The solution set of the inequality |x+2| ≤ 5 is x ∈ [-7,3].
What is inequality?
The word inequality means a mathematical expression in which the sides are not equal to each other.
Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.
What is modulus function?The modulus function, which is also called the absolute value function gives the magnitude or absolute value of a number irrespective of the number being positive or negative.
Modulus function is denoted as y = |x| or f(x) = |x|, where f: R→ (0,∞) and x ∈ R.
Here, we have an inequality |x+2| ≤ 5
Solving the modulus , we get
-5 ≤ x+2 ≤ 5
Subtracting -2 from both sides, we get
⇒ -5-2 ≤ x ≤ 5 -2
⇒ -7 ≤ x ≤ 3
⇒ x ∈ [-7,3]
Therefore, the solution set of the inequality is x ∈ [-7,3].
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NOTE : The question given here is not complete. The complete question is given below.
Question: What is the solution set of the inequality |x+2|≤ 5 ?
g at what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 18.4 cm/s? (use decimal notation. give your answer to three decimal places.) rate is cm/s
The diagonal of a cube increasing at a rate of 31.869 cm/s.
It is given that edges are increasing at a rate of 18.4 cm/s.
We know the formula of diagonal of cube which is
D = [tex]\sqrt{3}[/tex] a
where a is the edge.
Now we will differentiate the diagonal equation with respect to time er get,
[tex]\frac{dD}{dt}[/tex] = [tex]\sqrt{3}[/tex] [tex]\frac{da}{dt}[/tex]
Given that edges are increasing at a rate of 18.4 cm/s, this means
[tex]\frac{da}{dt}[/tex] = 18.4 cm/s
Therefore
[tex]\frac{dD}{dt}[/tex] = [tex]\sqrt{3}[/tex] (18.4) cm/s
[tex]\frac{dD}{dt}[/tex] = 1.732(18.4) cm/s
[tex]\frac{dD}{dt}[/tex] = 31.869 cm/s
Hence the diagonal of a cube increasing at a rate of 31.869 cm/s.
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How do you write three consecutive even numbers?.
Three consecutive even integers can be written with difference of two.
The even integers are defined as the numbers that are completely divisible by two. The complete division means that the result of division will be zero. The even integers are always present after a gap of one number in between.
This means that there is a difference of two numbers between integers. Firstly of all, the first even number is two. Following it four. There is a gap of number that is three. Hence, to find the consecutive even integers, add number two to the number.
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Is it possible to have a triangle with 3cm 5cm 8cm?.
No, it is not possible to have a triangle with 3cm 5cm 8cm because the total of the triangle's two sides, 3 cm and 5 cm, is not greater than the third side, 8 cm.
Define triangle.A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Given,
Sides 3cm, 5cm and 8 cm
Three sides are provided, measuring 3 cm, 5 cm, and 8 cm. We are aware that the third side is always greater than the sum of any two triangle sides. The triangle cannot exist because the total of the triangle's two sides, 3 cm and 5 cm, is not greater than the third side, 8 cm.
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:
Ethan needs to add together two whole numbers
and wants to estimate the answer first.
He rounds both numbers to 1 significant figure,
which gives him 300 and 600, and adds them
together to get an estimate of 900.
What is the greatest possible difference
between his estimate and the true answer to the
addition?
The required greatest difference between the estimate and the true value is 45.
Given that,
Ethan needs to add together two whole numbers and wants to estimate the answer first. He rounds both numbers to 1 significant figure, which gives him 300 and 600 and adds them together to get an estimate of 900.
The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.
Here,
For the estimated number 900, the least number that can be rounded to the number 900 is 855,
Now,
Difference = 900 - 855 = 45
Thus, the required greatest difference between the estimate and the true value is 45.
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se strong induction to show that every natural number can be expressed as the sum of distinct powers of 2. (for exam- ple, 21
It is proved that every natural number can be expressed as the sum of distinct powers of 2 using strong induction.
