tell me if im wrong

Good luck on your test!

Answer:

- 12 divided by 1/6 =n

Step-by-step explanation:

Let the total number of comic books collection be n

Number of comic books=12

Also, according to question number of comic books=1/6 of n

therefore,

1/6 of n=12

n=12×6

n=72

Thus, correct answer is option (a)

5×3/4=3.75

she needs 3.75 cups of sugar

Answer:

3√10

Step-by-step explanation:

27² + y² = x²

⇒⇒⇒ y² = x² - 27² ----------------- [ 1 ]

3² + y² = z²

⇒⇒⇒ y² = z² - 3² ----------------- [ 2 ]

Equate [ 1 ] and [ 2 ] :

x² - 27² = z² - 3²

x² - z² = 27² - 3²

x² - z² = 720 ----------------- [ 3 ]

x² + z² = 30²

x² + z² = 900 ----------------- [ 4 ]

[ 3 ] - [ 4 ] :

-2z² = -180

z² = 90

z = √90

z = 3√10

Answer:

4.9 I have to go and get the games and she said that she would be doing the same thing on my mind

Answer:

6.5 feet

Step-by-step explanation:

[tex]v = w \times h \times l[/tex]

We know the Volume is 234 ft

and we know the width is 4.5 ft and the length is 8 feet, we can set up or formula and solve for the height.

234=4.5 × 8 x h

234=36 x h

234÷36=h

6.5=height

Answer:For this item, we let x and y be the number of bushels of apple that will be used to produce apple cider and apple juice, respectively. The situation above is best represented by the following equations,

                                           x + y = 18

                                          20x + 15y = 330

The values of x and y from the equations above are 12 and 6, respectively. Therefore, 12 bushels will be used to make apple cider and 6 bushels will be used to make apple juice.

Step-by-step explanation:

Answer:

For this item, we let x and y be the number of bushels of apple that will be used to produce apple cider and apple juice, respectively. The situation above is best represented by the following equations,                                            x + y = 18                                           20x + 15y = 330The values of x and y from the equations above are 12 and 6, respectively. Therefore, 12 bushels will be used to make apple cider and 6 bushels will be used to make apple juice.

Step-by-step explanation:

Answer: 300 feet

The biggest challenge in this problem is that it includes a fraction.

So, we can make this question easier by figuring out how many feet this train travels in 1 second.

If we know how far it traveled in 1 second, then we can quickly figure out how far it goes in 4 seconds.

Since the train travels 25 feet in 1/3 of a second, then it must travel 3 times that far in 1 second:  

25 feet x 3 = 75

We now know that this train must travel 75 feet in 1 second. Now we can solve for 4 seconds quite simply.

If the train travels 75 feet in 1 second, then how far will it travel in 4 seconds? We need to multiply 75 by 4 to get our answer:

75 x 4 = 300 feet

A high-speed train travels 25 feet in 1/3 second. In 4 seconds, the train will have traveled 300 feet

In question, the distance traveled by a high-speed train in 1/3 seconds is 25 feet.

Therefore, If a train travels 25 feet in 1/3 second, then it must travel 3 times the distance in 1 whole second.

That means,

25*3 = 75 feet

If a train travels 75 feet in 1 second, then the distance traveled in 4 seconds is;

75*4 = 300 feet

Hence, in 4 seconds, the train will have traveled 300 feet

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Answer:

PS = 7

k = 9

Step-by-step explanation:

RS = PQ                   Given

3x  - 7 = x - 1            Substitute algebraic terms. Subtract x from both sides

3x-x - 7 = x - 1 - x    Combine

2x - 7 = - 1                Add 7 to both sides.

2x - 7+7 = -1+7         Combine

2x = 6                      Divide by 2

2x/2 = 6/2

x = 3

Length of PS = x - 1 + x + 3x - 7

Length of PS = 5x - 8

Length of PS = 5*3 - 8

Length of PS = 7

=========================

f(x) = k - x^2

x = 2

f(x) = 5  is the given point

5 = k - x^2      Substitute for x^2

5 = k - 2^2      Expand

5 = k - 4          Add 4 to both sides.

