Therefore, the area of the regular dodecagon with a side length of 8 units is approximately 1,843.21 square units.
What is area?In mathematics, area refers to the measure of the amount of space inside a two-dimensional shape or region. It is a measure of the size of a flat surface, and is typically expressed in square units, such as square meters (m²), square centimeters (cm²), or square feet (ft²). The area of a shape can be calculated using various formulas, depending on the type of shape. The concept of area is used in many areas of science and engineering, including physics, geometry, and architecture. It is particularly important in fields such as construction and landscaping, where the amount of material needed to cover a given area is often a key factor in planning and budgeting.
Here,
To find the area of a regular dodecagon, you can use the formula:
Area = (3 * √3 / 2) * s² * n
where s is the length of each side and n is the number of sides.
Substituting s = 8 and n = 12, we get:
Area = (3 * √3 / 2) * 8² * 12
Area = 3 * √3 * 64 * 12
Area = 1,843.21 square units (rounded to two decimal places)
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19.
Solve the problem.
2
Find the critical value XR corresponding to a sample size of 5 and a confidence
level of 98%.
(1 point)
O11.143
00.297
13.277
00.484
The critical value of the chi-square distribution corresponding to a sample size of 5 and a confidence level of 98% is given as follows:
0.297 and 13.277.
How to obtain the critical value?To obtain a critical value, we need three parameters, given as follows:
Distribution.Significance level.Degrees of freedom.Then, with the parameters, the critical value is found using a calculator.
The parameters for this problem are given as follows:
Chi-square distribution.1 - 0.98 = 0.02 significance level.5 - 1 = 4 degrees of freedom.Using a chi-square distribution calculator, the critical values are given as follows:
0.297 and 13.277.
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A net of a rectangular pyramid is shown.
A net of a rectangular pyramid with a base with dimensions of 13 inches by 17 inches. The two larger triangular faces have a height of 11 inches. The smaller triangular face has a height of 12.3 inches.
What is the surface area of the pyramid?
567.9 in2
457.4 in2
346.9 in2
283.95 in2
The surface area of the rectangular pyramid is approximately 567.9 in².
What is rectangular pyramid?
A rectangular pyramid is a type of pyramid that has a rectangular base and four triangular faces that meet at a common vertex. The rectangular base of a rectangular pyramid can be any rectangle, meaning that the length and width can be different. The four triangular faces of a rectangular pyramid are congruent, which means they are the same size and shape. The height of the rectangular pyramid is the distance between the vertex and the center of the base. The surface area of a rectangular pyramid can be calculated by finding the area of each face and adding them together.
To find the surface area of the rectangular pyramid, we need to find the area of each face and add them together.
First, let's find the area of the rectangular base:
Area of base = length x width = 13 in x 17 in = 221 in²
Next, let's find the area of the larger triangular faces:
Area of each larger triangular face = (1/2) x base x height = (1/2) x 17 in x 11 in = 93.5 in²
Total area of both larger triangular faces = 2 x 93.5 in² = 187 in²
Finally, let's find the area of the smaller triangular face:
Area of smaller triangular face = (1/2) x base x height = (1/2) x 13 in x 12.3 in = 79.95 in²
Now, we can find the total surface area of the rectangular pyramid by adding the areas of all the faces:
Total surface area = area of base + area of both larger triangular faces + area of smaller triangular face
Total surface area = 221 in² + 187 in² + 79.95 in²
Total surface area = 488.95 in²
Therefore, the surface area of the rectangular pyramid is approximately 567.9 in².
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 49 is the most appropriate measure of variability to use to represent the spread of donations received by the charity in this data set.
what is statistics?
Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It involves the study of methods for designing experiments and surveys, analyzing and interpreting data, and making decisions based on data. Statistics plays an important role in a wide range of fields, including science, social science, economics, finance, engineering, and many others. It is used to draw conclusions, make predictions, and inform decision-making by providing a quantitative and objective approach to understanding and analyzing data.
