Answers
Step-by-step explanation:
We have that
\((x + \frac{1}{x} ) {}^{2} = 3\)
We are trying to find the number value so that we can apply in the later equation.
Qe first simplify.
Remeber that
\((a + b) {}^{2} = a {}^{2} + 2ab + {b}^{2} \)
Also remeber that
\( \frac{1}{x} = {x}^{ - 1} \)
so
\((x + x {}^{ - 1} ) {}^{2} = {x}^{2} + 2x {}^{0} + {x}^{ - 2} = 3\)
We then simply remeber that x^0=1 so
\( {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 3\)
Multiply both sides by x^2.
\( {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{2} \)
Subtract both sides by 3x^2
\( {x}^{4} - {x}^{2} + 1 = 0\)
Notice that x^4= (x^2)^2.
So our reformed equation is
\(( {x}^{2} ) {}^{2} - {x}^{2} + 1 = 0\)
Let a variable , w equal x^2. This means that we subsitute variable, w in for x^2.
\(w {}^{2} - w + 1 = 0\)
Now we use the quadratic formula
\( w = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a} \)
and
\(w = - b - \frac { \sqrt{b {}^{2} - 4ac } }{2a} \)
Let a=1 b=-1 and c=1.
\(w = \frac{1 + \sqrt{1 - 4(1)} }{2} \)
\(w = \frac{1 - \sqrt{1 - 4} }{2} \)
Now, we get
\(w = \frac{1}{2} + \frac{i \sqrt{3} }{2} \)
and
\(w = \frac{1}{2} - \frac{ i\sqrt{3} }{2} \)
Now since we set both of these to the x^2 we solve for x.
and
\( {x}^{2} = \frac{1}{2} + \frac{i \sqrt{3} }{2} \)
and
\( {x}^{2} = \frac{1}{2} - \frac{i \sqrt{3} }{2} \)
We can represent both of these as complex number in the form of a+bi. Next we can convert this into trig form which is
\( {x}^{2} = 1( \cos(60) + i \: \sin(60) \)
and
\( {x}^{2} = 1( \cos(300) + i \: sin(300))\)
Next we take the sqr root of 1 which is 1, and divide the degree by two.
\( {x} = 1( \cos(30) + i \: sin \: 30)\)
and
\(x = 1( \cos(150) + i \: sin(150)\)
We are asked for the 2nd root so just add 180 degrees to this and we have
\(x = 1 \cos(210) + i \: sin \: 210)\)
and
\(x = 1( \cos(330) + i \: sin(330)\)
which both simplified to
\(x = - \frac{ \sqrt{3} }{2} - \frac{1}{2} i\)
and
\(x = \frac{ \sqrt{3} }{2} - \frac{1}{2} i\)
Now we must find
x^18+x^12+x^6+1.
We just use demovire Theorem. Which is a complex number raised to the nth root is
\( {r}^{n} (cos(nx) + i \: sin(nx)\)
So let plug in our first root.
\(1( \cos(330 \times 18)) + i \: sin \: (330 \times 18))) + 1( \cos(12 \times 330)) + i \: sin(12 \times 330) + 1( \cos(6 \times 330) + i \: sin(6 \times 330))) + 1\)
To save time we multiply the angle and use rules of terminals angle and we get
\(1( \cos(180) + i \sin(180) ) + 1( \cos(0) + i \: sin \:( 0) + 1( \cos(180) + i \: sin(180) + 1\)
And we get
\( - 1 + 1 + - 1 + 1 = 0\)
So one of the answer is x=0
And the other, let see
\(1 \cos(210 \times 18) + i \: \sin(210 \times 18) + 1 \: cos(210 \times 12) + i \: sin(210 \times 12) + 1 \cos(210 \times 6) + \:i sin(210 \times 6) + 1\)
\( \cos(180) + i \: sin(180) + 1 \cos(0) + i\sin(0) +1( \cos(0) + i \sin(0) + 1\)
We get
\( - 1 + 1 + 1 + 1 = 2\)
So our answer are 2.
So the answer to the second part is
0 and 2.
Related Questions
The coach fare to a theme park costs $21 for 3 people, what would be the cost for 6 people?
