what is the value of [3]\[n]{x}[/64}

Answer:

(a) The graph is an exponential growth curve.

(b) f(0) = 2,  f(1) = 10

(c) The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.

Step-by-step explanation:

Given function:

[tex]k(x)=2(5)^x[/tex]

[tex]\hrulefill[/tex]

The graph is an exponential growth curve.

The curve begins in quadrant II, crosses the y-axis at (0, 2) into quadrant I, and increases rapidly as x increases.

In general, an exponential growth function is in the form:

[tex]\boxed{y = ab^x}[/tex]

where:

In this case, the y-intercept is 2 and the base is 5.

As the value of a is positive, and the value of b is greater than 1, it indicates exponential growth.

[tex]\hrulefill[/tex]

The term "second coordinates" refers to the y-values of the points on a graph.

To find the second coordinates of the points with first coordinates 0 and 1, substitute x = 0 and x = 1 into the function and solve.

[tex]\begin{aligned}k(0)&=2(5)^{0}\\&=2(1)\\&=2\end{aligned}[/tex]

[tex]\begin{aligned}k(1)&=2(5)^{1}\\&=2(5)\\&=10\end{aligned}[/tex]

[tex]\hrulefill[/tex]

The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.

As 2(5)ˣ > 0, the graph is entirely above the x-axis.

The end behaviour of the function is:

Therefore, the graph increases from left to right.

In y = 2(5)ˣ, the base is 5, but it is multiplied by 2. This means that for every unit increase in x, the corresponding y-value is doubled compared to the graph of y = 5ˣ. Therefore, the multiplication by 2 makes the graph of y = 2(5)ˣ steeper than the graph of y = 5ˣ.

The graph is completely on the x-axis; It then increases from left to right. it is less steep that y = 5ˣ

The values are (0, 2) and (1, 10)

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

f(x) = 2(5ˣ)

The above function is an exponential growth curve

This means that

Here, we have

f(x) = 2(5ˣ)

This gives

f(0) = 2(5⁰)

f(0) = 2

f(1) = 2(5¹)

f(1) = 10

So, the values are (0, 2) and (1, 10)

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The function that satisfies the given condition is y = 3x + 2.

The correct answer to the given question is option B.

We are to find the function that satisfies the condition: When x increases from a to a + 2, y increases by a difference of 6.

A statement such as this represents a linear function, where y increases at a constant rate with respect to the increase in x.Let y = mx + b, be a linear function.

We know that when x increases from a to a + 2, y increases by a difference of 6. In other words, we can express this relationship using the following equation:

2m + b − m − b = 6 ⇒ m = 3

The function has been found to be y = 3x + b.

To find the value of b, we need to use the fact that when x increases from a to a + 2, y increases by a difference of 6: y(a + 2) − y(a) = 6 ⇒ 3(a + 2) + b − 3a − b = 6 ⇒ 6 = 6

Therefore, the function that satisfies the given condition is y = 3x + 2. The correct option is B) y = 3x + 2.

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Answer:

The slope-intercept equation is y = four-thirds x + 1

Step-by-step explanation:

slope:  [tex]\frac{4}{3}[/tex]

point: (3, 5)

y = mx + b

[tex]y=\frac{4}{3}x+b[/tex]

[tex]5=\frac{4}{3}(3)+b[/tex]

[tex]5=4+b[/tex]

[tex]b=5-4[/tex]

[tex]b=1[/tex]

Equation: [tex]y=\frac{4}{3}x+1[/tex]

[tex]-2=\frac{4}{3}(0)+1[/tex]

[tex]-2=0+1[/tex]

[tex]-2\neq 1[/tex]

Thus, the second statement is true!

=================================================

Explanation

I'll use the distance formula.

[tex](x_1,y_1) = (1,3) \text{ and } (x_2, y_2) = (-2,7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-(-2))^2 + (3-7)^2}\\\\d = \sqrt{(1+2)^2 + (3-7)^2}\\\\d = \sqrt{(3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

The distance is 5 units.

Answer:

5

Step-by-step explanation:

The most likely reason that Sora lists the activities of customers going through self-checkout is to prove the claim that self-checkout is eliminating jobs.

By observing and documenting the activities of customers using self-checkout, Sora may be gathering evidence to support the argument that self-checkout systems are replacing the need for human cashiers and leading to job loss in the retail industry.

By highlighting the tasks that customers can now perform independently, Sora may be emphasizing the efficiency and convenience of self-checkout systems, which can potentially lead to the reduction of cashier positions.

