In 2005, there were 12,458 fish in Hound's Tooth

Lake. After years of drought, there were only

968 fish in 2010. Find the rate of change in the

population of fish for 2005–2010.

The area of the given trapezoid is 24 square inches.

Area of trapezoid:

Area of the trapezoid is referred as the total space covered by its sides.

The formula to calculate the area of the trapezoid is

A = ½ (a + b) h

where

(A) is the area of a trapezoid,

'a' and 'b' are the bases that are parallel sides,

and 'h' is the height that is the perpendicular distance between a and b

Given,

Here we have the values 8 in, 6 in, and 4 in

Through the given values we have to find the area of the trapezoid.

Let us consider the base values of the trapezoid are 8in and 6 in and the height as 4 in.

Now, we have all the side value of the trapezoid.

Then we have to apply it on the formula,

Then we get,

Area = 1/2 (8 + 6) x 4

Area = 2 x (12)

Area = 24

Therefore, the area of the trapezoid is 24 square inches.

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Answer:

see the attachment photo!

Answer: he will be left with 31.74 dollars

Step-by-step explanation:

i first put 55.00 - 4.50 = 50.5

then you subtract 50.5 with 6.25  3 times so the and is 31.74

hope this helped !!

The choice which describes a sequence of transformations in which the blue figure is the image of the red figure is: 4. Rotate the triangle 90º clockwise about the origin and then translate it 1 unit left and 7 units down.

In Mathematics, the rotation of a geometric figure 90° about the origin in a clockwise or counterclockwise direction would produce a geometric figure that has these coordinates (y, -x).

From the information provided in the graph about the transformation applied to the red triangle to create the blue triangle, we have the following ordered pairs that represents a rotation of 90º clockwise:

(x, y)                                    →              (y, -x)

Ordered pair A = (-5, 2)            Ordered pair A' = (2, 5)

Ordered pair B = (-5, 6)             Ordered pair B' = (6, 5)

Ordered pair C = (-1, 2)             Ordered pair C' = (2, 1)

After a translation of 1 unit left and 7 units down, we have:

Ordered pair A' = (2, 5)       →     Ordered pair A' = (2 - 1, 5 - 7) = (-1, -2)

Ordered pair B' = (6, 5)       →     Ordered pair B' = (6 - 1, 5 - 7) = (.5, -2)

Ordered pair C' = (2, 1)        →     Ordered pair C' = (2 - 1, 1 - 7) = (-1, -6)

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Answer: K is greater than or equal to 18

Step-by-step explanation:

Answer:k>=-18

Step-by-step explanation:

Rewrite so k

is on the left side of the inequality.

2/5⋅(k−2)≥−8

Multiply each term in

2/5⋅(k−2)≥−8 by 5/2 to eliminate the fractions.

k−2≥−20

Move all terms not containing

k to the right side of the inequality.

k≥−18

The result can be shown in multiple forms.

Inequality Form:

k≥−18

Step-by-step explanation:

-(10x + 2) > 5x - 1 - 8x

combine x terms on right side:

-(10x + 2) > -3x - 1

remove ()'s from left side:

-10x - 2 > -3x - 1

add 10x to both sides:

-10x - 2 + 10x > -3x - 1 + 10x

-2 > 7x - 1

add 1 to both sides:

-2 + 1 > 7x - 1 + 1

-1 > 7x

divide both sides by 7:

-1/7 > 7x /7

-1/7 > x or x < -1/7

in interval notation: (-∞, -1/7)

Answer: $9.76

Step-by-step explanation: If you multiply f, the order of fries (5) by the cost of it ($1.08) you would get $5.40 & if you multiply d, the order of drinks (4) by the cost of it ($1.09) you would get $4.36. If you add up both the total numbers, you would get a final answer of $9.76.

Answer:

$9.76

Step-by-step explanation:

1.08f + 1.09d= Total

1.08(5)+1.09(4)= Total

5.40+4.36= Total

Answer:

(-1,4) (-3,0)

picture below (im assuming you meant x^2.)

if you meant x2, please look at the second image

FIRST PHOTO = y=x^2 + 6x + 9 & y=2x+6

SECOND PHOTO = y=x2 + 6x + 9 & y=2x+6

maximum height = 32ft

Given function  h(t) = -16t^2+40t+7

known data:

[tex]h{0}[/tex] = 7 ft

[tex]v_{0}[/tex] = 40 ft/s

we equate the first derivation to zero

and solve for time.

h(t) = -16t^2 + 40t+7

[tex]\frac{dh}{dt} (t)[/tex] = -32t+40 = 0

t = [tex]\frac{40}{32}[/tex] = 1.25s

second derivative and evaluate:

[tex]\frac{d^{2}h}{dt^{2}}[/tex] [tex]\frac{}{}(t)[/tex] = -32

the maximum height of the rocket with the respect to

the ground can be obtained by evaluating the function

h(1.25) = - 16[tex](1.25)^{2}[/tex]+40(1.25)+7 = 32 ft

therefore the rocket reaches maximum height at  h = 32ft.

