An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3500 feet and Plane 8 is at an altitude of 2285 feet. Plane A is gaining altitude
at 40.25 feet per second and Plane B is gaining altitude at 60.5 feet per second.

How many seconds will pass before the planes are at the same altitude?

What will their altitude be when they’re at the same altitude?

The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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The time required for the visit to the doctor should be more than 27 minutes.

It is given that the dose given by doctor is 14 mg radioactive dye. Dye remaining after 16 minutes is 4.25 mg.

Assuming the radioactive dye to decay exponentially then the amount present in body can be represented by the following expression

[tex]A(t) = A_0e^-^k^t[/tex] where, A(t) is the amount present after time t, k is a constant & t is the time elapsed

Initially,[tex]4.25=14e^-^1^6^k[/tex]

k=0.074/min

To calculate time such that 2mg of radioactive dye remains in the body substituting the values

[tex]2=14e^-^t^0^.^0^7^4[/tex]

t = 26.29 minutes.

Hence, the time required for doctor's visit must be more than 27 minutes to avoid the alarm.

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Answer:

9

Step-by-step explanation:

1 · 3 = 3

3 · 3 = 9

9 · 3 = 27

27 · 3 = 81

81 · 3 = 243

The median income from the given income distribution would be Rs. 34, 000.

The lowest income of the highest 10 % would be Rs. 40, 000.

Find the total number of earners sampled :

= 5 + 25 + 60 + 100 + 125 + 140 + 150 + 156

= 761 people

This means that the median income would be at :

= ( 761 + 1 ) / 2

= 381 position

The income at the 381 st position is Rs. 34, 000 so this must be the median.

The lowest of the highest 10 % would be the 90th percentile which would have the position of:

= 90 % x 761

= 685 position

The income at the 685 th position is Rs. 40, 000.

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The value of variables 'x' and 'y' will be 70 degrees and 75 degrees, respectively.

The value of 'x' is calculated as,

(140 - x) / 2 = 35

Simplify the equation, then the value of 'x' is calculated as,

(140° - x) / 2 = 35°

140° - x = 70°

x = 70°

The measure of the third arc is calculated as,

⇒ 360° - 70° - 140°

⇒ 150°

The value of y is calculated as,

y + [(180° - 150°) / 2] = 90°

y + 15° = 90°

y = 90° - 15°

y = 75°

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The required graph of the given equation y=x+2, y=-x+2, and y=|x|+2 has been shown.

The first equation, y = x + 2, represents a straight line with slope 1 and y-intercept 2. The graph passes through the point (0, 2) and has a positive slope, which means it slants upwards from left to right.

The second equation, y = -x + 2, also represents a straight line, but with slope -1 and y-intercept 2. The graph passes through the point (0, 2) and has a negative slope, which means it slants downwards from left to right.

The third equation, y = |x| + 2, represents the absolute value function of x translated up 2 units. The graph of y = |x| is a V-shape with its vertex at the origin, and when we add 2 to every y-coordinate, the graph is shifted upwards by 2 units. The resulting graph has a V-shape with its vertex at (0, 2).

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Answer:

1. [tex](x-3)^2+(y+15)^2=13[/tex]

2. [tex](x+9)^2+(y+14)^2=5[/tex]

3. [tex](x+3)^2+(y+11)^2=\sqrt{51}[/tex]

4. [tex](x+3)^2+(y-0)^2=25[/tex]

Step 1: Formula

The standard form of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex].

The h represents the x value of the coordinates of the circle's center and the k is the y value of the coordinates. The r is the radius.

So in the first problem h is going to be 3 and k is going to be -15. (In this problem the signs are flipped, so if you have a positive number it will be negative in the formula)

After inserting the values in the formula you have your answer of [tex](x-3)^2+(y+15)^2=r^2[/tex]. Now let us find the radius

Step 2: Find the radius

To find the radius of the first two problems what you can do is you can use the distance formula.

