Answers
Answer:
I don't understand what is your question?
Answer:
see explanation
Step-by-step explanation:
(sinA + cosA)² + (sinA - cosA)² ← expand using FOIL
= sin²A + 2sinAcosA + cos²A + sin²A - 2sinAcosA + cos²A ← collect like terms
= 2sin²A + 2cos²A
Related Questions
You have 3 fair 6-sided dice. You repeatedly roll all 3 at once, until all 3 of them show the same number. What is the probability that you have to try three or more times
Answers
The probability of having to try three or more times is = 431/46656.
How to find the probability of having to try three or more times to get all three dice to show the same number?To find the probability of having to try three or more times to get all three dice to show the same number, we need to consider the probabilities of different outcomes.
On the first roll, all three dice can show any number with equal probability, so the probability of not getting a match on the first roll is 1.
On the second roll, we want to calculate the probability of not getting a match again. There are two cases to consider:
All three dice show the same number as on the first roll: The probability of this is 1/6 * 1/6 * 1/6 = 1/216.At least one die shows a different number than on the first roll: The probability of this is 1 - 1/216 = 215/216.Since we want to calculate the probability of having to try three or more times, we are interested in the event where we do not get a match on the first two rolls.
Therefore, the probability of this event is \((215/216)^2\) = 46225/46656.
Thus, the probability of having to try three or more times is 1 - 46225/46656
= 431/46656.
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What is the formula of mm to m?
Answers
To convert from millimeters to meters, use the formula m = mm ÷ 1000 (or) m = mm x 0.001.
What are conversion factors?A conversion factor, which is an expression that depicts the relationship between the units, can be used to change the units of a measured quantity without changing the value.
If the numerator and denominator are the same value represented in different units, a conversion ratio (or unit factor) always equals one (1).
Utilizing conversion factors, one unit of measurement can be changed into another.
The conversion process comprises switching from a single-entry to a double-entry accounting system for the business.
m = mm / 1000 (or) m = mm x 0.001 is the formula for converting millimeters to meters.
Therefore, to convert from millimeters to meters, use the formula m = mm ÷ 1000 (or) m = mm x 0.001.
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If A and B are supplementary angles and A is times as large as B, find the measures of A and B.
Answers
If 15% of a number is 60 and 65% of the same number is 260, find 50% of that number.
Answers
Step-by-step explanation:
you can ask questions for clarification
50% of the number of 200.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number = x
15% of x = 60
(15/100)x = 60
x = (60 x 100)/15
x = 400
Now,
65/100 x 40
= 260
Now,
50% of 400
= 50/100 x 400
= 200
Thus,
200 is 50% of 400.
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g a piece of wire 9 m long is cut into two pieces. one piece is bent into a square and the other is bent into an equilateral triangle. (a) how much wire should be used for the square in order to maximize the total area? correct: your answer is correct. m (b) how much wire should be used for the square in order to minimize the total area? incorrect: your answer is incorrect. m
Answers
(a) The length of wire that should be used for the square in order to maximize the total area is 9 meters.
(b) Using the same 9 meters of wire for the square will result in the minimum total area as well as the maximum total area.
(a) To maximize the total area, we need to use as much wire as possible for the square and as little as possible for the triangle. Let x be the length of wire used for the square, then the length of wire used for the triangle is 9 - x.
For the square, we have:
4s = x, where s is the side length of the square.
For the equilateral triangle, we have:
3t = 9 - x, where t is the side length of the equilateral triangle.
Solving for x in terms of s and t, we get:
x = 4s and x = 9 - 3t/2.
Substituting x = 4s into x = 9 - 3t/2, we get:
4s = 9 - 3t/2
8s = 18 - 3t
t = (18 - 8s)/3
The area of the square is given by A = s^2, and the area of the equilateral triangle is given by A = (\(\sqrt{3}\)/4)t^2.
Substituting t = (18 - 8s)/3, we get:
A = (\(\sqrt{3}\)/4)((18 - 8s)/3)^2
To maximize the total area, we need to maximize A, which is a function of s. Taking the derivative of A with respect to s, we get:
dA/ds = -4\(\sqrt{3}\)(4s-9)/27
Setting dA/ds = 0, we get:
4s - 9 = 0
Solving for s, we get:
s = 9/4
Therefore, the length of wire that should be used for the square in order to maximize the total area is:
x = 4s = 9 meters.
