Put these numbers in order, from least to greatest. If you get stuck, consider using the number line. 3.5, -1, 4.8, -1.5, -0.5, -4.2, 0.5, -2.1, -3.5
Answers
The numbers are as follows, going from lowest to highest:
-4.2, -3.5, -2.1, -1.5, -1, -0.5, 0.5, 3.5, 4.8.
How are numbers on a number line determined?We must compare and organize these numbers from least to greatest in order to put them in numerical order. The two smallest figures, which are -4.2 and -3.5, can be used as a starting point. Afterwards, we add the remaining numbers to the list in ascending order of least to largest after comparing them to these two. We arrive at the list above after continuing this approach.
Visualizing these numbers in order can alternatively be done by using a number line. In the number line, we can mark each number and arrange them in ascending order from left to right. We can see from the number line that the least number is -4.2.
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Related Questions
please help me solve this problem
Answers
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]
using the unit normal table, find the proportion under the standard normal curve that lies between the following values. (hint: draw a picture.) do not round your answer. (a) the mean and z
Answers
The standard normal distribution is a bell-shaped curve that has a mean of 0 and a standard deviation of 1.
What is standard deviations?Standard deviation is a measure of how spread out numbers are. It is a measure of the amount of variation or dispersion from the average. For a data set, it is calculated as the square root of the variance. It is calculated by taking the square root of the variance (the average of the squared differences from the mean). The standard deviation can tell you how much variation there is from the average (mean) value in a data set.
The unit normal table is a statistical tool used to calculate probabilities related to the standard normal distribution. The standard normal distribution is a bell-shaped curve that has a mean of 0 and a standard deviation of 1. This table provides the probability of a given score falling within a certain range of the mean of the normal distribution.
For example, in part (a) the question is asking for the proportion between the mean and z = 1.96. Using the unit normal table, we can find this proportion to be 0.975. This means that 97.5% of the scores fall between the mean and z = 1.96.
In part (b), the question is asking for the proportion between the mean and z = 0. Since z = 0 is the mean, this proportion is 0.500, meaning that 50% of the scores fall between the mean and z = 0.
In part (c), the question is asking for the proportion between z = −1.90 and z = 1.90. This proportion can be found in the unit normal table to be 0.954. This means that 95.4% of the scores fall between z = −1.90 and z = 1.90.
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Complete questions as follows-
Using the unit normal table, find the proportion under the standard normal curve that lies between the following values. (Round your answers to four decimal places.)
(a) the mean and
z = 1.96
1
(b) the mean and
z = 0
2
(c)
z = −1.90 and z = 1.90
3
(d)
z = −0.40 and z = −0.30
4
(e)
z = 1.00 and z = 2.00
5
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.
Answers
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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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.
Answers
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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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)
Answers
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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What percent of light will pass through 10 panes?
Answers
If, for example, each pane blocks 10% of the light, then the percentage of light that passes through one pane is 100% - 10% = 90%. Therefore, the percentage of light that passes through 10 panes would be:
90% x 90% x 90% x 90% x 90% x 90% x 90% x 90% x 90% x 90% ≈ 34.87%
So, if each pane blocks 10% of the light, approximately 34.87% of the light will pass through 10 panes. However, the actual percentage of light that passes through 10 panes will depend on the percentage of light that is blocked by each pane.
could somebody please help
Answers
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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What do you believe is one of the most common mistakes students make when working with sequences and functions? Why do you believe they make that mistake? What suggestions would you offer to avoid the mistake in the future? (Answer should be at least 3 – 5 complete sentences.
Answers
Answer:
One of the most common mistakes students make when working with sequences and functions is misunderstanding the difference between the two. Sequences refer to a list of numbers or terms that follow a specific pattern, while functions are mathematical rules that relate one set of numbers to another. This confusion often arises because some sequences can be described by functions, but not all functions describe sequences.
To avoid this mistake, students should first understand the definitions of sequences and functions and practice identifying whether a given problem involves a sequence or a function. They should also pay attention to the language used in the problem and look for keywords that indicate whether they are dealing with a sequence or a function. Finally, they should practice using different methods to solve problems involving sequences and functions, including graphing, table-building, and algebraic manipulation, to gain a better understanding of the relationships between numbers in a sequence or a function.
