suppose sat writing scores are normally distributed with a mean of 497 and a standard deviation of 114 . a university plans to admit students whose scores are in the top 30% . what is the minimum score required for admission? round your answer to the nearest whole number, if necessary.
Suppose sat writing scores are normally distributed with a mean of 497 and a standard deviation of 114. A university plans to admit students whose scores are in the top 30%, the minimum score required for admission is 434
How we calculate the minimum score required for admission?Given information:
Mean (μ) = 497Standard Deviation (σ) = 114Probability (p) = 0.30 (for the top 30% of the scores)Let X be the random variable which represents the SAT writing scores. Then X ~ N(497, 114)Now we have to find the minimum score required for admission. We can solve the problem using the standard normal distribution table. Here we need to find the z-score.
The formula for z-score is given below:z = (X - μ) / σ z-score corresponding to the probability (p) can be calculated as:z = ZpWhere Zp is the standard normal variable, which gives the area to the left of the z-score. So, Zp = InvNorm(0.30) = - 0.524For the top 30% of the scores, we have Zp = -0.524. Now the z-score is known. So we can calculate the minimum score required for admission as :X = μ + z * σ = 497 + (-0.524) * 114 = 433.584 ≈ 434The minimum score required for admission is 434.
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A car is purchased for £8500
In its first year, the value of the car will depreciate
by 10%.
Each year after that, the value of the car will
depreciate by 5%.
What is the value of the car at the end of 3 years?
Answer:
£ 6904.13
Step-by-step explanation:
the final value is given by
[tex]8500 (0.90)[/tex] at the final of the first year
then you need to add (0.95) twice (one from second and one from third year)
Notice if the depreciation is 5% the final value is 0.95 of the initial value at the beginning of the year
finally:
[tex]8500 (0.90) (0.95)^2 = 6904.13[/tex] (rounded to nearest cent!)
the picture pls answer my picture.
Answer:
$63 more in tax
Step-by-step explanation:
Takis is 5.25 in tax
PlayStation is 68.25
well, we know the tax is 10.5% so let's get them for both.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]
[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]
(a) describe the relationship between distance and travel time. (select all that apply.) positive negative moderate weak linear nonlinear
The relationship between distance and travel time. It is not excessively strong or weak. In other words, the rate of change in journey time is moderate and constant with respect to distance.
positive negative moderate weak linear nonlinear relationship between distance and travel time can be described as follows:•
Positive• Linear• Moderate
Explain as we move from point A to point B, the distance covered and the travel time it takes to get there are positively correlated. As the distance increases, the travel time required to reach the destination also increases, resulting in a positive correlation.
The relationship between distance and travel time is linear because the rate at which distance is covered remains constant, resulting in a straight-line relationship on a graph. It means that if distance doubles, the travel time will also double, indicating a linear relationship.
Hence, the linear relationship is also referred to as a direct relationship. On a graph, the line that represents the relationship between distance and travel time is moderate. This implies that the slope of the line is neither too steep nor too gentle.
Thus, it is neither too strong nor too weak. In other words, the rate of change in travel time is consistent as distance changes, making it moderate.
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The inside diameters of bearings used in an aircraft landing gear assembly are known to have a standard deviation of A random sample of 15 bearings has an average inside diameter of 8. 2535 cm. (a) Test the hypothesis that the mean inside bearing diameter is 8. 25 cm. Use a two-sided alternative and (b) Find the P-value for this test. (c) Construct a 95% two-sided confidence interval on the mean bearing diameter
(a) The hypothesis that the mean inside bearing diameter is 8. 25 cm is 6.78.
(b) The p value is zero because if we observe a sample that is unlikely to fall below zero (if the statistician can detect it, we can get a p-value of exactly zero.
(c) At 95% two-sided confidence interval on the mean bearing diameter is 8.2527 or 8.2543.
Hypothesis:
Hypotheses (plural hypotheses) are proposed explanations for phenomena. For a hypothesis to be a scientific hypothesis, the scientific method requires that it can be tested. Scientists often base scientific hypotheses on past observations that cannot be satisfactorily explained by existing scientific theories. Although the words "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a tentatively accepted hypothesis that is proposed for further research in a process that begins with an educated guess or idea.