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The probability of getting 2 yellow apples and 1 red apple is 18/35 which is the D option.

This is a question of permutations and combinations.

Given that:-

Number of yellow apples = 4

Number of red apples = 2

We have to find the probability of getting 2 red apples and 1 yellow apple.

Number of ways of getting 2 yellow apples = [tex]^4C_2=6[/tex]

Number of ways of getting 1 red apple = [tex]^3C_1=3[/tex]

Total number of ways of finding 3 apples from 7 apples = [tex]^7C_3=35[/tex]

Hence,

Probability of getting 2 yellow apples and 1 red apple = 6*3/35 = 18/35.

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Answer:

ye it is I can't help sorry I need the points

3.  3.8 ft

5.  28

7.  .1

Step-by-step explanation:

5/20.5=15.5/x

solve for x

3.8

7/14=14/x

28

10/x=1/100

.1

Answer: 41.2

Step-by-step explanation: The rules of rounding are you round up if the number you're rounding is 5 or higher than five, and you keep the same number if it is 4 or lower. For this problem, the 1 is the digit being rounded, so to round it, look at the number to the right of the 1, which is a 5, which means we would round up.

hope this helps!

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Answer:

Step-by-step explanation:

The answer would be 24:600. One student is absent so there are 24 students present. The number of beads is still 600, so the ratio is 24:600 which simplifies to 1:25.

The cost of s and 20 songs are $1.25s and $25 respectively.

Multiplication is mathematical arithmetic operation. It is also a process of adding same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times or 3 is added 2 times.

Given that music services cost $6 per month to Nachelle.

And to download songs for offline listening, the service charges $1.25 per song.

If she wants to download s songs,

The cost of s songs = the cost of one song multiplied by s

The cost of s songs =$1.25 multiplied by s

The cost of s songs = $1.25s

Here s = 20 then

cost of 20 songs = $1.25 x 20

                           = $25

Therefore the cost of s and 20 songs are $1.25s and $25 respectively.

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Answer:
y = -1/3x + 1

Step-by-step explanation:

1) For a perpendicular line, the slope is the opposite reciprocal. What this means is that, the slope will be the opposite sign and flipped.

~-1/3 will be the new slope

2) Then you have to rewrite the problem using the point slope form which is y - y1 = m(x-x1). The values that we will be plugging in for x1 and y1 will be from the coordinate that you provided.

~ y - (-2) = -1/3(x-9)

3) Now simplify everything you can
~y+2 = -1/3(x-9)

4) Now distribute the -1/3
~y+2 = -1/3x + (9)(1/3)
~y+2 = -1/3x + 3

5) Now we need to subtract 2 from both sides to get y by itself.

~y = -1/3x + 1

Answer:

y = m x + b       equation for a straight line

when x = 4     y = 5

5 = m * 4 + b

m = (5 - b) / 4      solving for m

when x = -3      y = -1

-1 = (5 - b) / 4 * -3 + b = -3 * (5 - b) / 4 + 4 b / 4

-1 = (-15 + 3 b + 4 b) / 4

11 = 7 b      b = 11 / 7

Since m = (5 - b) / 4

m = (5 - 11/7) / 4  = 6/7

We then have y = 6 x / 7 + 11 / 7

Or 7 y = 6 x + 11

Check:

when (4 , 5)     35 = 24 + 11 = 35

For the specified requirements, 105 sample size are required.

Given that,

Confidence Interval = 90

Margin of error (m) =0.08

We know , to find Sample size for  estimating a population proportion

n = (Z*/m)² P(1-P)

where , m is margin of error

             P is estimated proportional value.

If we have no preconceived of the value of the population proportion

, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.

for a 90% confidence interval ,

Z* = 1.645 , m=0.08

Using equation we get

n = (1.645/0.08)²(0.5)( 1 - 0.5 )

By solving,

n =105.3 = 105

The necessary sample size is 105

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By using the concept of supplementary angle, it can be calculated that

The two angles are 47° and 133°

What are supplementary angles?

At first it is important to know about angle.

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Two angles are said to be supplementary if the sum of the angles is 180°

Let one angle be x

Other angle = 180 - x

The supplement of an angle is 8 less than three times the measure of the angle

By the problem

180 - x = 3x - 8

3x + x = 180 + 8

4x = 188

x = [tex]\frac{188}{4}[/tex]

x = 47°

Other angle = 180 - 47 = 133°

The two angles are 47° and 133°

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An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representations of the inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the inequality –3(2x – 5) < 5(2 – x)

First, we have to solve for x in the inequality

–3(2x – 5) < 5(2 – x)

Clear the parenthesis:

-6x + 15 < 10 - 5x

Collect like terms:

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1:

x > 5              ( Note:  Divide both sides by -1 will change the < to > )

This is what will determine our answer

Since our answer is x > 5.  An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)

Therefore, the correct representations of the inequality is  an open circle is at 5 and a bold line starts at 5 and is pointing to the right r

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The number of ways that a nine question true false quiz can be answered is; 512 ways

We are given;

Number of questions = 9

Options for each answer = 2 (True of false)

The power set is defined as the number of subsets of a set of n elements which is expressed as 2ⁿ

There are 2 ways to answer question 1 and as such it means that there are 2 ways to answer question 2.

