Wendy keeps her hamster, Fluffy, in a cage shaped like a rectangular prism that is 20 inches long, 14 inches wide, and has a volume of 4,340 cubic inches. Kenneth keeps his hamster, Speedy, in a cage that is the same length, but is 15 inches wide and has a volume of 5,250 cubic inches.

The mid point between the two points is at 13/8 .

A line segment is  a line of fixed measure .

The line segment extends from (-3/4) to  [tex]\rm 2 \dfrac{1}{2}[/tex]

i.e the line extends form -3/4 to 5/2

To find the mid point , the total distance needs to be determined

So the distance between the two point is

(5/2) + (3/4) = 13/8

The mid point is at half the distance of this

so it is at 13/8 from both the points

Any point at 13/8 distance from 5/2  towards (-3/4) will be

= (5/2) - (13/8)

= 7/8

So the mid point between the two points is at 13/8 .

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The angle of depression from the top of the flag pole to point A is 36.2 degrees.

From trigonometric ratio: cos(θ) = Adjacent / Hypotenuse

Given that;

cos(θ) = Adjacent / Hypotenuse

Cos(θ) = 25ft/31ft

Cos(θ) = 0.80645

θ = cos⁻¹( 0.80645 )

θ = 36.2°

Therefore, the angle of depression from the top of the flag pole to point A is 36.2 degrees.

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"Draw a ray with one endpoint" demonstrates the correct first step in copying an angle. This is further explained below.

In general, the distance (which is sometimes stated as a degree) that occurs between two crossing lines or surfaces at or near the point where they meet. This distance might be positive or negative.

The formation of an angle is caused by the conjunction of two rays at a single point in space. The split or 'opening' that can be seen between these two rays is referred to as a 'angle,' and the symbol denotes this particular angle. The degree is the standard unit of measurement for angles, and its values include things like 60 degrees and 90 degrees, amongst other possible combinations.

In conclusion, "Draw a ray with one terminal" illustrates the correct first step in duplicating an angle. This step shows how to replicate an angle.

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Pedro Fernández should advice his client to go with the second mutual fund named as Fund Corporation. This is because, it showed an higher average return over the five-year period at an average of 11% beating Trujix Inc by 3%.

To get the better fund, Pedro must calculate a simple average of the interest rates of the various funds over the past 5 year period.

Trujix Inc 5-Year Average

(12 + 10+ 3 +9 + 11)/5

= 45/5

=9%

Fund Corporation 5-Year Average

(13 + 12 +14 + 10+ 6)/5

= 55/5

= 11%

Hence, the better investment is the one by Fund corporation.

Full Question

Pedro Fernández is a manager at Avon Chic, Pedro was interested in the rates of return for the last five years of two different mutual funds. Trujix, Inc., showed a five-year period, rates of return of 12; 10; 3; 9 and 11%, while Fund Corporation showed 13; 12:14:10 and 6%. A client approached Pedro and expressed his interest in one of these mutual funds. Which one should Pedro choose for his client?

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The length and width of the toolbox given the diagonal is 45 inches and 15 inches respectively.

Hypotenuse ² = opposite ² + adjacent ²

30² = w² + (3w²)

30² = 4w²

900 = 4w²

w² = 900/4

= 225

w = √225

w = 15

Therefore,

Width of the triangle = w

= 15 inches

Length of the triangle = 3w

= 3(15)

= 45 inches

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The exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]

An exponential function is represented as:

y = b^x

Where b represents the base.

The base is given as:

b = 12

So, we have:

y = (12)^x

It is vertically compressed by a factor of 1/8.

So, we have:

y = 18(12)^x

When reflected across the y-axis, we have:

[tex]y = 18(12)^{-x}[/tex]

The horizontal asymptote is y = 2.

So, we have:

[tex]y = 18(12)^{-x} + 2[/tex]

It passes through the point (-3, 4).

So, we shift the function to the right by 4 units

[tex]y = 18(12)^{-x-4} + 2[/tex]

Express as a function

[tex]f(x) = 18(12)^{-x-4} + 2[/tex]

Hence, the exponential function is [tex]f(x) = 18(12)^{-x-4} + 2[/tex]

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The length of x will be 4 cm if is the angle bisector of A.

