According to the Central Limit Theorem, as the sample size increases, the sample distribution of the mean is closer to the normal distribution regardless of whether or not the distribution of the population is normal.
As the sample size increases, the sample distribution of the mean is closer to the normal distribution regardless of
whether or not the distribution of the population is normal. This is known as the Central Limit Theorem, which states
that as the sample size increases, the distribution of sample means will become approximately normal, regardless of
the distribution of the population, as long as the sample size is sufficiently large (usually n ≥ 30). This is an important
concept in statistics because it allows us to make inferences about population parameters based on sample statistics.
This theorem states that the distribution of sample means approaches a normal distribution as the sample size
increases, even if the original population distribution is not normal. The three rules of the central limit theorem are
The data should be sampled randomly.
The samples should be independent of each other.
The sample size should be sufficiently large but not exceed 10% of the population.
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Simplify this expression 3y + 6y + 8y
Answer:
the answer is 17y 3y+6y is 9y plus 8y is 17y
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{3y + 6y + 8y}[/tex]
[tex]\huge\textbf{Simplifying it:}[/tex]
[tex]\mathsf{3y + 6y + 8y}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathsf{(3y + 6y + 8y)}[/tex]
[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{\rightarrow 3y + 6y + 8y}[/tex]
[tex]\mathsf{\rightarrow 9y + 8y}[/tex]
[tex]\mathsf{\rightarrow 17y}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{17}\mathsf{y}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the P(1, 4) on 2 rolls of a die?
When you roll two number cubes, what are the odds in simplest form against getting two numbers greater than 3?
A. 4:1
B. 1:4
C. 3:1
D. 1:3
Answer:
1:3.
Step-by-step explanation:
Probability(getting > 3 on one roll) = 3/6 = 1/2.
So on 2 cubes rolled the probability of getting > 3 is 1/2 * 1/2 = 1/4.
As a ratio this is 1:3.
10 points
help me and hurry, please
The probability in all given conditions is 1/4.
According to the statement
Number of coin tossed = 3
Total outcomes = 8
Now, we have to find the probabilities on different conditions.
Probability of a head on each of the last two tossesProbability = A head on each of the last two tosses/ total outcomes
Probability = 2/8
Probability = 1/4.
Probability of alternating tale and headProbability = alternating tale and head / total outcomes
Probability = 2/8
Probability = 1/4.
Probability of a no tails on each of the last two tossesProbability = A No tails on each of the last two tosses/ total outcomes
Probability = 2/8
Probability = 1/4.
So, The probability in all given conditions is 1/4.
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Salma invests the following sums of money in common stocks having expected returns as follows: a. what is the expected return (percentage) on her portfolio
Calculate the total amount invested by summing up all the values of the investment.
Total = 50,000
Calculate the weight of each investment. For WOOPS, weight = 5000 / 50000 = 10% and so on.
Now, Expected Return = sum of weight x Returns = 10% x 0.14 + 20% x 0.16 + ... + 18%x 0.18 = 16.01%
b) Similarly,
Beta of the portfolio = sum of weight x beta = 10% x 0.6 + 20% x 0.8 + ... + 18% x 0.18 = 0.7605
c) Portfolio has less systematic risk as the beta for the average market is 1, which is above the portfolio
d) Using CAPM, Return = Rf + beta x (Rm - Rf) = 4% + 0.7605 x (14% - 4%) = 11.605%
To calculate the expected return of a portfolio, the investor needs to know the expected return of each security in the portfolio and the total weight of each security in the portfolio. This means that investors need to sum the weighted averages of the expected returns (RoRs) of each security.
Investors are based on estimates of the expected rate of return on securities, assuming that what has proven to be true in the past will be true in the future. Investors do not use the structural view of the market to calculate the expected return. Instead, it determines the weight of each security in the portfolio by dividing the value of each security by the total value of the security.
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What is the scale factor of this dilation? Triangle A B C. Side A C is 8, C B is 10, A B is 6. Triangle A prime B prime C prime. Side A prime C prime is 4, C prime B prime is 5, B prime A prime is 3. One-fifth One-half 1 2
Answer:
The scale factor from the original triangle to the image is 1/2. The scale factor from the image to the original is 2.
