The number we are looking for is N = 2 × 2^3 × 3^2 = 72.
Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say
n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k
then the number of divisors of n is given by
d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).
Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form
N = p_1^2 × p_2^2, or N = p_1^7,
where p_1 and p_2 are distinct prime numbers.
Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that
N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,
and
N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,
where q_1, q_2, r_1, and r_2 are distinct prime numbers.
To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by
p_1 = q_1^a × q_2^b,
p_2 = r_1^c × r_2^d,
N/2 = q_1^e × q_2^f,
N/3 = r_1^g × r_2^h.
Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:
a + 1 × (b + 1) = e + 1 × (f + 1) = 4,
c + 1 × (d + 1) = g + 1 × (h + 1) = 4,
2a × 2b = ef,
2c × 2d = gh.
We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get
(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.
We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.
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Maria downloads an unknown number of apps on her tablet in the month of June
The average number of applications downloaded in the month of June on the regular basis is calculated to be 5 apps.
Let's suppose that the unknown number of apps are downloaded in the month June i.e. suppose "x".
We know that the average number of apps downloaded daily in the previous month is 10. If we assume that the previous month has 30 days, then the total number of apps downloaded in the previous month is:
30 days × 10 apps/day = 300 apps
We also know that the total number of apps downloaded in June is half of the total number of apps downloaded in the previous month i.e. May. Therefore:
x = 1/2 × 300 apps
x = 150 apps
To find the average number of apps downloaded in June, we can divide the total number of apps downloaded in June by the number of days in June. If we assume that June has 30 days, then:
Average number of apps downloaded in June = 150 apps / 30 days
Average number of apps downloaded in June = 5 apps/day
Therefore, Maria downloaded an average of 5 apps per day in the month of June.
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The complete question is :
Maria downloads an unknown number of apps on her tablet in the month of June. The average of the number of apps downloaded daily in the previous month is 10. If the total number of apps downloaded in June is half of the total number of apps downloaded in previous month, find the average number of apps downloaded in June.
Select all the conclusions you can draw if you know that <1 is congruent to <8?
Knowing that <1 is congruent to <8 allows us to draw the following conclusions: The angles <1 and <8 have the same measure. They are alternate interior angles formed by a transversal intersecting two parallel lines. If <1 is part of a triangle or polygon, then <8 is also part of that same triangle or polygon.
What is Polygon?
In geometry, a polygon is a two-dimensional shape that is made up of straight lines. It is a closed figure with three or more line segments that connect at their endpoints to form a closed shape.
Polygons can have any number of sides, but they must have at least three sides. Some examples of polygons include triangles, rectangles, squares, pentagons, hexagons, and so on.
The properties of a polygon, such as its angles and sides, can be calculated and analyzed using mathematical formulas and principles. Polygons are commonly used in geometry, architecture, engineering, and many other fields.
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which statement about systematic errors is true? a.) they can occur when a selection bias is present. b.) they can be corrected by using a larger sample size. c.) they can be challenging to notice. d.) they can be eliminated if observations are repeated.
The statement about systematic errors that is true is: They can occur when a selection bias is present.
Systematic errors can be defined as a type of error that affects the accuracy of the results of an experiment or study. It is mostly caused by the tools, materials, or a particular problem with the instrument used in the experiment. A systematic error can be of different types, including the following:
Scale Error: Scale errors occur due to calibration issues. They can occur due to a problem with the measuring instruments, which may not provide accurate readings during an experiment.
Selection Bias: It occurs when a researcher deliberately selects a certain group of individuals or data that are not representative of the general population. This can lead to inaccurate results for the study.
Resolution Error: This error is common when researchers do not choose the correct measurement tools to measure the variables of interest.
Therefore, option A is correct. This is because systematic errors can occur when a selection bias is present.
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what is the assertiveness
Answer:
Confident or forceful behaviour
Step-by-step explanation: I have a dictionary
please help me solve this problem
Answer:
549.61
Step-by-step explanation:
5.5*10^2-3.9*10^-1
5.5*100-3.9*0.1
550-0.39
549.61
Answer:
Scientific notation: 5.4961 × 10²
Standard form: 549.61
Step-by-step explanation:
Scientific notation is written in the form [tex]a\times 10^n[/tex], where [tex]1 \leq a < 10[/tex] and [tex]n[/tex] is any positive or negative whole number.
