Step-by-step explanation:
greater than 6=0 cause no number on a dice is greater than six
an even number=1/2
less than 4=1/2
HELPPP PLEASE ASPPP!!!!!!
Examine the graph below. Calculate the slope.
Slope of line is 1/2.
What is slope?
In arithmetic, the slope or gradient of a line is a range that describes each the direction and therefore the gradient of the road.
Main body:
to find the slope from a graph , we need to fix two co-ordinates at slope for axis
let point at x be = (40,40)
let point y = (80,60)
Formula for slope ,
m = y₂-y₁/x₂-x₁
m = 60-40/80-40
m = 20/40
m = 1/2
hence , slope of line is 1/2.
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Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)=(x²-64)^{1/11} on the domain [-8,9]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The absolute maximum is , which occurs at x= (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.)
B. There is no absolute maximum.
The absolute maximum is 1.29, which occurs at x= 9
What is absolute extrema?
An absolute extremum of a perform in an exceedingly given interval is that the purpose at that a most or minimum worth of the perform is obtained. Frequently, the interval given is that the function's domain, and therefore the absolute extremum is that the purpose admire the most or minimum worth of the complete perform.
Main body:
Given =
f(x) = [tex](x^{2} -64)^{1/11[/tex]
f' (x) = derivative of function f(x)
f'(x) = 1/11[tex](x^{2} -64)^{-10/11[/tex] . 2x
= [tex]2 \frac{x}{11}[/tex][tex](x^{2} -64)^{-10/11[/tex]
putting f'(x) = 0
2x/11 [tex](x^{2} -64)^{-10/11[/tex] = 0
[tex](x^{2} -64)^{-10/11[/tex] = 0
[tex]x^{2} -64[/tex] = 0
x² = 64
x = ±8
We are given interval [-8,9].
Hence, calculating f(x) at -8, 8, 9.
f(-8) = 0
f(8) = 0
f(9) = [tex]17^{1/11}[/tex]
= 1.29
Hence, absolute maximum value is 1.29 at x=9.
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John paid $280 for a new mountain bicycle to sell in his shop. He wants to price it so that he can offer a 30% discount but still make 10% of the price he paid for it. At what price should the bike be marked?
By using the concept of discount, it can be calculated that
The bike should be marked at $440
What is discount?
Sometimes during sale, the items are sold at a reduced price from the original price of the item. The difference between the reduced price and the original price of the item is called discount.
Price paid by John for a new mountain bike = $280
Markup price = [tex]\frac{10}{100} \times 280[/tex] = $28
Price after markup = $(280 + 28) - $308
Let the marked price be $x
Rate of discount = 30%
Discount = [tex]\frac{30}{100}\times x[/tex]
Price after discount = [tex]x - \frac{30}{100}\times x[/tex]
= [tex]\frac{100x - 30x}{100}[/tex]
= [tex]\frac{70}{100}x[/tex]
By the problem,
[tex]\frac{70}{100}x = 308\\x = \frac{308 \times 100}{70}\\[/tex]
x = $440
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if you roll die, what is the probability of rolling a numbe rless than 4 or rolling an odd number
The probability of rolling an odd number or a number less than 4 is 2/3.
What is probability?
The degree to which something is likely; the probability that something will occur or will be the case.
Here, we have
Given
A single die is rolled.
Sample space = {1, 2, 3, 4, 5, 6}
Let P(A) be the probability of getting an odd number, where A = {1, 3, 5}
Let P(B) be the probability of getting a number less than 4,
where B = {1,2,3}
A ⋂ B ={1, 3}
P(A) = 3/6 = 1/2
P(B) = 3/6 = 1/2
P(A ⋂ B) = 2/6 = 1/3
Let P be the required probability of getting an odd number or a number less than 4
P = P( A ⋃ B ) = P(A) + P(B) - P(A ⋂ B)
P( A ⋃ B ) = 1/2 + 1/2 - 1/3
P( A ⋃ B ) = 1 - 1/3
P( A ⋃ B ) = 2/3
Hence, the probability of rolling an odd number or a number less than 4 is 2/3.
