After answering the presented question, we may conclude that the solution of the expressions are as follows.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
the solution of the expressions are as follows -
-3237-97196173396-4152-8172-196-176-12011084-177140undefined (division by zero is undefined)To know more about expressions visit :-
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Which table shows a proportional relationship between x and y?
Responses
x 1 2 3 4
y 4 10 12 16x 1 2 3 4 y 4 10 12 16 ,
x 2.5 3 5 6
y 5 6 10 15x 2.5 3 5 6 y 5 6 10 15 ,
x 7 14 28 35
y 1 2 4 5x 7 14 28 35 y 1 2 4 5 ,
x 1 3 4 7
y 2 5 8 14
(PLS HURRY I NEED TO GET THIS DONE)
(65 POINTS FOR THE RIGHT ANSWER)
The proportional relationship between x and y is shown by the table:
x 7 14 28 35
y 1 2 4 5
Explain about the proportional relationship:A connection among two factors that changes proportionally is referred to as a proportional relationship. If y=kx, where k is just the proportionality constant, can be used to represent two quantities, x and y, then they are said to be proportional.
This implies that the ratio between both always remains the same and that as x increases, y increases, and as x drops, y decreases.The proportional connection equation's graph is a line that passes directly through the origin.From the given options, consider the table:
x 7 14 28 35
y 1 2 4 5
As per proportional relationship.:
y=kx
k = y/x (must be same in all cases)
k = 1/7
k = 14/2 = 1/7
k = 4/28 = 1/7
k = 5/35 = 1/7
As all the k value for the given values of x and y are found equal.
Thus, the proportional relationship between x and y is shown by the table:
x 7 14 28 35
y 1 2 4 5
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calculate the side of a square with a perimeter 84cm
Answer:
441cm^2
Step-by-step explanation:
84 divided by 4 is 21
21cm*21cm is 441cm^2
I need help with questions 1,2, and 3. This class is microeconomics
Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.
What is budget?A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.
What is consumption?Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.
According to the given information:
To draw Ben's indifference curves, we need to plot different combinations of cookies and coffee that give Ben the same level of satisfaction. Since the slope of all his indifference curves is constant at -2, they will be downward-sloping straight lines. We can plot several indifference curves by varying the level of satisfaction they represent. The budget constraint is a straight line that represents all possible combinations of cookies and coffee that Ben can purchase with his $12 budget. The slope of the budget constraint is the ratio of the prices of coffee and cookies, which is 2:1. Ben optimally purchases the point where his budget constraint is tangent to his highest attainable indifference curve. In other words, he maximizes his satisfaction subject to his budget constraint. In the graph above, this point is labeled as "Optimal Consumption." At this point, Ben purchases 2 cookies and 2 coffees, spending $8 on coffee and $4 on cookies, which exhausts his $12 budget.To optimize his consumption, Ben should allocate his budget between cookies and coffee such that the ratio of their marginal utilities equals their prices. In other words, Ben should choose the combination of cookies and coffee where the marginal utility per dollar spent is the same for both goods. At his current consumption level of 3 coffees and 0 cookies, Ben's marginal utility per dollar spent on cookies is 2/2 = 1, and his marginal utility per dollar spent on coffee is 1/4 = 0.25. Since the marginal utility per dollar spent on cookies is higher than that of coffee, Ben should decrease his consumption of coffee and increase his consumption of cookies to achieve the optimal consumption level. He should continue adjusting his consumption until the marginal utility per dollar spent on each good is equal.To know more about budget and consumption visit:
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The bowling average of the players in the Capital Three bowling tournament is 158 with variance of 121. If Dr. Baker bowls an average of 169 during the tournament. Compute the appropriate statistic.
What proportion of bowlers performed better than Dr. Baker?
Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.
How to find the proportionStandard deviation (σ) = √(variance) = √(121) = 11
Now, we can calculate the z-score for Dr. Baker's average of 169 using the formula:
z = (X - μ) / σ
z = (169 - 158) / 11
z = 11 / 11
z = 1
Dr. Baker's z-score is 1, meaning his performance is one standard deviation above the mean.
The area to the left (or the cumulative probability) is approximately 0.8413
1 - 0.8413 = 0.1587
Approximately 15.87% of the bowlers in the Capital Three bowling tournament performed better than Dr. Baker.