(a) The hypothesis that the mean inside bearing diameter is 8. 25 cm. By Using the two sided alternative:
H₀= 8.25
H₁ ≠ 8.25
Z = X - 8.25÷ sd/√π
= x - 8.25÷ 0.002/3.14
= 6.78 > 1.96 (CV)
(b) the P-value for this test is:
p( value) = 0
because if we observe a sample that is unlikely to fall below zero (if the statistician can detect it, we can get a p-value of exactly zero.
(c) X ± Zᵃ ÷ sd/√π
= 8.2527 or 8.2543
At 95% two sided confidence interval on the mean bearing diameter is 8.2527 or 8.2543.
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If you have the following data about
a box of bouncy balls, about how
many bouncy balls are estimated to
be in the box?
Mass of Bouncy Balls + Box = 17,342
grams
Mass of 45 Balls = 505 grams
Mass of Box ONLY = 429 grams
Approximately, how many bouncy
balls are in the box?
Bouncy Balls in Box
Enter
there are approximately 1506 bouncy balls in the box.
What is mass ?
Mass is a physical property of matter, which refers to the amount of substance present in an object. It is typically measured in units of grams or kilograms, and can be thought of as a measure of the object's inertia or resistance to acceleration. Mass is often used interchangeably with weight in everyday language, but they are technically different concepts. Weight is a measure of the force of gravity acting on an object, and varies depending on the object's location in the gravitational field.
According to the question:
First, we need to find the mass of the bouncy balls in the box by subtracting the mass of the box only from the mass of the box and bouncy balls.
Mass of bouncy balls in box = Mass of box and bouncy balls - Mass of box only
Mass of bouncy balls in box = 17,342 - 429
Mass of bouncy balls in box = 16,913 grams
Next, we need to find the mass of one bouncy ball by dividing the mass of 45 balls by 45.
Mass of one bouncy ball = Mass of 45 balls / 45
Mass of one bouncy ball = 505 / 45
Mass of one bouncy ball = 11.222 grams
Finally, we can estimate the number of bouncy balls in the box by dividing the mass of the bouncy balls in the box by the mass of one bouncy ball.
Number of bouncy balls in box = Mass of bouncy balls in box / Mass of one bouncy ball
Number of bouncy balls in box = 16,913 / 11.222
Number of bouncy balls in box ≈ 1506
Therefore, there are approximately 1506 bouncy balls in the box.
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Solve for x, using the tangent lines.
X
46°
× = [ ? ]°
Please answer ASAP, if you could include an explanation that would also help!
Considering the tangent-secant theorem, the value of x is given as follows:
x = 55º.
What is the secant-tangent theorem?The secant-tangent theorem states that when a tangent and a secant line intersect at a point outside a circle, the measure of the angle of intersection is given by half the difference between the arc length of the far arc by the arc length of the near arc.
Hence the equation is given as follows:
y = (far arc - near arc)/2.
The parameters for this problem are given as follows:
far arc = 145º.near arc = 35º.Angle = x.Then, applying the theorem, the value of x is given as follows:
x = (145 - 35)/2
x = 55º.
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The product of two numbers is 19,200 and HCF is 40 find the LCM
If product of two numbers is 19,200 and HCF is 40, then the LCM is 480
Given that the product of two numbers is 19,200 and the highest common factor (HCF) is 40.
Let us assume the two numbers to be x and y.
Therefore, x × y = 19,200
Also, HCF of x and y is 40.
We can write x = 40a and y = 40b, where a and b are co-prime.
Then, x × y = 40a × 40b = 1600ab = 19,200
Therefore, ab = 12
Now, we need to find the LCM of x and y.
LCM(x, y) = (x × y)/HCF(x, y) --- (1)
Substituting the values of x, y and HCF in the above equation, we get,
LCM(x, y) = (40a × 40b)/40 = 40ab
= 40 × 12 (as ab = 12)
= 480
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for each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to 0. explain your choice. (a) weight of a car and gas mileage there is a positive correlation, because heavier cars tend to get lower gas mileage. there is a positive correlation, because heavier cars tend to get higher gas mileage. there is a negative correlation, because heavier cars tend to get lower gas mileage. there is a negative correlation, because heavier cars tend to get higher gas mileage. there is a correlation close to 0, because there is no reason to believe that weight of a car and gas mileage are related to each other. (b) size and selling price of a house there is a positive correlation, because larger houses tend to be more expensive. there is a positive correlation, because larger houses tend to be less expensive. there is a negative correlation, because larger houses tend to be more expensive. there is a negative correlation, because larger houses tend to be less expensive. there is a correlation close to 0, because there is no reason to believe that size and selling price of a house are related to each other. (c) height and weight there is a positive correlation, because taller people tend to be heavier. there is a positive correlation, because taller people tend to be lighter. there is a negative correlation, because taller people tend to be heavier. there is a negative correlation, because taller people tend to be lighter. there is a correlation close to 0, because there is no reason to believe that height and weight are related to each other. (d) height and number of siblings there is a positive correlation, because taller people tend to have more siblings. there is a positive correlation, because taller people tend to have fewer siblings. there is a negative correlation, because taller people tend to have more siblings. there is a negative correlation, because taller people tend to have fewer siblings. there is a correlation close to 0, because there is no reason to believe that height and number of siblings are related to each other.