A) $42 B) $63 C) $140
Answers
Answer:
42
Step-by-step explanation:
You add 21 twice because 3 is half of 6
Answer:
A - 42
Step-by-step explanation:
21 x 2 = 42
3 x 2 = 6
Complete the proof. Someone please help me answer this!
Answers
What is the cost of an item with a sales tax of $108?
Answers
The requried cost of the item is $2392, and the sale tax is 4.5% of the cost of the item.
As given in the question,
Total spent = $2500
Total sale's tax paid = $108
Sale's tax % = 108/[2500-108]×100%
Sale's tax % = 4.5%
The cost of the item is given as:
= $2500 - $108
= $2392
Thus, the requried cost of the item is $2392, and the sale tax is 4.5% of the cost of the item.
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The question seems to be incomplete,
The question must be,
What is the sale tax for a purchase of $2,500 and what is the cost of an item with a sales tax of $108?
3x - 5y = 15
x-intercept =
y-intercept =
Answers
Answer:
x-intercept is 5
y-intercept is -3
Step-by-step explanation:
For the x-intercept:
\(3x - 5(0) = 15\)
\(3x = 15\)
\(x = 5\)
For the y-intercept:
\(3(0) - 5y = 15\)
\( - 5y = 15\)
\(y = - 3\)
Answer:
Y intercept= -3
x-intercept = 5
Step-by-step explanation:
So you would want to get your y alone for it to be in slome intercept form (y=mx+b) so you would:
1. Subtract 3x from both sides to get -5y= -3x+15
2. then you would divide each side by -5 to get y= \(\frac{3}{5}\) x -3
And since in slope intercept form, b= the y-intercept, The y-intercept =-3 and to find the x-intercept you would have to solve for y=0 in your new-found equation.
sorry if this was long
suppose a political advisor is interested in the proportion of the vote an opponent will receive. if he samples voters randomly and tests hypotheses regarding p, the population proportion, what should he do to reduce his risk of making a type ii error? increase the number of voters he will sample decrease the number of voters he will sample increase the significance level decrease the significance level
Answers
So, on solving the provided question, we can say that to decrease that the Type II error, it is necessary to increase both the significance level and the sample size of voters.
A Type II mistake is what?When the experimenter fails to rule out a false null hypothesis, they commit a type II error, also referred to as a false-negative.Type II errors can also be decreased by increasing the significance level used throughout the testing method.
By employing more stringent criteria, the power of the testing technique can be increased while significantly reducing a type II error.
By raising the significance level employed throughout the testing procedure, Type II mistakes can also be reduced.
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Write each polynomial in standard form. What is the classification of each by degree? by number of terms?
a. 3x³ - x + 5x⁴ .
Answers
Please provide the dimensions of the bathroom floor (length and width) so I can help you calculate the number of boxes JoAnn will need.
To calculate the number of boxes JoAnn will need, we need to determine how many tiles are required to cover her bathroom floor.
Given that the tile size is 12" x 12", we can calculate the area of each tile:
Area of one tile = Length x Width = 12" x 12" = 144 square inches
Now, we need to find the total area of JoAnn's bathroom floor to determine the number of tiles required. However, you haven't provided the dimensions of the bathroom floor.
Please provide the dimensions of the bathroom floor (length and width) so I can help you calculate the number of boxes JoAnn will need.
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A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water so that the water level rises at a rate of 2 cm/sec. At what rate is water being poured into the cup when the water level is 9 cm
Answers
The required rate for water being poured into the cup when the water level is 9 cm = 40.5π cm³/sec
For given question,
We have been given the height of a conical paper cup i.e., h = 10 cm
and the radius of a conical paper cup r = 10 cm
The cup is being filled with water so that the water level rises at a rate of 2 cm/sec
We need to find the rate at which water being poured into the cup when the water level is 9 cm
We know that the volume of the cone is \(V=\frac{\pi r^2 h}{3}\)
We can relate h and r as we know that the slope = h/r
= 10/5
= 2
Now, we make the volume a formula in a single variable
\(\Rightarrow V=\frac{\pi (\frac{h}{2} )^2 h}{3}\\\\\Rightarrow V=\frac{\pi h^3}{12}\)
Differentiating above equation with respect to time,
\(\Rightarrow V'=\frac{3\pi h^2 h'}{12} \\\\\Rightarrow V'=\frac{\pi h^2 h'}{4}\)
Substituting values,
\(\Rightarrow V'=\frac{\pi \times 9^2\times 2}{4}\\\\\Rightarrow V'=40.5\pi~~cm^3/sec\)
Therefore, the required rate for water being poured into the cup when the water level is 9 cm = 40.5π cm³/sec
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Part C: Prove that the measure of ∠JKL is 90°.
