Therefore ,we reject the null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0
What is standard deviation ?The square root of the variance is used to calculate the standard deviation, a statistic that gauges a dataset's dispersion from its mean. The standard deviation, which is proportional to the square root of variance, is calculated by comparing the variance of each data point to its mean.
Here,
The null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0
Alternate hypothesis , [tex]H_{A}[/tex]= [tex]u_{d}[/tex] ≥ 0
thus,
[tex]d^{'}[/tex]=(14 + 11 + 7 + 11 -2 + 5 + 0 +5)/9
[tex]d^{'}[/tex]=4.44
[tex]S_{d}[/tex]=6.747
t=[tex]\frac{d^{'}-D}{\frac{S_{d}}{\sqrt{n} } }[/tex]
Putting values in above equation
[tex]d_{f}[/tex]=9-1=8
α=0.10 => t(0.1,8)
t=[tex]\frac{d^{'}-D}{\frac{S_{d}}{\sqrt{n} } }[/tex] = 1.397
Therefore ,we reject the null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0
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the length, x centimeters, of eels in a river may be assumed to be normally distributed with mean 53 and standard deviation 7. an angler catches an eel from the river. determine the probability that the length of the eel is less than 62 centimeters. round your answer to four decimal places.
The probability that the length of the eel is less than 62 centimeters is 0.0985.
In the given question, the length, x centimeters, of eels in a river may be assumed to be normally distributed with mean 53 and standard deviation 7.
An angler catches an eel from the river.
We have to determine the probability that the length of the eel is less than 62 centimeters.
Eels in a river may be assumed to be normally distributed with mean = μ = 53
Eels in a river may be assumed to be normally distributed with standard deviation = σ = 7
Now the probability that the length of the eel is less than 62 centimeters is
P(x > 62) = 1 - P(x < 62)
P(x > 62) = 1 - P((x - μ)/σ < (62 - 53)/7)
P(x > 62) = 1 - P(z < 1.29)
P(x > 62) = 1 - 0.9015
P(x > 62) = 0.0985
Hence, the probability that the length of the eel is less than 62 centimeters is 0.0985.
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the system below shows a periodic function and an absolute value function. how many solutions does the system have?
The system that contains periodic function and an absolute value function has two solution
In the given system there are two function, those are periodic function and absolute value function
The function is defined as the statement that shows the relationship between one dependent variable and other independent variables. The function consist of different types of variables numbers and the mathematical operators
The periodic function is a function that repeats its value at a regular interval of time
The absolute value function is a function that contains the mathematical expression with absolute value symbols
The system contains periodic and absolute value function and it will contains two solution
Therefore, the system has two solution
I have solved the question in general, as the given question is incomplete
The complete question is:
The system below shows a periodic function and an absolute value function. how many solutions does the system have?
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a tank contains 1,000 l of brine with 16 kg of dissolved salt. pure water enters the tank at a rate of 10 l/min. the solution is kept thoroughly mixed and drains from the tank at the same rate. (a) how much salt is in the tank after t minutes?
The salt that is left after t minutes is y = 16e^[-t/100]
We have to mix problems we use:
dy / dt = (rate in) - (rate out)
The water entering the tank at a speed of 10 L / min but it has no salt, therefore
rate in = 0
The tank has 1000 liters of brine with 16 kg of salt initially, therefore the concentration of salt at time "t" is:
y (t) / 1000
then rate out would be:
rate out = y (t) / 1000 * 10 = y (t) / 100
The difference equation would then be:
dy / dt = 0 - y (t) / 100
1 / y (t) * dy = 1/100 * dt
We integrate from both sides and we have:
ln y = - (1/100) * t + C1
y = e ^ [- (1/100) * t + C1]
y = e ^ [- (1/100) * t] * e ^ [C1]
We assume that C = e ^ [C1]
Thus:
y = C * e ^ [- (1/100) * t]
now y = 16 to t = 0, replacing:
16 = C * e ^ [- (1/100) * 0]
16 = C, therefore we would have:
y = 16*e ^ [- t / 100]
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What is the approximate total length of iron edging needed to create the square frame and the two diagonals?
43.5 inches
50.9 inches
54.0 inches
61.5 inches
The approximate total length of iron edging needed to create the square frame and the two diagonals is 43.5 inches. So, option A is correct.
What is a diagonal?When two vertices of a polygon or polyhedron are not on the same edge, a diagonal in geometry is a line segment that connects them. The term "diagonal" is a colloquial term for any sloping line.
