The difference between an independent sample and a dependent sample is that the dependent sample for one set of items is paired measurement while measurements made on two samples are termed an independent sample.
In statistics, while considering two samples and conducting a hypothesis test, one should be aware of which type of test should be conducted based on samples whether they are dependent or independent. If the value of another sample is affected by any one sample then the samples are dependent. If no information can be deduced from the other sample using one sample then the samples are independent.
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Given the equation F(x)=3x-1 what is f(x+9)?
f(x+9) = 3x + 26.
Given equation:
f(x)=3x-1
f(x+9) = 3(x+9) - 1
= 3x + 3*9 - 1
= 3x + 27 - 1
= 3x + 26.
Therefore f(x+9) = 3x + 26.
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people enter a gambling casino at a rate of 1 every 2 minutes. (a) what is the probability that no one enters between 12:00 and 12:05? (b) what is the probability that at least 4 people enter the casino during that time?
The probability that no one enters between 12:00 and 12:05 is 0.082.
The probability that at least 4 people enter the casino during that time is 0.242
Given that people enter the casino at the rate of 1 every 2 minutes. A random variable X is defined as the number of people entering the casino between the time period of 12:00 and 12:05. Since we are given in the question that people enter the casino at the rate of 1 every minute, hence in the given time period they enter at the rate of 2.5.
P(X=0) = [tex]e^{-2.5}[/tex] = 0.082
Hence the probability that no one enters between 12:00 and 12:05 is 0.082.
The required probability is simply
P(X≥4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)
= 1 - [tex]e^{-2.5}[/tex] - 2.5[tex]e^{-2.5}[/tex] - (((2.5)² / 2)[tex]e^{-2.5}[/tex] ) - (((2.5³)/3!)[tex]e^{-2.5}[/tex])
= 0.242
Hence, the probability that at least 4 people enter the casino during that time is 0.242
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Triangles geometry . I really neeed it. Teacher don’t explain at all.
The value of x is 32.5°(degree) when isosceles triangle has a base angle of (4x-3)degrees and non base angle is 54 degrees.
How to calculate the value of x?We know that an isosceles triangles is composed of a vertex angle and two base angles. The base angles are congruent to each other. We also know that the sum of a triangle's angles is 180°(degrees).
According to given data,
⇒ 180 - {(4x-3)+54}= 0
⇒180 - 4x + 3 - 54 = 0
⇒130 = 4x
∴ x = 32.5°(degree).
That means that each base angle is 32.5°(degree).
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At a baseball game, a vender sold a combined total of sodas and hot dogs. the number of sodas sold was three times the number of hot dogs sold. find the number of sodas and the number of hot dogs sold.
The number of sodas sold is 168
The number of hot dogs sold is 56
Total of sodas and hot dogs=224
Let the number of sodas sold be s, and the number of hot dogs sold be s
So we have the following:
s=3h.................i
s+h=224..........ii
we solve the two equation to find the value of s and h,
From equation ii, s=224-h, replacing this in equation i, we have:
224-h=3h
224=4h
h=56
Now, s=3*56
=168
s=168
Number of sodas=168
Number of hot dog sold=56
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The complete question is given below;
A vender sold a combined total of 224 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Write an absolute value equation representing all numbers x whose distance 7 is 3 units
Answer:
|x-7|=3
Step-by-step explanation:
x is 3 units away from 7
x-3=7
x-7=3
x+3=7
3=7-x
|x-7|=3
Compare these fractions by filling in the blank with the appropriate sign. 5/11 _____ 4/9
Answer:
5/11 > 4/9
Step-by-step explanation:
5/11 = 0.45454545....
4/9 = 0.44444444....
What’s the inequality for the sum of a number w is more than -12? Please help it’s already missing
The sum of a number w is more than -12 becomes w > -12
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
We have been given that the sum of a number w is more than -12.
Now the sum of a number = w
It is more than -12 means the inequality form as;
w > -12
Therefore, the overall expression becomes w > -12
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Can someone please help me
The proof that show show how ΔTRS ≅ ΔQRP by SAS congruence theorem is explained below.
What is the SAS Congruence Theorem?The SAS congruence theorem states that if two triangles have one pair of corresponding included angles that are congruent, and two pairs of corresponding sides that are also congruent, then both triangles are congruent to each other.
Using the SAS, the proof that shows both triangles are congruent is explained below.
Statements Reasons
1. SR ≅ PR 1. Given
2. SP bisects TQ 2. Given
3. TR ≅ QR 3. Definition of bisection
4. ∠TRS ≅ ∠QRP 4. Vertical ∠s theorem
5. ΔTRS ≅ ΔQRP 5. SAS congruence theorem
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a rectangular garden has a length of x and a y. the garden has its length reduced by 3 feet and its width extended by 2 feet. what is the area of the new garden?