A straight line that splits an angle in a triangle into two congruent angles is known as the angle bisector.

Given sides;

AB=12

AE=8

BD=6

DE=x

From the triangle angle bisector theorem;

[tex]\rm \frac{BD}{DE} = \frac{AB}{AE} \\\\ \frac{6}{x} =\frac{12}{8} \\\\ x=4[/tex]

Hence the length of x will be 4 cm.

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The following requires the submission of the details of the parabola related to the equations.

A parabola, simply defined, is a plane curve that is created by a point that is moving such that it's distance from a fixed locus is equal to it's distance from a line that is fixed.

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Answer: 65

Step-by-step explanation:
1 + 64 = 65

AMSWER :

Just remove the given angle from 180°

since , a straight line makes a angle of 180°

hence,

ROQ + ROP = 180°

144° + ROP = 180°

ROP = 180° - 144° = 36°

.

.

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The answer to the question is,

12 sin(∠B) = 2,           12 sin(∠C) = √3+√35

Sin rule is,

sin(A)/BC = sin(B)/AC = sin(C)/AB

sin(B) = (sin(A)×AC)/BC

sin(C) =(sin(B)×AB)/AC

To solve this question we apply sin rule,

Now we take

12 sin(∠B) =12 (sin(∠A)×AC)/BC

12 sin(∠B) =12 (sin(π/6)×(x/3x))          where ∠A =π/6 and AC=x, BC =3x

12 sin(∠B) =12 ((1/2)×(1/3))

12 sin(∠B) =12/6 = 2

12 sin(∠B) = 2

now we find the value of 12 sin(∠C)

12 sin(∠C) = 12(sin B)×(AB/BC)

now put the value of 12 sin(∠B) = 2

12 sin(∠C) = 2×(AB/BC)

12 sin(∠C) = (2/AC)×[AC×(cos(π/6))+BC×(cos B)]

12 sin(∠C) = 2×[cos(π/6)+(BC/AC)×(cos B)]

cos (π/6) = √3/2 and BC/AC =3

then

12 sin(∠C) = 2×[(√3/2)+3×(cos B)]

cos B= √1-sin²B

12 sin(∠C) = 2×[(√3/2)+3×√(1-sin²B)]

12 sin(∠B) = 2

sin B = 1/6

12 sin(∠C) = 2×[(√3/2)+3×√(1-(1/6)²]

12 sin(∠C) = 2×[(√3/2)+3×√1-(1/36)]

12 sin(∠C) = 2×[(√3/2)+3×√(36-1)/36]

12 sin(∠C) = 2×[(√3/2)+3×√(35/36)]

12 sin(∠C) = 2×[(√3/2)+(3/6)×√35]

12 sin(∠C) = 2×[(√3/2)+(1/2)×√35]

12 sin(∠C) = 2×[(1/2)(√3+√35)]

12 sin(∠C) = √3+√35

Hence the answer is,

12 sin(∠B) = 2,         12 sin(∠C) = √3+√35

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Answer: 6

Step-by-step explanation:

Because [tex]\overline{DE} \cong \overline{EF}[/tex], [tex]y=55[/tex]. So, because angles in a triangle add to 180 degrees, [tex]11x+4=70 \longrightarrow x=6[/tex]

Answer:

the answer

Step-by-step explanation:

Answer:

K?

Step-by-step explanation:

The answer of the answer is the answer.

Hope this helped :D

Since the correlation coefficient has an absolute value that is less than 0.6, it is not a strong relationship, hence the statement is False.

In this problem, the correlation coefficient is of 0.08, hence:

Thus, the given statement is False.

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73 is a 46% increase of 50.

What is percentage ?

A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount.

Percentage is defined as a specific part or amount out of a hundred. It is a fraction with the denominator 100 and is denoted by the symbol "percent."

The percent increase formula is as follows:

Percent increase = [(new value - original value)/original value] * 100.

Number of car parking (original value)=50

Number of car parking(new value)=73

The Percentage increase =[(73-50)/50]*100

                                          = [(23)/50]*100  

                                          =.46*100

                                         =46%

73 is a 46% increase of 50.

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Since there are only two (2) sellers in the town with many buyers, the competitive situation which Jameson's Grocery is experiencing is an oligopoly.

