The spinner is divided into 8 equal sections.

b. If the arrow lands on a number, what is the probability that it will land on an odd number?

Each party basket will have 73 pieces of candy

Felicia has 4.5 bags of candy for her party basket

Each bag has 146 pieces of candy

She has 9 party baskets, the number of candies in each party basket can be calculated by multiplying 4.5 by 146 and dividing the result by 9

4.5 × 146/9

= 657/9

= 73

Hence there are 73 pieces of candy in each basket

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The geometric mean between the pair of numbers, 18 and 1.5, is 3√3.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Solving for the geometric mean between 18 and 1.5 using the formula:

GM = n√x1 x2 . . . xn

where n = 2, x1 = 18, and x2 = 1.5

GM = √(18)(1.5)

GM = √27

GM = 3√3

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Solving the quadratic inequality, the solution set for x is given as follows:

x < -1 or x > 2.

For this problem, the inequality is given by:

x² - x - 2 > 0.

To graph a quadratic inequality, first we have to find the roots of the quadratic function, hence:

x² - x - 2 = 0

(x - 2)(x + 1) = 0.

Hence the roots are:

As the graph given at the end of the answer shows, any concave up quadratic function is positive to the left and to the right of the roots, hence the solution set for the inequality is:

x < -1 or x > 2.

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Answer:

1215

Step-by-step explanation:

The equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7) is; y = ³/₂x - 16

We want to find the equation of the line perpendicular to y = -²/₃x + 5 and passing through the point (6, -7).

Now, the slope that is perpendicular to that line is;

m = -1/(-²/₃) = 3/2

Thus;

Equation of the new line is;

y - (-7) = 3/2(x - 6)

y + 7 = 3x/2 - 9

y = ³/₂x - 16

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the answer is negative 41

Answer:  The answer would be D. I hope this is helpful :))

Answer:

A. The first mistake was made is Step 1

Step-by-step explanation:

The first mistake was in Step 1. Take a look below to see how Step 1 should've been.

4(2x +5)-(3x-4)=15

Use distributive property.

4(2x +5)-(3x-4)=15

8x+20-3x+4=15

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Answer:

1⁷/15

Step-by-step explanation:

2¾(3⅜-1½)

using the rule of BODMAS

change the fractions in the bracket into improper fraction

2¾(27/8-3/2)

find LCM of the fractions in the bracket

2¾(27-12)/8

2¾(15/8)

convert the other mixed fraction to an improper fraction

11/8(15/8)= 5.15625~ 5.2

Answer:

So the number is -48

Step-by-step explanation:

Lets say that the number is x

(x /6)+12=4

       x/6=-8

          x=-48

Step-by-step explanation:

1.

the length of the terminal side from (0, 0) to (4, -7) is the radius of the circle, while

x = 4 = cos(theta)×radius

y = -7 = sin(theta)×radius

so,

sin(theta) = -7/radius

radius² = (4 - 0)² + (-7 - 0)² = 4² + 7² = 16 + 49 = 65

radius = sqrt(65)

sin(theta) = -7/ sqrt(65) = -0.868243142...

FYI

theta = -60.2551187...°

or 299.7448813...°

2.

tan(theta) = 3/2

so,

sin(theta)/cos(theta) = 3/2

2×sin(theta) = 3×cos(theta)

square both sides

4×sin²(theta) = 9×cos²(theta)

completing the square

4×sin²(theta) + 9×sin²(theta) = 9×cos²(theta) + 9×sin²(theta)

13×sin²(theta) = 9×(cos²(theta) + sin²(theta)) = 9

sin²(theta) = 9/13

sin(theta) = 3/sqrt(13)

to make it a rational denominator we multiply by

sqrt(13)/ sqrt(13)

and we get

sin(theta) = 3×sqrt(13)/13

3.

because the sum of all angles in a triangle is 180°.

one angle is theta.

then we have the 90° angle at the origin (or center of the circle).

and that leaves 180 - 90 - theta = 90 - theta for the third angle.

this triangle can be flipped with putting 90 - theta in place of theta.

the flipped triangle is equivalent to the original triangle (all angles and side lengths are identical between the 2 triangles).

the baseline (radius) is the same length in both triangles.

in that flipped triangle the side formerly sin(theta) is now cos(90-theta) and cos(theta) is now sin(90-theta).

