prove identity trigonometric equation
[tex]2 \tan(x) = \frac{ \cos(x) }{ \csc(x - 1) } + \frac{ \cos(x) }{ \csc(x + 1) } [/tex]
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Answer:

hundreths

Step-by-step explanation:

After the decimal there is tenths, hundreths thousandnths, tens of thousands e.t.c

Answer:

Hello! The answer will be hundredths.

Step-by-step explanation:

The 5 means the thousandths.

The 0 means the hundredths.

The 8 means the tenths.

The 7 means the ones

And the 6 means the tens.

Hope this helps! :)

( below I attached a picture, which might be helpful.)

Answer:

(A) What is the z- score of the sample mean?

The z- score of the sample mean is 0.0959

(B) Is this sample significantly different from the population?

No; at 0.05 alpha level (95% confidence) and (n-1 =79) degrees of freedom, the sample mean is NOT significantly different from the population mean.

Step -by- step explanation:

(A) To find the z- score of the sample mean,

X = 75 which is the raw score

¶ = 74 which is the population mean

S. D. = 10.43 which is the population standard deviation of/from the mean

Z = [X-¶] ÷ S. D.

Z = [75-74] ÷ 10.43 = 0.0959

Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].

(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.

The estimated standard error of the mean is s/√n

S. E. = 16/√80 = 16/8.94 = 1.789

The Absolute (Calculated) t value is now: [75-74] ÷ 1.789 = 1 ÷ 1.789 = 0.559

Setting up the hypotheses,

Null hypothesis: Sample is not significantly different from population

Alternative hypothesis: Sample is significantly different from population

Having gotten T- cal, T- tab is found thus:

The Critical (Table) t value is found using

- a specific alpha or confidence level

- (n - 1) degrees of freedom; where n is the total number of observations or items in the population

- the standard t- distribution table

Alpha level = 0.05

1 - (0.05 ÷ 2) = 0.975

Checking the column of 0.975 on the t table and tracing it down to the row with 79 degrees of freedom;

The critical t value is 1.990

Since T- cal < T- tab (0.559 < 1.990), refute the alternative hypothesis and accept the null hypothesis.

Hence, with 95% confidence, it is derived that the sample is not significantly different from the population.

Answer:

see graph

Step-by-step explanation:

A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.

$1 = 5copies means

$5 = 25 copies obviously

then

$x = 100 copies

100 / 5 = $x

so she needs

$20

The cost of printing 100 copies of artwork is $20.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Suppose 2 pens cost $10, So the cost of 1 pen is (10/2) = $5.

From this unitary cost of pens, we can determine the cost of any no. of pens by multiplying the unit cost by the no. of pens.

Given, The cost of printing 5 artworks is $1.

∴ The cost of printing 100 copies is $(100/5),

= $20.

learn more about the unitary method here :

https://brainly.com/question/22056199

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Answer:

Surface area of the reflective glass is 543234.4 square feet.

Step-by-step explanation:

Given that: height = 311 feet, sides of square base = 619 feet.

To determine the slant height, we have;

[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]

   = 96721 + 95790.25

   = 192511.25

⇒ l = [tex]\sqrt{192511.25}[/tex]

      = 438.761

The slant height, l is 438.8 feet.

Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height

  area =  [tex]\frac{1}{2}[/tex] × 619 × 438.8

          = 135808.6

          = 135808.6 square feet

Since the pyramid has four reflective surfaces,

surface area of the reflective glass = 4 × 135808.6

                                                          = 543234.4 square feet

Answer:

Step-by-step explanation:

From the summary of the given statistics;

The null and the alternative hypothesis for confirming that the new engine has a mean emission level below the current standard can be computed as follows:

Null hypothesis:

[tex]H_0: \mu = 0.60[/tex]

Alternative hypothesis:

[tex]H_a: \mu < 0.60[/tex]

Type I  error: Here, the null hypothesis which is the new engine has a mean level equal to  .6g/ml is rejected when it is true.