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a circular plate has a radius of 12 inches complete the table included a number and a unit in the last column
The area and the circumference of the circular plate is 452.16 in² and 75.36 in
What is area and circumference of circular plate?
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle. It is typically expressed in units like cm or unit m.a closed circle geometric shape in space. A circle is a locus of a point moving around a fixed point at a defined distance from the point in mathematical terms. A circle is essentially a closed curve with an outer line that is equally spaced from the center.Area of circular plate , A = πr²
=3.14 * 12 * 12
= 452.16 in²
Circumference of the circular plate, C = π * 2r
= 3.14 * 2 * 12
= 75.36 in
Hence, the area and the circumference of the circular plate is 452.16 in² and 75.36 inches.
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Melvin and Sylvia are married with no children, and they're filing their federal income tax return. Melvin had a gross income of $44,500 last year, while Sylvia had a gross income of $51,200, and they plan to use the standard deduction. They're trying to decide whether to file their return jointly or separately, so they want to calculate how much less they would pay in federal income taxes if they filed jointly rather than separately. part 2
Answer: 3702
Step-by-step explanation: from plato
what is the solution for
an= -3an-1-3an-2-an-3, a0=1, a1=0, a2=5
a) (-1-4n+3n^2)(-1)^n
b) (1-4n-3n^2)(-1)^n
c) (1+4n+3n^2)(-1)^n
Answer:
none of the above
(1 -4n +3n^2)(-1)^n
Step-by-step explanation:
You have the recursive relation {a[0]=1, a[1]=0, a[2]=5, a[n]=-3a[n-1] -3a[n-2] -a[n-3]} and you want to know the explicit relation.
Test a fewThe given initial value a[0] = 1 rules out choice A.
The value a[1] = 0 rules out choices B and C.
Actual solutionWe observe that changing the sign of the constant in the first choice will make it match the sequence:
(1 -4n +3n^2)(-1)^n . . . . . . the solution for the recursive equation
Is 5/6 greater than 10/12
Answer:
Step-by-step explanation:
Clearly, it can be seen that 10/12 represents the largest fraction. Hence 5/6 (which is equivalent to 10/12) is larger than 2/3 or 3/4.
Answer: no they are equal either simplified to 5/6 or decimal 0.83 repeating decimal.
Step-by-step explanation:
The classroom outside bag had 5 frisbees in it. If 25% of the outside toys are frisbees, then how many total toys are in the bag?
Answer: 15, not including the frisbees. (The answer would be 20 if the frisbees were in there)
Step-by-step explanation: 25% is equivalent to 1/4, and 5 is equal to 1/4. The simplest way to solve this is to multiply 5 by 4, and you'll get 20. Then subtract 5 (the frisbees) and you'll get 15. (Sorry if that doesn't make much sense haha) Hope this helps!!
Are the two expressions x-5 and x-5 equivalent? Give evidence to support your yes or no answer.
Remember, for expressions to be equivalent, they must have the same value for all values of the input
variable, x.
The expressions x - 5 and x - 5 gives the equal value for the different values of x, therefore expressions are equivalent.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expressions are,
x - 5 and x - 5
To determine the expressions are equivalent,
Since, in the both, the expression x is a variable, and 5 is an integer,
Therefore, for the values of x the value of expression should be equal.
Substitute x = 0,
x - 5 = 0 - 5 = - 5
And
x - 5 = 0 - 5 = - 5
Substitute x = 1
x - 5 = 1 - 5 = - 4
and
x - 5 = 1 - 5 = - 4
Since, for the different values of x the values of expressions are equal.
Hence, expression x - 5 and x - 5 are equivalent.