It's important to note that without more context, we cannot definitively determine Sora's exact intentions or motivations. However, based on the given options and the mention of activities related to self-checkout, the claim that self-checkout is eliminating jobs appears to be the most plausible reason for listing the activities of customers going through self-checkout.

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Answer:

Step-by-step explanation:To determine which of the given numbers is closest to 7, we can calculate the absolute difference between each number and 7 and choose the number with the smallest absolute difference.

Let's calculate the absolute differences:

Absolute difference between √51 and 7:

|√51 - 7| ≈ 7.13 - 7 ≈ 0.13

Absolute difference between 50 and 7:

|50 - 7| = 43

Absolute difference between 46 and 7:

|46 - 7| = 39

Comparing the absolute differences, we can see that the number closest to 7 is √51. The absolute difference between √51 and 7 is the smallest among the given options.

Therefore, √51 is the number closest to 7.

The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.

To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.

The loan amount can be calculated by subtracting the down payment from the property value:

Loan amount = Property value - Down payment

           = $170,000 - $20,000

           = $150,000

Now we can calculate the LTV ratio:

LTV ratio = Loan amount / Property value * 100

         = $150,000 / $170,000 * 100

         = 88.24%

Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.

To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:

PMI payment = (Loan amount * PMI rate) / 12

           = ($150,000 * 0.30%) / 12

           = $450 / 12

           = $37.50

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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.

Use the table to find her monthly PMI payment

Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.

30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%

15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.

A. $51.25

B. $37.50

C. $23.75

D. $42.50

Answer:

379.2 in^2

Step-by-step explanation:

Each cylinder's side area is  pi *d * h = 43.98 in^2

  you need six    :     =263.89 in^2

each ned of the cylinder area = pi r^2 = 9.621 in^2

    and you have 12 ends  for 115.45 in^2

For total : 379.3  in^2       (slight difference due to the value of pi used and rounding)

Reason:

If CD was parallel to AB, then triangles CDE and ABE would be similar. In turn it would mean that EA/EC = EB/ED is a true proportion.

Let's calculate each side separately.

Both decimal values are approximate.

The two values don't match up which makes EA/EC = EB/ED to be false.

Since EA/EC = EB/ED is false, we know that triangles CDE and ABE are not similar. Therefore, CD is not parallel to AB.

Answer:

CD is not parallel to AB

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, if CD is parallel to AB, then EA : AC = EB : BD.

Substitute the values of the line segments into the equation:

[tex]\begin{aligned}EA : AC &= EB : BD\\\\28:20&=16:10\\\\\dfrac{28}{20}&=\dfrac{16}{10}\\\\1.4 &\neq 1.6\end{aligned}[/tex]

As 1.4 does not equal 1.6, then CD is not parallel to AB.

The antiderivative of the function is f(x) = 2x + 5x³ + 2x⁶ - 9.

To find an antiderivative of f(x), we can integrate each term of f'(x) individually.

Given:

f'(x) = 2 + 15x² + 12x⁵

To integrate 2, we get:

∫2 dx = 2x + C₁, where C₁ is the constant of integration.

To integrate 15x², we get:

∫15x² dx = 5x³ + C₂, where C₂ is another constant of integration.

To integrate 12x⁵, we get:

∫12x⁵ dx = 2x⁶ + C₃, where C₃ is another constant of integration.

Putting it all together, the antiderivative of f(x) is:

f(x) = 2x + 5x³ + 2x⁶ + C,

where C = C₁ + C₂ + C₃ represents the constant of integration.

To find the specific value of C, we are given that f(1) = 0. Substituting x = 1 into the antiderivative equation:

0 = 2(1) + 5(1)³ + 2(1)⁶ + C,

0 = 2 + 5 + 2 + C,

0 = 9 + C.

Therefore, C = -9.

The final expression for f(x) is:

f(x) = 2x + 5x³ + 2x⁶ - 9.

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The best estimate for the amount of juice Barry made is 235 cups.

In this question, Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. We need to find the best estimate for the amount of juice Barry made.

Let's begin by finding the amount of juice Barry actually made. Barry made 14 cups less than Jessica, which means he made: 235 - 14 = 221 cups of juice.

Now, let's compare this to Barry's estimate. Barry estimated that Jessica squeezed about 212 cups of juice. Since Jessica actually squeezed 235 cups of juice, her estimate was too low by:235 - 212 = 23 cups.