Answers
how can you evaluate 36^1/2
Answers
Answer:
6
Step-by-step explanation:
======================================================
Explanation:
Exponents of 1/2 are the same as square roots
\(36^{1/2} = \sqrt{36} = 6\)
If the exponent was say 1/3, then we'd be taking a cube root
\(36^{1/3} = \sqrt[3]{36}\)
and this is what a fourth root would look like
\(36^{1/4} = \sqrt[4]{36}\)
and so on
The volume of 10 drops of a liquid is 0.1 fluid ounces.
What is the volume of 100 drops?
Answers
Answer:
1 fluid ounce
Step-by-step explanation:
if 10 drops is equal to 0.1 fl and we multiply 10 by 10 to get 100, we have to multiply 0.1 by 10 as well, which is 1 fluid ounce.
Plz answer fast I need it done soon
Answers
Answer:
The correct answer is B
Step-by-step explanation:
.
Need Help here Please!
Answers
Answer:
Step-by-step explanation:
To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:
a) To find the value of \(\sf 3(x - y) \\\):
\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)
b) To find the value of \(\sf 6x - 6y \\\):
\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)
c) To find the value of \(\sf y - x \\\):
\(\sf y - x = - (x - y) = -4 \\\)
Therefore:
a) The value of \(\sf 3(x - y) \\\) is 12.
b) The value of \(\sf 6x - 6y \\\) is 24.
c) The value of \(\sf y - x \\\) is -4.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Based on climate data that have been collected in Bar Harbor, Maine, the average monthly
temperature, in degrees F, can be modeled by the equation
B(x)= 23.914 sin(0.508x-2.116) + 55.300. The same governmental agency collected average
monthly temperature data for Phoenix, Arizona, and found the temperatures could be
modeled by the equation P(x) = 20.238 sin(0.525x-2.148) + 86.729. Which statement can not
be concluded based on the average monthly temperature models x months after starting data
collection?
Answers
The statement that cannot be concluded based on the given temperature models is statement 2: "The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix."
Describe Equation?Equations can be simple or complex, and they can involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Equations can also be represented graphically using curves or surfaces.
We can compare the two given temperature models to make conclusions about the average monthly temperature variations in Bar Harbor and Phoenix.
First, let's compare the midline temperatures:
Midline temperature for Bar Harbor = 55.300 degrees F
Midline temperature for Phoenix = 86.729 degrees F
Since the midline temperature for Phoenix is higher than that of Bar Harbor, we can conclude that statement 2 cannot be concluded.
Next, let's compare the amplitude of the temperature variations:
Amplitude of temperature variation in Bar Harbor = 23.914 degrees F
Amplitude of temperature variation in Phoenix = 20.238 degrees F
Since the amplitude of temperature variation in Bar Harbor is greater than that of Phoenix, we can conclude that statement 1 is true.
Finally, let's use the temperature models to find the maximum and minimum temperatures:
Maximum temperature in Bar Harbor = 23.914 sin(0.508x-2.116)+55.300
To find the maximum temperature, we need to find the maximum value of the sine function, which is 1. Therefore, the maximum temperature occurs when:
0.508x-2.116 = 90 degrees
Solving for x, we get:
x = (90 + 2.116)/0.508 = 177.066
Plugging this value into the temperature model, we get:
Maximum temperature in Bar Harbor = 23.914 sin(0.508(177.066)-2.116)+55.300 = 78.986 degrees F
Therefore, statement 3 is false.
Minimum temperature in Phoenix = 20.238 sin(0.525x-2.148) + 86.729
To find the minimum temperature, we need to find the minimum value of the sine function, which is -1. Therefore, the minimum temperature occurs when:
0.525x-2.148 = 270 degrees
Solving for x, we get:
x = (270 + 2.148)/0.525 = 517.657
Plugging this value into the temperature model, we get:
Minimum temperature in Phoenix = 20.238 sin(0.525(517.657)-2.148) + 86.729 = 65.983 degrees F
Therefore, statement 4 is false.
