This table illustrates how many trials out of 100 resulted in each number of heads out of ten flips. Because it precisely depicts the possibility of each occurrence, this frequency table is the most likely to include the outcomes of the 100 trials.
The likelihood of receiving any number of heads out of ten flips is the same in a fair coin flip, therefore the table should show a fairly uniform distribution of trials across each number of heads. Overall, the frequency table most likely to capture the outcomes of the 100 trials has the number of heads out of 10 flips as rows and the number of trials out of 100 as columns.
This table may be used to precisely depict the data as well as determine the likelihood of each occurrence.
what is meant by frequancy table?
A frequency table is a way to organize and summarize data in a systematic way. It lists all of the different values (or categories) that appear in a dataset, along with the number of times each value appears. The goal of creating a frequency table is to get a better understanding of the data by seeing how frequently different values occur.
For example, let's say you have a dataset that contains the ages of a group of people. You could create a frequency table to see how many people are in each age range. The table might look something like this:
Age Range Frequency
0-9 5
10-19 8
20-29 12
30-39 10
40-49 7
50-59 4
60-69 3
70-79 2
80-89 1
90+ 1
In this frequency table, you can see that the most common age range is 20-29, with 12 people in that range. You can also see that there are very few people over the age of 80. This type of table can be helpful for understanding the distribution of values in a dataset and identifying patterns or trends.
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a line through the origin, rotates around the origin in such a way that the angle, theta, between the line and the positive x-axis changes at the rate of d/dt for time > 0. Which expression gives the rate at which the slope of the line is changing
The rate at which the slope of the line is changing with respect to time is dθ/dt.
The rate at which the slope of a line is changing with respect to time is a concept in calculus that is known as the derivative. The derivative measures the rate of change of a function with respect to one of its variables. In this case, we are looking at the rate of change of the slope of the line with respect to time. The slope of a line is determined by the angle, theta, between the line and the positive x-axis. Therefore, the rate of change of the slope of the line with respect to time is equal to the rate of change of the angle, theta, with respect to time. This can be expressed as dθ/dt, where dθ represents the change in theta and dt represents the change in time. Therefore, the expression which gives the rate at which the slope of the line is changing with respect to time is dθ/dt.
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One interior angle of a triangle is 43°, and the other two angles are congruent. Choose the equation that could be used to determine the degree measure of one of the congruent angles. 2x + 43 = 180 2x − 43 = 90 x + 43 = 180 x − 43 = 90
Answer:
x − 43 = 90
Step-by-step explanation:
2x + 43 = 180
2x − 43 = 90
x + 43 = 180
x − 43 = 90
there are $320 available to fence in a rectangular garden. the fencing for the side of the garden facing the road cost $6 per foot and the fencing for the other three sides is $2 per foot (see picture). a. determine the objective and constraint equations b. express the quantity to be maximized as a function of x. c. find the optimal values of x and y.
To answer this question, we first need to determine the objective and constraint equations.
The objective is to maximize the area of the rectangular garden, which is given by the equation $A = xy$.
The constraint is that the total cost of the fencing must not exceed $320. In other words, we have the equation $6x + 2(y+x) \le 320$.
To express the quantity to be maximized as a function of $x$, we can simply plug in the equation for the area of the rectangular garden into the objective equation. This gives us the function $f(x) = xy = x^2y$.
To find the optimal values of $x$ and $y$, we can use the method of Lagrange multipliers. Let $\lambda$ be the Lagrange multiplier. The Lagrange function is given by
$$L(x,y,\lambda) = x^2y + \lambda(6x + 2(y+x) - 320)$$
To find the optimal values of $x$ and $y$, we need to find the values of $x$ and $y$ that maximize $L(x,y,\lambda)$. To do this, we take the partial derivatives of $L(x,y,\lambda)$ with respect to $x$ and $y$ and set them equal to 0. This gives us the equations
$$\frac{\partial L}{\partial x} = 2xy + 6\lambda = 0 \quad \text{and} \quad \frac{\partial L}{\partial y} = x^2 + 2\lambda = 0$$
We can solve these equations simultaneously to find the optimal values of $x$ and $y$. First, we can solve for $y$ in the second equation to get
$$y = -\frac{x^2}{2\lambda}$$
Substituting this expression for $y$ into the first equation, we get
$$2x \left(-\frac{x^2}{2\lambda}\right) + 6\lambda = 0 \quad \Rightarrow \quad -x^3 + 12\lambda^2 = 0$$
Since $\lambda$ cannot be 0, we can divide both sides of this equation by $-12\lambda^2$ to get
$$x^3 = 12\lambda^2 \quad \Rightarrow \quad x = \sqrt[3]{12\lambda^2}$$
Substituting this expression for $x$ into the expression for $y$, we get
$$y = -\frac{\sqrt[3]{12\lambda^2}}{2\lambda}$$
Now we need to find the value of $\lambda$ that satisfies the constraint $6x + 2(y+x) \le 320$. Substituting the expressions for $x$ and $y$ into this equation, we get
$$6\sqrt[3]{12\lambda^2} + 2\left(-\frac{\sqrt[3]{12\lambda^2}}{2\lambda} + \sqrt[3]{12\lambda^2}\right) \le 320$$
Simplifying, we get
$$-\frac{\sqrt[3]{12\lambda^2}}{2\lambda} + 10\sqrt[3]{12\lambda^2} \le 320$$
Dividing both sides by $10\sqrt[3]{12\lambda^
please help me solve this
I don't see the picture. Can you send it in the message.
ABCD is a rectangle find the length of AC and find the measures of a and 0
In the given triangle, length of AC = 12.3 units
α= 45⁰ and θ = 45⁰
Using Pythagoras theorem,
[tex]AC^{2} = AB^{2} + BC^{2}[/tex]
[tex]AC^{2}[/tex] = 9 + 144
AC = 12.37
Now, to find the angles:
AC is the diagonal.
Then AD=BC and AB=CD
And ∠ABC=∠BCA=∠CDA=∠DAB=90⁰
In ΔABC and ΔADC
∠ABC=∠ADC (Angle of rectangle)
AB=DC (Opposite side of rectangle)
AC=AC (Common side)
∴ΔABC≅ΔADC
∴∠ACD=∠ACB
∵∠ACD+∠ACB=90⁰ ..........[Angle ACB is the angle of rectangle]
∴2∠ACD=90⁰
⇒∠ACD=45⁰
⇒θ = 45⁰
similarly, α = 45⁰
Pythagoras theorem:
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle.
This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
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Suppose the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection. Age Group Youths Young Adults Adults Seniors
Sample Size 102 258 319 31
x :2.00 3.10 3.06 2.81
s :1.59 1.66 1.69 1.87
For purposes of this exercise, assume that it is reasonable to regard the four samples as representative of the U.S. population in the corresponding age groups and that the distributions of social marginality scores for these four groups are approximately normal with the same standard deviation. Is there evidence that the mean social marginality scores are not the same for all four age groups? Test the relevant hypotheses using α = 0.01.
Calculate the test statistic. (Round your answer to two decimal places.) F = ?
What can be said about the P-value for this test?
P-value > 0.100
0.050 < P-value < 0.100
0.010 < P-value < 0.050
0.001 < P-value < 0.010
P-value < 0.001
What can you conclude?
Reject H0. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups.
Reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
Fail to reject H0. There is convincing evidence that the mean social marginality scores are not the same for all four age groups.
Fail to reject H0. There is not convincing evidence that the mean social marginality scores are not the same for all four age groups.
You may need to use the appropriate table in Appendix A to answer this question.
As per the given standard deviation, the Lana hypothesis is not equal to 25 point and the alternative hypothesis is greater.
The term standard deviation refers the measure of how dispersed the data is in relation to the mean.
Here we have given that the accompanying summary statistics for a measure of social marginality for samples of youths, young adults, adults, and seniors appeared in a research paper. The social marginality score measured actual and perceived social rejection, with higher scores indicating greater social rejection.
And we need to find if the mean social marginality scores are not the same for all four age groups
While we looking into the given the alternate hypothesis for this problem is μ greater than 115 point.
And here we have to find the test statistics which are equal to x, power, minus μ, divided by 10 point.
And the bar is 125 points in the x bar and 25.2 points in the me.
Then it can be written as,
=> x² = 125.2
Where as 1.5 and sigma equal to 30 and then equal to 25.
Now, we have to do the Minus 115 and then divided into 30 by root 5 and 25 by root.
Then we will get it as 1.70
Now we have to simplify it.
Which is, is that greater than 1.70, which is equal to 1 minus p p, is less than 1.70, which is equal to 1 minus 0.9554, which is equal to 0.0446.
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round 19.83 to the nearest tenth
Answer:
19.8
Step-by-step explanation:
19.83 rounded to the nearest tenth is 19.8.
The Smiths both work and their total household income is £36,000 per annum.
Their annual bills work out at £16,000 per annum.
What percentage of their annual income goes on bills to 2 decimal places?
%
Answer:
44.44 %
Step-by-step explanation:
16 000 / 36 000 = .4444 = 44.44%
21. Which statement is a good definition?
Right angles are angles formed by two intersecting lines.
Skew lines are lines that do not intersect.
A
square is a rectangle with four congruent sides.
Parallel lines are lines that do not intersect.
The statement that is a good definition is D. Parallel lines are lines that do not intersect.
How to illustrate the information?A type of quadrilateral with all sides being equal and all angles being 90 degrees is a square.
Lines that do not cross each other but have a constant perpendicular distance are known as parallel lines. Right angles and skew lines are perpendicular to one another but not parallel. Therefore, a square is a type of rectangle in which all four sides are parallel to one another.
Therefore, based on the information, the correct option is D
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Find the next permutation in lexicographic order About For each permutation of (1,2,3,4,5,6,7,give the next largest permutation or indicate that the permutation is the last one in lexicographic order (1,2,3,4,5,6,7) (7.6,5,4,3,2, 1) (1.7,6,4,2,3,5) (3,7,6,5,4,2,1) (5,4,7,6,3,2, 1)
On solving the provided question, we can say that In lexicographic order, the following variation will be (5,6,7,4,3,2,1).
What is a permutation?It is known as permuting the set in mathematics to rearrange the components of a set that is already ordered or, if the set is not already ordered, to place its members in a linear or sequential order. In this sense, "permutation" refers to the process of changing the linear order of an ordered set.It should be mentioned that a permutation is a mathematical concept that describes several potential arrangements of numbers or other objects.
The ascending numerical order is the lexicographic order when it comes to numbers. From left to right, the numbers are growing. The permutations of "1,2,3," for instance, are 123, 132, 213, 231, 312, and 321 in lexicographic order.
In lexicographic order, the following variation will be (5,6,7,4,3,2,1).
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In the xy-coordinate plane, the points (4, 2) and (-1, k) are on a line that is perpendicular to the line y=2x+1 . What is the value of k
A line of two points (4, 2) and (-1, k) is perpendicular to the line y=2x+1, then k = 9/2.
Given a line with equation y = mx + c, the slope is denoted by m.
Given 2 points with slopes m₁ and m₂, those two lines are perpendicular if:
m₁ x m₂ = -1
The given line equation is: y = 2x+1
Hence,
m₁ = 2
Compute the slope from 2 points: (4, 2) and (-1, k)
m₂ = (k - 2) / (-1 - 4)
m₂ = (-1/5) (k - 2)
Use the condition for perpendicular lines:
m₁ x m₂ = -1
2 x (-1/5) (k - 2) = -1
2k - 4 = 5
2k = 9
k = 9/2
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solve the following trigonomic equation for 0 < theta < 2pi
cos(theta) * csc(theta) - 2cos(theta) = 0
pls help
Answer:
To solve the given trigonometric equation, we can start by isolating the cos(theta) term on one side of the equation. We can do this by dividing both sides of the equation by csc(theta):cos(theta) * csc(theta) - 2cos(theta) = 0
cos(theta) * csc(theta) / csc(theta) - 2cos(theta) / csc(theta) = 0 / csc(theta)
cos(theta) - 2cos(theta) / csc(theta) = 0Next, we can combine like terms on the left side of the equation:cos(theta) - 2cos(theta) / csc(theta) = 0
-2cos(theta) / csc(theta) + cos(theta) = 0
(1 - 2 / csc(theta)) cos(theta) = 0Since cos(theta) cannot be equal to 0 (because the angle theta is between 0 and 2pi), the only solution to this equation is:1 - 2 / csc(theta) = 0
1 = 2 / csc(theta)
csc(theta) = 2This means that the value of csc(theta) is equal to 2. To find the value of theta, we can use the inverse cosecant function (arcsec) to solve for theta:theta = arcsec(2)The value of arcsec(2) is approximately 1.047198, which is the solution to the given equation for theta.Note that this is just one solution to the equation, as there may be other solutions for theta depending on the values of the trigonometric functions. It is important to check that the solution falls within the given range of 0 < theta < 2pi.
A chocolate chip cookie recipe calls for 2 3/4 cups of flour. You only have a 1/4-cup measuring cup and a 3/4-cup measuring cup that you can use.
a. What are different combinations of the measuring cups that you can use to get a total of 2 3/4 cups of flour?
b. Write each of the combinations as an addition equation.
The different combinations of the measuring cups that you can use to get a total of 2 3/4 cups of flour include 11 cups of 1/4 or 3.67 cups of 3/4.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the chocolate chip cookie recipe calls for 2 3/4 cups of flour. You only have a 1/4-cup measuring cup and a 3/4-cup measuring cup that you can use.
The combination will be:.
= 2 3/4 ÷ 1/4.
= 11
The second combination will be:
= 2 3/4 ÷ 3/4
= 3.67
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Determine the component representation and magnitude of the vector having the initial point P and the terminal point Q.
P(-3,2) and Q(5,17)
The component representation of the vector having the initial point P and the terminal point Q is....
The magnitude of the vector having the initial point P and the terminal point Q is ....
The magnitude of the vector having the initial point P and the terminal point Q is 17.
What is magnitude ?
Simply said, "distance or amount" is the definition of size. In terms of motion, it shows the absolute or relative size, direction, or movement of an item. It is used to describe something's size or scope. Magnitude in physics often refers to a size or amount.
Given: p (- 3,2) , q (5,17)
vector = (17-2)i + (5+3)j
= 15i + 8j
Magnitude = [tex]\sqrt{(15^{2}+8^{2} ) }[/tex]
magnitude =17
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If t less than s and s less than r what is the relationship between the values t and r?
If t is less than s and s is less than r then the relationship between the values t and r is - t is less than r.
We are given that-
t is less than s i.e. t < s
and
s is less than r i.e. s < r
Now, let us find the relationship between the values of t and r.
t < s and s < r
this implies that - t < s < r
Hence, we get t < r.
Thus, we get that if t is less than s and s is less than r then the relationship between the values t and r is - t is less than r i.e. t < r.
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The elephants at the Norfolk Zoo are fed 1/2 of a barrel of corn each day. The buffalo are fed 7/10 as much corn as the elephants. How many barrels of corn are the buffalo fed each day?
Addition
Subtraction
Multiplication
Division
If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.
How to solve word problems?
Recognize the issue, including all the terminology used to describe it. Recognize what we need to look for, Recognize the issue's context.
Convert the issue into an equation. Give the unknown a variable (or variables) to symbolize, Indicate exactly what the variable stands for.
Put the strategy into action and find a solution.
Given:
Elephants at the Norfolk zoo are fed = 1/2 of the barrel
Buffalo are fed 7/10 as much corn as the elephants = 7/10 * Elephants fed
= 7/10 * 1/2
= 7/20
Therefore, If buffalo are fed 7/10 as much corn as the elephants, then they are fed with 7/20 barrels of corn each day.
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PLEASE HELP IMMEDIATELY
Find the volume of a cylinder with a diameter of 16 inches and a height of 9 inches
What’s the volume of a NBA Basketball that has a diameter of 9.5 inches
The volume of the given cylinder is V = 1809.56 in³ and the volume of the NBA basketball is V = 448.92 in³.
What are the formulas for finding the volume of a cylinder and a sphere?The formula for the volume of a cylinder is V = π × r² × h cubic units.
Where the radius of the cylinder is represented by 'r' and the height of the cylinder is represented by 'h'.
The formula for the volume of the sphere is V = 4/3 × π × r³ cubic units.
Where the radius of the sphere is represented by 'r'.
Calculation:The given cylinder has a diameter is of 16 inches and a height of 9 inches.
I.e., d = 2r = 16 in and h = 9 in
Then the volume of the cylinder is
V = π × (d/2)² × h
= π × (16/2)² × 9
= π × 64 × 9
= 1809.56 in³
The shape of the NBA basketball is a sphere. The given sphere has a diameter of 9.5 inches.
I.e., d = 2r = 9.5 in
Then the volume of the sphere is
V = 4/3 × π × (d/2)³
= 4/3 × π × (9.5/2)³
= 4/3 × π × (4.75)³
= 4/3 × π × 107.172
= 448.92 in³
Therefore, the volume of the cylinder and the basketball are 1809.56 in³ and 448.92 in³ respectively.
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what is the answer to the question below
The equation of the area is 308 = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2) + 6 * (5 * 5) - 2 * (5 * 5)
How to determine the equation?From the question, we have the following parameters that can be used in our computation:
Area = 308
The formula used to calculate area
Area = S.A of the bottom + S.A of the top - 2 * Overlap
Using the given figure, we have
S.A of the top = 6 * (5 * 5)
S.A of the bottom = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2)
Overlap = 2 * (5 * 5)
So, we have
308 = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2) + 6 * (5 * 5) - 2 * (5 * 5)
Hence, the equation is (b)
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need help with this question cant figure it out
Let be independent random variables with the common distribution function F and suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N (b) Find P(M1} (d) Use (b) and (c) to rederive the probability you found in (a).
suppose they are independent of a geometric random variable with parameter p. Let M = max(x1,....,xN) (a) Find P{M<} by conditioning on N is nλe^(-nλx)
Given fx (x) = λe^λx
Fx (x) = 1 – e^-λx x…0
To find distribution of Min (X1,….Xn)
By applying the equation
fx1 (x) = [n! / (n – j)! (j – 1)!][F(x)]^j-1[1-F(x)]^n-j f(x)
For minimum j = 1
[Min (X1,…Xn)] = [n!/(n-1)!0!][F(x)]^0[1-(1-e^-λx)]^n-1λe^-λx
= ne^[(n-1) λx] λe^(λx)
= nλe^(-λx[1+n-1])
= nλe^(-nλx)
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BigPhone Company charges a connection fee of $200 and $0.15 per minute. LittlePhone Company charges a connection fee of $175 and $0.18 per minute.
Which phone plan would be cheapest if you spend 310 minutes on the phone?
Group of answer choices
LittlePhone Company is cheaper
Both companies will charge the same amount
BigPhone Company is cheaper
There is not enough information
The amount of Little phone company is $230.8 and of Big phone company is $246.5. Little Phone Company is cheaper. The correct option is B.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Big phone Company charges a connection fee of $200 and $0.15 per minute. Little phone Company charges a connection fee of $175 and $0.18 per minute.
The cost for both companies for time 310 minutes will be calculated as,
Cbc= 0.15t + 200
Cbc = ( 0.15 x 310) + 200
Cbc = $246.5
The cost of little company,
Clc = 0.18t + 175
Clc = ( 0.18 x 310 ) + 175
Clp = $230.8
From the above costs, it is observed that the Little Phone Company is cheaper.
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What is the range of the data set?
{6.2,9.1,2.9,1.6,9.3,5.5,8.3}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2
The range of the data set { 6.2 , 9.1 , 2.9 , 1.6 ,9.3 , 5.5 , 8.3 } is 7.7 .
Given :
the range of the data set {6.2,9.1,2.9,1.6,9.3,5.5,8.3}
Enter your answer as a decimal, rounded to the nearest tenth .
Range :
In statistics, the range is the spread of your data from the lowest to the highest value in the distribution.
Range = highest value - lowest value
Arrange in ascending order = { 1.6 , 2.9 , 5.5 , 6.2 , 8.3 , 9.1 , 9.3 }
Here highest value = 9.3
Lowest value = 1.6
Range = 9.3 - 1.6
= 7.7
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Suppose that the probability that the dart hit the area between the square of side length 14 and the square of side length 16
The probability of the area hit by the dart between the bigger square and the smaller square is equal to 0.7656.
As given in the question,
Total number of squares present = 2
Side length of the bigger square = 16 units
Side length of the smaller square = 14 units
Area of the bigger square = ( side length )²
= ( 16 )²
= 256 square units
Area of the smaller square = ( side length )²
= ( 14 )²
= 196 square units
Here favorable outcome is represented by small square and total outcome is represented by bigger square
Probability that the given dart hit the area between the square is
= 196 / 256
= 49/64
= 0.765625
≈ 0.7656
Therefore, the probability of the dart hitting the area formed by bigger square and smaller square is equal to 0.7656.
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A container that weighs 23 2/5pounds
holds sports equipment. Of the
equipment in the container, of the
1
3
weight is baseball equipment. What is the
weight of the baseball equipment?
The weight of the baseball equipment in the container is 7(4/5) pounds.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Container weight = 23(2/5) pounds
Baseball equipment.
= 1/3 of 23(2/5) pounds
= 1/3 x 117/5
= 39/5
= 7(4/5) pounds
= 7.8 pounds
Thus,
The weight of the baseball is 7.8 pounds.
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please help me please #1
Answer:
14.7
Step-by-step explanation:
You want the side opposite the 60° angle in a right triangle with hypotenuse 17.
SineThe sine relation is ...
Sin = Opposite/Hypotenuse
Solving for the opposite side gives ...
Opposite = Hypotenuse × Sin
x = 17·sin(60°) ≈ 14.7
The missing side is about 14.7.
a census is a statistical study in which an entire population is counted, not just a sample. which of the following stats is most likely to be based on a census?
true census is most likely to be based on a census There are many benefits to choosing a portion of the population selected to represent the population.