So, we can apply this error to Barry's estimate to get a better estimate for the amount of juice he made. If Barry's estimate was 212 cups, and he underestimated by 23 cups, then he actually made:212 + 23 = 235 cups of juice. Therefore, the best estimate for the amount of juice Barry made is 235 cups.

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Answer:

0

Step-by-step explanation:

theres only 2 people each district

The chords arc theorem and the angles of intersecting chords theorem indicates that we get;

a. CD = 32  

b. [tex]m\widehat{BD}[/tex] = 55°  

c. [tex]m\widehat{CD}[/tex] = 110°  

d. [tex]m\widehat{AB}[/tex] = 125°  

The angle of intersecting chords theorem states that the angle formed by the intersection of two chords in a circle is half the sum of the measure of the intercepted arcs.

The diameter of the circle AB indicates that we get;

PB is the perpendicular of the chord CD

CE = DE = 16

CD = CE + DE = 16 + 16 = 32

The chords CB and BD are congruent, therefore, according to the chords arc theorem, the arcs the chords intercepts are congruent.

Therefore; (4·x + 7)° = (5·x - 5)°

4·x + 7 = 5·x - 5

5·x - 4·x = 7 + 5 = 12

x = 12

[tex]m\widehat{BD}[/tex] = (5·x - 5)° = (5 × 12 - 5)° = 55°

[tex]m\widehat{BC}[/tex] = [tex]m\widehat{BD}[/tex] = 55°

[tex]m\widehat{CD}[/tex] = [tex]m\widehat{BC}[/tex] + [tex]m\widehat{BD}[/tex] = 55° + 55° = 110°

The angle of intersecting chords theorem indicates that we get;

90° = (1/2) × ((5·x - 5)° + m[tex]\widehat{AC}[/tex])

90° = (1/2) × ((4·x + 7)° + m[tex]\widehat{AD}[/tex])

Therefore; 2 × 90° = (4·x + 7)° + m[tex]\widehat{AD}[/tex]

(4·x + 7)° = 55°

Therefore; 2 × 90° = (4·x + 7)° + m[tex]\widehat{AD}[/tex] = 55° + m[tex]\widehat{AD}[/tex]

180° = 55° + m[tex]\widehat{AD}[/tex]

m[tex]\widehat{AD}[/tex] = 180° - 55° = 125°

m[tex]\widehat{AD}[/tex] = 125°

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The measure of an arc in a circle is determined by the central angle that subtends it. Let's analyze each given measure of the indicated arcs:

90°: A 90° arc spans one-fourth of the entire circle since a full circle has 360°.

80°: An 80° arc is smaller than a quarter of the circle but larger than a sixth since 360° divided by 4 is 90°, and by 6 is 60°. Therefore, it lies between these two values.

100°: A 100° arc is slightly larger than a quarter of the circle but smaller than a third, as 360° divided by 4 is 90°, and by 3 is 120°.

70°: A 70° arc is smaller than both a quarter and a sixth of the circle, falling between 60° and 90°.

H: The measure of an arc denoted by "H" is not provided, so it cannot be determined without further information.

40°: A 40° arc is smaller than a sixth of the circle but larger than a twelfth, as 360° divided by 6 is 60°, and by 12 is 30°.

F: Similarly, the measure of the arc denoted by "F" is not provided, so it remains unknown without additional data.

Thus, the measures of the indicated arcs are as follows: 90°, between 60° and 90°, between 90° and 120°, between 60° and 90°, unknown (H), between 30° and 60°, and unknown (F).

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The fraction that converts to a terminating decimal number is C. 3/8.

To determine which fraction converts to a terminating decimal number, we need to analyze the denominator of each fraction. A fraction will result in a terminating decimal if its denominator has only prime factors of 2 and/or 5.

Let's examine each option:

A. 1/6: The denominator is 6, which can be factored into 2 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.

B. 2/9: The denominator is 9, which can be factored into 3 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.

C. 3/8: The denominator is 8, which can be factored into 2 * 2 * 2. Since all the factors are 2, this fraction does convert to a terminating decimal.

D. 4/7: The denominator is 7, which cannot be factored into 2 or 5. Therefore, this fraction does not convert to a terminating decimal.

Based on our analysis, the fraction that converts to a terminating decimal number is C. 3/8.

