What are the domain and range of Y = sin X? select one choice for domain and one for range. (Answers in photo)

tan( 20 ) + 4 Sin( 20 ) =

( Sin( 20 ) / Cos( 20 ) ) + 4 Sin( 20 ) =

Sin( 20 ) + 4 Sin( 20 ).Cos( 20 ) / Cos( 20 ) =

Sin( 20 ) + 2 × 2 Sin(20).Cos(20)/ Cos(20) =

Sin( 20 ) + 2 × Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Cos( 50 ) / Cos ( 20 ) =

Sin( 20 ) + 2Cos( 20 + 30 ) / Cos( 20 ) =

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2 × Cos( 30 + 20 ) =

2 × [ Cos(30).Cos(20) - Sin(30).Sin(20) ] =

2 × [ √3/2 × Cos(20) - 1/2 × Sin(20) ] =

√3 Cos(20) - Sin(20)

_________________________________

Sin( 20 ) + 2Cos ( 20 + 30 ) / Cos( 20 ) =

Sin( 20 ) + √3 Cos(20) - Sin(20) / Cos(20) =

Sin(20) - Sin(20) + √3 Cos(20) / Cos(20) =

0 + √3 Cos(20) / Cos(20) =

√3 Cos(20) / Cos(20) =

Cos(20) simplifies from the numerator and denominator of fraction

√3 × 1 / 1 =

√3

And we're done ....

Answer:

Step-by-step explanation:

Answer:

for what? do you need a question answered?

Answer:

[tex]\begin{array}{cc}{Stem} & {Leaves} & {4} & {7} & {5} & {2, 7, 8, 8} & {6} & {1, 6, 6, 8, 8} & {7} & {0, 2, 2, 3, 3, 5, 6, 7} & {8} & {4, 4, 4, 5, 6, 6, 7, 9} & {9} & {0, 1, 1, 2, 3, 7} \ \end{array}[/tex]

Step-by-step explanation:

Given

See comment for complete part of the question

Required

Make a stem and leaf plot

We have:

[tex]58, 52, 68, 86, 72, 66, 97, 89, 84, 91[/tex]

[tex]91, 92, 66, 68, 87, 86, 73, 61, 70, 75, 72, 73[/tex]

[tex]85, 84, 90, 57, 77, 76, 84, 93, 58, 47[/tex]

Categorize the dataset according to tens

[tex]47[/tex]

[tex]52, 57, 58, 58[/tex]

[tex]61, 66, 66, 68, 68[/tex]

[tex]70, 72, 72, 73, 73, 75, 76, 77[/tex]

[tex]84, 84, 84, 85, 86, 86, 87, 89[/tex]

[tex]90, 91, 91, 92, 93, 97[/tex]

So, the stem and leaf plot is:

[tex]\begin{array}{cc}{Stem} & {Leaves} & {4} & {7} & {5} & {2, 7, 8, 8} & {6} & {1, 6, 6, 8, 8} & {7} & {0, 2, 2, 3, 3, 5, 6, 7} & {8} & {4, 4, 4, 5, 6, 6, 7, 9} & {9} & {0, 1, 1, 2, 3, 7} \ \end{array}[/tex]

Answer:

a) The null hypothesis is [tex]H_0: p \leq \frac{2}{3}[/tex] and the alternate hypothesis is [tex]H_1: p > \frac{2}{3}[/tex].

b) The sample proportion is 0.6710.

Step-by-step explanation:

Question a:

An airline promotion to business travelers is based on the assumption that no more than two-thirds of business travelers use a laptop computer on overnight business trips.

At the null hypothesis, we test if the proportion is two-thirds or less, that is:

[tex]H_0: p \leq \frac{2}{3}[/tex]

At the alternate hypothesis, we test if the proportion is of more than two-thirds, that is:

[tex]H_1: p > \frac{2}{3}[/tex]

b. What is the sample proportion from an American Express-sponsored survey that found 359 of 535 business travelers use a laptop computer on overnight business trips (to 4 decimals)?

359 out of 535 is 359/535 = 0.6710.

The sample proportion is 0.6710.

Answer:

b. The values X and Y are independent therefore, the mean is 34 seconds and the standard deviation is 50 seconds

Step-by-step explanation:

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds.

This means that [tex]\mu_X = 402, \sigma_X = 40[/tex]

After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds.

This means that [tex]\mu_Y = 368, \sigma_Y = 30[/tex]

Which of the following is true about the distribution of X-Y?

They are independent, so:

[tex]\mu = \mu_X - \mu_Y = 402 - 368 = 34[/tex]

[tex]\sigma = \sqrt{\sigma_X^2+\sigma_Y^2} = \sqrt{40^2+30^2} = 50[/tex]

This means that the correct answer is given by option b.

The values X and Y are independent therefore, the mean is 34 seconds and the standard deviation is 50 seconds.

What is the subtraction between normal variables?

The two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Before the training, the mean running mean  time for the students to runing a mile was 402 seconds with standard deviation 40 seconds.

