Answer:
[tex]P(x^{2} \geq 10.65) = 0.03\\[/tex]
Step-by-step explanation:
Since there are 5 categories, there are 5−1=4 degrees of freedom. The probability of obtaining a chi-square test statistic greater than or equal to 10.65 with 4 degrees of freedom is approximately 0.03, as found using technology.
A new cure has been developed for a certain type of cement that should change the mean compressive strength.It is known that a standard deviation is 130 kg/cm2and we may assume normal distribution. 9 pieces of cementhave been tested and the observed sample mean is ¯X= 4970. Find the 95% confidence interval for the mean.
(a) [4858.37,5081.63] (b) [4885.07,5054.93] (c) [4858.37,5054.93]
(d) [4944.52,4995.48] (e) [4858.37,5054.93]
(a) The 95% confidence interval for the mean of the compressive strength is 4885.1 < μ < 5054.9.
(b) The 95% confidence interval for the mean of compressive strength is 4975.2 < μ < 5012.4.
a) We have to find the 95% confidence interval for the mean of the compressive strength.
we are given
x = sample mean = 4970
n = sample size = 9
σ = population standard deviation = 130
The 95% confidence interval for population mean is
x - Za/2*(σ/√n) < μ < x + Za/2*(σ/√n)
For a = 0.05 Za/2 = Z0.025 = 1.96
4970 - 1.96*(130/√9) < μ < 4970 + 1.96*(130/√9)
4885.1 < μ < 5054.9
Hence, the 95% confidence interval for the mean of the compressive strength is 4885.1 < μ < 5054.9.
b) We have to find the 95% confidence interval for the mean of the compressive strength.
Since the population's standard deviation is unknown in this instance, the population mean's t confidence interval is used.
From the data n = 9
X = sample mean = 4993.8
s = sample standard deviation = 24.2
For a= 0.05 and degree of freedom = n -1 = 8
ta/2 , n-1 = t0.025,8 = 2.306
x - ta/2*(s/√n) < μ < x + ta/2*(s/√n)
4993.8 - 2.306*(24.2/√9) < μ < 4993.8 + 2.306*(24.2/√9)
4975.2 < μ < 5012.4
Hence, the 95% confidence interval for the mean of compressive strength is 4975.2 < μ < 5012.4.
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The complete question is:
A new cure has been developed for a certain type of cement that should change its mean compressive strength.
a) It is known that the standard deviation of the compressive strength is 130 kg/cm^2 and that we may assume that it follows a normal distribution. 9 chunks of cement have been tested and the observed sample mean is X = 4970. Find the 95% confidence interval for the mean of the compressive strength.
b) Now, assume that we do not know the standard deviation of the normal distribution. 9 chunks of cement have been tested, and the measurements are 5001, 4945, 5008, 5018, 4991, 4990, 4968, 5020, 5003. Find the 95% confidence interval for the mean of the compressive strength.
about 4% of the population has a particular genetic mutation. 100 people are randomly selected. round your answer to three decimal places. (a) Find the mean for the number of people with the genetic mutation in such groups of 600. (b) Find the standard deviation for the number of people with the genetic mutation in such groups of 600.
We got the mean value 4.167 and standard deviation 19.56.
What is mean value and standard deviation in statistics?In statistics, a mean value is the average value of all the available data. And it can be determined by adding all the data by dividing the amount of data.
A standard deviation is an estimation that implies how far each available data apart from the mean value.
How do we calculate the mean value and standard deviation?we are given, 4% of the population has a genetic mutation
Total people in the group =600
Now, total number of people who have genetic mutation = (4/100) ×600
= 24
the number of randomly selected people =100= X
Mean = Number of selected people/ people who have mutation
Mean = X/n = 100/24 = 4.167
the standard deviation = √∑(X-mean) ²/n
= √∑(selected people - mean) ²/ mutation number
=√(100-4.167) ²/24
standard deviation = 19.56
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Write the equation of the line that is perpendicular to the x-axis and passes through the point (6,-2).