Please help and answer. Much appreciated
Answers
The correct answer is A. a-c+b-d=0. This is because when two sets of numbers are both negative, the result of subtracting the larger number from the smaller number will always be negative.
What is subtraction?Subtraction involves taking one number or value away from another. It is one of the four basic operations in mathematics, along with addition, multiplication, and division.
When subtracting a from c and b from d, the result of either subtraction will always be a negative number. When the two negative numbers are added together, the result will always be 0.
The other options are not always true. In option B, ac > bd, this is not always true because when a, b, c, and d are all negative, it is possible for the result of ac to be less than the result of bd. In option C, a+c>b+d, this is not always true because when both sets of numbers are negative, it is possible for the result of a+c to be less than b+d. Finally, in option D, a/d < b/c, this is not always true because when both sets of numbers are negative, it is possible for the result of a/d to be greater than b/c.
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The correct answer is A. a-c+b-d=0 because the expression is always true when a, b, c and d are all less than zero.
What is expression?Expression is a combination of symbols and operators that evaluate to a single value. It could be a mathematical equation, an arithmetic expression, a logical expression, or a combination of these.
This is because the expression is equivalent to (a-c)+(b-d)=0, which is always true when a, b, c and d are all less than zero.
This can be proven through a simple calculation.
Let us assume that the values of a, b, c and d are -1, -3, 8 and -4 respectively.
Substituting these values into the expression gives us
(-1-3)+(8-4)=0, which is clearly true.
Therefore, A. a-c+b-d=0 is the correct answer as the expression is always true when a, b, c and d are all less than zero.
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2 reds and 18 blues
What is the ratio of red to blue squares in its simplest form?
Red Blue
Answers
Answer:
The ratio of red to blue squares in the given set of 2 reds and 18 blues can be written as:
Red:Blue = 2:18
To simplify the ratio, we can divide both the numerator and denominator by the greatest common factor (GCF) of 2 and 18, which is 2. Dividing both terms by 2, we get:
Red:Blue = 1:9
Therefore, the ratio of red to blue squares in its simplest form is 1:9.
The random variable x is known to be uniformly distributed between 10 and 20. Show the graph of the probability density function: Compute P(x 15). Compute P(12 =x= 18). St Compute E(x). Compute Var(x).
Answers
Compute P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.
Compute P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.
Compute E(x): The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15
Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.
The probability density function is as follows: As the random variable x is uniformly distributed between 10 and 20. Thus, f(x) = 1/(20-10) = 1/10 for 10 ≤ x ≤ 20.Compute P(x ≤ 15):Thus, P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.Compute P(12 ≤ x ≤ 18):Thus, P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.Compute E(x):The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15.Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.
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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?'
Answers
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:
In ΔKLM, l = 4.1 cm, m = 2.4 cm and ∠K=97°. Find the area of ΔKLM, to the nearest 10th of a square centimeter.
Answers
the area of the triangle KLM is 4.9 cm².
What is area?Area is the region bounded by a plane shape.
To calulate the area of the triangle, we use the formula below
Formula:
A = 1/2×absinCWhere:
A = Area of triangle ΔKLMa = Length of side lb = Lenth of side mC = Size of angle KFrom the question,
Given:
a = 4.1 cmb = 2.4 cmC = 97°Substitute these values into equation 1
A = 4.1×2.4×sin97°/2A = 4.9 cm²Hence, the area is 4.9 cm².
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what is the assertiveness
Answers
Answer:
Confident or forceful behaviour
Step-by-step explanation: I have a dictionary
D. On désire connaître la quantité de moulure dont on a besoin pour encadrer un tableau. Aire ou Périmètre
Answers
Answer:
Step-by-step explanation:
Perimeter
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You want to measure the height of an antenna on the top of a 125-foot building. From a point in front of the building, you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°. How tall is the antenna, to the nearest tenth of a foot?
Answers
The antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
What is an angle of elevationThe angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.
To get the height of the antenna, we subtract the height of the building from the height from the bottom of the building to the top of the antenna.
we shall represent the distance from the point of observation to the building with x and the height from the bottom of the building to the top of the antenna with y. so that;
tan 68° = 125/x {opposite/adjacent}
x = 125/ tan 68° {cross multiplication}
x = 50.5033
tan 71° = y/50.5033
y = 50.5033 × tan 71°
y = 144.6722
height of the antenna = 144.6722 - 125
height of the antenna = 19.6722
Therefore, the antenna which is having an angle of elevation 71° from the front of the it is on is 19.67 feet tall to the nearest tenth of foot.