What is natural number?Natural numbers are those in mathematics that are utilized for counting and ordering. Cardinal numbers are those used for counting, while ordinal numbers are those used for ranking. The positive integers, also referred to as non-negative integers, are a subset of the natural numbers. A few examples are 1, 2, 3, 4, 5, 6,.... In other words, the set of all whole numbers other than 0 (i.e., 23, 56, 78, 999, 100202, etc.) is known as the natural numbers.
Here,
The statement is obviously true for n=0.
Assume that we are given an n≥1 and that it is true for all m with 0≤m<n.
When n=2^m then m<n and therefore m=∑k2^pk with finitely many pk, all of them different. It follows that n=∑2^(pk+1) with all pk+1 different.
When n=2^(m+1) with an m as before then n=2^0+∑k2^(pk+1) with all pk+1 different and different from 0.
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find the 3x3 matrix that corresponds to the composite transformation of a scaling by 2, a rotation of 90o about the origin
The 3x3 matrix after composite transformation of scaling by 2, a rotation of 90° about origin is [tex]\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right][/tex].
Let A=[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex] be a 3x3 matrix
scaling the matrix A by 2 then the result will be
[tex]2A=2\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]\\\\=\left[\begin{array}{ccc}2a&2b&2c\\2d&2e&2f\\2g&2h&2i\end{array}\right][/tex]
now, rotating the resultant matrix by 90° in counterclockwise direction about the origin, we get
[tex]=\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right][/tex]
Thus, a 3x3 matrix after composite transformation of scaling by 2, a rotation of 90° about origin is [tex]\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right][/tex]
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Use the marginal tax rate chart to answer the question.
Marginal Tax Rate Chart
Tax Bracket
Marginal Tax Rate
$0–$10,275
10%
$10,276–$41,175
12%
$41,176–$89,075
22%
$89,076–$170,050
24%
$170,051–$215,950
32%
$215,951–$539,900
35%
> $539,901
37%
Determine the effective tax rate for a taxable income of $63,425. Round the final answer to the nearest hundredth.
10%
14.67%
15.18%
22%
The effective tax rate for a taxable income of $63,42 using the marginal tax rate chart rounded to the nearest hundredth is 15.18%.
The correct answer option is option C
What is the effective tax rate?Income = $63,425 and marginal rates
Find tax payable amount:
Tax bracket $0 - $10,275Marginal rate = 10%Amount taxable = $10275 -$0
= $10275
Tax payable = 10% of 10275
= 0.1 × 10275
=$1027.5
Tax bracket $10,276 - $41,175Marginal rate = 12%
Amount taxable = $41,175 - $10,276
= $30899
Tax payable = 12% of 30899
= 0.12 × $30899
= $3707.88
Tax bracket $41,176 - $89,075Marginal rate = 22%Amount taxable = $89,075 - $41,176
= $22249
Tax payable = 22% of 22249
= 0.22 × $22,249
= $4894.78
Total tax payable amount = $10275 + $3707.88 + $4894.78
= $9630.16
Effective tax rate = (Total tax payable amount/ income) × 100
= ($9630.16 / $63,425) × 100
= 15.18%
Therefore, the effective tax rate for a taxable income of $63,425 is 15.18%.
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You are shopping for a new computer monitor. It is regularly priced at $200 but it is now on sale for 25% off. After the sale discount is applied, you can also use your 20% off coupon. What is the final price?.
After calculating the individual discount and coupon percentages of the actual price, we find out that the final price of the new computer monitor is $40.
It is given to us that -
The new computer monitor is regularly priced at $200
It is now on sale for 25% off
After the sale discount, we can also use 20% off coupon
We have to find out the final price of the computer monitor.
The initial price of the new computer monitor = $200
After the sale discount of 25% off is applied to the product, the new price of the monitor can be calculated by finding out
25% of $200 = 0.25 * 200 = $50
Now, after calculating the price of the monitor after the sales discount, we have to find out the final price after the 20% off coupon is applied.
So, 20% of $50 = 0.20 * 50 = $10
So, we can conclude that after the sales discount and after a coupon of $10 off is applied, the final price of the computer monitor is -
$50 - $10
= $40
Thus, calculating the individual discount and coupon percentages of the actual price, we find out that the final price of the new computer monitor is $40.