Type II error:  Here, the alternative hypothesis which is the new engine has a mean level less than.6g/ml is rejected when it is true.

Similarly;

From , A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4.

Sample size n = 64

sample mean [tex]\overline x[/tex] = .5 g/ml

standard deviation σ = .4

From above, the normal standard test statistics can be determined by using the formula:

[tex]z = \dfrac{\bar x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{0.5- 0.6}{\dfrac{0.4}{\sqrt{64}}}[/tex]

[tex]z = \dfrac{-0.1}{\dfrac{0.4}{8}}[/tex]

z = -2.00

The p-value = P(Z ≤ -2.00)

From the normal z distribution table

P -value = 0.0228

Decision Rule: At level of significance ∝ = 0.05, If P value is less than or equal to level of significance ∝ , we reject the null hypothesis.

Conclusion: SInce the p-value is less than the level of significance , we reject the null hypothesis. Therefore, we can conclude that there is enough evidence that a new engine design has reduced the emissions to a level below this standard.

Answer:

( P -2w) /2 = l

Step-by-step explanation:

P= 2W + 2l

Subtract 2W from each side

P= 2W -2W + 2l

P -2W = 2l

Divide by 2

( P -2w) /2 = l

Answer:

A. [tex]\frac{P - 2w}{2} = l[/tex]

Step-by-step explanation:

Well in,

P = 2w + 2l

to solve for l we need to single it out.

P = 2w + 2l

-2w

P - 2w = 2l

divide everything by 2

[tex]\frac{P - 2w}{2} = l[/tex]

Thus,

the answer is A.

Hope this helps :)

Ans   k = 4

Step-by-step explanation:

Here g(x) =[tex]\frac{-1}{3}x + 1[/tex] and

        f(x) = [tex]\frac{-1}{3} x -3[/tex]

Now,  g(x) = f(x) + k

    or,      [tex]\frac{-1}{3}x + 1[/tex]  =  [tex]\frac{-1}{3} x -3 + k[/tex]

    or,      1 + 3 = k

    So,  k = 4   Answer.

Answer:

current population growth rate would be -3.1%

Step-by-step explanation:

We have to:

Growth rate = r * (1 - population / carrying capacity)

for 1960,

we have carrying capacity = 21 billion

population = 3 billion

r = Growth rate 1960 / (1 - population / carrying capacity)

replacing:

r = 0.021 / (1 - 3/21)

r = 0.0245

that is to say r = 2.45%

Now the current population would be:

= 0.0245 * (1 - carrying population / carrying capacity)

we replace:

= 0.0245 * (1 - 6.8 / 3)

= -0.031

current population growth rate would be -3.1%

The predicted growth rate compare to the actual growth rate of about 1.2% per year is -3.1% and this can be determined by using the formula of growth rate.

Given :

The growth rate is given by the formula:

[tex]\rm Growth \;Rate = r\times \left(1-\dfrac{Populatuion}{Carrying\;Capacity}\right)[/tex]

Given that the carrying capacity of the earth is 21 billion. The growth rate in 1960 is 2.1%. So, put the known values in the equation (1).

[tex]\rm 0.021 = r\times \left(1-\dfrac{3}{21}\right)[/tex]

[tex]0.021=r\times \dfrac{18}{21}[/tex]

0.0245 = r

So, r = 2.45%.

Now, the growth rate of the current population is:

[tex]\rm Growth \;Rate = 0.0245\times \left(1-\dfrac{6.8}{3}\right)[/tex]

[tex]\rm Growth\; Rate = 0.0245 \times \dfrac{-3.8}{3}[/tex]

0.031 = Growth Rate

So, the growth rate is -3.1%.

For more information, refer to the link given below:

https://brainly.com/question/2096984

Answer:

x=4

Step-by-step explanation:

5x - 17 = -x +7

Add x to each side

5x+x - 17 = -x+x +7

6x -17 = 7

Add 17 to each side

6x-17+17 = 7+17

6x =24

Divide each side by 6

6x/6 = 24/6

x = 4

Answer:

4

Step-by-step explanation:

5x - 17 = -x + 7

Add x on both sides.

