Answer the questions below to determine what kind of function is depicted below

If the kitchen is drawn 2 1/2 inches by 3 inches, the actual dimensions of the kitchen are 12.5 feet by 15 feet.

The given scale of 1 inch:5 feet means that for every 1 inch on the floor plan, the actual length in real life is 5 feet. To find the actual dimensions of the kitchen, we need to convert the length and width of the kitchen on the floor plan into real-life measurements.

The length of the kitchen on the floor plan is 2 1/2 inches, which in real life would be:

2.5 inches x 5 feet/1 inch = 12.5 feet

Similarly, the width of the kitchen on the floor plan is 3 inches, which in real life would be:

3 inches x 5 feet/1 inch = 15 feet

To verify this result, we can also use the scale to convert the actual dimensions of the kitchen back into the measurements on the floor plan. The length of the kitchen in real life is 12.5 feet, which on the floor plan would be:

12.5 feet x 1 inch/5 feet = 2.5 inches

Similarly, the width of the kitchen in real life is 15 feet, which on the floor plan would be:

15 feet x 1 inch/5 feet = 3 inches

As expected, these measurements match the dimensions of the kitchen as drawn on the floor plan.

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The measure of ∠L in Triangle JKL is 56.1 degrees.

In geometry, the measures in triangles refer to the angles and sides within a triangle. Triangles are three-sided polygons, and the measures of their angles and sides are important properties that determine their shape and characteristics.

In a triangle, the sum of the measures of all three angles is always 180 degrees. Therefore, to find the measure of ∠L in Triangle JKL, we can use the information given:

∠J is congruent to ∠L, which means they have the same measure.

∠K is given as 67.8 degrees.

Since ∠J is congruent to ∠L, we can denote their measure as "x".

So, the sum of the measures of ∠J, ∠K, and ∠L is 180 degrees:

∠J + ∠K + ∠L = 180

Substituting the given values:

x + 67.8 + x = 180

Simplifying the equation:

2x + 67.8 = 180

Subtracting 67.8 from both sides:

2x = 180 - 67.8

2x = 112.2

Dividing both sides by 2:

x = 112.2 / 2

x = 56.1

Hence, the measure of ∠L in Triangle JKL is 56.1 degrees.

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The probability of this random list is therefore the same as the example's random list, which is 25%.

To determine the number of groups containing at least three girls, we need to count the number of groups where there are at least 3 numbers between 0 and 4.

We can do this by counting the number of groups that have 0, 1, or 2 numbers between 0 and 4, and subtracting this from the total number of groups:

Number of groups with 0, 1, or 2 numbers between 0 and 4:

Number of groups with 0 numbers between 0 and 4 = 6 choose 0 * 94 choose 4 = 5,414,200

Number of groups with 1 number between 0 and 4 = 6 choose 1 * 94 choose 3 = 291,301,200

Number of groups with 2 numbers between 0 and 4 = 6 choose 2 * 94 choose 2 = 5,111,640

Total number of groups = 100 choose 5 = 75,287,520

Number of groups with at least 3 numbers between 0 and 4:

= Total number of groups - Number of groups with 0, 1, or 2 numbers between 0 and 4

= 75,287,520 - (5,414,200 + 291,301,200 + 5,111,640)

= 64,460,480

The amount of groups of this random list is the same as the example's random list (both have 100 groups).

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There is no fixed number of trials, so X is not a binomial variable. (Choice B) B is the right response.

Discrete random variables are within the category of binomial random variables. A binomial random variable keeps track of how frequently an event occurs over a predetermined number of trials. ALL of the following prerequisites have to be satisfied for a variable to qualify as a binomial random variable:

A predetermined sample size (number of trials) is used.

The relevant occurrence either takes place or doesn't in every trial.

On each trial, the likelihood of occurrence (or not) is the same.

Trials run separately from one another.

While Yoshi has a 30% chance of success for each shot and the trials are independent, the number of attempts is not fixed, as he continues until he makes the shot.

Thus, the correct answer is (Choice B) B. There is no fixed number of trials, so X is not a binomial variable.

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The height of the cuboid, after calculations, in the form (a+ b√3)m, is (6√3 - 9)/47 meters.

Let the height of the cuboid be h meters. The area of the square base is given by:

(2 + √3)² = 4 + 4√3 + 3 = 7 + 4√3 m²

The total surface area of the cuboid is the sum of the areas of the six rectangular faces. Since the base is a square, the area of each of the four vertical rectangular faces is also (2 + √3) × h = (2h + h√3) m². Therefore, we have:

Total surface area = 4(7 + 4√3) + 2(2h + h√3)(2 + √3) = 8h + 26 + (22 + 16√3)h

Since we know that one of the sides has area (2√3 - 3) m², we can set up another equation:

(2h + h√3)(2 + √3) = 2√3 - 3

Expanding the left side and simplifying, we get:

(2h + h√3)(2 + √3) = 2√3 - 3

4h + 7h√3 = 2√3 - 3

h(4 + 7√3) = 2√3 - 3

h = (2√3 - 3)/(4 + 7√3)

We can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:

h = [(2√3 - 3)/(4 + 7√3)] × [(4 - 7√3)/(4 - 7√3)]

h = (8√3 - 12 - 14√3 + 21)/(16 - 63)

h = (9 - 6√3)/(-47)

h = (6√3 - 9)/(47)

Therefore, the height of the cuboid is (6√3 - 9)/47 meters.

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The value of m by the given data is m=2

We are given that;

Number of elephants= 125000gram

The mass of african elephant= 3 x 10

Now,

To find the values of b and c, we need to write the given masses in scientific notation, which means that the coefficient must be between 1 and 10. For example, 6 x 10 grams is not in scientific notation, because 6 is not between 1 and 10. To fix this, we need to move the decimal point one place to the left and increase the exponent by one. We get:

6x106 grams=6.0x106 grams=6.0x106−1×101 grams=6.0x105×101 grams=6.0x105+1 grams=6.0x107 grams

Similarly, for the silverback gorilla, we get:

2x105 grams=2.0x105 grams=2.0x105−1×101 grams=2.0x104×101 grams=2.0x104+1 grams=2.0x105 grams

Therefore, the values of b and c are b=7,c=5

To find the value of m, we need to divide the mass of the African elephant by the mass of the silverback gorilla and write the result in scientific notation. We get:

Mass of silverback gorillaMass of African elephant​=2.0x105 grams6.0x107 grams​=2.06.0​×105107​=3.0×107−5=3.0×102

Therefore, by unitary method the answer will be m=2.

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Answer:

"Querido hijo, estás despedido" es una novela juvenil escrita por Jordi Sierra i Fabra que se divide en 17 capítulos. A continuación, se presenta un breve resumen de cada uno de ellos:

Capítulo 1: El protagonista, Leo, es un adolescente que vive en un hogar en el que sus padres son muy estrictos y le exigen que saque buenas notas en la escuela.

Capítulo 2: Leo tiene una discusión con su padre, quien le dice que si no mejora sus notas, lo echará de casa.

Capítulo 3: Leo tiene un accidente de bicicleta y es atendido por la enfermera del colegio, la señorita Rovira.

Capítulo 4: Leo recibe la noticia de que su padre ha muerto en un accidente de tráfico.

Capítulo 5: En el funeral de su padre, Leo se siente alejado de su familia y amigos.

Capítulo 6: Leo recibe una carta de su padre en la que le explica que ha dejado un testamento y que su hermana mayor, Berta, será la administradora de la herencia.

Capítulo 7: Berta le comunica a Leo que su padre le ha dejado una empresa de limpieza y que él será el encargado de dirigirla.

Capítulo 8: Leo descubre que la empresa está en quiebra y que tendrá que tomar medidas drásticas para salvarla.

Capítulo 9: Leo empieza a tomar el control de la empresa y a hacer cambios en su funcionamiento.

Capítulo 10: Leo contrata a un joven llamado Iván, quien se convierte en su mano derecha en la empresa.

Capítulo 11: Leo se encuentra con la señorita Rovira, quien lo ayuda a tomar una importante decisión en la empresa.

Capítulo 12: Leo tiene una reunión con los trabajadores de la empresa y les comunica los cambios que va a hacer.

Capítulo 13: Leo se siente muy presionado por las exigencias de la empresa y se desahoga con su amigo Santi.

Capítulo 14: Leo tiene un encontronazo con su hermana Berta, quien intenta influir en la gestión de la empresa.

Capítulo 15: Leo descubre que Iván le ha estado robando dinero a la empresa y tiene que tomar medidas para solucionar el problema.

Capítulo 16: Leo consigue salvar la empresa y hace balance de lo que ha aprendido en el proceso.

Capítulo 17: La historia termina con Leo en paz consigo mismo y con su familia, habiendo aprendido importantes lecciones sobre la vida y el trabajo.

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Answer:

48

Step-by-step explanation:

can be divided into two 4x6 rectangles. Therefore, the area is 4x6 + 4x6 = 48

If the area of a triangle is half of its base times height then the reasonable value of x is = 4.

A triangle-shaped table top with an area of 324 square inches has a base of 8x+4 inches and a height of 4x+2 inches. Given that the area of a triangle is half of its base times height, we can use the formula:

Area = (1/2) * base * height

Plug in the given values:

324 = (1/2) * (8x + 4) * (4x + 2)

Now, we need to solve for x. Follow these steps:

1. Multiply both sides of the equation by 2 to get rid of the fraction:

2 * 324 = (8x + 4) * (4x + 2)

2. Simplify the equation:

648 = (8x + 4) * (4x + 2)

3. Expand the equation by multiplying the terms in the parentheses:

648 = 32x^2 + 16x + 16x + 8

4. Combine like terms:

648 = 32x^2 + 32x + 8

5. Move all terms to one side of the equation to set it equal to zero:

32x^2 + 32x - 640 = 0

Now, we need to find a reasonable value of x. You can solve this quadratic equation using factoring, the quadratic formula, or a graphing calculator. Using a graphing calculator, we find that x is approximately 4.

Therefore, a reasonable value of x in this situation is 4.

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The percentage of males attending the sporting events that are adults is:

65.10%.

A percentage is one example of a proportion, as it is obtained by the number of desired outcomes divided by the number of total outcomes, and then multiplied by 100%.

The number of males attending sporting events is given as follows:

1235.

Of those 1235 males, 804 are adults, hence the percentage of males attending the sporting events that are adults is given as follows:

p = 804/1235 x 100%

p = 65.10%.

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The number of cubes of dimensions of [tex]\frac{1}{8}[/tex] foot that can fit into a rectangular prism of a length of 1 foot, a width of 1 [tex]\frac{3}{8}[/tex] foot, and a height of [tex]\frac{5}{8}[/tex] foot is 55.

Volume of cuboid = l * b * h

where l is the length

b is the breadth

h is the height

l = 1 foot

b = 1 [tex]\frac{3}{8}[/tex] foot = [tex]\frac{11}{8}[/tex] foot

h = [tex]\frac{5}{8}[/tex] foot

Volume of cuboid = 1 * [tex]\frac{11}{8}[/tex] * [tex]\frac{5}{8}[/tex]

= [tex]\frac{55}{64}[/tex] cubic foot

Volume of cube = [tex]s^3[/tex]

where s is the side

s = [tex]\frac{1}{8}[/tex] foot

Volume = [tex]\frac{1}{8}^3[/tex]

= [tex]\frac{1}{64}[/tex] cubic foot

Number of cubes = [tex]\frac{\frac{55}{64} }{\frac{1}{64} }[/tex]

= 55

The number of cubes that fit into the prism is 55.

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Answer:

1) 15.625% increase. 1850-1600=250. 250/1600=0.15625. 0.15625x100= 15.625.

2) 50%

Step-by-step explanation:

1) 1850-1600=250. 250/1600=0.15625. 0.15625x100= 15.625.

2) 75-50=25. 25/50=0.5. 0.5x100=50

The area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.

To find the area of a regular hexagon, you can use the formula , where A is the [tex]A =\frac{3\sqrt{3} }{2} (s^{2} )[/tex]area, s is the length of one side, and √3 is the square root of 3.

However, since the apothem length is given, you can also use the formula , where ap is the apothem length and p is the perimeter of the hexagon.

First, let's find the perimeter of the hexagon. Since a hexagon has six sides, the perimeter will be 6 x 12.7 = 76.2.

Next, we can use the apothem length of 11 and the side length of 12.7 to find the length of the radius of the circle inscribed in the hexagon. This is because the apothem is the distance from the center of the hexagon to the midpoint of any side, and the radius is the distance from the center to any vertex.

Using the Pythagorean theorem, we can find the radius:
[tex]r^2 = ap^2 + (\frac{s}{2} )^{2}[/tex]
[tex]r^2 = 11^2 + (\frac{12.2}{7} )^{2}[/tex]
[tex]r^2 = 121 + 40.1225[/tex]
[tex]r^2 = 161.1225[/tex]
[tex]r = \sqrt{161.1225}[/tex]
[tex]r = 12.69[/tex]

Now that we know the radius, we can use the formula for the area of a regular polygon in terms of the radius: A = (1/2) x r x ap x n, where n is the number of sides (which is 6 for a hexagon).

Plugging in the values we have:
[tex]A = \frac{1}{2} (12.69)(11)(6)[/tex]
[tex]A = 416.61[/tex]

Therefore, the area of the regular hexagon with a side length of 12.7 and apothem length of 11 is approximately 416.61 square units.

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The value of length ZY in nearest 10th place is 1,240.8 units.

The value of length ZY is calculated as follows;

Considering triangle XYZ;

tan 60 = ZY/XY

tan 60 = (ZY)/(240 + n)

ZY = 1.732(240 + n)   ------ (1)

Considering triangle WYZ;

tan 69 = ZY/WY

tan 69 = ZY/n

n = ZY/tan69

n = 0.384(ZY) ---------- (2)

The length ZY is calculated as;

Substitute the value of n into equation (1)

ZY = 1.732(240 + 0.384ZY)

ZY = 415.68 + 0.665ZY

0.335ZY = 415.68

ZY = 415.68 / 0.335

ZY = 1,240.8 units

From equation (2);

n = WY = 0.384 (1,240.8)

WY = 476.5 units

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The given data is tabulated for conditional relative frequency table as follows.

Total male = 145, Total female = 139

Total male votes for Santiago = 68, Total female votes for Measha = 89

Total female votes for Santiago = 50, Total male votes for Measha = 77

Now total votes for Santiago = 68+50=118

Total votes for Measha = 166

Total votes casted = 284

The above data is formulated in tables attached below.

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The difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.

The range of the 95% confidence interval for the actual difference between the proportions of probable voters who would support this candidate before and after the debate was (-0.014, 0.064). To find the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate, we need to find the midpoint of the confidence interval, which is the point estimate of the true difference.

In the given question, the interval is (-0.014, 0.064), then the expression for the likely difference is

(0.064 + (-0.014))/2 = 0.050/2

= 0.025

Hence, the difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.

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Answer:

92°

Step-by-step explanation:

All angles should add up to 360°

Opposite angles are equal so that means two angles are 88°

88+88=176

360 - 176 = 184

184 / 2 = 95

Measure of angle A is 92°

Based on the data, we can infer that Kallie needs 6 teaspoons of water conditioner for the 12 fish tanks.

To calculate how many teaspoons of water conditioner we must take into account the information on the capacity of each tank:

In accordance with the above, we do the following logical procedure.

We multiply the capacity of each tank by the number of tanks.

So we need 60 gallons of water to fill the tanks, and we divide by 10 to find how many teaspoons we need to fill all 12 tanks.

Based on the above, we need 6 teaspoons to condition the water in the 12 tanks.

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The option that represents the resulting transformation is: Option C

A reflection over line is defined as a transformation in which each point of the original figure which is also called the pre-image possesses an image that is the essentially the same distance from the reflection line as the original point, but then is on the opposite side of the line. In a reflection, the image is the same size and shape as the pre-image.

Now, looking at the letter Q, when we reflect it once, it should be the mirror image but when reflect it the second time about same line, it becomes exactly the original copy.

Thus, we can conclude that Option C represents the resulting transformation.

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Using the compounding interest formula:

a) His ending balance after the year will be $7,658.91.

b) The amount of interest he will earn is $358.91.

c) His annual percentage yield is 4.9166%.

a) To calculate the ending balance after one year, we'll use the compound interest formula: A = P(1 + r/n)^(nt), where A is the ending balance, P is the principal ($7,300), r is the interest rate (4.85% or 0.0485), n is the number of compounding periods per year (4 for quarterly), and t is the number of years (1).

A = 7300(1 + 0.0485/4)^(4*1) = 7300(1.012125)⁴ = 7300*1.049166 = $7,658.91

b) To find the interest earned, subtract the principal from the ending balance: Interest = A - P

Interest = $7,658.91 - $7,300 = $358.91

c) To calculate the annual percentage yield (APY), we'll use the formula: APY = (1 + r/n)^(n) - 1

APY = (1 + 0.0485/4)⁴ - 1 = 1.049166 - 1 = 0.049166 or 4.9166%

Paul's ending balance after one year is $7,658.91, he earns $358.91 in interest, and his annual percentage yield is 4.9166%.

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The value of the trigonometric expression sin c - cos c is: s - r

The three most common trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We are given that:

sinb = r and cos b = s

Thus, from the diagram attached, we can see that:

sin B = rh/h = r

cos B = sh/h = s

Thus, using trigonometric ratios, we can equally say that:

cos C = rh/h = r

sin C = sh/h = s

Thus:

sin c - cos c = s - r

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It should be noted that to craft a triangle with an edge measuring 5 units of length, another side 7 units in magnitude, we can get underway by sketching an uninterrupted line of 7-units duration.

Subsequently, draw an additional segment arriving at a peak of 5-units from the starting point of the former line. From the end-point of the line calculated as 7 units, draw a joined line towards the conclusion of the 5 unit-length section. This enables two distinctive triangles:

Also, to guarantee that just a single triangle can be drawn, it is imperative to recognize the angle resting between the two assigned sides. In case we are endowed with the inclination between both varying lengths of five and seven units, then only an original composition of triangle can be constructed.

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The Taylor series for f centered at 9, given f^(n)(9) = (-1)^n n!/6^n (n + 2), is f(x) = f(9) - (x-9)/2 + (x-9)^2/12 - (x-9)^3/432 + (x-9)^4/10368 - ... .

To find the Taylor series for f centered at 9, we need to use the formula

f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

where f'(x) represents the first derivative of f(x) with respect to x, f''(x) represents the second derivative of f(x) with respect to x, and so on.

In this case, we are given the nth derivative of f(x) evaluated at x = 9, so we can plug in the values and simplify the formula

f(9) = f(9) (since we're centering the series at 9)

f'(9) = (-1)^1 (1!/6^1)(1 + 2) = -1/2

f''(9) = (-1)^2 (2!/6^2)(2 + 2) = 1/6

f'''(9) = (-1)^3 (3!/6^3)(3 + 2) = -1/36

f''''(9) = (-1)^4 (4!/6^4)(4 + 2) = 1/216

and so on. So the Taylor series for f centered at 9 is

f(x) = f(9) - (x-9)/2 + (x-9)^2/2! * 1/6 - (x-9)^3/3! * 1/36 + (x-9)^4/4! * 1/216 - ...

or, simplifying the coefficients

f(x) = f(9) - (x-9)/2 + (x-9)^2/12 - (x-9)^3/432 + (x-9)^4/10368 - ...

This is the Taylor series for f centered at 9, based on the given information.

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The given question is incomplete, the complete question is:

Find the Taylor series for f centered at 9 if f^(n)(9) = (-1)^n n!/6^n (n + 2)

Anita will take 5 more weeks to save enough money for the snowboard. when she saved $43. 75 of the $112. 50 that she needs for a new snowboard.

Given data :

Total money needs for a new snowboard = $112. 50

Anita saved money = $43. 75

Money saved each week = $13. 75

From the given data we can write the equation to find the number of weeks  as,

13. 75w + 43. 75 = 112. 50

By solving the equation 13.75w + 43.75 = 112.50 we can find out how many more weeks it will take Anita to save enough money for the snowboard by using the elimination method.

Subtracting 43.75 from both sides of the equation, we get:

13.75w + 43.75 - 43.75 = 112.50 - 43.75

13.75w = 68.75

w = 68.75 / 13.75

w = 5

Therefore, Anita will take 5 more weeks to save enough money for the snowboard.

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Power is the rate at which work is done or energy is transferred. In this case, the girl used a force of 98 N to lift the painting to a height of 0.5 m in 0.75 seconds, resulting in 49 J of work done. The power used was calculated to be approximately 65.33 watts.

To calculate the power used by the girl while lifting the painting, we need to use the formula: Power (P) = Work (W) / time (t).

Firstly, we need to calculate the work done by the girl in lifting the painting. Work is defined as the product of force and distance. As there is no information about the force applied, we will assume that the girl lifted the painting with a constant force. Therefore, the work done can be calculated as:

Work (W) = force x distance

Here, the distance is 0.5 m, and we can use the formula for weight to calculate the force required to lift the painting. As we know that the mass of the painting is not given, we can assume it to be 10 kg (a medium-sized painting).

Weight (Wt) = mass x acceleration due to gravity
Wt = 10 kg x 9.8 m/s² = 98 N

Therefore, the work done by the girl is:

W = 98 N x 0.5 m = 49 J

Now, we can use the formula for power to calculate the power used by the girl.

P = W / t
P = 49 J / 0.75 s
P = 65.33 W (approx.)

Therefore, the girl used approximately 65.33 watts of power while lifting the painting.

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The girl used 65.3 watts of power to lift the painting.

To calculate power, we need to know the work done and the time taken.

We can use the formula:

power = work/time

The work done is equal to the force applied multiplied by the distance moved. Since we don't know the force, we can use the formula for work in terms of mass, gravity, and height:

work = mgh

where m is the mass, g is the acceleration due to gravity, and h is the height lifted.

Assuming the painting has a mass of 10 kg and the acceleration due to gravity is 9.8 m/s², the work done is:

work = (10 kg) x (9.8 m/s²) x (0.5 m) = 49 J

The time taken is 0.75 seconds.

So the power used is:

power = work/time = 49 J / 0.75 s = 65.3 watts

Therefore, the girl used 65.3 watts of power to lift the painting.

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The density of deer for 400 square miles is around 1:4 based on stated number of deers.

The density of deer will be given by the formula -

Population density of deer = number of deer/ area

Population density is the amount or number of individuals of a population on land per unit area.

Keep the value in formula to find the population density

Population density = 100/400

Cancelling zero as common in both numerator and denominator

Population density = 1:4

Thus, there is 1 deer for every 4 square mile.

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The LCM of 8 and 9 is 72. The GCF of 35 and 63 is 7.35 + 63 can also be written as 7 X 14.

Part A

Here we have been given 2 numbers 8 and 9. We need to find the LCM. LCM is the Lowest Common Multiple. It is the smallest number which can be divided by all the mentioned number. To take the LCM of 8 and 9 we first will factorize them

8 = 2 X 2 X 2

9 = 3 X 3

Here we see that 8 and 9 do not have any common factor. Hence we need to simply multiply them together to get

8 X 9 = 72

Part B.

We need to find GCF of 35 and 63. GCF or the Greatest common factor is the highest number that can divide all the given numbers. Here too we will first factorize 35 and 63.

35 = 5 X 7

63 = 3 X 3 X 7

Here we see that between the numbers, 7 is the only common factor

Hence, 7 is the GCF.

63 can also be written as 63 = 7 X 9

Hence we can write 35 + 3

= (7 X 5) + (7 X 9)

Taking 7 common we get

7(5 + 9)

= 7 X 14

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Considering "line-segment" defined by points A(0, 1) and B(4,6), then  effects of reflection across the "x-axis" are :

(b) The "y-coordinate" of "end-points" become opposites in sign.

(e) The length of reflection of AB is same as length of line-segment AB.

When reflecting a line segment across the x-axis, the x-coordinates of all points remain the same, but the y-coordinates become their opposites.

So, for the line segment AB, the x-coordinate of point A remains 0, and the x-coordinate of point B remains 4. However, the y-coordinate of point A becomes -1, and the y-coordinate of point B becomes -6. This results in a new line segment A'(0, -1) and B'(4, -6).

Since the reflection is across a horizontal line, the length of the reflection is the same as the length of the original segment.

Therefore, the correct options are (b) and (e).

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