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Un problema de derivadas de la vida cotidiana utilizando la siguiente función:
f(x)= 2x^3-3x^2-12x+1
Suppose you are driving a car with the velocity function represented by the following equation: f(x)= 2x^3-3x^2-12x+1. The derivative would be: f'(x) = 6x^2 - 6x - 12
How can we use the derivative of a function to analyze a car's motion?To find the acceleration of the car at a particular moment, we would need to calculate the derivative of the velocity function f(x). In this case, the derivative would be:
f'(x) = 6x^2 - 6x - 12
The result of this calculation would give us the instantaneous acceleration of the car at a given time x.
In terms of the car's motion, a positive value for f'(x) would indicate that the car is accelerating, while a negative value would indicate that the car is decelerating. The magnitude of the value would indicate the rate of change of the car's velocity, with larger values indicating a more rapid change.
Translated question "A derivative problem from everyday life using the following function: f(x)= 2x^3-3x^2-12x+1"
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What inequality matches this graph?
A} x > -5
B} x ≥ -5
C} x < -5
D} x ≥-5
According to the given condition. The inequality that matches this graph is option B) x ≥ -5.
What is an inequality equation?An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
According to the given information:The inequality that matches this graph is option B, "x ≥ -5". The graph represents a solid dot at x = -5 and a shaded region to the right of x = -5, including x = -5. This means that x can take on any value greater than or equal to -5, so the inequality can be written as x ≥ -5.
Therefore, According to the given condition. The inequality that matches this graph is option B) x ≥ -5.
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PLEASEE HELP ITS URGENT
The ratio of the areas is given as follows:
1:5.8.
How to obtain the ratio of the areas?The ratio of the areas is obtained applying the proportions in the context of the problem.
When a prism is dilated by a scale factor of k, we have that:
The ratio of the perimeters is k, as both the side lengths and the perimeter are measured in units.The ratio of the areas is k², as the side lengths are measured in units, while the areas are in units squared.The ratio of the volumes is k³, as the side lengths are measured in units, while the volumes are in units cubed.Hence the ratio of the areas is the cubic root of the ratio of the volumes squared, thus, as the ratio of the volumes is of 1:14, we have that:
(14²)^(1/3) = 5.8.
Hence:
1:5.8.
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15th term of 2, 10, 18, 26, 34
Step-by-step explanation:
a1 = 2
a2 = 10
d = a2 - a1 = 10 - 2 = 8
a15 = a + 14d = 2 + 14(8) = 2 + 112 = 114
Answer:
2, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114
Step-by-step explanation:
all you do is add 8 each time
81 smartphones is 45% of what number of smartphones? Please show work
Answer:
Let s be the number of smartphones.
81 = .45s, so s = 180
Answer:
36.45
Step-by-step explanation:
You make 45 into a percentage, which is 0.45%. Then, multiply 0.45 by 81 and you get 36.45. Hope this helps! And if you’re incorrect I deeply apologize. I tried my best and I’m 95% sure that I’m correct.
1) Find the APR for a $2400, two-year, add-on interest loan, that had a finance charge of $288.
2)) Suppose you have a loan for 4 years, with monthly payments of $185, and an APR of 9.0% (original finance charge of $1426). If you decide to pay it off in 3 years rather than 4 years, find the unearned interest.
3) Find the monthly payment necessary to amortize a $80,000 mortgage at 6% annual interest for 25 years.
1. the APR for this loan is 6%.
2. the unearned interest is $118.83.
3. the monthly payment necessary to amortize the $80,000 mortgage at 6% annual interest for 25 years is $506.69.
How do we calculate?APR = (finance charge / loan amount) / number of years * 100%
In this scenario, the loan amount is $2400 and the finance charge is $288. Since it's a two-year loan, the number of years is 2
APR = (288 / 2400) / 2 * 100%
APR = 0.06 * 100%
APR = 6%
b.
Number of payments = 4 years * 12 months/year = 48
If the loan is paid off in 3 years instead of 4 years, the number of payments made is:
Number of payments made = 3 years * 12 months/year = 36
Substituting these values into the formula, we get:
Unearned interest = (1426 / 48) * (48 - 36)
Unearned interest = $118.83
3.
To find the monthly payment necessary to amortize a mortgage, we need to use the formula:
M = P * (r / (1 - (1 + r)^(-n)))
where M is the monthly payment, P is the principal (loan amount), r is the monthly interest rate, and n is the total number of payments (in months).
In this scenario, the loan amount is $80,000, the annual interest rate is 6%, and the loan term is 25 years. To find the monthly interest rate, we divide the annual interest rate by 12 (since there are 12 months in a year):
Monthly interest rate = 6% / 12 = 0.005
To find the total number of payments, we multiply the number of years by 12:
Number of payments = 25 years * 12 months/year = 300
Substituting these values into the formula, we get:
M = 80000 * (0.005 / (1 - (1 + 0.005)^(-300)))
M ≈ $506.69
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If HI=square root 20, classify this triangle by sides. *
10
6
8
b
6
in
4
3₂2
(4
H
scalene
isosceles
3 4
O equilateral
none
I
5
6
7
G
8 9
10
According to the information provided, HI = 20, the triangle can be categorised by sides that are as follows:
what is a sequence?A collection of numbers or "terms" is called a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence.I have a code that tells me where to look for words in a sequence. A collection of objects in a peculiar order is called a sequence (or event) in mathematics. . It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.
We need further details regarding the triangle's side lengths in order to identify whether the cylinder is scalene, isosceles, etc equilateral. The cylinder with HI = 20 appears to have no relationship to the sides with lengths values 10, 6, & 8.
Given that the material after "b" contains symbols and numerals that do not make sense together, it can be incomplete or improperly structured. If you would kindly submit a thorough and correctly formatted inquiry, I would be pleased to assist you with sorting the triangle according to its sides or to offer any other information you might require.
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Solve 3/8 + n = 7/8
giving away 10 points for this
PLEASE HELP! An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1200, determine the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is what?
(Round to three decimal places as needed.) Thanks!
Therefore , the solution of the given problem of probability comes out to be z-score from a typical normal distribution.
What exactly is probability?Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.
Here,
The formula for the standard error of the mean (SEM), which is as follows:
=> SEM = the standard deviation / √(sample size).
We can enter these numbers into the SEM calculation to determine the SEM given that the standard deviation of the tariff rates is $1200 and the sample size is 400:
=> SEM=$1200/√(400)
=> $1200/20 =$60
It is possible to calculate the z-score for a $80 departure from the mean with a $60 SEM as follows:
=> z = (80 - 0) / $60 = 1.3333
Now that we have the probability corresponding to the z-score of 1.3333,
we can look up the cumulative distribution function (CDF) of the standard normal distribution using a z-table or a statistical calculator.
The CDF depicts the likelihood that a random variable will occur is less than or equal to a certain z-score from a typical normal distribution.
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In a large population of students, 60% feel like they can do better in their math class. In a random sample of 5 students, what is the probability that at least 2 students feel like they can do better in their math class?
0.0870
0.2304
0.3174
0.6826
0.9130
The probability that at least 2 students feel like they can do better in their math class is E. 0.9130.
How to calculate the probabilityTo find the probability that at least 2 students feel like they can do better, we need to calculate P(X >= 2). This can be done using the cumulative distribution function (CDF) of the binomial distribution:
P(X >= 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)
Using the binomial probability formula, we can calculate:
P(X = 0) = (5 choose 0) * 0.6^0 * 0.4^5 = 0.01024
P(X = 1) = (5 choose 1) * 0.6^1 * 0.4^4 = 0.07680
Therefore,
P(X >= 2) = 1 - 0.01024 - 0.07680 = 0.91296
Rounding this to four decimal places, we get: 0.9130
Therefore, the answer is option E: 0.9130.
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What is the greatest common factor of the polynomial below?
12x²9x
OA. 4x
OB. 3x
OC. 4x²
OD. 3x²
The greatest common factor (GCF) of the polynomial 12x²9x is 3x, therefore option B is correct.
How to Find the Greatest Common Factor of a Polynomial?The Greatest Common Factor (GCF) of a polynomial is the largest factor that all of the terms in the polynomial have in common.
To find the GCF, we need to find the largest factor that both terms have in common. Both terms have a factor of 3x, so that is the greatest common factor. Factoring out 3x from each term gives:
12x²9x = 3x(4x)3(3x) = 3x(4x3)
So the GCF of 12x²9x is 3x.
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Drag each value to the correct location on the equation. Not all values will be used. Convert radians to degrees. 4 /9
4[tex]\pi[/tex]/9 radians equals 80 degrees.
How will you convert radians into degrees?To convert a radian angle to a degree angle, multiply it by 180°/[tex]\pi[/tex]. To convert a degree angle to a radian angle, multiply it by [tex]\pi[/tex]/180°.
We utilize the conversion factor that 1 radian = 180/[tex]\pi[/tex] degrees to convert radians to degrees.
So we multiply 4[tex]\pi[/tex]/9 radians by the conversion factor to get degrees:
[tex]\\\frac{4\pi }{9} * \frac{180}{\pi } \\\frac{720}{9}[/tex]
On simplifying we get,
720 / 9 = 80 degrees
As a result, 4[tex]\pi[/tex]/9 radians equals 80 degrees.
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Complete question:
attach in the image form
PLEASE HELP ASAP!! (Please do this if ur good at Scientific Notation) please tell me which 4 should I put in the box! (Click picture) ‼️‼️
Answer:
1st one is 6.9 X 10^6
2nd one is 2 x 10^5
Step-by-step explanation:
The students in Mrs. Fishers class planted seeds. Each seed was given sunlight and water. Mrs. Fisher measured one plants height each week.
* After 4 weeks, the height was 2 centimeters.
* After 7 weeks the height was 4.5 centimeters.
* After 9 weeks, the height was 6 centimeters.
A student noticed the data suggest a linear association between the height of the plant, y, in centimeters, after x weeks.
What is a reasonable value for n?
Please answer as soon as possible due in an hour. Thank you.
Answer:
-9.5.
Step-by-step explanation
To find a reasonable value for n, we need to use the given data points and the equation of the line. We can plug in any pair of x and y values into the equation and solve for m or b. For example, using (4, 2), we get:
2 = m(4) + b
Solving for b, we get:
b = 2 - 4m
Now we can plug in another pair of x and y values, such as (7, 4.5), and use the value of b we just found:
4.5 = m(7) + 2 - 4m
Solving for m, we get:
m = 0.5
Now we have the slope and the y-intercept of the line. The equation is:
y = 0.5x + 2 - 4(0.5)
Simplifying, we get:
y = -1.5x + 4
To find n, we need to plug in x = 9 and solve for y:
y = -1.5(9) + 4
y = -9.5
Find the area of the circle. Round to the nearest square meter.
A. 63 m2
B. 314 m2
C. 897 m2
D. 1,257 m2
Answer:
B. 314 m²
Step-by-step explanation:
Area of circle = π · r²
r = 10 m
π = 3.14
Let's solve
3.14 x 10² = 314 m²
So, the area of the circle is B. 314 m²
Does anybody know this? I am a bit confused and please answer it right cause if you don't know it don't bother
The number of different passwords, considering 2 digits and 2 letters, is given as follows:
A. 6,760,000.
B. 3,276,000.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The password is composed by:
Four digits.Two letters.With repetition, we have that:
Each of the four digits have 10 possible outcomes.Each of the two letters have 26 possible outcomes.Hence the number of passwords is given as follows:
10^4 x 26² = 6,760,000.
Without repetition, we have that:
Digits: 10, 9, 8 and 7 outcomes.Letters: 26 and then 25 outcomes.Hence the number of passwords is given as follows:
10 x 9 x 8 x 7 x 26 x 25 = 3,276,000.
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HELP! A paper airplane is thrown from the top of a treehouse. The paper airplane flies 16 feet through the air and lands in a sandbox that is 9 feet from the base of the tree that the treehouse is in.
What is the angle of depression that the paper airplane is flying down at?
