The greatest common factor of two terms given as 21x⁴ and 49x³ is equal to 7x³.
To find the greatest common factor (GCF) of two terms, we need to find the highest factor that is common to both terms. In this case, we have 21x⁴ and 49x³.
To find the factors, we can break each term down into its prime factors:
21x⁴ = 3 * 7 * x * x * x * x
49x³ = 7 * 7 * x * x * x
The common factors are 7 and x³. To find the GCF, we multiply these common factors together:
GCF = 7 * x³
GCF = 7x³
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1.1 Convert 500 cm to m
Answer:
5 m
Step-by-step explanation:
To convert 500 cm to m, you simply divide by 100 since there are 100 centimeters in 1 meter.
So, 500 cm ÷ 100 = 5 m
One of the authors received a credit card bill for $2,559, but it included a charge of $1,825 th
values of the absolute and relative errors.
The value of the absolute error is $
The value of the relative error is%. (Round to the nearest integer as needed)
The absolute error is $1825, the relative error is 2
What is an absolute and relative error?An absolute error is a determinant of how large an error is. A relative error defines how good or bad an error is.
The formula for determining an absolute error is;
Absolute error = measured value - actual valueThe formula for determining a relative error is:
Relative error = absolute error ÷ actual valueFrom the parameters given:
The absolute error can be computed as:
Absolute error = 2559 - (2559 - 1825)
Absolute error = 2559 - 734
Absolute error = $1825
The relative error = 1825 ÷ 734
The relative error = 2.4
The relative error ≅ 2 (as an integer)
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Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
She needs to find the approximate surface area of the attic, including the walls, floor, and
ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes
the expression below to represent the surface area of the attic. Are Linda's net and
expression correct?
We have that Linda's net and expression incorrect.
Now, With the Expression of the surface area of attic
45 (40 + 25 + 25) + 1/2 (40 x 15)
Hence, Surface area is,
X = 4050 + 600
X = 4650 feet²
Hence, The answer is No, Because Her expression for the triangles are incorrect;
1/2(40 x 15)
Instead of,
1/2 x 40 x 15
Hence, Linda's net and expression incorrect,
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Complete question is,
Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
She needs to find the approximate surface area of the attic, including the walls, floor, and ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes the expression below to represent the surface area of the attic. Are Linda's net and expression correct?
Raj purchases a new home for $150,000. The value of the home increases by 9% every 3 years.
Determine the value of the home after 5 years.
The value of the home after 5 years would be $194,415.
How to calculate the value of the home after 5 years
First, let's calculate the increase in value for each 3-year period:
After the first 3 years:
Increase = 9% of $150,000 = 0.09 * $150,000 = $13,500
After the second 3 years:
Increase = 9% of ($150,000 + $13,500) = 0.09 * ($150,000 + $13,500) = $14,850
After the third 3 years:
Increase = 9% of ($150,000 + $13,500 + $14,850) = 0.09 * ($150,000 + $13,500 + $14,850) = $16,065
Now, let's add these increases to the initial value of the home to find the value after 5 years:
Value after 5 years = $150,000 + $13,500 + $14,850 + $16,065 = $194,415
Therefore, the value of the home after 5 years would be $194,415.
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Suppose the prices of a certain model of new homes are normally distributed with a mean of 150,000 use the 68 9599.7 route to find the percentage of buyers who paid between 150,000 and 153,300 if the standard deviation is 1100
The percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.
To solve this problem, we can use the properties of the normal distribution and the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of buyers who paid between 150,000 and 153,300.
According to the empirical rule, given a normal distribution:
approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the three standard deviations of the mean, the data are contained.
In this case, we want to find the percentage of buyers who paid between 150,000 and 153,300, which is one interval of length 3300 above the mean. To use the empirical rule, we need to standardize this interval by subtracting the mean and dividing by the standard deviation:
z1 = (150,000 - 150,000) / 1100 = 0
z2 = (153,300 - 150,000) / 1100 = 3
Here, z1 represents the number of standard deviations between 150,000 and the mean, and z2 represents the number of standard deviations between 153,300 and the mean.
Since the interval we are interested in is within three standard deviations of the mean (z2 <= 3), we can use the empirical rule to estimate the percentage of buyers who paid between 150,000 and 153,300:
Approximately 68% of the buyers paid within one standard deviation of the mean, which is between 149,000 and 151,000 (using z-scores of -1 and 1).
