i√5
Find the square of the imaginary number.

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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A formula that describes the average revenue per person is:

average revenue per person = 1.4w

Average revenue per person is the ratio of the total revenue received to the number of people. It is calculated by dividing total revenue by the number of people.

We have:

Total revenue formula, M = 350w⁴

Total number of people formula, T = 250w³

Thus,

Average revenue per person = M/T

Average revenue per person = 350w⁴/250w³

Average revenue per person = 1.4w

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Answer:

y=1/5x+11/5

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  y-y^1=m(x-x^1) to find line parallel to -x+5y=1

Hope this helps

Answer: y = 1/5x+ 2.2

Step-by-step explanation:

First, change the expression into y-intercept form

-x+5y=1

5y=x+1

y=1/5x+1/5

For a line to be parallel to another line, it must have the same slope.  Thus, the slope must be 1/5x.  Then, to find the y-intercept simply do:

y = 1/5x+b, where x = -1 and y = 2

2=1/5(-1)+b

2 = -1/5+b

b = 2 1/5.

Thus, the equation y = 1/5x+ 2.2

Hope it helps <3

The equation will be t = 3s where t is total cost and s is number of snow cones. this can be find out be relationship of number of snow cones and total cost in table .

In given table :

Number of snow cones               Total cost

2                                                      6

6                                                      12

5                                                      15

From above table, we can relate

1st case :
number of snow cones = 2 and total cost = 6

i.e. 3 times of number of cones.

2nd case:

number of cones = 4 and total cost = 12

i.e. 3 times the number of cones.

3rd case :

number of cones = 5 and total cost = 15

i.e. 3 times the number of cones.

So, we see same pattern is repeated in all.

Then equation will be t = 3s where t = total cost , s = number of snow cones.

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Given :

An automobile manufacturer introduces a new model that averages 27 miles per gallon in the city.

Standard deviation , S.D = 3 miles per gallon .

To Find :

The probability that the person will purchase a car that averages less than 20 miles per gallon for in-city driving.

Solution :

We have to find the probability , \(P(X\leq 20)\) .

Here , we will use the excel function

So ,

\(P(X\leq 20)=NORMADIST( 20, 27 , 3 , 1 )=0.009815\) .

Therefore , probability is 0.009815 .

Step-by-step explanation:

\(6(y + 1) > 6 \\ 6y + 6 > 6 \\ 6y > 0 \\ y > 0\)

Answer:

See in bold

1 x 1 = 1

1 x 2 = 2

1 x 3 = 2

1 x 4 = 4

1 x 5 = 5

2 x 1  = 2

2 x 2 = 4

2 x 3 = 6

2 x 4 = 8

2 x 5 = 10

3 x 1 = 3

3 x 2 = 6

3 x 3 = 9

3 x 4 = 12     Total 70

3 x 5 = 15

4 x 1 = 4

4 x 2 = 8

4 x 3 = 12

4 x 4 = 16   total 125

4 x 5 = 20

5 x 1 = 5

5 x 2  = 10

5 x 3  = 15  total 175

5 x 4 = 20

5 x 5 = 25  total 220

Total = 220

Algorithm Finding 142  =  220  - 78  = 142

-78 = 6 x 13 therefore 142six = 13

Algarithm Finding X 230six = X diagonal

X diagonal list on table shows;

1 x 1 = 1

2 x2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

Total = 91

230/91 = 2.52747253  if diagonal algorithm

or 230 taken from the last 5 x 5 algorithm total = 220

1 x 6 = 6   220 + 6 = 226   x = 4+  then 1 x 6

2 x 6 = 12  = 18    220 + 18 = 38  x = 8 - then 2 x 6

as X230 = 8- 230 = 2 x 6

or X230 = 4+ 230 = 1 x 6  

Vertex B is (6,6)

This point will go through two transformations:

• reflection, about x axis

• rotation, of 180 degrees counterclockwise

• First, ,reflection about x axis,:

If we have a point (x, y), the x-axis reflected point will have coordinate (x, -y). We leave the x coordinate as is and negate the y coordinate.