Therefore, the statement that cannot be concluded based on the given temperature models is statement 2: "The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix."
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Statement 2: "The midline average monthly climate for Bar Harbor is less than the midline temperature for Phoenix," cannot be proven based on the provided temperature models.
Describe Equation?In addition to variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation, equations can be simple or complex. Equations can also be graphically represented using surfaces or curves.
To draw conclusions regarding the average monthly temperature variations in Bar Harbor and Phoenix, we can compare the two provided temperature models.
Let's start by contrasting the midline temperatures:
Midline temperature for Bar Harbor = 55.300 degrees F
Phoenix's midline temperature = 86.729 degrees F
We can infer from the fact that Phoenix's median temperature is greater than Bar Harbor's that assertion 2 cannot be drawn.
Let's compare the temperature variations' amplitude next:
Bar Harbor's temperature variations' severity = 23.914 degrees F
The intensity of Phoenix's temperature variations = 20.238 degrees F
We can infer that assertion 1 is accurate since the amplitude of temperature change in Bar Harbor is bigger than that in Phoenix.
Let's use the temperature models to determine the highest and lowest temperatures.
Bar Harbor's highest temperature is equal to 23.914 sin (0.508x-2.116) + 55.300.
We need to determine the sine function's maximum value, which is 1, in order to determine the maximum temperature. Consequently, the highest temperature is reached when:
0.508x-2.116 = 90 degrees
Solving for x, we get:
x = (90 + 2.116)/0.508 = 177.066
When this value is entered into the temperature model, we obtain:
Bar Harbor's highest temperature record
= 23.914 sin(0.508(177.066)-2.116)+55.300
= 78.986 degrees F
Therefore, statement 3 is false.
Phoenix's low temperature = 20.238 sin(0.525x-2.148) + 86.729
We need to determine the sine function's minimal value, which is -1, in order to determine the minimum temperature. Consequently, the lowest temperature is reached when:
0.525x-2.148 = 270 degrees
Solving for x, we get:
x = (270 + 2.148)/0.525 = 517.657
When this value is entered into the temperature model, we obtain:
Phoenix's low temperature
= 20.238 sin(0.525(517.657)-2.148) + 86.729
= 65.983 degrees F
Therefore, statement 4 is false.
Statement 2: "The midline average month climate for Bar Harbor is lower than the midline temperature for Phoenix," cannot be proved based on the provided temperature models.
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A 95% confidence set for two or more coefficients is a set that contains: A) the sample values of these coefficients in 95% of randomly drawn samples. B) integer values only. C) the same values as the 95% confidence intervals constructed for the coefficients. D) the population values of these coefficients in 95% of randomly drawn samples.
Answers
A 95% confidence set for two or more coefficients is a set that contains: D) the population values of these coefficients in 95% of randomly drawn samples.
A 95% confidence set for two or more coefficients is a set that contains the same values as the 95% confidence intervals constructed for the coefficients. This means that the set includes all possible values for the coefficients that are consistent with the observed data and the level of uncertainty indicated by the confidence level. It is important to note that the confidence set is not guaranteed to contain the true population values of the coefficients in 95% of randomly drawn samples, as the true values are unknown.
The confidence set provides a range of plausible values that can be used for inference and decision making. The concept of a 95% confidence set.
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Line M passes through point (3,1) and is perpendicular to the line of the equation y=3x+4. Which equation describes the graph of M?
A) y=-3x+16
B) y=-1/3x+2
C)y=-1/3x+4
D)y=1/3x+6
Answers
Answer:
y = -1/3x + 2
Step-by-step explanation:
The gradient of the given line is 3 because (y = mx +c where m is the gradient)
Therefore, to find the gradient of the perpendicular line (at 90 degrees), you need to find the negative reciprocal.
The negative reciprocal of 3 is -1/3 because imagine if 3 = 3/1, to get the reciprocal, you flip it, and to get the negative, you just flip the sign.
Now we know that Line M is y = -1/3x + c, we need to find the y-intercept.
To do this, just input the point (3,1) into y = -1/3x + c, to get c. This is because we know (3,1) is on the line from the question.