The area of the new garden is found to be (x-3)(y+2) square units where x and y are the original dimensions.
What is the rectangle area formula?When calculating a rectangle's area, we multiply the length by the width of the rectangle.
What are examples of the area's practical applications?The area of the floors and walls must be measured before applying carpet or tiles on the floor, painting the walls, or installing cabinets in a space.
Given: A rectangular garden has x and y dimensions. The garden's width is increased by 2 feet while its length is decreased by 3 feet.
New length = x-3
New width = y+2
Area of new garden is given as:
=(length)(width)
= (x-3)(y+2)
Therefore, the area of the new garden is found to be (x-3)(y+2) square units where x and y are the original dimensions.
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A triangle has sides with lengths of 8 miles, 12 miles, and 17 miles. Is it a right triangle?
Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond. The bond pays 6.34% annual interest.
How much will Sascha receive in annual interest?
The amount that Sascha will receive in annual interest based on the information is $63.40.
How to calculate the interest?From the information, Sascha owns stock in Lewis Corp, and she bought a $1,000 corporate bond and the bond pays 6.34% annual interest.
In this case, it should be noted that the simple interest is calculated as:
Principal × Rate × Time
Principal = $1000
Time = 1 year
Rate = 6.34%
The interest will be:
= Principal × Rate × Time
= 1000 × 0.0634 × 1
= $63.40
The interest is $63.40.
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The depth of the water on the shore of a beach varies as the tide moves in and out. The equation
D(t) = 0.75 cos (t) + 1.5 models the depth of the water, D(t), in feet and t as time in hours.
1. When will the tide be at its lowest for the first time when t > 0?
A) 3
B) 6
C) 9
D) 12
Answer:
C) 9 hours
Step-by-step explanation:
as per your picture the equation is
D(t) = 0.75×cos(pi/6 × t) + 1.5
the function cosine continuously "waves" from +1 to -1 and back.
the lowest value of this function for the first time after t>0 is when the cosine part reaches -1 the first time.
that is at 270° or 3pi/2.
so,
pi/6 × t = 3pi/2
1/6 × t = 3/2
t = 3×6/2 = 3×3 = 9
Make x the subject:
Q1) 9y-5x = 4
Answer:
x = 9/5 y - 4/5
Step-by-step explanation:
Make x the subject:
9y - 5x =4
Subtract 9y from each side
9y-9y - 5x =-9y+4
-5x = -9y +4
Divide each side by -5
-5x/-5 = -9y/-5 + 4/-5
x = 9/5 y - 4/5
Answer:
x = (9/5)y - (4/5)
Step-by-step explanation:
Given equation,
→ 9y - 5x = 4
Solving for the required value of x,
→ 9y - 5x = 4
→ -5x = -9y + 4
→ x = (-9y + 4)/-5
→ [ x = (9/5)y - (4/5) ]
Hence, value of x = (9/5)y - (4/5).
What are the solutions of the quadratic equation?
`2x^{2}+12x+18=0`
show work
The solutions for the quadratic equation:
2x^2 + 12x + 18 = 0
are:
x₋ = -5.55
x₊ = -0.4
How to solve the quadratic equation?
Remember that for a general quadratic equation:
a*x^2 +b*x + c = 0
The solutions are of the form:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Here we have the quadratic:
2x^2 + 12x + 18 = 0
Then using the formula for the solutions we will get:
[tex]x = \frac{-12 \pm \sqrt{12^2 - 4*2*18} }{2*2} \\\\x = \frac{-12 \pm 10.2}{4}[/tex]
The two solutions of the quadratic equation are:
x₋ = (-12 - 10.2)/4 = -5.55
x₊ = (-12 + 10.2)/4 = -0.4
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Alonso went to the store to buy some almonds. The price per pound of
the almonds is $7.25 per pound and he has a coupon for $3.50 off the
final amount. With the coupon, how much would Alonso have to pay to
buy 5 pounds of almonds? Also, write an expression for the cost to buy
p pounds of almonds, assuming at least one pound is purchased.
The required price of almond and expression are $32.75 and c= $7.25P - $3.5 respectively.
What is pound?Pound is unit used to measure weight of quantity. It is used by the English speaking peoples.It equal to the 16 ounces and 0.454 kilogram.
