Which diagram depicts as a positive angle in standard position?

Answer:

The range of the number of seeds in the sample of oranges is 9.

The missing point of the rectangle is determined as (3, 8).

A rectangle is a four-sided flat shape in which the opposite sides are equal in length and parallel to each other, and all four angles are right angle.

The area of a rectangle is equal to the length multiplied by the width, and the perimeter is equal to the sum of the lengths of all four sides.

Since each angle of a rectangle must be 90 degrees, the length of each opposite side must be equal.

the missing side must be parallel to point (0, 8) and perpendicular to point (3, 7).

the side must be (3, 8)

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If professor Snozz earns 8% of "total-sales", then the amount that the professor make on selling of 300 copies is $708.

In order to find out how much Professor Snozz makes, we first calculate the "total-sales" revenue of the 300 copies of the book;

⇒ Total sales revenue = (number of copies sold) × (price per copy),

⇒ Total sales revenue = 300 × $29.50,

⇒ Total sales revenue = $8850;

Next, we calculate amount of royalty that Professor Snozz earns, which is 8% of the total sales revenue;

So, Royalty = 8% of "Total sales revenue";

⇒ Royalty = 0.08 × $8850,

⇒ Royalty = $708;

Therefore, Professor Snozz earns $708 as a royalty for selling 300 copies of his book.

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Answer:

Okay, let's break this down step-by-step:

   The initial point is P(-4, 5)

   The terminal point is Q(-2, 7)

To find the components of the vector V, we need to determine:

   The change in x-coordinate = -4 - (-2) = -2

   The change in y-coordinate = 5 - 7 = -2

So the vector components are:

<change in x-coordinate, change in y-coordinate>

= <-2, -2>

Therefore, the answer is choice (i): < -2,-2>

The other choices do not represent the correct changes between the given points P and Q.

Step-by-step explanation:

Amir's average speed for the whole journey was 51 km/h.

We have,

Let the total distance between Town A and Town B be D.

According to the problem,

Amir traveled 1/5 of the journey in the first two hours, which means he covered a distance of D/5 in 2 hours.

The remaining distance is 4D/5.

He then traveled 1/3 of the remaining journey in the next one hour, which means he covered a distance.

= (1/3) × (4D/5)

= 4D/15 in the next hour.

Therefore, the remaining distance.

= 4D/5 - 4D/15

= 8D/15.

It took him another 2 hours to cover the remaining distance of 136 km, so we have:

8D/15 = 136 km

Solving for D.

D = (136 km)×(15/8)

= 255 km

Therefore,

The total distance between Town A and Town B is 255 km.

The total time Amir took for the journey is 2 + 1 + 2 = 5 hours.

His average speed for the whole journey.

= Total distance ÷ Total time

= 255 km ÷ 5 hours

= 51 km/h

Therefore,

Amir's average speed for the whole journey was 51 km/h.

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Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).

To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.

One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.

Using the distance formula, we get:

[tex]\sqrt{(x-1)^{2} +(y-1)^{2} }[/tex] = 5

Simplifying and squaring both sides, we get:

(x-1)^2 + (y-2)^2 = 25

Expanding the left side and simplifying, we get:

[tex]x^{2}[/tex] - 2x + [tex]y^{2}[/tex] - 4y + 20 = 0

Completing the square for x and y, we get:

[tex](x-1)^{2}[/tex]  + [tex](y-1)^{2}[/tex]  = [tex]6^{2}[/tex]

This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.

Using this method, we can find several possible locations of the other vertices of the square. Three of them are:

(7, 2), (-5, 2), (1, 8)

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Answer:

To find g(26) when g(x) = 7x + 2, we simply need to substitute x = 26 into the expression for g(x):

g(26) = 7(26) + 2

g(26) = 184

Now, to find (g of f)(x), we need to substitute f(x) into the expression for g(x):

(g of f)(x) = g(f(x)) = 7(f(x)) + 2

Since f(x) = x - 2, we can substitute x - 2 for f(x) in the expression for g(x):

(g of f)(x) = g(x - 2) = 7(x - 2) + 2

Simplifying this expression, we get:

(g of f)(x) = 7x - 12

Now, to find (g of f)(26), we simply substitute x = 26 into the expression we just found:

(g of f)(26) = 7(26) - 12

(g of f)(26) = 182

Therefore, the answer is A) (not listed).

