When estimating a population mean (μ) with a known population standard deviation (σ), the proper distribution to use is the standard normal distribution. So, correct option is A.
This is because the sampling distribution of the sample mean follows a normal distribution when the population standard deviation is known. The central limit theorem guarantees that the sample mean will be normally distributed with mean μ and standard deviation σ/√n, where n is the sample size.
The formula for constructing a confidence interval for μ when σ is known is:
CI = x' ± zα/2 * (σ/√n)
where x' is the sample mean, zα/2 is the z-score corresponding to the desired confidence level (α), σ is the population standard deviation, and n is the sample size.
Since the standard normal distribution has a mean of 0 and a standard deviation of 1, we can use z-scores to find the appropriate values for zα/2. This is why the standard normal distribution is used for interval estimation when σ is known.
In summary, the standard normal distribution is used for interval estimation of μ when σ is known because the sampling distribution of the sample mean is normally distributed when the population standard deviation is known.
So, correct option is A.
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a) What is the size of angle ABC? b) Use your answer to part a) to work out the size of reflex angle CBD. Give your answers to the nearest degree.
Answer:
a) 110
b) 250
Step-by-step explanation:
Read the top row of numbers for a. We are starting at zero and going to 110
Reflex is when two angles add up to 360
360 - 110 = 250
HELP!!!
What is the slope of the line containing (-3, 5) and (6, -1)?
A. 2/3
B. 1
C. -1
D. -2/3
Answer:Slope is -2/3
Step-by-step explanation:
What you do is use the formula y2-y1/x2-x1.
y1 and y2 are at the end of the parenthesis so y1 is 5 and y2 is -1.
x1 and x2 are at the beginning of the parenthesis so x1 is -3 and x2 is 6.
Then you put it into the formula:
-1-5/6-(-3)
This then equals -2/3.
-2/3 is the answer.
How do you compare two graph functions?
Two graph functions can be compared by analyzing their shape, direction, and relative position.
To compare two graph functions, one must look at the overall shape of the graphs, which can be either linear, quadratic, cubic, or some other shape. The direction of the graph, whether it's increasing or decreasing, should also be considered. The relative position of the graph, including the x and y intercepts, as well as any asymptotes, should also be considered.
Additionally, it's important to examine the domain and range of the function, which are the set of input values and output values that the function can produce, respectively. By comparing these different aspects of the graph, one can determine the similarities and differences between the two functions and draw conclusions about their behavior.
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Why is there only 180 degrees in a triangle?
A triangle is a three-sided polygon and each of its interior angles must add up to 180°; so each angle can have at most 180°.
A triangle is a three-sided polygon with three interior angles. According to the mathematical rule known as the “sum of interior angles”, the sum of the three interior angles of any triangle must always equal 180 degrees. Therefore, if the three angles of a triangle are A, B, and C, then A + B + C = 180. Since the sum of the three angles must equal 180 degrees, it means that each angle can have at most 180 degrees; none of the angles can be greater than 180 degrees. In other words, the maximum possible value of the angles in a triangle is 180 degrees, so the triangle can have only 180 degrees in total.
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150% ×_____ = $6.75 find the unknown
Answer:
The answer is $4.50.
Step-by-step explanation:
To solve this problem, divide the result ($6.75) by the percentage (150%). This gives you the original number which was multiplied by the percentage. So,
$6.75 / 150% = $4.50.
Answer:
$4.50
Step-by-step explanation:
150% × □ = $6.75
First, we can rewrite 150% as the fraction 3/2.
[tex]\dfrac{3}{2} \times \square = \$ 6.75[/tex]
Then, we can also rewrite 6.75 as the fraction 27/4.
[tex]\dfrac{3}{2} \times \square = \$ \, \dfrac{27}{4}[/tex]
Next, we can isolate the unknown by multiplying both sides by 2/3 (the reciprocal of 3/2).
[tex]\left(\dfrac{2}{3} \right)\left(\dfrac{3}{2} \times \square \right) = \left(\$ \, \dfrac{27}{4}\right)\left(\dfrac{2}{3} \right)[/tex]
After that, simplify by multiplying out the numerators and denominators on the right side of the equation.
[tex]\square = \$ \, \dfrac{27 \times 2}{4 \times 3}[/tex]
[tex]\square = \$ \, \dfrac{54}{12}[/tex]
Finally, simplify the expression on the right side to a decimal form.
