The cost of changing the oil and filter during 2021, in total is $1512.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a transportation company has 8 shuttle buses. The company changed the oil and filter of each shuttle three times during the year 2021. If changing the oil and filter each time for each shuttle cost $63.
The cost will be calculated by multiplying the number of buses by the number of times it is changed with the cost of each time change.
Cost = 63 x 3 x 8
Cost = $1512
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A line passes through point (-6, 1) and has a slope of 4/3 write an equation in Ax+By=C
The equation in the form Ax+ By=C is 4x-3y=27 if the line passes through the point (-6, 1) and slope is 4/3.
What is meant by an equation?A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. The word equation and its translations in several languages might have slightly different meanings. For instance, in French, an equation is defined as including one or more variables, whereas in English, an equation is defined as any properly expressed formula that consists of two expressions joined by the equals sign.
The values of the variables that must fulfill the equality to make up the solution are referred to as the unknowns, together with the variables for which the equation must be solved.
Given point is (-6, 1)
Slope m=4/3
The equation of the line is:
y-y₁=m(x-x₁)
y-1=(4/3)(x+6)
3y-3=4x+24
4x-3y=27
Therefore, the equation in the form Ax+ By=C is 4x-3y=27
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PLEASE HELP IM GOING TO FAIL
4. What is the graph of the system? (1 point)
y≤x +4
2x+y≤-4
Answer:
A
Step-by-step explanation:
The answer is option A
Hope this helps :)
Using traditional methods, it takes 100 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 260 students and observed that they had a mean of 99 hours. Assume the standard deviation is known to be 6. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places.
The value of the Test statistic =z=-1.67
We have the value of sigma = 6, n = 260
In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.
Now using the formula of Test static
Test statistic will be: [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]
Where, n = total number of sample = 100
[tex]\bar x[/tex] = mean of the given data
[tex]\mu[/tex] = total number of hours taken to receive a basic driving licence.
So, putting the value given in the question,
We will get the value of test static as:
[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]
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7. Return on equity will not change if the firm increases its use of debt.
The statement "Return on equity will not change if the firm increases its use of debt" is false.
What is return in equity?Return on equity (ROE) is a financial ratio that shows how well a company is managing the capital that shareholders have invested in it. To calculate ROE, one would divide net income by shareholder equity.
Given is a statement, "Return on equity will not change if the firm increases its use of debt".
As we know that, The equity equals the assets minus total debt, a company decreases its equity by increasing the debt, or we can say, when debt increases, the equity decreases and since equity is ROE's denominator, ROE in turns gets a boost.
Hence, the statement "Return on equity will not change if the firm increases its use of debt" is false.
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Need help fast thank you
Calculate the average rate of change between x=-1 and x=1.
Between x=-1 and x=1, the average rate of change is 1.
What is meant by average rate of change?It represents the average change in the function's per-unit value during that time period. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity. As the slope of the straight line that links the two spots, the average rate of change between the two points is determined. Use the formula:
(f(b)-f(a))/(b-a) to get the average rate of change of f(x) between x=a and x=b.
Given line in the figure passes through the points A(4, 0), B(-1, -5)
Let the equation of the line be:
y=mx+ c
Slope m=(-5-0)/(-1-4)
m=1
Therefore, y=x+ c
It passes through (4, 0)
y+ c=0
c=-4
y=x-4=f(x)
f(-1)= -1-4=-5
f(1)= 1-4=-3
The average rate of change=(f(b)-f(a))/(b-a)
=(f(1)-f(-1))/1-(-1)
= -3-(-5)/(1+1)
=2/2
=1
Therefore, Between x=-1 and x=1, the average rate of change is 1.
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a population grows exponential. if it was 3190 initially and after 4 years grew to 3605 what is formula?
The exponential formula that shows population is y = y₀ (1.031)ˣ.
What is an exponential function?An exponential function is a function which can be defined as y = y₀ aˣ, Where 'x' is a variable and 'a' is a constant.