Explain your process
The angle of depression that the paper airplane is flying down at 55. 78 degrees
How to determine the valueNote that the different trigonometric identities in mathematics are;
sinetangentcotangentsecantcosecantcosineThese identities also have their ratios are;
sin θ = opposite/hypotenuse
cos θ = adjacent//hypotenuse
tan θ = opposite/adjacent
From the information given, we have;
Using the cosine identity
Adjacent = 9 feet
Hypotenuse = 16 feet
Substitute the values
cos θ = 9/ 16
divide the values
cos θ = 0. 5625
θ = 55. 78 degrees
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Answer:
55.8° (nearest tenth)
Step-by-step explanation:
The angle of depression is the angle between the horizontal line of sight at the top of the treehouse and line of sight to the sandbox (the flight path of the paper airplane). (See attached diagram).
To find the angle of depression, we can use the cosine trigonometric ratio. The cosine of an angle is equal to the ratio of the length of the side adjacent the angle to the length of the hypotenuse.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
In this case, the length of the side adjacent the angle of depression is equal to the distance between the base of the tree and the sandbox, so A = 9 ft. The hypotenuse is the distance the airplane flies through the air, so H = 16 ft.
Substitute these values into the cosine ratio and solve for θ:
[tex]\cos (\theta)=\dfrac{9}{16}[/tex]
[tex]\theta=\cos^{-1}\left(\dfrac{9}{16}\right)[/tex]
[tex]\theta=55.7711336...^{\circ}[/tex]
[tex]\theta=55.8^{\circ}\; \sf (nearest \; tenth)[/tex]
Therefore, the angle of depression that the paper airplane is flying down at is 55.8° (nearest tenth).
If the nth partial sum of a series n = 1 as it approaches infinity an is sn = 6 - n5^-n, find an and n = 1 as it approaches infinity an.
By using the partial sum of series is
[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]
and summation n=1 to infinity of [tex]a_{n}[/tex] is =6 .
How to find the nth term?To obtain the formula for the nth term of the series and its total, we must first discover the formula for the series' general term.
The formula for the series' nth partial sum is as follows:
[tex]sn = 6 - n*5^{-n}[/tex]
The nth term of the series can be obtained by subtracting the (n+1)th and nth partial sums, i.e.,
a = sn+1 - sn
When we substitute the formula for sn, we get:
[tex]a_{n} = [6 - (n+1)5^{(-(n+1))} ] - [6 - n5^{(-n)} ]\\a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]
As a result, the formula for the series' nth term is:
[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]
To calculate the series total, take the limit of the nth partial sum as n approaches infinity:
lim(n->inf) lim(n->inf) sn [6 - n*5^(-n)]
lim(n->inf) [n*5(-n)] = 6
= 6 - 0
= 6
As a result, the series' sum is 6.
As a result, the formula for the nth term in the series is:
[tex]a_{n} = 5^{(-n-1) } - (n+1)5^{(-(n+1))}[/tex]
And the series' total is:
a = sum(n=1 to inf) = 6
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Write an equation that you can use to solve for x.
Three lines intersect at the same point. Two of the lines intersect at a 90 degree angle. The third line divides one of the right angles into two adjacent angles. One of the adjacent angles is labeled 63 degrees and the other adjacent angle is labeled x degrees
Answer:
Ok so we know it has to equal=180 right?
90+90=180
180/4
45
Find the surface area of the rectangular prism. 2 m 5 m 2 m
Find the value of x. Then find the area of the triangle.
Step-by-step explanation:
first of all, remember, the sum of all angles in a triangle is always 180°.
now, we see that both bottom angles are 45°.
that means
180 = 45 + 45 + top-angle
90° = top-angle
aha ! we are dealing with a right-angled triangle, that is also isoceles (both legs are equally long, because the angles with the baseline are equal).
via Pythagoras
c² = a² + b²
where "c" is the Hypotenuse (the side opposite of the 90° angle), "a" and "b" are the legs.
in our case both legs are 7×sqrt(2) units long.
so,
baseline² = (7×sqrt(2))² + (7×sqrt(2))² = 49×2 + 49×2 =
= 98 + 98 = 196
baseline = sqrt(196) = 14 units
x is now the height of this triangle, and because of the isoceles form, it splits the baseline exactly in half.
so, one side of the baseline from x is 14/2 = 7 units.
and now Pythagoras for that sub-triangle :
(7×sqrt(2))² = 7² + x²
98 = 49 + x²
49 = x²
x = sqrt(49) = 7 units
the area of the triangle is
baseline × height / 2
in our case
14 × 7 / 2 = 7×7 = 49 units²
In need of assistance! If possible, I'd appreciate it!