[tex]\square = \$ \, \dfrac{54 \div 2}{12 \div 2}[/tex]
[tex]\square = \$ \, \dfrac{27 \div 3}{6 \div 3}[/tex]
[tex]\square = \$ \, \dfrac{9}{2}[/tex]
[tex]\square = \$ 4.50[/tex]
Could someone pls help me solve this ive been struggling for the past hour.no calculator allowed but im allowed a trigonometric circle.thx
The numeric value for each trigonometric expression is given as follows:
3. [tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \frac{5}{4}[/tex]
4. [tex]\frac{\sin{\left(\frac{\pi}{4}\right)}}{\cos^2{\left(\frac{\pi}{3}\right)}} = 2\sqrt{2}[/tex]
How to obtain the numeric value for the trigonometric expressions?The first trigonometric expression for this problem is defined as follows:
[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)}[/tex]
The numeric value of each term of the expression is given as follows, using equivalent angles on the trigonometric circle:
[tex]\sin{\left(-\frac{5\pi}{6}\right)} = \sin{\left(2\pi - \frac{5\pi}{6}\right)} = \sin{\left(\frac{7\pi}{6}\right)} = -\sin{\left(\frac{\pi}{6}\right)} = -\frac{1}{2}[/tex] (negative to positive, then find equivalent of the third quadrant angle on the first).[tex]\cos{\left(\frac{2\pi}{3}\right)} = -\cos{\left(\pi - \frac{2\pi}{3}\right)} = -\cos{\left(\frac{\pi}{3}\right)} = -\frac{1}{2}[/tex] (cosine on the second quadrant is negative).[tex]\cos{(-\pi)} = \cos{(\pi)} = -1[/tex] (cosine is an even function).Hence:
[tex]\sin{\left(-\frac{5\pi}{6}\right)}\cos{\left(\frac{2\pi}{3}\right)} - \cos{(-\pi)} = \left(-\frac{1}{2}\right)^2 + 1 = \frac{1}[4} + 1 = \frac{5}{4}[/tex]
For item 4, the angles are on the first quadrant, hence:
[tex]\sin{\left(\frac{\pi}{4}\right)} = \frac{\sqrt{2}}{2}[/tex][tex]\cos{\left(\frac{\pi}{3}\right) = \frac{1}{2}[/tex]Hence the numeric value of the expression is given as follows:
[tex]\frac{\frac{\sqrt{2}}{2}}{\left(\frac{1}{2}\right)^2} = 4 \times \frac{\sqrt{2}}{2} = 2\sqrt{2}[/tex]
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What does r equal?
Answer: r = ________
Answer:
[tex]r=\sqrt{\frac{3V}{\pi h} }[/tex]
Step-by-step explanation:
[tex]V=\frac{1}{3} \pi r^2h[/tex]
Lets solve for [tex]r[/tex].
Multiply both sides of the equation by 3.
[tex]3V=\pi r^2h[/tex]
Divide both sides of the equation by [tex]\pi h[/tex].
[tex]\frac{3V}{\pi h} =r^2[/tex]
Take the square root of both sides.
[tex]\sqrt{\frac{3V}{\pi h} } =r[/tex]
prove that the value of the expression does not depend on the value of x. (x-5)(x+8)-(x+4)(x-1)
The value of the expression is -44 and thus does not depend on the value of x
What are algebraic expressions?An algebraic expression can be described as a mathematical expression made up of variables, terms, factors, coefficients and constants.
They are also made up of mathematical or arithmetic operations, which includes;
MultiplicationSubtractionAdditionBracketParenthesesDivision, etcFrom the information given, we have that;
(x-5)(x+8)-(x+4)(x-1)
expand the bracket
x² + 8x - 5x - 40 - (x² -x + 4x - 4)
x² + 8x - 5x - 40 - x² + x - 4x + 4
collect like terms
3x - 3x - 40 - 4
add or subtract like terms
0 - 44
Hence, the expression does not depend o x
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Put the letters into the correct order to make worlds. Then match them to the definitions
oiffce psorin hlostipa ctotgae fcatyor gtues-hsoue
1. A room or building where people work at desks……..
2. A small hotel that is not very expensive………
3. A building where people are sent if they have committed a crime……..
4. A building where people go if they ill……..
5. A building where people make things, often using machines………
6. A small attractive house in the country……….
*************
1. A: Excuse me, can you tell me (1) the way to how far for the station?
B: Yes, sure. (2) Take/Turn left at the traffic lights and you'll see the station (3) in front / by
front of you.
2. A: Excuse me, (4) is it far / can you direct to the museum?
B: No. Just go (5) straight off / straight on for about half a kilometre and the museum is
(6) on / at your right.
Answer:
Step-by-step explanation:
What is the relationship between the ratios of sin x° and cos y°?