The most accurate measure of variability to use for this data set is the range of 49. The range is the difference between the highest and lowest values in the data set, which in this case is 59 - 10 = 49. The range provides a simple and straightforward measure of the spread of the data and is useful when the data is not too skewed.
While the data in this set is skewed, the range is still an appropriate measure of variability because there are no extreme outliers that would significantly affect the range. The IQR (interquartile range) is another measure of variability that is useful for skewed data, but in this case, it would not be the most appropriate choice because the data set is not divided into quartiles and the IQR would not provide additional information beyond what the range already shows.
Therefore, the range of 49 is the most appropriate measure of variability to use to represent the spread of donations received by the charity in this data set.
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Help please? I just need an answer. A clear explanation earns brainliest.
the simplified form of expression is: -(x² + 2x - 2)/((x+2)*(x+4))
what is expression ?
In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that represents a mathematical quantity or relationship. Expressions can be simple or complex
In the given question,
To evaluate the expression 1/(x+2) - (x+1)/(x+4), we need to find a common denominator for the two terms. The least common multiple of (x+2) and (x+4) is (x+2)(x+4).
So, we can rewrite the expression as:
(1*(x+4) - (x+1)(x+2))/((x+2)(x+4))
Expanding the brackets, we get:
(x+4 - x² - 3x - 2)/((x+2)*(x+4))
Simplifying the numerator, we get:
(-x² - 2x + 2)/((x+2)*(x+4))
Therefore, the simplified expression is:
-(x² + 2x - 2)/((x+2)*(x+4))
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rylie is a newly hired cybersecurity expert for a government agency. rylie used to work in the private sector. she has discovered that, whereas private sector companies often had confusing hierarchies for data classification, the government's classifications are well known and standardized. as part of her training, she is researching data that requires special authorization beyond normal classification. what is this type of data called? group of answer choices
Compartmentalized is the type of data that is discussed in the problem researched by an employee rylie who is a newly hired cybersecurity expert for a government agency and has working experience in the private sector.
Data classification is the way of organizing data into different categories that make it easy to retrieve, sort and store for future use. In simple words, compartmentalization means to separate into isolated compartments or categories. In data language, A nonhierarchical grouping of information used to control access to data more finely than with hierarchical security classification alone is called Compartmentalization. Now, we have a rylie who is a newly hired cybersecurity expert for a government agency. She has working experience in the private sector. On basis of her experience she has discovered that, the private sector companies often had confusing hierarchies for data classification as compared to the government's classifications which are well known and standardized. During her training, she is researching data that requires special authorization beyond normal classification. The data type that she researched and that is authorization beyond normal classification is called compartmentalized data.
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Using the graph, determine the coordinates of the x-intercepts of the parabola.
Answer:
x = -5, x = 1
As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).
Step-by-step explanation:
The x-intercepts are the x-values of the points at which the curve crosses the x-axis, so when y = 0.
From inspection of the given graph, we can see that the parabola crosses the x-axis at x = -5 and x = 1.
Therefore, the x-intercepts of the parabola are:
x = -5x = 1As (x, y) coordinates, the x-intercepts are (-5, 0) and (1, 0).
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent? (4 points)
Part A: A reasonable domain to plot the growth function would be from d = 0 to d = 11.
Part B: The y-intercept of the graph of the function f(d) is 7
Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.
Domine and y-intercept of a function:
The domain of a function represents the set of input values for which the function is defined and can produce a meaningful output.
The y-intercept of a function represents the value of the function when the input is equal to zero.
The average rate of change of a function from x = a to x = b is given by the slope of the secant line passing through the points (a, f(a)) and (b, f(b)).
Here we have
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
=> f(d) = 7(1.06)^d
Since it is given that the radius of the algae was approximately 13.29 mm when the biologist concluded her study, we can set f(d) = 13.29
=> 13.29 = [tex]7(1.06)^{d}[/tex]
=> ln(13.29/7) = d ln(1.06)
=> d = ln(13.29/7)/ln(1.06) ≈ 11
Therefore, A reasonable domain to plot the growth function would be from d = 0 to d = 11.
Part B: The y-intercept of the graph of the function f(d) represents the value of the function when d = 0.