Given that,
The growth of population is exponential.
Also,
The initial population y₀ = 3190.
And after 4 year the population y = 3605.
Use exponential formula
y = y₀ aˣ (1)
Where x = time
Substitute the values in the formula,
3605 = 3190 a⁴
3605/3190 = a⁴
1.13009 = a⁴
a = 1.031
Substitute the value of a in equation (1),
y = y₀ (1.031)ˣ
The required formula is y = y₀ (1.031)ˣ.
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Translate this phrase into an algebraic expression.
19 increased by twice a number
Use the variable n to represent the unknown number.
The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.
What is an algebraic expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.
To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:
Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).
Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.
Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:
19 + 2n
Hence, the expression represents the result of adding 19 to twice a number is 19 + 2n.
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The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.
What is an algebraic expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.
To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:
Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).
Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.
Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:
19 + 2n
Hence, the algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.
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P1.Suppose that the US population is growing by 0.94% each year and continues to grow at this rate everyyear.a. What is the overall growth factor for 30 years of population growth? (Round to 4 decimalplaces.) By what overall percentage will the US population grow over the next 30 years? (Roundto 2 decimal places.)
Answer:
Below
Step-by-step explanation:
.94 % is .0094 in decimal
this exponential growth is like a bank account compounded yearly
factor = ( 1+.0094)^30 = 1.3240
which would represent 32.40% growth
I NEED HELPPPPPPPPPPPPPPPPPP
Answer:
[tex]x = -2[/tex]
Step-by-step explanation:
[tex]\textsf {Square both sides:}\\\\(\sqrt{3x+12} )^2 = 3x + 12\\\\(\sqrt{x+8} )^2 = x + 8[/tex]
(The square of the square root of a value is the value itself
[tex](\sqrt{x} )^2 \;is\;x[/tex])
The original identity then becomes
[tex]3x + 12 = x + 8\\\\3x - x = 8 - 12\\\\2x = -4\\\\x = -4/2\\\\x = -2[/tex]
Question 2 of 10 A tessellation could be created using circles like the one shown below. A. True B. False
Answer:
B. False
Step-by-step explanation:
You want to know if it is true that a tessellation can be created from circles.
TessellationA tessellation is the covering of a plane, using one or more geometric shapes with no overlaps and no gaps.
As the attachment shows, it is not possible to cover a plane with circles, leaving no gaps.
A tessellation cannot be created using circles. The proposition is False.
Liana consumes only beer and chips. Her indifference curves are all bowed inward. Consider the bundles (2,6), (4,4), and (6,2). If Liana is indifferent between (2,6) and (6,2), then Liana must
prefer (4,4) to (6,2).
If Liana is indifferent between the bundles (2,6) and (6,2), then it means that she values these two bundles equally. This means that Liana does not have a preference for one bundle over the other.
If Liana's indifference curves are bowed inward, it means that she is willing to give up more units of one good in order to get more units of the other good, as she moves along the indifference curve. This implies that Liana has a diminishing marginal rate of substitution (MRS) between the two goods.
Therefore, if Liana is indifferent between (2,6) and (6,2), it does not necessarily follow that she prefers (4,4) to (6,2). It is possible that Liana may also be indifferent between (4,4) and (6,2), or she may prefer (6,2) to (4,4). This would depend on the specific shape and location of Liana's indifference curves.
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The mass of a sample of bacteria has increased by 2% each day for the past 10 days. The initial mass was 5 mg. If this growth continues, which equation can be used to determine M, the mass after d days?
The growth of the mass of the sample of a bacteria is represented by the exponential model m(x) = 5 · 1.02ˣ.