5x - 17 + x = -x + 7 + x

6x - 17 = 7

Add 17 on both sides.

6x - 17 + 17 = 7 + 17

6x = 24

Divide both sides by 6.

(6x)/6 = 24/6

x = 4

Answer:

-38

Step-by-step explanation:

it's subtracting 7 everytime, and -31-7=-38

Answer:

D. [tex]H_{0}[/tex] : μ = 1.70, [tex]H_{a}[/tex] : μ > 1.70

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Answer:

The 95% confidence interval for the mean score, , of all students taking the test is

        [tex]28.37< L\ 30.63[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is [tex]n = 59[/tex]

    The mean score is  [tex]\= x = 29.5[/tex]

     The standard deviation [tex]\sigma = 5.2[/tex]

Generally the standard deviation of mean is mathematically represented as

                [tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]

             [tex]\sigma _{\= x} = 0.677[/tex]

The degree of freedom is mathematically represented as

          [tex]df = n - 1[/tex]

substituting values

        [tex]df = 59 -1[/tex]

        [tex]df = 58[/tex]

Given that the confidence interval is 95%  then the level of significance is mathematically represented as

         [tex]\alpha = 100 -95[/tex]

        [tex]\alpha =[/tex]5%

        [tex]\alpha = 0.05[/tex]

Now the critical value at  this significance level and degree of freedom is

       [tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]

Obtained from the critical value table  

    So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as

      [tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]

substituting value

      [tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]

       [tex]28.37< L\ 30.63[/tex]

Answer:

y = 2666.67

Step-by-step explanation:

Well to solve this we can make a system of equations.

x = cost of car alone

y = cost of accesories,

[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]

So now we plug in 8y for x in x + y = 24000.

(8y) + y = 24000

9y = 24000

Divide both sides by 9

y = 2666.666666

or 2666.67 rounded to the nearest hundredth.

Now that we have y we can plug that in for y in x=8y.

x = 8(2.666.67)

x = 21,333.33 rounded to the nearest hundredth.

Thus,

accessories "y" cost around 2666.67.

Hope this helps :)

Answer:

Step-by-step explanation:

Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.

Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7

Mean = 76.2/7

Mean = 10.9

The mean score is 10.9 to 1 decimal place.

Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.

b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;

9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7

After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.

The median represents the center

c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.

The mode(s) does (do) not represent the center because it (one) is the largest data value.

Answer:

 Age                               Frequency                   Cumulative Frequency

 Less than 30                             28                                       28

 Less than 40                             37                                28 + 37  =  65

 Less than 50                              1 4                                 65 + 14   =  79

 Less than 60                               3                                  79 + 3   =  82

 Less than 70                                4                                 82 + 4   =  86

 Less than 80                                1                                     86 + 1  =  87

 Less than 90                                1                                    87 + 1  =  88

Step-by-step explanation:

Given:

The Frequency Distribution table of ages of best actresses when award was won

To find:

Construct the cumulative frequency distribution

Solution:

In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40  is 37 and the previous frequency (less than 30) is 28 so in order to calculate cumulative frequency 28 i.e. previous frequency is added to 37 (frequency of less than 30) and the cumulative frequency is 65. The complete table is given above.

Answer:

83,403

Step-by-step explanation: Take 74,145 and multiply it by 4%. Then take that number and add it to the 74,145 and that'll give you year one. For year 2 you'll take your total from year 1 and multiply it by the 4% growth rate then you'll add the 4% to what your ending from year 1 and that'll give you your total growth after 2 years. Then you'll take your ending total from year 2 and multiply it by 4% and then you'll add that 4% to the total end from year 2 and that'll give you your total growth of 4% every year for 3 consecutive years.

Hope this helps!

