Tan(x) times cos(x) simplify it to single trig

The data value corresponding to z = 0.55 is approximately 87.6075.

To find the data value corresponding to a given z-score, we need to use the formula:

z = (x - μ) / σ

where z is the standard score, x is the data value, μ is the mean, and σ is the standard deviation.

Rearranging this formula, we get:

x = z * σ + μ

Substituting the given values, we get:

x = 0.55 * 4.85 + 85.3

x = 87.6075

Therefore, the data value corresponding to z = 0.55 is approximately 87.6075.

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A normal distribution has a mean of 85.3 and a standard deviation of 4.85. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.) z = 0.55

Answer:

12 - 6n

Step-by-step explanation:

As this sequence decreases, rather than increases, this tell us that the nth term of this sequence will be minus. The difference from 6 and 0 is 6, telling us that the decrease is by 6 each time. So now we know the nth term of this sequence; -6n, but the sequence of -6n is -6,-12,-18 and so on. We need 6,0,-6. To find out the second part of the nth term find the difference from the sequence given and the sequence of -6n. The difference is 12 because the 6--6 = 12. So now we get the nth term of the sequence -6n + 12 which is written as 12-6n.  

The correct option is A.

The interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.

Given that, the box plots display the scores that two different groups of students got on their last math quiz.

We need to find the interquartile range of each data set.

So, the interquartile range of data set A = 80-65 = 15

the interquartile range of data set B = 90-80 = 10

Hence, the interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.

The correct option A.

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The missing length is 11.0818 unit.

We have,

Angle = 52 degree

H = 18

Using Trigonometry

cos 52 = B/H

cos 52 = x / 18

0.615661 = x  /18

x = 11.0818 unit

Thus, the missing length is 11.0818 unit.

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The radius of the diameter X is 6cm. Option D

To determine the radius of the circle, we have;

It is important to that the formula for diameter

The formula for calculating the diameter is given as;

d = r/2

Such that the parameters are given as;

From the information given, we have that;

Diameter, d = 12cm

Now, we have to substitute the values

Radius =diameter/2

Radius = 12/2

Radius = 6cm

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Answer:

Since the triangles are similar, their corresponding sides are in proportion. The ratio of sides AB to DE is 9:13.5, which simplifies to 2:3. Therefore, the ratio of their areas is the square of the ratio of their sides, which is 4:9.

If the area of triangle ABC is 34 cm, then the area of triangle DEF is:

Area of DEF = (Area of ABC) x (DE^2/AB^2) = 34 x (13.5^2/9^2) = 34 x 1.5^2 = 34 x 2.25 = 76.5 cm^2

Therefore, the area of triangle DEF is 76.5 cm^2.

Step-by-step explanation:

Answer:

check attachment

Step-by-step explanation:

First write in point-slope form:

y-y1=m(x-x1)

Now substitute:

y-(-1)=3/4(x-(-4))

And then just solve. You should get a y-intercept of 2.

The height of this parallelogram include the following: B. 12 cm.

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = b × h

Where:

By substituting the given parameters into the formula for the area of a parallelogram, we have the following;

Area of a parallelogram = 10 × 12

Area of a parallelogram = 120 cm².

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

The answer is A.

A graph passes through a point if its equation is equal to the coordinate of this point. In this exemple:

5x+4y=8

we replace the variables with 4 and -3 (x with 4 and y with -3):

5(4)+4(-3)=8

20-12=8

8=8 so it passes.

NOW , for the slope:

slope = - 5/4 ( the equation is 5x+4y=8 , the cartesian equation is 5x+4y-8=0. THE cartesian equation with variables is ax+by+c=0) NOW this is linked with the slope bcz the slope is linked to the director vector (-b;a) that gives (-4;5), this is the director vector's formula that we're going to call U. THEN with this formula you get the slope: Y of U / X of U = 5/-4 = - 5/4 (bcz you dont leave the denominator with a negative sign).

THAT'S it thats the answer.