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What is 18 ÷ 2/3.
What is -5/6÷9/10.
THESE ARE TWO SEPARATE QUESTIONS. 60 points because they are 2. If you figure them both out I will give Big Brain.
Answer:
18 ÷ 2/3 = 27
-5/6 ÷ 9/10 = -0.925
The um of firt 11 term of an A. P i 19 and the um of firt 19 term i 11. Find the um of the firt 30 term
The sum of the first 30 terms of this arithmetic expression (A.P) will be -30.
Let the first term of the Arithmetic progression be a
And the common difference of this progression be d
An be the nth term of the progression
Sn be the sum of the first nth term of the progression
As we know,
Sn = n/2( 2a + (n-1)d)
S11 = 11/2(2a + (11-1)d)
S11 = 11/2(2a + 10d) = 11(a + 5d)
As S11 = 19
Therefore, 19 = 11(a + 5d)
19 = 11a + 55d………….(i)
Again, S19 = 11 = 19/2 ( 2a + 18d )
11 =19( a + 9d)
11 = 19a + 171d………(ii)
Now, multiplying equation (i) by 19 and (ii) by 11 and then subtracting them, we get
361 = 209a + 1045d
121 = 209a + 1881d
240 = -836d
d = -240/836 = -60/209
Putting the value of d in equation (i), we get
11a - 55x60/209 = 19
11a = 3300/209 + 19
11a = 7271/209
a = 661/209
Therefore sum of first 30 terms are S30 = 30/2(2(661/209)+29(-60/209))
S30 = 15(1322/209 -1740/209) = 15 (-418/209) = 15(-2) = -30
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Does an X or y-axis scale have to always start at zero?.
No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero
Define axis.A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.
Given,
No, X or y-axis scale does not have to always start at zero.
A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.
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If $2x-y=7,$ what is the value of $7-8x+4y$?
Answer:
[tex]7-8x+4y=-21[/tex]
Step-by-step explanation:
[tex]2x-y=7 \implies 8x-4y=28 \\ \\ \implies 7-8x+4y=7-28=-21[/tex]
case sales price per unit variable costs per unit total fixed costs break-even in units 1 $20 $16 $40,000 2 25 5 5,000 3 30 81,000 9,000 4 4 48,000 8,000
Case 1: Break-even units are 10000
Case 2: Fixed cost is $1,00,000
Case 3: Variable cost is $20
Case 4: The sale price is $15
Break-even in units = Fixed cost/Selling price - Variable cost
Case 1:
Sales price = $20
Variable cost = $16
Fixed cost = $40,000
Break-even point = 40000/20-16
= 10000 units
Case 2:
Sales price = $25
Variable cost = $5
Break-even units = 5000
Finding fixed cost:
5000 = Fixed cost/25-5
Fixed cost = 5000* 20
= 1,00,000
Case 3:
Sales price = $29
Fixed cost = 81000
Break-even units = 9000
Finding variable cost:
9000 = 81000/29-variable cost
2,61,000 - 9000*Variable cost = 81000
Variable cost = 20
Case 4:
Variable cost = $9
Fixed cost = $48000
Break-even units = 8000
Finding sales price:
8000 = 48000/Sales price - 9
8000*Sales price - 72000 = 48000
Sale price = $15
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What are prime multiples of 10?.
2, 5 are prime multiples of 10 .
What is a number's prime multiple?
Prime numbers can only be divided by one and by themselves and are therefore never less than one. They can't be produced by adding the number to itself or by multiplying it by two additional whole numbers that aren't 1.What are multiples and prime factors?
A number is said to be prime if it only has the factors 1 and itself. Multiple: A number from the provided times table of numbers. Factor: A number that exactly divides another number. The smallest number that appears in the times tables of the given numbers is known as the LCM.Learn more about prime multiple
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1. If f(x) = x + 3 and g(x) = x² + 2x - 3, find [gxf](x).
