The equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x - 6*y +21 =0
Given that, the points (3,0) and (7,6)
(x1, y1) = (3,0) and (x2, y2) = (7,6)
We know that the formula for the equation of circle whose points of diameter are given is equal to :
(x - x1) * (x - x2) + (y - y1) * (y - y2)
So now,
(x - 3) * (x - 7) + (y - 0) * (y - 6) = x² + y² - 10*x - 6*y +21 =0
so the equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x - 6*y +21 =0
To know more about circle follow the given link :
https://brainly.in/question/2178053
Solve: 2x - 3= 2x - 5
A infinitely many solutions
B no solution
C 5/3
D 0
E -2
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.
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
Write 0.006655 in scientific notation
Answer: 6.655 * 10^-3
Step-by-step explanation:
0.006655 in scientific notation
6.655 × 10³
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).Please show me how to solve this problem?
Answer:
I think you forgot to show us the problem
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
Read more about Triangle congruence postulate at; https://brainly.com/question/29268713
#SPJ1
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
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
To learn more about empirical rule, click on below link:
https://brainly.com/question/15674025
#SPJ1
John started a home delivery service from several local restaurants. He charges a $5 tip on the delivery, plus $0.75 for every mile he travels.
Write an equation for the function that relates the total cost of a trip to the distance.
Answer:
y = total cost
x = mile
y = 5 + 0.75xStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Answer: y = 5 + 0.75x
Step-by-step explanation:
Please Help!!
Jamie and Hudson took a road trip to the beach. Their total distance traveled after getting on the highway can be found using the function d(h)=55h+10, where h is the number of hours they have been driving on the highway.
1) Explain why the relationship between total distance and hours is a function.
2) Is this function continuous or discrete? Explain how you know.
3) If the girls can drive a maximum of 8 hours, what is the domain for the function? Explain your answer.
4) If the girls can drive a maximum of 8 hours, what is the range for the function? Explain your answer.
5) Create a graph that models this function. Be sure to include a title and to label your x- and y-axis with the variable names, not just x and y.
6) What is the slope of the function? What does it represent?
7) What is the y-intercept? What does it represent?
The total distance is an illustration of a linear function.
(1) Why the relationship is a function
The relationship is a function because all input values of h, have exactly one corresponding output value of d
(2) The function type
The function is a discrete function, because the number of hours is an integer, and it cannot take decimal values (in this case)
(3) The domain for a drive of 8 hours
The domain is the set of time the girls drive.
So, the domain is: [0,8]
(4) The range
The function is given as:
d= 55h + 10
When h = 0,
d = 55(0) + 10 = 10
When h = 8,
d = 55(8) + 10 = 450
So, the range is: [10,450]
(5) The graph
Sorry
(6) The slope
A linear function is represented as:
y = mx + c
Where:
m represents the slope.
So, by comparison:
Slope = 55
The slope in this case represents the distance travelled per hour
(7) The y-intercept
In (6) above, c represents the y-intercept.
So, by comparison:
c = 10
The y-intercept in this case represents the initial distance
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
To learn more about Geometry from the given link
https://brainly.com/question/24375372
#SPJ1
In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by A. Delta y = f(x_1 + x_1, x_2, ....., x_k) - f(x_1, x_2, ... x_k). B. Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k). C. Delta Y = f(x_1 + Delta x_1, x_2 + Delta x_2, ...., x_k + Delta x_k) - f(x_1, x_2, ...., x_k). D. Delta Y = f(x_1 + x_1, x_1, .... x_k).
The expected change in the dependent variable for a change in one of the explanatory variables in a nonlinear model is given by Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k).
Any attribute that can have different values, such as height, age, temperature, or test results, is referred to as a variable in research.
To assess the causality of relationships, researchers frequently modify or measure independent and dependent variables in studies.
The cause is the independent variable. Its value is unaffected by the other study variables.
The effect is the dependent variable. Changes in the independent variable affect its value.
A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.
Dependent variables are also referred to as:
.response elements (they respond to a change in another variable)
.outcome factors (they represent the outcome you want to measure)
.Left-side parameters
To know more about dependent variable visit :
https://brainly.com/question/1479694?referrer=searchResults
#SPJ4
The expected change in the dependent variable for a change in one of the explanatory variables in a nonlinear model is given by Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k).
Any attribute that can have different values, such as height, age, temperature, or test results, is referred to as a variable in research.
To assess the causality of relationships, researchers frequently modify or measure independent and dependent variables in studies.
The cause is the independent variable. Its value is unaffected by the other study variables.
Effect is the dependent variable. Changes in the independent variable affect its value.
A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.
Dependent variables are also referred to as:
.response elements (they respond to a change in another variable)
.outcome factors (they represent the outcome you want to measure)
.Left-side parameters
To know more about dependent variable visit :
https://brainly.com/question/1479694?referrer=searchResults
#SPJ4
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
Read more about perimeter at
https://brainly.com/question/18019422
#SPJ1
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
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.
Learn more about scale factors:
https://brainly.com/question/25722260
#SPJ1
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
To know more about mean and standard deviation visit:
https://brainly.com/question/29262399
#SPJ4
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 )
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
The two graphs shown below detail the results of two independent response polls studying favorite movie genres.
Which genre had the same number of votes in each study?
a. action
b. horror
c. mystery
d. not enough information
Please select the best answer from the choices provided
• A
• B
• C
• D
The genre which had the same number of votes in each study is: B. horror.
What are the types of graph?In Mathematics, there are different types of graph and these include the following:
Box and whisker plotScatter plotBar graphDot graphLine graphHistogramPie chartWhat is a pie chart?A pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.
From the bar chart, the number of votes for horror movie is equal to 40 votes. Next, we would calculate the number of votes for horror movie in the pie chart as follows;
Number of votes = 16/100 × 250
Number of votes = 0.16 × 250
Number of votes = 40 votes.
In conclusion, we can logically deduce that horror is a movie genre that has the same number of votes in each independent study.
Read more on pie chart here: brainly.com/question/23608372
#SPJ1
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.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.
Learn more about probability, visit:
brainly.com/question/24756209
#SPJ1
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.
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
To learn more about variance and standard deviation link is here
brainly.com/question/29758680
#SPJ4
If a random variable that is normally distributed has a mean of 25 and a standard deviation of
3, convert the given value to a z-score.
a. x = 23
b. x = 33
c. x = 19
d. x = 45
Answer:
Step-by-step explanation:
To convert a value to a z-score, you need to subtract the mean and divide by the standard deviation. Here is how to convert each value to a z-score:
a. x = 23: (23 - 25) / 3 = -0.67
b. x = 33: (33 - 25) / 3 = 2.33
c. x = 19: (19 - 25) / 3 = -1.67
d. x = 45: (45 - 25) / 3 = 6.67
Therefore, the z-scores are -0.67, 2.33, -1.67, and 6.67 for values a, b, c, and d respectively.
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]
To learn more about Standard Deviation visit:https://brainly.com/question/23907081
#SPJ1
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
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.
To learn more about confidence interval link is here
brainly.com/question/24131141
#SPJ4
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.
For the following right triangle, find the side length x , round to the nearest hundredth.
Answer: 14.9
Step-by-step explanation:
Pythagoras Theorem States that for any right angled triangle.
a ^ 2 + b^2 = c ^2.
a = 10
b = 11
x = unknown
x^2 = a ^ 2 + b^2
x^2 = (10 * 10) + (11 * 11)
x = sqrt(100 + 121)
x = sqrt(221)
x = 14.9