According to given information:Alonso has a coupon of $3.5, let us consider P pound of almond. And price per pound of almond is $7.25
So, equation for the cost,
Cost(c) = $7.25P - $3.5
Then, the price of 5 pound of almond = $7.25×5 - $3.5
⇒ $36.25 - $3.5 = $32.75
Thus, the price of 5 pounds of almond is $32.75.
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A pencil is 712 inches long.
How long is the pencil in centimeters?
1 inch =2.54 centimeters
do you mean 712 or 7.12?
If for 712 it is 1808.48
if for 7.12 it is 18.0848
The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.
A line of best fit has also been drawn.
One of the points in an outliner.
a) Write down the coordinates of this point. (1)
b) For all the other points write down the type of correlation in just one word. (1)
On the same day, in another British town, the maximum temperature was 17.4C.
c) Estimate the number of hours of sunshine in this town on this day. (2)
You must use the drawing tool to show how the line of best fit has been used to get your answer.
A weatherman says that temperatures are lower on days when there is less sunshine.
d) Does the scatter graph support this? (1)
A yes B no C can't say
Total marks: 5
Answer:
See attached worksheet.
Step-by-step explanation:
The worksheet summarizes the steps for analyzing the data on the graph. Note that a "line of best fit" was drawn to help illustrate the linear behavior of the data, and to better the question concerning hours of sunshine in another British town. There are techniques for ensuring a line such as this fits the actual data as closely as possible. These techniques draw a line that has the least overall deviation from the actual data. For our purposes, a hand-drawn line appears to match the data reasonably well, so we are able to concule that the relationship is liner: There is a proportional change in y for every set change in x. That change is known as the slope. The slope of this liner would represent the direct relationship between hours of sun and maximum temperature.
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. If a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? Round your answer to four decimal places.
The probability that the sample mean would differ from the population mean by greater than 0.5 millimeters is 1
How to determine the probability value?From the question, the given parameters about the distribution are
Mean diameter = 127Variance = 36 The actual data value, x = Less than 0.5The standard deviation is the square root of variance
So, we have
Standard deviation = 6
The z-score is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (0.5 - 127)/6
Evaluate
z = -21.08
The probability is then calculated as:
P(x > 0.5) = P(z > -21.08)
From the z table of probabilities, we have;
P(x < 0.5) = 1
Hence, the probability is 1.0
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x + 3y = -18 in slope intercept form
Answer:
y=1/3x+6
Step-by-step explanation:
Use the formula "Y=mx+b"
Answer:
y= -1/3x - 6
Step-by-step explanation:
x+3y = -18
3y = -x -18
y= -1/3x - 6
The magnitude, M, of an earthquake is represented by the equation M=23log(EE0) where E is the amount of energy released by the earthquake in joules and E0=104.4 is the assigned minimal measure released by an earthquake. To the nearest tenth, what would be the magnitude of an earthquake releasing 3.4⋅1014 joules of energy?
Magnitude of an earthquake releasing 3.4*10^14 joules of energy is M ≈ 6.754.
Given:
The magnitude, M, of an earthquake is represented by the equation M=2/3log(E/E0) where E is the amount of energy released by the earthquake in joules and E0=10^4.4 .
E = 3.4*10^14
M = 2/3*log(3.4*10^14 / 10^4.4)
= 2/3*log(13535643798.8)
= 2/3*10.1314
= 20.2628 / 3
M = 6.754
Therefore Magnitude of an earthquake releasing 3.4⋅1014 joules of energy is M ≈ 6.754.
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The chart shows the distances, in miles, between three places.
a)Write down the distance
from Hereford to Chester.
b) Which town is 99 miles
from Kendal?
c)If Ellen drives from Kendal to
Hereford via Chester, how
many miles will she drive?
The spreadsheet that shows the distances between the cities, indicates that the distances between the cities are as follows;
a) From Hereford to Chester, the distance is 95 miles
b) Chester is the town that is 99 miles from Kendal
c) Ellen will have driven 201 miles if she drives from Kendal to Hereford through Chester
What is a spreadsheet?A spreadsheet application is used for the storage analysis, organization, and computation of data.
The interpretation of the distances in the chart which is in the form of a spreadsheet are;
The value in the cell corresponding to the distance from Kendal to Chester that is the cell which is on the same column as Kendal and on the same row as Chester is 99
Therefore, the distance from Kendal to Chester is 99 miles
The value in the cell that directly links Chester to Hereford that is the cell which is on the same column as Chester and on the same row as Hereford is 95
Therefore, the distance from Chester to Hereford is 95 miles
The value in the cell that connects Kendal to Hereford, that is the cell which is on the same column as Kendal and which is on the same row as Hereford is 201
Therefore the distance from Kendal to Hereford is 201 miles
a) The distance from Hereford to Chester is 95 miles
b) The town that is 99 miles from Kendal is Chester
c) The distance Ellen will have driven if she drives from Kendal to Hereford via Chester is 201 miles
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please help. what is the equation??
Answer:
y = -x + 4
Step-by-step explanation:
The equation of a line follows the form y=mx+c, where x and y are the coordinates, c is the y-intercept (the value of x where the line crosses the y-axis), and m is the slope.
We are given two points/coordinates - (-3,7) and (1,3) - so we know the following is true for our equation:
7=-3m+c
3=m+c
Rearranging the second equation above, we get c=3-m. Sub this into the first one, and we get
7=-3m+3-m
4=-4m
m=-1
Knowing c=3-m, we can say c=3-(-1)=3+1=4
Having found values for m and c, we can now write our equation:
y = -x + 4
Hope this helps :)
Complete both transformations below. Then enter the final coordinates of the figure. A (1.-2)
B (4,-1)
C (5.-3)
1) < -2.4 >
2) Dilate K = 3
Applying the transformation rule (x - 2.y + 4) and using the scale factor k = 3 for dilation gives
preimage translation image Dilation image
A (1.-2) A' (-1, 2) A'' (-3, 6)
B (4,-1) B' (2, 3) B'' (6, 9)
C (5.-3) C' (3, 1) C'' (9, 3)
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Translation refers to a type of transformation that involve a linear movement.
Applying the transformation rule (x - 2.y + 4 ) gives
A (1.-2) = (1 - 2, -2 + 4) = (-1, 2)
B (4,-1) = (4 - 2, -1 + 4) = (2, 3)
C (5.-3) = (5 - 2, -3 + 4) = (3, 1)
preimage image
A (1.-2) A' (-1, 2)
B (4,-1) B' (2, 3)
C (5.-3) C' (3, 1)
Dilation involves making the image bigger or smaller. In this case K > 1 hence the image is bigger
Using the scale factor k = 3 for dilation rule (kx, ky) gives
A' (-1, 2) = (-1 * 3, 2 * 3) = (-3, 6)
B' (2, 3) = (2 * 3, 3 * 3) = (6, 9)
C' (3, 1) = (3 * 3, 1 * 3) = ( 9, 3)
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what do you call the result of this opperation 2x+5
Answer:
addition?
Step-by-step explanation:
Commuting Distances (in miles)
The commuting distances in miles of 10 employees were used to make the box plot shown above. Which of the following is the median of the set of commuting distances? (please no long paragraphs or answers that aren't even there)
A. 30
B. 25
C. 28.5
D. 27.5
Answer:
The answer is gonna be B. Sorry if I’m late :((
Step-by-step explanation:
Answer: 25
Step-by-step explanation:
Bobbi wants to buy a bandana that costs 3.75$ But she has only 7.75$ in her budget what is her budget deficit
The budget deficit is how much less the budget is to buy a thing, thus Bobbi has the budget deficit as $3.75 - $0.75 = $3.00 thus option (B) is correct.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.
As per the given,
Cost of bandana = $3.75
Budget = $0.75
Budget deficit = $3.75 -$0.75
⇒ $3.00
Hence, "The budget deficit is how much less the budget is to buy a thing, thus Bobbi has the budget deficit as $3.75 - $0.75 = $3.00".
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The given question is incorrect, the correct question follows;
Bobbi wants to buy a bandanna that costs $3.75, but she has only $0.75 in her budget. What is her budget deficit?
A. $0.20
B.$ 3.00
C. $5.00
D.$4.50
On the interstate there is a ratio of 2 trucks to 4 cars to 3 SUVs, if there are a total of 1800 vehicles on the road, how many of each type of vehicle is on the road?
Answer:
Step-by-step explanation:
yes Saab do
If a, b, and c are positive prime numbers, in the equation a - b = c, either b or c must represent which number?
The value of prime numbers c in the equation is c = 2.
What is prime numbers?
Those greater than one are known as prime numbers. They simply have two variables, the number itself and factor 1.
We have given that a - b = c requires all of the integers to be positive prime numbers,
c can only have one outcome, which is 2.
[tex]e.g., 13 - 11 = 7 - 5 = 2.[/tex]
Hence in the given prime numbers c in the equation is c = 2.
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Any nonzero integer divided by 0 equals 0.
Answer: False
Step-by-step explanation:
Can not divide a number by 0.
What is the image of ( 0 , − 8 ) (0,−8) after a reflection over the line y = x y=x?
Answer:
(- 8, 0 )
Step-by-step explanation:
under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
(0, - 8 ) → (- 8, 0 )