The slope of a line that is perpendicular to the x-axis is undefined, so we cannot use the standard form of the equation of a line, y = mx + b, where m is the slope of the line. Instead, we can use the point-slope form of the equation of a line, which is given by y - y1 = m(x - x1). In this case, m is undefined, so we can simplify the equation to y = x1 - y1, where x1 and y1 are the coordinates of the point that the line passes through. In our case, this gives us the following equation:
y = 6 - (-2)
= 8
Therefore, the equation of the line that is perpendicular to the x-axis and passes through the point (6,-2) is y = 8.
Given f(x) = -x - 5 find f (0)
Answer: f(0)=-5
Step-by-step explanation:
f(0) means that x = 0
sub in 0 into the equation
f(0)=-0-5
f(0)=-5
Answer:
f(0) = -5
Step-by-step explanation:
Given f(x) = -x - 5
In order to find f(0), you need to replace x with 0
so f(0) = -(0) - 5
f(0) = -5
Answer and explain your answer.
With the help of Geometry We would make Australia 200 miles more wider.
What is geometry?
Geometry is a branch of mathematics that is concerned with the study of shapes, sizes, and relative positions of figures and the properties of space. It is one of the oldest branches of mathematics that has been around for centuries and is still relevant today. Geometry is used to explain many aspects of our lives, from the size of buildings and bridges to the path of a baseball in flight. It is a powerful tool for problem solving and understanding the world around us. Geometry is based on axioms, or accepted truths, that are used as the basis for forming logical proofs. These proofs are used to develop theorems and formulas which help us to understand and explain our world.
We would make Australia 200 miles more wider too or just give 200 miles long US to some other country to make their sizes equal.
Hence, we would make Australia 200 miles more wider
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Given the function g(x) = |x-3|, desvribe the graph of function
Answer:
The graph will be a V shape
Step-by-step explanation:
The graph will be a V shape because of the absolute value
The function g is defined as follows for the domain given.
g(x)=2x-2, domain = {-3, -2, 1, 5)
Write the range of g using set notation. Then graph g.
Answer:
1. range = {-8,-6,0,8}
2. My graph is attached to this response as a photo.
Step-by-step explanation:
1. ⭐What is the "domain" of a function?
Domain is another word for the x-values⭐What is the "range" of a function?
Range is another word for the y-values⭐What is the "set notation"?
Set notation is a way you can list numbers, such as x-values and y-values. When writing in set notation, you must list the numbers from least to greatest.Therefore, we have to find the corresponding y-values for the given x-values, and then write said y-values in set notation.
To find the corresponding y-values for the given x-values, substitute each given x-value into g(x) and solve for g(x).
✦ When x = -3
[tex]g(x) = 2x-2[/tex]
[tex]g(-3) = 2(-3) -2[/tex]
[tex]g(-3) = -6 -2[/tex]
[tex]g(x) = -8[/tex]
✧ y = -8
________________________________________________________
✦ When x = -2
[tex]g(-2) = 2(-2) -2[/tex]
[tex]g(-2) = -4-2[/tex]
[tex]g(-2) = -6[/tex]
✧ y = -6
________________________________________________________
✦ When x = 1
[tex]g(1) = 2(1) -2[/tex]
[tex]g(1) = 2-2[/tex]
[tex]g(1) = 0[/tex]
✧ y = 0
________________________________________________________
✦ When x = 5
[tex]g(5) = 2(5) -2[/tex]
[tex]g(5) = 10 -2[/tex]
[tex]g(5) = 8[/tex]
✧ y = 8
________________________________________________________
Next, we have to write the y-values in set notation. Make sure to write it from least to greatest.
range = {-8, -6, 0, 8}
I rent a gym for $150 for 30 students. Another time I rent the gym for $350 for 70 students. What is my rate per student?