Step-by-step explanation:
I make a sketch of the information. Look at the corresponding sides. Side AC on the big triangle is 8 and A'C' is 4. It is half of the size of the large triangle. That is true for each pair of sides.
If I went the other way, the original sides are twice as big as the images sides.
Se vendieron un total de 430 boletos para la obra de teatro escolar. Los boletos eran o de adulto o de estudiante. Se vendieron 70 boletos de estudiante menos que boletos de adulto. ¿Cuántos boletos de adulto fueron vendidos?
Resolviendo un sistema de ecuaciones, veremos que se vendieron 250 boletos de adulto.
¿Cuántos boletos de adulto fueron vendidos?
Definamos las variables:
x = boletos de adulto vendidos.y = boletos de estudiantes vendidos.Se vendieron un total de 430 boletos, entonces:
x + y = 430
Y se vendieron 70 boletos de estudiante menos que boletos de adulto:
y = x - 70
Tenemos el sistema de ecuaciones:
x + y = 430
y = x - 70
Para resolverlo, podemos reemplazar la segunda ecuación en la primera:
x + y = 430
x + (x - 70) = 430
2x = 430 + 70 = 500
x = 500/2 = 250
Se vendieron 250 boletos de adulto.
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which similar triangle, the ratios of all theee pairs of corresponding sides add never equal true or false
The ratio of all the corresponding sides of the triangle are equal to each other.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Two triangles are said to be similar if they have the same shape and the same corresponding angles.
Also, the ratio of all the corresponding sides of the triangle are equal to each other.
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what does -16t^2 mean in h(t)=5+100t-16t^2
-16t^2 represent the position on the graph on the negative side.
According to the statement
we have given equation is h(t)=5+100t-16t^2 -(1)
And we have to find representation of -16t^2
we know that the equation number (1) represent the Quadratic Equation
And in this we have to solve the Quadratic Equation and find the representation of the given terms. then
h(t)=5+100t-16t^2
5+100t-16t^2 = 0
16t^2 -100t-5 = 0
In this equation 16t^2 represent the equation on the graph.
It means that it shows the position on the graph.
Overall, -16t^2 represent the position on the graph on the negative side.
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Determine the missing information in the paragraph proof.
Given: Line PQ contains points (w, v) and (x, z) and line P'Q' contains points (w + a, v + b) and (x + a, z + b). Lines PQ and P'Q' are parallel.
Prove: Parallel lines have the same slope.
On a coordinate plane, 2 lines are shown. Line Q P goes through (w, v) and (x, z). Line Q prime P prime goes through (w + a, v + b) and (x + a, z + b).
Since slope is calculated using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction, the slope of both lines is equivalent to ________. It is given that the lines are parallel, and we calculated that the slopes are the same. Therefore, parallel lines have the same slopes.
The slope of both lines is mathematically equivalent to
[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]i
What is the slope of both lines is equivalent to?Generally, the equation for Slope is mathematically given as
[tex]S= dy / dx[/tex]
Therefore
[tex]Slope of PQ = \frac{(z - v)}{(x - w)}[/tex]
[tex]S of P'Q' =\frac{ (z + b - (v + b))}{((x + a) - (w + a))}\\\\S of P'Q' =\frac{ (z - v)}{(x - w)}[/tex]
The slopes of both lines are equivalent to
[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]
In conclusion, The slope of both lines is equivalent to
[tex]Slope=\frac{(z - v)}{ (x - w)}[/tex]
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Answer:
A: z - v | x - w
Step-by-step explanation:
Lowest common multiple of 12, 18,56
Answer: The lowest common multiple of 12, 18, and 56 would be 504. Why? Well, see below for an explanation!
Step-by-step explanation: What is the lcm? Well, the lcm of two or more numbers is the lowest possible number that each number has in common as a multiple. Because we are dealing with large numbers, we can tell that the lcm will be a multiple of these numbers times at least 5. I multiplied all the numbers by 10, and it was too large and did not work. However, I backed up and tried 9.