The ratios are both identical (three fifths and three fifths).
b
The ratios are opposites (negative three fifths and three fifths).
c
The ratios are reciprocals (three fifths and five thirds).
d
The ratios are both negative (negative five thirds and negative three fifths).
Answer:
A. The ratios are both identical (three fifths and three fifths).
Step-by-step explanation:
ratio means fraction
ratio also means division
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"SOHCAHTOA"
sine equals opposite over hypotenuse cosine equals adjacent over hypotenuse tangent equals opposite over adjacent
mathworldwolframcom
sine equals opposite over hypotenuse
sine X equals 3 over 5
cosine equals adjacent over hypotenuse
cosine Y equals adjacent over hypotenuse
cosine Y equals 3 over 5
side thats 3 is adjacent for y but
side thats 3 is also opposite for x
both identical, aka C on their question is right
its the 1st option for flvs
O. Test Practice Alaska has the longest coastline in the United States. Traveling at 62 miles per hour, how many hours would it take to travel along the Pacific Coast? A 17 hours B 89 hours 90 hours D 100 hours Alaska Coastline Coast Pacific Arctic Miles 5,580 1,060
Answer:
17
Step-by-step explanation:
How do you solve composite functions examples?
The composite function is the result of first applying the function (x^2 - 1) to the input and then applying the function (5x + 2) to the result. The final result of the composite function is 5x^3 + 2x - 3.
Step 1: Apply (x^2 - 1) to the input:
(x^2 - 1) = x^2 - 1
Step 2: Apply (5x + 2) to the result:
(5x + 2)(x^2 - 1)
= 5x^3 - 5x + 2x - 2
Step 3: Simplify:
5x^3 - 5x + 2x - 2
= 5x^3 + 2x - 3
A composite function is the result of applying two or more functions in succession. The order of operations for a composite function is to first apply the first function, then apply the second function to the result of the first, and so on. In the example given, the composite function
f(x) = (5x + 2) ∘ (x^2 - 1)
is the result of first applying the function
(x^2 - 1)
to the input and then applying the function (5x + 2) to the result. The calculation can be broken down into three steps: Step 1 is to apply (x^2 - 1) to the input to get x^2 - 1, Step 2 is to apply (5x + 2) to the result to get 5x^3 - 5x + 2x - 2,
and Step 3 is to simplify the result to get the final answer of
5x^3 + 2x - 3.
To summarize, the composite function
f(x) = (5x + 2) ∘ (x^2 - 1)
is the result of first applying the function (x^2 - 1) to the input, and then applying the function (5x + 2) to the
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What is Y + 4 = 3x + (-5) as a y = mx + b equation??
a) 3.2 ÷ 0.8 = ? please explain how you got it and b) 7.5 ÷ 0.5 also please explain how you got it i'll give the brain thing
Answer: To solve a division problem of the form a ÷ b = c, you need to find the value of c that makes the equation true. This means that if you multiply b by c, the result should be equal to a.
a) In the problem 3.2 ÷ 0.8 = ?, we are looking for the value of c that makes the equation true.
To solve this problem, we can multiply 0.8 by c to find the value of c that makes the equation true:
0.8 * c = 3.2
Dividing both sides of the equation by 0.8, we get:
c = 4
Therefore, the value of c that makes the equation 3.2 ÷ 0.8 = ? true is 4.
b) In the problem 7.5 ÷ 0.5 = ?, we are looking for the value of c that makes the equation true.
To solve this problem, we can multiply 0.5 by c to find the value of c that makes the equation true:
0.5 * c = 7.5
Dividing both sides of the equation by 0.5, we get:
c = 15
Therefore, the value of c that makes the equation 7.5 ÷ 0.5 = ? true is 15.
P.S. I don't need a brainliest, i am just happy that I am helping someone
Step-by-step explanation:
What ordered pairs are the solutions of the system of equations shown in the graph below?
Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).
Ordered pair: what is it?The term "ordered pair" refers to a pair of two variable that are shown in a way that they convey a specific order.
In an order pair, the first term denotes the x- and second term, the y-coordinates. The ordered pair is written in close brackets as shown in the example below.
Here ,
Is an equation system:
A set of equations is referred to as a system of equations when a limited set of equations is available and a common solution is sought.
The intersection of two lines, for the two equations drawn on a graph, represents the system's solution.
In the given graph, one linear line and one parabola is shown. In this graph the parabola intersect with the line at point (1,-4) and (4,-7).
Therefore ,the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).