Approximately 95% of the buyers paid within two standard deviations of the mean, which is between 148,000 and 152,000 (using z-scores of -2 and 2).
Therefore, the remaining percentage of buyers who paid between 152,000 and 153,300 is approximately (100% - 95%) / 2 = 2.5%.
So, the percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.
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Please help me find the function that explains how to get the output from the input
Answer:
The equation for those inputs and outputs is:
0.25 *input - 151.75 = Output
Step-by-step explanation:
For this, first search for the Slope of the funtion
THe slope can be found by calculating this :
(y2-y1)/(x2-x1) or in this case (output2 - output1)/ (input2 - input1)
IT continues as follows:
( -48.5 - 24) / (-413 - (-703) ) =
= (-72.5) / (290)
= -0.25
The slope is -0.25. If the function is a line then the equation is
-0.25*input + B = output
with any of the choices we can determine B.
-0.25 * (-703) + B = 24
175.75 + B = 24
175.75 +B - 175.75 = 24 - 175.75
B = - 151.75
The equation for those inputs and outputs is:
0.25 *input - 151.75 = Output
ill mark brainliest !
Answer:
Since the line is vertical and passes through the point (3, -5), it is a vertical line with undefined slope.
Step-by-step explanation:
Which equation choice could represent the graph shown below?
1) F(x) = (x - 4)(x + 1)(x - 6)
2) F(x) = (x - 4)(x - 1)(x - 6)
3) F(x) = (x - 4)(x - 1)(x + 6)
4) F (x) = (x + 4(x - 1)(x - 6)
The algebraic equation of the cubic function set on Cartesian plane is f(x) = (x + 6) · (x - 1) · (x - 4). (Correct choice: 3)
What equation does represent a cubic function?
In this problem we find the representation of a cubic function set on Cartesian plane, whose definition as algebraic equation is shown below:
f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Roots of the polynomial.Graphically speaking, the roots of the polynomials are the points of the curve on x-axis. If we know that a = 1, r₁ = - 6, r₂ = 1 and r₃ = 4, then the algebraic equation of the cubic function is:
f(x) = (x + 6) · (x - 1) · (x - 4)
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Answer:
3) f(x) = (x - 4)(x - 1)(x + 6)
Step-by-step explanation:
The x-intercepts of a function are the points at which the curve crosses the x-axis, so when f(x) = 0.
From inspection of the given graph, the curve crosses the x-axis at:
x = -6x = 1x = 4According to the Factor Theorem, if f(x) is a polynomial and f(a) = 0, then (x - a) is a factor of f(x).
Therefore, as f(x) = 0 when x = -6, x = 1 and x = 4, then (x + 6) and (x - 1) and (x - 4) are factors of the polynomial.
Therefore, the equation of the function is:
f(x) = (x - 4)(x - 1)(x + 6)Help me with this question pls. And do it fast I have to submit it soon in 3 minutes
The perimeter of the dilated rectangle M'N'O'P' is 54 centimeters.
If the area of the original rectangle is A, and the area of the dilated rectangle is A', then the relationship between their areas is:
A' = k² × A
Similarly, the relationship between their perimeters is:
P' = k × P
The original rectangle has an area of 14 square centimeters.
The dilated rectangle has an area of 126 square centimeters.
We need to find the perimeter of the dilated rectangle.
Let's denote the scale factor as "k."
126 = k² × 14
Dividing both sides by 14, we get:
9 = k²
k = 3
Now, we can find the perimeter of the dilated rectangle using the perimeter relationship:
P' = k × P
The original rectangle has a perimeter of 18 centimeters, so:
P' = 3 × 18
P' = 54 centimeters
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A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.
A coordinate plane.
What is the value of a?
–2
–1
1
2The table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. What is the rate of change?
Snowfall Amount
Length of Snowfall
(hours)
Amount of Snow on the Ground
(inches)
0
3.3
0.5
4.5
1.0
5.7
1.5
6.9
2.0
8.1
1.2 inches per hour
2.4 inches per hour
3.3 inches per hour
5.7 inches per hour
The value of a is given as follows:
a = 2.