56 x 9 = 504.
Why is this acceptable? Well, this is acceptable because I found that 504 can be divided by 12 and 18 both to get a whole number.
504 divided by 18 equals 28.
504 divided by 12 equals 42.
Using this principle, we will find that 504 is the lowest number that 12, 18, and 56 have in common.
Your final answer: 504 is the lowest common denominator. If you need extra help, let me know and I will gladly assist you.
To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.
This method consist of extracting the common and uncommon prime factors, then
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 18 \ \ \ 56}\\ \ 6 \ \ \ \ 9 \ \ \ \ 28\\ \ 3 \ \ \ \ 9 \ \ \ \ 14\\ \ 3 \ \ \ \ 9 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 3 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 1 \ \ \ \ \ 7\\ \ 1 \ \ \ \ 1 \ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 3\\ 3\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]
[tex]\sf{L.c.m.(12,18,56)=2\times2\times2\times3\times3\times7}[/tex]
[tex]\sf{L.c.m.(12,18,56)=2^{3}\times3^{2}\times7 }[/tex]
[tex]\boxed{\boxed{\sf{L.c.m.(12,18,56)=504}}}[/tex]
The lowest common multiple of 12, 18, and 56 is 504.
PLEASE HELP IM SUPER STUCK
Answer:
[tex]y = \frac{1}{4} x + 9[/tex]
Step-by-step explanation:
All lines take the form
[tex]y = mx + c[/tex]
Where m is the gradient (or slope), and c is the y-intercept. To find the gradient if a line perpendicular to another, we must find the negative reciprocal of the other line. The gradient of the line given is -4, so our negative reciprocal is 1/4.
To find our y-intercept, we must find the point where the line crosses the y-axis (in other words, when the X coordinate is 0). Helpfully, the coordinate given is already at this point, so we can simply take the y coordinate from here, and we know our y-intercept is 9. Putting this altogether, our equation is:
[tex]y = \frac{1}{4} x + 9[/tex]
Hey I appreciate the help thank you
Answer:
60 degrees
Step-by-step explanation:
The sum of the interior angles of a triangle are 180. The bottom triangle give you two of the angle measurements (43 and 35) Take 180 - 43 -35 = 102. Angle E is 102. Vertical angles are congruent so that mean that we can use that to find angle a. Again, the sum of the interior angles adds up to 180. 180 - 102 - 18 gives us the measurement of angle a (60)
What is the x-coordinate of the point that divides the directed line segment from j to k into a ratio of 2:5? x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 –4 –2 2 4
The x-coordinate of the point is -2
How to determine the coordinates of point C?The points are given as:
J = (-6, -2)
K = (8, -9)
m : n = 2 : 5
The x-coordinates of the point is calculated as:
[tex]jk = \frac{m}{m+n} *(x_2 -x_1) +x_1[/tex]
So, we have:
[tex]jk = \frac{2}{2+5} *(8+6) -6[/tex]
This gives
[tex]jk = \frac{2}{7} *14 -6[/tex]
So, we have:
jk = 4 - 6
Evaluate
jk = -2
Hence, the x-coordinate of the point is -2
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Find the surface area of the composite figure. Round to the nearest tenth if necessary.
The surface area of the composite figure shown in the figure attached is 233.6 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The surface area of the composite = (6 * 8) + 2(8 * 3.6) + 2(0.5)(6 + 2 + 6 + 2)(3) + (8)(2 + 6 + 2) = 233.6 cm²
The surface area of the composite figure shown in the figure attached is 233.6 cm²
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What is the perimeter of the contest area on the judo mat?
(please be quick)
The perimeter of the contest area on the judo mat will be 32 meters.
What is the perimeter of the square?For a square with a side length of a unit, we get:
Perimeter of the square = 4a unit
The side length of square is 8 m.
Then the perimeter of the contest area on the judo mat will be
P = 4 x 8
P = 32 m
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If mZMNO = 95°, mZADC = 101°, and mZMLO = 80°, then what is m/ABC, in degrees?
Answer:
This is your answer.
Step-by-step explanation:
There are different kinds of angles:
Angles below 90= Acute
90= Right
91–179= Obtuse
180= Straight Angle
181–359= Reflex Angle
360= Complete Angle or Circle.
Because 80 degrees is less than 90 degrees, Angle ABC is an acute angle.
Help please im bad at math!
Hello, the solution is in this photo.
The correct answer is 300
Answer:
300cm^2
Step-by-step explanation:
Replace pie by 3. 3(10)^2 which equals to 300cm^2. 10 is radius.
quadratic formula. pls help
Answer:
[tex]x=-1,\frac{5}{7}[/tex]
Step-by-step explanation:
1) Split the second term in [tex]7{x}^{2}+2x-5[/tex] into two terms.
1 - Multiply the coefficient of the first term by the constant term.
[tex]7\times -5=-35[/tex]
2 - Ask: Which two numbers add up to 2 and multiply to -35?
7 and -5.
3 - Split 2x as the sum of 7x and -5x.
[tex]7x^2+7x-5x-5[/tex]
2) Factor out common terms in the first two terms, then in the last two terms.
[tex]7x(x+1)-5(x+1)=0[/tex]
3) Factor out the common term x+1.
[tex](x+1)(7x-5)=0[/tex]
4) Solve for x.
1 - Ask: When will (x+1)(7x-5) equal zero?
When x + 1 0 or 7x-5=0
2 - Solve each of the 2 equations above.
[tex]x=-1,\frac{5}{7}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What are the quadratic formulas?}[/tex]
[tex]\bullet\rm{\ \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
[tex]\bullet\rm{\ ax^2 + bx + c = 0}[/tex]
[tex]\huge\textbf{What are we solving for?}[/tex]
[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]
[tex]\huge\textbf{What do we have to do?}[/tex]
[tex]\rm{7x^2 + 2x - 5 = 0}[/tex]
[tex]\huge\textbf{Factor the LEFT side of the given}\\\\\huge\textbf{equation:}[/tex]
[tex]\rm{(7x - 5)(x + 1) = 0}[/tex]
[tex]\rm{(7x - 5) \times (x + 1) = 0}[/tex]
[tex]\huge\textbf{Set 0 to the factors:}[/tex]
[tex]\rm{7x - 5 = 0\ or\ x + 1 = 0}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x = \dfrac{5}{7}\ or\ x = -1}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\mathsf x = \dfrac{5}{7}\ or\ \mathsf{x} = -1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Exhibit 2 Touchdowns Field Goals Patrick 39 13 Jimmy 25 5 Exhibit 2 presents the touchdowns and field goals two football players can make if they each specialize in being either a quarterback or a kicker, but not both. Who has the absolute advantage playing quarterback
Patrick has an absolute advantage in playing quarterback.
Given a table containing touchdowns and field goals by Partrik and Field goals as under:
Person Touchdowns Field goals
Patrik 39 13
Jimmy 25 5
We are required to find a person who has an absolute advantage in playing quarterback.
Absolute advantage is the ability of an individual, company to produce greater advantage of good or service than the individual.
Total of touchdowns and field goals by Patrik=39+13=52
Total of touchdowns and field goals by Jimmy=25+5=30
We can see that total of touchdowns and field goals by Patrik is greater than total of touchdowns and field goals by Jimmy. So Patrik has an absolute advantage playing quarterback.
Hence Patrick has an absolute advantage in playing quarterback.
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Question is incomplete as it should include the following table:
Person Touchdowns Field goals
Patrik 39 13
Jimmy 25 5
Can someone help me please
Answer:
D. (4,0) and (-4,0)
C. there is one discontinuity at x=3
Step-by-step explanation:
Roots can be found by setting f(x)=0:
f(x)=(x^2-16)/(x^2-2x-3)
0=(x^2-16)/(x^2-2x-3), multiply both sides by x^2-2x-3 to get rid of the denominator
0=x^2-16, use difference of squares to factor it
0=(x+4)(x-4)
x=4,-4
Therefore the roots are (4,0) and (-4,0)
Discontinuities are when f(x) is undefined, and f(x) is undefined when something is divided by 0
Set the denominator equal to 0:
0=x^2-6x+9, use the form a^2 - 2ab + b^2 to factor
0=(x-3)^2
x=3
Therefore, there is a discontinuity at x=3
What is the image of (-4,-4) after a dilation by a scale factor of 2 centered at the origin?
Answer:
multiply x and y coordinates by 2 since its a whole number dilation (make bigger basically) ... (-8,6)
Step-by-step explanation:
Margie is practicing for an upcoming tennis tournament. Her first serve is good 20 out of 30 times on average. Margie wants to know the estimated probability that her first serve will be good at least four of the next six times she serves. How could she design a simulation for this scenario
Probability that Margie's first serve will be good at least four of the next six times she serves is 0.68
What is Binomial Distribution in Probability?
Assume that n independent replications of a random experiment with exactly two outcomes are performed. Success has a probability of [tex]p[/tex], while failure has a probability of [tex]q[/tex]. Assume that out of these n times, we will experience success [tex]x[/tex] times and failure [tex]n-x[/tex] times. There are [tex]^nC_x[/tex] different ways in which we can succeed. If, [tex]X[/tex] has a binomial distribution, then,
[tex]P(X=x)=p(x)[/tex]
[tex]=[/tex] [tex]^nC_xp^xq^{n-x}[/tex]
for [tex]x[/tex] = 0, 1,..., n. Here, [tex]q=1-p[/tex]. A binomial variate is any such random variable [tex]X[/tex]. A group of n separate Bernoullian trials is known as a binomial trial. Binomial distribution requirements:
There are just two outcomes, success and failure, for each trial.The quantity "[tex]n[/tex]" of trials is finite.The trials run separately from one another.For each trial, the odds of success [tex]p[/tex], or failure [tex]q[/tex], remain constant.
Given,
Probability of good serves = Success
⇒ [tex]p=\frac{20}{30}[/tex]
⇒[tex]p=\frac{2}{3}[/tex]
Failure = [tex]q[/tex]
⇒ [tex]q=1-p[/tex]
⇒ [tex]q=1-\frac{2}{3}[/tex]
⇒ [tex]q=\frac{1}{3}[/tex]
Number of trials [tex]= n[/tex]
[tex]n=6[/tex]
Probability of at least four good serve = [tex]P(4 < X < 6)[/tex]
According to the binomial distribution,
Therefore,
[tex]P(4 \leq X \leq 6)=P(X=4)+P(X=5)+P(X=6)[/tex]
[tex]=[/tex] [tex]^6C_4(\frac{2}{3}) ^4(\frac{1}{3})^2+ ^6C_5(\frac{2}{3}) ^5(\frac{1}{3})^1+^6C_6(\frac{2}{3}) ^6(\frac{1}{3})^0[/tex]
[tex]=[/tex] [tex]15\times\frac{16}{729} +6\times\frac{32}{729} +1\times\frac{64}{729}[/tex]
[tex]=[/tex] [tex]\frac{496}{729}[/tex]
[tex]= 0.68[/tex]
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WILL MAKE BRAINLIEST!!!
Match each pair of angles to their relationship name (put letters next to the relationship name)
_1. Vertical
_2. Same side interior
_3. Alternate interior
_4. Corresponding
_5. Same-side exterior
_6. Alternate Exterior
_7. Supplementary
_8. No relationship
Answer:
corresponding, supplementary, alternate interior, same side interior, vertical, alternate exterior, corresponding, alternate exterior, vertical, and alternate interior
In the figure 10, the pair of angles are alternate interior angles.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
From the given figure,
1) corresponding angles
2) Adjacent angles (Supplementary)
3) Alternate interior angles
4) Allied angles (Same side interior)
5) Vertically opposite angles
6) Alternate exterior angles
7) corresponding angles
8) Alternate exterior angles
9) Vertically opposite angles
10) Alternate interior angles
Therefore, in the figure 10, the pair of angles are alternate interior angles.