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Maria downloads an unknown number of apps on her tablet in the month of June
Answers
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.
Use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 7 cos(20), [0, Phi/4]
Answers
The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.
To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.
A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.
To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°
Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.
The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)
So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.
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Your monthly take-home pay is $900. Your monthly credit card payments are about $135. What percent of your take-home pay is used for your credit card payments?
i came up with $765
Answers
Answer:15 percent
Step-by-step explanation:
Please simplify the following expression while performing the given operation.
(-3+1)+(-4-i)
Answers
Answer:
To simplify the expression (-3+1)+(-4-i), we can perform the addition operation within the parentheses first:
(-3+1)+(-4-i) = -2 + (-4-i)
Next, we can simplify the addition of -2 and -4 by adding their numerical values:
-2 + (-4-i) = -6 - i
Therefore, (-3+1)+(-4-i) simplifies to -6-i.
Step-by-step explanation:
Ty is a landscape architect. He needs to find the value of x in meters so that the sum of the areas of the patio, herb garden, and flower garden is 25% of the area of the entire rectangle. What in the area in square meters of the patio?
Answers
By using this value of x in the formula we previously discovered, we can get the patio's area Patio's size is equal to x2 + 4x + 4 = ((1 + 7)/3)2 + 4((1 + 7)/3) + 4 = 4.72 square meters.
What is a square's area?A square is a 2D shape with equal-sized sides on each side. The area would be length times width, which is equal to side side because all the sides are equal. As a result, a square's area is side square.
Let's first find the area of the entire rectangle:
A = lw = (3x + 6)(2x + 4) = 6x² + 30x + 24
Area of patio = (x + 2)² = x² + 4x + 4
Area of herb garden = (2x + 2)(x + 4) = 2x² + 10x + 8
Area of flower garden = (3x + 4)(x + 4) = 3x² + 16x + 16
Sum of areas = x² + 4x + 4 + 2x² + 10x + 8 + 3x² + 16x + 16
= 6x² + 30x + 28
0.25(6x² + 30x + 24) = 6x² + 30x + 28
Simplifying and solving for x, we get:
1.5x² - x - 1 = 0
Using the quadratic formula, we find that:
x = (1 ± √7)/3
x = (1 + √7)/3
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The area in square meters of the patio is 850 square meters.
What is a rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
Let's start by calculating the total area of the rectangle:
Area of rectangle = length x width = 100m x 40m = 4000 square meters
Now, let's denote the width of the herb garden as x meters. Then, the length of the herb garden would be 10 meters.
The area of the herb garden would be:
Area of herb garden = length x width = 10m x x = 10x square meters
The area of the patio can be calculated as:
Area of patio = (100 - x) x (40 - 2x) square meters
(100 - x) is the length of the patio, and (40 - 2x) is the width of the patio, since the herb garden takes up x meters of the width.
The area of the flower garden can be calculated by subtracting the area of the rectangle, the herb garden, and the patio from each other:
Area of flower garden = 4000 - 10x - (100 - x) x (40 - 2x) square meters
Now, we need to find the value of x so that the sum of the areas of the patio, herb garden, and flower garden is 25% of the area of the entire rectangle. In other words:
Area of herb garden + Area of patio + Area of flower garden = 0.25 x Area of rectangle
10x + (100 - x) x (40 - 2x) + 4000 - 10x = 0.25 x 4000
Simplifying this equation, we get:
-2x^2 + 30x + 1000 = 1000
-2x^2 + 30x = 0
-2x(x - 15) = 0
Therefore, x = 0 or x = 15. Since x cannot be 0 (since the herb garden would have no width), the value of x must be 15 meters.
Now we can calculate the area of the patio:
Area of patio = (100 - x) x (40 - 2x) = (100 - 15) x (40 - 2(15)) = 850 square meters
Therefore, the area in square meters of the patio is 850 square meters.