That is the [tex]\mu_x=402 , \sigma_x=40[/tex]

That is the after completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds.

That is [tex]\mu_y=368,\sigma_y=30[/tex]

which of the following is true about the distribution of X-Y?

They are independent

Therefore we get,

[tex]\mu=\mu_x-\mu_y=402-368=34[/tex]

[tex]\sigma=\sqrt{\sigma_x^2-\sigma_y^2}\\\sigma=\sqrt{40^2-30^2}\\\sigma =50[/tex]

Therefore the option b is correct.

To learn more about the distribution visit:

https://brainly.com/question/24756209

This means that the correct answer is given by option b.

Answer:

i think false

Step-by-step explanation:

Answer:

1,264

Step-by-step explanation:

a = 1000(1.06)^4

a = 1,262.47696

1,264

Answer:

True

Step-by-step explanation:

If a is negative then the shape of the graph is an upside down U, which intersects the x-axis. If a is positive it will never cross the X axis.

It is true that f(x)=[tex]a^{x}[/tex]+4 will never cross the x axis if a is positive.

Function is relationship between two or more that are variables expressed in equal to form. In a function each value of x must have a corresponding value of y.

We have been given that f(x)=[tex]a^{x} +4[/tex] and we have to find whether it will cross x axis or not.

when a line crosses the x axis the value of y becomes negative. We have to first check at y=0.

[tex]a^{x}+4[/tex]=0

[tex]a^{x}[/tex]=-4

taking log both sides,

log [tex]a^{x}[/tex]=log(-4)

x log a=0.602059991+1.3437635i

x=(0.602059991+1.3437635i)/log a

when we put the value of x in f(x) the value of f(x) cannot be negative so it cannot crosses the x axis.

Hence it is true that f(x)=[tex]a^{x}[/tex]+4 will never cross the x axis if a is positive.

Leaarn more about function at https://brainly.com/question/10439235

#SPJ2

Answer:

Step-by-step explanation:

the formula doesn't work for the answers shown,    

y = 2x +23 for 1980 should be 23  not 26.9

something is missing in your question

Answer:

D

Step-by-step explanation:

When you simplify the expression you start by subtracting 5 from both sides. This gives you 0.2x > -3. Then to isolate "x" you divide both sides by 0.2. This gives you x > -15, which is shown in the number line.

Answer:

.8

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome.

Given that the probability that Jane makes money in a given week is .6 and  the probability that Jane and Maria both make money in a given week is .48. Then the probability that Maria makes money in a given week...

Let the probability that Jane makes money in a given week be p(j) and that Maria makes money in a week be p(m) then

p(j) = .6 and

p(j) * p(m) = .48

.6 * p(m) = .48

p(m) = .48/.6

= .8

Answer:

7.14%

Step-by-step explanation:

A fair number cube has 6 sides while a normal spinner has 7 different colors. In order to find the probability of Jack getting a number less than 4 and lands on blue, we need to find the probability of each individual event and multiply them together. Since the cube has six sides and 3 options that are less than 4 then the probability of getting less than 4 is 3/6. On the wheel there are 7 colors and only one is blue, therefore, the probability is 1/7. Now we multiply these fractions together.

[tex]\frac{3 * 1}{6 * 7} = \frac{3}{42}[/tex] or 0.0714 or 7.14%

Therefore, the probability of this event happening is 7.14%

The probability of this event is 7.14%.

A fair number cube has 6 sides.

While a normal spinner has 7 different colors.

In order to find the probability of Jack getting a number less than 4 and lands on blue,

we have to find the probability of each individual event and then multiply them together.

The cube has six sides and 3 options that are less than 4 then the probability of getting less than 4 is 3/6.

On the wheel there are 7 colors and only one is blue.

Therefore, the probabilitiy is 1/7.

Now we multiply these fractions together.

[tex]\frac{3\times 1}{6\times 7} =\frac{3}{42}= 0.0714[/tex]

[tex]\frac{ 0.0714 }{100}=7.14\%[/tex]

Therefore, the probability of this event is 7.14%.

To learn more about the probability visit:

https://brainly.com/question/24756209

Answer:

volume = 7/8 cubic units

Step-by-step explanation:

[tex]volume = base \ area \times height = \frac{1}{2} \times \frac {7}{4} = \frac{7}{8} units^3[/tex]

Answer:

210.

Step-by-step explanation:

10.5 x 20 = 210

i hope that helps!!!

Given:

The function is:

[tex]f(x)=-4(2)^x[/tex]

The graph of the function [tex]g(x)=f(x)+k[/tex] is given.

To find:

The value of k.

Solution:

We have,

[tex]f(x)=-4(2)^x[/tex]

[tex]g(x)=f(x)+k[/tex]

Using these two functions, we get

[tex]g(x)=-4(2)^x+k[/tex]

From the given graph it is clear that the graph of g(x) passes through the point (0,2). It means the point (0,2) satisfies the function g(x).