The elements on the line connecting the top left corner and bottom right corner of a square matrix make up the diagonal of a matrix in matrix algebra.
Given, The diagonal of a square is 9 inches.
The side of the square be x as we have assumed.
We have to apply Pythagoras theorem for Δ ABC
AB²+BC²=AC²
x²+x²=9²
x=9/√2
We know that the diagonals in the square bisect each other.
OA = 4.5 inches=OC
OD = 4.5 inches=OB
Therefore, the total length of iron edge that is required for the window is:
=4×Length of square+2 diagonals
= 4×6.36+2×9=43.46 inches
The approximate total length of iron edging needed to create the square frame and the two diagonals is 43.5 inches.
Hence, option A is correct.
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Luke has blue and red ballsEvery day he wins 2 blue balls and loses 3 red onesAfter 5 days he has the same amount of blue and red ballsAfter 9 days, he has twice as many red balls as blue ballsHow many red balls did he have at the beginning?
The number of red balls Luke has at the start is 47.
blue ball per day = 2
red ball per day = -3 ('-' ve sign as he is loosing them)
let the number of red balls be represented by r
let the number of blue balls be represented by b
after 5 days
b+ 10 = r -15 -(i)
After 9 days
b + 18 =2(r-27)-(ii)
subtracting (i) from (ii)
b + 18 - b - 10 = 2r - r - 54 +15
8 = r - 39
r = 39 + 8
r = 47
The number of red balls Luke has at the start is 47
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Is 9 hundredths greater than 6/10
Step-by-step explanation:
9 hundredths = 9/100
is 9/100 > 6/10 ?
let's bring both to 1/100
9/100 > 6×10/100
9/100 > 60/100
no, this is wrong. 9/100 is not greater than 60/100 (or 6/10).
9/100 would be greater than 6/100. but not greater than 6/10.
Claudia spends $2.00 a day for lunch. Her cafeteria lunch account has a balance of $48.00. How many days, d, can Claudia eat without adding money to her lunch account?
Answer:
24 days
Step-by-step explanation:
you have to divide the balance by the spending money, so £48.00, divided by £2.00 will equal 24 meaning, Claudia can last 24 days without adding money to her account
Graph the function g(x)=2f(x-1)
x f(x)
0 0
-2 -4
4 -2
You need to draw y = 2 f (x-1)
So you need to choose x so that x-1 = 0, -2, 4 then you can use the above values.
New function
x-1 = 0, x = 1, y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0
x-1 = -2 x = -1 y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8
x-1 = 4 x = 5 y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4
So 3 points on the new graph are (1, 0) (-1, -8) and (5, -4)
Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move) y = f(x) a units to the right.
y = f(x) to y = 2 f(x), you dilate f(x) with center (0,0) factor 2, so (a,b) > (2a, 2b)
So basically here you are doing both things.
So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b).
what is graph?
A diagram or pictorial depiction of facts or values that is arranged might be referred to as a graph. The relationships between two or more items are frequently represented by the points on a graph.
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elect the correct answer. Which system of equations is satisfied by the solution shown in the graph? A coordinate plane linear graph on inequalities in which a line intersects Y-axis at 6 and another line intersects y-axis at 10. Both lines intersect X-axis at minus 2 and Y-axis at 8. A. x + 2y = 6 and x − y = 10 B. x + y = 6 and x − 2y = 10 C. x + 2y = 10 and x − y = 6 D. x + y = 6 and x − y = -10
We can factor this polynomial with 4 terms without grouping.
What is factor?Factor is a thing that influence decision or the situation.
How to factor polynomials with 4 term without groupingLet P(x) be a polynomial with four terms.
To factor P(x) without grouping, substitute
x = -1, 1, -2, 2, -3, 3.......
P(-1) = 0 ----> (x + 1) is a factor of P(x)
P(1) = 0 ----> (x - 1) is a factor of P(x)
P(-2) = 0 ----> (x + 2) is a factor of P(x)
P(2) = 0 ----> (x - 2) is a factor of P(x)
If P(-1) ≠ 0, then (x + 1) is not a factor of P(x).
Then, try x = 1, x = -2, x = 2 and so on.
Once one of the linear factors of P(x) is found, the other factors can bound easily (the rest of the process has been explained in the following examples).
Factor the following polynomials without grouping :
d as (x2 + ax + b).