The parametric equations graph as a portion of a parabola. The initial point is (5,0), and the terminal point is (3,4). The vertex of the parabola is (2,9). Arrows are drawn along the parabola to indicate motion right to left.
How to determine parametric equation?Parametric equations are a way of expressing a set of equations that define the coordinates of a point in terms of a third variable (parameter) that varies over a certain range. In the given problem, the parametric equations:
x(t) = 2 - t
y(t) = (t+3)²
To visualize the graph of these equations, we can substitute different values of t and plot the corresponding points (x(t), y(t)) on a coordinate plane. Since t ranges from -4 to 0, we can choose a few values of t such as t=-4, t=-2, and t=0 to get the corresponding points.
When plotted these points, a portion of a parabola that opens upwards. The vertex of the parabola is at the point (3, 4) where x=2-t and y=(t+3)² intersect. The initial point of the graph is when t=-4, which gives the point (6, 1) and the terminal point is when t=0, which gives the point (2, 9). The arrows are drawn along the parabola to indicate the direction of motion, which is from right to left in this case.
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Please help!!!!! Help please!! what is the value of x? is this right???
Answer:
x = 68
Step-by-step explanation:
X + 22 = 90 degrees
90 - 22 = 68 degrees
a) Use your calculator to solve sin x = 0.79 for 0° ≤ x ≤ 90°
b) Use the graph below to solve sin x = 0.79 for 90° ≤ x ≤ 180°
Give your answer to the nearest degree
Answer:
(a) 52°
(b) 128°
Step-by-step explanation:
You want the angle whose sine is 0.79 (a) in the interval [0, 90°], and (b) in the interval [90°, 180°].
a) Inverse sineThe inverse sine function is used to find the angle when its sine is known.
sin(x) = 0.79
x = arcsin(0.79) ≈ 52°
x ≈ 52° in the domain 0 ≤ x ≤ 90°.
b) Other valuesThe sine function is symmetrical about x = 90°, so other angles for which sin(x) = 0.79 can be found as 180° -x.
180° -52° = 128°
x = 128° in the domain 90° ≤ x ≤ 180°.
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Additional comment
The attachment shows the angles and that their sine is 0.79. Note that the calculator is set to Degrees mode.
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Given the following table of scores, calculate the indicated locator and percentile.
Do not round your results.
Here are the answers to the above questions:
Locator for the 52nd percentile, L52: 6.7252nd percentile, P52: 61.4Percentage of scores above the 52nd percentile: approximately 48%What is the explanation for the above response?To calculate the locator and percentile, we need to first arrange the scores in ascending order:
6, 8, 11, 12, 14, 17, 20, 34, 36, 38, 47, 48, 49
a) To calculate the locator for the 52nd percentile, we use the following formula:
Lp = (p/100) * (N + 1)
where Lp is the locator for the pth percentile, p is the percentile we are interested in, and N is the total number of scores.
For the 52nd percentile, p = 52 and N = 13. Substituting these values into the formula, we get:
L52 = (52/100) * (13 + 1) = 6.72
Therefore, the locator for the 52nd percentile is 6.72.
b) To determine the 52nd percentile, we need to find the score corresponding to the locator L52. Looking at the ordered list of scores, we see that the score at position 6 is 17 and the score at position 7 is 20. Since the locator L52 falls between positions 6 and 7, we can use linear interpolation to estimate the 52nd percentile:
P52 = (7 - L52) / (7 - 6) * 50 + (L52 - 6) / (7 - 6) * 50
P52 = (7 - 6.72) / (7 - 6) * 50 + (6.72 - 6) / (7 - 6) * 50
P52 = 38 + 0.48 * 50
P52 = 61.4
Therefore, the 52nd percentile is approximately 61.4.
c) To find the percentage of scores that are above the 52nd percentile, we subtract the 52nd percentile from 100:
100 - 52 = 48
Therefore, approximately 48% of the scores in the dataset are above the 52nd percentile.
Learn more about percentile at:
https://brainly.com/question/13638390
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What strategy could you use to figure out when Beau is likely to win 500 trophies
Answer:
I would say probability.