Answer:
a+b>0, a>0, b>0, a-b<0
Step-by-step explanation:
well, a>0 and b>0 since they're both positive
Answer:
sample answer
Step-by-step explanation:
The number further left on a number line is the smaller number. For positive numbers, the number closest to zero is smaller. For negative numbers, the number closest to zero is larger. If a is less than b, and they are both positive, then a is closer to 0 than b. The opposite of a is also closer to zero than the opposite of b, so the opposite of a must be larger than the opposite of b.
Find the missing length indicated
The calculated value of the indicated missing length x in the right triangle is 12
How to determine the value of the indicated missing lengthGiven the right triangle
We can start by calculating the value of x using the following equivalent ratio
x : 9 = 25 - 9 : x
Evaluate the difference
This gives
x : 9 = 16 : x
Next, we express the equivalent ratio as a fraction
So, the ratio becomes
x/9 = 16/x
Cross multiply the equation to calculate x
So, we have the following
x * x = 9 * 16
Evaluate the product
x² = 144
Take the square root of both sides
So, we have the solution to be
y = 12
Hence, the value of x is 12
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A pyrotechnician is running a test for a fireworks display he is providing for an event downtown. He launches a test shell from the top of a tower. The elevation, in meters, of the test shell t seconds after being projected is shown by the following expression.
Look at the picture attached and then choose your answer pls!
Select the best description of the term 29.4 in the expression.
A. the total time the test shell is in the air
B. the initial velocity of the test shell
C. the highest elevation the test shell reaches
D. the initial elevation of the test shell
The best description of that term 29.4 in the expression is the initial velocity of the test shell. That is option B.
Who is a pyrotechnician?A pyrotechnician is defined as the individual that has been trained for safe storage, handling, and functioning of pyrotechnics such as fireworks.
While testing the display of the fireworks, he took note of the following:
The elevation in meters
The time in seconds
The change in velocity should be noted as the velocity of distance covered by a moving object with time.
Therefore, the term 29.4 is the initial velocity of the fireworks he projected.
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What comes next in pattern
167,118,82,57,41,?
Answer: 32
Step-by-step explanation: got you broski
show that if x < y are real numbers then there are innitely many rational numbers b such that x < b < y. g
To show that there are infinitely many rational numbers between any two real numbers x and y, where x< y, we can use the Archimedean property of the real numbers.
The Archimedean property states that for any two positive real numbers a and b, there exists a positive integer n such that na>b. Let's choose a positive integer n such that 1/n< y-x. Then we can divide the interval(x,y) into n subintervals of equal length:
(x, y) = (x, x + (y - x)/n) ∪ (x + (y - x)/n, x + 2(y - x)/n) ∪ ... ∪ (x + (n - 1)(y - x)/n, y).
Each of these intervals has length(y-x)/n, which is less than 1/n. therefore, there must be at least one integer k such that x+k(y-x) is a rational number. This is because the numerator k(y-x) is an integer, and the denominator n is a positive integer.Since there are n subintervals, we have found at least n different rational numbers between x and y.
However, since the choice of n was arbitrary we can choose a larger n to find even more rational numbers between x and y. Therefore, there must be infinitely many rational numbers between x and y.
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Let x and y be reals with x<y. Show that there are infinitely many rationals b such that x<b<y.
Pls help me answer the questions thank you
A. The capacity of most of the trimmer Sara sells is [tex]1\tfrac{1}{5}[/tex]
B. The total gas she needs to fill all trimmers is [tex]$22 \frac{7}{8}[/tex]
What is the use οf expressiοns in mathematics?Expressiοns are used extensively in mathematics, including arithmetic, calculus, and geοmetry. They are used in mathematical fοrmula representatiοn, equatiοn sοlutiοn, and mathematical relatiοnship simplificatiοn.
Part A
The capacity of most of the trimmer Sara sells is [tex]1\tfrac{1}{5}[/tex]
Part B
The total gas she needs to fill all trimmers is:
[tex]$\Rightarrow (1 \times 1\frac{1}{2}) + (5 \times 1\frac{5}{8}) + (1 \times 1\frac{7}{8} )+ (3 \times 2\frac{1}{8} ) + (2 \times 2\frac{1}{2} )[/tex]
⇒ [tex]$22 \frac{7}{8}[/tex]
Thus, The total gas she needs to fill all trimmers is [tex]$22 \frac{7}{8}[/tex]
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For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal? А. A random sample of 8 taken from a normally distributed population B. A random sample of 50 taken from a normally distributed population C. A random sample of 10 taken from a population dintribution that is skewed to the right D. A random sample of 75 taken from a population distribution that is skewed to the left E. A random sample of 100 taken from a population that is uniform
The conditions in which is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal : (C) A random sample of 10 taken from a population distribution that is skewed to the right.
In statistics, the normal or Gaussian distribution is a continuous probability distribution for real-valued random variables.
The normal distribution is important in statistics and is often used in the natural and social sciences to represent real-valued random variables whose distribution is unknown. Their importance is partly due to the central limit theorem. It states that in some cases the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable - whose distribution converges to a normal distribution as the size of the l sample increases.
Now,
If we look at the options given below, we see that the random samples in options A and B are normally distributed, so their sample means will be approximately normally distributed.
Similarly, option E indicates that the population is uniform, so the sample mean will also be approximately normal.
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Pls help, due tmr and confused..
The nearest whole number, which is 9. So the middle apartment number for house 17 is 9.
What is apartment?An apartment is a self-contained housing unit that occupies only part of a building. Apartments typically consist of one or more bedrooms, a kitchen, a living room, and a bathroom, and usually include amenities such as heating, air conditioning, and appliances. Apartments are usually rented, though some are owned. Living in an apartment can be a great way to save money, as apartments are often more affordable than larger homes.
The rule is to take the house number and divide it by two and round up to the nearest whole number. This will give the middle apartment number. For example, if the house number is 17, divide it by two which equals 8.5, and then round up to the nearest whole number, which is 9. So the middle apartment number for house 17 is 9.
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The tread life (x) of tires follow normal distribution with µ = 60,000 and σ = 6000 miles. The manufacturer guarantees the tread life for the first 52,000 miles.
(i) What proportion of tires last at least 55,000 miles?
(ii) What proportion of the tires will need to be replaced under warranty?
(iii) If you buy 36 tires, what is the probability that the average life of your 36 tires will exceed 61,000?
(iv) The manufacturer is willing to replace only 3% of its tires under a warranty program involving tread life. Find the tread life covered under the warranty.
In linear equation, 48720 is the tread life covered under the warranty.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
1) µ = 60,000 and σ = 6000 miles.
P ( X >= 55000 ) = 1 - P ( X < 55000 )
Standardizing the value
Z = ( X - μ)/σ
Z = ( 55000 - 60000 ) / 6000
Z = -0.83
P((X - μ)/σ > ( 55000 - 60000)/6000
P ( Z > -0.83 )
P ( X >= 55000 ) = 1 - P ( Z < -0.83 )
P ( X >= 55000 ) = 1 - 0.2033
P ( X >= 55000 ) = 0.7967
Part v) What proportion of the tires will need to be replaced under warranty?
X ~ N ( μ = 60000 , σ = 6000 )
P ( X < 52000 )
Standardizing the value
Z = ( X - μ)/σ
Z = ( 52000 - 60000 ) / 6000
Z = -1.33
P((X - μ)/σ > ( 55000 - 60000)/6000
P ( X < 52000 ) = P ( Z < -1.33 )
P ( X < 52000 ) = 0.0918
Part c) If you buy 36 tires, what is the probability that the average life of your 36 tires will exceed 61,000?
X ~ N ( μ = 60000 , σ = 6000 )
P ( X > 61000 ) = 1 - P ( X < 61000 )
Standardizing the value
Z = ( X - μ)/(σ/√n)
Z = (61000 - 60000)/(6000/√36)
Z = 1
P(( X - μ)/(σ/√n) > (61000 - 60000)/(6000/√36)
P ( Z > 1 )
P ( X > 61000 ) = 1 - P ( Z < 1 )
P ( X > 61000 ) = 1 - 0.8413
P ( X > 61000 ) = 0.1587
Part d) The manufacturer is willing to replace only 3% of its tires under a warranty program involving tread life. Find the tread life covered under the warranty.