How to predict the growth of the mass of the sample of a bacteria
In this problem we find the case of mass of a sample of a bacteria (m(x)), in miligrams growing in time (x), in days. This growth is done exponentially, the exponential model is shown below:
m(x) = m' · (1 + r / 100)ˣ
Where:
m' - Initial mass, in miligrams.r - Growth rate, in percentage.x - Time, in days.We have that the mass of the sample was initially 5 miligrams and grows at a rate of 2 % during 10 days. If we know that m' = 5 mg and r = 2, then the exponential model for the sample is:
m(x) = 5 · 1.02ˣ
The exponential model for the sample of a bacteria is equal to m(x) = 5 · 1.02ˣ.
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Select the correct answer.
A solution to a quadratic function, f, is given below.
-3-51
Which statement is true about the given function?
O
The other solution to function fis 3 - 5i.
The other solution to function fis 3 + 5i.
Function f has no other solutions.
The other solution to function fis-3 + 5i.
Answer:
(d) The other solution to function f is -3 + 5i
Step-by-step explanation:
Given a solution to quadratic function f is -3-5i, you want to know the other solution.
ConjugateThe complex solutions to quadratic equations come in conjugate pairs. That is, if one solution is -3-5i, the other solution will be the same thing with the sign of the imaginary part reversed:
The other solution is -3+5i.
__
Additional comment
This is true only if the quadratic has real coefficients. (We typically don't study any other kind.)
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During one flu epidemic the proportion of adults nationwide who have come down with the flu is 8%. The manufacturer of a flu vaccine claims that those who have been vaccinated are less likely to catch the flu.
The hypotheses are as follows:
Null hypothesis: proportion of those vaccinated catching the flu = 8%
Alternative hypothesis: proportion of those vaccinated catching the flu < 8%
Select one:
A.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8%
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is less than 8%.
B.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is not equal to 8%
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
C.
Rejecting the null hypothesis means there is insufficient evidence that the proportion of those vaccinated catching the flu is equal to 8%
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
D.
Rejecting the null hypothesis means there is evidence that the proportion of those vaccinated catching the flu is less than 8%
Accepting the null hypothesis means there is evidence to conclude that the proportion of those vaccinated catching the flu is equal to 8%.
The test hypothesis is
H₀: p=0.08 (null hypothesis) and
Hₐ: p<0.08 (alternative hypothesis )
Given that,
8% of adults in the country contract the flu at any given time during a flu epidemic. The following are the hypotheses:
0% of people who received the vaccine contracted the flu.
8% or less of people who received the vaccine ended up getting the flu.
In order to reject the null hypothesis, there must be proof that 8% of individuals who received the vaccine did not also get the flu.
If the null hypothesis is not rejected, then there is insufficient data to draw the inference that the proportion of people who receive the flu shot is 8%.
The test hypothesis is H₀: p=0.08 (null hypothesis) and Hₐ: p<0.08 (alternative hypothesis )
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A rally car race course covers 631.95 miles. The winning car completed the course in 7.5 hours. What was the average speed of the winning car?
The average speed of the winning car is 79.38 miles per hour.
Given : Distance covered by rally car race course = 515.97 miles
Time taken to complete the course by winning car = 6.5 hours
The average speed of the winning car = ( Distance covered by rally car race course) ÷ (Time taken to complete the course by winning car)
= (515.97)÷ (6.5) miles per hour
= 79.38 miles per hour
Hence, the average speed of the winning car = 79.38 miles per hour.
What is average speed?Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.Average speed combines two ideas in two words: average, meaning a mean derived from a lot of individual data points, and speed, which is a change in position.You can calculate the average speed for any type of motion if you can time the motion and measure the distance.To learn more about Average speed refer to:
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Amy is going to spend What she saves from her rent budget on entertainment. How much will she’s have for entertainment each month?
Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.
How is the rent budget determined?The total budget for rent, utilities, and food for nine months is given as $12,798.
Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.
This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.
The total budget for rent, utilities, and food for nine months = $12,798
The percentage of the budget for rent = 60%
The amount for rent for nine months = $7,678.80 ($12,798 x 60%)
The monthly rent amount is $853.20 ($7,678.80/9)
Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.