The correlation close to 0, because there is no reason to believe that height and number of siblings are related to each other.
For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to 0. Explain your choice. (a) Weight of a car and gas mileage: There is a negative correlation, because heavier cars tend to get lower gas mileage. (b) Size and selling price of a house: There is a positive correlation, because larger houses tend to be more expensive. (c) Height and weight: There is a positive correlation, because taller people tend to be heavier. (d) Height and number of siblings: There is a correlation close to 0, because there is no reason to believe that height and number of siblings are related to each other.
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Shouldn't be correct answer be option 2?
2+1=3 is the solution to the differentiation equation.
What does a calculus differential equation mean?A differential equation is an equation that explains a function's unknown derivative or derivatives. Take the equation, for example. The expression d y d x = x sin expresses the derivative of an unknown function.
Chain rule evaluation of the derivative on the left hand side yields the following results:
[tex]dxd {( dxdy ) 3 } =0. ⇒3( dxdy ) 2 dx 2 d 2 y =0[/tex]
Because the highest order derivative that appears in the equation is second order, the order of this differential equation is 2.
Its highest order derivative's power is the degree. Degree in this instance is 1.
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FACTOR 6x²- 18x - 60
Answer: 6(x+2)(x-5)
Step-by-step explanation:
1: Factor by grouping- A 6 can be distributed in all 3 terms, when we do this we get 6(x²-3x-10).
2: This is in the form 6(x²+bx+c). So, to continue factoring, just forget about the six for a while and find two factors of c that add up to b. These two factors are -5 and 2.
3: Fill in the blanks with either factor. (x+?)(x+?) We get (x+2)(x-5).
4: Bring back the 6 to the beginning of the equation to get a final answer of 6(x+2)(x-5).
Due tomorrow!!! Pls help
Answer:
Step-by-step explanation:
[tex]P=\frac{\theta}{360} \pi d[/tex]
[tex]= \frac{120}{360} \pi \times 10[/tex] (diameter = 2 x radius)
[tex]=\frac{10\pi}{3}[/tex]
[tex]=10.5cm[/tex]
Miguel bought 22 pounds of flour for $12. How many dollars did he pay per pound of flour?
Which state is located at point C?
a map of the United States. New York, Indiana, and Kansas are labeled. There is an A marking the state south of New York along the Atlantic coast. There is a B marking the state east of Indiana. There is a C marking the state north of Indiana. There is a D marking the state northeast of Kansas. There is an E marking the state south of Kansas.
New Jersey
Ohio
Michigan
Iowa
According to the information provided, the state is at point C, Michigan.
Based on the information provided, the state located at point C is Michigan.
What is logical thinking?Logical reasoning consists of aptitude questions that require logical analysis to arrive at a suitable solution. Most of the questions are conceptual, the rest are unconventional.
Logical thinking follows he is divided into two types.
Oral reasoning:
It is the ability to logically understand concepts expressed in words and solve problems. Oral reasoning tests your ability to extract information and meaning from sentences. Non-verbal thinking:
It is the ability to logically understand concepts represented by numbers, letters, and combinations of numbers and words and solve problems. Nonverbal reasoning tests your ability to reason and guide the logic and implications of information in a problem.
Much of the logic curriculum can be classified into his two types above.
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Given a list (0, 1, 1, 2, 3, 5, 8, 13, 17), the binary search algorithm calls BinarySearch(list, 0, 8, 3). What is the index of the middle element?
The index of the middle element is 4.