Substituting [tex]g(x)=2[/tex] and [tex]x=0[/tex] in the above function, we get

[tex]2=-4(2)^0+k[/tex]

[tex]2=-4(1)+k[/tex]

[tex]2=-4+k[/tex]

[tex]2+4=k[/tex]

[tex]6=k[/tex]

Therefore, the value of k is 6.

Answer:

54°

Step-by-step explanation:

54°

Answer:

the missing angle is 54

Step-by-step explanation:

so first we need two triangle angles to get our measurement and we know straight lines add up to 180 so

180-123=57

57+69(other angle)=126

all triangle angles add up to 180 so subtract the two other angles to get your result

180-126=54

54 is your anwser

Answer:

4582.4

Step-by-step explanation:

Answer:

give me a heart first and then ill answer

Step-by-step explanation:

Answer:

The probability is "0.6406", this elevator isn't appear to be​ safe

Step-by-step explanation:

The given values are:

Mean,

[tex]\mu=165[/tex]

Standard deviation,

[tex]\sigma=35[/tex]

Number of male passengers,

[tex]n = 10[/tex]

Now,

⇒ [tex]z=\frac{161-165}{\frac{\sigma}{\sqrt{10} } }[/tex]

      [tex]=\frac{161-165}{\frac{35}{\sqrt{10} } }[/tex]

hence,

The probability will be:

= [tex]P(\bar {x}>161)[/tex]

= [tex]P(z > -0.3614)[/tex]

= [tex]0.6406[/tex]

Answer:

[tex]34 \leq x \leq 38[/tex]

Step-by-step explanation:

34 inches minimum

This means that x has to be at least 34, that is:

[tex]x \geq 34[/tex]

38 inches maximum

This means that x can be at most 38, that is:

[tex]x \leq 38[/tex]

Which inequality represents the required height?

The intersection of 34 minimum and 38 maximum is:

[tex]34 \leq x \leq 38[/tex]

Answer:

(2x+1) +x = -35

3x= -36

x= -12

Step-by-step explanation:

Given :

A new car depreciates each year by 2.8%. When the car is 8 years old, it has a value of $42,547.24.

To Find :

The car’s original value.

Solution :

Formula of car depreciation is :

[tex]A= P( 1- \dfrac{R}{100})^n\\\\42547.24 = P( 1 - \dfrac{2.8}{100})^8\\\\42547.24 = P\times 0.8\\\\P = \dfrac{42547.24}{0.8}\\\\P = \$53184.05[/tex]

Hence, this is the required solution.

Answer:

I'll setup the problem and you can do the calculations

Step-by-step explanation:

The formula for simple interest:

I = P*r*t

I = interest

P = principle or amount invested

r = interest rate per period (period is a year)

t = number of periods

P = 4920

r = .13

t = 8

if you have questions, send a comment

Here we have been provided with the principal , rate of interest and time period for which the sum of rupees is invested.

Now here we know that simple Interest is calculated by the formula,

Here in this formula,

Putting there values in the formula,

[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{4920 \times 13 \times 8}{100} }[/tex]

[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 13 \times 8}{10} }[/tex]

[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 13 \times \cancel{8}}{ \cancel{10}} }[/tex]

[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 13 \times 4}{ 5} }[/tex]

[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{492 \times 52}{ 5} }[/tex]

[tex]\longrightarrow \: \sf{S.I. \: = \: \dfrac{25584}{ 5} }[/tex]

[tex] \longrightarrow \: \sf{S.I. \: = \: \cancel\dfrac{25584}{ 5} }[/tex]

[tex] \longrightarrow \: \orange{\boxed{\bf{S.I. \: = \: 5116.8}}}[/tex]

[tex]\underline{\bf{Henceforth, \: interest \: paid \: is \: of \: Rs.5116.8}}[/tex]

Answer:

See Below

Step-by-step explanation:

The fibonacci sequence is a recursive type sequence where each term is the sum of the two previous terms. The sequence starts out as:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811...

The fibonacci sequence can be found in nature quite often. For example, it is found in "the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bract". It can also be found in the number of tree branches in each row.

Another cool place it can be found is in the diagonals of pascals triangle (shown in the image attached)

*Disclaimer: I do not own any of the images

Answer:

We need more info

Step-by-step explanation:

Answer:

What?

Step-by-step explanation:

You have to add more context to your question.

Answer:

$42

Step-by-step explanation:

less than 8 is supposed to be 7 or less 6×7=$42

Answer:

(0, 1):  Answer D

Step-by-step explanation:

The three given vertices are (0٫ 4)٫(8٫ 4) and (8٫ 1).  Note that the x-coordinates of two of these are both 8.  The remaining x-coordinate of the fourth vertex is 0.  Since the figure is a rectangle, there are two sets of parallel sides.  If one side is x = 8, the opposite vertical side must be x = 0, since the remaining coordinate is 0.  This side is a vertical line segment.  The fourth and last vertex is at the intersection of x = 0 and y = 1;  (0, 1):  Answer D.

Answer:

64

hope this helps

have a good day :)

Step-by-step explanation: