The correct answer is A. no; since np<5, the normal distribution should not be used. This is because np<5, which violates the condition for using the normal distribution approximation to the binomial distribution. In this case, np=15 which is less than 5, and therefore, the binomial distribution should be used. If np is greater than or equal to 5, a normal approximation to the binomial distribution can be used.
The binomial distribution can be used to model the probability of a certain number of successes in a fixed number of independent trials, where the probability of success in each trial is the same. However, if the number of trials is large and the probability of success is small, the binomial distribution can be approximated by a normal distribution.
In this case, we have
n = 100 trials and p = 0.15
probability of success in each trial.
Therefore, np = 15, which is less than 5. According to the rule of thumb, if np < 5 or n(1-p) < 5, the normal distribution approximation is not valid, and the binomial distribution should be used.
Since the probability of success is small (0.15), and the number of trials is relatively large (100), we could use a normal approximation to the binomial distribution. However, since np < 5, we cannot use the binomial probability formula directly. Instead, we would need to use a continuity correction and the standard normal distribution to estimate the probability. Therefore, option A is the correct answer.
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how to convert milliseconds to a second
1 millisecond is equal to 0 point 001 or 1/1000 of a second. Using the formula seconds = (milliseconds/1000), you can convert milliseconds to seconds.
As per the Time Relationships:
One minute equals 60 seconds.
One hour has 60 minutes.
One Day = 24 hours.
One week is comprised of 7 days.
Twelve months equal one year.
One year is made up of fifty-two weeks.
A year has 365 days (or 366 in leap years) in total.
Ten years equal one decade.
One century is equal to 100 years.
One millennium equals 1000 years.
In Conversion principle:
Multiply from big to little.
Separate, from small to large.
This implies that you must multiply if you change a larger unit to a smaller one. However, you must divide if you take a smaller unit and make it into a larger one.
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The first To Answer Gets Brainliest!!!
These lines never intersect, there are no solutions to the equation.
Describe Graph?In mathematics, a graph is a visual representation of a set of objects and the relationships between them. Graphs are widely used in many areas, including mathematics, computer science, engineering, social sciences, and more.
A graph consists of two main components: vertices (also known as nodes) and edges. The vertices represent the objects, and the edges represent the connections or relationships between them. The edges can be directed or undirected, meaning they can be one-way or two-way relationships.
There are many types of graphs, including:
Undirected graphs: Graphs in which edges have no direction.
Directed graphs: Graphs in which edges have a direction, often represented by arrows.
Weighted graphs: Graphs in which edges have weights or values, representing some kind of numerical data.
Bipartite graphs: Graphs in which the vertices can be divided into two distinct sets, with edges only connecting vertices in different sets.
Complete graphs: Graphs in which every vertex is connected to every other vertex by an edge.
Graphs are used to model and analyze various kinds of data, such as social networks, transportation systems, financial transactions, and more. They are also used in algorithms and data structures, such as shortest path algorithms and tree data structures. In addition, graphs are often visualized using software tools to help people better understand complex relationships and patterns in data.
The given equation is 3x + 1 = 3x + 2.
Subtracting 3x from both sides, we get:
1 = 2
This is a contradiction and there are no values of x that can satisfy this equation.
On a graph, this can be seen as follows:
Plotting the graphs of y = 3x + 1 and y = 3x + 2, we get two parallel lines.
Since these lines never intersect, there are no solutions to the equation.
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I need alottttt of hellp
The expressions that have 3 as the greatest common factor are b + 3 + 6c, 27n + 66p, and 36 - 9j + 6k.
Thus,
b + 3 + 6c - Yes
-30 - 24z - No
27n + 66p - Yes
36 - 9j + 6k - Yes
Determining the greatest common factorFrom the question, we are to determine if 3 is the greatest common factor of the given expressions
b + 3 + 6c
3(b + 1 + 2c)
The greatest common factor is 3
-30 - 24z
6(-5 -4z)
The greatest common factor is not 3. The greatest common factor is 6
27n + 66p
3(9n + 22p)
The greatest common factor is 3
36 - 9j + 6k
3(12 - 3j + 2k)
Thus, The greatest common factor is 3
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Can someone help on where to put the numbers?