Then,
(x + 1)((x2 + ax + b) = x3 - 2x2 - x + 2
Comparing the coefficients of x and constants,
b + a = -1 ----(1)
b = 2
Substitute b = 2 in (1).
2 + a = -1
a = -3
x2 + ax + b = x2 - 3x + 2
Factors of (x2 - 3x + 2) are (x - 1) and (x - 2).
Therefore,
x3 - 2x2 - x + 2 = (x + 1)(x - 1)(x - 2)
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y=-1/2X
thank you for your time
A Birr 1,000 deposits is made at a bank that pays 12% interest compounded monthly. How much will be in the account at the end of 10 years?
Answer:
$15400
Step-by-step explanation:
1 year = 12 month
10 years = 120 months
12% = month
1440% = 120 months
1440% = 14.4
Take 1000 times 14.4 = $14400
So, we add the two numbers
1000 + 14400 = $15400
So, $15400 will be in the account at the end of 10 years.
How do you write 82 in scientific notation?
The way is...
m x 10n
Ava made 5% of her free throws over the season. If she shot 120 free throws,
how many did she make?
The free throws she made by an accuracy of 5% in 120 is a total of 6
How to determine how many of the free throws she make?The given parametes from the question are
Free throw made = 5%
Total number of free throws = 120
The above means that we multiply the percentage of free throws made by the total number of free throws to determine the count of free throws made
Having mentioned that, we have
Free throw made = 5% * Total number of free throws
So, we have
Free throw made = 5% * 120
Evaluate
Free throw made = 6
Hence, she made 6 of 120 free throws
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AABC has vertices A(2, 1) B(4, 4) and C(4,1) . ADEF has corresponding vertices D(7, 3)
E(9, 6) and F(9, 3) Which of the following describes a translation that would produce ADEF from the pre-image of triangle ABC ?
To the right five units, and up two units To the left five units, and down two units
To the left five units, and up two units
To the right five units, and down two units
A statement which describes a translation that would produce ΔDEF from the pre-image of triangle ΔABC include the following: A. To the right five units, and up two units.
What is a translation?
In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.
Next, we would determine the translation rule as follows;
ΔABC → ΔDEF = (2 + 5, 1 + 2) = D (7, 3)
ΔABC → ΔDEF = (4 + 5, 4 + 2) = E (9, 6)
ΔABC → ΔDEF = (4 + 5, 1 + 2) = F (9, 3)
Therefore, the translation rule is given by this mathematical expression ΔABC → ΔDEF = (x + 5, y + 2). This ultimately implies that, triangle ABC (ΔABC) was translated by five units to the right and up two units in order to produce triangle DEF (ΔDEF).
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How do you simplify the fraction 10/20?
Answer:
by dividing
Step-by-step explanation:
by dividing them by a same factor that they both have like 2.
1. Stephen has discovered a blow-out sale at the music store in the mall. The cost of 3 sets of guitar
strings, 2 guitars, and 2 amps is $472. The cost of 2 sets of guitar strings and 1 guitar is $212. The cost
of 4 sets of strings and 1 guitar is $322. If x represents sets of guitar strings, y represents guitars, and z
represents amps, write a system of equations that can be used to determine the sale price of the sets
of strings, the guitars, and the amps? What is the cost for each amp?
Each amp costs_____?
The system of equations that can be used to determine the sale price of the sets of strings, the guitars, and the amps.
3x + 2y + 2z = 472
2x + y = 212
4x + y = 322
The cost of each amp is $51.
What is an equation?An equation is a mathematical statement made up of two expressions connected by an equal sign.
We have,
3x + 2y + 2z = 472 ____(1)
2x + y = 212 ____(2)
4x + y = 322 ____(3)
From (2) and (3) we get,
Multiply 2 on (2).
4x + 2y = 424
4x + y = 322
(-) (-) (-)
y = 102
Now,
2x + y = 212
2x = 212 - y
2x = 212 - 102
x = 110/2
x = 55
Now,
x = 55
y = 102
From (1) we get,
3x + 2y + 2z = 472
3 x 55 + 2 x 102 + 2z = 471
165 + 204 + 2z = 471
2z = 102
z = 51
Thus,
The system of equations that can be used to determine the sale price:
3x + 2y + 2z = 472
2x + y = 212
4x + y = 322
The cost of each amp is $51.
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g an epidemic of measles has started at what rate is the modeled by the funtion p epidemic spreading after 3 days
The modeled epidemic rate cannot be determined from the information provided.
The rate of an epidemic spreading is a complex process that is influenced by many factors such as the population density, the number of people who are vaccinated, and the infectiousness of the virus. Therefore, it is not possible to accurately model the rate of an epidemic spreading after 3 days based on the information provided. To accurately model the rate of an epidemic spreading, additional information such as the population density, the number of people who are vaccinated, and the infectiousness of the virus would be needed.
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Look carefully at the diagram.
The value of y is ___ °
The value of y in the triangle is 20°
How to find the value of y in the triangle?Consider the labeling on the image I attached
Since vertically opposite angles are equal. Thus:
x = 50°
Since the sum of angles on a straight line is 180°. Thus:
t + 70° = 180°
t = 180°-70°
t = 110°
Since the sum of angles in a triangle is 180°. Thus:
x + t + y = 180°
50 + 110 + y = 180°
160 + y = 180
y = 180 - 160
y = 20°
Therefore, the value of y is 20°
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Determine a series of transformations that would map polygon ABCD onto polygon A'B'C'D'?
Therefore , Due to a sequence of transformations, polygon ABCD will therefore overlap polygon A'B'C'D'.
What is polygon?A polygon is a closed, two-dimensional, flat or planar structure that is circumscribed by straight sides. There are no curves on its sides. The edges of a polygon are another name for its sides. A polygon's vertices (or corners) are the places where two sides converge.
Here,
a 4 unit translation to the left after reflecting polygon ABCD across the x-axis.
The coordinates for point A in the polygon ABCD are (1, -5).
ABCD's polygon should be mapped onto A'B'C'D',
Reflect the ABCD polygon across the x-axis in accordance with the rule,
A(x, y) → A'(x, -y) (x, -y)
Following this criterion, A's coordinates will be,
A(1, -5) → A'(1, 5) (1, 5)
ABCD is also moved four units to the left.
The rule for the translation is,
A'(x, y)=> A"(x - 4, y) (x - 4, y)
A'(1, 5) => A"(1 - 4, 5) (1 - 4, 5)
=> A"(-3, 5) (-3, 5)
Due to a sequence of transformations, polygon ABCD will therefore overlap polygon A'B'C'D'.
a 4 unit translation to the left after reflecting polygon ABCD across the x-axis.
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given forecast errors of -1, 4, 8, and -3, what is the mean absolute deviation? group of answer choices 2 16 3 8 4
Answer:
4
Step-by-step explanation:
Which expression is equivalent to (ab^7)^4? ab^28 ab^11 a^5b^11 a^4b^28
The expression that is equivalent to (ab⁷)⁴ is (a⁴b²⁸)
What is the integer exponent property?
Exponents that are integers are known as integer exponents. Exponents with positive integer values tell us how many times to multiply the base by itself. We are instructed by negative integer exponents to first flip the numerator and denominator before multiplying the result by the specified number of times.
Here, we have
Given expression: (ab⁷)⁴
We have to find the expression that is equivalent to this expression.
Using integer exponent property:
= (ab⁷)⁴
= (a⁴b²⁸)
Hence, the expression that is equivalent to (ab⁷)⁴ is (a⁴b²⁸).
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer:
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Step-by-step explanation:
m∠5 + m∠6 are linear pairs, so their sum has to be 180°.
m∠2 + m∠3 = m∠6 because of the exterior angle theorem, which states that the measure of an exterior angle is equal to the sum of the two opposite interior angles. (using this logic, m∠1 equals the sum of m∠5 and m∠3, and m∠4 equals the sum of m∠2 and m∠2).
m∠2 + m∠3 + m∠5 = 180° because the triangle sum property says that the sum of a triangle's interior angles will equal 180°.
Write the equation of the line in slope-intercept form (y=mx+b) for each of the following.
ill brainlist
The equation of the line in slope intercept form of y is -2x + 19
How to calculate the equation slope intercept ?When you know the slope of the line to be examined and the given point is also the y intercept, you can use the slope intercept formula, y = mx + b. The y value of the y intercept point is denoted by the symbol b in the formula.
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
To find this, we can use the point and the slope in point-slope form. The we solve for y.
y - y1 = m(x - x1)
y - 7 = -2(x - 6)
y - 7 = -2x + 12
y = -2x + 19
The equation would be y = -2x + 19
The complete question is : Write an equation in slope- intercept form y=mx=b of the line through point p(6,7) with slope -2
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Valeria has an action figure collection of 500 action figures. She keeps 235 of
the action figures on her wall. What percentage of Valeria's action figure
collection does she keep on her wall?
The percentage of Valeria's action figure collection is 47% which she keeps on her wall.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
To find the percentage of Valeria's action figure collection that she keeps on her wall, we need to divide the number of action figures she keeps on her wall by the total number of action figures in her collection and then multiply by 100%.
Since Valeria has a collection of 500 action figures and she keeps 235 of them on her wall, the percentage of her collection that she keeps on her wall is :
⇒ 235 / 500 × 100% = 47%.
Thus, the percentage of Valeria's action figure collection is 47%
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Alex tracked the number of cups of coffee he drank each day for the following month and
created a new probability distribution.
Number of Cups of Coffee, X 0
1 2 3 4
Relative Frequency, P(X) 0.035 0.579 0.286 0.080 0.020
According this new data, Alex is expected to drink 1.471 cups per day.
4. Calculate s(X) of Alex's new probability distribution. (1 point)
0.599
0.775
1.471
4.223
S(x) of Alex's new probability distribution will be 0.599.
What is Probability distribution ?
A mathematical function called a probability distribution explains how likely it is that a variable will take on several possible values. Utilizing graphs or probability tables, probability distributions are frequently represented.
Given, The no. of cups of coffee he drank with the probability.
If he drinks 1.471 cups per day, So the S(X) will be calculated in the following manner:
Step 1 : calculate the deviation of X from N.( here N = 1.471 )
Step 2 : find the square of (X- N).
Step 3 : multiply it with the given P(X).
Step 4 : find the sum of the (X-N)^2* P(X).
Hence, By following the given steps, we get S(X) as 0.599.
(Refer to the table given in Excel file).
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Please help it’s due today
a loaded coin has a 0.48 (48%) probability of coming up heads and 0.52 (52%) probability of coming up tails. if it is flipped seven times, what is the probability of getting exactly 4 heads?
The probability of getting exactly 4 heads is 0.26
A loaded coin has 0.48 probability of coming up heads
0.52 probability of coming up tails.
coin is flipped 7 times
let's assume n = 7.
The seven flips of the coin are separate from one another, so what happens on one flip is unaffected by the outcomes of the other tosses.
When calculating the likelihood that two events will occur simultaneously, we must multiply the probabilities of events 1 and 2, presuming that event 1 occurred.
Tosses never affect one another, so the "assuming event 1 happened" part is no longer necessary because it has no effect on the probability. As a result, we just need to multiply the chances for each toss. This supposition is essential. We would have needed to know exactly how tosses are dependent on one another if they were interdependent.
Typically, we would have [tex](n! /(r!)*(n - r)!)*p^r*(1-p)^(n-r)[/tex] is the probability of getting r heads out of n, without taking into account the order.
probability of getting exactly 4 heads r = 4.
out of 7 flipping n =7.
7!/(4!*3!) = 35
(0.48)^4 = 0.05308416
(0.52)^3 = 0.140608
35*0.05308416*0.140608 = 0.26124201492 = 0.26
so the probability of getting exactly 4 heads is 0.26.
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Kate wants to post three parcels Each parcels cost £1.20 how much changed should she get from £10 note
Answer: 6.40
Step-by-step explanation:
1.20 times 3 = 3.60
10 - 3.60 = 6.40
in the distribution system, the water main sizes most commonly in use in newer systems are what sizes?
In the distribution system, the water main sizes most commonly in use up to 3.65m to tiny 12.7mm.
Water pipes come in a variety of sizes, from enormous mains with a diameter of up to 3.65 m to tiny 12.7 mm pipes used to supply individual outlets within a building.
Any pipe or tube intended to deliver drinking water to consumers is referred to as a water pipe. Depending on the situation, water may be treated either before distribution or at the point of use (POU). Water is typically treated before distribution in well-thought-out water distribution networks, and occasionally it is also chlorinated, to prevent recontamination on the way to the end user.
Polyvinyl chloride (PVC), cast iron, copper, steel, and, in older systems, concrete or fired clay are materials frequently used to build water pipes. Long runs of water pipe can be joined together using flange, nipple, compression, or soldered joints (SCOTT 2011).
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solve for x
7/x =10
Give your answer as a fraction in its simplest form
Answer:
Step-by-step explanation:
Answer:
x = 7/10
Step-by-step explanation:
You multiply both sides by "x", to get 7 = 10x. Then divide both sides by 10 to get 7/10 = x, or 0.7 = x.
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