Substituting d = 0 into the given equation, we get:
f(0) = 7(1.06)⁰ = 7
Therefore, The y-intercept of the graph of the function f(d) is 7
Part C: The average rate of change of the function f(d) from d = 4 to d = 11 is given by the slope of the secant line passing through the points (4, f(4)) and (11, f(11)). Using the given equation, we can evaluate f(4) and f(11):
f(4) = 7(1.06)⁴ ≈ 8.84
f(11) = 7(1.06)¹¹ ≈ 13.29
The slope of the second line passing through these two points is:
Slope = (f(11) - f(4))/(11 - 4) = [ 13.29 - 8.84]/7 = 0.64
Therefore,
The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.64 mm/day.
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You roll a six sided die 30 times. A 5 is rolled 8 times. What is the theoretical probability of rolling a 5? What is the experimental probability of rolling a 5?
The theoretical and experimental probability of rolling a 5 are 1/6 and 4/15 respectively.
How do we derive the probability?We will calculate the theoretical probability by substituting 30 for the number of favorable outcomes as the die is rolled 30 times with one option each for 30 rolls and 180 for total number of outcomes in theoretical probability formula.
P(Theoretical probability of rolling a 5) = 30/180
P(Theoretical probability of rolling a 5) = 1/6.
The experimental probability is calculated by substituting 8 for the number of time the event occurs and 30 for the total number of trials.
P(Experimental probability of rolling a 5)= 8/30
P(Experimental probability of rolling a 5) =4/15
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A container built for transatlantic shipping is constructed in the shape of a right
rectangular prism. Its dimensions are 4 ft by 9.5 ft by 13 ft. If the container is entirely
full and, on average, its contents weigh 0.05 pounds per cubic foot, find the total
weight of the contents. Round your answer to the nearest pound if necessary
Thus, the on average the contents weight for the transatlantic shipping is found as 24.7 pounds.
Explain about the rectangular prism:a solid, three-dimensional object with six rectangular faces.It is a prism due to its uniform cross-section along its whole length.Volume is a unit of measurement for the amount of 3-dimensional space a thing occupies. Cubic units are used to measure volume.Given dimension of rectangular prism
Length l = 4ft
width w = 9.5 ft
height h = 13 ft
Volume of rectangular prism = l*w*h
V = 4*9.5*13
V = 494 ft³
Now,
1 ft³ = 0.05 pounds
So,
weight of 494 ft³ = 494*0.05 pounds
weight of 494 ft³ = 24.7 pounds
Thus, the on average the contents weigh for the transatlantic shipping is found as 24.7 pounds.
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The solid below is dilated by a scale factor of 1/2. Find the volume of the
solid created upon dilation.
24
26
10
34
Answer: 4080
Step-by-step explanation:
First you have to find the area of the triangle. 24*10 = 240. 240/2 = 120. Then you multiply the area of the triangle and multiply it by 34. 120 * 34 = 4080. This means the answer is 4080
in desperate need of help!! (i accidentally clicked the first answer)
Answer:
The answer is 28
Step-by-step explanation:
sin0=opp/hyp
let hyp be x
sin30=14/x
0.5x=14
divide both sides by 0.6
x=14/0.5
x=28
dora drove east at a constant rate of 75 kph. one hour later, tim started driving on the same road at a constant rate of 90 kph. for how long was tim driving, before he caught up to dora? a. 5 hours b. 4 hours c. 3 hours d. 2 hours
Tim was driving for 5 hours before he caught up to Dora.
The answer is (a) 5 hours.
To solve this problem, we can use the formula:
distance = rate × time
Let's denote the time Tim drove as t hours.
Since Dora started driving one hour earlier, her driving time would be (t + 1) hours.
Dora's distance: 75 kph × (t + 1)
Tim's distance: 90 kph × t
Since Tim catches up to Dora, their distances will be equal:
75(t + 1) = 90t
Now we can solve for t:
75t + 75 = 90t
75 = 15t
t = 5.
The answer is (a) 5 hours.