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What type of function is represented by the table of values below?
A. cubic
B. exponential
C. quadratic
D. linear
The table represents an exponential function:
[tex]f(x) = 3^x[/tex]
Then the correct option is B.
What type of function is represented by the table?
Here we have the table:
x y
1 3
2 9
3 27
4 81
5 243
You can see that each time that x increases by one unit, the value of is multiplied by 3. This is clearly an exponential function.
The function actually is:
[tex]f(x) = 3^x[/tex]
Evaluating it we get:
[tex]f(1) = 3^1 = 3\\\\f(2) = 3^2 = 9\\\\f(3) = 3^3 = 27\\...[/tex]
So the correct option is B, exponential.
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Use the interactive tool to find which of the following expressions have a sum of 6. Check all that apply.
8 + 2
(–4) + (-2)
(–3) + 9
7 + (–1)
The expressions that have a sum of 6 are Options C and D
How to determine the sum
In this case, we use the following rules
(-) + (-) = -
(+) + (+) = +
(+) + (-) = -
(-) + (+) = -
From the first case
8 + 2 = 10
(-4) + (-2) = -4 + -2 = -6
(-3) + 9 = -3 + 9 = 6
7 + (-1) = 7 - 1 = 6
Thus, the expressions that have a sum of 6 are Options C and D
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Can someone help me please. (TROLLS WILL BE REPORTED!!!)
Answer:
B.) 54π units²
Step-by-step explanation:
First, we need to find the height of the cone. We can do this using the Pythagreom Theorem.
a² + b² = c² <----- Pythagreom Theorem
3² + b² = 15² <----- Insert side lengths
9 + b² = 225 <----- Solve 3² and 15²
b² = 216 <----- Subtract 9 from both sides
b = 14.7 units <---- Take square root of 216
Now, we can use the surface area of a right cone equation to find the final answer.
r = 3 units
h = 14.7 units
SA = πr(r + √(h² + r²)) <----- Surface Area equation
SA = π(3)(3 + √(14.7² + 3²)) <----- Insert values
SA = π(3)(3 + √(216 + 9)) <----- Solve 14.7² and 3²
SA = π(3)(3 + √225) <----- Add 216 and 9
SA = π(3)(3 + 15) <----- Take square root of 225
SA = π(3)(18) <----- Add 3 and 15
SA = 54π units² <----- Multiply 3 and 18
Select the correct answer. consider this absolute value function. if function f is written as a piecewise function, which piece will it include?
x + 3, x > -3 is the piece which will be included in the given function f(x) = [ x + 3 ]. This can be obtained by removing modulus and finding the value for x.
Which piece will the function include?Given that,
f(x) = [ x + 3 ] which is an absolute value function.
Therefore,
| x+3 | > 0
By removing the modulus,
x+3 > 0
x > - 3
Hence x + 3, x > -3 is the piece which will be included in the given function f(x) = [ x + 3 ].
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Consider this absolute value function.
f(x) = [ x + 3 ]
If function f is written as a piecewise function, which piece will it include?
A. x + 3, x > 3
B. x + 3, x > -3
C. -x + 3, x < -3
D. -x - 3, x < 3
Answer:
The Answer is C. X+3, x > -3
for edmentum users
Step-by-step explanation:
Pentagon ABCDE ~ LMNOP. Find the value of x and the measure of Lc.
The value of x is 6 and the measure of ∠C is 86 degrees
How to solve for x and the measure of c?The complete question is added as an attachment
Given that:
ABCDE ~ LMNOP
It means that we have the following equivalent ratio
ED : BC = PO : MN
This gives
8 : 6 = 12 : x
Express as fraction
6/8 = x/12
Multiply both sides by 12
12 * 6/8 = x
Evaluate
9 = x
Rewrite as
x = 9
Also
ABCDE ~ LMNOP implies that the corresponding angles are equal
The corresponding angle of C is N
And, we have:
N = 86
This implies that
C = 86
Hence, the value of x is 6 and the measure of ∠C is 86 degrees
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