To use the distance formula you find have to identify the (x1, y1) and the (x2, y2)

In the first problem, the (x1, y1) would be the center of the circle. The reason for this is that on a graph you have to read it left to right (kinda like English) so to find the values you have to imagine what values would come first, in this case, the center point would come first.

So let us input the values in the formula. The formula is [tex]d = \sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]. This is the distance formula, this formula will be used in this problem.

Okay so the x1 is 3 and the y1 is -15. The x2 is 0 and the y2 is -13. So lets us input these values.

[tex]d = \sqrt{(0-3)^{2}+(-13--15)^2 } \\\\ = \sqrt{(-3)^{2}+(2)^2} \\\\=\sqrt{9+4}\\\\=\sqrt{13}\\\\= 3.605[/tex]

3.605 is our radius.

Now let us write our finished equation.

[tex](x-3)^2+(y+15)^2=\sqrt{13} ^2[/tex] or [tex](x-3)^2+(y+15)^2=13[/tex].

Doing these steps for the next problem gives us our second answer of [tex](x+9)^2+(y+14)^2=5[/tex]

Step 1: Midpoint Formula

To solve this problem you need to use the midpoint formula. The midpoint formula is [tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex]. In the first problem, the x1 would be -10, the y1 would be -13. The x2, on the other hand, is 4 and the y2 is -9. Now find the center of the circle.

Step 2: Find the center

To find the center of the circle we need to insert the values of x and the values of y into the midpoint formula. We can do this because they gave us the diameter and the diameter goes through the middle of the circle. So we can do this.

[tex]\frac{-10 + 4}{2} ,\frac{-13+-9}{2}\\\\\frac{-6}{2} ,\frac{-22}{2}\\\\(-3,-11)[/tex]

So (-3, -11) is the center of the circle.

Step 3: Find the radius

Now that we have the center of the circle we can use the distance formula to find the radius. We already have two of the ends of the radius so we can simply use the distance formula with the center and the ends.

[tex]d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\\\\=\sqrt{(4--3)^2+(-9--11)^2 }\\\\= \sqrt{(7)^2+(2)^2 }\\\\=\sqrt{49+4 }\\\\=\sqrt{51}[/tex]

Step 4: Write your final equation

Know we can insert all the values we have into the standard form of a circle equation.

[tex](x-h)^2+(y-k)^2=r^2\\\\(x+3)^2+(y+11)^2=\sqrt{51} ^2[/tex] or [tex](x+3)^2+(y+11)^2=\sqrt{51}[/tex]. This is our answer.

Doing these steps for the next problem gives us our answer of  [tex](x+3)^2+(y-0)^2=25[/tex]

The length of ST is 5.6 units.

Similar triangles are a set of given triangles which have some common relations when their corresponding properties are compared. Though they are similar, but not congruent.

Considering the given information, we have on comparison;

TU/ SU = OU/ CU

4/ SU = 5/ 12

5SU = 4 x 12

       = 48

SU = 48/5

     = 9.6

So that;

SU = ST + TU

9.6 = ST + 4

ST = 5.6

The length of ST is 5.6 units.

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Answer:

a=8

h=-1

k=19

Step-by-step explanation:

y=8(x^2+2x) + 20

completing the square:

y=8(x^2+2x+1)+20-1

y=8(x+1)^2+19

a=8, h=-1, k=19

Justin's painting will be 20 inches wide and 24 inches long to ensure it fits in the frame width of 2 1/2 inches.

In order to discern the ideal dimensions for Justin's painting, let us start by subtracting the wood frame width (2 1/2 inches) from the outside width and length of the frame set at 22 1/2 in and 26 1/2, respectively.  

total interior width = 22 1/2 - 2 1/2 = 20 in

interior length = 26 1/2 - 2 1/2 = 24 in

This leaves a total interior width of 20 in and an interior length of 24 in; ensuring Justin's painting is sized properly to fit within the specified parameters of the prearranged frame.