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hihihihihihihihihihihihihihihihihi
Answers
Six friends play a carnival game in which a person throws darts at balloons. Each person throws the same number of darts and then records the portion of the balloons that pop. A piece of paper shows the portion of balloons that popped in a game of darts. The portions are, Whitney, 16 percent; Chen, start fraction 2 over 25 end fraction; Bjorn, 0. 06; Dustin, start fraction 1 over 50 end fraction; Philip, 0. 12; Maria, 0. 4. Find the mean, median, and MAD of the data. The mean is. The median is. The mean absolute deviation is
Answers
The mean, median, and mean absolute deviation MAD of the data are 15%, 10%, and 8%.
To find the mean, median, and mean absolute deviation (MAD) of the data, we need to first convert all the fractions to percentages:
Whitney: 16%
Chen: 8%
Bjorn: 6%
Dustin: 2%
Philip: 12%
Maria: 40%
a) Mean:
To find the mean, we add up all the percentages and divide by the total number of friends (6):
Mean = (16 + 8 + 6 + 2 + 12 + 40) / 6 = 15%
Therefore, the mean is 15%.
b) Median:
To find the median, we need to arrange the data in order from smallest to largest:
2%, 6%, 8%, 12%, 16%, 40%
Since there are six values, the median is the average of the two middle values: (8 + 12) / 2 = 10%
Therefore, the median is 10%.
c) Mean Absolute Deviation (MAD):
To find the MAD, we first need to find the absolute deviation of each value from the mean:
Whitney: |16 - 15| = 1%
Chen: |8 - 15| = 7%
Bjorn: |6 - 15| = 9%
Dustin: |2 - 15| = 13%
Philip: |12 - 15| = 3%
Maria: |40 - 15| = 25%
Next, we find the average of these absolute deviations:
MAD = (1 + 7 + 9 + 13 + 3 + 25) / 6 = 8%
Therefore, the mean absolute deviation is 8%.
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a business give 30% discount on everyting. If a radio costed 1610 Dollars how much did it cost before discount
Can someone help with the calculation of this.
Answers
Answer:
$2300
Step-by-step explanation:
$1610 is 7/10 the original cost. Multiplying by 10/7 reverses that, and we get the starting cost of $2300
Hope this helps!
compute the zeros of the polynomial 4x2 - 4x - 8
Answers
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).
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
Answers
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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In Problems 47 through 56, use the method of variation of parameters to find a particular solution of the given differential equation. 47.y′′+3y′+2y=4ex48.y′′−2y′−8y=3e−2x
Answers
Eventually, the differential equation's general solution is:
y = y_h + y_p
y = c1e^(-2x) + c2e^(-x) - (1/6)e^(-x) + (2/3)
What is homogeneous solution?In the context of differential equations, the homogeneous solution of a differential equation is a solution that satisfies the equation when the right-hand side is equal to zero.
According to question:To find the particular solution of y'' + 3y' + 2y = 4e^x using the variation of parameters method, we first find the homogeneous solution of the differential equation by setting the right-hand side to zero:
y'' + 3y' + 2y = 0
The characteristic equation is r^2 + 3r + 2 = 0, which factors as (r + 2)(r + 1) = 0. Therefore, the solutions are y_h = c1e^(-2x) + c2e^(-x), where c1 and c2 are constants.
Next, we find the Wronskian of the homogeneous solution:
W(y1, y2) = |e^(-2x) e^(-x) | = e^(-3x)
To find the particular solution, we assume that it has the form y_p = u1(x)e^(-2x) + u2(x)e^(-x), where u1(x) and u2(x) are unknown functions to be determined.