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What is the length of side AB? please help
top I think he or she is right
The length of the AB in the given right triangle is √3/6
Given that, a right triangle with the base measure 6 units and an acute angle 30°,
We need to find the measure of side AB,
So, we will use the concept of trigonometric ratios,
Tan 30° = AB / AC
Tan 30° = AB / 6
1 / √3 = AB / 6
AB = √3/6
Hence the length of the AB in the given right triangle is √3/6
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7.) Given the following triangle, what is the value of x and the value of y ?
Answer: x = 36; y = 36
Step-by-step explanation:
This is an isosceles triangle, so the 2 "bottom" angles are equal:
2x = 72
x = 72/2 = 36
sum of interior angles = 180
180 - 72 - 72 = 36
Write the expression x2 - 6x-2 in the form (x + a)² + b
Answer:
(x - 3)² - 11--------------------------
GivenExpression x² - 6x - 2.Convert this to vertex form by completing the square.
Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:
x² - 6x - 2 = x² - 2*3*x + 3² - 3² - 2 = (x - 3)² - 9 - 2 = (x - 3)² - 11Answer:
[tex](x-3)^2-11[/tex]
Step-by-step explanation:
Given quadratic expression:
[tex]x^2-6x-2[/tex]
To write the given expression in the form (x + a)² + b, complete the square.
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies x^2-6x+\left(\dfrac{-6}{2}\right)^2-2-\left(\dfrac{-6}{2}\right)^2[/tex]
Simplify:
[tex]\implies x^2-6x+\left(-3\right)^2-2-\left(-3\right)^2[/tex]
[tex]\implies x^2-6x+9-2-9[/tex]
The first three terms x² - 6x + 9 form a perfect square trinomial.
A perfect square trinomial can be written as the square of a binomial.
Factor the perfect square trinomial:
[tex]\implies(x-3)^2-2-9[/tex]
Simplify:
[tex]\implies(x-3)^2-11[/tex]
Therefore, the given expression written in the form (x + a)² + b is:
[tex]\boxed{(x-3)^2-11}[/tex]
Question content area top Part 1 A motorboat is capable of traveling at a speed of 10 miles per hour in still water. On a particular day, it took 15 minutes longer to travel a distance of 6 miles upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that day? PLEASE HURRY
We can determine the stream's current velocity by solving a set of equations, which gives us S is 2 mi/h.
Calculate the stream's current flow rate on that particular day?The total speed of a motorboat traveling downstream is equal to the speed of the boat in still water plus the speed of the stream, whereas the total speed of a motorboat traveling upstream is equal to the speed of the stream minus one.
Therefore, the speed upstream is: (14 mi/h - S)
The speed downstream is (14 mph + S), where S is the stream's current flow rate.
We can construct the equations below after we know that it takes 15 minutes longer to walk 12 miles downstream:
14 mph plus speed (S) times the time (T minus 15 minutes) equals 12 miles.
In order to solve this, one of the variables in one of the equations needs to be isolated. I'll isolate T in the first equation:
T = (12 miles)/(14 miles per hour Plus S)
By substituting it in the other equation, we will obtain the following value: (14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi.
Taking only the favorable outcome, we obtain:
S = (24 - 25)/(-0.5) = 2 mph
2 mi/hr is the stream's current velocity.
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A person works at a vegetable farm and a paddy field. He earns Rs 200/- per hour from
vegetable farm and Rs 250/- per hour from paddy field. Last week, he worked for both jobs for a total of 30 hours, and earned a total of Rs 6900/-. How long did the person work at the vegetable farm last week, and how long did he work at the paddy field.. ?
Answer:
He worked 26 hours at the vegetable farm and 4 hours at the paddy field.
Step-by-step explanation:
Let us take the working hour at a vegetable farm be x and at paddy field be y
He worked for both jobs for a total of 30 hours.
So,
x + y = 30 ...(1)
He earns Rs 200/- per hour from vegetable farm and Rs 250/- per hour from paddy field, total of Rs 6900.