Thus, (6, 6) will becomes (6, -6).

• Secondly, we have ,counter-clockwise rotation of 180 degrees,:

If we have a point (x,y), the 180 degree counterclockwise rotated point will be (-x, -y). We negate both x and y coordinate.

Thus, (6, -6) will becomes (-6, 6).

The final vertex B would be (-6, 6).

Answer:

Given Figure has set of Stacked cubes.

To Draw the Base Plan, lets see its right side, Left Side and Front side view.

Right side:

It has 3 cubes in base.

2 cubes in 2nd layer clearly seen in figure and only 1 cube in 3rd layer.

Left Side:

It has 2 Cubes in base.

Both Cubes attached to 1st and 2nd cube of right side cubes.

Front Side:

It can be seen that, here base only has 2 rows of cubes.

Therefore,  1st Figure is correct Base Plan (or enclosed figure)

Note: Numbers in enclosed figure just shows the total no. of cubes in that stack.

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Answer:

1) 3( 2) - 1 = 6 - 1 = 5

2) 2(-1) - 3+4(-1) = -2 -7 = -9

3) 4^2-6(4)=9 = 16-24=9, = -8=9

TU is parallel to MN.

Given that the slope of a line MN is -3, we need to find a line which is parallel to the MN.
So we know that the parallel lines are having equal slope so the line which is parallel to the MN it must have slope of -3.

Therefore,

Considering the line TU, find the slope = y₂-y₁ / x₂-x₁

= 10-1 / 5-8 = -9/3 = -3

Since, the slope of the line TU is -3 therefore we can say the lines TU and MN are parallel liens.

Hence TU is parallel to MN.

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The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

h(x) = √(x - 7) + 5

The value inside the square root should be greater than or equal to zero. Then we have

x - 7 ≥ 0

x ≥ 7

The domain of the function h(x) = √(x - 7) + 5 should be greater than or equal to 7 that is [7, ∞).

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Answer:

$17.50

Step-by-step explanation:

$18.37=x+5%

18.37=1.05x

18.37/1.05=x

x=$17.50

Answer: C=2πr

r Radius

The value of the difference of composite function is (f-g)(144) = 0.

A composite function is one that uses the output of one function as the entry for another. The function f g (x) fg(x) fg(x) fg(x) fg(x) is also referred to as "f of g of x" or "f g fg fg of x," and it combines two functions if we have f and g.

To find the value of (f-g)(144), we first need to find f(144) and g(144).

We have:

\($$f(x) = \sqrt{x} + 12$$\)

So;

\($$f(144) = \sqrt{144} + 12 = 12 + 12 = 24$$\)

Similarly,

\($$g(x) = 2\sqrt{x}$$\)

So:

\($$g(144) = 2\sqrt{144} = 2 \cdot 12 = 24$$\)

Now we can calculate (f-g)(144):

\($$(f-g)(144) = f(144) - g(144) = 24 - 24 = 0$$\)

Therefore, (f-g)(144) = 0.

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Answer:

<A=42°

Step-by-step explanation:

If the exterior of angle C is 126, the interior is 54.

The sum of the other two angles must be 126. (Exterior Angle Theorem)

If B is twice A, we divide 126 into thirds. This is 42.

So A is 42, B is 84, and C is 54.

Answer:

42°

Step-by-step explanation:

An exterior angle is equal to the sum of the opposite interior angles.

A + B = 126

The measure of B is twice the measure of A.

B = 2A

Substitute:

A + 2A = 126

3A = 126

A = 42

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Answer:

365

Step-by-step explanation:

(20*x) / 100 = 73

Answer:

365

Hope this helps :)

Step-by-step explanation:

We already have our first value 73 and the second value 20. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

STEP 173 = 20% × Y

STEP 273 =  

20

100

× Y

Multiplying both sides by 100 and dividing both sides of the equation by 20 we will arrive at:

STEP 3Y = 73 ×  

100

20

STEP 4Y = 73 × 100 ÷ 20

STEP 5Y = 365

Finally, we have found the value of Y which is 365 and that is our answer.