Answer:
The rate is 5 dollars per student.
Step-by-step explanation:
The rate per student can be found with [tex]\frac{dollars}{student}[/tex]:
[tex]\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}[/tex]
The rate is 5 dollars per student.
Solve: 2x - 3= 2x - 5
A infinitely many solutions
B no solution
C 5/3
D 0
E -2
Please show me how to solve this problem?
Answer:
I think you forgot to show us the problem
Cai drove 189 miles in 7 hours. If he continued at the same rate, how far would he travel in 12 hours?
324 Miles
If you divide 189 by 7, you get 27. If you then multiply 27(miles per hour) by 12(hours) you get 324.
Rewrite 9x + 81 using a common factor.
9x(x + 81)
9x(x + 9)
9(x + 81)
9(x + 9)
Answer:
9 ( x + 9 )
Step-by-step explanation:
81 = 9 × 9
9x = 9 × x
9x + 81 = 9 ( x + 9 )
Solve the following inequality.8x-5>13-x
Answer:
x > 2
Step-by-step explanation:
8x - 5 > 13 - x Add x to both sides
8x + x - 5 > 13 - x + x
9x - 5 > 13 Add 5 to both sides
9x - 5 + 5 > 13 + 5
9x > 18 Divide both sides by 9
[tex]\frac{9x}{9}[/tex] > [tex]\frac{18}{9}[/tex]
x > 2
Answer:
x>2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
How can you find 50% of a number quickly in your head?
Answer:
Divide by 2
Step-by-step explanation:
I’ll give BRAINLIEST if correct pls need ASAP
Part A: given the function
g(x) = |x+3| describe the graph of the function including the vertex domain and range
Part B: if the parent function
f(x) = |x| is transformed to
h(x) = |x| - 2 what Transformation occurs from
f(x) to h(x) how are the vertex and range of h(x) affected
Answer:
A) The graph of function g(x) is V-shaped and has the following properties:
The vertex is (-3, 0)The axis of symmetry is x = -3The domain is the set of all real numbers: (-∞, ∞)The range is [0, ∞)B) Translation of 2 units down.
Therefore:
The vertex is (0, -2)The range is [-2, ∞)Step-by-step explanation:
The absolute value parent function, f(x) = |x|, is defined as:
[tex]f(x)=\begin{cases}x \; &\text{if}\;x > 0\\0 \; &\text{if} \; x=0\\-x\; &\text{if}\;x < 0\end{cases}[/tex]
Therefore:
The slope of the line where x > 0 is positive.The slope of the line where x < 0 is negative.Its graph is V-shaped and has the following properties:
The x-intercept and y-intercept are at the origin (0, 0).The vertex is at the origin (0, 0).The axis of symmetry is x = 0 (y-axis).The domain is the set of all real numbers: (-∞, ∞).The range is the set of all real numbers greater than or equal to 0: [0, ∞).Part AGiven absolute value function:
[tex]g(x)=|x+3|[/tex]
The graph of function g(x) is the parent function f(x) translated 3 units to the left.
As the graph has only been translated horizontally, the domain and range are the same as the parent function.
Therefore, the graph of function g(x) has:
Vertex = (-3, 0)Domain = (-∞, ∞)Range = [0, ∞)Part BGiven absolute value functions:
[tex]f(x)=|x|[/tex]
[tex]h(x)=|x|-2[/tex]
The graph of function h(x) is the parent function f(x) translated 2 units down.
As the graph has been translated vertically, the domain is the same as the parent function, but the vertex and range are different.
The y-value of the vertex of h(x) is 2 less than f(x).can someone help? i don't understand cos at all
Cos W as a fraction in the simplest terms is 2/3
Trigonometric ratios in a Right angled triangle:Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle.
