13. Final year students are selected at random from fiveuniversity colleges and are clas- sified according to whether they passed or not in the previous academic year. The results were as follows: Pass Engineering Medicine Science Education | Blašiness 693 585 1020 215 180 hline Fail If the critical value at 0.01 level of significance is 13.27. is there is sufficient statistical evidence to indicate a significant difference in the distribution of aggregates across the five colleges?
Answers
We fail to reject the null hypothesis and conclude that there is not sufficient statistical evidence to indicate a significant difference in the distribution of aggregates across the five colleges.
The answer to the question is that there is not sufficient statistical evidence to indicate a significant difference in the distribution of aggregates across the five colleges. This can be determined by carrying out a chi-square test of independence to determine the p-value and comparing it to the level of significance.
The observed frequencies are given below: Pass Fail
Total Engineering 693 307 1000Medicine 585 415 1000Science 1020 480 1500.
Education 215 285 500.
Business 180 320 500Total 2693 1807 4500.
We can calculate the expected frequencies using the formula: (row total x column total)/grand total .
For example, the expected frequency for pass in engineering is: (1000 x 2693)/4500 = 597.07 .
To determine whether there is a significant difference in the distribution of aggregates, we will use a chi-square test of independence. The formula for chi-square is: X² = Σ [ (O - E)² / E ] where O is the observed frequency and E is the expected frequency.
The degrees of freedom are calculated as df = (r - 1) x (c - 1) where r is the number of rows and c is the number of columns. In this case, df = (5 - 1) x (2 - 1) = 4.The critical value of chi-square at the 0.01 level of significance with 4 degrees of freedom is 13.27.
Using a calculator or software, we find that the calculated value of chi-square is 4.85,
which is less than the critical value of 13.27.
Therefore, we fail to reject the null hypothesis and conclude that there is not sufficient statistical evidence to indicate a significant difference in the distribution of aggregates across the five colleges.
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Related Questions
question if x, y, and z are integers and xy z is an odd integer, is x an even integer? (1) xy xz is an even integer. (2) y xz is an odd integer.
Answers
xy + xz is an even integer & x is even and y + xz is an odd integer & either (x-1) is even or (y-z) is even .
1. xy + xz is an even integer - SUFFICIENT
Given:
xy + z is odd ...(i)
xy + xz is even ...(ii)
subtracting (ii) from (i)
we get xz - z, which should be odd (* since odd - even = odd)
=> z(x-1) is odd
=> both z and (x-1) is odd
=> since (x-1) is odd, x must be even.
2. y + xz is an odd integer -INSUFFICIENT
Given:
xy + z is odd ...(i)
y + xz is odd ...(ii)
subtracting (ii) from (i)
we get xy + z - y - xz
= (x-1)(y-z) , which should be even
=> either (x-1) is even or (y-z) is even ....insufficient to determine
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If someone can ride a skateboard 2 miles in 10 minutes how many miles can still ride the skateboard and 1.5 miles
Answers
Answer:
7 and a half minutes. have a good one.
What does P’ in geometry. What does the ‘ mean when doing probability?
Answers
Answer:
I believe its proposition
Step-by-step explanation:
im almost 100% sure
all you need is in the photo please answer fast
Answers
To solve for d:
1. Remove parenthesis:
\(0.2d-1.2=0.3d+5-3+0.1d\)2. Leave the terms with d in one side of the equation:
-Add 1.2 in both sides of the equation:
\(\begin{gathered} 0.2d-1.2+1.2=0.3d+5-3+0.1d+1.2 \\ 0.2d=\text{0}.3d+5-3+0.1d+1.2 \end{gathered}\)-Substract 0.3d and 0.1d in both sides of the equation:
\(\begin{gathered} 0.2d-0.3d-0.1d=0.3d-0.3d+5-3+0.1d-0.1d+1.2 \\ 0.2d-\text{0}.3d-0.1d=5-3+1.2 \end{gathered}\)3. Opperate similar terms:
\(-0.2d=3.2\)4. Divide into (-0.2) both sides of the equation:
\(\begin{gathered} \frac{-0.2}{-0.2}d=\frac{3.2}{-0.2} \\ \\ d=-16 \end{gathered}\)Then, d is -16Write an equation for the word problem below.
"The YMCA summer camp charges an initial registration fee of $40 and then charges $100 per week of camp."
y = mx + b
Answers
Weekly (slope) - 100
Y=100x+40
Answer:
The equation is in slope-intercept form, Y = MX + B, where M is the slope and B is the y- intercept. in this case, the slope is 100 and the y- intercept us 40.
I hope this will help you!
Step-by-step explanation: The equation for the word problem is Y = 100x + 40. Where Y is the total cost of the summer camp, x is the number of weeks of camp, 100 is the cost per week of camp, and 40 is the registration fee.
Which number is equivalent to the improper fraction 35/4
Answers
Step-by-step explanation:
If you want to make the improper fraction into a mixed fraction/decimal;
35/4 = 32/4 + 3/4 = 8 3/4 = 8.75.
The number equivalent to the improper fraction 35/4 is 8 3/4.
We have,
To convert the improper fraction 35/4 into a mixed number, divide the numerator (35) by the denominator (4):
35 ÷ 4 = 8 remainder 3
The quotient, 8, represents the whole number part, and the remainder, 3, represents the numerator of the fractional part.
So, the equivalent mixed number is:
8(3/4)
Therefore,
The number equivalent to the improper fraction 35/4 is 8 3/4.