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Answer:

surface area=214cm2, volume=183 cm3

Step-by-step explanation:

slanted height=√5^2+7^2 (Pythagoras theorem)

= √74

area of bottom part=π(5)^2

=25π

area of top cone part=π(5)(√74)

surface area of cone=25π+π(5)(√74)

=214 cm2(to 3 s.f.)

volume of cone=1/3π(5)^2×7

=183 cm3(to 3 s.f.)

In the context of a Cartesian coordinate system, the term "(-,-) quadrant" refers to the third quadrant, also known as Quadrant III.

The Cartesian coordinate system consists of four quadrants, numbered from I to IV in a counterclockwise direction. Each quadrant is defined by the signs of the x and y coordinates.

In Quadrant III, the x-coordinates are negative (represented by the "-") and the y-coordinates are also negative. This means that any point located in this quadrant will have both x and y values that are less than zero.

Visually, Quadrant III is situated below the x-axis and to the left of the y-axis. It is characterized by its lower left position in the coordinate plane.

Points in Quadrant III can be thought of as having a negative horizontal position (to the left of the origin) and a negative vertical position (below the origin).

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Answer: 6+9x or 9x + 6

Step-by-step explanation:

Multiply 3 by each of the numbers inside the parentheses

The answer is:

Work/explanation:

To simplify this expression, we will use the distributive property:

[tex]\sf{3(2+3x)}[/tex]

Distribute the 3:

[tex]\sf{3\cdot2+3\cdot3x}[/tex]

Simplify

[tex]\sf{6+9x}[/tex]

Answer:

36)

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

The equation of the function is y = 1/(x + 3) - 1

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

The reciprocal function shifted down one unit and left three units

The equation of the reciprocal function is represented as

y = 1/x

When shifted down one unit, we have

y = (1/x) - 1

When shifted left three units, we have

y = 1/(x + 3) - 1

Hence, the equation of the function is y = 1/(x + 3) - 1

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The mapping shown does not represents a function

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

The mapping

From the mapping, we have

(1, 7), (8, 3), (8, -1) and (3, 0)

The above ordered pair is not a function

This is so because the input value 8 have different output values 3 and -1

i.e. it would not pass the vertical line test when represented on a graph

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Answer:

The correct option is the 3rd one

angle 1 = angle 4 = angle 5 = angle 8 = 60 degrees,

angle 2 = angle 3 = angle 6 = angle 7 = 120 degrees

Step-by-step explanation:

To solve this, we only need to look at the top two angles, 1 and 2

Since line l is a line, angle 1 and 2 must sum to 180,

Since angle 1 = 60 degrees, then,

angle 1 + angle 2 = 180

60 + angle 2 = 180

angle 2 = 120 degrees

the only option that corresponds to this is the third option,

angle 1 = angle 4 = angle 5 = angle 8 = 60 degrees,

angle 2 = angle 3 =

Answer:

A

Step-by-step explanation:

For a table of values to be a function, all inputs must have one unique output. The only table that doesn't violate this is table A.

Notice that while two different inputs (-4 and 1) have the same output of 7, it is still a function because both outputs of 7 are associated with two different inputs.

The values in the boxes that correctly complete the division model and quotient are presented as follows;

[tex]{}[/tex]                 10                   2                4    

6        [tex]{}[/tex]      60                 16                  

            76  ÷ 6 = 12 R 4  

A division area model comprises of the number being divided, representing the area of a rectangle, and a factor or the divisor, being a side length of the rectangle.

The number 76 divided by 6 using the division model can be evaluated by setting the area of the rectangle as 76 and the length of side of the rectangle as 6, asw follows;

The division model

The model for the division of 76 ÷ 6 can be presented as follows;

        [tex]{}[/tex]        10                2                 4  

6    [tex]{}[/tex]            60              16

Therefore; 76 ÷ 6 = 10 + 2 = 12 Remainder 4

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The value of a is 8 ln 9 - 36. Given an arithmetic sequence that has the first term Ina and a common difference In 3. The 13th term in the sequence is 8 ln 9.

We need to find the value of a.

Step 1: Finding the 13th term. Using the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

Substituting the given values, we get:an = a1 + (n - 1)d 13th term, a 13 = a1 + (13 - 1)3a13 = a1 + 36 a1 = a13 - 36 ...(1)Given that a13 = 8 ln 9.

Substituting in equation (1), we get: a1 = 8 ln 9 - 36.

Step 2: Finding the value of a. Using the formula for the nth term again, we can write the 13th term in terms of a as: a13 = a + (13 - 1)3a13 = a + 36a = a13 - 36.

Substituting the value of a13 from above, we get:a = 8 ln 9 - 36. Therefore, the value of a is 8 ln 9 - 36.