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The game starts at 1830. They play four eight minute quarters, and half-time lasts for thirty minutes. What time should you tell your parents to pick you up? Give your answer in both 12 and 24 hour clock notation
Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.
What is time?the idea that time was the fourth dimension and that space and time were therefore inseparably connected. According to his general theory of relativity (opens in new tab), the mass and momentum of adjacent matter influence how much space-time enlarges and compresses.
Here,
Given : The game starts at 18:30
Thus,
They play for eight minutes quarters and half time last for 30 minutes.
So,
To find the time to pick up by your parents:
=> 8*4 + 30
=> 32 + 30
=> 62
Thus time after 62 minutes is 7:32
Therefore , the solution to the given problem of time comes out to be the time to pick up by your parents is 7:32.
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cam someone please help me with this I don't know how it has to be reflection translation rotation pre image (By the way I said it out of order)
Answer:
it looks like a reflection or translation but my gut is saying translation
Solve for x in this triangle. Round your answer to the nearest tenth. 17 х° 6
Answer:
x ≈ 70.6°
Step-by-step explanation:
using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{17}{6}[/tex] , then
x = [tex]tan^{-1}[/tex] ( [tex]\frac{17}{6}[/tex] ) ≈ 70.6° ( to the nearest tenth )
Ayesha earns a 10 percent bonus based on her annual salary plus the number of sales shes earned and a 2,000 dollar bonus last year
The annual salary will be 49750
Gross salary would be the total amount of compensation that an employer or business pays an employee during their employment. The Cost of Company, as well as CTC, on the other hand, would represent the overall compensation of employees. The CTC seems to be an employee's gross pay, but their net compensation is how much they actually take home.
Now, According to the question:
Let x be the annual salary.
Then 10% of x+250 equates 0.1(x+250).
Thus, the bonus equates $5000, then we will get the equation:
0.1(250 + x) = 5000
Solving for 'x' we get:
250 + x = [tex]\frac{5000}{0.1}[/tex]
250 + x = 50000
x = 50000 - 250
x = 49750
CTC and gross salary are sometimes confused. But there is a distinction among the two. Before taxes, Employee Provident Fund (EPF) contributions, and gratuities deducted from the CTC, the amount paid to the employee would be known as their gross salary.
The complete question is this:
__"Ayesha earns a 10% bonus based on her annual salary plus the number of sales she makes. She made 250 and earned a $5,000 bonus last year. Write and solve an equation to find her salary last year__"
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Help! What’s the expression of m more than 2
Answer:
2 + m
Step-by-step explanation:
What is the value of x? (HINT: find the sum of the
interior angles of the pentagon first)
Answer:
(2x+10°) + (x°) +(2x-20°) = 540°
540 is the sum angle of the polygon
collect like terms
2x+x+2x+10°-20°=540°
5x-10°=540°
5x=540°+10°
5x=550°
x=550°/5
x=110°
(2(110)+10)+(110)+(2(110)-20)=540°
You work at an oil refinery and are in charge of draining a tank until the
are 635 gallons left inside. The tank starts with 859 gallons, and you can
drain it at a rate of 56 gallons per minute. How many minutes do you
need to drain the tank to the right level?
You need
minutes.
Answer:
To drain the tank to the right level, you need to remove 859 - 635 = <<859-635=224>>224 gallons.
So you need to work for 224 / 56 = <<224/56=4>>4 minutes.
Step-by-step explanation:
Which of the following 3 lengths can be combined to form a right triangle?
A. a = 1, b = 2, c = 3
B. a = 7, b = 12, c = 13
C. a = 9, b = 20, c = 21
D. a = 8, b = 15, c = 17
The 3 lengths that can be combined to form a right triangle will be 8, 15, and 17. Then the correct option is D.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The Pythagoras theorem formula is given as
H² = P² + B²
If the Pythagoras theorem is satisfied then the dimension is the dimension of the right triangle.
Let's check option D, then we have
17² = 8² + 15²
289 = 64 + 225
289 = 289
The 3 lengths that can be combined to form a right triangle will be 8, 15, and 17. Then the correct option is D.
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HELPPPPP
Jada rode her bike 5 days in a row. She rode the same distance each day. This model represents the situation. Each column represents one mile and the shaded parts of each column represent the fraction of a mile that Jada rode her bike each day.
Which expression can be used to determine the total distance in miles Jada rode her bike over the 5 days?
(A: 5 × 4/5
(B: 5 + 4/5
(C: 5 × 1/4
(D: 5 + 1/4
PLSSSS HELP
Answer: 5 x 4/5
Step-by-step explanation:
In each column there is 4/5 shaded . There are 5 columns .