P ( Z < ? ) = 3% = 0.03
Looking for the probability 0.03 in standard normal table to find the critical value Z
Z = - 1.88
Z = (X - μ)/σ
- 1.88 = ( X - 60000)/6000
X = 48720
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6TH GRADE MATH, WRITE THE EQUATION FOR THIS GRAPH IN THE FORM OF Y=MX+B, TYSM
Answer:
m = 0
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0,2) (1,2)
We see the y stay the same and the x increase by 1, so the slope is
m = 0/1 = 0
So, the slope is 0
determine whether the positive or negative square root should be selected. provide reasons to support as to why they are negative or positive.
1. Select the negative square root as sine function is negative for sin 195°. 2. Select the positive square root as cosine function is positive for cos 58°. 3. Select the negative square root as tangent function is negative for tan 225°.
4. Select the negative square root as sine function is negative and cosine of 20° is positive for sin(-10°) = √(1-cos(-20°))/2.
1. Since 195° is in the third quadrant, the sine function is negative. Therefore, we should select the negative square root.
2. Since 58° is in the first quadrant, the cosine function is positive. Therefore, we should select the positive square root.
3. Since 225° is in the third quadrant, the tangent function is negative. Therefore, we should select the negative square root.
4. Since -10° is in the fourth quadrant, the sine function is negative. Also, since cosine is an even function, cos(-20°) = cos(20°), which is positive since 20° is in the first quadrant. Therefore, we should select the negative square root.
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PLEASE HELP! 15 POINTS!!
Answer:
We can use similar triangles to solve this problem. Let's denote the height of the tree as h. Then, we can set up the following proportion:
h / 120 = 6 / 10
Cross-multiplying and simplifying, we get:
10h = 720
h = 72
Therefore, the height of the tree is 72 feet
123, 185, 143, 137, 192, 185, 129, 143, 154, 165, 143, 138, 187, 176
A bin size ofis most appropriate for the data shown above.
A. 69 B. 2 C. 10 D. 1
The answer of the given question based on statistics to find the most appropriate size of the bin from the data the answer is , the most appropriate bin size for this data set would be A. 69.
What is Statistics?Statistics is the practice of collecting, analyzing, and interpreting the data. It involves use of mathematical tools and techniques to gather insights and knowledge from numerical and categorical information. Statistics is essential in many fields, like business, medicine, social sciences, and engineering, as it enables researchers to draw conclusions from data and make informed decisions based on evidence.
It includes topics like probability, hypothesis testing, regression analysis, and data visualization. The application of statistical methods can help identify patterns, relationships, and trends in data, allowing researchers to make predictions and solve problems.
To determine the appropriate bin size, we need to consider the range of values in the data. The range is the difference between the largest and smallest values, which in this case is 192 - 123 = 69.
To get the bin size, we divide the range by the number of bins. So the bin size would be 69/4 = 17.25. However, since we can't have a fraction of a unit for bin size, we should round up to the nearest whole number. Therefore, the most appropriate bin size for this data set would be A. 69.
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The answer of the given question based on statistics to find the most appropriate size of the bin from the data the answer is , the most appropriate bin size for this data set would be A. 69.
What is Statistics?Statistics is the practice of collecting, analyzing, and interpreting the data. It involves use of mathematical tools and techniques to gather insights and knowledge from numerical and categorical information. Statistics is essential in many fields, like business, medicine, social sciences, and engineering, as it enables researchers to draw conclusions from data and make informed decisions based on evidence.
It includes topics like probability, hypothesis testing, regression analysis, and data visualization. The application of statistical methods can help identify patterns, relationships, and trends in data, allowing researchers to make predictions and solve problems.
To determine the appropriate bin size, we need to consider the range of values in the data. The range is the difference between the largest and smallest values, which in this case is 192 - 123 = 69.
To get the bin size, we divide the range by the number of bins. So the bin size would be 69/4 = 17.25. However, since we can't have a fraction of a unit for bin size, we should round up to the nearest whole number. Therefore, the most appropriate bin size for this data set would be A. 69.
