The probability of randomly drawing seven vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles is low. One time throughout the simulation's 500 iterations, all seven tiles were vowels.
Part A: What is the probability of randomly drawing 7 vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles?
Part B: To imitate one repetition of the process, you would use a table of random digits or a calculator to randomly generate seven digits, each between 0 and 9. The variable you would measure is the number of vowels drawn.
Part C:
Random Digits: 4, 2, 5, 7, 8, 8, 4
Vowels: 2, 8, 8, 4
Part D: This result suggests that it is possible to randomly draw all vowels in one draw, although it is unlikely.
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when people order books from a popular online source, they are shipped in boxes. suppose that the mean weight of the boxes is 1.5 pounds with a
The standard deviation of the total weight of the boxes that are shipped from this source is 3.02 pounds.
What is Standard Deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given:
Case A:
Standard Deviation= 0.3 pounds
mean weight= 1.5 pounds
Case B:
Standard Deviation= 0.1 pounds
mean weight= 0.5 pounds
Case C:
Standard Deviation= 3 pounds
mean weight= 12 pounds
let A is the Weight of boxes, B is the weight of packing and C is the weight of boxes.
ver(total)= ver A + ver B + ver C
Below is the Formula used:
SD = √variance
So, ver (total) = 0.3² + 0.1²+ 3²
ver (total) = 9.1 SD
ver (total) =√9.1
ver (total) = 3.02
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The complete Question is:
Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pound, the mean weight of the packing material is 0.5 pound with a standard deviation of 0.1 pound, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?
Here is the graph of a sequence:
1. Is this sequence arithmetic or geometric?
Explain how you know.
2. List at least the first five terms of the
sequence.
3. Write a recursive definition of the sequence.
A graph is a visual representation of data or information using points, lines, or bars.
How to plot the Graph?
To plot a graph, you need to have a set of x and y values that correspond to points on the graph. Once you have the data, you can use a tool such as a graphing calculator, spreadsheet software or specialized graphing software to plot the points and create the graph.
This sequence appears to be a geometric sequence. In a geometric sequence, the ratio between any two consecutive terms is always the same. In this case, the ratio between consecutive terms decreases by a factor of 1/4 each time.
The first five terms of the sequence are: (64,1), (16,2), (4,3), (2,4), (0,5)
A recursive definition of the sequence is a definition that expresses each term of the sequence in terms of one or more of the previous terms.
This definition says that each term of the sequence is the previous term divided by 4.
It's important to note that the graph you provided does not have a clear representation of the sequence, the points (64,1) (16,2) (4,3) (2,4) (0,5) does not represent a sequence as the x-coordinate does not represent the nth term of the sequence. The graph does not provide enough information to determine if it's arithmetic or geometric, or to list the first five terms of the sequence, or to write a recursive definition of the sequence.
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Which of the following is most likely the next step in the series?
The most likely the next step in the series wil be heptagon, the correct option is B.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Figure 1 has 4 sides
Figure 2 has 5 sides
Figure 3 has 6 sides
Now, from the three given figures;
The next figure will have 7 sides
Therefore, by algebra the next figure will be heptagon.
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PLEASE HELP There is a picture if you click on it haha
Answer:
120y + 720x = 600 (First option)Step-by-step explanation:
Correct answers only explained
------------------------------------------------------------------
We have the original equation as
72x + 12y = 60
If we multiply by 10 we get
720x + 120y = 600
First option
---------------------------------------------------------------
We can rewrite the original equation 72x + 12y = 60 as follows
Carry 72x to the right:
12y = 60 - 72x
Divide by 12
y = 5 - 6x
Second option
---------------------------------------------------------------
Rewrite 72x + 12y = 60 as
12y + 72x = 60 (same thing)
Divide by 6:
2y + 12x = 10
Third option
---------------------------------------------------------------
Rewrite 72x + 12y = 60 as
72x = 60 - 12y
Divide by 72
x = 60/72 -12y/72
Reduce to lowest fraction
x = 5/6 - y/6
Fifth option
------------------------------------------------
Find the value of x that satisfies the equation. 5t= 140.50 Using inverse operations, show all your steps.
The value of x that satisfies the equation 5^x = 140.50 is given as follows:
x = 3.07.
How to solve the exponential equation?The exponential equation for this problem is defined as follows:
5^x = 140.50.
We want to isolate the variable x, hence we have to apply the inverse operation to the base of 5 elevated to x, which is the logarithm of base 5.
Hence the solution for x is obtained as follows:
log5(5^x) = log5(140.50)
x = log(140.50)/log(5) -> change of base of logarithms.
x = 3.07.