To subtract two numbers in scientific notation, first write the numbers in the same form, with the same exponent (power of 10).
To convert 3.9 × 10⁻¹ so that the base 10 has an exponent of 2, move the decimal point 3 places to the left and add 3 to the exponent:
[tex]\implies 3.9 \times 10^{-1} = 0.0039 \times 10^2[/tex]
Therefore, we now have:
[tex]5.5 \times 10^2 - 0.0039 \times 10^2[/tex]
Factor out the common term 10⁻¹:
[tex]\implies (5.5 - 0.0039) \times 10^2[/tex]
Subtract the numbers:
[tex]\implies 5.4961 \times 10^2[/tex]
The answer has been given in scientific notation. If the answer should be in standard form then:
[tex]\implies 5.4961 \times 10^2=549.61[/tex]
Factorise 4x squared - 1
Answer:
(2x + 1) (2x-b)
Increase 80g by 25%
Help me i’ll give you 15 points!
Answer:
To increase 80g by 25%, you need to find 25% of 80 and then add that to 80.
25% of 80 is (25/100) x 80 = 20
So, to increase 80g by 25%, you add 20g to 80g:
80g + 20g = 100g
Therefore, an increase of 25% on 80g is 100g.
Step-by-step explanation:
If |z – 2| = |z – 6| then locus of z is given by :
a) a straight line parallel to x axis
b) none of these
c) a straight line parallel to y axis
d) a circle
c) The locus of z is a straight line parallel to the y-axis for x = 4.
What is a locus of line?The locus of a line is the set of all points that satisfy a given geometric condition related to that line. The term "locus" refers to the path or trajectory followed by a point or set of points that satisfy the given condition.
To determine the locus of z in the given equation |z-2| = |z-6|, we can use the definition of the absolute value of a complex number which is
[tex]|x + iy| = \sqrt{(x^2 + y^2)}[/tex]
So, we can square both sides of the given equation to get:
[tex]|z-2|^2 = |z-6|^2[/tex]
put z = (x + iy)
[tex]|x+iy-2|^2 = |x+iy-6|^2\\|(x-2)+iy|^2 = |(x-6)+iy|^2\\[/tex]
[tex][\sqrt{((x-2)^2 + y^2)} ]^{2} = [\sqrt{((x-6)^2 + y^2)} ]^{2}[/tex]
x² + 4 - 4x = x² + 36 - 12x
after simplification, x = 4
Therefore, the locus of z is a straight line parallel to the y-axis passing through the point x = 4.
Hence, the correct option is (c) a straight line parallel to the y-axis.
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The table gives some information about the heights of 30 plants.
Height, h in cm
Frequency
0
1
10 < h < 20
9
20 < h < 30
7
30 < h < 40
13
Which class interval contains the median?
Select your answer.
0sh<10 10 sh<20 20 sh<30 30 sh <40
A
B
D
the class interval that contains the median is "30 < h < 40".
What is median ?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the centre of a sequence to determine its value.
To calculate the cumulative frequency, we add the frequency of each class interval to the sum of frequencies of all previous class intervals.
Height, h in cm Frequency Cumulative Frequency
0 1 1
10 < h < 20 9 10
20 < h < 30 7 17
30 < h < 40 13 30
The total frequency is 30, which is an even number. To find the median, we need to find the value that lies in the middle of the dataset. Since the total frequency is even, the median will be the average of the two middle values.
The two middle values will be the 15th and 16th value. To find the corresponding class interval, we look at the cumulative frequency column and find the interval that contains the 16th value.
The 16th value is in the "30 < h < 40" interval, which means that this interval contains the median.
Therefore, the class interval that contains the median is "30 < h < 40".
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growth models like those used in forecastx usually model situations well where a process grows multiple choice a. until reaching saturation. b. at a more or less constant rate. c. at an exponential rate. d. in a linear fashion.