So it would be 1 = (-1/3 x 3) +c
Which would be 1 = -1 +c
And so c = 2
Put everything together and you get y = -1/3x + 2
1) 10x + 3y + 5x =
2) 2x + 7y+ 4x+6x? -
3) 9y+3y + 5x =
4) 2y + 7y + 4y + 6y' =
I
5) 8x + y - 2x =
6) x + 7y - 4y +9x?
7) 14x - 3x + 2 y = y + 3x -
8) 5y + 5y + 5y + 5x
What are the answer for these problems you need to simplify the expression by combining like terms
Answers
Answer:
Step-by-step explanation:
Terms with same variables are like terms
1) 10x + 3y + 5x
Here, 10x and 5x are like terms. so add them
10x + 5x + 3y = 15x +3y
2)2x + 7y +4x + 6x = 2x + 4x + 6x + 7y = 12x + 7y
3)9y+ 3y +5x = 12y +5x
4)2y +7y +4y +6y = 19y
5)8x + y - 2x = 8x -2x + y = 6x + y
6) x + 7y -4y +9x = x +9x + 7y - 4y = 10x + 3y
8) 5y +5y +5y +5x = 15y + 5x
Olivia volunteers at the hospital where her mother works. One Saturday, she answers phone calls at the information desk while the receptionist is away. Then she spends 25 minutes delivering flowers to patients' rooms. In all, Olivia volunteers at the hospital for 45 minutes that day.
Answers
The equation used to find the amount of time Olivia answers phone calls is t +25= 45
The amount of time Olivia answers phone calls is 20
Olivia volunteers at the hospital where her mother works
She answers phone calls
She spends 25 minutes delivering flowers to patient's room
She spends 45 meetings volunteering at the hospital
Let t represent the amount of time Olivia answers phone calls in the hospital
Hence the equation used to calculate the amount of time spent on calls is t + 25= 45
t + 25= 45
collect the like terms
t= 45-25
t= 20
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Select the correct answer. sara goes on a slingshot ride in an amusement park. she is strapped into a spherical ball that has a radius of centimeters. what is the volume of air in the spherical ball? use this formula: , where r is the sphere’s radius. a. b. c. d.
Answers
The volume of air in the spherical ball is \(\frac{4}{3}\cdot \pi\cdot 3^3\cdot 10^6\). So the option A is correct.
In the given question, we have to find the volume of air in the spherical ball.
A sphere's capacity is measured by its volume. It is the area the sphere calls home. Cubic units are used to express the volume of a sphere. The sphere has a three-dimensional, rounded shape. Its shape is defined by its three axes, which are the x, y, and z axes.
Since the cross-section of the sphere is a circle, the volume in this situation is dependent on the radius's diameter. A sphere's surface area is the area or region of its outside. The following formula can be used to determine the volume of a sphere whose radius is "r":
V = \(\frac{4}{3}\pi r^{3}\)
As given r = 3·10^2. So,
V = \(\frac{4}{3}\pi (3\cdot 10^2)^{3}\)
V = \(\frac{4}{3}\cdot \pi\cdot 3^3\cdot 10^6\)
V = \(4\cdot \pi\cdot 3^2\cdot 10^6\) cm^3
Hence, the option A is correct.
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The complete question is given below:
how to determine if a relation is a function calculator
Answers
Answer:
A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.
Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).
To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:
1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.
2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.
3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.
Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.
Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.
Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.
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Two dice are tossed. Let X be the random variable that shows the maximum of the two tosses. a. Find the distribution of X b. Find P(X S 3) c. Find E(x)
Answers
a. The distribution of X is:
X 1 2 3 4 5 6
P 1/36 1/6 2/9 1/2 8/9 1/36
b. P(X ≤ 3) = 5/12.
c. The expected value of X is 91/36.
a. To find the distribution of X, we can consider all possible outcomes of rolling two dice and determine the probability of each outcome for X = 1, X = 2, X = 3, X = 4, X = 5, and X = 6.
For X = 1, both dice must show a 1, which has probability 1/36.
For X = 2, one die shows a 2 and the other shows a number less than 2, which has probability (1/6)(1/2) = 1/12. There are two ways this can happen, so the total probability is 2/12 = 1/6.
For X = 3, one die shows a 3 and the other shows a number less than 3, which has probability (1/6)(2/6) = 1/18. There are four ways this can happen (the other die can show a 1, 2, 3, or 4), so the total probability is 4/18 = 2/9.
