Find all six trigonometric functions of θ if the given point is on the terminal side of θ. Answer exactly. ( − 4 , − 1 )

Answer: [tex]-\frac{9}{8}[/tex]

Step-by-step explanation:

If you are given two points of a line, the slope is defined as rise/run. Rise is the difference in y coordinates, (think about it, going UP is RISING), and Run is the difference in x coordinates, (again its pretty intuitive.)

So Slope = [tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]

This can be calculated with the coordinates of the two points, (order wont matter youll get the same answer).

Slope = (-3-6)/(6-(-2)) = -9/8

OR, (going the other way)

Slope = (6-(-3))/(-2-6) = 9/-8 = -9/8

Easy!

Answer:

Simple Interest

SI=PRT/100

P=€100

SI=€300-€100 = €200

T=10 years

rate = unknown

Rate = SIx100/(pxt)

Rate = 200x100/(100x10)

= 20%

b)Compound interest

CI = P(1+i)ⁿ

CI= €300

P =€100

n = 10

€300 = €100(1+i)¹⁰

take the tenth root of both sides

€1.77 = €1.58(1+i)

divide both sides by 1.58

1.12 = 1 + i

i = 1.12 - 1

i = 12%

c)si=prt/100

=(100x20x15)/100

= €300

total = 300+100

€400

CI = P(1+i)ⁿ

= 100(1+0.12)¹⁵

=€547.35

It is gathering more money with annual compound interest

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The angle relationship that will fill the correct angle are given below.

An angle is said to be generated when two or more lines intersect at a point. Thus series of angles which have some common relationship on comparison are formed. Some common angle relationships are; supplementary angles, complementary angles, vertical angles, etc.

The angle relationship to fill the correct angle are:

1. <AXE and <CXD are vertical angles.

2. <AXF and <DXF are supplementary angles.

3. <DXC and <BXC are complementary angles.

4. <CXB and <AXB are adjacent angles.

5. <AXC and <CXD are supplementary angles.

6. <DXE and <AXC are vertical angles.

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The total area of the composite figure is 258 squared centimeters.

The figure in the diagram is composed of two triangle and a rectangle?

The area of a triangle = 1/2 × base × height

Area of a rectangle = length × width

From the diagram;

Triangle 1

Triangle 2

Rectangle

To find the area of the composite figure, we find the area of the two triangle and rectangle and add.

Area = area of triangle 1 + area of triangle 2 + area of rectangle.

Area = ( 1/2 × base × height ) + ( 1/2 × base × height ) + ( length × width )

Area = ( 1/2 × 4 × 12 ) + ( 1/2 × 12 × 3 ) + ( 18 × 12 )

Area = ( 2 × 12 ) + ( 6 × 3 ) + ( 18 × 12 )

Area = 24 + 18 + 216

Area = 258cm²

Therefore, the area is 258 squared centimeters.

Option C) 258cm² is the correct answer.

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Answer:

258cm^2

Step-by-step explanation:

When the residual is negative it represents the predicted value is very much high.

Therefore, the negative residual value on the regression line represents the predicted value is very much high.

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Answer: 5,840,000

Step-by-step explanation:

96/24=4

365,000x2x2x2x2=5,840,000
or
365,000 x 2^4=5,840,000

The equation of the polynomial is P(x) = 0.16875(x + 8)(x - 10)

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

The graph

On the graph, we have the following readings:

A root of multiplicity 1 at x = -8

A root of multiplicity 1 at x = 10

y-intercept = -13.5

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

Using the above as a guide, we have the following:

P(x) = a * (x + 8)(x - 10)

The y-intercept is -13.5

So, we have

a * (0 + 8)(0 - 10) = -13.5

This gives

a = 0.16875

Hence, the expression is P(x) = 0.16875(x + 8)(x - 10)