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state the minimum or maxium value of y=2x^2
Since dy/dx > 0 for x = -7 and dy/dx < 0 for x = -9 , So this is a turning point.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and
constants.
So, the given expression ,
y = 2x^2 + 32x -4
So, first we have to find the derivative dy/dx
and than solve for dy/dx = 0
The derivative of any term x^n is equals to n*x^n-1 so for this polynomial
2x^2 + 32x - 4
The derivative could be
2.2x+1.32+0.-4
dy/dx = 4x+32
To calculate the turning points
let this equals to 0.
4x+32 = 0
x = -32/4
x = -5
By substituting this into the original equation, the turning point is at (-8,-137).
Therefore, Since dy/dx > 0 for x = -7 and dy/dx < 0 for x = -9 , So this is a turning point.
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1. Subtract
4 1/2
- 1 7/8
2. 20% of what amount is $6.50
The value obtained when we subtract the given fractions is 21/8 and the 20% of 32.5 gives the amount $6.50.
What are percentages?We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Given the following expression:
4 (1/2) - 1 (7/8)
Convert the mixed fractions into simple fractions:
9/2 -15/8
Take the LCM of the denominator:
36/ 8 - 15/8
21/8
2. 20% of x = 6.50
20/100 (x) = 6.50
20x = 650
x = 650/20
x = 32.5
Hence, the value obtained when we subtract the given fractions is 21/8 and the 20% of 32.5 gives the amount $6.50.
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a set of data has a mean that is much larger than the median. which of the following statements is most consistent with this information?
This suggests that the data set has a skewed distribution with a long tail of larger values.
This suggests that the data set has a skewed distribution, meaning that the data is not evenly distributed. The mean being much larger than the median indicates that there are a few larger values in the data set that are pulling the mean up and creating a long tail of larger values. This makes the distribution look lopsided, with a majority of the values being clustered around the median, and a few larger values that are skewing the mean higher.
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Rewrite in simplest rational exponent form (square root of x times the fourth root of x). Show each step of your process.
In the simplest rational exponent form of "square root of x times the fourth root of x" is [tex]x^{1/6}[/tex].
What is exponent?Exponentiation is one of the mathematics operation.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a time to itself.
So, a is the exponent of m.
Given:
We have a phrase:
Square root of x times the fourth root of x.
In numerator form:
(√x)[tex]\sqrt[1/4]{x}[/tex]
Simplifying,
(√x)[tex]\sqrt[1/4]{x}[/tex],
= [tex]x^{1/2} x^{1/4}[/tex]
= [tex]x^{1/2+1/4}[/tex]
= [tex]x^{1/6}[/tex]
Therefore, [tex]x^{1/6}[/tex]the required simple rational form.
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The circumference of a personal sized pizza at center court is 12.56 inches. Their large pizza is three times the diameter as the personalized sized pizza. What is the area of the large pizza?
The area of the large pizza is approximately equal to 112.984 square inches.
How to determine the area of a large pizza
Herein we need to determine the area occupied by a large pizza (A), in square inches, and based on given input by circumference of a small pizza (s), in inches. Then, we need the following formulas:
Circumference
s = π · D
Area
A = 0.25π · D²
Where D is the diameter, inches.
First, determine the diameter of the small pizza:
D = s / π
D = 12.56 / π
D ≈ 3.998 in
Second, calculate the diameter of the large pizza:
D' = 3 · (3.998 in)
D' = 11.994 in
Third, obtain the area of the large pizza:
A = 0.25π · (11.994 in)²
A ≈ 112.984 in²
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Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone
Plan B costs $50 per month but does not come with a phone. If you buy the $500 phone
and choose Plan B, how many months is it until your cost is the same as Plan A's?
The number of months before the cost is the same as Plan A is 25 months.
When the costs be the same?The linear equation that represents the cost of plan A = cost per month x number of months
$70 x m = $70m
The linear equation that represents the cost of plan B = (cost per month x number of months) + cost of the phone
($50 x m) + $500
= $50m + $500
When the costs are the same, the two equations would be equal
$70m = $50m + $500
Solve for m:
Combine similar terms: $70m - $50m = $500
Add similar terms: $20m = $500
Divide both sides of the equation by 20 = 500 / 20
m = 25 months
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Alexis is working with her English classes to make sure they are
all able to pass the upcoming state exam. From last year's data,
she predicts the number of students that will not pass the exam
is modeled by the linear equation:
y=-2.5t + 60,
where t is the number of weeks her students have been taking
the class.
The number of students from given linear equation after 6 weeks will be 45.
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
As given linear equation for students is
y=-2.5t + 60
where where t is the number of weeks her students have been taking
the class and y = no. of students.
To find students after 6 weeks put y=6
Therefore, y=-2.5*6+60
y=45
Hence,
The number of students from given linear equation after 6 weeks will be 45.
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Right question:-
Alexis is working with her English classes to make sure they are
all able to pass the upcoming state exam. From last year's data,
she predicts the number of students that will not pass the exam
is modeled by the linear equation:
y=-2.5t + 60,
where t is the number of weeks her students have been taking
the class and y = no. of students.
Find mo. of students after 6 weeks.
Each year, a physicist measures the remaining radioactivity in a sample. she finds that it reduces by 18% each year. if there was 1.52 g of radioactive material left after 4 years}
a. Find the initial quality of radioactive material
b. Hoy many more years will it take for the amount of radioactive material to reduce to 0.2 g?
a. The initial quantity of radioactive material is 0.68 g.
b. It will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.
a. In order to find the initial quality of radioactive material, we will use the formula:
Initial Quality = Final Quantity * (1 - Reduction Rate)^Years
We know that -
the final Quantity is 1.52 g, the reduction rate is 18% (or 0.18), and the number of years is 4.
Initial Quantity = 1.52 g * [tex](1 - 0.18)^4[/tex]
Initial Quantity = 1.52 g * 0.452
Initial Quantity = 0.68 g
Hence, the initial quantity of the radioactive material is 0.68 g.
b. In order to find how many more years it will take for the amount of radioactive material to reduce to 0.2 g, we will use the formula:
Years = log(Final Quality / Initial Quality) / log(1 - Reduction Rate)
We know that -
the final quality is 0.2 g, the initial quality is 0.68 g, and the reduction rate is 18% (or 0.18).
Years = log(0.2 / 0.0.68) / log(1 - 0.18)
Years = 7.15
Therefore, it will take an additional 7.15 years for the amount of radioactive material to reduce to 0.2 g.
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Triangle ABC is congruent to triangle XYZ, as shown below. 4. If AEFG = AHIJ, which of the following statements must be true?
From the given options, option B is the only statement that is not true is ∠C ≅ ∠E for congruent
What is the congruence theorem?
Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
If Δ ABC is congruent to Δ DEF, then its corresponding parts must be congruent.
segment AB ≅ segment DE
segment BC ≅ segment EF
segment AC ≅ segment DF
∠A ≅ ∠D
∠B ≅ ∠E
∠C ≅ ∠F
Therefore, from the given options, option B is the only statement that is not true is ∠C ≅ ∠E.
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"Your question is incomplete, probably the complete question/missing part is:"
If triangle ABC is congruent to triangle DEF, which statement is not true?
A) Segment AB ≅ segment DE
B) ∠C ≅ ∠E
C) Segment BC ≅ segment EF
D) ∠A ≅ ∠D
From the given options, option B is the only statement - 1
In a certain college, 55% of the students are women. Suppose we take a sample of two students. Use a probability tree to find the probability
(a) that both chosen students are women.
(b) that atle a stone of the two students is a woman.
The probability that both chosen students are women is 0.3025 and the probability that at least one of the two students is a woman is 0.8075.
a) Probability of both chosen students being women = P(W1 ∩ W2) = P(W1) * P(W2)
= 0.55 * 0.55 = 0.3025
b) Probability of atleast one of the two students being a woman = P(W1 ∪ W2)
= P(W1) + P(W2) - P(W1 ∩ W2)
= 0.55 + 0.55 - 0.3025 = 0.8075
Therefore, the probability that both chosen students are women is 0.3025 and the probability that at least one of the two students is a woman is 0.8075.
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Equivalent expression
The equivalent expression of the given expression is {4/y - 56}.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
8(1/2y - 7)
The given expression is -
8(1/2y - 7)
(8 x 1/2y - 8 x 7)
4/y - 56
Therefore, the equivalent expression of the given expression is {4/y - 56}.
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{Complete question is
Write an equivalent expression for 8(1/2y - 7)}
The perimeter of a rectangular field is 52 yards. The length is 4 more yards than the width. Find the length and width of the field.
The the length and width of the rectangular field are respectively; 15 yards and 11 yards
How to find the perimeter of a rectangle?The perimeter of a rectangle is given by the formula;
Perimeter = 2(Length + width)
We are given;
Perimeter = 52 yards
Length(L) = W + 4
Width = W
Thus;
2(W + W + 4) = 52
2W + 4 = 52/2
2W + 4 = 26
2W = 22
W = 11 yards
L = 11 + 4
L = 15 yards
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Use the figure below to select the classification of each set of angles in a)-d)
The classification of the angles are;
a) ∠3 and ∠5; Alternate Angles
b) ∠1, ∠2 and ∠3; three interior angles of a triangle.
c) ∠2 and ∠3; Complementary angles
d) ∠4 and ∠5; Supplementary angles
How to classify angles?We know that the sum of angles in a triangle is 180 degrees and as such it means that ∠1, ∠2 and ∠3 are classified as three interior angles of a triangle.
We know that alternate angles are defined as angles that occur on opposite sides of the transversal line and have the same size. Thus;
∠3 and ∠5 are alternate angles.
Since ∠1 is 90 degrees, then it means that ∠2 and ∠3 are complementary angles.
Similarly, ∠4 and ∠5 are called supplementary angles because they sum up to 180 degrees.
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A ladder leans against the side of a house. The angle of elevation of the ladder is 74° when the bottom of the ladder is 12 ft from the side of the house. Find the length of the ladder. Round your answer to the nearest tenth.
?
12
74°
Answer: We can use trigonometry to solve this problem.
Let x be the length of the ladder, and h be the height of the ladder.
We can use the tangent function to relate the angle of elevation, the length of the ladder, and the height of the ladder:
tan(74°) = h / x
We know that x = 12 ft and we can find h.
We can cross multiply and solve for h:
x * tan(74°) = h
12 * tan(74°) = h
We can use a calculator to find the value of h, this will give us the height of the ladder.
Finally, we can use the Pythagorean theorem to find the length of the ladder:
x^2 = h^2 + 12^2
x = √(h^2 + 12^2)
Round your answer to the nearest tenth, we have x = √(h^2 + 12^2)
We can use the value of h to find the length of the ladder.
However, without the value of h it is not possible to find the length of the ladder.
Step-by-step explanation:
Compare Slopes: Are these lines parallel, perpendicular, or neither?
Y = 3x - 5
Y = 3x + 6
Answer:
parallel
Brief explanation:
Well parallel lines have the same slopes sooo
these two lines are parallel
hence the answer
study hard
Due to gravity, an object falls 16t^2 feet in t seconds. You drop a rock from a bridge that is 75 feet above the water. Will the rock hit the water in 2 seconds?
Explain
If due to gravity, an object falls 16t^2 feet in t seconds. You drop a rock from a bridge that is 75 feet above the water. The rock will hit the water in 2 seconds?
How to find seconds the rock will hit the rock?Given data:
Object falls = 16t² feet in t seconds
Rock from a bridge = 75 feet above the water
So,
72 =16t²
t² = 72/16
t²= 4.5
t = √4.5
t = 2.12 seconds to hit the water
Therefore we can conclude that the rock will hit the water in 2 seconds.
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In order to use the formula sigma x = sigma/ calculate the standard deviation of the sampling distribution of the sample mean, which of the following condition must be met? n ge 30 The population's distribution is approximately Normal. The sample size is less than 10% of the population size. I only II only III only III and either I or II All three conditions must be met.
The standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.
In order to use the formula sigma x = sigma/ to calculate the standard deviation of the sampling distribution of the sample mean, all three conditions must be met. The first condition is that n must be greater than or equal to 30. This is because the larger the sample size, the more likely it is that the population's distribution is approximately normal. The second condition is that the population's distribution is approximately normal. This is because the Central Limit Theorem states that when the sample size is large enough (usually n ≥ 30) the sample means will have an approximately normal distribution. The third condition is that the sample size is less than 10% of the population size. This is because samples that are too large can lead to sample means that are not representative of the population.
To calculate the standard deviation of the sampling distribution of the sample mean, we can use the following formula:
σx = σ/√n
Where σ is the population standard deviation, and n is the sample size. For example, if the population standard deviation is 5, and the sample size is 30, then the standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.
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Order the correlation coefficients from least to greatest -0.50,0.60,,98,-0.10,0.68
answer: In this case, -0.50, -0.10, 0.60, 0.68, 0.98 are all correlation coefficients and -0.50 is the least and 0.98 is the greatest among the given correlation coefficients.
but why? The correlation coefficients can be ordered from least to greatest as:
-0.50, -0.10, 0.60, 0.68, 0.98
A correlation coefficient is a measure of the strength and direction of a linear relationship between two variables. The value of the coefficient ranges from -1 to 1, where:
A coefficient of -1 represents a perfect negative correlation, meaning that as one variable increases, the other variable decreases.
A coefficient of 0 represents no correlation, meaning that there is no linear relationship between the two variables.