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The complete question is as fpllows:
123, 185, 143, 137, 192, 185, 129, 143, 154, 165, 143, 138, 187, 176
A bin size of is most appropriate for the data shown above.
A. 69
B. 2
C. 10
D. 1
find the cayley Hamilton theorem for the matrix 3,1,1,4
[tex]\left[\begin{array}{ccc}0&0\\0&0&\\\end{array}\right][/tex] is the solution of the cayley Hamilton theorem for the matrix .
What does Cayley-Hamilton theorem mean?
Theorem of Cayley-Hamilton: Every square matrix satisfies its own characteristic equation, according to this theorem. For the stress polynomial p(), this means that the scalar polynomial p() = det(I ) also holds true.
A = [tex]\left[\begin{array}{ccc}3&1\\4&1&\\\end{array}\right][/tex]
Cayley Hamilton Theorem states that Every square matrix A must satisfy its characteristic equation | A - kI |.
So, first find characteristic equation.
⇒ A - kI
[tex]\left[\begin{array}{ccc}3&1\\1&4&\\\end{array}\right][/tex] - k[tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}3&1\\1&4&\\\end{array}\right] - \left[\begin{array}{ccc}k&0\\0&k&\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}3 -k&1\\1&4-k&\\\end{array}\right][/tex]
So,
Characteristic equation is given by
⇒ l A - kI l = 0
⇒ l 3 - k 1 l
l 1 4 - k l
= ( 3- k )(4 - k ) - 1 = 0
= k² - 7k + 11 =0
So, We have to show that A must satisfy
k² - 7k + 11 =0
thus
A² - 7A + 11I =0
So, Consider
A² - 7A + 11I =0
[tex]\left[\begin{array}{ccc}3&1\\1&4&\\\end{array}\right] \left[\begin{array}{ccc}3&1\\1&4&\\\end{array}\right] - 7\left[\begin{array}{ccc}3&1\\1&4&\\\end{array}\right] + 11\left[\begin{array}{ccc}3&1\\1&4&\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}9+1&3+4\\3+4&1+16&\\\end{array}\right][/tex] [tex]- \left[\begin{array}{ccc}21&7\\7&28&\\\end{array}\right] + \left[\begin{array}{ccc}11&0\\0&11&\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}10&7\\7&17&\\\end{array}\right] + \left[\begin{array}{ccc}-10&-7\\-7&-17&\\\end{array}\right][/tex]
[tex]= \left[\begin{array}{ccc}0&0\\0&0&\\\end{array}\right][/tex]
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Triangle ABC is similar to triangle DEF. What is AC?
Answer:
i think side AC is 14 because if you do subtract BC (18) from EF(12) you get 6, so u add 6 to DF(8) and get 14.
if its confusing ask me questions!!
Answer:
12
Step-by-step explanation:
When triangles are similar, their side ratios are the same. The ratio of EF to BC is 18/12, or 3/2. To find the side AC, we would multiply the corresponding part of DEF by 3/2, the same ratio. The corresponding part of DEF would be DF. DF = 8. 8 times 3/2 is 12. So AC is 12.
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find the following answer
The Venn diagram here shows the cardinality of each set. The cardinality of the n(A∩B∩C) is 6.
Describe Venn Diagram?Venn diagrams can be used to visually represent many different types of information, such as mathematical relationships, logical relationships, and sets of data. They are a useful tool for organizing and visualizing complex information.
A Venn diagram is a graphical representation of the relationships between different sets of objects. It consists of overlapping circles or other shapes that represent each set. The portions of the circles that overlap represent the objects that are in common to the corresponding sets.
Using the principle of inclusion-exclusion, we have:
n(A∩B∩C) = n(An) + n(B∩C) + n(C∩A) - 2n(A∩B) - 2n(B∩C) - 2n(C∩A) + 3n(A∩B∩C)
Substituting the given values, we get:
n(A∩B∩C) = 10 + 9 + 7 - 2(4) - 2(9) - 2(7) + 3(3) = 6
Therefore, n(A∩B∩C) = 6.
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The dot plots below show the number of students in attendance each day in Mr. Wilson's class and Mr. Watson's class in April. What is the difference of the medians as a multiple of the interquartile range? A. B. C. D.