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By Using the Cumulative distributed Function(CDF)m we get:

a) P (x <= 3 ) = 0.36

b) P ( 2.5 <= x <= 3  ) = 0.11

c) P (x > 3.5 ) = 1 - 0.49 = 0.51

d) x = 3.5355

e) f(x) = x / 12.5

f) E(X) = 3.3333

g) Var (X) = 13.8891  , s.d (X) = 3.7268

h) E[h(X)] = 2500

Given:

The cdf is as follows:

F(x) = 0                    x < 0

F(x) = (x^2 / 25)     0 < x < 5

F(x) = 1                   x > 5

Now,

a) Evaluate the CDF given with the limits 0 < x < 3.

So, P (x <= 3 ) = (x^2 / 25) | 0 to 3

P (x <= 3 ) = (3^2 / 25)  - 0

P (x <= 3 ) = 0.36

b) Evaluate the CDF given with the limits 2.5 < x < 3.

So, P ( 2.5 <= x <= 3 ) = (x^2 / 25) | 2.5 to 3

P ( 2.5 <= x <= 3  ) = (3^2 / 25)  - (2.5^2 / 25)

P ( 2.5 <= x <= 3  ) = 0.36 - 0.25 = 0.11

c) Evaluate the CDF given with the limits x > 3.5

So, P (x > 3.5 ) = 1 - P (x <= 3.5 )

     P (x > 3.5 ) = 1 - (3.5^2 / 25)  - 0

    P (x > 3.5 ) = 1 - 0.49 = 0.51

d) The median checkout for the duration that is 50% of the probability:

   So, P( x < a ) = 0.5

         ⇒ (x² / 25) = 0.5

          ⇒ x² = 12.5

          ⇒ x = 3.5355

e) The probability density function can be evaluated by taking the derivative of the cdf as follows:

      pdf f(x) = d(F(x)) / dx = x / 12.5

f) The expected value of X can be evaluated by the following formula from limits - ∞ to +∞:

      E(X) = integral ( x . f(x)).dx          limits: - ∞ to +∞

       E(X) = integral ( x² / 12.5)    

        E(X) = x³ / 37.5                    limits: 0 to 5

        E(X) = 5³ / 37.5 = 3.3333

g) The variance of X can be evaluated by the following formula from limits - ∞ to +∞:

 Var(X) = integral ( x² . f(x)).dx - (E(X))^2          limits: - ∞ to +∞

 Var(X) = integral ( x³ / 12.5).dx - (E(X))^2    

 Var(X) = x⁴/ 50 | - (3.3333)^2                         limits: 0 to 5

 Var(X) = 5⁴/ 50 - (3.3333)^2 = 13.8891

Standard Deviation (s.d) (X) = sqrt (Var(X)) = sqrt (13.8891) = 3.7268

h) Find the expected charge E[h(X)] , where h(X) is given by:

      h(x) = (f(x))^2 = x^2 / 156.25

The expected value of h(X) can be evaluated by the following formula from limits - ∞ to +∞:

E(h(X))) = integral ( x . h(x) ).dx          limits: - ∞ to +∞

E(h(X))) = integral ( x^3 / 156.25)    

E(h(X))) = x^4 / 156.25                      limits: 0 to 25

E(h(X))) = 25^4 / 156.25 = 2500

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The formula for given sequence is aₙ = 0.3(-0.2)ⁿ⁻¹ i.e. E.

What exactly is a sequence?

A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. Can you figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.

Now,

Given sequence is 0.3,-0.06, 0.012, -0.0024, 0.00048, ...

Of all given options only E satisfies the given sequence because

for E

a₁=0.3*-0.2¹⁻¹

=0.3*1

=0.3

a₂=0.3*-0.2²⁻¹

=-0.3*0.2

=-0.006

a₃=0.3*-0.2³⁻¹

=0.3*0.04

=0.012

hence,

          The formula for given sequence is aₙ = 0.3(-0.2)ⁿ⁻¹.

