Let (-5,-4) be a point on the terminal side of (theta). Find the exact values of cos, csc, and tan.

The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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Answer: the mode is 67.2

Step-by-step explanation:

Given that;

Data               Frequency

30 - 34                 1

35 - 39                0

40 - 44                3

45 - 49                7

50 - 54                5

55 - 59               10

60 - 64               10

65 - 69              21

70 - 74               12

Mode = ?

we know that mode is the number that has the highest number of appearance of frequency, so in this case, the data group that has the highest frequency (21) is 65 - 69  

Lower class boundary of the modal group; L = 65

Frequency of the group before the modal group; Fm-1 = 10

Frequency of the modal group; Fm = 21

Frequency of the group after the modal group; Fm+1 = 12

Group width; G = 4

Now using the formula

Mode = L + [ (Fm - Fm-1) / ( (Fm - Fm-1) + (Fm - Fm+1) ) ] × W

so we substitute

Mode = 65 + [ (21 - 10) / ( (21 - 10) + (21 - 12) ) ] × 4

= 65 + [ 11 / 20] × 4

= 65 + 2.2

= 67.2    

Therefore the mode is 67.2

The point charges placed 0.500 m apart are 10.4 nC and 43.9 nC. Then, the electric field halfway between these charges will be -4824 N/C.

The physical field that surrounds particles with an electrical charge is called an electric field. All other charged particles in the field are affected by it, either being attracted to it or being repelled by it.

The electric field because of a point charge q is written as \(E=\frac{kq}{r^2}\)

Positive point charges cause the electric field to point away from the point, whereas negative point charges cause the electric field to point in the direction of the point. Then, the electric field of the midpoint p in the diagram is written as,

\(\begin{aligned}E_p&=\mathrm{\frac{k(10.4\;nC)}{(0.25\;m)^2}-\frac{k(43.9\;nC)}{(0.25\;m)^2}}\\&=\mathrm{\frac{k(10.4-43.9)\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{\frac{9\times 10^9\;Nm^2/C^2\times 33.5\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{4824\;N/C}\end{aligned}\)

The required answer is -4824 N/C.

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Answer:

.048

Step-by-step explanation:

6 thousandths = 0.006

So, 0.006 times 8 would be...

.006

x    8

.048

Hope this helps you out! I'm not exactly sure how to explain how to multiply, but if you're confused, you can always ask someone for help...have a great day :)

Answer:

x = - 1

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1

Answer:

Step-by-step explanation:

The domain and range of a linear function is always real numbers (T or F)

It is True. This is because of a couple of reasons.

    1.) You cannot divide by 0.

     2. A negative number cannot have its square root taken.

The range is determined by the domain in a linear function, and thus it must always consist of real numbers.

A member of the senate will serve for (h+4) years.

An expression, in mathematics, is a finite set of combinations and/ or numbers and variables that accurately represents the the context in question. When two or more expressions are connected using the equality sign then an equation is formed.

Here, we are given that in the US government a member of the senate serves for 4 years longer than a member of the House of Representatives.

Also the House of Representatives serves for- h years

Thus, the number of years a member of the Senate will serve will be 4 more than the number h

= h + 4

Thus, a member of the senate serves for (h+4) years.

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The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.

Let's solve the system of linear equations correctly.

The given system of linear equations is:

x = y + 3z = 6

x - 2y = 5

2x - 2y + 5z = 9

To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:

From equation 1, we have:

x = y + 3z

Substituting this value of x in equation 2:

(y + 3z) - 2y = 5

y + 3z - 2y = 5

-z + 3z = 5 - y

2z = 5 - y

Now, let's substitute the value of x in equation 3:

2(y + 3z) - 2y + 5z = 9

2y + 6z - 2y + 5z = 9

11z = 9

Simplifying the equation, we find:

z = 9/11

Now, substituting this value of z back into the equation 2z = 5 - y, we get:

2(9/11) = 5 - y

18/11 = 5 - y

18/11 - 5 = -y

18/11 - 55/11 = -y

-37/11 = -y

y = 37/11

Finally, we can substitute the values of y and z into equation 1 to find the value of x:

x = y + 3z

x = 37/11 + 3(9/11)

x = 37/11 + 27/11

x = 64/11

Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).

The system has exactly one solution.