The difference of the medians as a multiple of the interquartile range is 0.5,So the correct answer is option (A) 0.5.
What is median?The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in numerical order.
For example, consider the data set {3, 5, 2, 6, 1, 4}. When the values are ordered from smallest to largest, we get {1, 2, 3, 4, 5, 6}. The median in this case is the middle value, which is 3.
We can first find the medians and interquartile ranges of the two dot plots.
For Mr. Wilson's class:
Median = 12
Q1 = 10
Q3 = 14
IQR = Q3 - Q1 = 14 - 10 = 4
For Mr. Watson's class:
Median = 10
Q1 = 8
Q3 = 12
IQR = Q3 - Q1 = 12 - 8 = 4
The difference of the medians is |12 - 10| = 2. Therefore, the difference of the medians as a multiple of the interquartile range is:
$$\frac{2}{4} = \boxed{0.5}$$
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As an equity analyst, you have developed the following return forecasts and risk estimates for two different stock mutual funds (Fund T and Fund U):Forecasted Return CAPM Beta Fund T 9.0% 1.20Fund U 10.0 0.80a. If the risk-free rate is 3.9 percent and the expected market risk premium (i.e., E(RM) − RFR) is 6.1 percent, calculate the expected return for each mutual fund according to the CAPM.b. Using the estimated expected returns from Part a along with your own return forecasts, demonstrate whether Fund T and Fund U are currently priced to fall directly on the security market line (SML), above the SML, or below the SML.c. According to your analysis, are Funds T and U overvalued, undervalued, or properly valued?
For Fund T: Expected Return = 11.32% For Fund U: Expected Return = 8.94%,,For Fund T:Expected return (11.32%) > Our forecasted return (8%) .
Thus, Fund T is priced below the SML and is undervalued. For Fund U Expected return (8.94%) < Our forecasted return (10%) Thus, Fund U is priced above the SML and is overvalued and Fund T is undervalued and Fund U is overvalued.
a. To calculate the expected return for each mutual fund according to the CAPM, we can use the following formula:
Expected Return = Risk-free rate + (Market Risk Premium × Beta)
For Fund T:
Expected Return = 3.9% + (6.1% × 1.20) = 11.32%
For Fund U:
Expected Return = 3.9% + (6.1% × 0.80) = 8.94%
b. To determine whether Fund T and Fund U are currently priced to fall directly on the security market line (SML), above the SML, or below the SML, we need to compare their expected returns with our own return forecasts. Let's assume that we have forecasted returns of 8% for Fund T and 10% for Fund U.
If the expected return for a mutual fund is higher than our own return forecast, it is considered to be priced below the SML and thus undervalued. Conversely, if the expected return is lower than our own forecast, the mutual fund is considered to be priced above the SML and therefore overvalued. If the expected return and our own forecast are the same, the mutual fund is priced directly on the SML and is considered to be properly valued.
Using the CAPM expected returns calculated in part (a), we can compare with our own return forecasts:
For Fund T:
Expected return (11.32%) > Our forecasted return (8%)
Thus, Fund T is priced below the SML and is undervalued.
For Fund U:
Expected return (8.94%) < Our forecasted return (10%)
Thus, Fund U is priced above the SML and is overvalued.
c. Based on our analysis, Fund T is undervalued and Fund U is overvalued. This suggests that investors should consider buying Fund T, as it is expected to provide higher returns than the market return, while Fund U may not provide sufficient returns to compensate for the higher risk. However, it is important to note that other factors such as fund expenses, management quality, and investment strategy should also be considered when making investment decisions.
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Given f(x)=x^2 - 6x + 8 and g(x) = x - 2, solve f(x) = g(x) using a table of values.
Please show your work.
Answer:
Table solves f(x)=g(x)
Victor.
Given f(x)=x^2 - 6x + 8 and g(x) = x - 2, solve f(x) = g(x) using a table of values.
Please show your work.
To solve f(x) = g(x) using a table of values, we can create two columns, one for f(x) and one for g(x), and fill in values of x and the corresponding values of f(x) and g(x) until we find a value of x that makes f(x) equal to g(x).