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Answer:

y = 28

Step-by-step explanation:

(20 + 5y + 4)/2 = 3y - 2

5y + 24 = 6y - 4

y = 28

The value of tan( 5π/6) is -1/√3

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

The values of function of angles depends on the quadrant they fall on.

First quadrant ( 0-90°) = all functions are positive

Second quadrant ( 91°-180°) = only sine is positive

Third quadrant ( 181°- 270°) = only tan is positive

Fourth quadrant ( 271° -360°) = only cos is positive

Pi is a measurement of angle in radians and it is equivalent to 180°

therefore;

5π/6 = 5×180/6

= 150°

the equivalent of 150° is

180° -150 = 30°

since 150 falls on the second quadrant, tan of 150 will be negative.

Tan 150 = -tan 30

= -1/√3

therefore the value of tan 150 = -1/√3

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The exact values of x for x² - 8x - 5 = 0 are x = 4 + √21 or x = 4 - √21

To solve for x in the equation x² - 8x - 5 = 0, we can use the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

Using this formula, we can identify the values of a, b, and c in the equation x² - 8x - 5 = 0.

Here, a = 1, b = -8, and c = -5.

Substituting these values into the formula, we get:

x = (-(-8) ± √((-8)² - 4(1)(-5))) / 2(1)

Simplifying this expression, we get:

x = (8 ± √(64 + 20)) / 2

x = (8 ± √84) / 2

Now, we can simplify the square root of 84 as 2√21:

x = (8 ± 2√21) / 2

We can further simplify this expression by factoring out 2 from the numerator:

x = 2(4 ± √21) / 2

Canceling out the 2s, we get:

x = 4 ± √21

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Statement           Reason

We are given that M is the midpoint of CD and that MD = 3. To prove that CM = 3, we need to show that CM is equal to the difference between CD and MD, and that CD is equal to twice MD because M is the midpoint of CD.

Using the segment addition postulate, we can express CM as CD - MD. From the definition of midpoint, we know that CD is twice MD, so we can substitute 2MD for CD in the expression for CM.

Simplifying the expression for CD, we get CD = 6. Substituting CD = 6 and MD = 3 into the expression for CM, we get CM = 6 - 3 = 3. Therefore, we have proven that CM is equal to 3.

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Answer:

-7√2 + 7√2 i.

Step-by-step explanation:

To convert a complex number from polar form to rectangular form, we use the following formula:

a + bi = r(cos θ + i sin θ)

where a and b are the rectangular coordinates, r is the modulus or magnitude, and θ is the argument or angle.

In this case, we have:

r = 14

θ = 135°

So, we can plug these values into the formula and simplify:

a + bi = 14(cos 135° + i sin 135°)

a + bi = 14(-√2/2 + i * (-√2/2))

a + bi = -7√2 + 7√2 i

Therefore, the complex number in rectangular form is -7√2 + 7√2 i.

The sum of the lengths of the longest and shortest bulb = 16 1/3 inches

The correct answer is an option (c)

Here, the line plot represents the Length of Hyacinth Bulbs inches.

We need to find the sum of the lengths of the longest and shortest bulb.

We knnow that a Line plot displays data as check marks above a number line that represents the frequency of each value.

From the attached line plot, we can observe that the length of the longest bulbs = 10 in. and the length of the shortest bulbs = 6 1/3

So,  the sum of the lengths of the longest and shortest bulb would be,

10 + 6 1/3 = 16 1/3

Therefore, the correct answer is an option (c)

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An attractive tax credit or deduction that can be considered is a reward for those who expend in renewable energy sources, such as solar power systems, wind turbines, or geothermal technology.

This payment can take the form of a tax credit, awarding taxpayers with a dollar-for-dollar payoff to lessen their tax debt for the year they initiated the investment.

