Answer:
hence the value of w is 12
Step-by-step explanation:
[tex]area = 2 {w}^{2} - 16w \\ by \: the \: question \: if \: area \: is \: equal \: to \: 8w \\ 8w = 2w {}^{2} - 16w \\ 8w + 16w = 2 {w}^{2} \\ 24w = 2 w {}^{2} \\ w = 12[/tex]
A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The percentage of people who said they preferred Candidate A was 80%. The margin of error for the survey was 4%. Which of the following is not a reasonable value for the actual percentage of the population that prefers Candidate A? Group of answer choices 75.6% 82.4% 76.4% 83.3%
83.3% is outside the range and therefore not a reasonable value.
How to determine which value is not a reasonable value?
We need to take into account the margin of error in order to determine which value is not a reasonable one for the actual proportion of the population that favors Candidate A. The range within which the actual population value is likely to fall is shown by the margin of error.
We can determine the likely range of the true population value as follows if the sample contained 80% of those who preferred Candidate A and the margin of error was 4%:
The lower bound of the range is 80% - 4% = 76%
The upper bound of the range is 80% + 4% = 84%
Therefore, any value outside of this range is not a reasonable value for the actual percentage of the population that prefers Candidate A.
75.6% is within the range and therefore a reasonable value.
82.4% is within the range and therefore a reasonable value.
76.4% is within the range and therefore a reasonable value.
83.3% is outside the range and therefore not a reasonable value.
So the answer is 83.3%.
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Mehnaj has a set of blocks that are all the same hight the cone-shaped block has a volume of 125 cubic inches the sphere--shaaped block has a volume of 250 cubic inches what do you know about the raduis of the base of the cone-shaped block explain?
The radius of the base of the cone-shaped block is approximately 10.69 inches.
To solve this problemWe can use the formula for the volume of a cone to find the radius of its base. The volume of a cone is given by the formula :
V = (1/3)πr^2h
Where
V is the volume r is the radius of the baseh is the heightWe know that the volume of the cone-shaped block is 125 cubic inches, and we know the height is the same for all blocks. So we can solve for the radius:
125 = (1/3)πr^2h
125 = (1/3)πr^2h
375 = πr^2h
r^2 = 375/π
r ≈ 10.69
So we can conclude that the radius of the base of the cone-shaped block is approximately 10.69 inches.
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4/7+1/4 in its simplest form
Which do you think would have a higher value if c and d are positive decimal numbers:
4c + 2d or 6c + 3d? How can you be sure?
we can be sure that 6c + 3d will have a higher value than 4c + 2d if c and d are positive decimal numbers.
Explain variableA variable in mathematics is a symbol or letter that is used to indicate a quantity in a mathematical statement or equation that can have many values. It is a symbol that may be used to represent an arbitrary or undefined integer in algebraic expressions and equations.
Both expressions have the same common factor of 2, so we can simplify them as follows:
4c + 2d = 2(2c + d)
6c + 3d = 3(2c + d)
Since c and d are positive decimal numbers, we know that both 2c + d and 3(2c + d) are positive. Therefore, the expression with the higher value will be the one with the larger coefficient, which is 3 in the second expression.
So, we can be sure that 6c + 3d will have a higher value than 4c + 2d if c and d are positive decimal numbers.
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(a) How many strings of seven hexadecimal digits do not have any repeated digits? 43680 x (b) How many strings of seven hexadecimal digits have at least one repeated digit? 21856 X (c) What is the probability that a randomly chosen string of seven hexadecimal digits has at least one repeated digit? (Round your answer to the nearest tenth of a percent. ) 33. 4 X % Need Help? Read It Talk to a Tutor
a) the total number of strings of seven hexadecimal digits that do not have any repeated digits is 450,450
b) The number of strings of seven hexadecimal digits have at least one repeated digit is 267,985,006
c) the probability that a randomly chosen string of seven hexadecimal digits has at least one repeated digit is 99.8%
How is this so?The total number of strings of seven hexadecimal digits is 16⁷.
For a string to not have any repeated digits, the first digit can be chosen in 16 ways, the second in 15 ways (since one digit has already been used),
the third in 14 ways, and so on, giving a total of 16 * 15 * 14 * 13 * 12 * 11 * 10 = 13,608,960 strings.