The domain is 0 ≤ x ≤ 52. The maximum number of laws that she can mow with 13 gallons is of 52, and the minimum number is of 0.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when the graph touches/crosses the y-axis.The graph touches the y-axis at y = 13, hence the intercept b is given as follows:
b = 13.
When x increases by 20, y decays by 5, hence the slope m is given as follows:
m = -5/20
m = -0.25.
Hence the function is:
y = -0.25x + 13.
From the intercept, the minimum amount can be mowed is given as follows:
0.
The maximum amount is given as follows:
-0.25x + 13 = 0
0.25x = 13
x = 13/0.25
x = 52.
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FIND THE LENGTH OF SEGMENT BD. ROUND TO THE NEAREST TENTHS PLACE HELP
Answer:
BD = 2.4
Step-by-step explanation:
see your other posting for details explanation
A box contains 3 red marbles, 6 blue marbles, and 1 white marble. the marbles are selected at random, one at a time, and are not replaced. find each compound probability
The compound probability is P(R and then R) = P(R) x P(R|R) = (3/10) x (2/9) = 0.0667 or 6.67% (rounded to two decimal places)
Describe Probability?Probability is a measure of the likelihood or chance that an event will occur. It is a mathematical concept used to quantify the degree of uncertainty of a particular outcome in a random process.
The probability of an event occurring is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur. The probability of an event occurring can also be expressed as a percentage, with 0% indicating that the event is impossible and 100% indicating that the event is certain to occur.
The calculation of probability involves determining the number of possible outcomes that satisfy the condition of interest and dividing that number by the total number of possible outcomes in the sample space.
For example, if you toss a fair coin, the probability of getting heads is 0.5 or 50%, since there are two possible outcomes (heads or tails), and each outcome is equally likely. Similarly, if you roll a fair six-sided die, the probability of getting a 4 is 1/6 or approximately 0.167, since there is only one possible outcome of rolling a 4, out of six possible outcomes.
Probability is used in various fields, such as statistics, economics, engineering, and science, to analyze data, make predictions, and make decisions based on uncertain outcomes. It is an essential concept in many areas of study, and its applications are widespread.
Let's denote the events as follows:
R = selecting a red marble
B = selecting a blue marble
W = selecting a white marble
a) The probability of selecting a blue marble on the first draw, followed by a red marble on the second draw:
The probability of selecting a blue marble on the first draw is 6/10 (since there are 6 blue marbles out of a total of 10 marbles). If a blue marble is selected on the first draw, then there are 9 marbles left in the box, including 3 red marbles. The probability of selecting a red marble on the second draw, given that a blue marble was selected on the first draw, is 3/9. Therefore, the compound probability is:
P(B and then R) = P(B) x P(R|B) = (6/10) x (3/9) = 0.2 or 20%
b) The probability of selecting a white marble on the first draw, followed by a blue marble on the second draw, followed by a red marble on the third draw:
The probability of selecting a white marble on the first draw is 1/10. If a white marble is selected on the first draw, then there are 9 marbles left in the box, including 6 blue marbles. The probability of selecting a blue marble on the second draw, given that a white marble was selected on the first draw, is 6/9. If a blue marble is selected on the second draw, then there are 8 marbles left in the box, including 3 red marbles. The probability of selecting a red marble on the third draw, given that a white marble was selected on the first draw and a blue marble was selected on the second draw, is 3/8. Therefore, the compound probability is:
P(W and then B and then R) = P(W) x P(B|W) x P(R|W and B) = (1/10) x (6/9) x (3/8) = 0.025 or 2.5%
c) The probability of selecting a red marble on the first draw, followed by another red marble on the second draw:
The probability of selecting a red marble on the first draw is 3/10. If a red marble is selected on the first draw, then there are 9 marbles left in the box, including 2 red marbles. The probability of selecting another red marble on the second draw, given that a red marble was selected on the first draw, is 2/9. Therefore, the compound probability is:
P(R and then R) = P(R) x P(R|R) = (3/10) x (2/9) = 0.0667 or 6.67% (rounded to two decimal places)
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Based on the results, what is the probability of needing more than 6 rolls to get doubles??
___
The probability of needing more than 6 rolls to get doubles is,
⇒ 3 / 20
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
Each student in Mr. Jones class has two standard number cubes.
Hence, The probability of needing more than 6 rolls to get doubles is,
Total number of cubes = 20
More than 6 rolls = 3
Thus, The probability of needing more than 6 rolls to get doubles is,
⇒ 3 / 20
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5^-2
what is the answer
Answer: 0.04
Step-by-step explanation:
Just do the Math.
Answer:
1/25 or 0.04
Step-by-step explanation:
Calculate the amount that will be in the bank after 5 years if R4 700 is invested at 5% simple interest
The amount after 5 years with a simple interest of 5 % is A = $ 875
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the amount in the bank after 5 years be A
Let the simple interest be represented as I
Now , the principal amount invested = $ 700
The rate of interest r = 5 %
The number of years n = 5 years
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
On simplifying , we get
Simple Interest I = ( 700 x 5 x 5 ) / 100
Simple Interest I = 25 x 7
Simple Interest I = $ 175
Now , the amount after 5 years = P + I = 700 + 175
The amount after 5 years = $ 875
Hence , the amount after 5 years in the bank is $ 875
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One angle of an isosceles triangle measures 120 degrees. Which other angles could be in that isosceles triangle?
Answer: The other angle would be 60 degrees.
Step-by-step explanation:
If y is inversely proportional to x, and y = 60 when x = 3, what are the values of y when x = 5 and x = 4?
A
35 and 46
B
20 and 36
C
36 and 45
D
45 and 20
Answer:
The correct answer is A. 35 and 46. When y is inversely proportional to x, it means that the ratio of x to y remains constant. In this case, when x = 3, y = 60, which means that the ratio of x to y is 3/60. Since the ratio is constant, we can use that ratio to find the values of y when x = 5 and x = 4. When x = 5, y = (3/60) x 5 = 35 and when x = 4, y = (3/60) x 4 = 46.
Answer:
Option A 35 and 46
Step-by-step explanation:
the senior classes at high school A and high school B planned separate trips to Yellowstone national park. the senior class at high school A rented and filled 3 vans and 7 buses with 263 students High school B rented 12 vans and 3 buses with 177 students. every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?
The number of students in the van are 6 and in the bus are 35.
What are system of equations?A system of equations is a combination of equations with a common solution pair.
Given is that the senior class at high school A rented and filled 3 vans and 7 buses with 263 students. High school B rented 12 vans and 3 buses with 177 students. every van had the same number of students in it as did the buses.
Assume that there are {x} students in each van and {y} students in each bus. We can write the system of equations as -
3x + 7y = 263
12x + 3y = 177
Now, we can write -
3x + 7y = 263
3x = 263 - 7y
4 x 3x = 4(263 - 7y)
12x = 1052 - 28y
So -
1052 - 28y + 3y = 177
25y = 1052 - 177
25y = 875
y = 35 ... { 1 }
and
3x + 7 x 35 = 263
3x = 18
x = 6 ... { 2 }
Therefore, the number of students in the van are 6 and in the bus are 35.
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The Click-O Pen Company produced 1.8×106 pencils each year for 4 years. What was the total number of pencils the Click-O Pen Company produced during those 4 years?
The Click-O Pen Company produced a total of 7.2×106 pencils during those 4 years.
What is the arithmetic operations?
The basic arithmetic operations are the fundamental mathematical operations used in arithmetic, which include:
Addition: combining two or more numbers to find their total or sum.Subtraction: finding the difference between two numbers by subtracting one from the other.Multiplication: finding the product of two or more numbers, which is the result of repeated addition.Division: dividing a number into equal parts or groups.To find the total number of pencils produced by the Click-O Pen Company during the 4 years, we need to multiply the number of pencils produced each year by the number of years.
We are given that the company produced 1.8×106 pencils each year for 4 years. Therefore, the total number of pencils produced is:
1.8×106 pencils/year × 4 years = 7.2×106 pencils
Hence, the Click-O Pen Company produced a total of 7.2×106 pencils during those 4 years.
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Answer:
The Click-O Pen Company produced 1.8 x 10^6 pencils each year for 4 years.
To find the total number of pencils produced during those 4 years, we need to multiply the number of pencils produced per year by the number of years:
Total number of pencils produced = (1.8 x 10^6) x 4
= 7.2 x 10^6
Therefore, the Click-O Pen Company produced a total of 7.2 million pencils during those 4 years.
Step-by-step explanation:
Start by identifying the number of pencils produced each year by the Click-O Pen Company. According to the problem statement, the company produced 1.8 x 106 pencils per year.
Next, determine how many years the company produced pencils for. In this case, we know that the company produced pencils for 4 years.
To calculate the total number of pencils produced during those 4 years, we need to multiply the number of pencils produced per year by the number of years. This gives us:
Total number of pencils = 1.8 x 106 pencils/year x 4 years
We can simplify this expression by multiplying 1.8 x 4 to get:
Total number of pencils = 7.2 x 106 pencils
Therefore, the Click-O Pen Company produced a total of 7.2 x 106 pencils during the 4-year period.
At 2:45 P.M, you are 117 miles from Tampa. You want to be in Tampa at 5:00 P.M. How many miles per hour must you average to be on time?
Answer:
93.6
Step-by-step explanation:
First, convert the time you have to work with to hours:
1 hour 15 minutes = 1.25 hours
required speed to cover 117 miles in 1.25 hours =
distance ÷ time = 117 miles ÷ 1.25 hours = 93.6 miles per hour (apprx.)
HELP PLEASEEE
Write en equation of a Line that goes through (1, 2) slope = 7. Put in point slope
Alex constructs a scatter plot. He realizes that he needs to add one more point, which will be an outlier. Which of the ordered pairs does he still need to plot? Responses (2,12) left parenthesis 2 comma 12 right parenthesis (18,10) left parenthesis 18 comma 10 right parenthesis (10,6) left parenthesis 10 comma 6 right parenthesis (14,2)
Any of the given ordered pairs could be the outlier depending on the overall distribution of the data.
Why is it known as a "ordered pair"?A pair of items that have a specific significance for the order of their placements is called an ordered pair, as the name suggests.
A point that deviates significantly from the general trend of the other data points is referred to as an outlier. The outlier point would be one that does not fit the pattern, if we assume that the other plotted points constitute a general pattern or trend.
We cannot identify with certainty which point would be the outlier without knowing the other plotted points or the context of the scatter plot. Depending on the overall distribution of the data, any of the ordered pairings that are presented could be an outlier.
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\left\ {{9x-6y=4 \atop {15x-10y=7}} \right
Answer: The answer is {x,y}={17/5,-68/5}
As it is used in line 19, the phrase paid out most nearly
means:
F. dispensed.
G. ascertained.
H. suggested.
J. compensated.
Answer:
Dispensed
Step-by-step explanation:
two vectors are linearly dependent if and only if they are collinear. True/False?
The two vectors are indeed considered linearly dependent if they are collinear. So the given statement is true about two linear dependent vectors.
The set [tex]\{v_1, v_2,.....,v_k\}[/tex] is considered as linearly dependent if numbers [tex]\{x_1, x_2, ....,x_k\}[/tex]are not equal to zero. Then, [tex]x_1v_1+x_2v_2+.....+x_kv_k=0[/tex]. This equation is referred to as the equation of linear dependence or linear dependence relation.
When two vectors are collinear, or when one is a scalar multiple of the other, they are said to be linearly dependent. These collinear vectors are also referred to as parallel vectors and these vectors will lie along the same line or parallel line. The given statement is therefore true.
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pleaseeee helpppppppppppppp
5) Practice: Summarizing
Find the slope of the line passing through (6, −1) and (7, 3). Let (x1, y1) = (6, −1) and (x2, y2) = (7, 3). List the coordinates, fill in the slope formula, and then simplify.
x1 = ___________ x2 = ___________ y1 = ___________ y2 = ___________
The slope is ____________.
We can fill in the given blanks as follows:
x1 =6, x2 = 7 , y1 = -1, y2 =3. The slope is 4.
What is meant by the slope of a line?
We have seen lines drawn on the coordinate plane in geometry. The best approach to determine without using any geometrical tools if the lines are parallel, perpendicular, or at any angle is to measure the slope. A line's steepness can be determined by looking at its slope. A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinates. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
Given,
(x1, y1) = (6, −1)
(x2, y2) = (7, 3)
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = 3 -(-1) / 7-6 = 4/1 = 4
Therefore we can fill in the given blanks as follows:
x1 =6, x2 = 7, y1 = -1, y2 =3. The slope is 4.
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A new car is purchased for 21,100 dollars. The value of the car depreciates at a rate of 2% per year. Which equation represents the value of the car after 5 years?
the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08
How to calculate the equation that represents the value of the car after 5 yearsGiven:
The cost price of the car, P = $21100,
The depreciation rate = 2%
Calculate the value of the car after 6 years by the following formula,
A = P (1- r / 100)ⁿ
Here A is the value of the car after 6 years.
Substitute the values,
A = 21100 × (1- 2 / 100)^5,
A = $19,105.08
Therefore, the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08
Which equation, written in the form of y=x+b, represents the table of values?
X y
2 7
3 8
4 9
5 10
A.y=x+2
B.y=x+5
C.y=x+7
D.y=x+9
Answer:
Option B. y=x+5
Step-by-step explanation:
If x=2 and y=7
Inserting the values into y=x+5
7=5+2
7=7
If x=3 and y=8
y=x+5
8=3+5
8=8
If x=4 and y=9
y=x+5
9=4+5
9=9
If x=5 and y=10
y=x+5
10=5+5
10=10
how to calculate for percent difference?
Percent difference is a measure of the difference between two values expressed as a percentage of their average.
The formula for percent difference is:
Percent difference = (|value 1 - value 2| / ((value 1 + value 2) / 2)) x 100%
where |value 1 - value 2| is the absolute value of the difference between the two values
((value 1 + value 2) / 2) is their average.
So the Percent difference is a measure of the difference between two values expressed as a percentage of their average.
To calculate percent difference, follow these steps:
Determine the two values you want to compare.
Calculate the absolute difference between the two values by subtracting one from the other and taking the absolute value of the result.
Calculate the average of the two values by adding them together and dividing by 2.
Divide the absolute difference by the average, and multiply by 100% to get the percent difference.
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how is bsa calculated
The BSA or Body surface area can be calculated by the formula is as follows: Body Surface Area= 0.007184 x (Height(m)^0.725) x (Weight(kg)^0.425)
Body surface area was developed as a metric to be used as such in the modulation of many various pharmaceutical treatments and as a standard index to various physiological measurements like glomerular filtration rate and cardiac output.
The Du Bois and its formula is one of the most widely used methods to determine a person's body surface area, in despite the fact that there are actually numerous variations on this concept. In the measurement of physiological and pharmacological data, the body surface area metric is much highly valued. The most typical reference point for chemotherapeutic drug dosing is body surface area.
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The height h (in feet) of a swing above the ground can be modeled by the function h=−8cosθ+10 , where the pivot is 10 feet above the ground, the rope is 8 feet long, and θ is the angle that the rope makes with the vertical. Graph the function. What is the height of the swing when θ is 45º? Round your answer to the nearest tenth. The height is about feet.
the height of the swing when θ is 45º is about 3.7 feet. Graph is attached below.
What is the significant use of graphs in real life?Graphs are a not unusual place technique to visually illustrate relationships within side the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately within side the textual content and in much less space.
Given, The height h (in feet) of a swing above the ground can be modeled by the function h=−8cosθ+10
Where,
the pivot is 10 feet above the ground,
the rope is 8 feet long,
To find the height of the swing when θ is 45º, we can substitute θ = 45º into the function and evaluate:
h(45º) = -8cos45º + 10
Using the fact that cos(45º) = √2/2, we get:
h(45º) = -8(√2/2) + 10
h(45º) = 10 - 4√2
Rounding to the nearest tenth, we get:
h(45º) ≈ 3.7 feet
Therefore, the height of the swing when θ is 45º is about 3.7 feet.
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To mix his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix.
Twenty-two people are running in tomorrow's
Road race and Jerome thinks they will each want two cups of energy drink.
