There is enough proof that the mean raw score for the school's applicants is more than 30 at a significance level of α = 0.01, therefore we reject the null hypothesis.
The null hypothesis H0: μ ≤ 30 mean raw score for the school's applicants is less than or equal to 30 and the alternative hypothesis Ha: μ > 30
We can utilize a one-tailed t-test since we don't know the population standard deviation and our sample size is less than 30. The test statistic is evaluated
t = (x' - μ) / (s / √n)
here
x'= sample mean = 31,
μ = hypothesized population mean = 30,
s = standard deviation = 2.5,
n = sample size = 50.
t = (31 - 30) / (2.5 / √50)
= 3.16
Applying t-distribution table with degrees of freedom (df) = n - 1 = 49 and a significance level of α = 0.01, we find that the critical value is
t-critical = 2.404.
The calculated t-value (3.16) is greater than our critical value (2.404), we reject the null hypothesis since there is enough evidence to support the student's claim that the mean raw score for the school's applicants is more than 30 at a significance level of α = 0.01.
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Solve for x. Round your answer to the nearest tenth and type it in the blank without "x=".
Answer:
13.5
Step-by-step explanation:
We can solve for x using the side splitter theorem, assuming that the two triangles' bases are parallel.
[tex]\dfrac{\text{segment of left side}}{\text{left side}} = \dfrac{\text{segment of right side}}{\text{right side}}[/tex]
↓ plugging in the lengths given in the diagram
[tex]\dfrac{4}{4 + 5} = \dfrac{6}{x}[/tex]
[tex]\dfrac{4}{9} = \dfrac{6}{x}[/tex]
↓ cross-multiplying
[tex]4x = 9(6)[/tex]
[tex]4x = 54[/tex]
↓ dividing both sides by 4
[tex]x = 13.5[/tex]
What is the solution of the equation, x–11=16?
x=
in this question you need to find what x is what ever x is, is the answer
Answer:
x=27
Step-by-step explanation:
x-11=16
add 11 to both sides
x=27
The list shows the numbers of hours 5 employees worked at a store.
14 23 26 40 26
What is the mean of the numbers of hours worked by the employees?
Enter your answer as a decimal in the box provided.
Therefore, 25.8 hours per employee each week is the mean number of hours worked.
What does that mean?The mean in mathematics is the average value among a group of numbers. It is calculated by adding up all of the set's numbers, then dividing the result by the total number of numbers in the set.
You may calculate the mean, for instance, if you have the set of numbers 2, 4, 6, and 8, by adding them all together and dividing by the total number of numbers:
(2 + 4 + 6 + 8) / 4 = 20 / 4 = 5
Consequently, 5 is the mean of these numbers.
In this instance, a store employed 5 workers for varying shifts. The list displays each individual's hours worked.
14 23 26 40 26
We add up all of these numbers and divide by the total number of numbers to determine the mean:
(14 + 23 + 26 + 40 + 26) / 5
= 129 / 5 mean of the numbers of hours worked by the employees = 25.8
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3. The horizontal distance "d" of the tip of a pendulum from its
vertical position at rest can be represented by a sinusoidal function.
The tip of the pendulum has a maximum displacement of 7.5 inches
and completes one cycle in 3.1 sec. Assume that the pendulum is at
rest at t= 0 and swings forward first.
Determine the value of y when t = 3.1 s:_
Approximate the value of t when y = 4 for the second time:
The second time that d = 4 is approximately 2.275 seconds after the pendulum starts swinging forward from its vertical position at rest.
What is the sinusoidal function?
A sinusoidal function is a mathematical function that describes a repetitive oscillation that resembles a sine or cosine wave. It can be expressed in the general form:
f(x) = A sin (Bx + C) + D
We can use the general form of a sinusoidal function to model the horizontal distance "d" of the tip of the pendulum from its vertical position at rest:
d = A sin(ωt + φ) + C
where:
A = amplitude (maximum displacement) = 7.5 inches
ω = angular frequency = (2π)/T, where T is the period = 3.1 seconds
φ = phase shift (initial horizontal displacement) = 0 (since the pendulum is at rest at t=0)
C = vertical displacement = 0 (since the pendulum is at rest at its vertical position)
Plugging in the given values, we get:
d = 7.5 sin((2π/3.1)t)
Now we can use this equation to answer the given questions:
Determine the value of d when t = 3.1 s:
We simply plug in t = 3.1 into the equation:
d = 7.5 sin((2π/3.1)(3.1))
d = 7.5 sin(2π)
d = 0 inches
Therefore, when t = 3.1 seconds, the horizontal distance of the tip of the pendulum from its vertical position is 0 inches.
Approximate the value of t when d = 4 for the second time:
To find when d = 4 for the second time, we need to find the two values of t for which the sinusoidal function equals 4. We can use the fact that the sine function repeats itself every 2π radians to solve this problem.
First, we find the period of the sinusoidal function:
T = 2π/ω = 2π/(2π/3.1) = 3.1 seconds
Next, we find the time it takes for the function to complete half a cycle, or π radians:
t1 = (π/ω) + kT, where k is an integer
t1 = (π/(2π/3.1)) + k(3.1)
t1 = (3.1/2) + 3.1k
We want to find the second time that d = 4, so we need to find the smallest integer value of k for which t2 > t1, where t2 is the time when d = 4 for the second time.
t2 = (3π/ω) + kT
t2 = (3π/(2π/3.1)) + k(3.1)
t2 = (9.3/2) + 3.1k
We want to find the smallest integer value of k such that t2 > t1 and d = 4:
7.5 sin((2π/3.1)t1) = 4
7.5 sin((2π/3.1)t2) = 4
calculating
t1 ≈ 0.604 s
t2 ≈ 2.275 s
Therefore, the second time that d = 4 is approximately 2.275 seconds after the pendulum starts swinging forward from its vertical position at rest.
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A survey conducted in 2005 found that the State of Louisiana was the happiest State in the United States. The survey was completed before Hurricane Katrina destroyed most of New Orleans and the surrounding area. The information quality for this survey is probably not:
The information quality of the survey is not reliable for understanding the current happiness level in the state.
The information quality for this survey is likely outdated and not
representative of the current state of Louisiana, particularly after the
devastating impact of Hurricane Katrina in 2005.
The survey was conducted before the hurricane, which significantly
affected the region, including the mental health and well-being of its
residents.
Thus, the survey's results may not accurately reflect the current level of
happiness or satisfaction among Louisiana residents.
Therefore, the information quality of the survey is not reliable for
understanding the current happiness level in the state.
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pls help (show work)
Step-by-step explanation:
okay as we know a circle is a quarter 360° in total therefore all you have to do is say 360° multiplied by 165
If a cube that is 8cm long is painted orange and then cut into 1cm cubes how many cubes have exactly 2 sides painted orange
The solution is: number of cubes are 1120.
Here, we have,
Volume of wood block :
V = (n+5)(n+8)(n+14)
Number of cubes = Volume of wood block/ Volume of small cubes
Number of cubes, N = (n+5)(n+8)(n+14) ....1)
Number of cubes with on sides painted is :
n = (n+5-2)(n+8-2)(n+14-2)
n = (n+3)(n+6)(n+12)
It is given that :
n = N/2
(n+3)(n+6)(n+12) = (n+5)(n+8)(n+14)/2
Solving above equation, we get :
n = 2
Putting value of n in equation 1, we get :
N = (2+5)(2+8)(2+14)
N = 7×10×16
N = 1120 cubes
Therefore, number of cubes are 1120.
Hence, this is the required solution.
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complete question:
A block of wood is in the shape of a rectangular prism with dimensions n+5 cm, n+8 cm, and n+14 cm. All faces of the block are painted, and then the block is cut into 1cm cubes using parallel cuts to each face. If exactly half of the cubes have no paint on them, find the total number of cubes.
In a long run, what does new technology do to the LRATC?
In the long run, new technology can have a significant impact on the long-run average total cost (LRATC) of a company.
The LRATC curve represents the lowest possible average cost at which a company can produce a particular level of output in the long run. New technology can reduce the costs of production by improving efficiency, reducing waste, and increasing productivity, leading to lower LRATC. This can lead to a shift in the LRATC curve downward, indicating that the company can now produce the same output at a lower cost than before. This can make the company more competitive and increase its profitability.
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JK and YA intersect at point C.
Find the measure of ZJCA.
C
123°
A
K
Angles
The measure of angle JCA is 57°
What are verically opposite angles?When two lines intersect, the opposite (X) angles are equal. This means ;
123° = JCY
and JCA = YCK ( verically opposite angles)
The sum of angle at a point is 360. This means the addition of all the angles above is 360°.
Representing angle JCA by x , therefore,
x+x +123+123 = 360°( angle at a point)
2x + 246 = 360
2x = 360-246
2x = 114
divide both sides by 2
x = 114/2
x = 57°
therefore the measure of angle JCA is 57°
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how many 3 digit numbers can we make using the digits 2,3,4,5,6 without repetition
Answer:
60
Step-by-step explanation:
5x4x3=60 therefor you would get 60 3 digit numbers
A prism has a pentagonal base. The area of the pentagon is 45 cm up 2, the height of the prism is 13 cm. Find the volume of the prism.
The volume of the prism is approximately 4519.16 cubic centimeters.
We have,
To find the volume of the prism, we need to multiply the area of the base by the height.
The area of a regular pentagon can be found using the formula:
[tex]$A = \frac{5}{4} s^2 \cot(\frac{\pi}{5})$[/tex]
where s is the length of the side of the Pentagon.
We are given that the area of the pentagon is 45 cm².
Solving for s:
[tex]$45 = \frac{5}{4} s^2 \cot(\frac{\pi}{5})$\\[/tex]
[tex]$s^2 = \frac{4}{5} \cdot \frac{45}{\cot(\frac{\pi}{5})}$\\[/tex]
[tex]$s^2 \approx 28.478$\\[/tex]
[tex]$s \approx 5.334$[/tex]
Now that we know the length of a side of the pentagon, we can find the area of the base of the prism:
[tex]$A_{base} = 5 \cdot \frac{1}{2} s \cdot h$[/tex]
[tex]$A_{base} = 5 \cdot \frac{1}{2} \cdot 5.334 \cdot 13$[/tex]
[tex]$A_{base} \approx 346.935$[/tex]
Finally, we can find the volume of the prism:
[tex]$V = A_{base} \cdot h$[/tex]
[tex]$V = 346.935 \cdot 13$[/tex]
[tex]$V \approx 4519.16$[/tex]
Therefore,
The volume of the prism is approximately 4519.16 cubic centimeters.
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Clara is taking a medicine for a common cold. The table below shows the amount of medicine f(t), in mg, that was present in Clara's body after time t:
t (hours) 1 2 3 4 5
f(t) (mg) 236.5 223.73 211.65 200.22 189.41
Heidi was administered 300 mg of the same medicine. The amount of medicine in her body f(t) after time t is shown by the equation below:
f(t) = 300(0.946)t
Which statement best describes the rate at which Clara's and Heidi's bodies eliminated the medicine?
Heidi's rate of elimination is also decreasing over time, but at a slower rate than Clara's which decreases exponentially over time
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
f(t) = 300(0.946)^t
For Clara, we can calculate the rate of elimination by finding the difference in the amount of medicine present between two consecutive time points, and dividing by the time elapsed:
From t=1 to t=2: f(2) - f(1) = 223.73 - 236.5 = -12.77 mg
Rate of elimination = -12.77 mg / (2-1) hours = -12.77 mg/hour
From t=2 to t=3: f(3) - f(2) = 211.65 - 223.73 = -12.08 mg
Rate of elimination = -12.08 mg / (3-2) hours = -12.08 mg/hour
From t=3 to t=4: f(4) - f(3) = 200.22 - 211.65 = -11.43 mg
Rate of elimination = -11.43 mg / (4-3) hours = -11.43 mg/hour
From t=4 to t=5: f(5) - f(4) = 189.41 - 200.22 = -10.81 mg
Rate of elimination = -10.81 mg / (5-4) hours = -10.81 mg/hour
Hence , this expression tells us that the rate of elimination for Heidi is proportional to the amount of medicine in her body at any given time, and decreases exponentially over time as the amount of medicine decreases
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Lena, Alan, and Bill sent a total of 104 text messages over their cell phones during the weekend. Lena sent 8 fewer messages than Alan. Bill sent 2 times as many messages as Lena. How many messages did they each send?
So, Lena sent 24 messages, Alan sent 32 messages, and Bill sent 48 messages.
Let's denote the number of messages Lena, Alan, and Bill sent as L, A, and B, respectively. We are given the following information:
L + A + B = 104 (Total messages)
L = A - 8 (Lena sent 8 fewer messages than Alan)
B = 2L (Bill sent 2 times as many messages as Lena)
Now, we'll use the second equation to express A in terms of L:
A = L + 8
Next, substitute the expressions for A and B from equations 2 and 3 into equation 1:
L + (L + 8) + 2L = 104
Combine like terms:
4L + 8 = 104
Subtract 8 from both sides:
4L = 96
Divide by 4:
L = 24
Now that we have the number of messages Lena sent, we can find the number of messages Alan and Bill sent:
A = L + 8 = 24 + 8 = 32
B = 2L = 2 * 24 = 48
what is the sample size need to reduce the margin of error to 3.1% for a 95% confidence interval given that the proportion is unknown.
We need a sample size of at least 753 to reduce the margin of error to 3.1% for a 95% confidence interval when the proportion is unknown.
To determine the sample size needed to reduce the margin of error to 3.1% for a 95% confidence interval when the proportion is unknown, we need to use the following formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
n = sample size
Z = Z-score for the desired confidence level (95% confidence corresponds to a Z-score of 1.96)
p = proportion (since it's unknown, we use 0.5 to get the maximum sample size)
E = margin of error (in decimal form)
Plugging in the given values, we get:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.031^2
n = 752.61
Therefore, we need a sample size of at least 753 to reduce the margin of error to 3.1% for a 95% confidence interval when the proportion is unknown.
To determine the sample size needed to reduce the margin of error to 3.1% for a 95% confidence interval when the proportion is unknown, you can use the formula for sample size calculation in a proportion estimation:
n = (Z^2 * p * (1-p)) / E^2
Here,
- n is the sample size
- Z is the Z-score corresponding to the desired confidence level (1.96 for a 95% confidence interval)
- p is the proportion, which is unknown (since we don't know the proportion, we use the most conservative estimate, p=0.5)
- E is the margin of error (0.031 for 3.1%)
Now, let's plug in the values:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.031^2
n = (3.8416 * 0.5 * 0.5) / 0.000961
n = 1.0004 / 0.000961
n ≈ 1040.58
Since we cannot have a fraction of a participant, you should round up to the nearest whole number. Therefore, you would need a sample size of 1,041 to reduce the margin of error to 3.1% for a 95% confidence interval when the proportion is unknown.
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A sample size of at least 754 is needed to reduce the margin of error to 3.1% for a 95% confidence interval when the population proportion is unknown.
The formula for calculating the sample size needed to estimate a population proportion with a specified margin of error at a certain level of confidence is:
[tex]$n = \frac{z^2 \cdot p \cdot (1-p)}{E^2}$[/tex]
where:
n is the sample size needed
z is the critical value of the standard normal distribution corresponding to the desired level of confidence (for a 95% confidence interval, z = 1.96)
p is the estimated proportion of the population (since the proportion is unknown, we will use the conservative estimate of 0.5 to obtain the maximum possible sample size)
E is the desired margin of error (in decimal form)
Substituting the given values, we get:
[tex]$n = \frac{1.96^2 \cdot 0.5 \cdot (1-0.5)}{0.031^2} \approx 753.68$[/tex]
Therefore, a sample size of at least 754 is needed to reduce the margin of error to 3.1% for a 95% confidence interval when the population proportion is unknown.
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5. What information would you need in order to determine the absolute data of a rock
sample?
Answer:
natural radioactive decay, examples: postassium and carbon. Three ways to classify their physical properties mineralogical composition, grain size, and texture
Step-by-step explanation:
can someone help me PLEASE BE CORRECT
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 12.
The IQR is the best measure of variability, and it equals 12.
The range is the best measure of variability, and it equals 3.
The IQR is the best measure of variability, and it equals 3.
The appropriate measure of variability for the data in the box plot is the interquartile range (IQR), which is a measure of the spread of the middle 50% of the data.
From the box plot, we can see that the lower quartile (Q1) is located at 17, the upper quartile (Q3) is located at 20, and the median is located at 19. The IQR can be calculated as the difference between the upper and lower quartiles:
IQR = Q3 - Q1 = 20 - 17 = 3
Therefore, the IQR is 3 and it is the best measure of variability for the given data. The range, which is the difference between the maximum and minimum values (24 - 12 = 12), is not the best measure of variability in this case because it is affected by extreme values that may not be representative of the typical spread of the data.
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suppose the heights of professional horse jockeys are normally distributed with a mean of 62 in. and a standard deviation of 2 in. which group describes 16% of the population of horse jockeys?
The groups that describes 16% of the population of horse jockeys are option (c) jockeys who are shorter than 60 in. and (d) jockeys who are between 60 in. and 64 in.
To solve this problem, we need to use the standard normal distribution, where we can find the z-score associated with the given percentages using a z-table or calculator. The z-score tells us how many standard deviations a value is from the mean.
First, we can standardize the values using the formula
z = (x - μ) / σ
where z is the z-score, x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
a) To find the jockeys who are shorter than 58 in., we can standardize the value as
z = (58 - 62) / 2 = -2
Using a z-table, we can find that the percentage of values below z = -2 is approximately 0.0228, which is less than 16%. Therefore, a) is not correct.
b) To find the jockeys who are taller than 64 in., we can standardize the value as
z = (64 - 62) / 2 = 1
Using a z-table, we can find that the percentage of values above z = 1 is approximately 0.1587, which is also less than 16%. Therefore, b) is not correct.
c) To find the jockeys who are shorter than 60 in., we can standardize the value as
z = (60 - 62) / 2 = -1
Using a z-table, we can find that the percentage of values below z = -1 is approximately 0.1587, which is less than 16%. Therefore, c) is correct.
d) To find the jockeys who are between 60 in. and 64 in., we can standardize the values as
z1 = (60 - 62) / 2 = -1
z2 = (64 - 62) / 2 = 1
Using a z-table, we can find the percentage between z1 and z2, which is approximately 0.6826. Therefore, d) is also correct.
Therefore, the correct answers are (c) jockeys who are shorter than 60 in. and (d) jockeys who are between 60 in. and 64 in.
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The given question is incomplete, the complete question is:
Suppose the heights of professional horse jockeys are normally distributed with a mean of 62 in. and a standard deviation of 2 in.
Which group describes 16% of the population of horse jockeys?
Select each correct answer.
a) jockeys who are shorter than 58 in.
b) jockeys who are taller than 64 in.
c) jockeys who are shorter than 60 in.
d) jockeys who are between 60 in. and 64 in.
what’s the answer to this? I need help pls ease
die
Step-by-step explanation:
Two numbers have a sum of 80 and a difference of 16. what are the two numbers?
Answer: 48 and 32
Step-by-step explanation:
When a 99% con interval is calculated instead of a 95% con inter with n being the same, the margin of error will be
When calculating a confidence interval, the level of confidence chosen determines the range of values within which the true population parameter is expected to fall.
A 95% confidence interval means that if we repeatedly sample from the population and construct confidence intervals, 95% of those intervals will contain the true population parameter.
On the other hand, a 99% confidence interval means that if we repeatedly sample from the population and construct confidence intervals, 99% of those intervals will contain the true population parameter.
The margin of error, which is the amount by which the interval may vary due to sampling error, is directly affected by the level of confidence chosen.
As the level of confidence increases, the margin of error also increases. Therefore, when a 99% confidence interval is calculated instead of a 95% confidence interval with n being the same, the margin of error will be wider.
This means that the range of values within which the true population parameter is expected to fall will be larger with a 99% confidence interval, making the interval less precise but more conservative.
It is important to note that choosing a higher level of confidence comes at the cost of a wider margin of error, which may not always be practical or necessary depending on the research question and context.
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PLS HELP DUE TODAY!!!!
The values of the positive intergers a and b is 2 and 3 respectively and the value of 2a+3b is 13.
What is algebraic expression?An algebraic expression are the expression which consist the variables, coefficients of variables and constants. In the given problem, a and b are positive integers. The given expression in the problem is: ^2b^3=108.
Let us the hit and trial method to make both the equation equal. For a=1 and b= 1 the expression will be equal to 1. For a =2 and b=3,
(2)^2(3)^3 = 108
(4)(27) = 108
108 = 108
Here, left hand side of the expression is equal to the right hand side of the expression for a =2 and b=3. Thus the value of a and b are,
a = 2
b = 3
The value of the expression we have to find is, 2a+3b. Put the values of a and b in the above expression, we get,
2a+3b = 2^(2)+3^(3)
2a+3b = 4+9
2a+3b = 13
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a certain drug has a half-life in the body of . what should the interval between doses be, if the concentration of drug in the body should not fall below of its initial concentration? round your answer to significant digits.
The interval between doses should be approximately 10.4 hours to maintain a minimum concentration of 30% of the initial concentration in the body.
The interval between doses of a drug depends on its half-life and the desired minimum concentration in the body. The half-life of a drug is the time it takes for half of the initial dose to be eliminated from the body.
To determine the interval between doses, we can use the following formula
t = (t1/2 × ln(Cmin/Cmax)) / ln(2)
Where:
t1/2 is the half-life of the drug
Cmin is the desired minimum concentration in the body (expressed as a fraction of the initial concentration)
Cmax is the initial concentration of the drug
ln represents the natural logarithm function.
Substituting the given values, we get
t = (6.0h × ln(0.3)) / ln(2)
t ≈ 10.4h
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The given question is incomplete, the complete question is:
A certain drug has a half-life in the body of 6.0h. What should the interval between doses be, if the concentration of drug in the body should not fall below 30.% of its initial concentration?
What is the area of this figure? 10 mi 17 mi 3 mi 4 mi 4 mi 6 mi 4 mi 18 mi
The area of the figure is 197 square miles
How to find the area of the figure.To find the area of the figure, we need to first identify the shape of the figure. From the given dimensions, it appears to be an irregular quadrilateral with a triangle on top.
We can divide the figure into two parts: a rectangle with dimensions 17 mi by 10 mi, and a triangle with base 18 mi and height 3 mi.
The area of the rectangle is:
Area of rectangle = length x width = 17 mi x 10 mi = 170 mi^2
The area of the triangle is:
Area of triangle = (base x height) / 2 = (18 mi x 3 mi) / 2 = 27 mi^2
Therefore, the total area of the figure is the sum of the areas of the rectangle and triangle:
Total area = 170 mi^2 + 27 mi^2 = 197 mi^2
So the area of the figure is 197 square miles.
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B. Solve:
1. If there are 13 yellow balls and 25 brown balls in a jar, what is the probability that Jaide will pick out a brown ball from the jar?
2. From a pack of 52 cards, a card is drawn at random. What is the probability of getting a king?
Answer:
Step-by-step:
1.The probability of picking a brown ball can be calculated as:
Probability of picking a brown ball = Number of brown balls / Total number of balls
Number of brown balls = 25
Total number of balls = 13 + 25 = 38
Probability of picking a brown ball = 25/38
Probability of picking a brown ball is approximately 0.658 or 65.8%
Therefore, the probability of Jaide picking a brown ball from the jar is approximately 0.658 or 65.8%.
2.There are four kings in a pack of 52 cards (one king for each suit). Therefore, the probability of drawing a king from a pack of 52 cards can be calculated as:
Probability of drawing a king = Number of kings / Total number of cards
Number of kings = 4
Total number of cards = 52
Probability of drawing a king = 4/52
Probability of drawing a king is approximately 0.077 or 7.7%
Therefore, the probability of getting a king when drawing a card at random from a pack of 52 cards is approximately 0.077 or 7.7%.
The Phillips curve describes the relationship between... a. The output gap and potential GDP. O b. The money supply and interest rates. C. The unemployment rate and the rate of change of wages. O d. A
The Phillips curve describes the relationship between the unemployment rate and the rate of change of wages. Option C is the correct option.
What is Phillips curve?
The relationship between the rate of inflation and the unemployment rate is represented by the Phillips curve. The analysis of wage inflation and unemployment in the United Kingdom from 1861 to 1957 by A. W. H. Phillips, despite having forerunners, is a significant development in the field of macroeconomics. When unemployment was high, wages rose slowly; when unemployment was low, wages rose quickly, according to Phillips' research.
According to Phillips' hypothesis, as the unemployment rate declines, the labor market becomes more competitive and firms are forced to raise wages more quickly in order to recruit qualified workers. The pressure decreased as unemployment rates rose. The average relationship between wage behavior and unemployment over the course of the business cycle was represented by Phillips' "curve."
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The Central Limit Theorem is an important tool that provides the information you will need to use ___ to make ___ about a population mean
The Central Limit Theorem is an important tool that provides the information you will need to use sample means to make inferences about a population mean.
The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that if we take repeated random samples of size n from any population with a finite mean and variance, then the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.
This means that if we take a large enough sample size from a population, the distribution of the sample means will be approximately normal, even if the population distribution is not normal. This is important because the normal distribution is well understood and has many useful properties that make it easier to work with in statistical analyses.
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If you know the length of the longer leg of a 30-60-90 triangle, how do you find the length of the other, shorter leg?
As per the triangle, the length of the other, shorter leg is 3.46 units.
We know that a is twice the length of b, so we can write:
a = 2b
We also know that c is the square root of three times b, or:
c = √3b
Now, let's say we're given the length of the longer leg, a. We can use our equation a = 2b to solve for b:
a = 2b
b = a/2
So, we know that the shorter leg is half the length of the longer leg. For example, if a is 8, then b is 4.
To double-check our answer, we can use the equation for the hypotenuse:
c = √3b
c = √3(4)
c = 2√3 = 3.46
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Sally is 6ft tall there is a lamppost 15ft away from her and a building 45ft away from her how tall is the building
If Sally is 6ft tall there is a lamppost 15ft away from her and a building 45ft away from her, the building is 12ft tall.
We can use similar triangles to solve this problem. Let's assume that Sally's height is represented by the vertical line segment AB, the height of the building is represented by the vertical line segment CD, and the lamppost is represented by the point E.
We know that the distance between Sally and the lamppost is 15ft and the distance between Sally and the building is 45ft.
To find the height of the building, we need to find the length of the line segment CD. We can use the property of similar triangles that states that the ratio of corresponding sides in two similar triangles is equal.
Let's form two right triangles by drawing line segments AE and AC. We know that triangle ABE and triangle ABC are similar. We can set up a proportion as follows:
AB/AC = BE/BC
Substituting the known values, we get:
6/45 = x/15
Simplifying the equation, we get:
x = 2
Therefore, the height of the building is 2 times Sally's height, or:
2 * 6ft = 12ft
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The point (2, 3) is plotted on the coordinate plane.
Plot four points with integer coordinates that are each 3 units away from (2, 3).
A graph of four points with integer coordinates that are each 3 units away from (2, 3) is shown in the image attached below.
What is a translation?In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N).
Where:
N represents an integer.g(x) and f(x) represent functions.In order to write an equation that models the four points with integer coordinates that are each 3 units away from (2, 3), we would have to apply a set of translation to f(x) by 3 units:
A (5, 3)
B (-1, 3)
C (2, 6)
D (2, 0)
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Answer all of these questions. 1) If a total of 160 people bought drinks at the stadium on Friday, how many could be expected to have ordered a medium?
2) If a total of 480 people bought drinks at the stadium on Saturday, how many could be expected to have ordered a small?
3) If a total of 100 people bought drinks at the stadium on Monday, how many could be expected to have ordered a small, medium, or large?
The number that could be expected to have ordered a medium was 64 people.
The number that could be expected to have ordered a small would be 108 people.
The number that could have been expected to have ordered a small, medium, or large was 75 people.
How to find the expected sales ?The number that could have been expected to have ordered a medium was :
= 16 / ( 9 + 16 + 5 + 10 ) x 160 people
= 64 people
The number that could have been expected to have ordered a small would be :
= 9 / ( 9 + 16 + 5 + 10 ) x 480 people
= 108 people
The number that could have been expected to have ordered a small, medium, or large was :
= ( 9 + 16 + 5 ) / ( 9 + 16 + 5 + 10 ) x 100
= 75 people
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