So
(16 * 15 * 14 * 13 * 12 * 11 * 10)/ (2 * 2 *2* 2* 2 *2* 2)
= 450,450
b) the number of strings with no repeated strings is 450450, so the nubmer of strings with at least one rpeated digit is
16⁷ - 450450 = 267,985,006
c) the probability that a a randomly chosen string of seven hexadecimal digits has at least one repeated digit
= 267,985,006/ 16⁷
= 0.99832194298
= 99.8%
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If the mRP = 130 , what is the measure of RSP
Answer:
230°
Step-by-step explanation:
Because Arc RSP had three letters that means its a major arc or greater than 180°
Arc RP is the portion of the circle not intercepted by the angle so 360 minus the measure of RP is RSP
360 - 130 = 230
Which choice shows (4+9)+11 correctly rewritten using the associative property and then correctly simplified ?
o 11+(4+9)=11+13=24
o 4+(9+11)=4+20=24
o 4+(91+1)=4+92=96
o 11+(9+4)=11+13=24
The associative property of addition:
[tex](a + b) + c = a + (b + c)[/tex]
We now apply the associative property of addition to the expression in this problem.
[tex](4+9)+11=4+(9+11)[/tex]
Now we follow the correct order of operations by adding the numbers inside the parentheses first.
[tex]= 4 + 20[/tex]
[tex]= 24[/tex]
Answer: B
what are the domain and range of the function represented by the set of ordered pairs? {(-10,-6),(-4,-10),(3,8),(9,-2)}. APEX
The domain of the data set {(-10,-6),(-4,-10),(3,8),(9,-2)} are {-10, -4, 3, 9} and the range are {-6, -10, 8, -2}.
How to find the domain and range?The domain of a function is the set of all possible inputs for the function. In other words, the domain of a function is the independent value of a function. The domain are usually the x values.
The range of a function refers to all the possible values y could be. Therefore, the range is the dependent values. The range are usually the y values.
Hence,
The domain of the data set are {-10, -4, 3, 9}
The range of the data sets are {-6, -10, 8, -2}
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Express the number 77 ten in base two
The binary representation of the number 77 ten is 1001101 two . This can be found by repeatedly dividing 77 by 2 and writing down the remainders in reverse order.
What is binary representation?Binary representation is a system of representing numbers using only two digits, usually 0 and 1. It is used extensively in digital electronics and computer programming.
What is remainder?The remainder is the amount left over after dividing one number by another. It represents the part of the dividend that could not be evenly divided by the divisor.
According to the given information:
To convert the number 77 ten to base two, we need to find the binary representation of this number.
One way to do this is to repeatedly divide the number by 2 and keep track of the remainders. We continue dividing until the quotient is 0. Then, we read the remainders in reverse order to get the binary representation.
Here's how the calculation works:
77 divided by 2 is 38 with a remainder of 1. Write down the remainder (1).38 divided by 2 is 19 with a remainder of 0. Write down the remainder (0).19 divided by 2 is 9 with a remainder of 1. Write down the remainder (1).9 divided by 2 is 4 with a remainder of 1. Write down the remainder (1).4 divided by 2 is 2 with a remainder of 0. Write down the remainder (0).2 divided by 2 is 1 with a remainder of 0. Write down the remainder (0).1 divided by 2 is 0 with a remainder of 1. Write down the remainder (1).Reading the remainders in reverse order gives us 1001101, which is the binary representation of 77 ten. Therefore, 77 ten = 1001101 two .
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The Normal model is a goodâ first-choice to model data if the data are suspected to be
The Normal model is a good first-choice to model data if the data is normally distributed or approximately normally distributed
Normally distributed or approximately Normally distributed. The Normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is widely used in statistical modeling due to its mathematical properties and practical applications in many fields.
When the data is Normally distributed, the Normal model provides a good approximation of the underlying distribution of the data. This means that the parameters of the Normal distribution can be estimated from the data using methods such as maximum likelihood estimation, and the resulting model can be used to make predictions and conduct statistical inference.
However, it is important to note that the Normal model may not be appropriate for all types of data, particularly if the data exhibits significant departures from Normality. In such cases, other distributional models or non-parametric methods may be more appropriate.