Answer:

[tex]84n-27[/tex]

Step-by-step explanation:

[tex]-9(1-10n) -2(3n+9)[/tex]

[tex]-9+90n-6n-18[/tex]

[tex]{84n-27}[/tex]

Answer: (3, -7) and (3, -1)

Step-by-step explanation:

Distance formula: a^2 + b^2 = c^2

c is the distance between different points which is 5 in this case

a=3-(-1)

a=3+1

a=4 ==> distance between x-coordinates

4^2+b^2=5^2

16+b^2=25

b^2=9

b=3

Distance from -4 and y-coordinate of a different point is equaled to 3.

How to express this in the form of an equation?

|-4-y|=3    ==> where y is the y-coordinate of a different point

-4-y=3

-4+4-y=3+4

-y=7

y=-7  ==> (3, -7)

-4-y=-3

-4+4-y=-3+4

-y=1

y=-1  ==> (3, -1)

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

2.25 kilometers on the ground is represented by 9cm on the map

According to the question, the scale on the map is in the ratio 1 : 25000

That is the     length on the map = length of the ground

                               1cm = 25000 cm

                                1 cm = 25000/100000 km

                                1 cm = 0.25 km

Now we have to find the length of the ground in kilometres which is represented by 9cm on the map

That is we have to find the ratio,  9cm : x km

As from above, we know that,

                          1cm = 0.25 km

                           9 cm = 0.25*9 km

                                    = 2.25 km

Hence 2.25 km on the ground is represented by 9 cm on the map

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Answer:14.

Step-by-step explanation:

14.2 is closer to 14 than 15

Answer:

14

Step-by-step explanation:

The nearest whole number in 14.2 is 4.

Since 2 is less than 5, the 4 stays the same.

We get left with 14.

The difference is -3/4.

Given,

(5/2) - (13/4)

Solution:

Taking L.C.M,

(5/2) - (13/4) = 10/4 - 13/4

                    = -3/4

The difference is -3/4.

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The equation of the slant asymptote of the rational function is; y = 2x - 3

We want to find the equation of the slant asymptote of the rational function given as;

f(x) = (10x³ - 15x² + x - 1)/(5x² - 2)

To solve this question, we will divide the numerator by the denominator.  The result (not including the remainder) will be the equation of the slant asymptote.

We can tell the first term of the quotient will be 2x since 10x³/5x² = 2x. Thus, the answer from the given options will be either 2x − 3 or 2x − 11/5.

The easiest method to apply here is to simply multiply these options by the denominator to get;

(5x² − 2) (2x − 3) = 10x³ − 15x² − 4x + 6

(5x² − 2) (2x − 11/5) = 10x³ − 11x² − 4x + 22/5

So the answer must be 2x − 3

Thus, the equation of the slant asymptote of the rational function is; y = 2x - 3

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The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

IT is given that year ago, a radio program was aired on r stations across the country.

Also Today, the number of stations airing the radio program can be represented by the following expression; 0.82r

Therefore, the equivalent expression that represents this situation is r+0.82r

Hence, The set of statements is true; B. The number of stations airing the program increased by 82%. the equivalent expression that represents this situation is r+0.82r.

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Stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have to determine the price of sold tomatoes at the least expensive price per pound.

The price of sold tomatoes at stand A:

⇒ 2/(3/4) = 2/0.75  = 2.67 per pound.

The price of sold tomatoes at stand B:

⇒ 3.45/(5/4) = 3.45/1.25  = 2.76 per pound.

The price of sold tomatoes at stand C:

⇒ 14.85/(11/2) = 14.85/5.5= 2.70 per pound.

Here is the least expensive price per pound at stand C.

Hence, the stand C sold their tomatoes at the least expensive price per pound that price is 2.70 per pound.

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Answer:

-48

Step-by-step explanation:

2 x 4 = 8

8 x -6 = -48

Answer:

r = (n - p)/c

Step-by-step explanation:

n = p + cr

Subtract p from both sides

n - p = p + cr - p

n - p = cr

Divide both sides by c.

(n - p)/c = cr/c

r = (n - p)/c

The magnitude of vector →JK is 4

And the direction of vector →JK is given by an angle 360°

For given question,

Let J(-6, -4) = (x1, y1) and

K(-10,-4) = (x2, y2)

By distance formula, the magnitude of vector is,

[tex]|\vec{JK}|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|\vec{JK}|=\sqrt{(-10+6)^2+(-4+4)^2}\\\\ |\vec{JK}|=\sqrt{(-4)^2}\\\\ |\vec{JK}|=4[/tex]

To find the direction of the vector JK:

[tex]tan\theta=\frac{y_2-y_1}{x_2-x_1} \\\\tan\theta=\frac{-4+4}{-10+6}\\\\ tan\theta=0\\\\\theta=0^{\circ}[/tex]

However, the angle is in the fourth quadrant, so we add  360°  to obtain a positive angle.