(b) To minimize the total area, we need to use as little wire as possible for the square and as much as possible for the triangle. Let x be the length of wire used for the square, then the length of wire used for the triangle is 9 - x.
Using the same equations as in part (a), we get:
t = (18 - 8s)/3
A = (\(\sqrt{3}\)/4)((18 - 8s)/3)^2
Taking the derivative of A with respect to s, we get:
\(dA/ds = -4\sqrt{3}(4s-9)/27\)
Setting dA/ds = 0, we get:
4s - 9 = 0
Solving for s, we get:
s = 9/4
This is the same value as in part (a), which means that using 9 meters of wire for the square will result in the minimum total area as well as the maximum total area.
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What is the value of s in the equation 3r= 10+5s when r = 10
Answers
Answer:
s = 4
Step-by-step explanation:
Given: 3r = 10+5s
Fill in r: 3(10) = 10 + 5s
Multiply: 30=10+5s
Subtract: 30-10=5s
Divide: 20/5=s
Answer: 4=s
In 2009, the average compensation for CEOs in the U.S. was approximately $10,800,000, and by 2016, this had risen to about $12,800,000. By comparison, the average compensation for workers was $54,700 in 2009 and $55,800 in 2016. Assume that both values are growing exponentially. Find the growth rate r for both salaries. State your answers as percentages rounded to the nearest tenth of a percent.For CEOs: r= %For workers: r = %
Answers
The exponential growth formula is given by
\(C=a(1+r)^t\)where C is the average compensation, a is the initial amount and t is the time (in years).
For the CEO's case, we have that
\(\begin{gathered} \text{for t=2009, C=10800000} \\ \text{for t=2016, C=12800000} \end{gathered}\)Then, we can find a and r with these values. By substituting the first values, we have
\(10800000=a(1+r)^{2009}\)By substituting the second values, we get
\(128000000=a(1+r)^{2016}\)By isolating a in both case, we have that
\(\begin{gathered} a=\frac{10800000}{(1+r)^{2009}} \\ \text{and} \\ a=\frac{12800000}{(1+r)^{2016}} \end{gathered}\)Then, we can state the following equation:
\(\frac{10800000}{(1+r)^{2009}}=\frac{12800000}{(1+r)^{2016}}\)or equivalently,
\(\begin{gathered} \frac{(1+r)^{2016}}{(1+r)^{2009}}=\frac{128000000}{108000000} \\ \frac{(1+r)^{2016}}{(1+r)^{2009}}=1.185185 \end{gathered}\)By applying natural logarithm in bot sides, we have
\(\begin{gathered} \ln (\frac{(1+r)^{2016}}{(1+r)^{2009}})=\ln 1.185185 \\ \ln (\frac{(1+r)^{2016}}{(1+r)^{2009}})=0.169899 \end{gathered}\)By the properties of logarithms:
\(\ln (\frac{A}{B})=\ln A-\ln B\)we obtain
\(\ln (1+r)^{2016}-\ln (1+r)^{2009}=0.169899\ldots.(a)\)By the property of logaritm:
\(\ln A^x=x\ln A\)The last result is equivalent to
\(\begin{gathered} 2016\ln (1+r)-2009\ln (1+r)=0.169899 \\ which\text{ gives} \\ 7\ln (1+r)=0.169899 \end{gathered}\)then, by moving the number 7 to the right hand side, this yields,
\(\begin{gathered} \ln (1+r)=\frac{0.169899}{7}\ldots(b) \\ \ln (1+r)=0.024271 \end{gathered}\)Now, by applying the exponential function in both sides, we have
\(\begin{gathered} 1+r=e^{0.024271} \\ 1+r=1.024568 \end{gathered}\)then, r is given by
\(\begin{gathered} r=1.024568-1 \\ r=0.0245 \end{gathered}\)Now, by converting this result into percent form. The answer for the CEO's case is
\(r=2.45\text{ \%}\)Now, for the workers case, we can do the same procedure and get an equation similar to equation (a). That is,
\(\begin{gathered} \ln (1+r)^{2016}-\ln (1+r)^{2009}=\ln (\frac{55800}{54700}) \\ \ln (1+r)^{2016}-\ln (1+r)^{2009}=\ln (1.020109) \\ \ln (1+r)^{2016}-\ln (1+r)^{2009}=0.0199 \end{gathered}\)and find somthing similar to equation (b)
\(\begin{gathered} \ln (1+r)=\frac{0.0199}{7}\ldots \\ \ln (1+r)=0.0028 \end{gathered}\)and finally,
\(\begin{gathered} 1+r=e^{0.0028} \\ 1+r=1.0028 \end{gathered}\)then, r will be
\(\begin{gathered} r=1.0028-1 \\ r=0.0028 \\ In\text{ percent form is} \\ r=\text{ 0.28 \%} \end{gathered}\)In summary,by rounding the answers to the nearest tenth percent, the answers are
\(\begin{gathered} \text{For CEO's:} \\ r=2.5\text{ \%} \\ \text{For workers:} \\ r=0.3\text{ \%} \end{gathered}\)What value of b^2 is needed for there to be exactly one real solution of a quadratic equation? Explain.