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A collegiate basketball player hits 80% of his free throw attempts. Assuming free throw attempts are independent, he will try 100 free throws this season the answers are as follows:

a) The mean of X is 80.

b) The standard deviation of X is 4.

c) The probability that the basketball player makes at least 90 of these attempts is approximately is 0.0062.

d) If the basketball player instead attempts only 10 free throws, the probability that he makes at most 4 of these is 0.0064.

As per the question given,  

a) The mean of X is given by the formula: mean = n * p, where n is the number of trials and p is the probability of success on each trial. In this case, the player attempts 100 free throws with a probability of success of 0.8, so the mean is:

mean = 100 * 0.8 = 80

Therefore, the correct answer is 80.

b) The standard deviation of X is given by the formula: standard deviation = sqrt(n * p * (1 - p)). Substituting the values, we get:

standard deviation = sqrt(100 * 0.8 * 0.2) = 4

Therefore, the correct answer is 4.

c) To find the probability that the player makes at least 90 free throws, we can use the normal approximation to the binomial distribution. The mean is 80 and the standard deviation is 4, so we can standardize the value of X as follows:

z = (90 - 80) / 4 = 2.5

Using a standard normal distribution table, we can find the probability that Z is greater than 2.5, which is approximately 0.0062.

Therefore, the correct answer is 0.0062.

d) If the player attempts only 10 free throws, the number of successful attempts X follows a binomial distribution with n=10 and p=0.8. The probability that he makes at most 4 of these attempts is:

P(X <= 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

Using the binomial distribution formula, we can calculate each of these probabilities and sum them up. Alternatively, we can use a binomial probability table or a calculator to find the cumulative probability.

Using a binomial probability calculator, we get:

P(X <= 4) = 0.0064 (rounded to four decimal places)

Therefore, the correct answer is 0.0064.

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the assumption being that h(t) is the height of the rock in "t" seconds, so by the time the rock hits the ground h(t) = 0, namely it has reached 0 height because, well, is on the ground :)

[tex]h(t)=36t^2 - 64\implies 0=36t^2 - 64\implies 64=36t^2\implies \cfrac{64}{36}=t^2 \\\\\\ \sqrt{\cfrac{64}{36}}=t\implies \sqrt{\cfrac{16}{9}}=t\implies \cfrac{4}{3}=t\implies 1.\overline{33}=t[/tex]

Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.

Yes, measures of variability are used to describe the extent to which scores in a distribution differ from one another.

Measures of variability include the range, variance, and standard deviation, and they give us a sense of how spread out the scores in a distribution are. These measures help us understand the variability or dispersion of the data and how far the individual scores in a distribution deviate from the mean or other measures of central tendency.

Measures of central tendency, such as the mean, median, and mode, describe the central or typical value of a set of scores. They provide a summary of the data and a single value that represents the center of the distribution.

The decisions regarding graph size, shape, and style are usually based on the type of data being presented and the message being conveyed. A histogram, for example, may be used to visually display the distribution of a set of scores, and the size, shape, and style of the graph can be adjusted to highlight important features of the data.

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Answer:

[tex]10[/tex] four point questions and [tex]30[/tex] two point questions

Step-by-step explanation:

Let's say [tex]f =[/tex] [tex]\text{number of four point questions}[/tex] and[tex]t = \text{number of two point questions}[/tex]. The total number of questions is [tex]40[/tex], therefore [tex]t + f = 40[/tex]. We know the test is worth [tex]100[/tex] points so we can write [tex]2t + 4f = 100[/tex]. We have a system of equations: [tex]t + f = 40 \text{ and } 2t + 4f = 100[/tex]. We can rewrite [tex]t[/tex] as [tex]t = 40 - f[/tex]. We rewrite this in the equation [tex]2t + 4f = 100[/tex]. Since [tex]t = 40 - f[/tex], we have [tex]2 \cdot (40 - f) + 4f = 100[/tex]. Distributing & simplifying gives