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IF 168=18 ⋅ x + 12 ⋅ 2x
what does x equal?
During a single day at radio station WMZH, the probability that a particular song is played is 0.58. What is the probability that this song will be played on at most 2 days out of 4 days? Round your answer to the nearest thousandth.
Thus, the probability that this song will be played on no more than two out of every four days is 35.60%.
Explain about the term combinations:Combination as well as permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in whatsoever order when combined. The components of the subset usually listed in a permutation in a certain order.
Since this is a combination issue, we must first determine the combination of 4 select 2, and then multiply that result by the chance of each possible outcome:
Choose 2 from a combination of 4:
C(4, 2) = 4! / (2! * 2!) = 4*3/2 = 6
This figure indicates that there are 6 alternative ways that the 2 days we want to be allocated in the 4 days could be used.
The probability of every event is now:
2 days of song playback: (0.58)²
The song wasn't played for two days: (0.42)².
Hence, the final probability is
P = C(4,2) * (0.58)² * (0.42)²
P = 6 * (0.58)² * (0.42)²
P = 0.3560
Thus, the probability that this particular song will be played on no more than two out of every four days is 35.60%.
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why does an angle formed by a tngent and a chord have the same measure as an insribed angle that intercepts the same arc
An angle formed by a tangent and a chord in a circle is called an "angle between tangent and chord" while an inscribed angle is an angle whose vertex is on the circle and whose sides intersect the circle at two distinct points.
When a tangent line and a chord intersect at a point on the circle, the tangent line is perpendicular to the radius drawn to the point of intersection.
This means that the angle between the tangent and the chord is equal to the angle between the radius and the chord.
Now, consider an inscribed angle that intercepts the same arc as the chord.
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that it intercepts.
Thus, the measure of the inscribed angle is equal to the measure of the arc that the chord intercepts.
Since the angle between the tangent and the chord is equal to the angle between the radius and the chord, and the inscribed angle intercepts the same arc as the chord, it follows that the angle between the tangent and the chord is equal to the inscribed angle that intercepts the same arc.
Therefore, an angle formed by a tangent and a chord has the same measure as an inscribed angle that intercepts the same arc.
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what does the equal 2,000,005,679,876=?
Answer:
N/A
Step-by-step explanation:
If you're looking for a significance or interpretation of the number 2,000,005,679,876, it's just a number. Unless utilized in a certain mathematical, financial, or another applicable context, it has no meaning or relevance. It is a big number with thirteen digits that can signify a quantity, amount, or value in a variety of scenarios depending on the context.
solve by substitution
-8y=5x+17
-7y=-2x-17
Therefore , the solution of the given problem of equation comes out to be the system of equations has an answer of x = -10.51 and y = 6.26.
Define equation.In intricate algorithms, variable words are typically employed to demonstrate consistency between two opposing arguments. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider the specifics of the above x + 7 suggestions. improving in this case provides b + 7 while constructing y + 7 before integrating.
Here,
Let's apply these steps to the provided equation system:
=> -8y = 5x + 17 ...(1)
=> -7y = -2x - 17 ...(2)
Solve equation (1) for x in terms of y in step 1:
=> -8y = 5x + 17
=> 5x = -8y - 17
=> x = (-8y - 17)/5
Step 2: Replace the value of x in equation (2) with the expression from step 1:
=> -7y = -2((-8y - 17)/5) - 17
Step 3: Address the equation that results for y.
=> -7y = (-16y - 34)/5 - 17
=> -35y = -16y - 34 - 85
=> -35y + 16y = -119
=> -19y = -119
=> y = (-119)/(-19)
=> y = 6.26
Step 4: Replace the formula for x from step 1 with the value of y obtained in step 3:
=> x = (-8(6.26) - 17)/5
=> x = -10.51
Consequently, the system of equations has an answer of x = -10.51 and y = 6.26.
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resting pulse rates for a random sample of 26 smokers had a mean of 80 beats per minute (bpm) and a standard deviation of 5 bpm. among 32 randomly chosen nonsmokers, the mean and standard deviation were 74 and 6 bpm. both sets of data were roughly symmetric and had no outliers. a. create a 95% confidence interval for the difference in the resting pulse rates between smokers and nonsmokers.
We can be 95 % confident that for smokers the pulse rate is between 3.1 and 8.9 beats per minute higher than for nonsmokers.
We are given that the total number of samples taken to observe the resting pulse rates of smokers is 26 with a mean and standard deviation of 80 bpm and 5 bpm respectively while samples taken for nonsmokers is 32 with a mean and standard deviation of 74 bpm and 6 bpm respectively.
We have independent random samples, each less than 10 % of the population, and the data appears to be approximately normal.
For smokers, n1 = 26, y1 = 80, s1 = 5
For non smokers, n2 = 32, y2 = 74, s2 = 6
t = [tex]((y1-y2) - H0)/ \sqrt{(s1^2/n1) + (s2^2/n2}[/tex]
t = [tex]((80 - 74) - 0)/ \sqrt{(5^2/26) + (6^2/32)}[/tex]
t = 4.15
P ≈ 0.0001
df ≈ 56
as the P-value is very small, the difference observed is not a sampling error. We have strong evidence of a difference in mean pulse rates for smokers and nonsmokers.
To find how big is that difference,
[tex](y1-y2)[/tex] ± t* SE(y1-y2)
= [tex](80 - 74)[/tex] ± [tex]t*(\sqrt{5^2/26 + 6^2/26})[/tex]
= (3.1, 8.29)
Therefore, we can be 95 % confident that the difference in resting pulse rates between smokers and nonsmokers is between the interval of 3.1 and 8.29 beats per minute.
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I need help converting 20000 lb into tons please
Answer:
10
20,00/2000=10
Step-by-step explanation:
Hope this helps! =D
Mark me brainliest! =D
Answer: 10 tons.
Step-by-step explanation: There are 2000 pounds in one ton. Hence:
20000 lb ÷ 2000 lb/ton = 10 tons
Solve for x. Type your answer as a number in the blank without "x=".
Answer:
17
Step-by-step explanation:
The midpoint theorem states that “The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”
therefore 2(x+5) = 3x-7
distribute
2x+10 = 3x-7
subtract 2x from both sides
2x+10 -2x = 3x-7 -2x
x-7 = 10
add 7 to both sides
x- 7 +7 = 10 + 7
x = 17
Answer:
Step-by-step explanation:
I think you are in 11th grade
we can use the theorem midpoint theorem.
as the mid-point theorem,
2(x+5)=3x-7
2x+10=3x-7
x=17
I really love your profile picture, is it real?
Round your answer to the nearest tenth, and type it in the blank without units.
According to the given data the length of the cable is 257.6ft.
What is meant by angle?An angle is formed by two rays, also called sides or arms, that extend from the vertex in different directions. The amount of turn between the two rays is the angle's measure, usually expressed in degrees or radians. A full turn, or a complete revolution, is 360 degrees or 2π radians.
According to the given information:To find the length of the cable, we can use trigonometry. Let "x" be the length of the cable. The tower height forms a right angle with the ground, so we can use the sine function:
sin(50) = opposite/hypotenuse
sin(50) = height/x
We know the height of the tower is 200 ft, so we can solve for x:
x = height/sin(50)
x = 200/sin(50)
x ≈ 257.6 ft
Therefore, the length of the cable is approximately 257.6 ft.
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Find the values of c that make f continuous everywhere: x² – ² f(x) CX + 9 smaller c = if < 15 if x > 15 larger c = Use at least 3 decimal places in your answers. Submit Question 2 -5 4 -3 -2 1 2 3 4 5 1 -2 3 -4 -5+ Use the graph of f(x) above to estimate the value of f'(-2) to one decimal place. f'(-2) = Question Help: P Viden 1 d. 6+ 5 4 3 2 1 -6 -5 -4 -3 -2 2 3 4 5 -Z -1 5 6 -2 ده -4 -5 -6+ a In the graph above the slope of the tangent at 2 is
To find the values of c that make f continuous everywhere, Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.
For x < 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c = 201 - 15c
Solving for c, we get c = 13.4 (rounded to 3 decimal places).
For x > 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c ≤ 15 Solving for c, we get c ≥ 12.9 (rounded to 3 decimal places).
Therefore, the values of c that make f continuous everywhere are 13.4 ≤ c ≤ 12.9.
To estimate the value of f'(-2), we can look at the slope of the tangent line at x = -2 on the graph. From the graph, it looks like the slope of the tangent at x = -2 is around -2.5. Rounding to one decimal place, we estimate f'(-2) to be -2.5.
Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.
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The temperature at the point (x,y) on a metal plate is
T=x/x2+y2
Find the direction of greatest increase in heat from the point (2, 5).
The direction of the greatest increase in heat from the point (2, 5) is in the direction of the vector (-21, -20).
To find the direction of the greatest increase in heat from point (2, 5), we need to find the gradient vector of the temperature function T(x,y) at that point, and then determine the direction in which the gradient vector points.
The gradient vector of T(x,y) is given by:
∇T(x,y) = (∂T/∂x)i + (∂T/∂y)j
where i and j are the unit vectors in the x and y directions, respectively.
Taking the partial derivatives of T(x,y) with respect to x and y, we get:
∂T/∂x = (x² - y²)/(x² + y²)²
∂T/∂y = -2xy/(x² + y²)²
Substituting x = 2 and y = 5, we get:
∂T/∂x = (4 - 25)/(29)² = -21/1681
∂T/∂y = -20/1681
Therefore, the gradient vector of T(x,y) at the point (2, 5) is:
∇T(2,5) = (-21/1681)i - (20/1681)j
The direction of the greatest increase in heat from points (2, 5) is in the direction of the gradient vector. We can normalize the gradient vector to get the unit vector in this direction:
u = (∇T(2,5))/|∇T(2,5)|
where |∇T(2,5)| is the magnitude of the gradient vector, given by:
|∇T(2,5)| = √((-21/1681)² + (-20/1681)²) = sqrt(841)/1681 = 1/41
Thus, the unit vector in the direction of greatest increase in heat from the point (2, 5) is:
u = (-21/1681i - 20/1681j)/(1/41) = -21i - 20j
Therefore, the direction of the greatest increase in heat from points (2, 5) is in the direction of the vector (-21, -20).
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How many flowers, spaced every 3 in., are needed to surround a circular garden with a 175-ft radius? Use 3.14 for pi.
First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:
[tex]\text{C}=2\pi \text{r}[/tex]
If we substitute 175 ft for [tex]\text{r}[/tex] and use 3.14 to approximate [tex]\pi[/tex] we get a circumference of:
[tex]\text{C}=2\times3.14\times175 \ \text{ft}[/tex]
[tex]\text{C}=6.28\times175 \ \text{ft}[/tex]
[tex]\text{C}=1099 \ \text{ft}[/tex]
We can now convert the circumference in feet to inches:
[tex]1099 \ \text{ft}\times \dfrac{12 \ \text{in}}{1 \ \text{ft}} \implies[/tex]
[tex]1099\times12 \ \text{in}\implies[/tex]
[tex]=13188[/tex]
To find how many flowers we need we can divide the circumference in inches by the 3 inches between flowers giving:
[tex]13188 \ \text{in}\times\dfrac{1 \ \text{flower}}{3 \ \text{in}}\implies[/tex]
[tex]13188 \ \text{in}\times\dfrac{1 \ \text{flower}}{3 }\implies[/tex]
[tex]\dfrac{13188 \ \text{flower}}{3 }\implies[/tex]
[tex]=4396 \ \text{flower}[/tex]
You would require 4,396 flowers
3 Marcus has 500 g of flour. He uses 200g to bake
bread and 120g to make biscuits.
Work out the percentage of the flour:
A he uses for bread
B he uses for biscuits
C he does not use
Answer:
40% , 24% , 36%
Step-by-step explanation:
first express each as a fraction then multiply the fraction by 100%
A
[tex]\frac{200}{500}[/tex] × 100% = 0.4 × 100% = 40% used for bread
B
[tex]\frac{120}{500}[/tex] × 100% = 0.24 × 100% = 24% used for biscuits
C
percentage not used = 100% - (40 + 24)% = 100% - 64% = 36%
216,36,6,... Find the 8th term. Find the 8th term.
Answer:
t8 term is
[tex] \frac{ 1}{1296} [/tex]
What is the domain and range of each relation?
Answer:
Table:
Domain: {-1, 3, 6}
Range: {4, 5, 6}
Set of coordinates:
Domain: {-4, -3, 1}
Range: {1, 3, 4}
3-3 The slope of a simple fable roof may be defined as:A. The rise of the roof times the run of the roof.B. The rise of the roof divided by the run of the roof.C. The rise of the roof divided by 1/2 the run.D. The run of the roof times the rise squared.
The slope of a simple gable roof can be defined using the terms rise and run.
The correct definition is:
B. The slope of a simple gable roof is the rise of the roof divided by the run of the roof.
To calculate the slope, follow these steps:
Measure the rise of the roof (the vertical distance between the highest and lowest points).
Measure the run of the roof (the horizontal distance between the edge of the roof and the point directly below the highest point).
Divide the rise by the run to find the slope.
Remember, the slope is a ratio representing the steepness of the roof, and it is important for proper drainage and structural stability.
Option B. The slope of a simple gable roof is the rise of the roof divided by the run of the roof.
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Convert 4.6 cm = ________mm
In the picture below Pac-Man, from the video game PAC-MAN, is shown eating ghosts. In the picture his mouth is open 60° and the radius of the circle is 13 mm. What is the area of the Pac-Man, to the
nearest tenth mm²?
The area of Pac-Man to the nearest tenth mm² is 11.4 mm².
What is area of circle?A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius.
To find the area of Pac-Man, we need to calculate the area of the sector that corresponds to the angle of his open mouth and subtract the area of the isosceles triangle formed by the two radii of the sector and the chord that represents the straight edge of his mouth.
First, we need to calculate the angle in radians that corresponds to the 60° angle given:
angle in radians = (60/360) x 2π = π/3 radians
Next, we can use the formula for the area of a sector:
Area of sector = (angle in radians / 2π) x πr²
where r is the radius of the circle.
Area of sector = (π/3 / 2π) x π(13mm)² ≈ 84.95 mm²
Now, we need to calculate the area of the triangle. We can use the formula for the area of an isosceles triangle:
Area of triangle = (1/2) x base x height
where the base is the chord that represents the straight edge of Pac-Man's mouth, and the height is half the length of the chord times the sine of half the angle of the mouth opening.
The base of the triangle is given by the formula:
base = 2r x sin(angle/2)
base = 2(13mm) x sin(30°) ≈ 22.52 mm
The height of the triangle is given by the formula:
height = (base / 2) x sin(angle/2)
height = (22.52 mm / 2) x sin(30°) ≈ 6.53 mm
Therefore, the area of the triangle is:
Area of triangle = (1/2) x base x height ≈ 73.5 mm²
Finally, we can subtract the area of the triangle from the area of the sector to get the area of Pac-Man:
Area of Pac-Man ≈ 84.95 mm² - 73.5 mm² ≈ 11.4 mm²
Therefore, the area of Pac-Man to the nearest tenth mm² is 11.4 mm².
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A line passes through the point (-4, -3) and has a slope of 5.
Write an equation in slope intercept form for this line.
The equation of the line is y=5x+17.
What is slope intercept form of the equation?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.
Here the given the point [tex](x_1,y_1)=(-4,-3)[/tex] and slope m = 5.
Now using equation formula then,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y -(-3)=5(x-(-4))
=> y+3 = 5(x+4)
=> y+3 = 5x+20
=> y = 5x+20-3
=> y = 5x+17
Hence the slope intercept form of the equation is y = 5x+17.
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In 9-11,use the dot plot at the right.
A dot plot is a simple type of graph that represents data using dots. It is a one-dimensional display of data where each dot represents a single data point. Dot plots are useful for showing the distribution of a set of values, particularly when the data set is small.
What is a dot plot?To create a dot plot, you simply draw a horizontal or vertical line and plot a dot above or beside the line for each data point. The dots are usually stacked vertically or horizontally if there are multiple data points with the same value.
| x
8 | x
7 | x x x
6 | x x x x
5 | x x x x
4 | x x x x x
3 | x x x x x
2 | x x x x x x
1 | x x x x x x x
---------------
1 2 3 4 5 6 7
In this example, the dot plot shows the number of times a dice roll resulted in a particular value. The x's represent the data points, and the numbers on the left indicate the frequency of each value.
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