Answer: THe slope is 2

SO answer d

Step-by-step explanation:

-4X + 2Y = 16 add 4x to the other side so equation is

2y=16+4x divided by 2

y=8+2x

Answer: 0.18

Step-by-step explanation:

P(1 unit is defective)= C2  1* P^1*Q^1

C2 1= 2!/(1!*(2-1)!)=2

P=0.1 - probability that items from a production line are defective  

Q=1-0.1=0.9 - probability that items from a production line are functional.

P(1 unit is defective)= 2*0.1*0.9=0.18

Answer:

a) the angle of ascent is 8.2°

b) the horizontal distance traveled is 4375 m

Step-by-step explanation:

depth of ocean = 626 m

distance traveled in the ascent = 4420 m

This is an angle of elevation problem with

opposite side to the angle = 626 m

hypotenuse side = 4420 m

a) angle of ascent ∅ is gotten from

sin ∅ = opp/hyp = 626/4420

sin ∅ = 0.142

∅ = [tex]sin^{-1}[/tex] 0.142

∅ = 8.2°  this is the angle of ascent of the submarine.

b) The horizontal distance traveled will be gotten from Pythagoras theorem

[tex]hyp^{2}[/tex] = [tex]opp^{2}[/tex] + [tex]adj^{2}[/tex]

The horizontal distance traveled will be the adjacent side of the right angle triangle formed by these distances

[tex]4420^{2}[/tex] = [tex]626^{2}[/tex] + [tex]adj^{2}[/tex]

adj = [tex]\sqrt{4420^{2}-626^{2} }[/tex]

adj = 4375 m  this is the horizontal distance traveled.

Answer:

x = -8

Step-by-step explanation:

When h(x) = 48, you can simply just plug it back into the first equation. Don't let the h(x) confuse you!

Think of it like saying y = -4x + 16, y = 48.

48 = - 4x + 16

32 = - 4x

8 = -x

Divide by -1 both sides.

-8 = x

Answer:

[tex]f(x) = x^3 -sinx +Cx+D[/tex]

Step-by-step explanation:

Given that:

[tex]f ''(x)= 6x +sinx[/tex]

We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.

We will have to integrate it twice to find the value of f(x).

Let us have a look at the basic formula of integration that we will use in the solution:

[tex]1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C[/tex]

[tex]\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\[/tex]

Now, integrating it again to find f(x):

[tex]f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D[/tex]

Answer:

Please refer to the graph in the attached area.

Step-by-step explanation:

Given:

Total money available with the customer is $10.

Cost of each hotdog is $2.

Cost of each drink is is $2.50.

To find:

The graph of inequality.

Solution:

Let number of hotdogs bought = [tex]x[/tex]

Total cost of hotdogs = [tex]2x[/tex]

Let number of drinks bought = [tex]y[/tex]

Total cost of drinks = [tex]2.5y[/tex]

Total cost = [tex]2x+2.5y[/tex]

And total money available is $10.

So, the total cost calculated above must be lesser than or equal to $10.

Hence, the inequality is:

[tex]2x+2.5y<10[/tex]

Also there will be two conditions on variables [tex]x[/tex] and [tex]y[/tex]:

[tex]x\ge0\\y\ge0[/tex]

To graph this, let us find the points on the equivalent equation:

[tex]2x+2.5y = 10[/tex]

Finding two points on the equation.

First put x = 0 [tex]\Rightarrow[/tex] y = 4    

Then put y = 0, [tex]\Rightarrow[/tex] x = 5

So, two points are (0, 4) and (5, 0).

Now, plotting the line.

Having point (1,2) in the inequality:

2 + 5 < 10 (True) hence, the graph of inequality will contain the point (1,2)

Please refer to the graph of inequality in the attached graph.

Answer:

You'll need 2.8 gallons of the 80% solution.