[tex]2 \cdot (40 - f) + 4f = 100\\(80 - 2f) + 4f = 100,\\\text{Remove parentheses} 80 - 2f + 4f = 100,\\80 + (-2f) + 4f = 100\\80 + 2f = 100,\\\text{Subtract 80 from both sides} 2f = 20,\\\text{Divide 2 by both sides} f = 10.\\[/tex]

Since we determined [tex]t = 40 - f[/tex] and [tex]f = 10[/tex], subtracting [tex]10[/tex] from [tex]40[/tex] will give [tex]t = 30[/tex].

Therefore, there are [tex]10[/tex] four point questions and [tex]30[/tex] two point questions.

Hope that helps!

Answer:482 in ^2

Step-by-step explanation:

The equation of the graph is y = (5x + 10)/(x²-1).

The correct option is c.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

The graph of the equation is given in the image.

From the graph:

When x = 0, then y = -10.

And when y = 0, then x = -2.

y = (5x + 10)/(x²-1)

Substituting the values,

we get,

when x = 0, then y = -10.

And when y = 0, then x = -2.

From the given choices:

The equation,

y = (5x + 10)/(x²-1) satisfies the points.

Hence, the equation is y = (5x + 10)/(x²-1).

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The probability of selecting the fair coin when a gambler has both a fair coin and a two-headed coin in his pocket is 50%.

This is because, when he selects one of the coins at random, it is equally likely that he has chosen either the fair coin or the two-headed coin. If he flips the coin and it shows heads, then the probability that it is the fair coin is still 50%, because either coin could have been selected and both would show heads.This is an example of a classical probability problem, which is based on the law of equal chances. This law states that when an event has multiple possible outcomes, each of those outcomes is equally likely to occur. In this case, there are two possible coins that could have been chosen, so each coin has a 50% chance of being selected. This means that the probability of selecting the fair coin is 50%.This also applies to events that have multiple outcomes which are not equally likely. For example, if a gambler has a fair coin, a two-headed coin, and a three-headed coin in his pocket, the probability of selecting the fair coin is still 50%. This is because the gambler has an equal chance of selecting any of the coins, regardless.

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Answer:

x=1 , y=1

Step-by-step explanation:

2x+y=3 - - (1)

4x+6=10y
=> 4x-10y=-6 - - (2)
Multiply eq (1) by 2, and we get ;

4x+2y=6 - -(3)

Now subtract eq (3) by eg (2)
4x+2y=6
-4x+10y=+6

12y=12

y=1

Sub value of y in eq (1)

2x+1=3

2x=2

x=1

Answer:

32 markers

Step-by-step explanation:

Ty has 8 x 3 = 24 markers.

Together, they have 8 + 24 = 32 markers.

Answer:

no solution

Step-by-step explanation:

- x + 6y = 9 → (1)

- 4x + 24y = 48 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x and y

4x - 24y = - 36 → (3)

add (2) and (3) term by term

0 + 0 = 12

0 = 12 ← false statement

this false statement indicates the system has no solution

Answer:

It would equal 2/5. First flip the 5/6 so then it would be 6/5. Then the 3 and 6 can cross cancel so it would equal to 2 in the numerator.

Answer: A. [tex]92cm^{3}[/tex]

Step-by-step explanation:

[tex]V= \frac{4}{3} \pi r^{3}[/tex]

[tex]V=\frac{4}{3}\pi 2.8^{3}[/tex]

[tex]4/3=1.33333333333[/tex]

calculate in calculator

[tex]1.33333333333\pi 2.8^3=91.9523225755[/tex]

round to nearest ones (9 tells 1 to go to 2)

Therefore, A. 92cm^3

Answer:

the area of the isosceles triangle is approximately 104.49 cm^2.