These investments in green energy assets facilitate diminishing greenhouse gases emissions, providing ecological welfares by dropping one's carbon footprint. Moreover, this spending can lower an individual’s obligation on traditional energy options, economizing them long term on utility costs. In turn, supplying these incentives encourages people to invest in recyclable energy resources, ultimately leading to a decrease in global climate change elements alongside propelling the globe into a more sustainable future.

Overall, any brand new regulation on taxation allowance needs to bear mindful inspection by assembly members, carefully examining financial and revenue implications.

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The mean and standard deviation of each physician's examination room times are:

The mean and standard deviation of each physician's examination room times are found using the formulas below:

Mean = sum of values/number of values

Standard deviation,  σ = √(Σ(x-μ)² / N)

where

For Physician 1:

Sum: 36 + 26 + 27 + 30 + 27 + 32 + 23 = 201

n: 7

Mean = 201 / 7

Mean = 28.71

σ = √{(36-28.71)² + (26-28.71)² + (27-28.71)² + (30-28.71)² + (27-28.71)² + (32-28.71)² + (23-28.71)²} /7

σ = 4.67

For Physician 2:

Sum: 32 + 33 + 29 + 31 + 43 + 33 = 201

n: 6

Mean = 201 / 6

Mean = 33.5

σ  = √{(32-33.5)² + (33-33.5)² + (29-33.5)² + (31-33.5)² + (43-33.5)² + (33-33.5)²} / 6

σ = 3.37

For Physician 3:

Sum: 17 + 31 + 30 + 28 + 31 + 38 + 28 + 30 = 233

n = 8

Mean = 233 / 8

Mean = 29.13

σ = √{(17-29.13)² + (31-29.13)² + (30-29.13)² + (28-29.13)² + (31-29.13)² + (38-29.13)² + (28-29.13)² + (30-29.13)²} / 8

σ = 2.82

For Physician 4:

Sum: 28 + 35 + 33 + 25 + 33 + 35 + 42 = 231

n = 7

Mean = 231 / 7

Mean = 33

σ = √{(28-33)² + (35-33)² + (33-33)² + (25-33)² + (33-33)² + (35-33)² + (42-33)²} / 7

σ = 4.28

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The volume of the shaded portion of the cone is V = 621.667 inches³

Given data ,

Let the volume of the shaded region be V

Now , the volume of the larger cone be A

Let the volume of the smaller cone be B

Volume of Cone = ( 1/3 ) πr²h

V = A - B

And , A = ( 1/3 ) ( 9 )² ( 25 )

On simplifying , we get

A = ( 1/3 ) ( 81 ) ( 25 )

A = 675 inches³

And , B = ( 1/3 ) ( 4 )² ( 10 )

B = ( 160/3 ) inches³

So , Volume of shaded region V = A - B

V = 675 inches³ - ( 160/3 ) inches³

V = ( 1,865/3 ) inches³

V = 621.667 inches³

Hence , the volume of cone is 621.667 inches³

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Answer: 8 weeks

Step-by-step explanation:

The perimeter of the figure is 8x+16

Perimeter is a math concept that measures the total length around the outside of a shape. We can calculated perimeter is a shape by adding all the sides together.

The perimeter of circle is 2πr, where r is the radius, perimeter of a square is 4l and a parallelogram is 2(l+b)

Perimeter of a rectangle is expressed as;

P = 2(l+b)

P= 2(3x+6+x+2)

P= 2(4x+8)

P= 8x+16

Therefore the perimeter of the figure is 8x+16

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Answer:

2 1/5 or 35/14

Step-by-step explanation:

The arithmetic mean is adding all the numbers up and dividing by how many # there are.

Add:

0+2+4+3+1+1+5+0+4+3+2+5+3+2 = 35

Divide:

35/14 = 2 1/5

Answer:

2.5

Step-by-step explanation:

mean=sum of all numbers/total number

=35/14

=2.5

The value of ratio is,

⇒ 1 : 9

We have to given that;

Volume of cones are,

⇒ V₁ = 27 in³

⇒ V₂ = 343 in³

Hence, The value of ratio is,

⇒ V₁ : V₂

⇒ 27 : 243

⇒ 27 / 243

⇒ 9/81

⇒ 1 / 9

Thus, The value of ratio is,

⇒ 1 : 9

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Since the coordinates of the translated triangle are (3,5), (5, 6), and (2, 9), the translation vector is (x, y)   → (x + 2, y + 1).

In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

By translating the pre-image of this triangle vertically upward by 1 unit and horizontally right by 2 units, the coordinates of the image include the following:

(x, y)                               →                  (x + 2, y + 1)

(1, 4)                        →                  (1 + 2, 4 + 1) = (3, 5).

(3, 5)                        →                  (3 + 2, 5 + 1) = (5, 6).

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The values of μ, μ² and σ² of the random variable X in the probability density function are μ = -1/2, μ² = -3/10 and σ² = -11/20

Given that

g(x) = 6x(1 - x)

The expected value, μ is calculated as

[tex]\mu = \int\limits^a_b {x \cdot f(x)} \, dx[/tex]

So, we have

[tex]\mu = \int\limits^1_0 {x \cdot 6x(x - 1)} \, dx[/tex]

Integrate

μ = 1.5x⁴ - 2x³

So, we have

μ = 1.5(1)⁴ - 2(1)³ + 1.5(0)⁴ - 2(0)³

Evaluate

E(x) = μ = -1/2

The variable, μ² is calculated as

[tex]\mu^2 = \int\limits^a_b {x^2 \cdot f(x)} \, dx[/tex]

So, we have

[tex]\mu^2 = \int\limits^1_0 {x^2 \cdot 6x(x - 1)} \, dx[/tex]

Integrate

μ² = 3x⁴(4x - 5)/10

So, we have

μ² = 3(1)⁴(4(1) - 5)/10 - 3(0)⁴(4(0) - 5)/10

Evaluate

E(x²) = μ² = -3/10

Calculating the variance σ², we have

σ² = E(x²) - E(x)²

This gives

σ² = (-3/10) - (-1/2)²

Evaluate

σ² = -11/20

Hence, the variance is -11/20

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The identity of each of the hidden lines are:

A is a continuous thin single arrow head line.

B is a continuous thick short dashes line.

C is a long thin dashed and single dashed line.

D is a continuous thin double arrow head line.

E is a continuous thin zig-zag line.

A line is either a straight or curved path that joins to points of reference. Or it extends from one point to another point. There are various types of lines especially used in technical drawing, and each has its major purpose of use.

From the types of line given in the question, the identity of the hidden lines are;

i. A is a continuous thin single arrow head line.

ii. B is a continuous thick short dashes line.

iii. C is a long thin dashed and single dashed line.

iv. D is a continuous thin double arrow head line.

v. E is a continuous thin zig-zag line.

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The experimental probability that the next spin falls in a black region is given as follows:

0.205 = 20.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

205 out of the previous 1000 trials fell in the black region, hence the experimental probability is given as follows:

p = 205/1000

p = 0.205.

p = 20.5%.

The problem asks for the experimental probability that the next spin falls in a black region.

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The length of BE in given figure of ABCD rectangle is 7.2 units.

Given that the length of the rectangle ABCD is = 12 units

Breadth of the rectangle ABCD is = 9 units

Area of the rectangle ABCD = Length*Breadth = 12*9 = 108 square units.

In another way, In triangle ABC, BE is the height on the side AC which is diagonal of the rectangle.

So diagonal AC = square root of (12² + 9²) = square root of 225 = 15 units.

So the area of triangle ABC = (1/2)*BE*AC = (1/2)*BE*15 = 15BE/2 square units.

Since diagonal of a rectangle divides the rectangle into two similar triangles.

So the area of ABCD = 2*area of triangle ABC = 2*(15BE/2) = 15BE square units.

According to condition now,

15BE = 108

BE = 108/15 = 7.2 units

Hence, the length of BE is 7.2 units.

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