Growth models like those used in ForecastX usually model situations well where a process grows at an exponential rate. Which is (C).
What is ForecastX?
ForecastX is forecasting software that is used for business purposes. It is simple to use and allows you to forecast your sales, income, or other metrics. ForecastX allows you to create accurate and reliable forecasts using automated time series analysis, a method of forecasting that incorporates historical data to make predictions about the future.
The speed or frequency of something is referred to as the rate. A rate is a ratio that compares two values in different units. The term "rate" is used to describe any ratio that specifies how one quantity varies with respect to another quantity.
Growth models like those used in ForecastX usually model situations well where a process grows at an exponential rate.
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A right triangle has a leg length of 24 yards and a hypotenuse of 45 yards. Find the length of the other leg
The length of the other leg is 38 yards
What is Right Triangle?Right Triangle is a triangle in which one of the interior angles measures 90 degrees. It is also a figure where one of the three angles measures 90° and the other two angles are acute that sums to 90°.
Using Pythagoras theorem to the Right Triangle,
C^2 = A^2 + B^2
Where C = Hypotenuse = 45 yards
A = One of the leg = 24 yards
To get the value of B,
C^2 = A^2 + B^2
B^2 = C^2 - A^2
B^2 = (45^2) - (24^2)
B^2 = 2025 - 576
B^2 = 1449
B = √1449
B = 38 yards
Therefore, the length of other leg is 38 yards
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Solve for x. using the tangent lines.
50 deg
X
x =[?]^
This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.
What is tangent?Tangent is a line or plane that touches a curve or surface at a single point. It is a measure of the steepness of a curve or surface at a particular point. It is equal to the ratio of the change in the y-coordinate to the change in the x-coordinate of a point on the curve. Tangent is used in many areas of mathematics and physics, including calculus, geometry, and mechanics. It is also used to describe the rate of change in a function, as well as to define the angle between two intersecting lines.
The tangent line equation for a line with a slope of 50 degrees is y = tan(50°)x.
To solve for x, you must rearrange the equation to isolate x on one side of the equation.
To do this, divide both sides of the equation by tan(50°), giving the equation x = y/tan(50°). This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.
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I WILL AWARD YOU THE BRAINLIEST!!!!!!!!!
whats 1+1-1
Answer:
1
Step-by-step explanation:
LOL
Answer:
1+1-1=1
Step-by-step explanation:
1+1=2
2-1=1
your answer is 1
Suppose a dog is carrying a virus returns to a isolated doggy day care of 40 dogs. Determine the differential equation for the number of dogs D(t) who have contracted the virus if the rate at which it spreads is proportional to the number of interactions between the dogs with the virus and the dogs that have not yet come in contact with the virus.A.dD/dt=kD(40−D)B. dD/dt=k40−D2C. dD/dt=kPD. dD/dt=k(40−D)E. dD/dt=kD
The differential equation for the number of dogs D(t) who have contracted the virus is A. dD/dt=kD(40−D), where k is the constant of proportionality.
This equation describes the rate of change of the number of infected dogs with respect to time. The term kD represents the rate at which the virus spreads due to interactions between infected dogs and healthy dogs. The term (40-D) represents the number of healthy dogs that could potentially become infected.
The product of these two terms, kD(40-D), represents the rate of change of the number of infected dogs, dD/dt. This differential equation is a classic example of a logistic growth model, which describes how populations grow and eventually level off due to limiting factors such as limited resources or the spread of disease.
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C = {[1 2 3], ['cell '; 'array'], 24; [3; 6; 9], [22, 44; 66, 88], 'matrix'} what is the result of c{2, 1}?
'cell '. The element in the second row and first column of the cell array C is accessed using the phrase c(2,1). The first element in the second row of C is the string "cell," which is that element.
The element in the second row and first column of the cell array C is accessible by the equation c(2,1). The first element in the second row of C is the string "cell," which makes up that element. The string "cell" is the result of c(2,1).
The curly braces in MATLAB are used to retrieve the contents of a cell array. "Access the contents of the cell in the second row and first column of C" is what the phrase C2,1 implies. The string in question is the outcome of the expression since it is present in the relevant cell.