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Question Completion:The percentage of the rent to the total rent, utilities, and food budget is 60%.
in the equation y = 75 - 6x, what is the slope and what is the y-intercept ?
The slope and y intercept of the equation are -6 and 75 respectively.
What is slope?The slope of a line is a number that describes both the direction and the steepness of the line.
Given that, the equation of a line is y = 75 - 6x
Comparing to the standard equation of the line, y = mx+c
m = slope and c is the y intercept.
In the equation, we can see,
The slope (m) = -6
The y intercept (put x = 0) = y = 75 - 6x0
y = 75
Hence, the slope is -6 and y intercept is 75.
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Find x to the nearest tenth.
After using trigonometric function the value of to the nearest tenth digit is 11.11
What is Trigonometric function ?
Trigonometric functions are mathematical functions that are used to describe relationships between certain angles and lengths in a triangle. They are based on the ratios of the sides of a right triangle and are used in a variety of applications including surveying, navigation, engineering, and physics. Trigonometric functions are commonly referred to as sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions can be used to calculate the angle of a triangle, the length of the sides, or the area of the triangle.
Function of Sine
The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.
Sin a =Opp/Hypot = CB/CA
Cos Function
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.
Adjacent/Hypotenuse = AB/CA is the cosine of.
Functional Tan
The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
Tan a = Opposite/Adjacent = CB/BA
In terms of sine and cos, tan is also equivalent to:
Tan = cos a/sin a
Sin 46° = 8/x
x = 8/Sin 46°
x= 8/0.72
x=11.11
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Factor x^3-125 as shown in the image attached
Answer:
Factored form is (x - 5) (x² + 5x + 25)
Step-by-step explanation:
You can get the factors directly by using the formula for a³ - b³.
landon's ice cream machine produced 1.2 cups of ice cream in 3 minutes. If it produced the same amount each minute, how much ice cream did the machine produce during the 2nd minute?
The ice cream that the machine produces during the 2nd minute will be 0.8 cups of ice cream.
How to illustrate the rate?Rate demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Typically, a rate is defined as the ratio of two quantities expressed in different units. The first quantity is typically written as the numerator of a fraction, and the second quantity is written as the denominator. By condensing them into the simplest form possible, we can calculate the rate.
A rate is a ratio that contrasts two distinct quantities represented by various units. A comparison of two numbers with various quantities or units is called a rate. A ratio or a rate out of 100 is what is known as a percentage.
Here, landon's ice cream machine produced 1.2 cups of ice cream in 3 minutes. If it produced the same amount each minute, the ice cream that the machine produces during the 2nd minute will be:
= (1.2 / 3) × 2
= 0.4 × 2
= 0.8 cups.
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What integer is tripled when 9 is added to three-fourths of it?
Answer:
4
Step-by-step explanation:
let n be the integer , then n tripled is 3n, so
[tex]\frac{3}{4}[/tex] n + 9 = 3n ( multiply through by 4 to clear the fraction )
3n + 36 = 12n ( subtract 3n from both sides )
36 = 9n ( divide both sides by 9 )
4 = n
the required integer is 4
19 points all i have really..Gavin is hoping to buy his first car in 3 years. He is considering two options to help him save and grow his money. If he currently has $800, should he deposit his money into a savings account that is compounded annually at an interest rate of 9% or in a savings account that is compounded quarterly at an interest rate of 3%?
Gavin should deposit his money into a savings account that is compounded annually at an interest rate of 9%.
What is compound interest?
The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.
Given that the current balance is $800.
There were two types of schemes.
First scheme offer compounded annually at an interest rate of 9%
Second scheme offer compounded quarterly at an interest rate of 9%.
The formula of compound interest annually is
A = P(1+r)^t
P = principal = 800
r = rate of interest = 9% = 0.09
t = time = 3 year
A = 800(1+0.09)³
A = 1036.02.