Answers
Answer:
4ac
Step-by-step explanation:
Assuming you're referring to the equation \(ax^2+bx+c=0\).
Since the discriminant \(D=b^2-4ac\) has to be equal to 0 in order for there to be exactly one real solution, then we have the following:
\(0=b^2-4ac\\b^2=4ac\)
Therefore, b² needs to be the same value as 4ac.
Will give brainliest
Answers
Answer:
21
Step-by-step explanation:
.Independent random samples of business managers and college economics faculty were asked to respond on a scale from 1 (strongly disagree) to 7 (strongly agree) to this statement: Grades in advanced economics are good indicators of students’ analytical skills. For a sample of 70 business managers, the mean response was 4.4 and the sample standard deviation was 1.3. For a sample of 106 economics faculty, the mean response was 5.3 and the sample standard deviation was 1.4.
a) Test, at the 5% level, the null hypothesis that the population mean response for business managers would be at most 4.0. (10marks)
b) Test, at the 5% level, the null hypothesis that the population means are equal against the alternative that the population mean response is higher for economics faculty than for business managers. Assume unequal variance.
Answers
Step-by-step explanation:
a) The test statistic is (4.4-4)/(1.3/sqrt(70)) = 2.83. The p-value is 0.0023. Since the p-value is less than 0.05, we reject the null hypothesis.
b) The test statistic is (5.3-4.4)/sqrt((1.4^2/106)+(1.3^2/70)) = 4.09. The p-value is less than 0.0001. Since the p-value is less than 0.05, we reject the null hypothesis.
nearest thousand of 10391 please give me answer fast
Answers
Answer: 10,000
Step-by-step explanation:
a local ice cream shop has a special deal on thursdays: buy a waffle cone for $3 and get each scoop of ice cream for $1.50. what would be the rate of change in this word problem?
Answers
In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.
That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.
We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.
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Need help ASAP!!!!!!!
Answers
2. X+2
4. X = -2 √6 and x= 2 √6
Which of the following examples would constitute a discrete random variable?
I. Total number of points scored in a football game
II. Height of the ocean's tide at a given location
III. Number of near collisions of aircraft in a year
Answers
The examples that would constitute a discrete random variable are;
I. Total number of points scored in a football game
III. Number of near collisions of aircraft in a year
What is discrete random variable?A discrete random variable has only a countable number of different values that it can assume. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values. A variable whose value is determined by counting is referred to as a discrete variable.
A continuous variable is one whose value may be determined through measurement. A random variable is a variable whose value is the resultant number of an unpredictable event.
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hello people does anyone
Answers
Answer:
The answer is 24. Yes we do.
All three points displayed are on the line. Find an equation relating x and y.