Thus,  0° + 360° = 360°

Therefore, the magnitude of vector →JK is 4

And the direction of vector →JK is given by an angle 360°

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The correct names for the given angle is ∠PHV.

How to name the any angle?

For naming any angle, the common vertex must come in the middle of the name.

But it could start with any of the end point.

Thus, the angle given can be named either ∠PHV or  ∠VHP.

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Answer: y = -55

Step-by-step explanation:

-57 = y -2

-57 + 2 = y

-55 = y

Answer:

Get natural log on both sides and subtract 8 to subject the unknown x.

Step-by-step explanation:

                        [tex]\begin{aligned}\\e^{x+8} &= 15\\\\ln(e^{x+8}) &=\small ln(15)\\\\(x+8) ln(e)&=\small ln(15)\\\\x+8&=\small ln(15) \cdots\cdots\cdots[ ln(e) = 1]\\\\x&=\small ln(15) -8\end{aligned}[/tex]

Answer:

x = -5.29

Step-by-step explanation:

e^(x+8) = 15

==> take log of both sides

log(e) * (x+8) = log(15)

==> divide both sides by log e (log(15)/log(e) = 2.70805)

x + 8 = 2.70805

==> subtract both sides by 8

x = -5.29 (rounded to the nearest tenth)

[tex]log_{5} \sqrt{14}[/tex] ≈ 0.82

The property of logarithms log ab = log a + log b , log a/b = log a - log b

[tex]log_{5} 2[/tex] ≈ 0.43

[tex]log_{5} 7[/tex] ≈ 1.21

We need to find,

[tex]log_{5} \sqrt{14}[/tex]

= 1/2[tex]log_{5} 14[/tex]

= 1/2[tex]log_{5} 2*7[/tex]     ( log ab = log a + log b)

= 1/2 ([tex]log_{5} 2[/tex] + [tex]log_{5} 7[/tex])  

=1/2( 0.43 + 1.21)

= 1/2 × 1.64

= 0.82

Hence logarithms of [tex]log_{5} \sqrt{14}[/tex] = 0.82

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The number of people who can go to the amusement park is 3 people

89.50 = 7.75 + 27.25p

89.50 - 7.75 = 27.25p

81.75 = 27.25p

p = 81.75 / 27.25

p = 3

Therefore, the number of people who can go to the amusement park is 3 people.

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Answer:

50 pounds of raspberries and 45 pounds of apples is sold

Solution:

Let  "a" be the number of pounds of raspberries sold

Let "b" be the number of pounds of apples sold

Cost of each pound of raspberry = $ 4

Cost of each pound of apple = $ 1.50

Austin made $267.50 from selling a total of 95 pounds of raspberries and apples

Therefore,

a + b = 95

b = 95 - a ------ eqn 1

Austin made $267.50. Therefore,

number of pounds of raspberries sold x Cost of each pound of raspberry + number of pounds of apples sold x Cost of each pound of apple = 267.50

4a + 1.50b = 267.50 --------- eqn 2

Substitute eqn 2 in eqn 1

4a + 1.5(95 - a) = 267.50

4a + 142.5 - 1.5a = 267.50

2.5a = 125

a = 50

Substitute a = 50 in eqn 1

b = 95 - 50

b = 45

Thus 50 pounds of raspberries and 45 pounds of apples is sold

Step-by-step explanation:

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A person 11 miles west and 12 miles south of the tower will not have coverage.

A circle is a closed curve that is drawn from a fixed point. This point is called the center. All points on the curve are equidistant from this center point.

The cell phone tower covers a circular area with radius 15 miles. This means that there will be coverage in all directions from center up to 15 miles.

The person is 11 miles west and 12 miles south of the tower.

Distance of person from center will be calculated using distance formula

[tex]d = \sqrt{(11^{2} + 12^{2} }[/tex]

∴ [tex]d = \sqrt{121 + 144}[/tex]

∴ [tex]d = 16.27[/tex] miles.

Since this distance is greater than the radius of circle (15 miles), the person will not have cell phone coverage.

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