The formula of compound interest annually is
A = P(1+(r/n))^tn
P = principal = 800
r = rate of interest = 3% = 0.03
t = time = 3 year
n = 4
nt = 4×3 =12
A = 800(1+0.03/4)¹²
A = 875.04
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The data below shows the numbers of hours Mrs. Diaz works at the library each month fir eight months. The mean of the data set is 22 hours. What is the mean absolute deviation of the data
The mean absolute deviation of the data 20, 12, 27, 23, 18, 20, 30, and 26 will be 4.5.
What is the mean absolute deviation?It is the average distance between each data point and the mean.
The mean absolute deviation is given as
[tex]\rm MAD = \dfrac{\Sigma _{i = 1}^n|x_i - \mu|}{n}[/tex]
The information underneath shows the quantities of hours Mrs. Diaz chipped in at the library every month for a very long time.
20, 12, 27, 23, 18, 20, 30, 26
The mean of the informational index is 22 hours.
Then the mean absolute deviation of the data will be given as,
MAD = [|20 - 22| + |12 - 22| + |27 - 22| + ... + |30 - 22| + |26 - 22|] / 8
MAD = (2 + 10 + 5 + 1 + 4 + 2 + 8 + 4) / 8
MAD = 36 / 8
MAD = 4.5
The mean absolute deviation of the data will be 4.5.
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The complete question is given below.
The data below show the numbers of hours Mrs. Diaz volunteered at the library each month
for eight months.
20, 12, 27, 23, 18, 20, 30, 26
The mean of the data set is 22 hours. What is the mean absolute deviation of the data?
You are making snack bags to sell at the fair. You want each bag to contain the same combination of carrot and celery sticks. You have 75 carrot sticks and 40 celery sticks and want to use them all.
What is the greatest number of snack bags you can make
The greatest number of snack bags is 10.
Highest Common Factor:The largest of all the common factors between two or more numbers is known as the Highest Common Factor (HCF). It is also known as the Greatest Common Element (GCF).
HCF is a fundamental method that allows you to equally distribute items throughout a group or set.
We can use the idea of HCF to determine the same when you are organizing a party and want to make sure that nothing is wasted or you require a proper calculation.
Here we have
Number of carrots = 75
Number of celery sticks = 40
Here we are making snack bags such that each bag contains the same combination of carrot and celery sticks.
To find the greatest number of snack bags we need to find HCF of 70 and 40 as given below
Write given numbers as the product of prime numbers
=> 70 = 2 × 5 × 7
=> 40 = 2 × 2 × 2 × 5
List out the common factors
=> 2 × 5
=> HCF (70, 40) = 10
Therefore,
The greatest number of snack bags is 10.
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14=6+z over -2 whats the answer please i need help
Answer:
Hi!
If you're trying to solve for z, the answer would be -34.
I hope this helps you :)
A line on a graph passes through the points (15,10) and (60,20) what is the slope of the line
Answer:
The slope is 2/9.
Step-by-step explanation:
(15, 10) and (60, 20)
m = 20-10/60-15
m = 10/45
m = 2/9
Please help me with this and show work!! I’ll give brainliest
Answer:
The original price of the tie was 20 dollars
Step-by-step explanation:
The price of the t-shirt was originally 24, but because he bought it on sale, he would have payed 12 because 24x.5=12. This means we can subtract the value payed for the shirt from the total money payed. 22(total)-12(shirt)=. 10 (tie). However, 10 is the price he payed for the tie, not its original value. We can find this by multiplying 10x2, which gives us our answer.
Answer:
20 dollars is the original price
25%498.60 how much in total
TRUE/ FALSE. A researcher compares the BMI of two populations of individuals from different socioeconomic backgrounds and finds that the proportion of individuals considered obese and from a poor background is .37 (n = 112), and the proportion of individuals considered obese and from an affluent background is .27 (n = 87); a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).
True , a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).
The critical value for alpha is 0.05 and z is 1.96 .
The corresponding confidence interval is ( 6.235 , 7.165).
Therefore the above statement is true.
Confidence Interval, to put it simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.
The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.
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