The list (0, 1, 1, 2, 3, 5, 8, 13, 17), the binary search algorithm calls Binary Search (list, 0, 8, 3). The index of the middle element is 4. The binary search algorithm works by dividing a list into halves and looking at the value in the middle of the list. This is compared with the target value, and based on the comparison, one-half of the list is discarded as the search is continued in the other half. This is continued until the target value is found or it is clear that it is not on the list. In the given case, the list is (0, 1, 1, 2, 3, 5, 8, 13, 17), and the algorithm calls Binary Search(list, 0, 8, 3).
Here, the first parameter of the Binary Search function is the list, the second parameter is the lower index of the part of the list being searched, the third parameter is the upper index, and the fourth parameter is the value being searched. In the given case, the lower index is 0, the upper index is 8, and the value being searched is 3. The index of the middle element in the list is calculated as (0 + 8) / 2 = 4.
Therefore, the index of the middle element is 4.
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If the block suppported by the pulley system has a weight of 20N what is the input force(effort) on the rope?(Assume the pulley system is frictionless ).
Answer: The input force (effort) on the rope is 20 N.
Step-by-step explanation:
In a frictionless pulley system, the tension in the rope is constant throughout. Therefore, the force applied to the rope on one side of the pulley system is equal to the force exerted on the other side of the system.
In this problem, we know that the weight of the block is 20 N. This means that there is a force of 20 N acting downwards on one side of the pulley system.
Since the pulley system is frictionless, the tension in the rope is also 20 N. Therefore, the force applied to the rope on the other side of the pulley system (i.e., the input force or effort) must also be 20 N in order to balance the weight of the block.
So the input force (effort) on the rope is also 20 N.
I NEED HELP ON THIS ASAP, IT'S DUE TODAY!
The inequalities which the number lines represent are as follows;
x > 3
x <= 2.
What are inequalities ?A mathematical comparison and expression of the relationship between two expressions is known as an inequality.
It can be seen as a generalization of an equation and is denoted by a symbol like ">", "", "", or "".
In contrast to an equation, which only has one solution, an inequality may have several answers or none at all.
The values that give rise to an inequity are its remedies.
The range of potential values for a variable is one example of how inequality models limits or limitations in the real world.
They can also be used to describe how two variables relate to one another, such as when one is more than or less than the other.
According to our question-
the inequality is; x <= 2
the inequality is; x > 3
x > 3
x <= 2
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The probability that a person in a certain town has brown eyes is 2 out of 5. A survey of 450 people from that same town was taken. How many people would be expected to have
brown eyes?
A. 45
B. 90
C. 180
D. 225
From the given information provided, the number of people having brown eyes in town is 180.
If the probability that a person in the town has brown eyes is 2/5, then we can expect that 2 out of every 5 people have brown eyes.
To find the number of people in the survey who would be expected to have brown eyes, we can use the following proportion:
(2/5) = (x/450)
where x is the number of people expected to have brown eyes.
Solving for x, we can cross-multiply:
5x = 2 × 450
5x = 900
x = 180
Therefore, the expected number of people in the survey who would have brown eyes is 180.
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Rewrite the following in the form log(c).
log(15) -log(3)
The logarithmic expression given as log(15) -log(3) when simplified is log(5).
How to rewrite the logarithmic expressionGiven that
log(15) -log(3)
The form is
log(c)
Using the logarithmic identity that states log(a) - log(b) = log(a/b), we can rewrite the given expression as:
log(15) - log(3) = log(15/3)
And simplifying the expression inside the logarithm, we get:
log(15) - log(3) = log(5)
So the given expression, log(15) - log(3), can be written in the form log(c) as log(5).
This means that the logarithm of 5 is equivalent to the difference between the logarithms of 15 and 3.
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A team of 3 identical robotic lawn mowers can cut 15.6 acres of grass in a garden for
a single battery charge. How many acres can cut a team of 5 identical robotic lawn
mowers for a single battery charge?
Answer:
HOPE THIS HELPS
Step-by-step explanation:
Midsize robot lawnmowers cut up to half an acre or about 22,000 square feet. Large robot lawnmowers can cut up to 1 acre, or 43,560 square feet, or more
Answer: 26 acres
Step-by-step explanation:
26 acres
Divided 15.6/3 to get unit rate, then multiply by 5 to get answer.
use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.
the volume of the solid is [tex]V = π r2 (sqrt(3/4)r) / 3 = π r3 sqrt(3/4) / 3.[/tex]
Plugging in the given values, we get[tex]V = π (3)3 sqrt(3/4) / 3 = 27π/4.[/tex]
The volume of a solid with a circular base and cross sections taken parallel to one of the diameters that are equilateral triangles can be found using the slicing method. The formula for the volume of such a solid is:[tex]V = π r2 h/3,[/tex]where π is the constant pi, r is the radius of the circular base, and h is the height of the solid.