You can easily calculate 73 is 20 percent of what number by using any regular calculator, simply enter 73 × 100 ÷ 20 and you will get your answer which is 365

The formula of the graph of f(x) = 8x⁴-5x³-2x²+6x+5 is reflected across the y-axis as g(x) = 8x⁴ + 5x³- 2x²-6x + 5 .

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Reflection across the y-axis is defined as reflecting a point across they = x,  the x-coordinate, and y-coordinate places, the line y = -x is the coordinates (-x, y).

So reflected across the y-axis: f(x) → f(-x),

⇒ (x,y) → (-x , y)

We have to determine the equation of the graph of f(x) = 8x⁴-5x³-2x²+6x+5 is reflected across the y-axis.

Since reflected across the y-axis: f(x) → f(-x), So substitute the value x = -x

⇒ f(-x) = 8(-x)⁴-5(-x)³-2(-x)²+6(-x)+5

⇒ f(-x) = 8x⁴ + 5x³- 2x²-6x + 5 = g(x)

Hence, the equation of the graph of f(x) = 8x⁴-5x³-2x²+6x+5 is reflected across the y-axis as g(x) = 8x⁴ + 5x³- 2x²-6x + 5 .

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The probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

Let's use the formula for calculating the probability of the intersection of two events: P(A and B) = P(A) × P(B|A), where P(B|A) is the probability of event B occurring given that event A has occurred.

Let A be the event that it is raining, and B be the event that the flight is delayed. We are looking for P(A and B).

We know that:

P(A) = 0.1 (the probability that it will rain)

P(B) = 0.11 (the probability that the flight will be delayed)

P(not A and not B) = 0.88 (the probability that it will not rain and the flight will leave on time)

We can use the complement rule to find P(A or B):

P(A or B) = 1 - P(not A and not B)

P(A or B) = 1 - 0.88

P(A or B) = 0.12

Now we can use the formula for the intersection of two events:

P(A and B) = P(A) × P(B|A)

We know that P(A) = 0.1, and we need to find P(B|A), the probability of the flight being delayed given that it is raining.

We can use Bayes' theorem to find P(B|A):

P(B|A) = P(A and B) / P(A)

P(B|A) = (P(A) × P(B|A)) / P(A)

P(B|A) = P(B and A) / P(A)

We can rearrange this to get:

P(A and B) = P(B|A) × P(A)

Substituting the values we know:

P(B|A) = P(A and B) / P(A)

0.11 = P(A and B) / 0.1

P(A and B) = 0.11 × 0.1

P(A and B) = 0.011

Therefore, the probability that it is raining and the flight is delayed is 0.011, or approximately 0.011 rounded to the nearest thousandth.

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Answer:

15x

Step-by-step explanation:

Both of these numbers can be divided by 15x.

If this helps please mark as brainliest

Answer:

23 1/4

Step-by-step explanation:

3/6 ^ 2 = 1/4

7 * 4 = 28

28 + 1/4 = 113/4

113/4 - 5 = 93/4

93/4 = 23 1/4

Answer:

40°

Step-by-step explanation:

z+90+y+x=180°

z+90+30+40=180°

z=40°

Angle Z would be 40°

The top half of the image is 180° In total and the red square represents 90°,

And since angle X is 20° and angle Y is 30° thats 50° total leaving a total of 40° unknown for the top half making that 40°

Answer: Z=40°

Answer:

Step-by-step explanation:

( 2, 7)

is the point where the lines intersect

Answer:

(2,7)

Step-by-step explanation:

The answer will always be where the lines intersect.

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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\(\huge\textbf{Use the distributive property.}\)

\(\begin{aligned}A.&&3(x+2)&=18\\ B.&&3x+6&=18 \end{aligned}\)

You can use the distributive property to get equation B from equation A.

The distributive property proves that \(a(b+c)=ab+ac\). Use this same logic on equation A, distributing \(3\) to \((x+2)\).

\(\begin{aligned}3(x+2)&=18\\3x+3(2)&=18\\3x+6&=18\end{aligned}\)

so, The solution is the B option