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Answer:

a) 1/1

b) 3/2

c) 2/1

d) 17/13

Step-by-step explanation:

a) 1 sun for every 1 moon

b) 12 circles for 8 triangles = 12/8 = 3/2 (divide 12 and 8 by the highest number possible for both at the same time, which is 4 in this case)

c) 8/4 = 2/1

d) 17/13

code: 7591-5917-1759-9175

Answer:

A) -8x+2

Step-by-step explanation:

-8x + 7 - 5 - 5x + 5x

-8x -5x + 5x + 7 - 5

- 8x+2

Answer:

x = 1

Step-by-step explanation:

Recall: adjacent angles supplementary

Therefore,

65x + 115° = 180°

Subtract 115° from each side

65x + 115° - 115° = 180° - 115°

65x = 65

Divide both sides by 65

65x/65 = 65/65

x = 1

Answer:

y intercept = -41/9

Step-by-step explanation:

y = mx + b

y = -1/9x + b

-5 = -1/9(4) + b

-5 = -4/9 + b

add 4/9 to both sides

-45/9 + 4/9 = b

-41/9 = b

the y intercept is equal to -41/9

linear equation: y = -1/9x - 41/9

Answer:

I think its telling you to done o and up and like 2y 1x

Step-by-step explanation:

Answer: I'm sorry, I dont really know but here are some notes to help you with this.

Step-by-step explanation:   https://www.hopewell.k12.pa.us/Downloads/Representing%20Proportional%20Relationship%20-%20NOTES%20COMPLETE2.pdf

Note that the longest segment in the shapes shown is DC (Option B).

The longest side of a triangle is opposite to greatest angle.

To determine the longest side in a triangle, compare the lengths of all three sides. The side with the greatest length is the longest side.

You can use a ruler or a measuring tool to measure the lengths of the sides or compare the numerical values if they are provided.

In this case,

∠A = ∠DBA = 60°

So ∠ ABD is an equilateral triangle.

So, AB = BD = AD

Since

AB = BC

Then

∠BDC = ∠C ∠ 38°

so ∠DBC > 90°

This means that DC is the longest side.

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The standard deviation of the sampling distribution is 0.06.  

Standard deviation is a statistical value used to determine the closeness of a statistical sample to the average of a data. The higher the standard deviation value, the wider the range of data variations.

Thus, the standard deviation can provide an overview of the gap between the sample values and the average. The standard deviation formula is used to analyze whether the sample can represent the population in the study. The standard deviation can also describe the quality of the sample data obtained.

Given that

Its 29% of American adults do not sit on public toilet seats.

Probability that American adults do not sit on public toilet seats, p=0.29

sample size, n = 51

\(Standard deviation = \frac{p(1 - p)}{n} \\ = \frac{0.29( 1 - 0.29)}{5.1} = 0.06\)

Therefore, the standard deviation of the sampling distribution is 0.06.  

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Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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The length of the second trial will be equal to 2(⁵/₈) miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.

The length of the second trial will be calculated as,

Length =  3/4 x ( 3¹/₂ )

Length = 2(⁵/₈)

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The inequality that represents the number of each type of calculator she can buy will be 25x + 65y ≤ 800

Given that teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each.

Consider that x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators.

The inequality that represents the situation becomes as;

25x + 65y ≤ 800

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Answer:

C = L + B(x)

Step-by-step explanation:

First, make Laser Tag "L" and Bowling "B." Make the total cost "C." Then, make the equation, with "x" being the number of bowling games. So, the equation is:

Total Cost = Laser Tag Price + (Price of Bowling x Number of Games Bowled)

or in simpler terms,

C = L + B(x).

Hope this helps!

Using equivalent angles, the solutions to the equation are given as follows:

\(\theta = 255^\circ, \theta = 285^\circ\)

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the equation is:

\(\sin{\theta} = -0.966\)

Applying the inverse relation:

\(\theta = \arcsin{-0.966} = 255^\circ\)

Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:

\(270^\circ + (270^\circ - 255^\circ) = 285^\circ\)

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The percentage of drivers who are at least 45 is 62%

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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Remember that given any function, if we subtitude

for

We're moving the function's graph a units horizontaly

Note that a could be negative, and we would end up with

That means we move the graph a units to the left.

In this case, we have

That means that the graph of the function moves 3 units to the right

Answer:

line b

Step-by-step explanation:

you can tell because x and y equal the same number on line b

Answer:

switch them up

Step-by-step explanation:

8÷5 and 8/5 are just equal to each other because the symbol "÷" means division as well as the fraction bar "/".

8÷5 = 1.6

8/5 = 1.6 as well.

The coordinate of point R after the rotation is determined as = ( - 4, 7).

option A.

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.

You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.

When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.

The initial coordinate of point R = ( 4, 7),

The new coordinate of point R after the rotation = ( - 4, 7)

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