From a Right-angled triangle with an angle θ
sin θ = Opposite side/Hypotenuse
cos θ = Adjacent side/Hypotenuse
tan θ = Opposite side /Adjacent side
Here we have
A triangle UVW
where VW = 10 units
And WU = 15 units
As we know
cos θ = Adjacent side / Hypotenuse
cos W = VW/WU = 10/15
cos W = 2/3 [ divided by 5 ]
Therefore,
Cos W as a fraction in the simplest terms is 2/3
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Assume that the distribution
A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and
weighed the bags. They weighed 10.8, 10.7, 10.2, and 10.8 pounds.
of weights is Normal. Find a 95% confidence interval for the mean weight of all bags of oranges. Use
technology for your calculations. Answer parts a and b below.
a. Choose the correct interpretation of the confidence interval below and, if necessary, fill in the
answer boxes to complete your choice.
and. A.There is a 95% chance that all intervals will be between
B. We are 95% confident the population mean is between
C. We are 95% confident that the sample mean is between
D. The requirements for constructing a confidence interval are not satisfied.
(Type integers or decimals rounded to the nearest thousandth as needed. Use ascending order.)
95% confident the population mean is between (9.1,9.9).
We are given the following data set:
9.3, 9.7, 9.2, 9.7
What is Standard Deviation?
Standard Deviation [tex]$=\sqrt{\frac{\sum\left(x_i-\bar{x}\right)^2}{n-1}}$[/tex]
where[tex]$x_i$[/tex] are data points, [tex]$\bar{x}$[/tex]is the mean and [tex]$\mathrm{n}$[/tex] is the number of observations.
Mean [tex]$=\frac{\text { Sum of all observations }}{\text { Total number of observation }}$[/tex]
Mean [tex]$=\frac{37.9}{4}=9.475$[/tex]
Sum of squares of differences [tex]$=0.2075$[/tex]
S.D[tex]$=\sqrt{\frac{0.2075}{3}}=0.262$[/tex]
[tex]$95 \%$[/tex] Confidence interval:
[tex]$\bar{x} \pm t_{\text {critical }} \frac{s}{\sqrt{n}}$[/tex]
Putting the values, we get,
[tex]$t_{\text {critical }}$[/tex] at degree of freedom 3 and[tex]$\alpha_{0.05}=\pm 3.182$[/tex]
[tex]$9.475 \pm 3.182\left(\frac{0.262}{\sqrt{4}}\right)=9.475 \pm 0.416842=(9.058158,9.891842) \approx(9.1,9.9)$[/tex]
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(Equivalent Algebraic Expressions MC)
25x¹⁰/y⁶ is equivalent to expression to (5x⁻⁵ y³)⁻².
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given
Expression
(5x⁻⁵ y³)⁻²
25x¹⁰ y⁻⁶
25x¹⁰/y⁶
25x¹⁰/y⁶ is equivalent to expression to (5x⁻⁵ y³)⁻².
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at a cafeteria the price of a salad depend on it weight in ounces. the graph shows the relationship what is the slope of the line
Answer:
slope = 1/4
Step-by-step explanation:
at a cafeteria the price of a salad depend on it weight in ounces. the graph shows the relationship what is the slope of the line
Find two places where the line neatly intersects the graph. For example, we will use the points: (0 , 0) and (4 , 1)
slope = change in y / change in x
[tex]slope = \frac{(y_{1} -y_{2} )}{(x_{1} -x_{2} )}[/tex]
slope = (0 - 1) / (0 - 4)
slope = -1 / -4
slope = 1/4
Answer: 1/4
Step-by-step explanation:
I just did it
Find the perimeter of the figure shown below
The perimeter of the figure with the varied side length is 52 cm
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
Shape = composite figure
Smaller shapes = squares and rectangles
Side lengths = varied values
The perimeter of the figure is calculated as
Perimeter = Sum of the sides lengths of the shape
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 12 + 7 + 3 + 4 + 3 + 7 + 6 + 10
Evaluate the sum in the above equation
Perimeter = 52 cm
Hence, the perimeter is 52 cm
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A random sample of 55 standard hotel rooms in the Philadelphia area has a mean nightly cost of $154.17. From previous studies, it has been found that the standard deviation of the price of all hotel rooms in Philadelphia is $38.60. Construct a 99% confidence interval for the population mean cost . Round to the nearest penny. Show work below . (5 points )
The 99% confidence interval for the population mean cost is 38.37 to 269.97.