Answer:

0.375

Step-by-step explanation:

The minimum height the second beaker must be so it does not overflow is 9.55 inches.

Given that a beaker has a radius of 1.8 inches and height of 4.6 inches. we need to find the height of another beaker which has the radius of 1.25 in and has same volume,

Volume of a cylinder = π × radius² × height

= 3.14 × 1.8² × 4.6

= 46.8 in³

Now, the second beaker =

46.8 = 3.14 × 1.25² × h

h = 46.8 / 3.14 × 1.25²

h = 9.55

Hence, the minimum height the second beaker must be so it does not overflow is 9.55 inches.

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The result of 1/11 in the base 10 system is given as is 0.09.

To visualize the long division of 1 ÷ 11 in a base ten system:

Set up the long division: 11 outside and 1.00 inside the division bracket.

Place the decimal point in the quotient above the dividend's decimal point.

Bring down the first digit (0) and divide 11 into 10; it goes 0 times.

Subtract the product (0) from 10, leaving 10.

Bring down the next digit (0) and divide 11 into 100; it goes 9 times.

Subtract 99 from 100, leaving a remainder of 1.

The result is 0.09.

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The missing values are 60, 100 and 40 if the Median and Mode of the  wage distribution are known to be $33.5 and $34 respectively

Wages (in Rs)_freq____        CF

0-10________4___________4

10-20_______16________20

20-30_______x________20+x

30-40______y_________20+x+y

40-50______z________20+x+y+z

50-60______6_______26+x+y+z

60-70______4______30+x+y+z

Since total 230

So, 30+x+y+z=230

x+y+z=200

Mode =34

Median = 33.5

By solving the equations we get x=60, y=100 and z=40

Hence, the missing values are 60, 100 and 40

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Answer:60, 6.75

Step-by-step explanation:

To solve the first prompt, we must create an equality statement.

[tex]\frac{10}{45}=\frac{x}{270}[/tex] X being the distance he can go in 4.5 hours.

In order to have came up with 270, we needed to take 4.5 hours and turn it into a measure of minutes to correspond to the minute value of 45.

This is found by multiplying 4.5 by 60.

Now that we have this done, we can cross multiply the equality statement.

[tex]10\cdot270=45x[/tex]

Simplify the first side

[tex]2700=45x[/tex]

Divide both sides by 45

[tex]\frac{2700}{45}=\frac{45x}{45}[/tex]

[tex]60=x[/tex]

This means that Jacob can bike 60 miles in 4.5 hours.

For the second prompt, we need to find how long it would take for him to bike 90 miles given the amount of time it took for him to bike 10 miles.

We can use an equality statement like this:

[tex]\frac{45}{10}=\frac{x}{90}[/tex]

Now we cross multiply:

[tex]45\cdot90=10\cdot x[/tex]

Simplify:

[tex]4050=10x[/tex]

Now we can divide both sides by 10.

[tex]\frac{4050}{10}=\frac{10x}{10}[/tex]

[tex]405=x[/tex]

This means that it would take Jacob 405 MINUTES to bike 90 miles.

To turn this into a measure of hours, we need to divide 405 by 60, which comes out to 6.75.

It would take Jacob 6.75 hours to bike 90 miles.

The correct statement regarding the relations in this problem is given as follows:

Only relation A could represent a linear relationship.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

From the first bullet point, we have that what classifies a linear relation is a constant rate of change.

For relation K, we have that it is not linear, as:

For relation R, we have that it is linear, as it has a constant rate of change.

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This capital gain  problem that can be modelled using this equation is one that relates to the price of a stock or share.

It can be writen as follows.....

Suppose that one purchased 900 shares of a stock at a price of $  12.55 per share .

After a year, the stock price rose to $ 13.25 per share, but you sold the shares at a price of $8. 14 per share due to financial difficulties.

You also incurred a transaction cost of $25.

What is the capital gain or loss made on the stock?

given the above question, if we solved for for the problem, we would get....