The rate of change is given as follows:
2.4 inches per hour.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope, which is the rate of change of the output variable y relative to the input variable x.b is the intercept, which is the value of y when x = 0.The line passes through the points (–1, –5) and (4, 5), hence the slope m is obtained as follows:
m = (5 - (-5))/(4 - (-1))
m = 2.
Hence:
y = 2x + b.
When x = -1, y = -5, hence the intercept b is obtained as follows:
-5 = -2 + b
b = -3.
Hence:
y = 2x - 3.
Then the value of a is obtained as the value of x when y = 1, hence:
2x - 3 = 1
2x = 4
x = 2.
The rate of change in the snowfall is given as follows:
m = (8.1 - 2.3)/2
m = 2.4 inches per hour.
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(Worth 100 Brainly points help fast)Solve the following system of equations and show all work.
y = 2x²
y = -3x -1
The solutions are : solution of the following system of equations are:
(- 1/2, 1/2)
(- 1, 2)
Here, we have,
The given system of equations is expressed as
y = 2x²- - - - - - - - - - - - - - -1
y = - 3x - 1- - - - - - - - - -- - - -2
We would apply the method of substitution by substituting equation 1 into equation 2. It becomes
2x² = - 3x - 1
2x² + 3x + 1 = 0
We would find two numbers such that their sum or difference is 3x and their product is 2x².
The two numbers are 2x and x. Therefore,
2x² + 2x + x + 1 = 0
2x(x + 1) + 1(x + 1) = 0
2x + 1 = 0 or x + 1 = 0
x = - 1/2 or x = - 1
Substituting x = - 1/2 into equation 1, it becomes
y = 2(-1/2)² = 1/2
Substituting x = - 1 into equation 1, it becomes
y = 2(-1)² = 2
Hence, The solutions are : solution of the following system of equations are:
(- 1/2, 1/2)
(- 1, 2)
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Suppose you'd like to save enough money to pay cash for your next car. The goal is to save an extra $22,000 over the next 3 years. What amount must be deposited quarterly into an account that earns 4.7% interest, compounded quarterly, in order to reach your goal? Round your answer to the nearest cent, if necessary.
The initial deposit needed for the account is given as follows:
$19,257.37.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
[tex]A = 22000, t = 3, r = 0.0447, n = 4[/tex]
Hence the initial deposit P is obtained as follows:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]22000 = P\left(1 + \frac{0.0447}{4}\right)^{4 \times 3}[/tex]
1.142657P = 22000
P = 22000/1.142657
P = $19,257.37.
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The question is :
Which expression is a factor of both
x^2-9 and x^2+8x+15
Can you please explain this to me like you are talking to an elementary schooler, i kinda get it but im honestly so confused.
The expression that is a factor of both x² - 9 and x² + 8x + 15 is (x + 3).
What is the common factor between the given polynomials?Given the polynomials in the question:
x² - 9
x² + 8x + 15
To find a factor that is common to both x² - 9 and x² + 8x + 15, we can factorize the two expressions and look for any common factors.
First, factorize x² - 9:
Using the difference of sqaure formula
a² - b² = ( a + b )( a - b )
x² - 9
x² - 3² = (x - 3)(x + 3)
Next, factorize x² + 8x + 15:
Using AC method
( x + 3 )( x + 5 )
From the factorizations, we can see that both expressions have a common factor of (x + 3).
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the martins bought a condominium for $85,000. assuming that the value of the condo will appreciate at most 5% a year, how much will the condo be worth in 5 years?
Answer:
Step-by-step explanation:
Answer:181,250
Step-by-step explanation:
Basically, the cost would go up 5 percent, and you’re asking how much it would go up in 5 years. So 5x5=25, so you’d multiply 145,000 by 25%, which is 36,250. So, you’d add that to 145,000 which would get you 181,250.
A cruise ship can cover 19 nautical miles in 437 minutes. How many nautical miles will it travel in 345 minutes?
The cruise ship will travel approximately 15 nautical miles in 345 minutes.
How did we get the value?Use a proportion to solve this problem. Let "d" be the number of nautical miles the cruise ship will travel in 345 minutes. Then:
19 nautical miles / 437 minutes = d nautical miles / 345 minutes
To solve for "d", cross-multiply:
19 nautical miles x 345 minutes = d nautical miles x 437 minutes
Then, divide both sides by 437 minutes to isolate "d":
d nautical miles = (19 nautical miles x 345 minutes) / 437 minutes
Simplifying this expression, we get:
d nautical miles = 15 nautical miles (rounded to the nearest whole number)
Therefore, the cruise ship will travel approximately 15 nautical miles in 345 minutes.