What is confidence interval?
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.
Given that the standard hotel rooms in the Philadelphia area has a mean nightly cost of $154.17.
The standard deviation of the price of all hotel rooms in Philadelphia is $38.60.
According to the empirical rule,
P(μ - 3σ ≤ X ≤ μ - 3σ) = 99%.
Here μ = 154.17 and σ = 38.60.
Calculating the confidence interval:
154.17 - (3 × 38.60) ≤ X ≤ 154.17 + (3 × 38.60)
38.37 ≤ X ≤ 269.97
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a map has a scale of 1cm to 12km
on a map ,the distance between cardiff and london is 20cm
what is the real distance,in km, between cardiff and london
By using the given scale, we will see that the real distance is 240km
What is the real distance between Cardiff and London?We know that the scale of the map is 1 cm to 12km, so we just need to take the distance in centimeters on the map, and multiply that number by 12 km.
We know that on the map, the distance between Cardiff and London is 20cm, then the real distance is 12km times that, so we will get:
real distance = 20*12km = 240km
The real distance between Cardiff and London is 240 kilometers.
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Differentiate with respect to x
a) 2 + sin x
Answer:
cos x
Step-by-step explanation:
d( 2 + sin x )/DX
= d( 2 )/dx + d( sin x )/dx
= 0 + cos x
= cos x
Note : -
Differentiation of any number with respect to any variable ( here x ) is 0.Differentiation of sin x is cos x.d/dx is the notation to denote Differentiate with respect to x.Given m is parallel to n, find the value of x
Answer:
x = 44
Step-by-step explanation:
Given that line m is parallel to line n, the angles that we see are same-side exterior angles, meaning that these two angles add up to 180°.
Set up the equation: [tex]112 + (2x - 20) = 180[/tex] and solve for x.
. . . . . . . . . . . . 112 - 112 + 2x - 20 = 180 - 112
. . . . . . . . . . . . 2x - 20 + 20 = 68 +20
. . . . . . . . . . . . 2x /2 = 88 /2
. . . . . . . . . . . . ∴ x = 44
NO LINKS!! Please help me with these questions. Part 3cc
3. Loretta is a single mom with two kids. On 2009, her gross income was $61,840. She filed her taxes as Head of Household and claimed herself and her 2 children. Using the tables above, find Loretta's taxable income.
4. Mike and Lisa are a married couple with 2 kids. On 2009, they made $79,480. They filed jointly. Find Mike and Lisa's taxable income.
Answer:
3. $42,540
4. $53,480
Step-by-step explanation:
Question 3Income
Gross income = $61,840
Allowances
Head of household (2009) = $8,350
Single with 2 dependents = $3,650 + $3,650 · (2) = $10,950
Total allowances = $8,350 + $10,950 = $19,300
Taxable Income
Gross income - total allowances = $61,840 - $19,300 = $42,540
Question 4Income
Gross income = $79,480
Allowances
Married filing jointly (2009) = $11,400
Married with 2 dependents = $7,300 + $3,650 · (2) = $14,600
Total allowances = $11,400+ $14,600 = $26,000
Taxable Income
Gross income - total allowances = $79,480 - $26,000 = $53,480
In Exercises 1-3, decide whether enough information is given to prove that the triangles are congruent using either the SSS Congruence Theorem (Theorem 5.8) or the HL Congruence Theorem (Theorem 5.9). Explain.
The congruency proofs that can be used for each of the triangles are;
1) SSS Congruency
2) None
3) HL Congruence
How to prove the triangle congruency postulate?