For X = 4, one die shows a 4 and the other shows a number less than 4, which has probability (1/6)(3/6) = 1/12. There are six ways this can happen, so the total probability is 6/12 = 1/2.
For X = 5, one die shows a 5 and the other shows a number less than 5, which has probability (1/6)(4/6) = 1/9. There are eight ways this can happen, so the total probability is 8/9.
For X = 6, both dice must show a 6, which has probability 1/36.
Therefore, the distribution of X is:
X 1 2 3 4 5 6
P 1/36 1/6 2/9 1/2 8/9 1/36
b. To find P(X < 3), we can sum the probabilities for X = 1 and X = 2:
P(X < 3) = P(X = 1) + P(X = 2) = 1/36 + 1/6 = 7/36
To find P(X = 3), we can use the probability for X = 3 from part a:
P(X = 3) = 2/9
Therefore, P(X ≤ 3) = P(X < 3) + P(X = 3) = 7/36 + 2/9 = 5/12.
c. To find E(X), we can use the formula:
E(X) = Σxi P(X = xi)
where xi are the possible values of X and P(X = xi) are their respective probabilities. From the distribution of X in part a, we have:
E(X) = (1/36)(1) + (1/6)(2) + (2/9)(3) + (1/2)(4) + (8/9)(5) + (1/36)(6) = 91/36
Therefore, the expected value of X is 91/36.
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What would you choose as x in the given series of clicks to calculate formulas automatically: file < options < x < automatic?
Answers
We should choose Formulas as X in the given series of clicks to calculate formulas automatically.
File < Options < (A) Formulas < Automatic
What are Formulas?In science, a formula is a concise way of symbolically expressing information, such as a mathematical formula or a chemical formula. In science, the term formula refers to the general construct of a relationship between given quantities. In mathematics, a formula is an identity that equates one mathematical expression to another, the most important of which are mathematical theorems. A formula (also known as a well-formed formula) is a logical entity that is constructed using the symbols and formation rules of a given logical language.We should choose Formulas as X in the given series of clicks to calculate formulas automatically.
Therefore, File < Options < (A) Formulas < Automatic
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The complete question is given below:
What would you choose as X in the given series of clicks to calculate formulas automatically: File < Options < X < Automatic?
a. Formulas
b. Language
c. Proofing
d. Advanced
what is Alternate interior angles give an example
Answers
Hey there!
Basically, the alternate interior angles is/are the inside of the given lines but it’s unlikeable sides of your transversal
Basically, ∠1 & ∠2 are alternative interior angles
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Answer:
in the above pic you can see 12345678 marked angles
the alternate interior angles are angle3,5,4and6
they are pairs of alternat interior angles
Step-by-step explanation:
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using separation of variables, solve the differential equation, use c to represent the arbitrary constant. 10 x^8
Answers
Since C is any arbitrary constant, \(y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C\) is the final solution of the differential equation.
The equation given to us is:
\((3 + x^{10})\frac{dy}{dx} = \frac{x^{9}}{y}\)
We can re-write the above equation:
\(y dy = \frac{x^9}{3 + x^{10}} dx\)
This is separation of variables.
A separable differential equation is any equation that can be written in the form y′=f(x)g(y). The method of separation of variables is used to find the general solution to a separable differential equation.
Now, if we differentiate the denominator,
\(\frac{d}{dx} (3 + x^{10} ) = 10x^9\)
Integrating both sides,
\(\frac{y^2}{2} = \frac{1}{10} ln (3 + x^{10})\) + C
⇒ \(y^{2} = \frac{1}{5} ln (3 + x^{10})\) + 2C
Since C is any arbitrary constant, \(y^{2} = \frac{1}{5} ln (3 + x^{10}) + 2C\) is the final solution of the differential equation.
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A kite has vertices at (2, 4), (5, 4), (5, 1), and (0, –1). What is the approximate perimeter of the kite? Round to the nearest tenth. 11. 3 units 13. 6 units 16. 8 units 20. 0 units.
Answers
The given problem involves finding the approximate perimeter of a kite with specified vertices.We need to determine closest approximate perimeter value by calculating lengths of the sides and summing them.
A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. To find the perimeter, we need to calculate the lengths of the four sides of the kite using the given vertices.