Let's start by creating the table:
x f(x) = x^2 - 6x + 8 g(x) = x - 2
0 8 -2
1 3 -1
2 0 0
3 1 1
4 0 2
5 3 3
Looking at the table, we see that f(2) = 0 and g(2) = 0, so the solution to f(x) = g(x) is x = 2.
Therefore, the solution to f(x) = g(x) is x = 2.
pls help with this question
Answer:
4/3 or d
Step-by-step explanation:
) Solve t + t + t = 12
Answer:
Step-by-step explanation:
t+t+t= 3t
3t = 12
12/3=t
4=t
determine the amount of mass possessed by the blue mass. show your data and explain your reasoning or show the math
Since I added three 4 kg weights and one 1 kg weight to the left side of the fulcrum, the blue mass is 13 kg and is completely balanced. In light of this, the blue mass's mass is 13 kg.
To keep the beam horizontal for a beam balance, a body with gravitational mass m1 and a standard weight of m2 are placed in the left and right pans, respectively. If a1 = a2, then m1 = m2, and vice versa. Alternatively, the gravitational mass of the body in the left pan is equal to the gravitational mass in the right pan.
For calibrating masses between 13 mg and 4+1 = 5 kg, a beam balance is utilised. Depending on the calibre and sharpness of the knife edge used to make the pivot, a given measurement can be made with a given resolution and accuracy.
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The actual question is :
Determine the amount of mass possessed by the blue mass. Show your data and explainyour reasoning or show the math. The amount of the blue mass is 13 kg since I placed three 4 kg and 1 kg on the left side of the fulcrum and it is completely balance . Therefore the mass possessed by the blue mass is 13 kg .
use reference angles and the trigonometric function values for angles in special right triangles to find each trigonometric value
The cosine of 330 degrees is sqrt(3)/2.
To find the cosine of 330 degrees, we need to use the concept of reference angles. A reference angle is the acute angle formed between the terminal side of an angle and the x-axis.
First, we need to determine the reference angle for 330 degrees. Since 330 degrees is in the fourth quadrant, we can subtract it from 360 degrees to find the equivalent acute angle in the first quadrant
360 degrees - 330 degrees = 30 degrees
Therefore, the reference angle for 330 degrees is 30 degrees.
Next, we need to use the trigonometric function values for angles in special right triangles. For a 30-60-90 degree triangle, the ratios of the sides are
sin(30 degrees) = 1/2
cos(30 degrees) = sqrt(3)/2
tan(30 degrees) = 1/sqrt(3)
Since the reference angle for 330 degrees is 30 degrees, we can use the cosine value of 30 degrees to find the cosine value of 330 degrees
cos(330 degrees) = cos(360 degrees - 30 degrees) = cos(30 degrees) = sqrt(3)/2
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The given question is incomplete, the complete question is:
Use reference angles and the trigonometric function values for angles in special right triangles to find each trigonometric value . cos 330 degrees
Use the power of a power property to simplify the numeric expression.
THANKS!!
Answer:
[tex] 9^{\frac{7}{8}} [/tex]
Step-by-step explanation:
[tex] (9^{\frac{1}{4}})^{\frac{7}{2}} = [/tex]
[tex] = 9^{\frac{1}{4} \times \frac{7}{2}} [/tex]
[tex] = 9^{\frac{7}{8}} [/tex]
Determine the following standard normal (z) curve areas. (Round all answers to four decimal places.)
(a) The area under the z curve to the left of 1.73
(b) The area under the z curve to the left of
−0.69
(c) The area under the z curve to the right of 1.3
(d) The area under the z curve to the right of
−2.82
(e) The area under the z curve between −2.22 and 0.52
(f) The area under the z curve between
−1
and 1
(g) The area under the z curve between
−4
and 4
(a) The area under the standard normal curve to the left of 1.73 is 0.9582.
(b) The area under the standard normal curve to the left of -0.69 is 0.2454.
(c) The area under the standard normal curve to the right of 1.3 is 0.0968.
(d) The area under the standard normal curve to the right of -2.82 is 0.9974.
(e) The area under the standard normal curve between -2.22 and 0.52 is 0.6851.
(f) The area under the standard normal curve between -1 and 1 is 0.6826.
