17. A biologist studying ants started on day with a population of 1500 ants. On day 2, there were 3000 ants, and on day 3, there were 4500 ants. The increase in an ant population can be represented using a geometric sequence. What is the ant population on day 5?​

The relationship between the angle of elevation and the angle of depression between two points is that they are alternate interior angles and are equal when measured from the same horizontal line.

The angle of elevation and the angle of depression are related to each other as follows. The angle of elevation is the angle between the horizontal line and the line of sight when an observer is looking upwards to an object. The angle of depression is the angle between the horizontal line and the line of sight when an observer is looking downwards to an object.

The two angles are complementary, which means that they add up to 90 degrees. This is because the horizontal line and the line of sight form a right angle.

So, if the angle of elevation is x degrees, then the angle of depression is (90 - x) degrees, and vice versa.

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A negative answer makes no sense because y is an angle and cannot be negative. As a result, we can conclude that there is no solution because the specified angles do not form a proper triangle.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

The total of a triangle's angles is 180 degrees. As a result, we may begin by locating the missing angle in the triangle containing the angle denoted by y:

Angle missing = 180° - 40° - y = 140° - y

y + 160° + 30° = 180°

Mixing like terms and calculating y:

y = 180° - 160° - 30° = -10°

A negative answer makes no sense because y is an angle and cannot be negative. As a result, we can conclude that there is no solution because the specified angles do not form a proper triangle.

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An angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.

Vertex, the intersection of two lines, is used to measure angles. Internal angles are created by the sides of geometric shapes like triangles and rectangles.

With the triangles that are presented, prove the angle bisector theorem:

There will be equality in the side ratios.

AB / BC = AD / DC

AB = 9 ; BC = 11.7 AD = 3.6

Put the values.

9/11.7 = 3.6 / AD

AD = 3.6*11.7 / 9

AD = 4.68

Thus, an angle bisector theorem is used to determine AD = 4.68 as the length of the side of the triangle AD.

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Answer:

1. It's a quadratic expression bcs the highest power in a quadratic expression is 2. Hence its in standard form. basically anything that follows ax^2 + bx + c
2. x^2-6x+8 (separate the coefficient into 2, where they add to get the coefficient number (-6), and multiply to get the number (8)
x^2-4x-2x+8 (separate it into 2 parts, and factorize each part)
x(x-4)-2(x-4)
(x-2)(x-4)
Hence, x^2-4x-2x+8 is equivalent to (x-2)(x-4)

Answer:

-8

Step-by-step explanation:

-0.5(3q+15) = 1.5(q+11)

3q + 15 = -3q - 33

6q = -48

q = -8

Step-by-step explanation:

Using the trig identity for  sin ( a- b) , this reduces to

sin ( pi/12 -7 pi/12)   = sin ( -6pi/12 )  = sin ( - pi/2)

The sum of the units 3 ft. 9 in, 4 ft. 7 in. and  10 ft. 3 in. is 18 ft. 7 in.

To add these lengths, we need to first convert all the measurements to the same units.

Let's convert everything to inches.

3 ft. 9 in. = (3 x 12) + 9 = 45 in.

4 ft. 7 in. = (4 x 12) + 7 = 55 in.

10 ft. 3 in. = (10 x 12) + 3 = 123 in.

Now we can add the lengths:

45 in. + 55 in. + 123 in. = 223 in.

We have 223 inches in total.

To convert this back to feet and inches, we can divide by 12 to get:

18 ft. 7 in.

So the final answer is 18 ft. 7 in.

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The experimental probability closest to the theoretical probability is O.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: A game has 15 balls for each of the letters B, I, N, G, O. The table shows the results of drawing balls 1,250 times.

Each letter should have the same probability of occurring since there are 15 of each.

There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability of 15/75 = 1/5 of being drawn.

This means one would expect a theoretical frequency of 1250/5 = 250, i.e. any given letter should get drawn 250 times.

Hence, the experimental probability closest to the theoretical probability is O.

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Answer:

9.9

Step-by-step explanation:

Turn Fractions into decimals. 3 3/5 turns to 3.6 and 5 1/2 turns to 5.5

Multiply them and get 19.8 and divide by 2 to get 9.9

Answer:

Step-by-step explanation:

Area = s x s. So 3 3/5 x 5 1/2 = 99/5 = 19 4/5

The speed of the wind is 10km/hr.

What is the speed?

A scalar quantity, speed is defined as the size of the change in an object's location over time or the size of the change in an object's position per unit of time.

Here, we have

Given: An airship flies 150km with the wind and then turns around and flies back, taking 6 hours and 15 minutes for the round trip.

We have to find the speed of the wind if the speed of the airship in calm weather is 50 km/hr.

150 = (50-c)(6.25-t)

6.25-t = 150/(50-c)

(6.25×50 - 6.25c -150)/(50-c) = t

t = (162.5 - 6.25c)/(50-c).....(1)

150=(50+c)t  

t = 150/(50+c)

Now, we put the value of t in equation (1) and we get

150/(50+c) = (162.5 - 6.25c)/(50-c)

150 = (50+c) (162.5 - 6.25c)/(50-c)

150 = (50+c)(162.5 - 6.25c)/(50-c)

150 = (8125 - 312.5c +162.5c - 6.25c²)/(50-c)

7500 - 150c = 8125 - 312.5c + 162.5c - 6.25c²

7500 - 150c = 8125 - 150c  - 6.25c²

7500 = 8125 - 6.25c²

8125 - 6.25c² - 7500 = 0

6.25c² - 625 = 0

c² = 100

c = 10

Hence, the speed of the wind is 10km/hr.

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The required cost of 34 inches of wire as per the cost of 23 inches of wire is 92 cents is equals to 136 cents.

Let x be the cost (in cents) of 34 inches of wire.

We know that 23 inches of wire costs 92 cents,

Use a proportion to solve this problem,

23 inches / 92 cents = 34 inches / x cents

To solve for x, apply cross-multiply and simplify,

⇒ 23 inches × x cents = 92 cents × 34 inches

⇒ 23x = 3128

⇒ x = 3128/23

⇒ x ≈ 136.00 cents

Therefore, the cost of 34 inches of wire will be approximately 136 cents.

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In conclusion Sample: A subset of the population, which could be a randomly selected group of home runs hit during one week in July of the 2014-2015 baseball season, used to estimate the average number of home runs hit during that week.

What does average number mean?

Average number is a measure of central tendency that is calculated by adding up a set of numbers and dividing the sum by the total number of numbers in the set. It is also known as the mean.

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Complete question:

What is the population and sample in a study of the number of home runs hit during one week in July of the 2014-2015 baseball season?

Population: The population in this study would be all home runs hit during one week in July of the 2014-2015 baseball season by all players and teams in the league.

Sample: The sample in this study would be a subset of the population, such as the home runs hit during one week in July of the 2014-2015 baseball season by a specific team or a specific player.

The solution of the inequality is 7 < x < 13 and graph is attached.

The inequality 5 < x - 2 < 11 represents a range of values for x that satisfy the inequality. To graph its solution, we can start by adding 2 to each part of the inequality:

5 + 2 < x - 2 + 2 < 11 + 2

This will be simplified to:

7 < x < 13

This solution represents all values of x that make the inequality true. To graph this on a number line, we can draw a line with a point at 7 and a point at 13, and shade in the region between them. The shaded region represents all values of x that satisfy the inequality.

In words, the solution can be described as follows: x is greater than 7 and less than 13. Alternatively, we can use interval notation to represent the solution as (7, 13).

It is important to note that the solution to the inequality is not a single value, but rather a range of values. The graph helps to visualize this range and make it easier to understand.

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Answer:

So first you'll want to line your numbers in order. 0,3,4,6,6,7,7,7,

The median refers to number that is in the middle, so 6 is the median.

To find the range, you subtract the biggest number with the smallest. So 9 is the range.

And 7 is the mode because it's repeated the most.

hope this helps

median:6

range: 9

mode: 7

The correct order is: 2%, 0.09, 19/100, 7/10, 0.1. We can calculate it in the following manner.

First, we need to convert all the fractions and percentages to decimals, and then we can compare them in ascending order:

0.09, 0.1, 0.02, 0.7, 0.19

Therefore, the ascending order of the given numbers is:

0.02, 0.09, 0.19, 0.7, 0.1

So the correct order is: 2%, 0.09, 19/100, 7/10, 0.1

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

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Answer:

Step-by-step explanation you have to do this

Answer:

Saanvi recorded the number of math problems she did for homework each night for 10 days.

Step-by-step explanation:

The result (f•g)(12) = 382 represents the overall cost of catering the event when 12 fewer guests than 100 attend.

In mathematics, a function is a rule that gives each input value in a set a distinct output value. It is a relationship between a collection of inputs and a set of potential outputs, where each input has a single, precise counterpart in each possible outcome. f(x) = x2, where f is the function, x is the input, and x2 is the output, is a common function notation used to represent functions. Functions are used to model and analyse interactions between variables in many branches of mathematics as well as in many fields of science and engineering.

given

We must first locate the composite function f(g(x)) before substituting x = 12 to calculate (f•g)(12):

430 - 4x = f(g(x)) = f(100 - x) = 30 + 4(100 - x)

Thus, 430 - 4x = (f•g)(x) = f(g(x)).

If we replace x with 12, we get:

(f•g)(12) = 430 - 4

(12) = 382

Interpretation: Taking into account the cost per guest as modelled by f(x) = 30 + 4x and the number of attendees as modelled by g(x) = 100 - x, the result (f•g)(12) = 382 represents the overall cost of catering the event when 12 fewer guests than 100 attend.

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Answer:

second option: 6

Step-by-step explanation:

The general term of a geometric sequence is given by: [tex]a_{n} = a_{1} r^{n-1}[/tex]

∴ [tex]a_{1}[/tex] is the first term

[tex]a_{8} = a_{1} (3)^{8-1}[/tex]

13122 = [tex]a_{1}[/tex] [tex](3)^{7}[/tex]

13122 = [tex]a_{1}[/tex] x 2187

13122/2187 = [tex]a_{1}[/tex]

6 = [tex]a_{1}[/tex]

Answer: y intercept = (0.6)

Step-by-step explanation:

plug in 0 for x since the y-intercept is when x=0. then solve the equation. 2y=12. divide both sides by 2. y=6

i’m sorry i’m not sure about the slope

Point (D) (-7, 4) must be on the graph of the inverse function F¹(x)  if point (7,-4) is on the graph of the function F(x).

If there is just one value of x in the domain where f(x)=y, then a function f does not have an inverse function.

The term "f inverse" is widely used to refer to this particular inverse function, which is singular.

A function's inverse will cause the input and output to be inverted.

If a function has an inverse, one can use algebra to find it by setting the function equal to y.

Then, swap x and y and solve for y in terms of x.

So, we have the coordinates:
(7, -4)

It lies in the 4th quadrant.

Then, its inverse would be in the 2nd quadrant.

Which would be:

(-7, 4)

Therefore, point (D) (-7, 4) must be on the graph of the inverse function F¹(x)  if point (7,-4) is on the graph of the function F(x).

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Answer:

Step-by-step explanation:

it's (-4,7)

The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

A numerical expression is characterized as the assortment of numbers factors and works by utilizing operations like expansion, deduction, multiplication, and division.

Considering that;

The expression is,

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

Presently, We can place x and y in the above expression as;

⇒ ([x/(y - 1)](- 4) - [xy + (- 3)]/(- 1)

⇒ [- 5/(- 2 - 1) ] (- 4) - [-5×-2 + (- 3)]/(- 1)

⇒ [ - 5/ - 3 ] (- 4) - [10 - 3]/(- 1)

⇒ - 20/3 + 7

⇒ 1/3

In this way, The worth of expression at x = - 5 and y = - 2 is,

⇒ 1/3

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Answer:

28

Step-by-step explanation:

2x+10+2(5y+3)

2×1+10+2(5×1+3)

2+10+10+6

28

In Linear equation, 5/8 golf balls per ounce are the number of golf balls per Ounce.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Number of golf balls (n) = 20

Total weight (w) = 32 ounces

total weight = number of balls (n) * weight of 1 golf ball

∴ weight of 1 golf ball = w/n =32/20 ounces

⇒ the weight distribution is 1.6 ounce per golf ball

Now, apply unitary method :

32 ounces is total weight of 20 golf balls

∴ 1 ounce amounts to 20/32 golf balls

⇒ there are 5/8 golf balls per ounce

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Based on proportions, the numbers of students in the senior form and junior form are 615 and 885, respectively.

Proportion refers to the equation of two ratios.

Proportion is a fractional value depicted using ratios, percentages, fractions, and decimals.

The percentage of senior form students in the school = 41%

The percentage of junior form students = 59% (100% - 41%)

The additional percentage of junior over senior students = 18% (59% - 41%)

The additional number of junior form students over the seniors = 270

Proportionately, if 18% = 270, the total number of students (both junior and senior) = 1,500.

Therefore, the number of senior and junior students is as follows:

Check:

The difference in the numbers = 270 (885 - 615)

Thus, using proportions, we can state that there are 1,500 students in the school, consisting of 615 seniors and 885 juniors.

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The graph should show a parabolic shape, opening upwards. The points are (0,0), (0.5, 2.5), (1,5), (1.5, 22.5), and (2,20).

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output.

Using the table provided, we can fill in the values for distance traveled:

Given function d=5t²

Putting t=0, d=0

t=0.5, d=1.25

t=1, d=5

t=1.5, d=11.25

t=2, d=20

Hence, d(meters) are 0,1.25,5,11.25 and 20.

To plot this data on a coordinate plane, we can use the values of t as the x-coordinates and the values of d as the y-coordinates.

The graph should show a parabolic shape, opening upwards. The points (0,0), (0.5, 2.5), (1,5), (1.5, 22.5), and (2,20) should be plotted and connected with a smooth curve.

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The angle measures that satisfy cos theta = 1/2 are

To find all angle measures for which cos theta = 1/2, we can use the unit circle and look for the x-coordinate of the point where the angle intersects the unit circle.

The x-coordinate (cosine) is equal to 1/2 at two points on the unit circle:

However, the given angle measures are not all within one revolution (360 degrees or 2pi radians), so we need to find equivalent angles within one revolution.

To do this, we can add or subtract multiples of 360 degrees or 2pi radians from the given angles until they are within one revolution.

-120° = 360° - 120° = 240°

-60° = 360° - 60° = 300°

120° = 120°

600° = 600° - 1(360°) = 240°

660° = 660° - 2(360°) = 60°

So the angle measures that satisfy cos theta = 1/2 are -120° (or 240°), -60° (or 300°), and 660° (or 60°).

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The measure of angle x and y in the cyclic quadrilateral are 93 and 59 degrees.

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. The sum of angles in a cyclic quadrilateral is 360 degrees.

The opposite angles in a cyclic quadrilateral add up to 180°. The opposite angles of a cyclic quadrilateral are supplementary.

Therefore, let's find the measure of x and y in the cyclic quadrilateral.

Hence,

x + 87 = 180

x = 180 - 87

x = 93 degrees

y + 121 = 180

y = 180 - 121

y = 59 degrees

Therefore,

x = 93°

y = 59°

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To find the value of x in the triangle, we can use the law of sines, which states that in any triangle ABC, the following relationship holds:

a/sin A = b/sin B = c/sin C

where a, b, and c are the side lengths of the triangle opposite to the angles A, B, and C, respectively.

In this case, we can write:

x/sin 80° = 7/sin 50°

Using the properties of sines, we can simplify this expression to:

x = (7 x sin 80°) / sin 50°

Using a calculator, we can evaluate this expression to get:

x ≈ 9.05

Therefore, the value of x in the triangle is approximately 9.05.

For this situation, the example size is 45 and the standard deviation is 3.1 inches, which is known. Hence, a one-example t-test is fitting for testing the scientist's hypothesis about the normal length of salmon getting back to generate from the Alaskan waterway.

The proper test for the scientist's hypothesis that the typical length of salmon getting back to generate from an Alaskan river is not exactly the verifiable normal length of 24 inches is a one-example t-test for a populace mean.

This is on the grounds that the specialist is looking at the example mean length (22 inches) to a realized verifiable populace mean (24 inches), and needs to decide whether the contrast between the two means is measurably huge. A one-example t-test is utilized to contrast an example mean with a realized populace mean and is suitable when the example size is little and the populace standard deviation is obscure.

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