Answer: the area of the triangle is 150 cm².

Step-by-step explanation:

To solve this problem, we need to use the formula for the area of a triangle:

Area = (1/2) x base x height

From the diagram, we can see that the base of the triangle is 20 cm and the height is 15 cm. Plugging these values into the formula, we get:

Area = (1/2) x 20 cm x 15 cm

Area = 150 cm²

Therefore, the area of the triangle is 150 cm².

Answer:

A quadrilateral is a shape that has four straight sides and four angles.

A triangle is a shape that has three straight sides and three angles.

A square is a special type of quadrilateral that has four straight sides of equal length and four right angles.

Answer: 7725.5775

Step-by-step explanation:

d=27

r=d/2=27/2=13.5

the volume of the spherical balloon= 3.14*r^3

                                                       = 3.14*(13.5)^3

                                                       = 7725.5775

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The resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.

The problem we are trying to solve is to determine if the sample proportion of heads obtained from spinning a penny 300 times (134 heads) is significant evidence against equal probabilities of heads and tails. To do this, we will be testing the null hypothesis H0: p = 0.5, which states that the probability of getting heads is equal to 0.5.

We can calculate the z-test statistic using the formula z = (sample proportion - hypothesized proportion) / (standard error). In this case, the z-test statistic is z = (0.444 - 0.5) / (√(0.5 * 0.5 / 300)) = -0.86. This means that the sample proportion of heads is 0.86 standard errors away from the hypothesized proportion of 0.5.

Therefore, the resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.

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The function whose graph matches this one y= 4 sin (π/7 x) - 2

As, The general form of a sine function is

y= A sin (kx) + C........(1)

From the given graph the maximum value of the function is 2 and minimum value of the function is -6.

So, Amplitude= (Max- Min)/2

A = (2- (-6))/2

A= 8/2

Amplitude= 4

Now, The function complete a cycle in 14 units, so period of the function is 14.

2π/k= 14

k = π/7

and, Midline= (Min + Max)/2 = (2-6)/2 = -2

So, the function is

y= A sin (kx) + C.

y= 4 sin (π/7 x) - 2

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Answer:

5.25

Step-by-step explanation:

7 divide 8 = 0.875

0.875 × 6 = 5.25

The money invested by the teacher to have at least 125,000 in her account after 40 years of a 6.95% annual interest rate compounded continuously is 7755. Hence, the right solution to the question is option D

Compound interest is given by

A = P[tex](1+r)^t[/tex]

where A is the amount

P is the principal

r is the rate of interest

t is the time

Given in the question,

A = $125,000

r = 6.95% or 0.0695

t = 40 years

P is to be found

A = P[tex](1+r)^t[/tex]

125000 = P [tex](1 + 0.0695)^{40[/tex]

125000 = P * [tex]1.0695^{40[/tex]

125000 = 16.118P

P = 7755

The teacher should invest $7755 initially.

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Answer:

SA = 48 cm²

Step-by-step explanation:

the surface area (SA) is the sum of the areas of the 5 faces.

1 square and 4 congruent triangles form the pyramid

area of square = 4 × 4 = 16 cm²

area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 4 and h = 4

area = [tex]\frac{1}{2}[/tex] × 4 × 4 = 2 × 4 = 8 cm²

area of 4 triangles = 4 × 8 = 32 cm²

SA = 16 + 32 = 48 cm²

The total length of the nylon rope that Jamie will use would be 15.3 feet of nylon rope.

Within this scenario specifically, one side of the right-angled triangle comprises the height of the tent (standing at 6.5-feet), and the other forms as the measure from the center of the tent to where Jaime stakes the ropes stretching outwards in another direction (with a calculated measure of 4-feet). Subsequently, we will refer to the extent of the nylon rope as R.

The Pythagorean theorem formula is:

R ² = 6.5 ² + 4 ²

R ² = 42. ²25 + 16

R ² = 58.25

R = 7. 63 ft

There are two ropes so the length would be :

= 7. 63 + 7. 63

= 15. 3 ft

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Answer:

x ≈ 6.5

Step-by-step explanation:

using the tangent ratio in the right triangle

tan25° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{14}[/tex] ( multiply both sides by 14 )

14 × tan25° = x , then

x ≈ 6.5 ( to the nearest tenth )

The area of the different types of polygon with given dimensions are,

Area of octagon= 391.07 cm²

Area of pentagon = 232m²

Area of triangle = 21.22in²

Area of hexagon = 11.24square units.