We then find y_p' and y_p'':
[tex]y_p' = u1'(x)e^(-2x) + u2'(x)e^(-x) - 2u1(x)e^(-2x) - u2(x)e^(-x)y_p'' = u1''(x)e^(-2x) + u2''(x)e^(-x) - 4u1'(x)e^(-2x) - 2u2'(x)e^(-x) + 4u1(x)e^(-2x) + u2(x)e^(-x)u1''(x)e^(-2x) + u2''(x)e^(-x) + u1'(x)e^(-2x) + u2'(x)e^(-x) - 4u1'(x)e^(-2x) - 2u2'(x)e^(-x) + 4u1(x)e^(-2x) + u2(x)e^(-x) = 4e^x[/tex]
Simplifying and grouping terms, we get:
[tex]u1''(x)e^(-2x) - 3u1'(x)e^(-2x) + u2''(x)e^(-x) - u2'(x)e^(-x) = 4e^x[/tex]
To solve for u1(x) and u2(x), we use the method of undetermined coefficients and assume that they are both linear combinations of the exponential function and its derivative:
u1(x) = A(x)e^x
u2(x) = B(x)e^(2x)
Substituting these expressions into the previous equation and solving for A(x) and B(x), we get:
A(x) = -e^x/6
B(x) = 2e^x/3
Therefore, the particular solution is:
[tex]y_p = (-e^x/6)e^(-2x) + (2e^x/3)e^(-x)y_p = (-1/6)e^(-x) + (2/3)[/tex]
Eventually, the differential equation's general solution is:
y = y_h + y_p
y = c1e^(-2x) + c2e^(-x) - (1/6)e^(-x) + (2/3)
Therefore, the particular solution of the given differential equation y′′+3y′+2y=4ex is
[tex]y(x)=c_1e^{-x} + c_2e^{-2x} - 4 + 2e^{x}.[/tex]
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the weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. what is the effect on the weight when the distance is multiplied by 2?
Answers
The weight becomes 1/4 of its original value when the distance is multiplied by 2.
According to the question, "the weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth." We need to determine the effect on the weight when the distance is multiplied by 2.
Let w be the weight of a body, d be the distance from the center of the earth, and k be the constant of variation. According to the question,
w = k / d²
When the distance is multiplied by 2, the new distance is 2d. Therefore, the new weight is given by:
w' = k / (2d)²
w' = k / 4d²
w' = w / 4
Therefore, the weight becomes 1/4 of its original value when the distance is multiplied by 2.
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a survey found that 10% of americans believe that they have seen a ufo. for a sample of 10 people, find each probability: a. that at least 2 people believe that they have seen a ufo b. that 2 or 3 people believe that they have seen a ufo c. that exactly 1 person believes that he or she has seen a ufo
Answers
The probability that at least 2 people believe that they have seen a ufo is 0.1937102445. The probability that exactly 1 person believes that he or she has seen a ufo is problem: P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890.
What is the probability?The probability that at least 2 people believe that they have seen a UFO would be 0.1937102445. For this we use the binomial distribution formula.
P(X ≥ 2) = 1 − P(X = 0) − P(X = 1)P(X = 0) = (9/10)¹⁰
P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890 (rounded to 10 decimal places)
P(X ≥ 2) = 1 − 0.3874204890 − 0.3486784401 = 0.1937102445 (rounded to 10 decimal places)
The probability that 2 or 3 people believe that they have seen a UFO would be 0.1937102445. Using the formula of binomial distribution again we can solve for the probability of this event.
P(2 ≤ X ≤ 3) = P(X = 2) + P(X = 3)P(X = 2) = 10C₂ (0.10)² (0.90)⁸= 0.1937102445 (rounded to 10 decimal places)
P(X = 3) = 10C₃ (0.10)³ (0.90)⁷= 0.0573956280 (rounded to 10 decimal places)
P(2 ≤ X ≤ 3) = 0.1937102445 + 0.0573956280 = 0.2511058725 (rounded to 10 decimal places)
The probability that exactly 1 person believes that he or she has seen a UFO would be 0.3874204890. Using the binomial distribution formula to solve this problem:
P(X = 1) = 10C₁ (0.10) (0.90)⁹= 0.3874204890 (rounded to 10 decimal places)
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Look at the simultaneous equations below.
(1) x-2y=10
(2) x-2=6y
a) Rearrange equation (2) to make x the subject.
b) Using your answer to part a), solve the simultaneous equations using substitution.
Answers
Answer:
a) To make x the subject of equation (2), we need to isolate x on one side of the equation. We can do this by adding 2 to both sides, and then dividing both sides by 6:
x - 2 = 6y
x = 6y + 2
b) We can now substitute the expression 6y + 2 for x in equation (1):
6y + 2 - 2y = 10
Simplifying the left-hand side, we get:
4y + 2 = 10
Subtracting 2 from both sides, we get:
4y = 8
Dividing both sides by 4, we get:
y = 2
Now we can substitute y = 2 back into either equation to find x. Let's use equation (2), since we have already rearranged it to make x the subject:
x = 6y + 2
x = 6(2) + 2
x = 14
Therefore, the solution to the simultaneous equations is x = 14 and y = 2.
Step-by-step explanation: