The sum of two draws from a box containing 11 tickets labeled 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 is equivalent to the sum of two dice rolls, as the outcomes are not equally likely
What are dice rolls?
Dice rolls are a random event used in various games and activities. A dice typically has six sides, each side marked with a different number of , ranging from 1 to 6. To roll a dice, the player tosses it in the air, causing it to spin and land on a random side.
Dice rolls are often used in games of chance, such in role-playing games, where they are used to determine the outcome of actions or events. They are also used in probability theory, where the probability of a certain outcome can be calculated based on the number of sides on the dice and the number of times it is rolled.
The sum of two dice that are independently rolled and the sum of two draws from a box containing six tickets labeled 1, 2, 3, 4, 5, 6 are indeed equivalent. This is because there are 36 possible outcomes when rolling two dice, and each outcome is equally likely. The sum of the two dice can range from 2 (when both dice show a 1) to 12 (when both dice show a 6).
Similarly, when drawing two tickets from a box containing six tickets labeled 1, 2, 3, 4, 5, 6, there are 36 possible outcomes, with each outcome being equally likely. The sum of the two draws can range from 2 (when both draws yield a 1) to 12 (when both draws yield a 6).
However, if we use a box containing 11 tickets labeled 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, the outcomes will not be equally likely, and the sum of the two draws will not be the same as the sum of two dice rolls. For example, there is only one way to get a sum of 2 with two dice (rolling two 1s), but there are two ways to get a sum of 2 when drawing from the box (drawing a 1 and a 1 or drawing a 2 and a 0).
Therefore, we cannot say that the sum of two draws from a box containing 11 tickets labeled 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 is equivalent to the sum of two dice rolls, as the outcomes are not equally likely.
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The point-slope form ofthe equation of the line that passes through ( 4, -3) and (12, 1) is y - 1 = 4(x - 12). What
the standard form of the equation for this line?
O x- 4y = 8
О x-4y = 2
О 4x-y=8
• 4x-y = 2
Answer:
4x - y = 2,
Step-by-step explanation:
The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, we are given that the line passes through the points (4, -3) and (12, 1). The slope of the line is then m = (1 - (-3)) / (12 - 4) = 1/4.
Substituting the slope and the point (4, -3) into the point-slope form of the equation, we get y - (-3) = 1/4(x - 4). Simplifying, we get y + 3 = 1/4x - 1.
To convert the equation to standard form, we multiply both sides of the equation by 4. This gives 4y + 12 = x - 4. Simplifying, we get 4x - y = 8.
Therefore, the standard form of the equation of the line is 4x - y = 8.
how to find the scale factor of 10 cm=5m
The scale factor of 10cm to 5m is 50.
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures.
For example ,if a length of 5cm is doubled and it gives a length 10cm, the scale factor is 10/5 = 2. This means that we can express scale factor with a formula;
scale factor = new dimension / old dimension
Here, the old dimension is 10cm and the new dimension is 5m. We need to convert the 5m into cm
therefore 5m = 5× 100 = 500cm
therefore scale factor = 500/10 = 50
This means the scale factor of 10cm = 5m is 50
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Find B in degrees. 4 B 3 round to the nearest hundredth
Step-by-step explanation:
For right triangles tan B = opposite leg / adjacent leg
tan B = 3/4
arctan (3/4) = B = 36.87 degrees
A surveyor interviews a random sample of 85,349 adults in Florida and finds that 72% state that they have visited a doctor within the past year. Records from the state board of health indicate that of the 21 million Florida residents, 12 million visit a doctor annually. Identify the population, parameter, sample, and statistic. Population: 57%; parameter: 21 million; sample: 72%; statistic: 85,249
Population: 21 million; parameter: 57%; sample: 85,249; statistic: 72%
Population: 21 million; parameter: 72%; sample: 85,249; statistic: 57%
Population: 85,249; parameter: 72%; sample: 21 million; statistic: 57%
Answer:
Population: 21 million; parameter: 57%; sample: 85,349; statistic: 72%.
Explanation:
The population is the entire group being studied, which in this case is all the residents of Florida, with a total population of 21 million.
The parameter is a numerical summary of the population, which in this case is the proportion of residents who visit a doctor annually and is stated as 57% in the problem.
The sample is a subset of the population that is selected for study, which in this case is the 85,349 adults surveyed by the surveyor.
The statistic is a numerical summary of the sample, which in this case is the proportion of adults in the sample who stated that they have visited a doctor within the past year and is stated as 72% in the problem.
PLS HELP SOLVE W STEPS!!!! THANK YOU
Answer:
see what you got to do is you have to find n
Algebraic expression for a number divided by 12
Answer:
hope this helps
Step-by-step explanation:
Let "x" be the number.
The algebraic expression for "a number divided by 12" can be written as:
x/12
Here, "x" is being divided by 12, which means that we are finding the quotient of "x" when it is divided by 12.
Answer:
The answer is *some variable* upon 12 or *some variable* ÷ 12
Examples:
x÷12 or x upon 12
y÷12 or y upon 12
m÷12 or m upon 12
Step-by-step explanation:
You must apply a variable, such as "x,y,m,... etc" to "some number." Your expression then changes to the examples I have given above.
Hope this helped you :)
1.12x - 2.24y= 4.96 -3.56- 2.48y= -7.32
What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
[tex]2((1 \frac{1}{3} )(1 \frac{1}{2} ) + (1 \frac{1}{2} )(5) + (1 \frac{1}{3}) (5))[/tex]
[tex]2(( \frac{4}{3} )( \frac{3}{2} ) + ( \frac{3}{2} )(5) + ( \frac{4}{3} )(5))[/tex]
[tex]2(2 + \frac{15}{2} + \frac{20}{3} )[/tex]
[tex]2( \frac{12 + 45 + 40}{6} )[/tex]
[tex] \frac{97}{3} = 32 \frac{1}{3} [/tex]
The surface area of this rectangular prism is 32 1/3 square feet.
AD BE
DC EC
Given:
Prove: AB || DE
A
MN
2
E
3 C
B
Complete the steps of the proof.
1.
2
3.
4.
DC
Statements
BE
EC
+1= 8+1
-DC =BE+EC
BE+EC
EC
=
AD + DC
DC
5. AC=AD+DC;
BC=BE+EC
6. ACB
EC
7.23 23
8. AABC-ADEC
9.21 22
1. given
2. addition property
3. property of proportion
4. addition of fractions
5. segment addition
postulate
Reasons
6. substitution property
7. reflexive property
8.
9.+
The two statements that completes the above proof are:
ΔABC ~ ΔDEC - Side - Angle - Side Postulate
∠1≅∠2 - Corresponding angles.
What is the Side - Angle - Side postulate?The Side-Angle-Side (SAS) postulate states that if two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent.
Corresponding angles are equal because of the congruence of the triangles. Two angles are corresponding if they occupy the same relative position in two distinct intersecting lines, such that they are on the same side of the transversal and are in the same position in relation to the intersection. Corresponding angles are equal if the two intersecting lines are parallel.
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true or false the decimalformat class is part of the java api so it is automatically available to your programs.
The statement is true. The DecimalFormat class is part of the Java API, specifically within java.text package, so it is automatically available to your programs. You can use it to format numbers in various ways, such as for displaying currency or percentages.
DecimalFormat is a concrete subclass of NumberFormat that formats decimal numbers. It has a variety of features designed to make it possible to parse and format numbers in any locale, including support for Western, Arabic, and Indic digits. It also supports different kinds of numbers, including integers (123), fixed-point numbers (123.4), scientific notation (1.23E4), percentages (12%), and currency amounts ($123). All of these can be localized.
To obtain a NumberFormat for a specific locale, including the default locale, call one of NumberFormat's factory methods, such as getInstance(). In general, do not call the DecimalFormat constructors directly, since the NumberFormat factory methods may return subclasses other than DecimalFormat. If you need to customize the format object, do something like this:
NumberFormat f = NumberFormat.getInstance(loc);
if (f instanceof DecimalFormat) {
((DecimalFormat) f).setDecimalSeparatorAlwaysShown(true);
}
A DecimalFormat comprises a pattern and a set of symbols. The pattern may be set directly using applyPattern(), or indirectly using the API methods. The symbols are stored in a DecimalFormatSymbols object. When using the NumberFormat factory methods, the pattern and symbols are read from localized ResourceBundles
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True. The Decimal Format class is a part of the Java API and is included in the java.text package.
It is automatically available to Java programs without the need for any additional installations or imports.
The Decimal Format class is part of the Java API, and it is automatically available to your programs.
The Java API is a collection of pre-written classes, methods, and interfaces that are part of the Java Development Kit (JDK).
These classes and methods provide a wide range of functionalities that can be utilized by Java developers to build robust applications.
The Decimal Format class, specifically, is a subclass of the Number Format class and is used to format decimal numbers according to a specific pattern.
The class provides methods to format and parse decimal numbers and can be used to specify the number of digits after the decimal point, the use of a thousand separator, and the currency symbol.
The Decimal Format class in your Java program, you simply need to import the class using the import statement, and then create an instance of the class.
For example:
import java. text. Decimal Format.
public class MyClass
{
public static void main (String [] args) {
Decimal Format df = new Decimal Format("#.00");
double num = 1234.5678
System.out.println(df.format(num));
}
}
The Decimal Format class using the import statement, and then create an instance of the class called df.
We then use the format method of the class to format the decimal number 1234.5678 with two decimal places.
The Decimal Format class is an essential part of the Java API and is automatically available to your programs.
Its inclusion in the Java API makes it easier for Java developers to format decimal numbers in their applications.
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In trapezoid ABCD, O is the point of intersection from the diagonals. The area of AOD is 15 ft^2. The altitudes from B and O to the longer base are in a 5:3 ratio. Find the area of ABD and the area of MOC if M is the midpoint of the leg CG
If M is the midpoint of the leg CG, then the
a) Area of ABD = 18.75 ft^2
b) Area of MOC = 15 ft^2
To solve this problem, we need to use the properties of trapezoids and their diagonals. Let's start with finding the area of ABD.
First, notice that ABD and COD are similar triangles because they share angle O. Thus, we can write
AB/CD = AD/CO
Since AD = BC (opposite sides of a trapezoid are parallel), we can simplify to:
AB/CD = BC/CO
We also know that the area of AOD is 15 ft^2
Area of ABD/ Area of COD = AB/CD
We can substitute the ratio AB/CD from the similarity relation above to get
Area of ABD/ Area of COD = BC/CO
Since the bases of the trapezoids are parallel
Area of ABD/ Area of COD = BD/CO
Finally, we can use the fact that the altitudes from B and O to the longer base are in a 5:3 ratio to write
Area of ABD/ Area of COD = 5/3
Area of ABD = 5/8 × Area of COD
We know that the area of AOD is 15 ft^2, so the area of COD is twice that, or 30 ft^2. Therefore
Area of ABD = 5/8 × 30 = 18.75 ft^2
Next, we need to find the area of MOC. To do this, we can use the fact that the diagonals of a trapezoid divide it into four triangles, and the areas of these triangles are proportional to the lengths of the diagonals.
Let x be the length of OC, and let y be the length of OG. Then we have
Area of MOC/ Area of MOG = x/y
Also, since M is the midpoint of CG, we have
x = 2y
Substituting this into the first equation, we get
Area of MOC/ Area of MOG = 2
We know that the area of MOG is half the area of AOD, so
Area of MOG = 15/2 ft^2
Therefore, we have
Area of MOC = 2 × Area of MOG = 15 ft^2
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(Repost because urgency)
Not sure how to go about tackling this question?
Should I try to get [tex]y=\frac{x(k+1)}{k-1}[/tex] into the form of the ratio by rationalizing first then simplify?
Answer:
y = [tex]\frac{x(k+1)}{k-1}[/tex]
Step-by-step explanation:
First, recall that in a proportion (a set of equivalent ratios), the product of means is equal to the product of extremes. For example,
if [tex]\frac{a}{b} = \frac{c}{d}[/tex] (or a:b = c:d) the product of means (b and c) is equal to the product of extremes (a and d), and we have ad = cb.
Using this knowledge, in the proportion (y+x):(y-x) = k:1, let us find the product of means and extremes and set them equal, like so:
(y+x):(y-x) = k:1 =
k(y-x) = y+x =
ky - kx = y+x
To solve for y, move all terms including y to one side, like so:
ky - kx = y+x =
ky - y = kx + x
Now, factor out y.
ky - y = kx + x =
y(k - 1) = kx + x
Then, factor out the common term x.
y(k - 1) = kx + x =
y(k - 1) = k(x + 1)
Now, finish isolating the variable by dividing by (k-1), and we have:
y = [tex]\frac{x(k+1)}{(k-1)}[/tex]
The diameter of a circle is 3.6 m. Find the radius, circumference and area. Show your working.
Step-by-step explanation:
Given :
d = 3.6m
r = d/2
r = 3.6/2
r = 1.8 m
We know that,
C = 2πr
C = 2 * 22/7 * 1.8
C = 11.3 m
Now,
A = π r²
A = 22/7 × (1.8)²
A = 22/7 × 3.24
A = 10.1 m²
Answer:
The Radius is 1.8, The circumference is 11.3 ,The area is 10.2
Step-by-step explanation:
The radius of a circle from diameter: if you know the diameter d , the radius is r = d / 2 .
To calculate the circumference, you need the radius of the circle: Multiply the radius by 2 to get the diameter. Multiply the result by π, or 3.14 for an estimation.That's it; you found the circumference of the circle.Or you can use the circle's diameter:Multiply the diameter by π, or 3.14.The result is the circle's circumference.
Diameter of circle= 3.6cm So, radius of circle=3.6/2Radius of circle = 1.8 Now ,Area of circle =πr². [r=radius] so 3.14 times 1.8 times 1.8 and you get 10.17 then round it to the nearest tenth and it is 10.2
Please help me!
see attached item for more info
Answer:
csc θ + cot θ
Step-by-step explanation:
(z + y)/x = z/x + y/x
sin θ = x/z
csc θ = 1/sin θ
csc θ = z/x
tan θ = x/y
cot θ = 1/tan θ
cot θ = y/x
z/x + y/x = csc θ + cot θ
HELP PLS WILL GIVE BRAINLIST DUE TODAY AND SOON
Part A: Given the function g(x) = |x + 3|, describe the graph of the function, including the vertex, domain, and range. (5 points)
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| − 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Answer:
A: description: graph of f(x) shifted left 3 units. Domain: (-∞, ∞); range: [0, ∞); vertex: (-3, 0).
B: description: graph of f(x) shifted down 2 units. Range: [-2, ∞); vertex: (0, -2).
Step-by-step explanation:
Given parent function f(x) = |x|, you want descriptions of g(x) = |x+3| and h(x) = |x| -2, including the vertex, domain, and range.
TransformationsThis question is concerned with translations of functions. The translations of interest are ...
f(x -h) — shifts the graph right h unitsf(x) +k — shifts the graph up k unitsAbsolute valueThe function f(x) = |x| is defined for all values of x. Its domain is all real numbers: (-∞, ∞). Shifting the function left or right does not affect the domain.
The vertex of the function is at (0, 0), and is a minimum. That means the range of the function is all non-negative numbers: [0, ∞). Shifting the function up or down affects the range by the same amount.
G(x)The function g(x) = |x+3| is equivalent to g(x) = f(x+3). Comparing to the transformations above, we see h = -3. So the graph of f(x) will be shifted left 3 units to make the graph of g(x).
vertex: (-3, 0)domain: (-∞, ∞)range: [0, ∞)H(x)The function h(x) = |x| -2 is equivalent to h(x) = f(x) -2. Comparing to the transformations above, we see k = -2. So the graph of f(x) wil be shifted down 2 units to make the graph of h(x).
vertex: (0, -2)range: [-2, ∞)Find the difference in the place value of the two seven in the number 872574
The difference in the place value of the two seven in the number 872574 is 69,930.
In the given value we have to find the place value of two 7. To find the place value of the two seven we need to find the occurrence of seven in the value.
In the given value of 8,72,574,
the first 7 occur at ten thousand place
Its place value = 7 × 10000 = 70000
The second 7 occurs at ten’s place
Its place value = 7 × 10 = 70
The difference between the two place values of 7
= 70000 - 70
= 69930
Therefore, the difference in the place value of two 7 is 69,930
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If you have the following data about bag of chocolate chips, about how many chocolate chips are estimated to be in the bag?
Mass of Chocolate Chips + Bag= 2041 grams
Mass of 100 Chocolate Chips= 31 grams
Mass of Bag ONLY= 67 grams
How many chocolate chips are in the bag? Round answer by using significant figures.
Answer:
6,368 chocolate
Step-by-step explanation:
First, we need to find the mass of chocolate chips in the bag:
Mass of Chocolate Chips=Mass of Chocolate Chips + Bag - Mass of Bag ONLY
Mass of Chocolate Chips = 2041 g - 67 g
Mass of Chocolate Chips = 1974 g
Next, we need to use the given information to estimate the number of chocolate chips in the bag:
31 grams of chocolate chips = 100 chips
1 gram of chocolate chips = 100/31 chips
Using this conversion factor, we can find the estimated number of chocolate chips in the bag:
1974 g of chocolate chips = (100/31) x 1974 chips
1974 g of chocolate chips ≈ 6,368 chips (rounded to four significant figures)
Therefore, it is estimated that there are about 6,368 chocolate chips in the bag.
consider these functions f(x)=3x^3+8x-2 k(x)=4x what is the value of k(f(x)
The value of function k(f(x)) is 12x³ + 32x - 8.
What is Function composition:Function composition is a way to combine two or more functions to form a new function. In this case, we are given two functions f(x) and k(x), and we need to find the value of k(f(x)), which means we need to apply the function k(x) to the output of the function f(x).
Here we have
Functions f(x)= 3x³ +8x -2 and k(x) = 4x
To find k(f(x)), we need to substitute the expression for f(x) into k(x) wherever we see x. So, we have:
k(f(x)) = 4(f(x)) = 4(3x³ + 8x - 2)
We can simplify this expression by distributing the 4:
k(f(x)) = 12x³ + 32x - 8
Therefore,
The value of function k(f(x)) is 12x³ + 32x - 8.
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A survey is taken at a movie theater in Wayside. The first 200 people who entered the theater were asked about their favorite type of movie. What is true about this situation?
The population is the first 200 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Wayside.
The population is the total number of people who go to the movie theater, and the sample is the first 200 people at the theater.
The population is the number of people in the town of Wayside, and the sample is the number of people who go to the movie theater.
A survey is taken at a movie theater in Wayside. The first 200 people who entered the theater were asked about their favorite type of movie. The true about this situation is: The population is the total number of people who go to the movie theater, and the sample is the first 200 people at the theater.
In this situation, the population refers to the entire group of people who go to the movie theater in Wayside. The population includes all individuals who have the potential to be surveyed about their favorite type of movie.
The sample, on the other hand, is a subset of the population and represents the first 200 people who entered the theater. These 200 individuals are selected to provide information about the preferences of the larger population.
It is important to note that the sample is not the entire population but rather a smaller representative group. By surveying the sample, we aim to gather insights and make inferences about the preferences of the larger population of moviegoers in Wayside.
The correct answer is: The population is the total number of people who go to the movie theater, and the sample is the first 200 people at the theater.
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Algunos números irracionales no tienen inverso aditivo
The statement " Some irrational numbers do not have an additive inverse" is false because every real number, whether rational or irrational, has an additive inverse.
Every real number, whether rational or irrational, has an additive inverse. The additive inverse of a real number x is the number that, when added to x, gives zero as the result. For any real number x, its additive inverse is -x.
This is a fundamental property of the real numbers and is true regardless of whether a number is rational or irrational. Therefore, any irrational number, such as the square root of 2 or pi, also has an additive inverse. For example, the additive inverse of the irrational number √2 is -√2, since √2 + (-√2) = 0.
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What ordered pair is represented by the function g(4) = 22?
Ordered pair is represented by the function g(4) = 22 is (4,22)
Define ordered pairAn ordered pair is a pair of mathematical elements written in a specific order, typically represented by the notation (a, b). The first element in the pair is called the x-coordinate, while the second element is called the y-coordinate. The order of the elements is important, so (a, b) is not the same as (b, a) unless a = b.
Ordered pairs are commonly used in mathematics to represent points in the Cartesian plane, where the x-coordinate represents the horizontal distance from the origin and the y-coordinate represents the vertical distance from the origin. They can also be used to represent solutions to equations, inputs and outputs of functions, and many other mathematical concepts.
Given Function
g(4)=22
For the value of x=4
The output of function is y=22
So, the ordered pair is (4,22).
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consider a dataset of towers in every state which is normally distributed. consider a sample of 40 towers. the sample data has a mean of 68 with a standard deviation of 15. how many degrees of freedom we use to find the t-critical statistic value?
39 degrees of freedom will be used to find the t-critical statistic value.
We need to find degrees of freedom for the t-critical statistic value with 40 sample towers and a normally distributed population. According to the given dataset we can assume that we have the 95% confidence interval which is taken as default if nothing is mentioned about it.
The degrees of freedom (df) for a t-distribution are calculated as given below:
df = n - 1
where n is the sample size of the problem.
In this case, the sample size is 40, so the degrees of freedom would be:
df = 40 - 1 = 39
Therefore, we would use 39 degrees of freedom to find the t-critical statistic value for a 95% confidence interval.
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The prism below is made of cubes which measure of a centimeter on one side.
Which of the following represents the volume of the prism?
There are multiple answers.
3/2 cubic cm
1/216 cubic cm x 24
4/3 cubic cm
1/18 cubic cm x 24
1/9 cubic cm
(4 x 1/6cm) + (2 x 1/6cm) + (3 x 1/6cm)
(4 x 1/6cm) X (2 x 1/6cm) X (3 x 1/6cm)
NO LINKS NO FILES
The prism has an 8/27 cubic centimetre volume.
What is the volume of a cube?The following formula determines a cube's volume:
V = s³
where V is the volume of the cube and s is the length of one of its sides.
In other words, to find the volume of a cube, you simply need to raise the length of one of its sides to the third power (cube it).
The volume of a cube = s³
Given that the prism is composed of cubes with a one-third-centimeter side measurement.
Volume of a cube = (1/3)³ = 1/27
There are 8 cubes in the prism.
Therefore, the volume of the prism is;
=8(1/27)
= 8/27 cubic centimeter.
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The complete question is:
The prism below is made of cubes which measure of a centimeter on one side. What is the volume?
Note: Figure is not drawn to scale.
The prism below is made of cubes which measure 1/3 of a centimeter on one side. What is the volume?
Image is attached below.
the mean age of 5 students whose ages are 8,x,13,12,and 10 is 10. calculate the value of x in years
Answer:
x = 7 years
Step-by-step explanation:
The mean (M) is defined as the average of the sum of all the data points in a set:
[tex]M=\frac{r_{1}...r_{n} }{n}[/tex]
Thus, since there are five data points and we're given the mean, we can use the following formula to find x:
[tex]M=10\\10=\frac{(8+x+13+12+10)}{5}\\ 50=43+x\\7=x[/tex]
The hour marks on a clock face are 30° apart. What is the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line?
Circle I and circle L are shown. Sector HIJ and sector KLM have the same area.
BLANK 1: Which formula should be used to solve this problem?
BLANK 2: What is the area of sector HIJ? Use 3.14 for pi.
BLANK 3: What is the measure of angle KLM?
1. Formula for the area of a sector of a circle, which is A = (θ/360)π[tex]r^2[/tex] 2. The area of sector HIJ is 2.51 square units. 3. The measure of angle KLM is approximately 0.29 degrees
What is circle?A circle is a geometric shape consisting of all the points in a plane that are a fixed distance (called the radius) away from a given point (called the center).
According to given information:BLANK 1: To solve this problem, we can use the formula for the area of a sector of a circle, which is A = (θ/360)π[tex]r^2[/tex], where θ is the central angle of the sector, r is the radius of the circle, and π is pi (approximately 3.14).
BLANK 2: To find the area of sector HIJ, we need to know the radius of circle I and the measure of angle HIJ. From the given information, we know that circle I has a radius of 8, and angle HIJ is 45 degrees. Therefore, the area of sector HIJ is:
A = (45/360) x 3.14 x [tex]8^2[/tex]
A = 3.14 x 8 x (45/360)
A = 3.14 x 8 x 0.125
A = 2.51 square units (rounded to two decimal places)
Therefore, the area of sector HIJ is 2.51 square units.
BLANK 3: We know that sector KLM has the same area as sector HIJ, and circle L has a radius of 10. Therefore, we can use the formula for the area of a sector of a circle again to find the measure of angle KLM. Let x be the measure of angle KLM in degrees. Then:
A = (x/360) x 3.14 x [tex]10^2[/tex] = 2.51
Simplifying this equation gives:
(x/360) = 2.51/(3.14 x [tex]10^2[/tex])
(x/360) = 0.0008
x = 360 x 0.0008
x = 0.288
Therefore, the measure of angle KLM is approximately 0.29 degrees (rounded to two decimal places).
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See image. If you can show work please do so otherwise thank u in advanced
From the figures, AB is a tangent to the C because they make a right angles (90⁰)
What is a tangent to a circle?Recall that in n Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.
We shall be determining the angle at C to see if it gives 90⁰
Using trigonometrical ratios of tangent
TanB = Opposite/Adjacent
Tan B. = 4.8/7.2
Tan B = 0.6667
B = Tan⁻¹0.6667
<B = 33.69⁰
Also in the same manner,
TanS = opp/Adj
Tan S = 7.2/4.8
Tan S = 1.5
S = Tan⁺¹1.5
< S = 56.31⁰
Npw <S + <B = 56.32 + 33.69 = 89.9999247 = 90⁰
Therefore AB makes tangent at C
20.
Tan C = Opp/Adj
Tan C = 15/11.2
Tan C = 1.3393
C = Tan⁺¹1.3393
< C = 53.25
Also, Tan B = 11.2/15
Tan B = 0.7467
B = 36.75
<B + <C = 36.75 + 53.25 = 89.9986 = 90⁰
Therefore AB makes a tangent at C
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Himpunan penyelesaian dari :
18 - 2x < 3.(2x - 1) - 3
adalah ….
Step-by-step explanation:
18-2x<3(2x-1)-3
21-2x<6x-3
24<8x
3<x
Interval notation
(3, ∞)
how many ways are there to seat n couples around a circular table so that no couple sits together? (note: rotated seatings are considered to be the same, but reflected seatings are considered to be different.)
Each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.
Let's consider the number of ways to seat n couples around a circular table without any restrictions first.
Since there are 2 people in each couple, there are a total of 2n people. The number of ways to seat 2n people around a circular table is (2n-1)!/2n,
where we divide by 2n to account for rotations of the same seating arrangement.
Now, let's consider the restriction that no couple can sit together.
We can start by fixing one person in a couple, and then there are (2n-2) ways to seat the other person in that couple so that they don't sit together.
After that, we can fix another person and their partner, and there are (2n-4) ways to seat the remaining two people in their couple so that they don't sit together.
We can continue this process until all couples are seated.
Therefore, the total number of ways to seat n couples around a circular table so that no couple sits together is:
[tex](2n-2)(2n-4)(2n-6)...2 = 2^{n-1} * (n-1)![/tex]
We multiply by[tex]2^{n-1}[/tex] to account for the fact that each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.
Note that reflected seatings are considered to be different, so we don't need to worry about dividing by 2 as we did in the unrestricted case.
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Consider continuous functions f, g, h, and k. Then complete the statements. Graph shows an upward parabola labeled f of x equals x squared minus 2x minus 6 with vertex at X-axis 1 and Y-axis minus 7. The parabola goes through (minus 2, 2) and (4, 2). Function h is two times the square of the difference of x and 1. Select the correct answer from each drop-down. The function that has the least minimum value is function . The function that has the greatest minimum value is function .
k(x) can have any minimum value, which means it can have the greatest minimum value among the given functions.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output.
According to given information:The given graph represents the function [tex]f(x) = x^2 - 2x - 6[/tex], which is an upward-opening parabola with vertex at (1, -7) and passes through the points (-2, 2) and (4, 2).
Function [tex]h(x) = 2(x - 1)^2[/tex] is a quadratic function that opens upwards and its vertex is at (1, 0). The minimum value of h(x) is 0, which is the value at the vertex. Therefore, h(x) has the least minimum value among the given functions.
Function k(x) can be any linear function or a constant function. If k(x) is a linear function, then its minimum value is either negative infinity or 0, depending on the slope of the function. If k(x) is a constant function, then its minimum value is the same as its constant value.
Therefore, k(x) can have any minimum value, which means it can have the greatest minimum value among the given functions.
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