In this case, the radius of the circular base is 3 and the height is equal to the length of the sides of the
equilateral triangles. To find the height, we can use the Pythagorean Theorem. The hypotenuse of the triangle is 2r, so the length of the sides is sqrt(r2 - (r/2)2), which simplifies to sqrt(3/4)r.
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what are the dimensions of the soup can of greatest volume that can be made with a 150 square inches of tin
The dimensions of the can of greatest volume that can be made with 150 square inches of tin are a radius of approximately 5.78 inches and a height of approximately 3.85 inches.
What are the dimensions?The dimensions of the soup can of greatest volume that can be made with 150 square inches of tin are given by the formula [tex]V = \pi r^2h[/tex], where V is the volume of the can, r is the radius of the base, and h is the height of the can. We can solve for the radius and height of the can using the given information.
Let the radius of the base be r and the height of the can be h. Then, the surface area of the can is given by the formula [tex]A = 2\pi rh + 2 \pi r^2[/tex]. We are given that the surface area of the can is 150 square inches, so we can write the equation [tex]2 \pi rh + 2 \pi r^2 = 150[/tex]. We need to find the dimensions of the can that maximize its volume, V. To do this, we can use the formula for the derivative of V with respect to r, which is [tex]dV/dr = 2 \pi rh + \pi r^2 dh/dr[/tex].
Setting this equal to zero and solving for h, we get [tex]h = -2r/3[/tex]. Substituting this into the equation for A, we get the equation [tex]2 \pi r(-2r/3) + 2 \pi r^2 = 150[/tex], which simplifies to [tex]-4 \pi r^2/3 + 2 \pi r^2 = 150[/tex]. Solving for r, we get [tex]r = 5.78[/tex] inches. Substituting this into the equation for h, we get [tex]h = -3.85[/tex] inches.
Since we cannot have a negative height, we must discard this value and take the positive value of h, which is approximately 3.85 inches. Therefore, the dimensions of the can of greatest volume that can be made with 150 square inches of tin are a radius of approximately 5.78 inches and a height of approximately 3.85 inches.
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Find the derivative of the function h(w), below. It may be to your advantage to simplify before differentiating: h(w) = 7w arcsin w h' (w)=
Therefore, the derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7.[/tex]
The derivative of the function h(w) is h'(w) = [tex]7*arcsin(w) + w*cos(w)*7[/tex]. To find this, first simplify the original function using the identity arcsin(w) = sin-1(w), then use the chain rule. We get:
h'(w) = 7*sin-1(w) + w*cos(sin-1(w))*7
Since sin-1(w) is the inverse of sin(w), we can substitute w for sin(w). This gives us:
h'(w) = 7*sin-1(w) + w*cos(w)*7[tex]7*sin-1(w) + w*cos(w)*7[/tex]
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Dos veces un número es a lo sumo 24? Ayuda porfavor
After solving the linear inequality, the number can have any value less than or equal to 12 (x ≤ 12). So the maximum possible value of the number is 12.
Let's suppose the number be "x".
From the given statement, we can write the following inequality:
2x ≤ 24
To solve for x, we can divide both sides by 2:
x ≤ 12
Therefore, the number "x" is at most 12. The exact value of "x" could not be found out. As it could be any number less than or equal to 12 that satisfies the inequality.
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The complete question is :
If twice a number is at most 24, find the number.
The new town jewelry company purchased 501 carat diamond rings for $125,000 based on the following information find the selling price purring to the nearest cent
The selling price of the 501 carat diamond rings is approximately $168,750.00, rounded to the nearest cent.
To find the selling price of the 501-carat diamond rings, we need to use the information given about the cost of the purchase and the markup percentage.
Let's assume the markup percentage is m. Then, the selling price S can be calculated as:
S = C * (1 + m/100)
where C is the cost of the purchase ($125,000 in this case).
If the markup percentage is not given, we can use another piece of information to calculate it. For example, if we know that the company wants to earn a profit of P dollars on the sale, we can set the equation:
S - C = P
and solve for the markup percentage:
m = (P/C) * 100
Assuming a markup percentage of 35%, we can calculate the selling price as:
S = 125,000 * (1 + 35/100)
S ≈ $168,750.00
Therefore, the selling price of the 501 carat diamond rings is approximately $168,750.00, rounded to the nearest cent.