The answer is g(f(x)) =(x+6)(x+2)
From the question, we have
f(x) = x + 3 and g(x) = x² + 2x - 3
g(f(x)) = g(x + 3)
=(x + 3)² + 2(x + 3) - 3
=x² + 9+6x+2x+6-3
=x² + 8x+12
=x² + 6x+2x+12
=(x+6)(x+2)
The answer is g(f(x)) =(x+6)(x+2)
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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How many solutions does this linear system have Y =- 6x 2?.
The linear system of equation y =-6x+2 has infinitely many solutions.
The linear equation is y = -6x+2 .
Now for any value of x we find the value of y ,
at x=0 ,y = 2
at x=1 , y = -4
at x=-2 , y = 14
Hence there are infinitely many solutions on the line . All points on the straight line are solutions.
The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." In order to model real-world issues, linear equations include unknown quantities as one or more variables.
The locations where the lines or planes used to illustrate the linear equations intersect or meet are known as the solutions. The set of values for each variable in a system of linear equations is known as the solution set.
Disclaimer: the complete question is :
How many solutions does this linear system have Y =- 6x + 2?.
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inductive or deductive all numbers divisible by 6 are also divisible by 3. 36 is divisible by 6. so, 36 is divisible by 3.
Answer:
deductive
Step-by-step explanation:
In triangle ABC points X and Z are in AB and Y is on AC such that XY and BC are parallel and ZY and XC are parallel. If AZ=8, ZX=4, then what is XB?
If length of AZ=8 units and the length of ZX=4, then the length of the side XB is 6 units
Consider the triangle ABC
The points X and Y are on the line AB and Y is on the line AC
The lines XY and BC are parallel
Therefore
AX / XB = AY / YC
Similarly, the lines ZY and XC are parallel
AZ / ZX = AY / YC
Therefore the the proportion will be
AX / XB = AZ / ZX
The length of the line AX = AZ + ZX
= 8 + 4
= 12 units
Then the proportion will be
12 / XB = 8 / 4
Cross multiply the terms
12 × 4 = 8 × XB
XB = (12 × 4) / 8
XB = 48 / 8
XB = 6 units
Hence, the length of the side XB is 6 units
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suppose i have an orgnization that has 60 members, i'm going to pick one person at random to be the president, another person to be the vice president, and a third person to be the treasurer. how many ways can this be done
There are [tex]\frac{60!}{57!}[/tex] ways we can do it.
Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,
the president can be select in 60c1 = [tex]\frac{60!}{1! 59!}[/tex]
= [tex]\frac{60 *59!}{1*59!}[/tex]
= 60 ways
After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.
and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.
∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58
= [tex]\frac{60 * 59 * 58 * 57!}{57!}[/tex]
= [tex]\frac{60!}{57!}[/tex]
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John read the quarter of the time that tom read. Tom read only two-fifth of the time that sasha read. Sasha read twice as long as mike. If mike read 5 hours, how long did john read?.
The required read time taken by the John in the given question is 2 hours.
How ratio help us to solve this problem?A ratio can be characterized as the relationship or examination between two quantities of a similar unit to check how greater is one number than the other one.
According to question:Sasha read = 2(mike read)
given, mike read 5 hours
Then, Sasha = 10 hours
Similarly,
Tom read = (Sasha read)2/5
Tom read = 4 hours
Now, john read = (Tom read)/4 = 4/2
John read = 2 hours
Thus, read time of John is 2 hours.
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A random sample of 49 statistics examinations was taken. The average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examinations is
76.00 to 84.00
77.40 to 86.60
83.00 to 85.00
68.00 to 100.00
The 95% confidence interval for the average examination score of the population of the examinations is (82.99, 85.01).