B) how much water and how much drink mix should Jerome use to make enough energy drink for all the runners?
Answer: He needs 32 cups of water and 12 cups of drink mix.
Step-by-step explanation: 8 cups + 3 cups = 11 cups
So we know that 8 cups of water + 3 cups of drink mix = 11 cups of 'special energy drink'. Now, Jerome assumes that each person wants 2 cups so we perform the following equation: 22 people x 2 cups = 44 cups. We know that 8 cups of water and 3 cups of drink mix is equal to 11 cups so we just divide: 44 cups/11 cups = 4. Now we need to multiply 8 and 3 by 4 because he needs 4 x 11 cups, that is why we need to multiply
each of the numbers that make up 11 by 4. 8 cups x 4 = 32 cups,
3 cups x 4 = 12 cups
Answer: He needs 32 cups of water and 12 cups of drink mix.
Step-by-step explanation:
If θ is an angle in standard position and its terminal side passes through the point (2,7), find the exact value of tan � tanθ in simplest radical form.
Therefore , the solution of the given problem of trigonometry comes out to be the exact value of tanθ in simplest radical form is:
tanθ = 7/2.
What exactly does trigonometry mean?connections between trigonometry and cubic slope The field of mathematics is believed to have been established around the fourth millennium BC, when scientists and professions came together. Many geometric problems can be resolved using precise mathematical techniques, and these techniques can also be used to predict the results of calculations. Trigonometry is the study of the six basic trigonometric operations.
Here,
We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the terminal side of the angle θ and the x and y axes.
The distance from the origin to the point (2,7) is the hypotenuse, so we have:
r = √{2²+7²} = √53
Since $\tan\theta$ is the ratio of the opposite side to the adjacent side, we have:
tanθ = 7/2
Therefore, the exact value of tanθ in simplest radical form is:
tanθ = 7/2.
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What is the conversion of 175 cm to inches ?
The conversion factor for converting centimetres to inches (in.) is 0.3937. Thus, the conversion of 167 centimetres to inches is equals to the 68.89 inches.
To convert from one unit to another, multiply by a conversion factor. The centimeter (cm) is the fractional part of the meter, the international standard unit of length, and is approximately equal to 39.37 inches. An inch is a unit of length or distance in measurement system of common American units and British Imperial units. One inch is defined as 1/12 of a feet. To convert a centimeter value to its equivalent inch value, simply multiply the centimeter value by 0.39370078740 (the conversion factor). The formula to convert centimeters to inches is: Inches
= Centimeters × 0.39370078740.
The factor 0.39370078740 is the result of dividing 1/2. So the best formula is inches = centimeters / 2.54. Now we need to convert 175 cm to inches. So, according to the formula, inches = 175 cm / 2.54
= 68.8976377953 ~ 68.89
Hence, required value is 68.89 inches.
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Ashley and Alexandro have to determine if the two lines, y = -2x + 7 and 6x + 3y = 21, are parallel, perpendicular, or neither. Ashley thinks the lines are parallel. Alexandro thinks the lines are neither. Who is correct?
Ashley thinks the lines are parallel is correct. Meanwhile, Alexandro is wrong, he thinks the lines are neither.
The two lines, y = -2x + 7 and 6x + 3y = 21, are parallel because they have the same slope.
To determine if two lines are parallel, we need to check if their slopes are equal.
The slope of the first line, y = -2x + 7, is -2.
The slope of the second line, 6x + 3y = 21, can be found by rearranging the equation to solve for y:
3y = -6x + 21, divided by 3
y = -2x + 7
The slope of the second line is also -2. Since the slopes are equal, the lines are parallel.
However, to determine if two lines are perpendicular, we need to check if the product of their slopes is -1. The slope of the first line is -2, and the slope of the second line is -2.
The product of their slopes is (-2)(-2) = 4, which is not equal to -1. Therefore, the lines are not perpendicular.
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Can someone help on where to put the numbers?
The domain is 0 ≤ x ≤ 52. The maximum number of lawns she can mow with 13 gallons is 52, and the minimum is 0 lawns.
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {0, 52}.
Range = {0, 13}.
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