5+4=k-4+4      Combine

k = 9

Answer:

V = 60

Step-by-step explanation:

The formula for the volume of a square based pyramid is: V = a² × h/3 where a = the edge and h = the height

to solve we just plug it in:

V = 6² × 5/3

V = 36 × 5/3

V = 36/1 ×5/3 (another way of writing the above)

V = 180/3 <-- simplify

V = 60

Answer:

48

Step-by-step explanation:

Formula: a^2*(h/3)

We know a is 6ft, but to find h, the height, we'll need to use Pythagoreon Theorem. The hypothenuse of the triangle is 5 and one of the legs is 3, because you need to divide 6 by 2.

3^2+b^2=5^2

9+b^2=25

b^2=16

b=4

Now plug in a and h into the formula to get 48.

Step-by-step explanation:

A six sided die has three even numbers, and each roll is independent, so P(success) is constant at 3/6 = 0.5.  Since it's constant, the variable X does indeed have a binomial distribution.

So the answer is the second one, which you have selected.

Answer:

It is B.

Step-by-step explanation:

The probability of success of rolling an even number in 1 roll = 3/6 = 0.5. This is a constant and  Probability of failure = 0.5. There are 2 possible outcomes so it is a Binomial Distribution.

Answer:

17 units

Step-by-step explanation:

The sides of all right triangles share the same relationship known as the Pythagorean Theorem a² + b² = c². Substitute the lengths of the triangle into the theorem and solve for the unknown side. Since the problem does have an attached a picture, assume that a = 8, b = 15, and c = x.

8² + 15² = x²

64 + 225 = x²

289 = x²

√289 = √x²

17 = x

Final answer:

To find the length of side x in the right triangle, we use the Pythagorean theorem, which yields a hypotenuse value of 17 units. The exact value does not require rounding to the nearest hundredth.

Explanation:

To find the side length of x in a right triangle with a perpendicular side of 15 and a base of 8, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here's how you do it:

Let's call the perpendicular side a, the base b, and the hypotenuse c.

According to the theorem, we have the equation a2 + b2 = c2.

Insert the known values into the equation: 152 + 82 = c2.

Solve for c: 225 + 64 = c2, which simplifies to 289 = c2.

Take the square root of both sides to solve for c: c = √289.

Calculate the square root, which gives us c = 17.

Therefore, the length of side x (which is the hypotenuse in our case) is 17 units. We don't need to round our answer because 17 is already to the nearest hundredth.

Answer:

The graph of [tex]y=cos(x)[/tex] is:

*Stretched vertically by a factor of 3

*Compressed horizontally by a factor  [tex]\frac{1}{10}[/tex]

*Moves horizontally [tex]\pi[/tex] units to the rigth

The transformation is:

[tex]y=3f(10(x-\pi))[/tex]

Step-by-step explanation:

If  the function [tex]y=cf(h(x+b))[/tex]  represents the transformations made to the graph of [tex]y= f(x)[/tex]  then, by definition:

If  [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.

If  [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c

If [tex]c <0[/tex]  then the graph is reflected on the x axis.

If [tex]b> 0[/tex] The graph moves horizontally b units to the left

If [tex]b <0[/tex] The graph moves horizontally b units to the rigth

If [tex]0 <h <1[/tex] the graph is stretched horizontally  by a factor [tex]\frac{1}{h}[/tex]

If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]

In this problem we have the function [tex]y=3cos(10(x-pi))[/tex] and our parent function is [tex]y = cos(x)[/tex]

The transformation is:

[tex]y=3f(10(x-\pi))[/tex]

Then [tex]c =3>1[/tex]  and [tex]b =-\pi < 0[/tex] and [tex]h=10 > 1[/tex]

Therefore the graph of [tex]y=cos(x)[/tex] is:

Stretched vertically by a factor of 3.