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The x- and y-intercept values in the graph for the function f and in the table for the function g(x), indicates that the correct option is option C

The x-intercept is the point at which the y-value is 0, and the coordinates of the point is specified as the x-intercept.

The x-intercept is the point at which the x-value is 0, and the coordinates of the point is specified as the y-intercept

The question compares the x- and y-intercepts of the graph and the function in the table

The x-intercept of the function f in the graph are; (0, 3)

The y-intercept of the function f in the graph are; (4, 0)

The function g(x) in the table indicates that the x- and y-intercepts are;

The value of g(x) is 0 at the ordered pair (1, 0), therefore, the x-intercept of g(x) is (1, 0)

The value of x is 0 at the ordered pair (0, 4), therefore, the function, g(x) has a y-intercept at the point (0, 4)

Therefore, the function f and g have different intercepts, but the value in the table and the graph indicates that as x approaches infinity, the y-value, approaches -1, the correct option is therefore, option C

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The reason why Figure A is congruent to Figure C is that they undergo the same sequence of transformations: a translation followed by a reflection.

The statement "Figure A is translated 3 units right and 2 units up. The translated figure is labeled Figure B. Figure B is reflected over the x-axis. The reflected figure is labeled Figure C" describes a sequence of transformations applied to Figure A to obtain Figure C.

When Figure A is translated 3 units right and 2 units up, it undergoes a rigid transformation known as a translation. This transformation preserves the shape and size of the figure. The translated figure, Figure B, will have the same dimensions and orientation as Figure A but will be shifted to the right and up.

When Figure B is reflected over the x-axis, it undergoes a reflection. This transformation flips the figure vertically, changing the sign of the y-coordinates of its vertices while keeping the x-coordinates the same. The reflected figure, Figure C, will have the same shape and size as Figure B, but it will be oriented in the opposite direction.

Since translations and reflections are both rigid transformations, they preserve congruence. Therefore, Figure A and Figure C are congruent because they undergo the same sequence of transformations (translation followed by reflection) from Figure A.

In conclusion, Figures A and C go through the same set of transformations, a translation and a reflection, which explains why they are congruent.

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Answer: 28

Step-by-step explanation:

If [tex]a = 7[/tex] and [tex]b = 2[/tex], then [tex]2ab[/tex] can be worked out as follows:

[tex]\Large 2ab = 2 \times a \times b[/tex]

Substituting the values of [tex]a[/tex] and [tex]b[/tex], we get:

[tex]2 \times 7 \times 2 = 28[/tex]

Therefore, [tex]2ab[/tex] is equal to 28 when [tex]a = 7[/tex] and [tex]b = 2[/tex].

________________________________________________________

The answer is:

Work/explanation:

To evaluate the expression [tex]\sf{2ab}[/tex], I begin by plugging in 7 for a and 2 for b:

[tex]\large\pmb{2(7)(2)}[/tex]

Simplify by multiplying.

[tex]\large\pmb{2*14}[/tex]

[tex]\large\pmb{28}[/tex]

Answer:

1/12 is the correct answer

Cameron has 1 book left over after sorting it into group of 5

To determine the number of book left,

we need to first divide 56 by 5         [56 ÷ 5]

Quotient = 11

then find the remainder which is 1

therefore there os only 1 book left over

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The best answer that matches the calculated values is C. sin θ = -1/3, tan θ = -3/(2√2)

Let's break down the given values and find the values of sine and tangent.

We are given:

cos θ = √(8/9)

csc θ < 0

Using the Pythagorean identity, sin^2θ + cos^2θ = 1, we can find the value of sin θ.

sin^2θ + (√(8/9))^2 = 1

sin^2θ + 8/9 = 1

sin^2θ = 1 - 8/9

sin^2θ = 1/9

Taking the square root of both sides, we get:

sin θ = ±1/3

Since csc θ is negative (csc θ < 0), we can conclude that sin θ is negative. Therefore, sin θ = -1/3.

Next, let's find the value of tan θ.

tan θ = sin θ / cos θ

tan θ = (-1/3) / (√(8/9))

tan θ = -√9/√8

tan θ = -√9/√(4*2)

tan θ = -√9/(2√2)

tan θ = -3/(2√2)

So, the values are:

sin θ = -1/3

tan θ = -3/(2√2)

The best selection from the available options that matches the calculated values is:

C. sin θ = -1/3, tan θ = -3/(2√2)

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