We have given that,
Sample mean{[tex]\overline x[/tex]} = 84
Sample standard deviation(S) =3.5
Sample size(n) =49
Level of significance=1-0.95=0.05
Degree of freedom =48
t critical value is (by using t table)(t)= 2.011
Confidence interval formula is
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex]
Now putting the value
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}=84\pm 2.011\times\frac{3.5}{\sqrt{49}}[/tex]
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = 84 ± 2.011 × 3.5/7
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = 84 ± 2.011 ×0.5
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = 84 ± 1.01
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = (84-1.01, 84+1.01)
[tex]\overline{x}\pm t\times\frac{S}{\sqrt{n}}[/tex] = (82.99, 85.01)
Lower confidence limit= 82.99
Upper confidence limit=85.01
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Given that the polynomial f(x) has 5 intercepts, which of the following most accurately describes the degree of f(x)? Select the correct answer below: O The degree of f(x) is at most 5. O The degree of f(x) is at least 4. O The degree of f(x) is at most 4 O The degree of (x) is at most 2 O The degree of (x) is at least 2. O The degree of f(x) is at least 5.
The solution is the degree of f(x) is at least 5.
Given info,
The polynomial f(x) has 5 intercepts.
The solution required,
The polynomial f(x) has 5 intercepts.
→ if the function has n intercept then the polynomial function has at least n degrees.
→ There is 5 intercept, then the polynomial function has at least 5 degrees.
→ The degree of f(x) is at least 5.
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Where is the outlier in a data set?.
Answer:
It is data outside what you would expect.
Step-by-step explanation:
An example would be if I asked everyone is a class how many dogs they dad living with them. I would expect to get answers like 0, 1, 2, 3 or 4. If someone answered 115 that would be be an outlier, it is outside all of the data that I have collected.
what is a perpendicular
Answer:
at an angle of 90° to a given line, plane, or surface.
"dormers and gables that extend perpendicular to the main roofline
Step-by-step explanation:
How do you determine if a graph crosses or touches the x-axis?.
Answer:The zeros of a function f correspond to the x-intercepts of its graph. If f has a zero of odd multiplicity, its graph will cross the x-axis at that x value. If f has a zero of even multiplicity, its graph will touch the x-axis at that point.
a triangular parcel of land has sides of lengths 590 feet, 980 feet and 1423 feet. a) what is the area of the parcel of land? area
The area of the parcel of land is 226934.799 square feet.
Given:
a triangular parcel of land has sides of lengths 590 feet, 980 feet and 1423 feet.
a).
Let a = 590 , b = 980, c = 1423 lengths
s = semi-perimeter
= 1/2(a+b+c)
= 1/2(590+980+1423)
= 1496.5
s-a = 1496.5-590
= 906.5
s-b = 1496.5-980
=516.5
s-c = 1496.5-1423
= 73.5
Heron's formula for area:
A = [tex]\sqrt{(s(s-a)(s-b)(s-c))}[/tex]
= √1496.5(906.5)(516.5)(73.5)
= √51499402997.4
≈ 226934.799
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As part of a study of corporate employees, the director of human resources for PNC Inc. wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 35 Cincinnati employees showed they travel a mean of 370 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month. The population standard deviations for the Cincinnati and Pittsburgh employees are 30 and 26 miles, respectively. At the 0.05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees? a. Is this a one-tailed or a two-tailed test? O One-tailed test O Two-tailed test b. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) c. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
1) Given data information.