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Gabe learns more than just
math in Mrs. Zemla's class. Today he
learned that buying a car is a bad
investment because a car's value decreases
each year. So when Gabe was looking to
buy a 2024 Porsche Boxster for $54792,
he also reasearched the projected resale
value of the vehicle. He found that the
vehicle is expeced depreciate 19% each
year after the car is purchased. What is
the expected vaule of the car 7 years after
it was purchased?
The expected value of the car 7 years after it was purchased is $47,029.12.
To solve this problem, we need to calculate the expected value of the car after 7 years. To do this, we need to use the formula for calculating the value of a depreciating asset:
Value after n years = Initial Value - (Initial Value × (Depreciation Rate/100)×n)
In this case, the initial value of the car is $54792, the depreciation rate is 19%, and n = 7. Thus, the expected value of the car 7 years after it was purchased is:
Value after 7 years = 54792 - (54792 × (19/100)×7)
Value after 7 years = 54792 - (54792 × 0.19×7)
Value after 7 years = 54792 - 7762.88
Value after 7 years = $47,029.12
Therefore, the expected value of the car 7 years after it was purchased is $47,029.12.
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The photo is kinda blurry but please help me with it
The perimeter of rectangle M'N'O'P' is given as follows:
54 cm.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The ratio between the areas is given as follows:
126/14 = 9.
The area is measure in square units, while the perimeter is measured in units, hence the ratio of the perimeters is the square root of the ratio of the areas, that is:
3.
Hence the perimeter of rectangle M'N'O'P' is given as follows:
3 x 18 = 54 cm.
Missing InformationThe complete problem is:
Rectangle MNOP has a perimeter of 18 cm and an area of 14 cm2. After rectangle MNOP is dilated, rectangle M'N'O'P' has an area of 126 cm2. What is the perimeter of rectangle M'N'O'P'?
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x+3 is a factor of p(x)=x^3-7x^2+15x-9
true or false
The statement "x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex]" is false.
To determine whether x + 3 is a factor of p(x) = [tex]x^3 - 7x^2 + 15x - 9[/tex], we can use the factor theorem.
According to the factor theorem, if a polynomial p(x) has a factor (x - a), then p(a) = 0.
In this case, we have x + 3 as a possible factor. To check if it is indeed a factor, we substitute -3 for x in the polynomial p(x):
[tex]p(-3) = (-3)^3 - 7(-3)^2 + 15(-3) - 9[/tex]
= -27 - 63 - 45 - 9
= -144
Since p(-3) is not equal to zero, we conclude that x + 3 is not a factor of p(x).
Therefore, the statement "x + 3 is a factor of [tex]p(x) = x^3 - 7x^2 + 15x - 9[/tex]" is false.
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Can someone help me with this please?
Applying linear functions, we have: a. Bakery B charges a higher delivery fee b. Bakery A charges a higher price per cookie
c. Bakery B is cheaper.
How to Solve Linear Functions?In order to solve this problem, we will need to write the linear function for bakery A and bakery B.
Where:
b = the initial delivery fee which is the y-intercept
m = price per cookie
x = number of cookies
y = total cost
For Bakery A:
b = 5 (initial delivery fee)
m = price per cookie = change in y/change in x = 10 - 5 / 2 - 0
m = 5/2 = $2.5.
The linear function for bakery A is: y = 2.5x + 5.
For Bakery B:
b = 7 (initial delivery fee)
m = price per cookie = change in y/change in x = 16 - 7 / 4 - 0
m = 9/4 = $2.25.
The linear function for bakery A is: y = 2.25x + 7.
Therefore, we have:
a. The bakery that charges a higher delivery fee is Bakery B.
b. The bakery that charges a higher price per cookie is Bakery A.
c. Substitute x = 12 into both linear functions:
Bakery A: y = 2.5(12) + 5 = $35
Bakery B: y = 2.25(12) + 7 = $34
The bakery that is cheaper is: Bakery B.