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true or false: a linear programming problem can have an optimal solution that is not a corner point. select one: true false
It is true that a linear programming problem can have an optimal solution that is not a corner point.
How given statement is true? Explain further?In linear programming, the optimal solution represents the point where the objective function is optimized while still satisfying all the constraints.
In some cases, the optimal solution may occur at a corner point of the feasible region, where two or more of the constraints intersect.
However, it is possible for the optimal solution to occur at a point that is not a corner point, but rather lies on an edge or a line segment of the feasible region.
This can occur when the objective function is parallel to one of the constraint lines or when there are redundant constraints that limit the feasible region.
Therefore, it is true that a linear programming problem can have an optimal solution that is not a corner point.
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Solve for x to make A||B.
A = x + 12
B = x + 48
X = [?]
Answer:
Step-by-step explanation:= x+48=180 ( linier pair )
= x=180-48
= x=132
= x+12=180 (liner pair)
= x=180-12
= x=168
An animal population N(t) is modeled by the differential equation:
dN/dt = -0. 001N(N - 110)(N - 99). If N(0)=A, where A is a positive integer, what is the maximum value of the positive integer A such that extinction will occur?
For the given integer, the maximum starting population size that will eventually lead to extinction is 98, since any larger value will result in the population either stabilizing at a positive value or growing indefinitely.
The equation in question is:
dN/dt = -0.001N(N - 110)(N - 99)
Here, N represents the population size, and dN/dt represents the rate of change of the population with respect to time. The right-hand side of the equation tells us how the population size changes over time, and it's determined by the current population size N, as well as the two constants 110 and 99.
We can do this by setting dN/dt equal to zero and solving for N:
dN/dt = -0.001N(N - 110)(N - 99) = 0
=> N = 0, N = 99, N = 110
We can then plot the direction field (i.e., arrows indicating the direction of change) on each interval, and use this to determine the behavior of the solution curve. In this case, we can see that the direction of the arrows changes at each critical point, indicating that the population behavior switches between growing and declining as we move from one interval to the next.
Specifically, we can see that if the initial population size A is less than 99, the population will decline to extinction. If the initial population size is between 99 and 110, the population will initially decline but then grow and eventually stabilize at N = 110. If the initial population size is greater than 110, the population will grow exponentially and tend towards infinity.
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Find the surface area and width of a rectangular prism with height of 6 cm, length of 5 cm, and the
volume of 240 cm³.
Answer:
236 cm^2 and 8 cm
Step-by-step explanation:
width=w
240=6(5)(w)
w=8 cm
area=2[(6)(5)+(6)(8)+(5)(8)]
area=236 cm^2
pyriamid a square base that measures 140 m on each side. the height is 91 m. what is the volume of the pyramid?
The volume of the pyramid is approximately 574,533.33 cubic meters.
To find the volume of a pyramid, you use the formula: V = (1/3) × base area × height, where B is the area of the base and h is the height of the pyramid.
Given that the side length of the square base is 140 m and the height is 91 m.
Since the base of the pyramid is a square with a side length of 140 m, we can find its area by multiplying the side lengths: B = 140m x 140m = 19,600 square meters.
By calculating this expression, you'll find the volume of the pyramid.
Now we can plug in the values for B and h into the formula: V = (1/3)(19,600 square meters)(91 meters) = 574,533.33 cubic meters.
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9) Given f-¹(x)=-3x+2, write an equation
that represents f(x).
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so for this inverse, since finding the inverse of the inverse, will give us the original function :)
[tex]f^{-1}(x)=-3x+2\implies y~~ = ~~-3x+2\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~-3y+2} \\\\\\ x-2=-3y\implies \cfrac{x-2}{-3}=y\implies \cfrac{2-x}{3}=y=f(x)[/tex]
A bottle of water that is 80°F is placed in a cooler full of ice. The temperature of the water decreases by 0. 5°F every minute. What is the temperature of the water, in degrees Fahrenheit, after 5 1/2
minutes? Express your answer as a decimal
After 5 and a half minutes, the temperature of the water will be 77°F.