Also as [tex]h=10[/tex] the graph is compressed horizontally by a factor  [tex]\frac{1}{10}[/tex] .

Also, as [tex]b =-\pi < 0[/tex] The graph moves horizontally [tex]\pi[/tex] units to the rigth

Answer:

Step-by-step explanation:

Keep in mind that the derivative of ln(u) = u'/u.  Here, our u is x^2 + y^2, so the derivative of that will fit in for u'.  Let's do this step by step:

[tex]xy=ln(x^2+y^2)[/tex]

Working on the left first, using the product rule, the derivative (implicite, of course!) is:

[tex]x\frac{dy}{dx}+1y=ln(x^2+y^2)[/tex]

Now we will work on the right side, keeping in mind the rule above for derivatives of natural logs:

[tex]x\frac{dy}{dx}+1y=\frac{2x+2y\frac{dy}{dx} }{x^2+y^2}[/tex]

Now we are going to get rid of the donominator on the right by multiplication on both sides:

[tex](x^2+y^2)(x\frac{dy}{dx}+1y)=2x+2y\frac{dy}{dx}[/tex]

Distribute on the left to get

[tex]x^3\frac{dy}{dx}+x^2y+xy^2\frac{dy}{dx}+y^3=2x+2y\frac{dy}{dx}[/tex]

Now collect all the terms with dy/dx in them on one side and everything else goes on the other side:

[tex]x^3\frac{dy}{dx}+xy^2\frac{dy}{dx}-2y\frac{dy}{dx}=2x-x^2y-y^3[/tex]

Factor out the common dy/dx:

[tex]\frac{dy}{dx}(x^3+xy^2-2y)=2x-x^2y-y^3[/tex]

and divide on the left to isolate the dy/dx:

[tex]\frac{dy}{dx}=\frac{2x-x^2y-y^3}{x^3+xy^2-2y}[/tex]

And there you go!

I don't know the area of a parallelogram off the top of my head but you can use the area of the rectangle and the area of the triangle and add those. The area of the triangle is 1/2*base*height and use the pythagorean theorem to find the base. 3² + b² = 5²; 9 + b² = 25; b² = 16; b = 4. The area of the triangle is 1/2*4*3 or 6 in. Since there are two of them, the total area of the triangles are 12 in. The area of the rectangle is length*width or (12 - 4) * 3 which is 8 * 3 or 24in. Add these areas together to get 36in total

The area of the given rectangle is 36 inch^2.

The area of a parallelogram is off the top of my head but you can use the area of the rectangle and the area of the triangle and add those.

The area of the triangle is 1/2*base*height

use the Pythagorean theorem to find the base.

3² + b² = 5²

9 + b² = 25

b² = 16

b = 4.

The area of the triangle is 1/2*4*3 or 6 in.

Since there are two of them, the total area of the triangles are 12 in.

The area of the rectangle is length*width or (12 - 4) * 3 which is 8 * 3 or 24in.

Add these areas together to get 36in total.

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Answer:

Volcanic Ash

Step-by-step explanation:

Answer: Option D

Step-by-step explanation:

Answer:

The original equation must have been:

[tex]7x^{2} -5x-2=0[/tex]

Step-by-step explanation:

A quadratic equation is in the form of :

[tex]ax^{2} +bx+c=0[/tex]

And it is solved in the form of :

[tex]x=\frac{-b+\sqrt{b^{-4ac} } }{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^{-4ac} } }{2a}[/tex]

Now the given equation is :

[tex]x=\frac{-(-5)+-\sqrt{(-5)^{2} -4(7)(-2)} }{2(7)}[/tex]

We can see that here;

a = 7

b = -5

c = -2

So, the original equation must have been:

[tex]7x^{2} -5x-2=0[/tex]

Answer:

Look at the picture