Answers
Answer:
y = 2x - 3
Step-by-step explanation:
The graph is a straight line, thus linear with equation
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (3, 3) and (x₂, y₂ ) = (6, 9) ← 2 points on the line
m = \(\frac{9-3}{6-3}\) = \(\frac{6}{3}\) = 2 , thus
y = 2x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 3 ), then
3 = 6 + c ⇒ c = 3 - 6 = - 3
y = 2x - 3 ← equation relating x and y
The equation whigh relates x and y points on the graph can be expressed in slope-intercept form as y = 2x - 3
The general form of a slope - intercept equation is :
y = bx + cb = slope ; c = interceptSlope, b = Rise / Run
Rise = 9 - 3 = 6 Run = 6 - 3 = 3Slope, b = 6/3 = 2
Taking a pair of point on the graph :
(3, 3)
3 = 2(3) + c
3 = 6 + c
3 - 6 = c
c = - 3
Therefore equation can be expressed thus :
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A baseball player hits a triple and ends up on third base. each side of length 25.740650945432 m, with home plate and the three bases on the four corners. what is the magnitude of his displacement?
Answers
The magnitude of his displacement is 77.221952836296 m
In this question,
A baseball player hits a triple and ends up on third base.
A baseball "diamond" is a square, each side of length 25.740650945432 m, with home plate and the three bases on the four corners.
We need find the the magnitude of his displacement.
The magnitude of his displacement is the distance from home plate to the third base.
the distance from home plate to the third base is
= 3 × 25.740650945432
= 77.221952836296 m
Therefore, the magnitude of his displacement is 77.221952836296 m
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2y^n - y'= 0. Sketch the phase portrait (including equilibria, orientations/directions of arrows), do not need to give solutions
Answers
The phase portrait of the differential equation 2y^n - y' = 0 will consist of a single equilibrium point at (0, 0) and arrows diverging away from the equilibrium in both positive and negative y directions.
To sketch the phase portrait of the differential equation 2y^n - y' = 0, we need to analyze the equilibriam and the orientations or directions of the arrows.
First, let's find the equilibria by setting y' to zero and solving for y. In this case, we have:
2y^n - y' = 0
2y^n - 0 = 0
2y^n = 0
From this equation, we can see that the only equilibrium occurs when y = 0. Thus, the phase portrait will have a single equilibrium point at (0, 0).
Next, we need to determine the orientations or directions of the arrows around the equilibrium point. To do this, we can choose some test points to the left and right of the equilibrium and evaluate the sign of y' to determine whether the arrows are pointing towards or away from the equilibrium.
Let's consider a test point y = -1, which is to the left of the equilibrium at y = 0. Substituting this value into the differential equation, we have:
2(-1)^n - y' = 0
2(-1)^n = y'
For even values of n, we get:
2 - y' = 0
y' = 2
Since y' is positive (2 > 0), the arrows at y = -1 will be pointing away from the equilibrium.
Now let's consider a test point y = 1, which is to the right of the equilibrium at y = 0. Substituting this value into the differential equation, we have:
2(1)^n - y' = 0
2 - y' = 0
y' = 2
Again, we find that y' is positive (2 > 0), indicating that the arrows at y = 1 will be pointing away from the equilibrium.
Based on this analysis, we can sketch the phase portrait of the differential equation. Since the orientations of the arrows are pointing away from the equilibrium at y = 0 for both positive and negative y values, the phase portrait will show arrows diverging away from the equilibrium in both directions.
The phase portrait will have a single equilibrium point at (0, 0), with arrows diverging away from it in both the positive and negative y directions. It is important to note that the specific shape and scale of the phase portrait will depend on the value of n, which is not specified in the given equation.
In summary, the phase portrait of the differential equation 2y^n - y' = 0 will consist of a single equilibrium point at (0, 0) and arrows diverging away from the equilibrium in both positive and negative y directions.
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For box plot data where Q1 = 200, Q2 = 250, and Q3 = 290, the
IQR
Answers
The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.
Given that,
For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290
We have to find the data of IQR.
We know that,
IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.
IQR Formula is Q₃ - Q₁
So,
Q₃ = 290
Q₁ = 200
Then ,
IQR = Q₃ - Q₁
IQR = 290 - 200
IQR = 90
Therefore, The value of IQR is 90.
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I need help PLEASE!!
Answers
Answer:
Step-by-step explanation:
thats an allien ow may gad
Students in a sixth grade class are raising money for an end-of-the-year
camping trip. So far, they have raised $240. This is ⅖ of the cost of the trip. How
much does the trip cost?