(g) The area under the standard normal curve between -4 and 4 is 0.9998.
(a) Using a standard normal table, the area under the standard normal curve to the left of 1.73 is 0.9582.
(b) Similarly, the area under the standard normal curve to the left of -0.69 is 0.2454.
(c) The area to the right of 1.3 is the same as the area to the left of -1.3. Using a standard normal table, this area is 0.0968.
(d) The area to the right of -2.82 is the same as the area to the left of 2.82. Using a standard normal table, this area is 0.9974.
(e) To find the area under the standard normal curve between -2.22 and 0.52, we need to find the area to the left of 0.52 and subtract the area to the left of -2.22. Using a standard normal table, we find that the area to the left of 0.52 is 0.6990 and the area to the left of -2.22 is 0.0139. Therefore, the area between -2.22 and 0.52 is 0.6990 - 0.0139 = 0.6851.
(f) To find the area under the standard normal curve between -1 and 1, we need to find the area to the left of 1 and subtract the area to the left of -1. Using a standard normal table, we find that the area to the left of 1 is 0.8413 and the area to the left of -1 is 0.1587. Therefore, the area between -1 and 1 is 0.8413 - 0.1587 = 0.6826.
(g) The area under the standard normal curve between -4 and 4 is the same as the area to the left of 4 minus the area to the left of -4. Using a standard normal table, we find that the area to the left of 4 is 0.9999 and the area to the left of -4 is 0.0001. Therefore, the area between -4 and 4 is 0.9999 - 0.0001 = 0.9998.
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Consider g(x) = {a sin x + b, if x 2pi .
A. Find the values of a and b such that g(x) is a differentiable function.
B. Write the equation of the tangent line to g(x) at x = 2pi.
C. Use the tangent line equation from part B to write an approximation for the value of g(6).
Do not simplify
Answer:
A. For g(x) to be differentiable, the derivative of g(x) must exist at every point in its domain. The derivative of a sin x + b is a cos x, which exists for all values of x. Therefore, any values of a and b will make g(x) a differentiable function.
B. To find the equation of the tangent line to g(x) at x = 2π, we need to find the slope of the tangent line, which is the derivative of g(x) evaluated at x = 2π.
g'(x) = a cos x, so g'(2π) = a cos(2π) = a
Therefore, the slope of the tangent line at x = 2π is a. To find the y-intercept of the tangent line, we can plug in x = 2π into g(x) and subtract a times 2π:
y = g(2π) - a(2π)
= (a sin 2π + b) - a(2π)
= b - 2aπ
So the equation of the tangent line is:
y = ax + (b - 2aπ)
C. We can use the tangent line equation to approximate g(6) by plugging in x = 6 and using the equation of the tangent line at x = 2π.
First, we need to find the value of a. Since g'(2π) = a, we can use the derivative of g(x) to find a:
g'(x) = a cos x
g'(2π) = a cos (2π) = a
g'(x) = a = 2
Now, we can plug in a = 2, b = any value, and x = 2π into the tangent line equation:
y = ax + (b - 2aπ)
g(2π) = 2πa + (b - 2aπ)
a sin 6 + b ≈ 12π + (b - 4π)
Since we don't know the value of b, we can't find the exact value of g(6), but we can use the approximation:
g(6) ≈ 12π + (b - 4π)
3 and below, then the player will lose 3 times the number that turns up.
The rule of a single-die game states that "If the number that turns up is
However, if the number that turns up is 4 and above, then the player will
gain 4 times the number that turns up." Marvin tosses a 5, then a 2, and
4. Did he win or lose the game? By how many points?
Marvin won the game by 30 points.
How to calculate the won ponits?Marvin tossed three times and got the following numbers: 5, 2, 4.
For the first toss, he tossed a 5, which is 4 or above, so he gains 4 times the number that turns up. Therefore, he gains:
4 x 5 = 20
For the second toss, he tossed a 2, which is below 3, so he loses 3 times the number that turns up. Therefore, he loses:
3 x 2 = 6
For the third toss, he tossed a 4, which is 4 or above, so he gains 4 times the number that turns up. Therefore, he gains:
4 x 4 = 16
To find out whether Marvin won or lost the game, we need to add up his gains and losses.