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Make a number line and mark the points that represent the following values of x. x²=16
please show with numberline for brainliest :) please help my class is tomorrow and im finishing homework
Answer:
See below.
Step-by-step explanation:
Here's a number line showing the points that represent the values of x that satisfy the equation x² = 16
|---------------------------|---------------------------|
-4 0 4
On this number line, I have marked the points -4, 4, which are the two solutions to the equation x² = 16. These values of x make the left-hand side of the equation equal to 16.
Katherine is going to invest in an account paying an interest rate of 3.8%
compounded daily. How much would Katherine need to invest, to the nearest dollar,
for the value of the account to reach $1,180 in 17 years?
619 would Katherine need to invest, to the nearest dollar, for the value of the account.
What is interest in simple words?
When you borrow money, you must pay interest, and when you lend money, you must charge interest. The most common way to represent interest is as a percentage of a loan's total amount every year. The interest rate for the loan is denoted by this proportion.
x. (1 + 3.8%/365)¹⁷ˣ³⁶⁵ = 1180
= x * ( 1 + 38/365000)¹⁷ˣ³⁶⁵ = 1180
= x * ( 1 + 19/182500)¹⁷ˣ³⁶⁵ = 1180
= common denominator and write the numerators above common denominator x * ( 182500 + 19/182500)⁶²⁰⁵ = 1180
= x * (182519/182500)⁶²⁰⁵ = 1180
Divide both sides of the equation by the coefficient of variable
x = 1180/(182519/182500)⁶²⁰⁵
x = 1180 * 182500⁶²⁰⁵/182519⁶²⁰⁵
x = 619
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Determine all solutions to the equation 2sin2x = 1 − cos x on the interval [0, 2π).
a: x equals pi over 2 comma 2 times pi over 3 comma 4 times pi over 3
b: x equals 0 comma pi over 3 comma 5 times pi over 3
c: x equals pi over 2 comma pi over 3 comma 5 times pi over 3
d: x equals 0 comma 2 times pi over 3 comma 4 times pi over 3
The solution to the given equation 2sin2x = 1 − cos x on the interval [0, 2π) as required is; Choice D; x equals 0 comma 2 times pi over 3 comma 4 times pi over 3.
What are the solutions to the given equations?It follows from the task content that the solutions to the given equation be determined.
On this note, since the give equation is;
2sin²x = 1 − cos x on the interval [0, 2π).
Recall sin²x = 1 − cos²x; therefore we have that;
2 - 2cos²x = 1 - cos x
2cos²x - cos x - 1 = 0.
let y = cos x so that we have;
2y² - y - 1 = 0
x = 1 or x = -1/2.
Therefore; cos x = 1 or cos x = -1/2.
Ultimately, the values of x in the given interval are; 0, 2π/3, 4π/3.
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during the computer daze special promotion, a customer purchasing a computer and printer is given a choice of three free software packages. there are 8 different software packages from which to select. how many different groups of software packages can be selected?
Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.
There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.
To calculate this, the total number of possibilities can be found by using the formula nPr,
where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]
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find the circumference of each circle
Answer:
[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]
[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked for the circumference of this circle.}[/tex]
[tex]\textsf{Let's review what the Circumference of a circle actually is.}[/tex]
[tex]\large\underline{\textsf{What is the Circumference?}}[/tex]
[tex]\textsf{The Circumference is is the length 'on' the circle.}[/tex]
[tex]\textsf{Circumference is the Perimeter of the Circle; The sum of all the curved edges.}[/tex]
[tex]\large\underline{\textsf{How do we find the Circumference?}}[/tex]
[tex]\textsf{To find the Circumference, we should use a common, and simple formula.}[/tex]
[tex]\mathtt{Circumference=(Diameter) \pi}[/tex]
[tex]\textsf{Pi will be multiplied by the Diameter of the Circle.}[/tex]
[tex]\textsf{Because we are given the Diameter, we can start solving for x.}[/tex]
[tex]\large\underline{\textsf{Substitute;}}[/tex]
[tex]\mathtt{Circumference \ (C)=(100 \ in.) \pi}[/tex]
[tex]\large\boxed{\mathtt{C=100 \pi \ in.}}[/tex]
[tex]\large\boxed{\mathtt{C \approx314.16 \ in.}}[/tex]