Answers
Answer:
$600
Step-by-step explanation:
We know
2/5 = $240
1/5 = $120
5/5 - 2/5 = 3/5
So, we need to find the 3/5 missing
1/5 = $120
3/5 = $360
So, we add both numbers to find the trip cost
240 + 360 = $600
So, the trip costs $600
If you can, please give me a Brainliest; thank you, and Happy New Year!
HELP PLEASE IM STRUGGLING
Answers
Answer:
121°
Step-by-step explanation:
Since we are working with a parallelogram, A and C will have the same angle measure and B and D will as well. We can form an equation and solve for x.
9x - 5 = 10x - 19
~Add 5 to both sides
9x = 10x - 14
~Subtract 10x to both sides
-x = -14
~Divide -1 to both sides
x = 14
Find angle B with what we found for x.
9x - 5
9(14) - 5
126 - 5
121
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Mr Keag's swimming pool is 15 feet long, 12 feet wide and 10 feet deep. How much water would it take to fill it half way to the top
Answers
Answer:
900 cubic feet
Step-by-step explanation:
\( \frac{1}{2} (15 \times 12 \times 10) = \frac{1}{2} (1800) = 900\)
. Importance of hydrologic cycle The role of water is central to most natural processes - Transport - Weathering, contaminant transport - Energy balance - transport of heat, high heat capacity - Greenhouse gas - 80% of the atmospheric greenhouse effect is caused by water vapor - Life - for most terrestrial life forms, water determines where they may live; man is exception
Answers
The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.
The importance of the hydrologic cycle can be understood by considering its various functions:
Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.
Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.
Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.
Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.
Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.
It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.
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f(x) = -3x- 6 and g(x) = -4x + 9, find g(g(y))
Answers
9514 1404 393
Answer:
g(g(y)) = 16y -27
Step-by-step explanation:
Simplify from the inside out, as the order of operations tells you.
g(g(y)) = g(-4y +9) = -4(-4y +9) +9
g(g(y)) = 16y -36 +9
g(g(y)) = 16y -27
The vertices of a trapezoid are A(1,2), B(4,4), C(4,0). D(1.6).
Rotate the trapezoid 270 degrees counterclockwise about
the vertex a. What are the coordinates of the image?
Answers
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.
Henry is buying bagels for a family gathering. Each bagel costs $0.75. Answer the
questions below regarding the relationship between the total cost and the number of
bagels purchased.
Answers
Answer:
0.75x=(total cost)
Step-by-step explanation:
Answer:
The independent variable, x, represents the number of bagels purchased, and the dependent variable is the total cost of the bagels, because the total cost of the bagels depends on the number of bagels purchased.
A function relating these variables is A(x) =0.75x .
So A(12) = 9, meaning 12 bagels will cost 9 dollars.
Step-by-step explanation:
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Have a good day
T/F: solving a linear programming model and rounding the optimal solution down to the nearest integer value is the best way to solve a mixed integer programming problem.
Answers
False. While it may be tempting to round the optimal solution of a linear programming model down to the nearest integer value to solve a mixed integer programming problem, this approach is not always guaranteed to produce an optimal solution.
In fact, mixed integer programming problems require specialized algorithms and techniques that are specifically designed to handle integer variables in the objective function and constraints. These methods search for feasible solutions within the space of integer values, which can be more computationally intensive than solving a linear programming model.
So, while rounding the optimal solution of a linear programming model may sometimes provide a good approximate solution to a mixed integer programming problem, it is not always the best or most reliable way to solve these types of problems.
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I need answer Immediately!!!!!!!
Answers
The answer is x=10
(x, 7) (3, -1) has a slope that is undefined. Find the value of x
Answers
Based on the fact that the slope of the line is undefined, the value of x can be found to be 3.
What is an undefined slope?When a slope is said to be undefined, it means that the slope of the line does not show any horizontal movement. In other words, the value of the x points used to calculate the give a product of zero when subtracted.
The slope of a line can be found by the formula:
= (y2 - y1) / (x2 - x1)
For the slope to be undefined, the denominator needs to be zero:
= (-1 - 7) / (3 - x)
x will need to subtract 3 such that the result would be zero. So x will be 3.
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