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Tommy looks around at an assembly. He notices his younger sister to his right and his older brother 4 meters ahead of him. If Tommy's brother and sister are 5 meters apart, how far apart are Tommy and his younger sister?
Answer: Tommy's sister is four meters away from him.
Step-by-step explanation:
If Tommy's older brother is 4 meters ahead and he is 5 meters from his sister,subtract 1 from that since it is described she is right next to him,and you get four.
This is my first time answering anyone so I hope it helps.
Can someone please answer and provide an explanation for these problems?
The area of the sector is: 21) 177.0 cm² 22) 58.6 in.²
The missing sides are: 23) 12 24) 8
How to Find the Area of a Sector of a Circle?The area of the sector of any circle is given as:
Area = ∅/360 * πr², where r is the radius.
21. ∅ = 120°
r = 13 cm
Substitute:
Area = 120/360 * π * 13² = 177.0 cm²
22. ∅ = 105°
r = 8 in.
Substitute:
Area = 105/360 * π * 8² = 58.6 in.²
Since the lines appear tangents in the circles given, then the triangle formed is a right triangle, therefore, we will apply the Pythagorean Theorem in each case:
23. Missing side = √[(9 + 6)² - 9²]
Missing side = 12
24. Let the missing side be x. Therefore, we have:
12 + x = √(16² + 12²)
12 + x = 20
12 + x - 12 = 20 - 12
x = 8
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At a football game, a vender sold a combined total of 233 sodas and hot dogs. The number of hot dogs sold was 51 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
The vendor sold 142 sodas and 91 hotdogs.
According to the question:
The vendor sold 233 sodas and hotdogs combined
The number of hot dogs sold was 51 less number of sodas sold
To find:
Number of sodas sold(S)
Number of hotdogs sold(H)
From the question, it is clear that:
S + H = 233 ...(i)
S - H = 51 ...(ii)
These two are simultaneous linear equations.
Adding equations (i) and (ii):
S + H + S - H = 233 + 51
2S = 284
S = 284/2
S = 142
Substitute this value of S in equation (i):
142 + H = 233
H = 233 - 142
H = 91
Therefore, the vendor sold 142 sodas and 91 hotdogs.
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At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds
The graph below displays a fire department's
response time, which measures the time from when
the alarm is sounded at the firehouse to the time the
first fire engine leaves the station.
Fire Department Response Times
0.4
Relative Frequency
10
02
0
10
20 30 40 50 60 70 80 90
Response Time (Seconds)
Which of the following correctly describes the shape of
the distribution?
uniform
skewed left
skewed right
roughly symmetric
The correct description of the shape of the distribution is D. Roughly Symmetric.
What is a symmetric distribution ?Symmetric distribution is an often-referenced term in statistics, representing a type of probability with data segments evenly dispersed around the mean. This denotes the perfect mirror image of the right and left halves when the distribution is split; arriving at an equal size and shape on either side when drawn at the midpoint of the line.
Looking at the distribution of a fire department's response time, we can see that the distribution is roughly symmetric because the values on the left seem to match those on the right.
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22. Which of the following is NOT a rational expression?
O(x+3)(2x-1)
x+3
O3x²+3x
4x+5
3x+4√x-7
2x+2
2x²-3x³+5
5x
The correct expression which is not a rational expression,
⇒ (x+3)(2x-1) / (x+3)
We have to given that;
All the expressions are,
⇒ (x+3)(2x-1) / (x+3)
⇒ (3x²+3x) / (4x+5)
⇒ (3x+4√x-7) / (2x+2)
⇒ (2x²-3x³+5) / 5x
Since, A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
Hence, We can simplify all the expressions as,
⇒ (x+3)(2x-1) / (x+3)
⇒ (2x - 1)
Hence, It is not a rational expression.
⇒ (3x²+3x) / (4x+5)
⇒ 3x (x + 1) / (4x + 5)
Hence, It is a rational expression.
⇒ (3x+4√x-7) / (2x+2)
⇒ (3x + 4√x - 7) / 2 (x + 1)
Hence, It is a rational expression.
⇒ (2x²-3x³+5) / 5x
Hence, It is a rational expression.
Thus, The correct expression which is not a rational expression,
⇒ (x+3)(2x-1) / (x+3)
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The value of side TS is,
⇒ TS = 28
First, we are going to divide the figure and named new points X and Y as:
Now, we know that TS is the sum of TX and XS.