1) The SSS congruency postulate states that If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
Now, we see that we are shown 2 corresponding sides that are congruent. However, the third side is automatically congruent using the reflexive property of congruence.
Thus, we conclude that the congruency can be proved using SSS Congruency postulate.
2) In this one, we are given 2 congruent sides and the included angle and so it is SAS Congruency and neither SSS nor HL congruency can be used.
3) The HL congruence Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
In this case, we see that the hypotenuse is congruent to itself by reflexive property of congruence while the one leg is also congruent and so we can use HL Congruence Theorem
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A dog allergy test for people has a 98% accuracy rate. Only one percent of the population has an allergy to dogs actually it is much smaller than that. Use a group of 100,000 people who have taken the test and the information provided to complete the table and answer the following question if you tested positive what is the probability you have a dog allergy
The probability that one has a dog allergy when tested positive will be 0.3311.
What do you mean by probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
According to the given question,
We have the given information:
1% of the population has an allergy to dogs.
This will be:
= 1% × 100000
= 1000
So, 1000 people have an allergy to dogs.
The number of people who doesn't have allergy to dogs will be:
= 100000 - 1000
= 99000
Those that have allergies = 2% × 1000 = 20
So, the probability that one has dog allergy will be:
= P(has allergy and test positive)
= (0.01 × 0.98) + (0.098 + 0.0198)
= 0.0098/0.0296
= 0.3311
Therefore, the probability is 0.3311.
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Shaina is 55 kg. What is Shaina's weight in grams
Answer: 55000 grams
Step-by-step explanation:
4. The wholesale price of a commodity for seven consecutive days in month is as follows: Days: 2 3 4 5 6 7 1 260 270 245 255 286 264 Commodity Price: 240 Calculate variance and standard deviation. 5. Calculate the standard deviation and variance from the following frequency distribution X: 10 12 14 16 18 20 22 F: 3 5 9 16 8 7 2 6. 6.Calculate Standard Deviation from the following Distribution C.I.: 10-20 20-30 30-40 40-50 50-60 60-70 70-80 8 Freq: 4 8 16 12 6 4
The variance is 206 and standard deviation is 14.353.
In the given question, we have to find the standard deviation and variance from the following frequency distribution X.
Days: 1 2 3 4 5 6 7
Commodity Price: 240 260 270 245 255 286 264
x (x-X) (x-X)^2
240 (240-260) = -20 400
260 (260-260) = 0 0
270 (270-260) = 10 100
245 (245-260) = -15 225
255 (255-260) = -5 25
286 (286-260) = 26 676
264 (264-260) = 4 16
Total = 1820 Σ(x-X)^2 = 1442
X = Total of x/total number
X = 1820/7
X = 260
Variance = Σ(x-X)^2/n
Variance = 1442/7
Variance = 206
Standard Deviation = √(Variance)
Standard Deviation = √206
Standard Deviation = 14.353
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Write x² + 10x + 29 in the form (x + c)² + d, where c
and d are numbers.
What are the values of c and d?
Answer:Write x² + 10x + 29 in the form (x + c)² + d, where c
Step-by-step explanation:
Answer:
(x+5)² + 4, so c is 5 and d is 4
Step-by-step explanation:
x² + 10x + 29 is a quadratic equation which can be witten as x² + bx + c, where b is 10 and c is 29.
We need to complete the square to get it in the form
(x + c)² + d
Completing the square uses the form:
[tex](x + \frac{b}{2} ) {}^{2} - ( \frac{b}{2} ) {}^{2} + c[/tex]
substitute b = 10 and c = 29 in this form:
[tex](x + \frac{10}{2}) {}^{2} - ( \frac{10}{2} ) {}^{2} + 29[/tex]
Simplify further:
[tex](x + 5) {}^{2} - 25 + 29[/tex]
[tex](x + 5) {}^{2} + 4[/tex]
c = 5, d = 4