• Reducing the cost and time needed to conduct research. Researchers will save more time and money analyzing sample than the whole population.
• Reducing resource deployment. The manpower needed to analyze a sample is less than the manpower needed to analyze the whole population.
• Increasing data accuracy. Data taken from the sample will be more accurate than data taken from the whole population because the sample is more willing to join the research.
• Creating an intensive and exhaustive data. The data taken from a sample will be more intensive and exhaustive because the respondents are minimum.
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write the equation of the parabola in vertex form that has the following information: vertex: (2, -8) directrix: x
The Equation of parabola ( y + 8 )² = 12( x - 2 )
In math, what is a parabola?
A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line.
All of the parabola-related ideas are discussed here because it is a crucial component of the conic section topic.
Given,
Directrix is known as x=a Directrix=a=3 Equation of parabola
(Y-y1)²= 4a(X-x1)
Vertex (X1,Y1) = (2,-8)
Directrix=a=3
Equation of parabola
( y - y₁ )² = 4a( x - x₁)
( y - ( -8))² = 4 * 3(x - 2 )
( y + 8 )² = 12( x - 2 )
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Suppose that the functions u and w are defined as follows.
u(x)=x² + 3
w (x)=√x+2
Find the following.
(wu) (2) =
(uw) (2) =
The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
What is composite function?
Function composition is an operation о used in mathematics that takes two functions, f and g, and creates a function, h = g о f, such that h(x) = g. The function g is applied in this operation to the outcome of applying the function f to x.
Given:
u(x) = x^2 + 3
w(x) = √x+2
We have to find (w о u)(2) and (u о w)(2).
First to find (w о u)(x)
(w о u) = w(u(x))
= w(x^2 + 3)
(w о u) = √(x^2 + 3) + 2
⇒ (w о u)(2) = √(2^2 + 3) + 2
(w о u)(2) = √7 + 2
Now to find (u о w).
(u о w)(x) = u(w(x))
= u(√x+2)
= (√x+2)^2 + 3
= x + 4√x + 4 + 3
(u о w)(x) = x + 4√x + 7
⇒ (u о w)(2) = 2 + 4√2 + 7
(u о w)(2) = 9 + 4√2
Hence,
The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
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Which is the simplified form of the expression three 7/5 X +4-232 -5/4 X
The simplified form of the expression is 123/20 x - 228
How to determine the simplified form of the expression?From the question, we have the following parameters that can be used in our computation:
three 7/5 X +4-232 -5/4 X
Rewrite the above expression properly
So, we have the following representation
37/5 x + 4 - 232 - 5/4 x
Collect the like terms in the above expression
So, we have the following representation
37/5 x - 5/4 x + 4 - 232
Evaluate the like terms in the above expression
So, we have the following representation
123/20 x + 4 - 232
Solving further, we have
123/20 x - 228
Hence, the solution is 123/20 x - 228
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Four-Sided Dice A pair of four-sided dice-each with the numbers from 1 to 4 on their sides- -are rolled, and the num bers facing down are observed. (Note: A four-sided die is sim- ilar to a pyramid with a triangular base.) (a) List the sample space. (b) Describe each of the following events as a subset of the sample space i) Both numbers are even. (ii) At least one number is odd. iii Neither number is less than or equal to 2. (iv) The sum of the numbers is 7. (v) The sum of the numbers is greater than or equal to 6. (vi) The numbers are the same. (vii) A 2 or 3 occurs, but not both 2 and 3. (viii) No 4 appears.
Previous question
Answer:
Step-by-step explanation:
(a)
The sample space is
{(1,1), (2,2), (3,3), (4,4), (1,2), (1.3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2) (3,4), (4,1),(4,2), (4.3)}
(b)
i {(2,2), (4,4), (2,4), 4,2)}
ii {(1,1), (1,2), (3,3), (1,3), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4), (4,1), (4,3)}}
iii {(1,1)}
iv {3,4), (4,3)}
v {(3,3), (2,4), (4,2), (3,4), (4, 3), (4,4)}
vi {(1,1), (2,2), (3,3), (4,4)}
vii {(1,2), (1,3), (2,1), (3,1), (2,2), (2,4), (3,3), (3,4), (4,2), (4,3)}
viii {(1,1), (2,2), (3,3), (1,2), (1.3), (2,1), (2,3), (3,1), (3,2)}