Step-by-step explanation:

Let the volume of 30% alcohol =x gallons

Then the volume of 80% alcohol =(14-x) gallons

Since we want to obtain a 40% alcohol solution, we have:

0.3x+0.8(14-x)=0.4(14)

0.3x+11.2-0.8x=5.6

0.8x-0.3x=11.2-5.6

0.5x=5.6

x=11.2

Therefore, the volume of 80% alcohol

=14-11.2

=2.8 gallons

You'll need 2.8 gallons of the 80% solution.

Complete Question

Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.

Answer:

The  sample size is  [tex]n = 1537 \ gallons[/tex]

Step-by-step explanation:

From the question we are told that

    The margin of error is  [tex]MOE = 0.5[/tex]

     The confidence level is  [tex]C = 95[/tex]%

Given that the confidence level is  95% the level of significance is mathematically represented as

         [tex]\alpha = 100 - 95[/tex]

         [tex]\alpha = 5[/tex]%

         [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is  [tex]Z_{\frac{\alpha }{2} } = 1. 96[/tex]

The reason we are obtaining critical values of  

[tex]\frac{\alpha }{2}[/tex]

instead of  

[tex]\alpha[/tex]

is because  

[tex]\alpha[/tex]

represents the area under the normal curve where the confidence level interval (

[tex]1-\alpha[/tex]

) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex]

is just the area of one tail which what we required to calculate the sample size

Now the sample size is mathematically represented as

          [tex]n = \frac{[Z_{\frac{\alpha }{2} }] ^2 * \sigma ^2}{MOE^2}[/tex]

substituting values

         [tex]n = \frac{1.96^2 * 10 ^2}{0.5^2}[/tex]

         [tex]n = 1537 \ gallons[/tex]

Answer:

30

Step-by-step explanation:

24 - (-6)

Apply rule : -(-a) = a

Negative (-) times a negative (-) is positive (+).

24 + 6

= 30

Answer:

-6 is in parentheses because it is a negative number. this prevents the equation from looking like a too long subtraction sign (24--6); therefore it is written as 24 - (-6).

this simplifies to 24 + 6 = 30

to negatives = a positive

Answer:

[tex]cos57 = 0.5446[/tex]

[tex]sin57 = 0.8387[/tex]

[tex]tan57 = 1.5399[/tex]

Step-by-step explanation:

Given

[tex]cos 94\° cos 37\° + sin 94\° sin 37\°[/tex]

Required

Determine the

- sin

- cosine

- tangent

of an angle

The given expression can be represented as follows;

[tex]cosAcosB + sinAsinB[/tex]

Where A = 94 and B = 37

In trigonometry:

[tex]cosAcosB + sinAsinB = cos(A - B)[/tex]

Substitute 94 for A and 37 for B

[tex]cos(A - B) = cos(94 - 37)[/tex]

[tex]cos(A - B) = cos(57)[/tex]

Hence, the angle is 57;

Since 57 is not a special angle; I'll solve using a calculator

[tex]cos57 = 0.5446[/tex]

[tex]sin57 = 0.8387[/tex]

[tex]tan57 = 1.5399[/tex]

Answer:

See the attachment for sketch

Thr region is unbounded

DNE

Step-by-step explanation:

y≤ -2x + 10

The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.

Answer:

The standard deviation of the sample mean is  [tex]\sigma _ {\= x } = 2.711[/tex]

Step-by-step explanation:

From the question we are told that

   The mean is  [tex]\= x = 60[/tex]

    The standard deviation is  [tex]\sigma = 21[/tex]

     The sample size is [tex]n = 60[/tex]

Generally the standard deviation of the sample mean is mathematically represented as  

               [tex]\sigma _ {\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

               [tex]\sigma _ {\= x } = \frac{ 21 }{\sqrt{60} }[/tex]

               [tex]\sigma _ {\= x } = 2.711[/tex]

Answer:

h^2 means h²

(h squared)

Step-by-step explanation:

Step 1: Write equation

144 + h² = 225

Step 2: Subtract 144 on both sides

h² = 81

Step 3: Take square root

√h² = √81

h = 9