2) z = (Xcin -Xpit)/ (σ^2cin/n[tex]c_i_n[/tex] + σ^2pit/n[tex]p_i_t[/tex] ) ...(1)
3) [tex]z = \frac{370-380}{\sqrt{\frac{30^2}{35} -\frac{26^2}{40} } } = -1.532[/tex]
[tex]P_v[/tex] = 2 × P(Z < -1.532) = 0.126
4) Comparing the p value with the significance level α = 0.05 we see that
[tex]P_v[/tex] > α so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a wouldn't be a significant difference in the average of the two groups
Given,
In the question:
1) Data given and notation
[tex]X_c_i_n[/tex] = 370 represent the mean for the sample of Cincinnati
[tex]X_p_i_t[/tex] = 380represent the mean for the sample Pittsburgh
σ[tex]_c_i_n[/tex] = 30represent the population standard deviation for the sample Cincinnati
σ[tex]p_i_t[/tex] = 26 represent the population standard deviation for the sample Pittsburgh
[tex]n_c_i_n[/tex] = 35 sample size for the group Cincinnati
[tex]n_p_i_t[/tex] = 40 sample size for the group Pittsburgh
z would represent the statistic (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:
Null hypothesis: μ[tex]c_i_n[/tex] = μ[tex]p_i_t[/tex]
Alternative hypothesis: μ[tex]c_i_n\neq[/tex] μ[tex]p_i_t[/tex]
We have the population standard deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:
z = (Xcin -Xpit)/ (σ^2cin/n[tex]c_i_n[/tex] + σ^2pit/n[tex]p_i_t[/tex] ) ...(1)
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
3) Calculate the statistic
With the info given we can replace in formula (1) like this:
[tex]z = \frac{370-380}{\sqrt{\frac{30^2}{35} -\frac{26^2}{40} } } = -1.532[/tex]
4) Statistical decision
Since is a bilateral test the p value would be:
[tex]P_v[/tex] = 2 × P(Z < -1.532) = 0.126
Comparing the p value with the significance level α = 0.05 we see that
[tex]P_v[/tex] > α so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a wouldn't be a significant difference in the average of the two groups.
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You are facing north. You turn 45 degrees to your left. Take two steps forward. Turn 180 degrees. Turn 45 degrees to your right. Take one step back. Turn 90 degrees to your right. Which one of these statements is true?* You are facing the same direction you started. You are facing east. You are facing south. You are standing on the same spot you started out on. You are facing west.
Answer: Northeast - unless you are at the South Pole, in which case you are still facing North.
Step-by-step explanation
Sequence:
Facing North
90 degrees left = facing West
180 degrees right = facing East
reverse = facing West
45 degrees left = facing Southwest
reverse = facing Northeast
you have weekly store-level unit sales data as well as binary promotion information about if the product was on display or not. you run a linear regression model (yunit.sales
~ xdisplay.promotion. This means that the promotion has a positive effect on unit sales, and the model can accurately predict unit sales based on whether the promotion is present or not.
What are regression models?Regression models are statistical models that are used to forecast a continuous result information based on one or more predictor variables. These models are employed to comprehend how the predictor and outcome variables relate to one another as well as to forecast the result variable. In disciplines like economics, finance, and psychology, regression models are frequently employed to forecast variables like future sales or psychological health. Regression models can be either linear or nonlinear, and they can also have numerous predictor variables. These models typically include an intercept and a slope for each predictor variable, which are used to calculate the predicted outcome.
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Prove the theorem by first setting up a one-to-one correspondence between permutations of nn objects with nini indistinguishable objects of type ii, ii=1, 2, 3, ..., kk, and the distributions of nn objects in kk boxes such that nini objects are placed in box ii, ii=1, 2, 3, ..., kk and then applying that the number of different permutations of nn objects, where there are n1n1 indistinguishable objects of type 1, n2n2 indistinguishable objects of type 2, ...., and nknk indistinguishable objects of type kk is n!n1!n2!...nk!n1!n2!...nk!n!.Theorem: The number of ways to distribute nn distinguishable objects into kk distinguishable boxes so that nini objects are placed into box ii, ii=1,2,...,kk, equals
In every distribution of k boxes containing n distinct objects, where box i receives ni. Let Si stand for the set that includes those ni identifiable items for i = 1, 2,..., k.
Given,
he collection of objects can be expressed equivalently as k, i = 1 Si has the following object types: left| S 1 |right| = n 1S number of items of type 1, left |S2| right| = n 2S number of objects of type 2, and so on.
In this case, type i denotes objects that fit into box i and are therefore interchangeable. By simply permuting these sets, one can obtain all conceivable distributions of objects. kS I 1, 2, and S i
The number of distribution options is equal to the number of these permutations for i=1, 2,..., k.
n!/(n₁!,n₂!...nₐ!)
That is,
In every distribution of k boxes containing n distinct objects, where box i receives ni. Let Si stand for the set that includes those ni identifiable items for i = 1, 2,..., k.
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