So , 5 x 4/5
Answer:
A) 5 × 4/5
Step-by-step explanation:
The shaded part each column in the model represents what fraction of a mile that Jada rode her bike each day.
There are 5 columns.
Therefore, to determine the total distance in miles that Jada rode over the days, we can multiply the distance that she rode each day by the number of days that she rode that distance (5 days):
A) [tex]5 \textrm{ days} \times \dfrac{4}{5} \textrm{ mile each day}[/tex]
would you earn a greater total commission with Sara or Ravi?
The current ratio of Sara's sales to Ravi's sales is 100:2
Sara's pieces of art sell for $25 each your commission is 60%
Ravi's pieces of art sell for $2000 each your commission is 25%
as a professional artist assume you will make pieces of art that sell at the same sales ratio as the artist with whom you apprenticed. would you earn more as a professional after apprenticed for Sara or Ravi?
As a professional artist and judging from the current sales ratio and commission rates, one would earn more if one apprenticed for Sara.
Which of Sara and Ravi guarantees more earnings after apprenticeship?As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.
Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.
Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.
Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.
Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.
On this note, one would earn more if one apprenticed for Sara.
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Geometry - Should be pretty easy
Answer:
DQR
Step-by-step explanation:
DEF is complentary to DQR
Answer:
∆DQR
Step-by-step explanation:
You want the similarity statement if the triangles shown are similar.
SimilarityTriangles will be similar if they have congruent corresponding angles, or proportional corresponding sides.
No angles are shown in the figure, but side lengths are given.
We expect that if the triangles are similar that the corresponding sides will be ...
DE ⇔ DQEF ⇔ QRFD ⇔ RDProportionThe attached calculator display shows the ratios of these side lengths are the same: 14/3. That means ...
∆DEF ~ ∆DQR
<95141404393>
An entertainment center is 52 inches wide and 40 inches high. Will a tv with a 60 inches diagonal fit ?
No, a TV with a 60 inch diagonal would not fit in an entertainment center that is 52 inches wide and 40 inches high.
What is diagonal?Diagonal is a line connecting two or more points that are not in a straight line. It is used to describe the shape of a polygon and also used in mathematics to refer to lines, angles, and shapes. It can also refer to a line, or direction, that is not parallel or perpendicular to something else. In geometry, diagonal lines are used to divide shapes into equal parts, and are used in the construction of polygons. In linear algebra, diagonal lines are used to calculate the determinant of a matrix.
The diagonal measurement of a TV is the length of a line drawn between the opposite corners of the TV. For a 60 inch diagonal TV, the width of the TV would be around 52 inches and the height would be around 33 inches. As the entertainment center is only 40 inches high, the TV would not fit in it.
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If b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
Hence option (B) is a correct choice and rest all other options are incorrect
1/b^2 ∑ (-1)^k(t^2/b^2)^k
Step-by-step explanation:
Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r
S=a/1 - r
Wherever the common ratio r falls within the interval (-1,1)
When the given series is compared to the infinite sum:
First term=a
Common ratio=r
S= a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:
Hence option (B) is a correct choice.
What are real numbers simple definition?
Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.
INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k
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A triangle ha an area of 142. 74 quare feet and a height of 18. 3 feet. What i the length of the bae?
A triangle having an area of 142. 74 ft^2 and a height of 18. 3 ft, has a base of 15.6 ft.
What is the area of a triangle?
In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.
The area of the triangle is 142.74 ft^2.
The height of the triangle is 18.3 ft.
Let the base of the triangle be x.
The formula for area of a triangle is -
Area = (height × base)/2
Plugging in the values in the equation -
142.74 = (18.3 × x)/2
142.74 = 18.3x/2
18.3x = 285.48
x = 285.48/18.3
x = 15.6
Therefore, the base of the triangle measures 15.6 ft.
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What is meant by halting problem?
Therefore , the solution of the given problem of tractable problem comes out to be halting problem claims that no computer can be created that can anticipated.
Describe a tractable problem.an algorithm that takes a polynomial amount of time to solve a tractable issue. The upper bound is described by a polynomial. Any issue that cannot be addressed in a polynomial period of time is considered to be intractable. The lowest limit is exponential.
Here,
The halting problem claims that no computer can be created that can anticipated.
the likelihood that any other program will halt after a certain number of steps, making it an unsolved algorithmic challenge.
Software development is directly affected in practice by the stopping problem's insoluble nature.
Therefore , the solution of the given problem of tractable problem comes out to be halting problem claims that no computer can be created that can anticipated.
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