Solving for x, we get:

((900 )(x )-(900 )(x)(.01))-(900) (x-4)  +25)

= 15,740

Simplifying this expression, we get:

(0.99900x) - (36 x 900) + 25

= 15,740

0.99900 x = 15,655

x = 17.39

Therefore, the current stock price is $17.39

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Full Question:

1. Examine the equation below used for determining the capital gain made on a stock. Look through this chapter and your notes to help you write a problem that could be modeled by this equation.

.((900)(12.55)-(900)(12.55)(.01))-(900)(8.14)+25)=3,831.05

∠ AFE is supplementary to ∠ AFB and the measure of ∠ AFE = 102⁰.

option A.

Supplementary angles are the two angles that sum up to 180 degrees.

That is, if the sum of two angles is equal to 180 degrees, then the two angles are supplementary.

From the given diagram we can form the following equation;

∠ AFE + ∠ AFB = 180 (sum of angles on a straight line is equal to 180⁰ )

∠ AFE = 180 - ∠ AFB

∠ AFE = 180 - 78

∠ AFE = 102⁰.

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Answer:

Answer:Radians = Degrees × 3.14/180

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174135×0.0174

Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174135×0.0174 = 2.355

Answer:

0.1 oz

Step-by-step explanation:

1000=10 oz

10 drops

1000/100=10

10/100=O.1 oz

Answer:

Step-by-step explanation:

4. A. Im not sure but that seems like the most logical.

5. D.

6. B.

7. B.

8. I think it's A. maybe-

9.- id-k sorry-

10. i--dk..]

11. C

12. D

13. B.

15. C.

16. C

17. A.

18. D

19. C.

21. D.

22. -(x+1)/(x-1)(x+2) x does not equal -3, -2, 1, and 6

23. i d-ksorry

24.i-d-k sorry

25. D.

Hope this helped sorry i culdn't get them all-

The answers to all parts are shown below.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

1. x⁴ + 5x³ + 7x² -3x - 10 = 0

= (x-1)(x+2)(x² + 4x + 5)

Thus, the rational roots are 1 and -2.

2. 3x² -4 = - x⁴

x⁴ + 3x² -4 = 0

(x-1)(x+1)(x² + 4) =0

Thus, the zeroes are 1, -1, -2i, +2i.

3. We can write the zeroes as

p(x)=(x-1)(x-2)(x+2)(x+3).

So, p(x) = x⁴ + 2x³ -7x² -8x +12

4. x³ -3x² +4x- 12=0

(x-3)(x²+4) =0

x= 3, -2i, 3i

5.  x= 1,2,4,6,8,10,11

y= 0,-1,0,4,8,9,8

So, equation of line

(y- 0) = (-1-0)/(2-1)(x-1)

y = -1(x-1)

y + x +1=0

6. x= 2,5,12,20 and y= 30,12,5,3

k = 30/2

k = 15

So, the relationship is y= 15x.

7. cn = constant(k)

n= 44

then, c= 30/44 = 0.68

and, k = 44 x 0.68

k = 30

So, c = 1.5 dollars per person.

8. 125¹/³

= (5³)¹/³

= 5

9. y = 293(1.06)⁴ = 370

10. log₃ 2187

= log₃ 3⁷

= 7

11. log₄ 22

= 2.29

12 . y= 4/x

The new equation is  y = 4/(x - 7) + 6.

13. (6-x)/ (x² + 2x - 3) / (x² -4x- 12)/ (²x² + 4x + 3)

= - (x+1)/ (x+1)(x+2)

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According to the line plot, the statement that best describes the spread and distribution of the data is "The data is bimodal with an approximate range of 24. The most frequent number of activities was either 16 or 28, which might show that the entire class needed to choose an activity.". (option c).

The horizontal number line starts at 0 and increases by units of two up to 30. The dots above the numbers represent the number of schools that offer a certain number of activities. For instance, there is one dot above 4, 6, 14, and 28, which means that only one school offers four activities, one school offers six activities, one school offers 14 activities, and one school offers 28 activities.