So,
200x + 250y = 6900
2x + 5y = 138 ...(2)
From equation 1 we get,
x = 30 - y
Put the value of x = 30 - y in equation 2 we get,
2x + 5y = 138
2(30 - y) + 5y = 138
60 - 2y + 5y = 138
60 + 3y = 138
3y = 138 - 60
3y = 78
y = 26
Now, put the value of y in equation 1 we get,
x + y = 30
x + 26 = 30
x + 26 - 26 = 30 - 26
x = 4
Thus, He worked 26 hours at the vegetable farm and 4 hours at the paddy field.
Please do this I have to turn it in to pass
Answer:
I've solved all of the above for you :)
Step-by-step explanation:
3q² + 7 = 55
3q² = + 7 - 7 = 55 - 7
3q² = 48
3q²/3 = 48/3
q² = 12
q = 2√3
√p - 4 = - 5
p - 4 = (-5)²
p - 4 + 4 = 25 + 4
p = 29
5√a/2 = 40
5√a/2 × 2 = 40 × 2
5√a = 80
5√a/5 = 80/5
√a = 16
a = 256
c³ - 4 = 23
c³ - 4 + 4 = 23 + 4
c³ = 27
c = 3
(k + 3)² = 4
k² + 6k + 9 = 4
k² + 6k + 9 - 4 = 0
k² + 6k + 5 = 0
k² + k + 5k + 5 = 0
k(k + 1) + 5(k + 1) = 0
(k + 5) (k + 1) = 0
k = (-5) or (-1)
√s + 4 = 6
s + 4 = (6)²
s + 4 - 4 = 36 - 4
s = 32
(√f - 5) = (√7 - f)
(√f - 5)² = (√7 - f)²
f - 5 = 7 - f
f - 5 + 5 + f = 7 + 5 - f + f
2f/2 = 12/2
f = 6
∛j + 9 = 0
∛j + 9 - 9 = -9
∛j = (-9)
j = (-9)³
j = (-729)
b² - 1 = 24
b² - 1 + 1 = 24 + 1
b² = 25
√b² = √25
b = 5
13 = (w - 2)² + 5
13 = w² - 4w + 4 + 5
13 - 9 = w² - 4w
w² - 4w = 4
w² - 4w - 4 = 0
w² - 2w - 2w - 4 = 0
w(w - 2) - 2(w - 2) = 0
(w - 2) (w - 2) = 0
w = 2 or 2
12 = 4√2x + 1
12/4 = 4√2x + 1/4
3 = √2x + 1
√2x + 1 = 3
2x + 1 = 9
2x + 1 - 1 = 9 - 1
2x/2 = 8/2
x = 4
(g + 1)³ = (-8)
g³ + 1³ + 3g(g + 1) = (-8)
g³ + 1 + 3g² + 3g = (-8)
g³ + 3g² + 3g = (-8) - 1
g³ + 3g² + 3g = -9
g³ + 3g² + 3g + 9 = 0
g = (-3)
∜(5m + 1) = 4
[∜(5m + 1)]⁴ = (4)⁴
5m + 1 = 256
5m + 1 - 1 = 256 - 1
5m/5 = 255/5
m = 51
∛(y³ - 19) = 2
(y³ - 19) = (2)³
y³ - 19 = 8
y³ - 19 + 19 = 8 + 19
y³ = 27
y = 3
Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)
The compound interest is 61.342 years.
What is compound interest?
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
To find the time period the interest must be compounded quarterly.
Calculated twelve times a year is interest that is compounded monthly. Interest is calculated on a quarterly compound basis, four times a year.
Given that;
A = 1700 P = 500
r = 2% n = 4
= 2/100
r = 0.02 /year
Using the formula A=P(1+r/n)ⁿt find the time period (t)
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.02/4)] )
t = ln(1,700.00/500.00) / ( 4 × [ln(1 + 0.005)] )
t = 61.342 years
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Hassan is cooking some rice the recipe says he needs 450 grams of rice for 6 people how many kilograms or rice would he need for 18 people?
Answer:
450 g = 6 people
? kg = 18 people
450 x 18 = 8100
8100 = 6x
8100/6 = 6x/6
x = 3150 kg of rice is needed for 18 people.
Suppose you can afford to pay $ 325 a month for 9 years towards a new car with no down payment. If the current interest rates are 4.75%, how expensive a car can you afford?
Car sticker price =
Based on the given parameters, the car would be $497.9 expensive in 9 years
How to determine the amount in nine years?The given parameters about the compound interest are
Principal Amount, P = $325Interest Rate, R = 4.75%Time, t = 9 yearsCompound interests are different from simple interest, and they are calculated using the following compound interest formula
CI = P(1 + R)^t - P
To calculate the amount, we have:
A = P + CI
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this case, we introduce the variable n
So, we have
A = P(1 + R/n)^nt
Where n is the number of times in a year
i.e. n = 12
Substitute the known values in the above equation
A = 325 * (1 + 4.75%/12)^(12 * 9)
Evaluate the percentages and the quotients
A = 325 * (1 + 0.0039583)^(108)
Evaluate the sum
A = 325 * (1 .0039583)^(108)
Evaluate the exponent
A = 325 * 1.532
Evaluate the product
A = 497.9
Hence, the value of the investment after 9 years is $497.9
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16
22
34
52
76
?
Select one:
a.
106
b.
137
c.
89
d.
105
Answer:
106
Step-by-step explanation:
The pattern goes +6, +12, +18, etc
Thus, the final term is simply +30.
76+30 = 106
Hope it helps :) and let me know if you want me to elaborate.
tell how you can use the structure of mathematics to complete the task
Answer: It is crucial for students to look for and make use of a structure because this practice requires them to reason about the underlying mathematical structure and unity of mathematics ideas.
bus company uses a grid to locate bus stops. The bus station is at (3, 4). The point (7, 6) represents the first bus stop. The location of each stop after that is determined using the same relationships as those between the coordinates of the bus station and the first bus stop. A coordinate plane is titled Which point represents the fourth bus stop? A. (11, 8) B. (13, 12) C. (15, 10) D. (19, 12) 7 / 7 6 of 7 Answered
Answer:
I think that's 11,8
Step-by-step explanation:
Hope its right
Select the correct answer. What happens if the correlation coefficient equals 0? A. There is a strong negative linear relationship between x and y. B. There is not a linear relationship between x and y. C. There is a strong positive linear relationship between x and y. D. There is a weak negative linear relationship between x and y. Reset Next
By the Definition of a Correlation Coefficient,
x and y do not have a linear relationship.
Option B is the correct answer.
What Is the Definition of a Correlation Coefficient?The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.
What does a correlation between 0 and +1 mean?The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.
According to the question, If the correlation coefficient is zero, there is no linear relationship.
If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.
By the Definition of a Correlation Coefficient,
Option B is the correct answer.
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By the Definition of a Correlation Coefficient, X and Y do not have a linear relationship. Option B is the correct answer.
What Is the Definition of a Correlation Coefficient?The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.
What does a correlation between 0 and +1 mean?The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.
According to the question, If the correlation coefficient is zero, there is no linear relationship.
If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.
By the Definition of a Correlation Coefficient,
Option B is the correct answer.
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DIRECTIONS: Use this information to answer Parts A and B.
A faucet supplies water at a constant rate. After 3 minutes, the faucet supplies 12 liters of water.
Part A
Use the Line Tool to graph the proportional relationship that gives the number of liters of water the facet supplies, y, after x minutes.
The required proportional relationship is given as y = 4x and shown in the graph.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
According to the question,
The proportional relationship gives the number of liters of water the facet supplies, y, after x minutes,
y = kx - - - - - (1)
Put x = 3 so y = 4
12 = k[3]
k = 4
From equation 1,
y = 4x
Thus, the required proportional relationship is given as y = 4x and shown in the graph.
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Suppose your gross monthly income is $6,500 and your current monthly payments are $525. If the
bank will allow you to pay up to 38% of your gross monthly income (less current monthly payments)
for a monthly house payment, what is the maximum loan you can obtain if the rate for a 25-year
mortgage is 8.65%?
The maximum loan you can obtain if the rate for a 25-year mortgage is 8.65% is $298,853.76
How to find monthly payment?A monthly payment can be calculated as;
Monthly payment = (Monthly income - payment)(percentage payment)
38% of your gross monthly income is
0.38 × $6,500 = $2470
If you're already spending $525 on monthly payments, the amount the bank says you can afford for a mortgage loan;
Then
$2470-525= $1945
The amortization formula can be used to find the corresponding loan value.
A = P(r/25)/(1 -(1 +r/25)^(-25t))
where A is the monthly payment on a loan of P at interest rate of r for time t years.
Filling in the known values, we have ;
1945= P(.0525/25)/(1 -(1 +.0525/25)^(-12·30))
≈ 0.00515636808·P
Then the maximum loan can obtain is
P = $1945/0.00515636
P ≈ $298,853.76
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a building has a height of 250 in length of 160 m on a scale drawing of the building the height is 50 cm what is the length of the building on the scale drawing a centimeters
The required length of the building is given as 32 cm.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
The height of the building is 250 meters, the length of the building is 160m, and on the drawing, the height of the building is 50 cm,
Scale factor = height on drawing / original height
Scale factor = 50 / 250
Scale factor = 1/5
Now,
Length in drawing = scale factor × original length,
length in drawing = 1 / 5 × 160
= 31
Thus, the length of the building as of the scale factor 1/5 is given as 31 cm.
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Write a function g whose graph is a horizontal shrink by a factor of 1/3
of the graph of f. F(x)=2|x+3|-2
Answer:
g(x) = 6|x + 1| - 2-----------------------------------------
Given:
Function f(x) = 2|x + 3| - 2Find a function g which is a horizontal shrink by a factor of 1/3 of f(x).
Horizontal shrink by a factor of k is:
g(x) = f(x/k)Apply this to the given function:
g(x) = f(x : 1/3) = f(3x) = 2|3x + 3| - 2 = 6|x + 1| - 2Solve x2 = 36 for x.
Answer:
x=18
36/2=18
all good.
Help Please! This is 6th grade k12
Answer:Put a one under the five then sop he last faction and start multiplying
Step-by-step explanation:
A sample of 38 observations is selected from one population with a population standard deviation of 3.0. The sample mean is 100.5. A sample of 50 observations is selected from a second population with a population standard deviation of 5.2. The sample mean is 98.8. Conduct the following test of hypothesis using the 0.02 significance level.
P value?
A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
What is the hypotheses in research?A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.Hypotheses are used to support scientific research and create breakthroughs in knowledge. These brief statements are what form the basis of entire research experiments. Thus, a flaw in the formulation of a hypothesis may cause a flaw in the design of an entire experiment.a. two-tailed test
b. reject H0 if Z>1.96 or Z<-1.96
c. Z = 1.73
d. we have failed to reject the null hypothesis
e. P-value = 0.0418
We will use a Z test to resolve this, an it will be a two-tailed test because the hypothesis statements are not indicating a specific direction for the significant difference (H0 : μ1 = μ2 ; H1 : μ1 ≠ μ2), this also means that the significanclevel will be divided between the both tails (2.5% en each tail for the rejection regions). See attached drawing for reference.We need to find our critical value:
Zα/2 = Z(0.05/2) = 0.025
If we look for 0.025 in a Z table we will find that the critical value is 1.96 to the right, and by symmetry -1.96 to the left. So our decision rule will be to reject H0 if Z>1.96 or Z<-1.96The Z test will be done using the next equation:
Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2
Because we are testing the null hypothesis we know that μ1 - μ2 must be zero if they are supposed to be equal (H0 : μ1 = μ2), so we calculate as follows:Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73
Z<1.96, therefore we have failed to reject the null hypothesis
The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis
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