For question 2; 2² = 4 ways

For question 3; 2³ = 8 ways

For question 4; 2⁴ = 16 ways

For question 5; 2⁵ = 32 ways

For question 6; 2⁶ = 64 ways

For question 7; 2⁷ = 128 ways

For question 8; 2⁸ = 256 ways

For question 9; 2⁹ = 512 ways

Thus we we conclude that, there are 512 ways to answer 9 true-false tests.

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Answer:

[tex]x^3-10[/tex]

Step-by-step explanation:

Let the number be x.

"A number cubed" refers to x³.

"Difference" means to subtract, so the answer is [tex]x^3-10[/tex].

In order to get the same outcomes as a form mirrored across the y-axis and turned counterclockwise, a shape can be reflected across the x-axis and then rotated 90 degrees in a clockwise manner around the origin. This suggests a similarity between these two transformative sequences.

What does mathematics mean by reflection?

A flip is the term used in geometry to describe a reflection. The mirror image of the form is a reflection. An image can reflect through a line known as the line of reflection. When all of the points in a figure are evenly spaced away from one another, the two figures are said to reflect each other.

(X, Y) > when a form is rotated 90 degrees counterclockwise (y, -x).

When the picture is reflected across the y-axis, (x, y) > (-x, y).

When those two transformations are used, it is the same as reflecting a shape across the line y = -x, where (x, y) > (-y, -x).

For instance: After being rotated 90 degrees clockwise and reflecting across the y-axis,

(2, 1) > (1, -2) > (-1, -2); and

(2, 1) > (-1, -2)

after being reflected across the y = -x line

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The number of pennies they lose altogether is 288 pennies.

How to find the number of pennies they lost together?

Together, Katya and Mimi have 480 pennies in their piggy banks.

Therefore, there total amount of pennies is 480.

After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.

Therefore,

let

x = number of pennies Katya have

y = number of pennies Mimi have

Hence,

x + y = 480

x = 480

Katya pennies left = x - 1 / 2x = 1 / 2x

Mimi pennies left = y - 2 / 3 y = 1 / 3 y

1 / 2 x  = 1 / 3 y

2y = 3x

y = 3  / 2 x

Substitute the value in equation(i)

x + 3 / 2 x  = 480

2.5x = 480

x = 480 / 2.5

x = 192

Therefore,

192 + y = 480

y = 480 - 192

y = 288

The number of pennies they lose can be calculated as follows;

Katya losses = 1 / 2 × 192 = 96

Mimi losses = 2 / 3 × 288  = 192

Therefore, they lost 96 + 192 = 288 pennies altogether.

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The 4.89 hours after midnight did the temperature first hit 63 degrees.

A sinusoidal function can be used to mimic the daily variation in outdoor temperature. Assume you are aware that the daily average temperature starts at 9 am and swings between 60 and 70 degrees throughout the day.

We have to find to two decimal places, how many hours after midnight did the temperature first hit 63 degrees.

Max T=70 and Min T=60

D = (Max + Min)/2

   = 70+60/2

   = 65

A = Max- D

   = 70 - 65

   = 5

Since,

Period is 24 hours,

So,

W = 2π/24

   = π/12

The function will be:

T(t) = 5 Sin (π/12(t-C)) + 65

Given average temperature occurs at 8 am so,

T(9)=65

Solving this we get

C=9

Hence,

T(t)= 5Sin(π/12( t-9))+65

Now,

We need to find t such that T(t)=63

63=5Sin(π/12( t-9))+65

t = 4.89 hours.

Therefore, The 4.89 hours after midnight did the temperature first hit 63 degrees.

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Coordinates of the original figure: (-2, 2), (-2, 0), and (2, 2).

Coordinates of the final transformed figure: (-4, 4), (-4, 2), and (4, 4).

What is a coordinate system?

In geometry, a coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the location of points or other geometric elements on a manifold, such as Euclidean space.

In the original figure, we can plot the coordinates, and we get

                     For dark blue dot = (-2, 2)                      

                     For red dot = (-2, 0)

                     For light blue dot = (2, 2)

After applying a scale factor of '2', we get the new coordinates as

                     For dark blue dot = (-4, 4)                      

                      For red dot = (-4, 2)

                      For light blue dot = (4, 4)

Hence,

Coordinates of the original figure: (-2, 2), (-2, 0), and (2, 2).

Coordinates of the final transformed figure: (-4, 4), (-4, 2), and (4, 4).

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