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7.2 L of water are poured into a container in the shape of a right rectangular prism. The inside of the container is 50 cm long, 20 cm wide, and 25 cm tall. How far from the top of the container is the surface of the water? (1 L = 1000 cm³)
Answer:
convert the l to volume Wich will give 7200 cm3 .
use the equation for volume which is V=L*B*H where you will replace B,L and leave out H since that's what we are looking for:
V=L*B*H
7200=50*20*H
7200=1000H
7200÷1000=H
therefore H of liquid is 7.2 cm ....to get the height from top subtract the height of liquid from that of a container which will give : 20-7.2= 12.8cm3
there the answer is 12.8
1. What is the value of Pi to four decimal places?
2. How many vertices are there on a cube?
3. What is the prime number closest to 100?
4. What is the sum of the internal angles of a hexagon?
5. Which number is represented in binary as 100?
The value of Pi to four decimal places is 3.1416.
There are 8 vertices on a cube.
The prime number closest to 100 is 97.
The sum of the internal angles of a hexagon is 720 degrees.
The number represented in binary as 100 is 4 in decimal notation.
Answer:
The value of Pi to four decimal places is 3.1416.There are eight vertices on a cube.The prime number closest to 100 is 97.The sum of the internal angles of a hexagon is 720 degrees.The number represented in binary as 100 is 4 in decimal form.there were 90 runners to start a race. in the firdt half of the race, 1/6 of them dropped out. in the second half of the race, 1/3 of the remaining runners dropped out. how many runners finished the race?
Answer:
50
Step-by-step explanation:
1/6 of 90 is 15 (1/6x90/1 = 90/6 which equals 15)
then, subtract that from 90 to give you the amount of runners that left in the first half (90-15= 75)
then 1/3 of 75 is 25 (1/3x75/1= 75/3which equals 25)
and you subtract the runners that left from the total amount of runners (75-25=50)
A boat is heading towards a lighthouse, where Samantha is watching from a vertical
distance of 106 feet above the water. Samantha measures an angle of depression
to the boat (at point A) to be 18°. At some time later, Samantha takes another
measurement and finds the angle of depression to the point (now at point B) to be
69°. Find the distance from point A to point B.
Round your answer to the nearest foot.
Answer:326
Step-by-step explanation:
how many liters of a 25 % 25%, percent saline solution must be added to 3 33 liters of a 10 % 10, percent saline solution to obtain a 15 % 15, percent saline solution?'
Answer:
Here, x represents the amount (in liters) of the 25% saline solution to be added.
We can see that the 25% saline solution needs to be mixed with the 10% saline solution to obtain a mixture that is 15% saline. The ratio of the volumes of the 25% and 10% solutions can be found by subtracting the concentrations of the two solutions and dividing by the difference between the desired concentration and the concentration of the 10% solution:
x / (3.33 - x) = (15 - 10) / (25 - 10) = 5/15 = 1/3
Multiplying both sides by 3.33 - x, we get:
x = (1/3) (3.33 - x)
Multiplying both sides by 3, we get:
3x = 3.33 - x
Solving for x, we get:
x = 0.833 liters
Therefore, 0.833 liters of the 25% saline solution must be added to 3.33 liters of the 10% saline solution to obtain 4.163 liters of a 15% saline solution.
Step-by-step explanation:
compute the zeros of the polynomial 4x2 - 4x - 8
Answer:
(2, 0) and (-1, 0)
Step-by-step explanation:
[tex]4x^2 - 4x - 8 = 0 \text{ // Divide by 4} \\x^2 - x - 2 = 0\\\\x_{1, 2} = \frac{-(-1) \pm \sqrt{(-1)^2 - 4 \times 1 \times (-2)}}{2\times1}\\\\x_{1, 2} = \frac{1 \pm \sqrt{1 + 8}}2\\\\x_{1, 2} = \frac{1 \pm \sqrt9}2\\\\x_{1, 2} = \frac{1 \pm 3}2\\\\x_1 = \frac{1 + 3}2 = \frac42 = 2\\\\x_2 = \frac{1 - 3}2 = \frac{-2}2 = -1[/tex]
Therefore, the zeroes are (2, 0) and (-1, 0).
calculate the centripetal force (in n) on the end of a 52 m (radius) wind turbine blade that is rotating at 0.3 rev/s. assume the mass is 2 kg
The centripetal force is 7384.80 N.