Step-by-step explanation:

The perimeter of the triangle is 100 cm, so we can write an equation using the lengths of the sides:

x + x + (x + 10) = 100

3x + 10 = 100

3x = 90

x = 30

So the equal sides of the triangle have length 30 cm and the side that is 10 cm greater has length 40 cm.

To find the area of the triangle, we can use the formula for the area of an equilateral triangle:

Area = (sqrt(3) / 4) * (side length)^2

Area = (sqrt(3) / 4) * 30^2

Area = (sqrt(3) / 4) * 900

Area = (sqrt(3) / 4) * 30 * 30

Area = (sqrt(3) / 4) * 900

Area = (30 * sqrt(3)) / 2

Area = 45 sqrt(3)

The required after 8 years, the investment will be worth approximately $156,753.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,
To calculate the future value of Joshua's investment after 8 years with an interest rate of 6% compounded daily, we can use the formula:

In this case, P = $97,000, r = 6% = 0.06, n = 365 (since the interest is compounded daily), and t = 8.

So, we have:

[tex]A = $97,000 \times (1 + 0.06/365)^{365 * 8}[/tex]

A = $195,239.00

Therefore, after 8 years, the investment will be worth approximately $156,753.

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Answer:

NOT

Step-by-step explanation:

There are no pairs of congruent sides.

X = 11 when y = 4 when X=a+b+4 and a directly proportional to y squared , b is inversely proportional to y.

Given that a is directly proportional to y^2 and b is inversely proportional to y, we can write the following two relationships:

[tex]a = k * y^2[/tex]

[tex]b = m / y[/tex]

where k and m are constants. From the first equation, we can find the value of k when y = 2:

[tex]a = k * 2^2[/tex]

[tex]k = a / 4[/tex]

And from the second equation, we can find the value of m when y = 2:

[tex]b = m / 2[/tex]

[tex]m = 2b[/tex]

Substituting these values into the equation X = a + b + 4, we can find X when y = 2:

[tex]X = (k * 2^2) + (m / 2) + 4[/tex]

[tex]X = (a / 4) * 4 + 2b + 4[/tex]

[tex]X = a + 2b + 4[/tex]

[tex]X = 18[/tex]

We can now use the value of k and m to find X when y = 4:

[tex]X = (k * 4^2) + (m / 4) + 4[/tex]

[tex]X = (a / 4) * 16 + (2b) / 4 + 4[/tex]

[tex]X = 4a + 2b + 4[/tex]

Substituting the value of X = 18 when y = 2, we can solve for a and b:

18 = 4a + 2b + 4

14 = 4a + 2b

7 = 2a + b

Solving the system of equations for a and b, we find:

a = 5

b = 2

Finally, substituting these values into the equation X = a + b + 4, we can find X when y = 4:

X = (5) + (2) + 4

X = 11

Therefore, X = 11 when y = 4.

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The answer is 309,600 cubic inches, which is option B.

What is the volume?

Volume is the total amount of space inside a three-dimensional shape. Volume is measured in cubic units, such as “cubic inches” or in³.

Volume is the amount of space matter takes up. The matter is anything that has mass and takes up space. Volume is used to describe the size of an object.

The volume of each case is 16.00 inches * 10.75 inches * 5.00 inches = 880 cubic inches.

So, the volume of 360 cases is 360 * 880 cubic inches = 309,600 cubic inches.

Therefore, the answer is 309,600 cubic inches, which is option B.

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Answer:

Step-by-step explanation:

Convers 95 min into hours

95/60 = 1.58 Hours

Sara can read 19 pages per hour

Total pages in 95 min or 1.58 hours =

19 * 1.58 = 30.02

Rounding off to nearest whole number- 30

Hope it helps

Answer:

X = 48

Step-by-step explanation:

x/4 - 6 = x/12 + 2​

= 3x-72=x+24

= 3x=x+96

= 2x=96

= x=48

Answer:

x=48

Step-by-step explanation:

You can solve by x by simplifying both sides of the equation, then isolating the variable