In this scenario, we are given that the initial temperature of the water is 80°F. We also know that the temperature of the water decreases by 0.5°F every minute. We want to find out what the temperature of the water will be after 5 and a half minutes.
To solve this problem, we need to use a bit of math. We know that the temperature of the water is decreasing by 0.5°F every minute. So after 1 minute, the temperature of the water will be 80°F - 0.5°F = 79.5°F. After 2 minutes, the temperature will be 79.5°F - 0.5°F = 79°F. We can continue this pattern to find the temperature after 5 and a half minutes.
After 5 minutes, the temperature of the water will be 80°F - (0.5°F x 5) = 77.5°F. And after another half minute (or 0.5 minutes), the temperature will decrease by another 0.5°F, so the temperature will be 77.5°F - 0.5°F = 77°F.
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3. Technology required. Here are the data for the population f, in thousands, of a city d decades after 1960 along with the graph of the function given by f(d) = 25 - (1.19)ª. Elena thinks that shifting the graph off up by 50 will match the data. Han thinks that shifting the graph of f up by 60 and then right by 1 will match the data. a. What functions define Elena's and Han's graphs? b. Use graphing technology to graph Elena's and Han's proposed functions along with f. population (thousands) c. Which graph do you think fits the data better? Explain your reasoning.
The relationship between the functions are indicated in the attached graph. see further explanation below.
a. Elena's graph is obtained by shifting the original function f up by 50 units, so her function is g(d) = f(d) + 50 = 75 - (1.19)ª.
Han's graph is obtained by shifting the original function f up by 60 units and then to the right by 1 unit, so his function is h(d) = f(d - 1) + 60 = 85 - (1.19)^(a-1).
b. Using graphing technology, we can graph the three functions f, g, and h to compare how well they fit the given data. Here's an example graph:
graph of f, g, and h
c. From the graph, it appears that Han's function h fits the data better than Elena's function g. The graph of h seems to align more closely with the plotted data points than the other two functions. Moreover, the shift to the right and up of the graph of f seems to better capture the overall trend of the data, as it appears that the population increased and shifted slightly to the right over time.
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During a flood, there were 6000 acres of land under water. After 2 days, only 3375 acres of land were under water. Assume that the water receded at an exponential rate. Write a function to model this situation that has a B-value of 1.
where t is measured in days, and A(t) represents the amount of flooded land at time t. This function has a B-value of -0.3118.
To model the situation of the flood, we can use an exponential decay function, which represents the decreasing amount of flooded land over time. The function can be written as:
[tex]A(t) = A0 * e^{(-kt)}[/tex]
where A(t) is the amount of flooded land at time t, A0 is the initial amount of flooded land, k is a constant representing the rate of decay, and e is the mathematical constant approximately equal to 2.718.
To determine the value of k, we can use the given information that after 2 days, only 3375 acres of land were under water. Substituting t = 2 and A(t) = 3375 into the equation above, we get:
[tex]3375 = A0 * e^{(-2k)[/tex]
We also know that initially, there were 6000 acres of land under water. Substituting A0 = 6000 into the equation above, we get:
Dividing both sides by 6000, we get:
ln(0.5625) = -2k[tex]ln(0.5625) = -2k[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(0.5625) = -2k[/tex]
Solving for k, we get:
[tex]k = -ln(0.5625)/2[/tex]
k ≈ 0.3118
Therefore, the function to model the situation of the flood is:
[tex]A(t) = 6000 * e^{(-0.3118t)}[/tex]
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Find the three trigonometric ratios. If needed, reduce fractions.
A rectangular prism is shown in the image.
A rectangular prism with dimensions of 5 yards by 5 yards by 3 and one half yard.
What is the volume of the prism?
twenty eight and one half yd3
forty one and one fourth yd3
eighty seven and one half yd3
166 yd3
The volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]
What is the volume of the prism?The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length is 5 yards, the width is 5 yards, and the height is 3 and 1/2 yards. We can convert the height to a mixed number fraction of 7/2 yards.
Therefore, the volume of the prism is:
V = lwh = 5 yards × 5 yards × 7/2 yards = 87.5 cubic yards
So, the volume of the prism is 87 and 1/2 cubic yards or 87.5 [tex]yd^{3}[/tex]
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The right triangle shown is enlarged such that each side is multiplied by the value of the hypotenuse, 3y. Find the expression that represents the perimeter of the enlarged triangle. TRIANGLE AND ANSWER CHOICES BELOW!
Answer:
c.
Step-by-step explanation:
The original triangle has two sides with length 4x each, and the hypotenuse has length 3y.
After the enlargement, each of the sides with length 4x becomes 3y × 4x = 12xy, and the hypotenuse becomes 3y × 3y = 9y^2.
Therefore, the perimeter of the enlarged triangle is the sum of the lengths of its three sides:
12xy + 12xy + 9y^2 = 24xy + 9y^2 = 9y^2 + 24xy
So the answer is (C) 9y^2 + 24xy.
Using trig to find angles.
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x ≈ 39.5°
Step-by-step explanation:
using the cosine ratio in the right triangle
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{OP}{NP}[/tex] = [tex]\frac{64}{83}[/tex] , then
x = [tex]cos^{-1}[/tex] ( [tex]\frac{64}{83}[/tex] ) ≈ 39.5° ( to the nearest tenth )
In triangle ∆ABC, m<A = 33°, m<C = 58°, and AB = 25 in. What is AC to the nearest tenth of an inch?
1. 16.1 in.
2. 38.9 in
3. 42 in.
4. 12 in.
The value of AC to the nearest tenth is 29.5
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
Angle B = 180-(33+58)
= 180-91 = 89°
using sine rule
represent AC by x
x/ sin89 = 25/sin 58
xsin58 = 25sin89
0.848x = 0.9998×25
0.848x = 24.995
x = 24.995/0.848
x = 29.5( nearest tenth)
therefore the value of AC is 29.5.
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Write the functions in standard form:
h(x)=2(x-3)²-9
h(x)=
p(x) = -5(x + 2)² + 15
p(x)=
Answer:
[tex]h(x)=2x^2-12x+9[/tex], [tex]p(x)=-5x^2-20x-5[/tex]
Step-by-step explanation:
To get to the standard form of a quadratic equation, we need to expand and simplify. Recall that standard form is written like so:
[tex]ax^2+bx+c[/tex]
Where a, b, and c are constants.
Let's expand and simplify h(x).
[tex]2(x-3)^2-9=\\2(x^2+9-6x)-9=\\2x^2+18-12x-9=\\2x^2+9-12x=\\2x^2-12x+9[/tex]
Thus, [tex]h(x)=2x^2-12x+9[/tex]
Let's do the same for p(x).
[tex]-5(x+2)^2+15=\\-5(x^2+4+4x)+15=\\-5x^2-20-20x+15=\\-5x^2-5-20x=\\-5x^2-20x-5[/tex]
Thus, [tex]p(x)=-5x^2-20x-5[/tex]
1. suppose we know that the average weight of coyotes is 14.5kg with a standard deviation of 4kg. what is the probability of trapping a coyote that is 17kg or larger?
The probability of trapping a coyote that is 17kg or larger, given an average weight of 14.5kg and a standard deviation of 4kg is approximately 0.2743 or 27.43%.
To solve the problem, we first need to standardize the weight of the coyote using the formula:
z = (x - μ) / σ
Where:
x = the weight of the coyote we want to find the probability for (17kg in this case)
μ = the population mean (14.5kg in this case)
σ = the population standard deviation (4kg in this case)
z = the standardized score
Substituting the given values in the formula, we get:
z = (17 - 14.5) / 4
z = 0.625
Next, we need to find the probability of getting a coyote weighing 17kg or more, which is equivalent to finding the area under the normal distribution curve to the right of z = 0.625. We can use a standard normal distribution table or a calculator to find this probability.
Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the area under the curve to the left of a specified z-score. Since we want the area to the right of z = 0.625, we can subtract the CDF from 1 to get the area to the right.
Using a standard normal distribution table or calculator, we find that the CDF for z = 0.625 is approximately 0.734. Therefore, the area to the right of z = 0.625 is 1 - 0.734 = 0.266 or 26.6%.
Thus, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.
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Using a standard normal distribution table or a calculator, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.
What exactly is a standard normal distribution?The standard normal distribution is a probability distribution that is used to calculate probabilities associated with a random variable that has a normal distribution with mean 0 and standard deviation 1. Any normally distributed random variable can be standardized by subtracting its mean and dividing by its standard deviation to obtain a new variable with mean 0 and standard deviation 1.
In this case, we are given that the weight of coyotes has a normal distribution with a mean of 14.5kg and a standard deviation of 4kg. We want to find the probability of trapping a coyote that is 17kg or larger.
To calculate this probability, we need to standardize the weight of a 17kg coyote using the formula:
z = (× - μ) / σ
where:
x is the value we want to standardize (in this case, 17kg),
μ is the mean of the distribution (14.5kg),
σ is the standard deviation of the distribution (4kg).
Substituting the values we have:
[tex]z =\frac{(17 - 14.5)}{4} = 0.625[/tex]
This value of 0.625 is the z-score for a coyote weighing 17kg. The z-score represents the number of standard deviations that a particular value is above or below the mean.
Next, we need to find the probability of a randomly selected coyote weighing 17kg or larger, which can be calculated using the standard normal distribution table or a calculator.
The standard normal distribution table gives the probability associated with a given z-score. However, since the table only gives probabilities for z-scores less than 0, we need to use the fact that the standard normal distribution is symmetric about the mean (0) to find the probability of a z-score greater than 0.625.
Specifically, we can use the property that:
P(Z > z) = 1 - P(Z < z)
where Z is a standard normal random variable and z is a z-score. This formula tells us that the probability of a z-score greater than a certain value is equal to 1 minus the probability of a z-score less than that value.
Using this formula, we can calculate:
P(Z > 0.625) = 1 - P(Z < 0.625)
We can look up the value of P(Z < 0.625) in a standard normal distribution table or calculate it using a calculator. For example, using a standard normal distribution table, we can find that P(Z < 0.625) = 0.734.
Substituting this value into the formula, we get:
P(Z > 0.625) = 1 - 0.734 = 0.266
Therefore, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.
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past data shows that the standard deviation of apartments for rent in the area is $200. suppose we want a 98% confidence interval with margin of error of 50. what sample size do we need?
A sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50.
How to calculate sample size?To calculate the sample size required for a 98% confidence interval with a margin of error of 50, we need to use the following formula:
n = [Z*(σ/ME)]^2
where:
n = the sample size needed
Z = the Z-score for the desired confidence level (98% or 2.33)
σ = the standard deviation of apartments for rent in the area ($200)
ME = the margin of error ($50)
Plugging in the given values, we get:
n = [2.33*(200/50)]^2
n = [9.32]^2
n ≈ 86.7
Since we cannot have a fractional sample size, we round up to the nearest whole number to get the final answer.
Therefore, a sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50, given that the standard deviation of apartments for rent in the area is $200.
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a random sample of n equal to 64 scores is selected from a normally distributed population with mu equal to 77 and sigma equal to 21. what is the probability that the sample mean will be less than 79? hint: this is a z-score for a sample.
The probability of the sample mean being less than 79 is 77.64%
In order to solve the given problem we have to take the help of Standard error mean
SEM = ∑/√(n)
here,
∑ = population standard deviation
n = sample size
hence, the z-score can be calculated as
z = ( x' - μ)/σ/√(n)
here,
x' = sample mean
μ = population mean
σ = population standard deviation
n = sample size
adding the values into the formula
SEM = σ / √(n)
= 21/√64
= 2.625
z = (x' - μ)/SEM
= (79-77)/2.625
= 0.76
now, using standard distribution table we find that probability of a z-score is less than 0.77 then converting it into percentage
0.77 x 100
= 77%
The probability of the sample mean being less than 79 is 77.64%
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