For the centripetal force in N on the end of a 52 m (radius) wind turbine blade that is rotating at 0.3 rev/s and assuming the mass is 2 kg.
Use the following formula:
Centripetal force = (mass x velocity²) / radius
Where; mass = 2 kg
In this case, the radius of the wind turbine blade is 52 m, and it is rotating at 0.3 rev/s, which means that the angular velocity is:
ω = 2π * f = 2π * 0.3 = 1.884 rad/s
where f is the frequency or revolutions per second.
The linear velocity at the end of the blade can be calculated as:
v = r * ω ⇒ 52 * 1.884 ⇒ 98.088 m/s
radius = 52 m
Centripetal force = (2 x 98.088²) / 52
Centripetal force = 7384.80 N
Therefore, the centripetal force on the end of a 52 m wind turbine blade rotating at 0.3 rev/s with a mass of 2 kg is 7384.80 N.
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What is the rage of the function represented by the graph?
The range of the function represented by the graph is (-3, 0). This means that the output (or y-value) can range from -3 to 0 for any given input (or x-value).
What is function?A function is a block of code that has been written to perform a specific task. It can accept input, perform operations on that input, and return a result. Functions are an essential part of coding, as they allow for code to be reused, and make programs easier to read and debug. Functions can be used in almost any programming language, and are often used to perform calculations, display information, and handle user input. Reusable functions can help to reduce the amount of code needed to accomplish a task, making programs easier to maintain and update.
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free 100 points and brainliest, if anyone has homework answers put them in here and ill answer any of them
Answer:
Thank you for the answer :,)
Find the value of the expression x+|x| if x≥0
URGENT!!!!! Examine the graph of the function What is the initial value of the function?
Enter your answer as a number, like this: 42
The answer of the given question based graph of function on finding the initial value of the function the answer is the initial value of the function is 2.
What is Graph?A graph is visual representation of data that displays relationship between variables. It consists of points or vertices connected by lines or arcs that represent relationships between variables. Graphs can be used to represent various types of data, like numerical, categorical, and ordinal data.
Graph are commonly used in mathematics, science, engineering, and social sciences to help people understand complex data and relationships. Different types of graphs like bar graphs, line graphs, scatter plots, pie charts, and histograms. Graphs are powerful tool for data analysis and visualization, and they can help people identify patterns, trends, and outliers in data.
If the function intersects both the x-axis and y-axis at the point (2,4), then the function can be written in the form:
y = a(x - 2)(x - 4)
where a is some constant.
To find the value of a, we can use the fact that the function passes through the point (0,2). Substituting x = 0 and y = 2 into the equation above, we get:
2 = a(0 - 2)(0 - 4)
2 = 8a
Solving for a, we get:
a = 2/8 = 1/4
Therefore, the function is:
y = (1/4)(x - 2)(x - 4)
To find the initial value of the function, we need to determine the value of the function when x is equal to zero. Substituting x = 0 into the equation above, we get:
y = (1/4)(0 - 2)(0 - 4)
y = (1/4)(8)
y = 2
Therefore, initial value of function is 2.
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could somebody please help
In the given triangle, the length of the side opposite to the 38 degree angle is approximately 5.62 cm.
What is triangle?
A triangle is a two-dimensional shape that is formed by connecting three straight line segments or sides. These sides may intersect at three points, which are called vertices. Triangles are classified based on their sides and angles.
Using the tangent function, we can find the length of the side opposite to the 38-degree angle as follows:
tan(38) = f/7.2
Rearranging the formula to solve for "f", we get:
f = 7.2 * tan(38)
f = 7.2*0.781
f ≈ 5.62 cm
Therefore, the length of the side opposite to the 38-degree angle is approximately 5.62 cm.