A coefficient of 1 represents a perfect positive correlation, meaning that as one variable increases, the other variable also increases.
helpppppppppppppppppp
We need to calculate the area bounded by the given arcs . As we know that if [tex]\theta[/tex] is the angle subtended at the centre by the arc , then ; the area is given by ,
[tex]\longrightarrow Area =\dfrac{\theta}{360^o}\times \pi r^2 \\[/tex]
And here ,
[tex]\theta = 120^o[/tex][tex] r = 6m [/tex]Therefore on substituting the respective values, we have;
[tex]\longrightarrow Area =\dfrac{120^o}{360^o}\times \pi (6m)^2 \\[/tex]
Simplify,
[tex]\longrightarrow Area =\dfrac{1}{3}\times 3.14 \times 36m^2 \\[/tex]
[tex]\longrightarrow \underline{\underline{ Area = 37.68 \ m^2}} \\[/tex]
And we are done!
The championship record for a baseball team in a certain year was 52 games won and 14 games lost. What is the win percentage?
The win percentage is 79%
How to find the percentage?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
Number of games won=52
Number of games lost=14
Now, total games played= 14+52=66
Percentage of games won;
=(games won/total games)x100
= 52x100/66
=78.78
Therefore, the win percent will be 79%
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A television show aired once a week for 4.5 years. How many weeks did the show last?
For 235 weeks the show lasts.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
A television show aired once a week for 4.5 years.
So, In four years number of weeks are
= 52.1429 weeks
and, in 6 months the number of weeks
= 4.34524 weeks
So, the number weeks the show last
= 52.1429 x 4 + 4.34524 x 6
= 234.6431
= 235 weeks
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two planes take off from the same airstrip. the first plane flies west for 150 miles and then flies 30 degrees south of west for 220 miles. the second plane flies east for 220 miles and then flies x degrees south of east for 150 miles. if x < 30, which plane is farther from the airstrip after the second leg? justify your answer.
The first plane is farther from the airstrip after the second leg
Which plane is farther from the airstrip after the second leg?The first plane
Initial distance = 150 miles west
Additional distance = 220 miles 30 degrees SW
This means that
Additional distance = 220 * cos(30) miles SW
Additional distance = 190.53 miles
Total distance = 150 + 190.53 = 340.53
The second plane
Initial distance = 220 miles east
Additional distance = 150 miles x degrees SE
This means that
Additional distance = 150 * cos(x) miles SW
Total distance = 220 + 150 cos(x)
Given that
x < 30
We have
Second plane < First plane
220 + 150 cos(x) < 340.53
Evaluate
cos(x) < 0.8035
Take the arc cos of both sides
x < 36
x < 36 is not the same as x < 30
Hence, the first plane is farther
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The question is in the photo
From given pie chart, The percentage of students for 12th grade is 20%.
What is a pie chart?
The “pie chart” is also known as a “circle chart”, dividing the circular statistical graphic into sectors or sections to illustrate the numerical problems. Each sector denotes a proportionate part of the whole. A pie chart requires a list of categorical variables and numerical variables. To find out the composition of something, Pie-chart works the best at that time. In most cases, pie charts replace other graphs like the bar graph, line plots, histograms, etc.
The total value of the pie is always 100%.
Now
As
The total value of the pie is always 100%.
12th+9th+10th+11th=100
12th+30+27+23=100
12th=100-80
12th=20%
Hence,
The percentage of students for 12th grade is 20%
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Grade 5 Fractions how do you simplify fractions for 15/30
Answer:
Step-by-step explanation:
by selecting the filled-in regions on the graph, you can determine that the area of the canvas covered by the barn door is equal to 15 square inches.By selecting the filled-in regions on the graph, you can determine that the area of the canvas covered by the road is equal to [ ] square inches.
Area of the road 4 (in both selected sides)
Which of the following statements are true regrading areas?
-Each palette icon will always allow you to drag only one fill area onto the graph.
-Areas can be used to shade a region of any shade.
-Changing the position of the other objects on the graph may change the shape of the possible regions you may fill.
The statements that are true regarding the areas are that each palette icon will always allow you to drag only one fill area onto the graph. Changing the position of the other objects on the graph may change the shape of the possible regions you may fill.
The statement "Each palette icon will always allow you to drag only one fill area onto the graph." is true.
The statement "Areas can be used to shade a region of any shade." is false. Areas can be used to shade a region in a specific colour or pattern, but not necessarily any shade.
The statement "Changing the position of the other objects on the graph may change the shape of the possible regions you may fill." is true.
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