An oligopoly can be defined as a market structure which comprises a small number of business firms (sellers) that are offering identical (similar) products to many buyers, wherein none of the sellers can limit the significant influence of others.

In this scenario, we can infer and logically deduce that the competitive situation which Jameson's Grocery is experiencing is an oligopoly because there are only two (2) sellers in the town with many buyers (1,000 students).

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Answer:

B

Step-by-step explanation:

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

a = 7 × 2 = 14

Answer:

[tex]\boxed{\boxed{\bf x = 7}}[/tex]

Step-by-step explanation:

[tex] \sf \cfrac{4x - 4}{20} = \cfrac{30}{25} [/tex]

[tex]\sf 4x - 4 = \cfrac{(20)(30)}{25} [/tex]

[tex]\sf 4x - 4 = \cfrac{600}{25} [/tex]

[tex]\sf 4x - 4 = 24[/tex]

[tex]\sf 4x = 24 + 4[/tex]

[tex]\sf \cfrac{4x}{4} = \cfrac{28}{4} [/tex]

[tex]\sf x = 7[/tex]

Using proportions, the selling prices are given as follows:

1. $46.92.

2. $15.29.

3. $17.16.

4. $20,280.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

To find the selling prices, we have to multiply the original prices by either 1.02(2% sales tax) or 1.04(4% sales tax), hence they are given as follows:

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Step-by-step explanation:

Answer:

80?

hshsshjsjsjjsjajjsjsnnsnsnnw

Step-by-step explanation:

hhddussisusuis

The number 2007 is in the 63rd row

The pattern is given as

1

2  3

4  5  6

The sum of n natural numbers is:

Sum = 0.5n(n + 1)

Assume n = 62

Sum = 0.5 * 62 * (62 + 1)

Sum = 1953

Assume = 63

Sum = 0.5 * 63 * (63 + 1)

Sum = 2016

2007 is between 1953 and 2016

Since 2016 is greater than 1953, we can conclude that 2007 is in row 63

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Answer:

3/2

Step-by-step explanation:

We can use the slope formula to find the slope of the line

m = ( y2-y1)/(x2-x1)

Using the points (0,-4) and (2,-1)

m = ( -1 - -4)/( 2 - 0)

   = (-1+4)/ (2 -0)

   = 3/2

Answer: Function 1 has the larger maximum at (4,1).

Step-by-step explanation:

The vertex of f(x) is at [tex]x=-\frac{2}{2(-1)}=1[/tex], and [tex]f(1)=-2[/tex].

For the graph, the maximum is obviously at (4,1).

So, Function 1 has the larger maximum at (4,1).

The point that is a solution to the system of inequalities on the coordinates grid is A.

It should be noted that form the information given, the expression is y < −2x + 10. In this case, draw the solid line y = -2x + 10.

Shade the region below the like for x = 5.

y = -2(5) + 10

= -10 + 10

= 0

For x= 0

y = -2(0) + 10

= 0 + 10

= (0, 10)

The diagram is attached.

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Answer:

a₃ = 19

Step-by-step explanation:

to find the third term substitute n = 3 into the nth term rule

a₃ = 4(3) + 7 = 12 + 7 = 19

Answer:

a₃ = 19

Step-by-step explanation:

the relationship between any two terms of an arithmetic sequence (in our case the relationship between the 3rd term and nth term)  gives us this equality :

[tex]a_n - a_3 = 4(n-3)[/tex]

Then

4n + 7 - a₃ = 4n - 12

Then

7 - a₃ = - 12

Then

7 + 12 = a₃

Then

a₃ = 19

The full set is;

(x + 7) (3x + 1) = 3x² + 22x + 7

This question introduces the concept of polynomial long division.

This is what we are

Given: (3x² + 22x + 7) ÷ (x + 7) = 3x + 1

Now, from the concept of polynomial long division, we can see that:

if, f (x) ÷ g (x) = h (x),

This means that we can write:

f (x) = g (x) × h (x)

Applying the same concept to the question, we can also say:

(3x² + 22x + 7) ÷ (x + 7) = 3x + 1,

Next; (x + 7) (3x + 1) = 3x² + 22x + 7

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Answer:900

Step-by-step explanation: