One possible null hypothesis for this paired sample study could be: "There is no significant difference in the amount of caffeine (in milligrams) ingested before and after lunch among the 45 volunteer citizens from the small community."
Based on your question, we can construct a null hypothesis for this paired sample study involving 45 volunteer citizens from a small community. The terms "studies," "samples," and "small" are included in the context of the question. Here's a possible null hypothesis:
Null Hypothesis (H0): There is no significant difference in the mean amount of caffeine ingested by the 45 volunteer citizens before and after lunch each day.
The null hypothesis is a statistical assumption that says there is no statistical significance in a group of observations. Hypothesis testing is used to test the reliability of a hypothesis using sample data. It is sometimes called "blank" and stands for H0. The null hypothesis, also known as the Conjecture, is used in quantitative analysis to test a theory about business, investment, or the economy to determine whether the idea is true or false.
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What is | –10 |
Ignore thissssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answer: 10
Step-by-step explanation:
| –10 | = 10
Because that's the number of spaces it's from 0. :-)
The histogram shows the numbers of magazines read last month by the students in a class.
A histogram, titled Magazines. The vertical axis is labeled frequency. The horizontal axis is labeled magazines read and has bins with the following intervals: For 0 to 1, the bar height is 2. For 2 to 3, the bar height is 15. For 4 to 5, the bar height is 0. For 6 to 7, the bar height is 3.
a. Which interval contains the fewest data values?
Responses
0–1
0–1
2–3
2–3
4–5
4–5
6–7
6–7
Question 2
b. How many students are in the class?
The class has
students.
c. What percent of the students read fewer than six magazines?
% read fewer than six magazines.
Skip to navigation
The histogram shows the numbers of magazines read last month by the students in a class.
A histogram, titled Magazines. The vertical axis is labeled frequency. The horizontal axis is labeled magazines read and has bins with the following intervals: For 0 to 1, the bar height is 2. For 2 to 3, the bar height is 15. For 4 to 5, the bar height is 0. For 6 to 7, the bar height is 3.
a. Which interval contains the fewest data values?
Responses
0–1
0–1
2–3
2–3
4–5
4–5
6–7
6–7
Question 2
b. How many students are in the class?
The class has
students.
c. What percent of the students read fewer than six magazines?
% read fewer than six magazines.
Skip to navigation
The histogram shows the numbers of magazines read last month by the students in a class.
A histogram, titled Magazines. The vertical axis is labeled frequency. The horizontal axis is labeled magazines read and has bins with the following intervals: For 0 to 1, the bar height is 2. For 2 to 3, the bar height is 15. For 4 to 5, the bar height is 0. For 6 to 7, the bar height is 3.
a. Which interval contains the fewest data values?
Responses
0–1
0–1
2–3
2–3
4–5
4–5
6–7
6–7
Question 2
b. How many students are in the class?
The class has
students.
c. What percent of the students read fewer than six magazines?
% read fewer than six magazines.
Skip to navigation
The histogram shows the numbers of magazines read last month by the students in a class.
A histogram, titled Magazines. The vertical axis is labeled frequency. The horizontal axis is labeled magazines read and has bins with the following intervals: For 0 to 1, the bar height is 2. For 2 to 3, the bar height is 15. For 4 to 5, the bar height is 0. For 6 to 7, the bar height is 3.
a. Which interval contains the fewest data values?
Responses
0–1
0–1
2–3
2–3
4–5
4–5
6–7
6–7
Question 2
b. How many students are in the class?
The class has
students.
c. What percent of the students read fewer than six magazines?
% read fewer than six magazines.
Skip to navigation
The histogram shows the numbers of magazines read last month by the students in a class.
A histogram, titled Magazines. The vertical axis is labeled frequency. The horizontal axis is labeled magazines read and has bins with the following intervals: For 0 to 1, the bar height is 2. For 2 to 3, the bar height is 15. For 4 to 5, the bar height is 0. For 6 to 7, the bar height is 3.
a. Which interval contains the fewest data values?
Responses
0–1
0–1
2–3
2–3
4–5
4–5
6–7
6–7
Question 2
b. How many students are in the class?
The class has
students.
c. What percent of the students read fewer than six magazines?
% read fewer than six magazines.
Skip to navigation
The histogram shows the numbers of magazines read last month by the students in a class.
A histogram, titled Magazines. The vertical axis is labeled frequency. The horizontal axis is labeled magazines read and has bins with the following intervals: For 0 to 1, the bar height is 2. For 2 to 3, the bar height is 15. For 4 to 5, the bar height is 0. For 6 to 7, the bar height is 3.
a. Which interval contains the fewest data values?
Responses
0–1
0–1
2–3
2–3
4–5
4–5
6–7
6–7
Question 2
b. How many students are in the class?
The class has
students.
c. What percent of the students read fewer than six magazines?
% read fewer than six magazines.
Skip to navigation
The histogram shows the numbers of magazines read last month by the students in a class.
A histogram, titled Magazines. The vertical axis is labeled frequency. The horizontal axis is labeled magazines read and has bins with the following intervals: For 0 to 1, the bar height is 2. For 2 to 3, the bar height is 15. For 4 to 5, the bar height is 0. For 6 to 7, the bar height is 3.
a. Which interval contains the fewest data values?
Responses
0–1
0–1
2–3
2–3
4–5
4–5
6–7
6–7
Question 2
b. How many students are in the class?
The class has
students.
c. What percent of the students read fewer than six magazines?
% read fewer than six magazines.
Skip to navigation
1. The interval contains the fewest data values is 4-5.
2. The total number of students are 20.
3. The percent of the students read fewer than six magazines is 85%.
We have histogram that shows the numbers of magazines read last month by the students in a class.
1. The interval contains the fewest data values is 4-5 as it has 0 data.
2. The total number of students are
= 2 + 15 + 0 + 3
=20
3. The percent of the students read fewer than six magazines
= 17/20 x 100
= 85%
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Taylor Polynomial: Consider the approximation of the exponential by its third degree Taylor Polynomial: ex≈P3(x)=1+x+x^2/2+x^3/6
Compute the error e^x−P3(x) for various values of x.
The error between the exponential function e^x and its third degree Taylor polynomial P3(x) is given by e^x - P3(x).
Let's compute this error for various values of x:
For x = 0, we have e^0 - P3(0) = 1 - 1 = 0.
For x = 1, we have e^1 - P3(1) = e - (1 + 1 + 1/2 + 1/6) = e - 2.16667 ≈ -0.0803.
For x = -1, we have e^-1 - P3(-1) = 1/e - (1 - 1 + 1/2 - 1/6) = 0.581976 ≈ 0.582.
For x = 2, we have e^2 - P3(2) = e^2 - (1 + 2 + 4/2 + 8/6) = e^2 - 5.33333 ≈ 2.995.
For x = -2, we have e^-2 - P3(-2) = 1/e^2 - (1 - 2 + 4/2 - 8/6) = 0.133151 ≈ 0.133.
Overall, we can see that the error between the exponential function and its third degree Taylor polynomial decreases as x gets closer to 0. This is because the Taylor polynomial is centered at x = 0 and becomes a better approximation as x gets closer to the center. However, for larger values of x, the error can become quite significant.
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find exact values for each of the following quantities without using a calculator by applying definition of logarithms and logarithmic functions. (Simplify your answers completely.) (a) log3(27) =____ because 3 = _____ (b) log2(2,048) = _____ because 2 = _____(c) log3(1/81) = ______ because 3 = _____ (d) log2 (1) = _____ because 2 = _____(e) log 10(1/10) = _____because 10 = _____(f) log 6(6) = _____ because 6= ____(g) log3(3k) = ______ because 3=____
All the solutions of the logarithmic function,
a. log₃(27) = 3 because 3³ = 27.
b. log₂(2,048) = 11 because 2¹¹ = 2,048.
c. log₃(1/81) = -4 because 3⁻⁴ = 1/81.
d. log₂(1) = 0 because 2⁰ = 1.
e. log₁₀(1/10) = -1 because 10⁻¹ = 1/10.
f. log₆(6) = 1 because 6¹ = 6.
g. log₃(3k) = 1 + log₃k
(a) The expression is log₃ (27),
Now, the exponent to which 3 must be raised to obtain 27.
Since 3³ = 27
log₃ (27) = log₃ (3³)
= 3 log₃3
= 3
log₃(27) = 3 because 3³ = 27.
(b) Similarly, to find log_2(2,048), we need to determine the exponent to which 2 must be raised to obtain 2,048.
Since 2¹¹ = 2,048
Here, we have;
log₂(2,048) = log₂ (2¹¹)
= 11 log₂ (2)
= 11
log₂(2,048) = 11 because 2¹¹ = 2,048.
(c) For log₃(1/81), we need to determine the exponent to which 3 must be raised to obtain 1/81.
Since 3⁻⁴ = 1/81
So, we have
log₃(1/81) = -4 because 3⁻⁴ = 1/81.
(d) In the case of log₂(1), we need to determine the exponent to which 2 must be raised to obtain 1.
Since any number raised to the power of 0 equals 1, we have;
log₂(1) = 0 because 2⁰ = 1.
(e) For log₁₀(1/10), we need to determine the exponent to which 10 must be raised to obtain 1/10.
Since 10⁻¹ = 1/10
Hence, we have;
log₁₀(1/10) = -1 because 10⁻¹ = 1/10.
(f) When calculating log₆(6), we need to determine the exponent to which 6 must be raised to obtain 6.
Since any number raised to the power of 1 is equal to itself, we have
log₆(6) = 1 because 6¹ = 6.
(g) Lastly, for log₃(3k)
log₃(3k) = log₃3 + log₃k
= 1 + log₃k
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The logarithm method is used to determine the number of times to multiply the base number to obtain another number. The given expressions convert into respective powers of the base to give the final exact values. The values obtained depict the fundamental property of logarithms.
Explanation:The logarithm function is a method of determining how many times one number must be multiplied by itself to reach another number. It is usually denoted as logb(x), where 'b' is the base, 'x' is the result of the multiplication, and the result of the log function is the number of times we need to multiply.
log3(27) = 3 because 3^3 = 27log2(2048) = 11 because 2^11 = 2048log3(1/81) = -4 because 3^-4 = 1/81log2(1) = 0 because 2^0 = 1log10(1/10) = -1 because 10^-1 = 1/10log6(6) = 1 because 6^1 = 6log3(3k) = k if k is a positive integer, because 3^k = 3k.Learn more about Logarithms here:https://brainly.com/question/37245832
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Solve linear equation by substitution. check solution
y = -2x + 4
-x + 3y = -9
The required solution (x, y) = (3, -2) satisfies both equations, and it is the correct solution.
To solve the linear equation -x + 3y = -9 by substitution using the equation y = -2x + 4, we can substitute y in the second equation with -2x + 4 from the first equation, as follows:
-x + 3(-2x + 4) = -9
x - 6x + 12 = -9
-7x = -21
x = 3
Now, we can use the value of x to find the value of y from the first equation,
y = -2x + 4:
y = -2(3) + 4
y = -2
So the solution to the system of equations is (x, y) = (3, -2).
To check the solution, we can substitute the values of x and y in both equations and verify that they are true:
y = -2x + 4 becomes -2 = -2(3) + 4, which is true.
-x + 3y = -9 becomes -3 + 3(-2) = -9, which is also true.
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the number of hours worked per year per person in a state is normally distributed with a standard deviation of 39. a sample of 15 people is selected at random, and the number of hours worked per year per person is given below. calculate the 98% confidence interval for the mean hours worked per year in this state. round your answers to the nearest integer and use ascending order. time 2051 2061 2162 2167 2169 2171 2180 2183 2186 2195 2196 2198 2205 2210 2211 provide your answer below:
Using a t-distribution with 14 degrees of freedom (n-1) and a 98% confidence level (α = 0.02/2 = 0.01 for each tail), we have:
sample mean (x) = (2051+2061+2162+2167+2169+2171+2180+2183+2186+2195+2196+2198+2205+2210+2211)/15 = 2180.6
sample standard deviation (s) = 39
standard error of the mean (SEM) = s/√n = 39/√15 ≈ 10.077
t-score for a 98% confidence level and 14 degrees of freedom (from t-distribution table or calculator) = 2.977
Margin of error (ME) = t-score × SEM = 2.977 × 10.077 ≈ 30.05
Therefore, the 98% confidence interval for the mean hours worked per year in this state is:
(x- ME, x+ ME) = (2180.6 - 30.05, 2180.6 + 30.05) = (2150, 2211)
Rounding to the nearest integer and putting the limits in ascending order, we get:
(2150, 2211)
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Evaluate the Riemann Sum forf(x)=2x^2if0\leq x \leq 2with four equal subintervals using right-hand endpoints as the sample points.
\frac{15}{4}
\frac{7}{2}
\frac{15}{2}
15
\frac{30}{2}
Answer:
the Riemann Sum for $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points is $\frac{15}{2}$.
Step-by-step explanation:
To evaluate the Riemann Sum for the function $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points, we first need to determine the width of each subinterval. Since we have four subintervals to cover the interval $[0, 2]$, each subinterval has a width of $\Delta x = \frac{2-0}{4} = \frac{1}{2}$.
Next, we need to choose a sample point from each subinterval to evaluate the function. Since we are using right-hand endpoints as the sample points, we choose the endpoint of each subinterval as the sample point. The four subintervals are:
$[0, \frac{1}{2}]$, with sample point $x_1 = \frac{1}{2}$
$[\frac{1}{2}, 1]$, with sample point $x_2 = 1$
$[1, \frac{3}{2}]$, with sample point $x_3 = \frac{3}{2}$
$[\frac{3}{2}, 2]$, with sample point $x_4 = 2$
The Riemann Sum is then given by:
∑i=14f(xi)Δx=f(x1)Δx+f(x2)Δx+f(x3)Δx+f(x4)Δx=2(12)2⋅12+2(1)2⋅12+2(32)2⋅12+2(2)2⋅12=12+2+92+4=152i=1∑4f(xi)Δx=f(x1)Δx+f(x2)Δx+f(x3)Δx+f(x4)Δx=2(21)2⋅21+2(1)2⋅21+2(23)2⋅21+2(2)2⋅21=21+2+29+4=215
Therefore, the Riemann Sum for $f(x)=2x^2$ with four equal subintervals using right-hand endpoints as the sample points is $\frac{15}{2}$.
The Riemann Sum is 15/2 or 7.5.
To evaluate the Riemann Sum for the function f(x) = 2x^2 on the interval [0, 2] using 4 equal subintervals and right-hand endpoints, follow these steps:
1. Determine the width of each subinterval:
Δx = (b - a) / n = (2 - 0) / 4 = 0.5
2. Identify the right-hand endpoints of each subinterval:
x1 = 0.5, x2 = 1, x3 = 1.5, x4 = 2
3. Evaluate the function at each right-hand endpoint:
f(x1) = 2(0.5)^2 = 0.5
f(x2) = 2(1)^2 = 2
f(x3) = 2(1.5)^2 = 4.5
f(x4) = 2(2)^2 = 8
4. Calculate the Riemann Sum using these values:
Riemann Sum = Δx * (f(x1) + f(x2) + f(x3) + f(x4))
Riemann Sum = 0.5 * (0.5 + 2 + 4.5 + 8)
Riemann Sum = 0.5 * (15)
Riemann Sum = 7.5
The Riemann Sum for the given function using 4 equal subintervals and right-hand endpoints is 7.5, which is not among the provided options. However, the closest answer choice would be 15/2 or 7.5.
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suppose that the mean daily viewing time of television is 8.35 hours. use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household (a) what is the probability that a household views television between 4 and 12 hours a day? (round your answer to four decimal places.)
Therefore, it is approximately 0.8911, or 89.11% (rounded to four decimal places), that a household watches television for between 4 and 12 hours per day.
z = (x - μ) / σ
For part (a), we want to find the probability that a household views television between 4 and 12 hours a day. We can translate this into finding the probability that a random variable X with mean μ = 8.35 and standard deviation σ = 2.5 falls between 4 and 12:
P(4 ≤ X ≤ 12)
To find this probability, we first standardize the values 4 and 12:
z1 = (4 - 8.35) / 2.5
= -1.74
z2 = (12 - 8.35) / 2.5 = 1.46
Now that we have the area under the curve between these two z-scores, we can use a normal distribution table or calculator to determine it:
P(-1.74 ≤ Z ≤ 1.46) ≈ 0.8911
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A circle has a circumference of 7{,}8507,8507, comma, 850 units. What is the radius of the circle?
Use 3. 14 for pi and enter your answer as a decimal
Cuál de las siguientes ecuaciones modela una recta creciente?
A. 2x+4y+12=0
B. 3x−2y+3=0
C. −x−3y−12=0
D. −5x+3y+9=0
The equations that models a growing line include the following:
B. 3x − 2y + 3 = 0
D. −5x + 3y + 9 = 0
What is a steeper slope?In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.
In order to determine an equation with a growing line, we would have to determine the slope of each line graphically and then taking note of the line with a positive slope because it indicates an increasing function.
In this context, we can reasonably infer and logically deduce that both 3x − 2y + 3 = 0 and −5x + 3y + 9 = 0 are equations that models a growing line.
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Complete Question:
Which of the following equations models a growing line?
A. 2x+4y+12=0
B. 3x−2y+3=0
C. −x−3y−12=0
D. −5x+3y+9=0
13 Consider the system of equations below.
5x + 2y = -3
8x-6y= -14
Which of the following is a graph of this system of equations?
The graph of the system of linear equation is attached below
What is graph of system of linear equationsThe graph of a linear equation is a line. Each point on the line is a solution to the equation. For a system of two equations, we will graph two lines. Then we can see all the points that are solutions to each equation. And, by finding what the lines have in common, we’ll find the solution to the system.
In this given problem, we can use a graphing calculator to plot the lines of the graph as well as find the point of intersection which will give us our solution.
The equations given are;
5x + 2y = -3 ...eq(i)
8x - 6y = -14 ...eq(ii)
Plotting this in a graphing calculator;
We can see that the solution to this graph which is the point of intersection is at (1, 1)
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a banker is interested in the percentage of banking customers who have a money market savings account. based on a recent banking newsletter, 50% of banking customers have a money market savings account. the banker believes this percent has decreased in recent months. if the banker wants to convert their test statistic to a probability, what is this called in hypothesis testing?
In hypothesis testing, converting a test statistic to a probability is called p-value. The p-value is the probability of obtaining a test statistic as extreme as the observed one or more extreme, assuming the null hypothesis is true.
If the p-value is less than the chosen level of significance, typically 0.05 or 0.01, the banker would reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis, which is that the proportion of banking customers with a money market savings account has decreased. If the p-value is greater than the chosen level of significance, the banker would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion has decreased.
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How much energy is required to raise the temperature of 12.2 grams of gaseous nitrogen from 24.5 °C to 39.3 °C ?
Approximately 187.97 Joules of energy is required to raise the temperature of 12.2 grams of gaseous nitrogen from 24.5 °C to 39.3 °C.
To calculate the energy required to raise the temperature of 12.2 grams of gaseous nitrogen from 24.5°C to 39.3°C, we need to use the following formula:
Q = m x c x ΔT
Where Q is the energy required (in joules), m is the mass of the substance (in grams), c is the specific heat capacity of the substance (in J/g°C), and ΔT is the change in temperature (in °C).
The specific heat capacity of nitrogen gas at constant pressure is approximately 1.04 J/g°C. Therefore, we can calculate the energy required as follows:
Q = 12.2 g x 1.04 J/g°C x (39.3°C - 24.5°C)
Q = 163.52 J
Therefore, it would require 163.52 joules of energy to raise the temperature of 12.2 grams of gaseous nitrogen from 24.5°C to 39.3°C.
To calculate the energy required to raise the temperature of 12.2 grams of gaseous nitrogen from 24.5 °C to 39.3 °C, you can use the formula:
q = mcΔT
where:
- q is the energy required (in Joules)
- m is the mass of the substance (in grams)
- c is the specific heat capacity of the substance (in J/g°C)
- ΔT is the change in temperature (in °C)
For gaseous nitrogen, the specific heat capacity (c) is approximately 1.04 J/g°C.
Now, let's calculate the energy required:
1. Calculate the mass (m): 12.2 grams
2. Calculate the change in temperature (ΔT): 39.3°C - 24.5°C = 14.8°C
3. Use the formula q = mcΔT:
q = (12.2 g) * (1.04 J/g°C) * (14.8 °C)
q ≈ 187.97 Joules
So, approximately 187.97 Joules of energy is required to raise the temperature of 12.2 grams of gaseous nitrogen from 24.5 °C to 39.3 °C.
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What is the correct set of image points for trapezoid W’X’Y’Z’?
W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
W’(4, 2), X’(3, 4), Y’(1, 4), Z’(0, 2)
W’(–2, –4), X’(–4, –3), Y’(–4, –1), Z’(–2, 0)
W’(2, 4), X’(4, 3), Y’(4, 1), Z’(2, 0)
The correct set of image points for trapezoid W’X’Y’Z’ for 180 degrees rotation is (a) W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
The set of image points for trapezoid W’X’Y’Z’From the question, we have the following parameters that can be used in our computation:
W(-4, 2), X(-3, 4), Y(-1, 4), Z(0, 2)
Rule: 180 degrees rotation
The rule of 180 degrees rotation is
(x, y) = (-x, -y)
Substitute the known values in the above equation, so, we have the following representation
W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
Hence, the image = W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
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Find
(sec A x sin C - tan A x tan C)/sin B
where
A triangle ABC is right angled at B
The given expression, (sec A x sin C - tan A x tan C)/sin B, simplifies to (x/40) x AB, where AB is the length of the side opposite the right angle in triangle ABC.
Since triangle ABC is right-angled at B, we can use the following trigonometric ratios:
sin A = opposite/hypotenuse = AC/BC
cos A = adjacent/hypotenuse = AB/BC
tan A = opposite/adjacent = AC/AB
sin C = opposite/hypotenuse = AB/BC
cos C = adjacent/hypotenuse = AC/BC
tan C = opposite/adjacent = AB/AC
Using these ratios, we can simplify the given expression as follows:
(sec A x sin C - tan A x tan C)/sin B
= [(1/cos A) x sin C - tan A x tan C]/sin B (using sec A = 1/cos A)
= [(1/cos A) x (AB/BC) - (AC/AB) x (AB/AC)]/sin B (substituting sin C and tan C)
= [(AB/BCcos A) - (AC/BC)]/sin B (simplifying)
= [(AB/BC) - (ACcos A/BCcos A)]/sin B (getting a common denominator)
= [(AB - ACcos A)/BC]/sin B (simplifying)
= [(AB - ABsin A)/BC]/sin B (substituting)
Since triangle ABC is right-angled at B, we can use the following trigonometric ratios:
sin A = opposite/hypotenuse = AC/BC
cos A = adjacent/hypotenuse = AB/BC
tan A = opposite/adjacent = AC/AB
sin C = opposite/hypotenuse = AB/BC
cos C = adjacent/hypotenuse = AC/BC
tan C = opposite/adjacent = AB/AC
Using these ratios, we can simplify the given expression as follows:
(sec A x sin C - tan A x tan C)/sin B
= [(1/cos A) x sin C - tan A x tan C]/sin B (using sec A = 1/cos A)
= [(1/cos A) x (AB/BC) - (AC/AB) x (AB/AC)]/sin B (substituting sin C and tan C)
= [(AB/BCcos A) - (AC/BC)]/sin B (simplifying)
= [(AB/BC) - (ACcos A/BCcos A)]/sin B (getting a common denominator)
= [(AB - ACcos A)/BC]/sin B (simplifying)
= [(AB - ABsin A)/BC]/sin B (substituting sin A = AC/BC)
= [AB(1 - sin A)/BC]/sin B (factoring out AB)
= [(AB/BC) x (cos A/sin A)]/sin B (using sin A = opposite/hypotenuse and cos A = adjacent/hypotenuse)
= [cot A x (AB/BC)]/sin B (using cot A = cos A/sin A)
= (AB/BC) x (cos A/sin A) x (1/sin B) (multiplying fractions)
= (AB/BC) x (cos A/sin A) x csc B (using csc B = 1/sin B)
= (AB/BC) x cot A x csc B (using cot A = cos A/sin A)
= (BC/AB) x tan A x sin B (taking the reciprocal of both sides)
= (2BC/2AB) x (sin B/cos B) x (sin A/cos A) (multiplying and dividing by cos B and cos A)
= (BC/AB) x (2sin Bcos A)/(2sin A cos B) (simplifying)
= (BC/AB) x (sin (B + A)/sin (A + B)) (using sum and difference formulae)
= (BC/AB) x (sin C/sin 90) (since A + B + C = 90 degrees in a right-angled triangle)
= (BC/AB) x sin C
Substituting the given values, we get:
= [(2x + 20)/80] x AB
= (x/40) x AB
Therefore, the final answer is (x/40) x AB.
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Round 8,631 to the nearest ten thousand
Answer:
9,000
Step-by-step explanation:
Answer: 9,000
Step-by-step explanation:
When the next number over is 5 or above, you round up. This would give you 9,000. If you needed to round to the nearest hundred it would be 8,600 for example.
what is the diameter of a hemisphere with a volume of 557 m 3 , 557 m 3 , to the nearest tenth of a meter?
The diameter of the hemisphere with a volume of 557 m³ is approximately 12.8 m, to the nearest tenth of a meter.
The volume of a hemisphere can be calculated using the formula V = (2/3)πr³, where V is the volume and r is the radius. Given that the volume of the hemisphere is 557 m³, we can find the radius by solving for r:
557 = (2/3)πr³
To find the radius, first, we need to isolate r³ by multiplying both sides by 3/(2π):
r³ = (3 * 557) / (2 * π)
r³ ≈ 265.18
Now, take the cube root of both sides to find the radius:
r ≈ 6.4 m
To find the diameter, simply multiply the radius by 2:
d ≈ 2 * 6.4
d ≈ 12.8 m
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The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
Explain what the ratio 8:73 represents.
The ratio 8:73 represents the ratio of total athletes to 7th grade football players.
The ratio 8:73 represents the ratio of 6th grade football players to total athletes.
The ratio 8:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 8:73 represents the ratio of 6th grade athletes to total athletes.
Answer:
Step-by-step explanation:
/,
The ratio 8:73 represents the ratio of 6th grade football players to total athletes. The Option B is correct.
How do we derive the answer?We must add up the number of football players in each grade to get the ratio/
Data:
6th grade: 8 football players
7th grade: 15 football players
8th grade: 10 football players
The total number of football players is:
= 8 + 15 + 10
= 33.
The total number of athletes is:
6th grade: 2 (basketball) + 1 (baseball) + 7 (soccer) + 8 (football) = 18
7th grade: 4 (basketball) + 6 (baseball) + 4 (soccer) + 15 (football) = 29
8th grade: 7 (basketball) + 5 (baseball) + 4 (soccer) + 10 (football) = 26
The total number of athletes is:
= 18 + 29 + 26
= 73.
Therefore, the ratio of 6th grade football players to total athletes is 8:73.
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A recipe that makes s for 2/3 cup of flour how much flour is required to make 20 servings.
Answer:
14/13
Step-by-step explanation:
40/3
five hundred teenagers were sampled at random about their favorite movie genre. the results are listed in the table below. out of a population of three thousand teenagers, about how many will prefer action movies?
Out of the 500 teenagers sampled at random, the table presents their preferences in terms of favorite movie genres. To estimate the number of teenagers out of a population of 3,000 who prefer action movies, we can use the proportion of action movie fans from the sample.
Let's say the table shows that "x" out of the 500 sampled teenagers prefer action movies. To find the proportion of action movie fans in the sample, we divide the number of action movie fans by the total number of teenagers in the sample:
Proportion of action movie fans = (x / 500)
Now, we can use this proportion to estimate the number of teenagers who prefer action movies in the entire population of 3,000 teenagers. To do this, multiply the proportion of action movie fans by the total population:
[tex]Estimated action movie fans = Proportion of action movie fans * Total population[/tex]
Estimated action movie fans = (x / 500) * 3,000
By calculating this value, we can estimate the number of teenagers in the population of 3,000 who will prefer action movies based on the results of the random sample.
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given that z is a standard normal random variable what is the probability that z ≥ -2.12?
a. 0.966
b. 0.017
c.4830
0.9830
From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. The standard error of the mean is
a. 3
b. 2
c. greater than 2
d. less than 2
The probability that z ≥ -2.12 can be found using a standard normal distribution table or calculator. The answer is approximately 0.9830. 2. For a sample of 49 elements with a sample mean of 56 and a sample standard deviation of 14, the standard error of the mean is: b. 2
The standard error of the mean can be calculated using the formula:
[tex]standard error = sample standard deviation / square root of sample size[/tex]
In this case, the sample standard deviation is 14 and the sample size is 49. Therefore, the standard error of the mean is:
standard error = 14 / √49
standard error = 14 / 7
standard error = 2
So the answer is (b) 2.
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Select ALL that are properties of isosceles trapezoids.
Group of answer choices
consecutive angles are supplementary
One pair of opposite parallel sides
Diagonals are congruent
Two pairs of opposite parallel sides
Opposite angles are congruent
base angles are congruent
Diagonals bisect each other
The answer is: one pair of opposite parallel sides, congruent diagonals, and congruent base angles.
What are the properties of an isosceles trapezoids?An isosceles trapezoid has the following properties:
- One pair of opposite parallel sides
- Diagonals are congruent
- Congruent base angles
As a result, the right options are:
- One set of opposite parallel sides
- Congruent diagonals
- Congruent base angles
Hence, answer is: one pair of opposite parallel sides, congruent diagonals, and congruent base angles.
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Average Cost Graph The total daily cost in dollars) of producing a mountain bikes is given by C(x) = 936 +80+ 0.12 The average cost function C(x) decreases until e = cand increases afterwards. If the goal of the company is to make the mountain bike as affordable as possible, they should target the production level of c mountain bikes daily Find c Round to 2 decimal places. mountain bikes daily
The given function is C(x) = 936 + 80x + 0.12x^2, where x represents the number of mountain bikes produced daily. The average cost function is also given by C(x).
To make the mountain bike as affordable as possible, the company should target a production level of 333.33 mountain bikes daily, where the average cost function is at its minimum. Rounded to 2 decimal places, the answer is
c = 333.33.
First, let's correct the given cost function: C(x) = 936x + 80x^2 + 0.12x^3. Now, we'll use the terms "function," "average," and "increases."
To find the average cost function, we need to divide the total cost function, C(x), by the number of mountain bikes produced daily, x. Let A(x) represent the average cost function:
A(x) = C(x) / x
Now, let's substitute C(x) into this equation:
A(x) = (936x + 80x^2 + 0.12x^3) / x
Simplify by canceling out an x term:
A(x) = 936 + 80x + 0.12x^2
To find the production level c where the average cost function decreases and then increases, we need to find the minimum point on the A(x) curve. To do this, we'll differentiate A(x) with respect to x to obtain the first derivative:
A'(x) = 80 + 0.24x
Now, set the first derivative equal to zero and solve for x:
80 + 0.24x = 0
0.24x = -80
x = c = -80 / 0.24
Round to 2 decimal places:
c ≈ 333.33
So, to make the mountain bike as affordable as possible, the company should target a production level of approximately 333.33 mountain bikes daily.
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Pablo recorded the colors of cars driving by his house. The table below shows the colors of the last 250 cars that drive by Pablo’s house
The probability that the next car to drive by Pablo's house will be red or blue is 12 / 25.
How to calculate the probabilityFor given data probabilities are,
color no. of cars probability
blue 70 0.28
green 30 0.12
red 50 0.2
white 80 0.32
yellow 20 0.08
total 250 1
Hence, the probability that the next car to drive by Pablo's house will be red or blue is,
= P(car drived will be red) + P(car drived will be blue)
= (50 / 250) + (70 / 250)
= 12/25
The probability is 12/25
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Calculate the area and circumference of a circle with diameter 8cm
Education: College Graduates - A local professor claims that college graduates in his program earn an annual salary of $53,500 or more in the first year after the completion of their master's degree. A rival university's faculty dispute that claim and claim that the actual value is less than that. A random sample of 20 program graduates found they earned an annual salary of $50,994 in the first year after the completion of their master's degree with a standard deviation of $521. Use a 5% error. What is the critical value for this problem? O-1.729 0-1.645 1.645 1.729
The critical value for this problem would be 1.729, as this corresponds to a 5% error level and a two-tailed test.
To explain further, we can use hypothesis testing to determine whether the claim made by the local professor is supported by the sample data.
H0: The true mean salary for college graduates in the program is equal to or less than $53,500.
And our alternative hypothesis as:
Ha: The true mean salary for college graduates in the program is greater than $53,500.
We can then use the sample mean and standard deviation to calculate the test statistic:
t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
t = (50994 - 53500) / (521 / sqrt(20))
t = -2.01
Using a t-distribution table with 19 degrees of freedom (sample size minus 1), and a significance level of 0.05 (corresponding to a 5% error), we can find the critical value for a two-tailed test:
t_critical = +/- 2.093
Since our calculated test statistic falls outside of the critical value range, we can reject the null hypothesis and conclude that there is evidence to suggest that the true mean salary for college graduates in the program is less than $53,500. Therefore, the rival university's faculty may have a valid point in disputing the local professor's claim.
To find the critical value for this problem, we will use a one-tailed t-test since we want to test if the actual value is less than $53,500.
Given:
- Sample size (n) = 20 graduates
- Significance level (α) = 5% or 0.05
- Degrees of freedom (df) = n - 1 = 20 - 1 = 19
Now, let's find the critical value (t) using the t-distribution table. For a one-tailed test at a 5% significance level and 19 degrees of freedom, the critical value is -1.729.
So, the critical value for this problem is -1.729.
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between clock skew and clock jitter, which is preferable and why? group of answer choices jitter is preferred because it is predictable jitter is preferred, because it increases max frequency skew is preferred, because it is more predictable and can sometimes increase max frequency skew is preferred because it is unpredictable
Between clock skew and clock jitter, skew is preferred because it is more predictable and can sometimes increase max frequency. This makes it easier to manage in electronic systems and can provide benefits in certain scenarios.
Jitter is preferred because it is predictable. Clock jitter refers to the variability of the clock signal and can be predicted and compensated for. On the other hand, clock skew refers to the difference in arrival time of the clock signal at different points in the circuit and can sometimes increase maximum frequency. However, skew is preferred because it is more predictable and can be compensated for, while jitter is preferred because it is unpredictable and can't be compensated for. Therefore, in general, jitter is considered more preferable than skew.
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There is a drawer with 10 red socks, 10 blue socks, and 10 white socks what is the least number of socks?
The least number of socks you need to pick is 10 red socks, 10 blue socks, and 10 white socks to ensure you have a matching pair. The least number of socks that can be taken from the drawer is one.
Follow these steps:
1. Pick one sock from the drawer (it could be any color, let's say red).
2. Pick a second sock from the drawer (if it's red, you have a matching pair; if not, let's say it's blue).
3. If you don't have a matching pair yet, pick a third sock from the drawer (now, it's either red, blue, or white, and you'll have a matching pair for sure).
So, the least number of socks you need to pick to ensure a matching pair is 3.
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If these two shapes are similar, what is the measure of the missing length q?
[tex]\cfrac{q}{10}=\cfrac{98}{49}\implies \cfrac{q}{10}=2\implies q=20[/tex]
solve the proportion 9/3x-15 = 3/12