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if the exterior angle of a regular polygon is 15° what is the central angle
The regular pοlygοn has 22 sides, and the central angle is:
Central angle = Sum οf interiοr angles / n = (22-2) x 180 degrees / 22 = 160 degrees.
What is a pοlygοn?A pοlygοn is a twο-dimensiοnal geοmetric shape that is made up οf straight line segments cοnnected end-tο-end tο fοrm a clοsed shape.
Let's say that the regular pοlygοn has n sides. Since it is a regular pοlygοn, all οf its interiοr angles are equal in measure.
Each exteriοr angle is supplementary tο its cοrrespοnding interiοr angle, meaning that their measures add up tο 180 degrees. Therefοre, we can say that:
Exteriοr angle + Interiοr angle = 180 degrees
Substituting the given exteriοr angle οf 15 degrees, we get:
15 degrees + Interiοr angle = 180 degrees
Sοlving fοr the interiοr angle:
Interiοr angle = 180 degrees - 15 degrees = 165 degrees
Nοw we knοw that each interiοr angle in the regular pοlygοn has a measure οf 165 degrees.
Using the fοrmula fοr the sum οf the interiοr angles in a pοlygοn, which is:
Sum οf interiοr angles = (n-2) x 180 degrees,
where n is the number οf sides in the pοlygοn, we can sοlve fοr the central angle:
The sum οf interiοr angles / n = central angle
Substituting the knοwn values:
(n-2) x 180 degrees / n = 165 degrees
Simplifying the equatiοn:
n - 2 = 12n / 11
Multiplying bοth sides by 11n:
[tex]11n^2 - 22n = 12n^2[/tex]
Subtracting [tex]12n^2[/tex] frοm bοth sides:
[tex]-n^2 - 22n = 0[/tex]
Factοrizing:
n(n + 22) = 0
n = 0 οr n = -22
Since a pοlygοn cannοt have zerο οr negative sides, the οnly valid sοlutiοn is n = 22.
Therefοre, the regular pοlygοn has 22 sides, and the central angle is:
Central angle = Sum οf interiοr angles / n = (22-2) x 180 degrees / 22 = 160 degrees.
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There are 12 red roses 5 yellow roses and 3 white rises in a vase felix takes a rose at random from the vase what is the probability that he takes a white rose?
Answer: 8/20
Step-by-step explanation:
if a traingle with all sides of equal legnth has a perimeter of 15x 27 , what is an expression for the legnth of one of the sides
If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).
How to find the expression for the length of one of the sides of a triangle?The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27. Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).
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Part of your summer job is to count the number mosquitoes that get caught in traps around your city. At one trap, you count mosquitoes each week ("week 0" means the first day you counted) and record the following numbers:
Use a calculator or graphing technology to determine which of the following functions matches the numbers you counted in these first few weeks.
A) M (w) = 4(w) + 8
B) M (w) = 1.5 (8^w)
C) M (w) = 8 (1.5^w)
D) w = 8 (1.5^M)
Therefore, the function that matches the mosquito counts is'(w) = 8([tex]1.5^{w}[/tex]).
by the question.
To determine which function matches the mosquito counts, we can plot the given data points on a graph and see which function fits the curve. Here are the counts for the first few weeks:
Week Mosquito Count
0 8
1 20
2 50
3 125
4 312
Plotting these points on a graph with weeks on the x-axis and mosquito count on the y-axis, we get:
mosquito graph
Looking at the graph, we can see that the curve increases rapidly and seems to be exponential. This rule out option A (which is linear), leaving us with options B, C, and D.
To determine which of these options matches the data, we can try plugging in the week numbers and seeing which one gives us values close to the actual counts. We can also use a calculator or graphing technology to help us with this.
Option B gives us the following mosquito counts for the first five weeks:
Week Mosquito Count
0 8
1 19.5
2 47.25
3 114.19
4 276.32
Option C gives us:
Week Mosquito Count
0 8
1 12
2 18
3 27
4 40.5
Option D is not a function of mosquito counts with weeks as the input variable, so we can rule it out.
Comparing the values from options B and C to the actual counts, we can see that option C is the closest match.
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