Using the distance formula, the length of a line segment between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Calculating the lengths of the sides:
Side AB: dAB = sqrt((5 - 2)^2 + (4 - 4)^2) = sqrt(3^2 + 0^2) = 3 units
Side BC: dBC = sqrt((5 - 5)^2 + (1 - 4)^2) = sqrt(0^2 + (-3)^2) = 3 units
Side CD: dCD = sqrt((0 - 5)^2 + (-1 - 1)^2) = sqrt((-5)^2 + (-2)^2) = sqrt(25 + 4) = sqrt(29) ≈ 5.4 units
Side DA: dDA = sqrt((0 - 2)^2 + (-1 - 4)^2) = sqrt((-2)^2 + (-5)^2) = sqrt(4 + 25) = sqrt(29) ≈ 5.4 units
The perimeter is the sum of all four sides:
Perimeter = AB + BC + CD + DA = 3 + 3 + 5.4 + 5.4 ≈ 16.8 units
Therefore, the closest approximate perimeter value to the given options is 16.8 units.
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Find the solutions to (x, y) y = -0.5x + 2 y = 0.5x + 6
Answers
Answer:
y=-0.5x+2 (-4,0) (0,2) y=0.5x+6 (0,6)(12,0)
Step-by-step explanation:
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show that there is no choice of the constant c that will make the solution in part a yield the solution y= -1.
Answers
This is not possible since the square of a real number can never be negative. Therefore, there is no choice of the constant c that will make the solution in part (a) yield the solution y = -1.
The given differential equation is given by;dy/dx
= x - y² ….(i)We will solve this differential equation by separating variables;dy / (x - y²)
= Integrating both sides, we have;1/2 * ln |x - y²|
= x + c Squaring both sides, we have;ln |x - y²|
= 2x + c‘e’ to the power of the left hand side is given by;x - y²
= e^(2x + c) ….(ii)Given;y
= -1 and x
= 0 When x
= 0, equation (ii) above becomes;0 - y²
= e^c (since e^0
= 1)⇒ y²
= - e^c⇒ y² < 0 This is not possible since the square of a real number can never be negative, thus we cannot find the constant ‘c’ that will make the solution in part (a) yield the solution y
= -1.The given differential equation is dy/dx
= x - y² ….(i). We can solve this differential equation by separating variables. After , we will be left with ln |x - y²|
= 2x + c. Squaring both sides will result in the equation x - y²
= e^(2x + c) ….(ii). Now we are given y
= -1 and x
= 0. When we substitute these values in equation (ii), we get; 0 - y²
= e^c (since e^0
= 1). Simplifying this, we have y²
= - e^c. This is not possible since the square of a real number can never be negative. Therefore, there is no choice of the constant c that will make the solution in part (a) yield the solution y
= -1.
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How does the graph of g(x) = (x − 2)3 + 6 compare to the parent function of f(x) = x3?
Answers
The graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.
How does the graph of g(x) compare to the one of f(x)?
Here we have:
\(f(x) = x^3\\\\g(x) = (x - 2)^3 + 6\)
You can notice that if we take f(x), and we shift it 2 units to the right, we have:
g(x) = f(x - 2)
Then if we apply a shift upwards of 6 units, then we have:
g(x) = f(x - 2) + 3
Replacing f(x) by the cubic parent function, we have:
\(g(x) = (x - 2)^3 + 6\)
So we conclude that the graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.
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The sum of a number and its square is 42. which equation can be used to find the two numbers for which this is true? x2 x = 42 x2 2x = 42 x2 x 42 = 0 x2 2x 42 = 0
Answers
The equation is a quadratic equation that is x + x² = 42. Then the correct option is A.
What is Algebra?Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.
The sum of a number and its square is 42.
Let x be the number. Then the square of that number will be x².
Then we have
x + x² = 42
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Answer:
a
Step-by-step explanation:
Choose equal less or greater
Answers
Answer:
C is greater
D is less
Step-by-step explanation:
There are 20 triangles and 4 circles. What is the simplest ratio of circles to total shapes?
PLS HURRY HELP
Answers
Answer:
Im pretty sure its 5
Step-by-step explanation:
5:1 due to 20/4 would be 5. I can give you more of an explaination if needed.
Answer:
5 triangles to 4 circles.