Based on this line plot, we can conclude that the data is not symmetric because there is not an equal number of dots on either side of the plot. Therefore, we can rule out the first and fourth options.

We can observe that there are more dots on the left-hand side of the plot, indicating that there are more schools that offer fewer activities. Additionally, the most frequent number of activities is 16, which means that about half of the schools offer this number of activities.

Furthermore, we can estimate the range of the data to be approximately 24, as the number line goes up to 30, and the highest number of activities offered by any school is 28.

Hence the correct option is (c).

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Let's assume the price of a citron is "x" units and the price of a fragrant wood apple is "y" units.

From the given information, we can form two equations:

7x + 9y = 135 ...(1)

9x + 7y = 137 ...(2)

We can solve this system of equations using the elimination method. Multiplying equation (1) by 9 and equation (2) by 7, we get:

63x + 81y = 1215 ...(3)

63x + 49y = 959 ...(4)

Subtracting equation (4) from equation (3), we get:

32y = 256

y = 8

Substituting the value of y in equation (1), we get:

7x + 9(8) = 135

7x + 72 = 135

7x = 63

x = 9

Therefore, the price of a citron is 9 units and the price of a fragrant wood apple is 8 units.

The total gain at the end of the second year for both accounts combined is $509.09.

We have,

Amount saved = $8500

40% of 8500 is saved in saving account = 0.4 x 8500 = $3400

Remainder amount in stock plan = 8500 - 3400 = 5100

Working for savings plan

A = P(1 + r/n[tex])^{nt[/tex]

A = 3400(1 + 0.042/1)²

A = $3691.60

So, we gain = 3691.6 - 3400 = $291.6

Working for stock plan:  

The stock plan decreases 3% in the first year

= 5100 x 0.97

= $4947

and increases 7.5% in the second year.

= 4947 x 1.75

= $5318.03

So, we gain = 5318.03 - 5100 = $218.03

Thus, the total gain is

= 291.06 + 218.03

= $509.09

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namely, what is "t" when f(t) = 2000

[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(t)}{2000}=500e^{0.195t}\implies \cfrac{2000}{500}=e^{0.195t}\implies 4=e^{0.195t} \\\\\\ \log_e(4)=\log_e\left( e^{0.195t}\right)\implies \log_e(4)=0.195t\implies \ln(4)=0.195t \\\\\\ \cfrac{\ln(4)}{0.195}=t\implies 7.11\approx t[/tex]

The interest on the loan using the Banker's Rule is $139.20.

The formula for calculating interest using the Banker's Rule is:

Interest = Principal x Rate x Time / 360

where:

Principal is the amount of the loan

Rate is the interest rate as a decimal

Time is the time period in days

Using this formula, we can calculate the interest on the loan as:

Interest = 4800 x 0.088 x 105 / 360

Interest = 139.20

Therefore, the interest on the loan using the Banker's Rule is $139.20.

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To complete the proof below, we have;

<EFC is right angle; definition of a right angle

m<EFC = 90 degrees; definition of a tangent line

m<EFC + m<FEC + m<ECF = 180; Triangle sum theorem

90° + m<FEC + m<ECF = 180; Substitution property of equality

m<FEC + m<ECF = 90; Subtraction property of equality

<FEC + <ECF are complementary angles; definition of complementary angles

To match the statement with their corresponding equations, we need to know the following;

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Corellian Engineer used the Bottom up (Micro) approach to estimate the total cost of developing a new navigation system for its YT-1300 Freighter. The total cost estimate of $17,500. So, the correct option is C).

The process that Corellian used for this estimate is the Bottom up (Micro) approach, which involves estimating costs for each component or task in the project and then summing them up to get the total cost estimate.

In this case, they estimated the costs for programming, beta testing, installation, and final shake down, and then added them up to get the total cost estimate of $17,500.

So, the correct answer is C).

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