TS = TX + XS
Additionally, TX has the same length of HJ, so:
TX = HJ = 14
Now, we want to know the length of YK, and we can calculate it using the following equation:
LK = LY + YK
LY = HJ,
so, LY = 14
And, 42 = 14 + YK
42 - 14 = YK
28 = YK
Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:
XS = YK/2
XS = 28/2
XS = 14
Therefore, TS is equal to:
TS = TX + XS
TS = 14 + 14
TS = 28
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Alfred says that the line shown on the scatter plot is a good line of fit because the line goes through the middle of all the data points. Do you agree? Explain your reasoning
No, I disagree because a good line of fit has to minimize the sum of the squared distance between all the points in the data.
Line of fitA line of fit is used to mathematically model the relationship between variables in a data. A line of fit is drawn such that the best line would minimize the sum of the squared distances between the plotted points.
This means that, the line of fit should not aim to go through the middle of the data points but minimize the sum of the squared distances between them.
Hence, Alfred's reasoning is Incorrect .
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Please help. Is the answer even there?
The critical values t₀ for a two-sample t-test is ± 2.0.6
To find the critical values t₀ for a two-sample t-test to test the claim that the population means are equal (i.e., µ₁ = µ₂), we need to use the following formula:
t₀ = ± t_(α/2, df)
where t_(α/2, df) is the critical t-value with α/2 area in the right tail and df degrees of freedom.
The degrees of freedom are calculated as:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
n₁ = 14, n₂ = 12, X₁ = 6,X₂ = 7, s₁ = 2.5 and s₂ = 2.8
α = 0.05 (two-tailed)
First, we need to calculate the degrees of freedom:
df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]
= (2.5²/14 + 2.8²/12)² / [(2.5²/14)²/13 + (2.8²/12)²/11]
= 24.27
Since this is a two-tailed test with α = 0.05, we need to find the t-value with an area of 0.025 in each tail and df = 24.27.
From a t-distribution table, we find:
t_(0.025, 24.27) = 2.0639 (rounded to four decimal places)
Finally, we can calculate the critical values t₀:
t₀ = ± t_(α/2, df) = ± 2.0639
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Your brain needs caffeine! You decide to walk from home to the coffee shop located at point (-8,-5). What coordinate would you be standing on if you stood on a point “K” so that it directed the line segment in a ratio of 5:2?
The coordinates you would be standing on would be coordinate (-5.71, -3.57).
How to calculate the coordinatesTo discover the arrangement of point "K" that partitions the line section interfacing the beginning point to the coffee shop in a proportion of 5:2, we are able to utilize the concept of the area equation.
We should expect the starting point to be meant as A with orchestrates (- x1, - y1), and the café is implied as B with works with (- x2, - y2). The ratio of 5:2 suggests that segment AB is divided into two parts and five parts, each accounting for 7 percent of the length.
The x-direction of point K can be determined as:
xK = (5 * x2 + 2 * x1)/7
Basically, the y-direction of point K can be determined as:
yK = (5 * y2 + 2 * y1) / 7
Stopping within the arranges of the coffee shop (-8, -5) as (-x2, -y2) and accepting the beginning point as the beginning (0, 0), we have:
xK = (5 * (-8) + 2 * 0) / 7 = -40/7 ≈ -5.71
yK = (5 * (-5) + 2 * 0) / 7 = -25/7 ≈ -3.57
Hence, in case you stood on point K, you'd be around at coordinate (-5.71, -3.57).
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The box plots show the data distributions for the number of customers who used a coupon each hour for two days of a store sale. What is the difference of the medians? 0 2 4 7
The difference of medians is given as follows:
2.
What does a box and whisker plot shows?A box and whisker plots shows these five metrics from a data-set, listed and explained as follows:
The minimum non-outlier value.The 25th percentile, representing the value which 25% of the data-set is less than and 75% is greater than.The median, which is the middle value of the data-set, the value which 50% of the data-set is less than and 50% is greater than%.The 75th percentile, representing the value which 75% of the data-set is less than and 25% is greater than.The maximum non-outlier value.The median for each day is given as follows:
Day 1: 6.Day 2: 8.Hence the difference is given as follows:
8 - 6 = 2.
Missing InformationThe box plot is given by the image presented at the end of the answer.
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