His total gain is:
20 + 16 = 36
His total loss is:
6
Therefore, his net gain is:
36 - 6 = 30
Marvin won the game by 30 points.
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The graph ABC has coordinates A(-3,-1) B(-4,-4) and C(-1,-2). And then graph the translation of 4 units right and 1 unit up.
Answer:45
Step-by-step explanation:
Answer:
A' = (1, 0)
B' = (0, -3)
C' = (3, -1)
Step-by-step explanation:
4 units right is adding 4 to the x value.
1 unit up is adding 1 to the y value.
A' = (1, 0)
B' = (0, -3)
C' = (3, -1)
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Angela is riding on a circular Ferris wheel that has a 59-foot radius. After boarding the Ferris wheel, she traveled a distance of 44.3 feet along the arc before the Ferris wheel stopped for the next rider.
a) Make a drawing of the situation and illustrate relevant quantities.
b) The angle that Angela swept out along the arc had a measure of how many radians?
c) The angle that Angela swept out along the arc had a measure of how many degrees?
The motion of Angela, riding on the 59 feet radius Ferris wheel indicates;
a) Please find attached the drawing represent the situation created with MS Word
b) The angle Angela swept out along the ard is about 0.751 radians
c) The measure of the angle Angela swept out in degrees is about 43.02°
What is the radius of a circular figure?The radius of a circular figure is the distance from the center of the figure to the circumference.
The specified parameters are;
Radius of the Ferris wheel = 59 feet
The distance along the arc, traveled by Angela, s = 44.3 feet
Let θ represent the angle Angela swept out along the arc, we get;
a) Please find attached the drawing of the situation created with MS Word
b)The formula for the arc length, s, of a circular motion is; s = r × θ
Where;
r = The radius of the circular motion, therefore;
θ = s/r
θ = 44.3/59 ≈ 0.751
The angle that Angela swept out, θ ≈ 0.751 radians
c) The angle swept out in degrees can be found as follows;
s = (θ/360) × 2 × π × r
Therefore;
44.3 = (θ/360) × 2 × π × 59
θ = 44.3° × 360°/(2 × π × 59) ≈ 43.02°
The angle Angela swept out is approximately 43.02°
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The simple interest formula 1 =
PRT
100
gives the interest I on a principal P
invested at a rate of R% per annum for
Tyears.
a) Find the interest when GH 2500 is
invested at 5% p.a. for 4 years.
b) Find the principal that gains an interest
of GH 2590 in 5 years at 7% per
annum,
The interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.
The principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.
What is simple interest ?
Simple interest is a type of interest that is calculated on the principal amount of a loan or investment at a fixed rate for a specified period of time. It is based only on the principal amount, and does not take into account any interest earned on previous periods.
The formula for simple interest is:
I = P * R * T
where:
I is the interestP is the principal amountR is the interest rate per periodT is the number of periodsAccording to the question:
a) Using the simple interest formula, we have:
I = (P * R * T) / 100
Substituting P = GH 2500, R = 5%, and T = 4 years, we get:
I = (2500 * 5 * 4) / 100 = 500
Therefore, the interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.
b) Using the same formula, we can solve for the principal P:
I = (P * R * T) / 100
2590 = (P * 7 * 5) / 100
2590 = (35P) / 100
35P = 2590 * 100
P = (2590 * 100) / 35
P ≈ GH 7400
Therefore, the principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.
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what will be the range of the random numbers generated by the following code snippet? rand() % 50 5;
The given function rand() % 50 + 5 will generate random numbers in the range of 5 to 54 inclusive.
The code snippet you provided contains a syntax error.
It seems like there is a typo between the '%' and '5' characters.
Assume that it meant to write,
rand() % 50 + 5;
Assuming that rand() function generates a random integer between 0 and RAND_MAX
Which may vary depending on the implementation.
The expression rand() % 50 will generate a random integer between 0 and 49 inclusive.
Then, adding 5 to the result will shift the range of the generated numbers up by 5.
Producing a random integer between 5 and 54 inclusive.
Therefore, the range of the random numbers generated by the code snippet rand() % 50 + 5 will be from 5 to 54 inclusive.
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