Polygon name = octagon,

Side length = 9cm

Degree of central angle = 360° /8

                                        = 45°

To find Apothem ,

draw right triangle .

base is half of the side length = 4.5

Top angle of the right triangle = (1/2) × 45°

                                                  = 22.5°

Using tangent ratio considering top angle as α

tanα = 4.5/ Apothem length

⇒Apothem length = 4.5 / tan22.5°

⇒Apothem length = 4.5 / (√2 - 1 )

⇒Apothem length = 4.5 / 0.414

⇒Apothem length = 10.86cm.

Area of octagon = 2 ( 1 + √2 ) × (side length)²

                           = 2 × 2.414 × 9²

                           = 391.07 cm²

Polygon name = Pentagon,

Apothem= 8m

Degree of central angle = 360° /5

                                        = 72°

To find Side length ,

Let 'x' be the side length

draw right triangle .

base is half of the side length = x/2

Top angle of the right triangle = (1/2) × 72°

                                                  = 36°

Using tangent ratio considering top angle as α

tanα =   half of side length /Apothem length

⇒(1/2) side length  = 8 × tan36°

⇒ side length = 16 ×  (0.7265)

⇒ side length= 11.62m

Area of pentagon

= 5/2 × side length × distance from the center of sides to the center of pentagon

= 5/2 × 11.6 × 8

= 232m²

Polygon name = triangle,

Apothem= 2in

Degree of central angle = 60°

To find Side length ,

Let 'x' be the side length

draw right triangle .

base is half of the side length = x/2

Top angle of the right triangle =60°

Using tangent ratio considering top angle as α

tanα = half of side length / Apothem length

⇒(1/2) side length  = 2 × tan60°

⇒ side length = 4 (√3)

⇒ side length= 6.928in

                      ≈ 7 in

Area of triangle = √3/4 × 7²

                          = 21.22in²

Polygon name = hexagon,

Apothem= 5

Degree of central angle = 60°

To find Side length ,

Let 'x' be the side length

draw right triangle .

base is half of the side length = x/2

Top angle of the right triangle =30°

Using tangent ratio considering top angle as α

sinα = half of side length / Apothem length

⇒(1/2) side length  = 5 × sin30°

⇒ side length = 10 (0.5)

⇒ side length= 5

distance from center of sides to the center of hexagon

= √5² - 2.5²

=4.33

Area = (3√3)/2 × distance from center of sides to the center of hexagon

        = (3√3)/2 × 4.33

        = 11.24square units.

Therefore, the area of the given polygon are octagon = 391.07 cm² , pentagon =  232m² , triangle = 21.22in² , and hexagon = 11.24square units.

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We can see here that the measure that Raul should use to find the distance that the ball travels during each hit varies, on average, from the mean distance is the measure of variability known as standard deviation.

The mean, commonly referred to as the arithmetic mean or average, is a statistic that depicts the usual or centre value of a dataset. It is determined by adding up all of the dataset's values, then dividing by all of the values.

We can see here that standard deviation actually refers to the statistical measure that represents the amount of dispersion or variability in a dataset.

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The surface area of the rectangular prism in this problem is given as follows:

A. 426 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.

By the net method, the prism is divided as follows:

Hence the surface area of the prism is given as follows:

S = 2(5 x 12 + 5 x 9 + 12 x 9)

S = 426 m².

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The equation (x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2 has no solution for x

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

(x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2

Divide through the equation by x^2

so, we have the following representation

(x+7) -(x-3) = (x+35) -(x+34)

When the brackets are removed and the like terms are evaluated, we have

2x + 10 = 2x - 1

Evaluate the like terms again

So, we have

10 = -1

The above equation is false

Hence, the equation has no solution for x

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a) The probability that exactly one of them will be a girl = 0.3407

b) The probability that at least one of them will like the football = 0.7672

a) If we select three students then the probability that exactly one of them will be a girl

From the attached two way table we can observe that the total number of girls = 22

the total number of boys = 18

and the total number of students = 40

The possible outcomes for selecting 3 students from 40 would be,

⁴⁰C₃

Using combination formula,

⁴⁰C₃ = 40! / (3! × (40 - 3)!)

      = 9880

If there is exactly one girl then other two must be boys in the set of 3 selected students.

So, the required probability would be,

P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃

P = (22 × 153)/9880

P = 0.3407

b) The number of students like the football = 15

and the number of students who don't like the football are 40 - 15 = 25

The probability that at least one of them will like the football would be,

P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃

P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880

P = 0.7672

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Answer:

The points that are on the line given by the equation y = x are:

A. (3, 3)

B. (2, 2)

D. (-1, -1)

E. (1, 1)

To check if a point is on the line, you can substitute its coordinates into the equation and see if the equation is true. For example, for point (3, 6), we have:

y = x

6 = 3

This is not true, so the point (3, 6) is not on the line. Repeat this process for each point to determine which points are on the line.

Answer:

<ABC + <CBD =180⁰

<ABC =180⁰ - <CBD

<ABC =180⁰ - 47⁰

<ABC =133⁰

Answer:

110

Step-by-step explanation:

nth term = 3n + 2

3 (36) + 2

108 + 2 = 110

Answer:

The 36th term in the sequence is 104.

Here's how to find it:

- Start with the first number in the sequence: 5.

- Add the common difference, which is 3, to get the second number in the sequence: 8.

- Add the common difference to the second number to get the third number: 11.

- Continue adding the common difference to each subsequent number to find the next term in the sequence.

- The 36th term is three less than 37 times the common difference added to the first term.

- Using that formula, we can calculate the 36th term as: 5 + (36 - 1) * 3 = 5 + 105 = 110.

- Therefore, the 36th term in the sequence is 104.

Answer: 5

Step-by-step explanation:

Since x is directly related to the square of y, we can write the equation:

x = ky^2

where k is a constant of proportionality. We can solve for k using the given values of x and y:

16 = k(2^2) -> 16 = 4k -> k = 4

Now that we know k, we can use it to find y when x = 100:

100 = 4y^2 -> 25 = y^2 -> y = ±5

Since y cannot be negative, the only possible value of y is 5. Therefore, when x = 100, y could be 5.

Answer:

One possible value of y when x = 100 is y = 5.

Step-by-step explanation:

Using the direct variation formula, we know that x = ky^2, where k is a constant. Given that x = 16 and y = 2, we can solve for k:

16 = k(2)^2

k = 4

Now we can use this value of k to find y when x = 100:

100 = 4y^2

y^2 = 25

y = 5 or -5 (since the question only asks for one possible value, we can choose either solution)

Therefore, one possible value of y when x = 100 is y = 5.

If the temperature outside is 86°F and the relative humidity is 55%, the heat index is: C. 89°F.

In this scenario, the relative humidity would be plotted on the x-axis (x-coordinate) of the scatter plot while the heat index would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot which models the relationship between the x-values and y-values, a quadratic equation for the line of best fit when the temperature outside is 86°F, is given by:

y = 0.004x²- 0.1243x + 84.028

when x = 55%, the heat index can be calculated as follows;

y = 0.004(55)²- 0.1243(55) + 84.028

y = 89.2915 ≈ 89°F

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The vector in component form whose tail is the point (−1,5), and whose head is the point (8,−6) is (-9, 11)

A vector is a physical quabntity thet has both magnitude and direction.

To find  the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6), we proceed as folows

Since we have the points (-1, 5) and (8, -6) and we want the head to be at (8, -6),

Let A = (8, -6) and B = (-1, 5)

So, AB = B - A

= (-1, 5) - (8, -6)

= (-1 - 8), (5 - (-6))

= (-9, 5 + 6)

= (-9, 11)

So, the vector in component form is (-9, 11)

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Answer:

(10, 5π/3)

Step-by-step explanation:

To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:

r = √(x^2 + y^2)

θ = arctan(y/x)

Substituting the given values, we get:

r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10

θ = arctan((-5√3)/5) = arctan(-√3) = -π/3

Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:

θ = -π/3 + 2π = (5π/3)

Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).

Answer:

[tex]a(1) = 144[/tex]

[tex]a(n) = 144{( - \frac{1}{6} )}^{n - 1} [/tex]

[tex]a(n) = - \frac{1}{6} a(n - 1)[/tex]