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While attempting to measure its risk exposure for the upcoming year, an insurance company notices a trend between the age of a customer and the number of claims per year. It appears that the number of claims keeps going up as customers age. After performing a regression, they find that the relationship is (claims per year) = 0.217 * (age) + 9.04. 1f a customer is 48.282 years old, how many claims would you expect them to make in a given year?
a. 180.84
b. 10.48
c. 19.52
d. 436.69
e. We do not know the observations in the data set, so we cannot answer that question
Answers
If a customer is 48.282 years old, we would expect them to make approximately 19.52 claims in a given year.
According to the regression relationship provided by the insurance company, the number of claims per year is determined by the customer's age. The equation given is: (claims per year) = 0.217 * (age) + 9.04.
To find the expected number of claims for a customer who is 48.282 years old, we substitute the age value into the equation:
Claims per year = 0.217 * 48.282 + 9.04
Claims per year ≈ 10.48
Therefore, if a customer is 48.282 years old, we would expect them to make approximately 10.48 claims in a given year. The correct answer is option B.
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Using the Normal approximation, the probability that sample average of the heights falls
within 2 centimeter of the population average is 0.9253374
Feedback
Using the Normal approximation, the computation of a probability associated with the random
variable is conducted with the functions of the Normal distribution for the same expectation and
standard deviation as the original distribution.
The expectation is μ = 170.035. The standard deviation is σ = 1.122.
The event corresponds to the interval [μ - 2, μ + 2]. Therefore, the approximated probability is
mu + 2]. Therefore, the approximated probability is
> mu <- 170.035
> sig <- 1.122
> pnorm(mu+2,mu,sig) - pnorm(mu-2,mu,sig)
[1] 0.9253374
The correct answe
Answers
Using the Normal approximation, the probability that sample average of the heights falls between [μ - 2, μ + 2] is approximately 0.9253374.
The Normal approximation is used for estimating the probabilities of a random variable. It is applied when the sample size is large enough, and the mean and variance of the population are known. In this case, the sample size is large enough, and the mean and variance of the population are known.The event corresponds to the interval [μ - 2, μ + 2]. Therefore, the approximated probability is 0.9253374, which is calculated using the standard Normal distribution table. The Z-score for μ - 2 is -2/σ, and the Z-score for μ + 2 is 2/σ. The probability between the two Z-scores is calculated by finding the difference between the two values in the table.
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(9* 1010) - (4 * 1010) =
How to answer
Answers
(9090) - (4040)
Then subtract both of them.
5050
Answer: 5050
Scale Factor: 1/2; Center: point N
Answers
The new coordinates of points M and O is determined as;
M = (0.5, - 1)
O = (2.5, -2).
What is the new coordinate of points of M and O?The new coordinate of points M and O after applying the scale factor is calculated as follows;
The given scale factor = 1/2
The current coordinates of point M and O is;
M = (1, - 2)
O = (5, - 4)
A scale factor can be used to either enlarge a figure or decrease a figure.
When the scale factor is less than 1, it means the new figure will be smaller than the original figure.
However, if the scale factor is greater than 1, the new figure will be greater than the original figure.
The new coordinates of points M and O is determined as follows;
M = (1 x 1/2, -2 x 1/2) = (0.5, - 1)
O = (5 x 1/2, -4 x 1/2) = (2.5, -2)
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masses of 200 and 800 g are 12 cm apart. (a) find the gravitational force on a 100 g object situated at a point on the line joining the masses 4.0 cm from the 200 g mass. (
Answers
The gravitational force on the 100 g object situated 4.0 cm from the 200 g mass is approximately \(2.66972 \times 10^-11 N.\)
What is gravitational force?Gravitational force is the force of attraction that exists between two objects with mass. It is one of the fundamental forces of nature and is described by Newton's law of universal gravitation. According to this law, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
To find the gravitational force on a 100 g object situated at a point on the line joining the masses, we can use the formula for gravitational force:
\(F = (G * m1 * m2) / r^2\)
Where:
F is the gravitational force,
G is the gravitational constant (approximately \(6.67430 \times 10^-11 N(m/kg)^2),\)
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, the masses are 200 g and 800 g, which can be converted to 0.2 kg and 0.8 kg respectively. The distance between the masses is 12 cm, which is equivalent to 0.12 m.
We want to find the gravitational force on a 100 g object situated at a point on the line 4.0 cm from the 200 g mass. This distance is 0.04 m.
Substituting the values into the formula, we have:
\(F = (6.67430 \times 10^-11 N(m/kg)^2) \times (0.2 kg) \times (0.1 kg) / (0.04 m)^2\)
Calculating this expression:
\(F = (6.67430 \times 10^-11 N(m/kg)^2) \times(0.2 kg) \times (0.1 kg) / (0.04 m)^2= 2.66972 \times 10^-11 N\)
Therefore, the gravitational force on the 100 g object situated 4.0 cm from the 200 g mass is approximately \(2.66972 \times 10^-11 N.\)
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Write and equivalent fraction using the picture.3/5=
Answers
Answer:
An example is 6/10
Step-by-step explanation:
We can multiply the numerator and denominator by the same number to get an equivalent fraction. I multiplied by 2. 3 times 2 = 6. 5 times 2 = 10. Therefore, it is 6/10.
I hope this helped and please mark me as brainliest!
What is the value of x in the equation 3/4(14x+8)-(1/2x+2)=3/8(4-x)-1/4
Answers
Answer:
-37/68
Step-by-step explanation:
3/4(14x+8)-(1/2x+2)=3/8(4-x)-1/4
(21/2x+6)-(1/2+2)=(3/2x-3/8)-1/4
(21/2x-1/2x)+(6-2)=3/2x-3/8-1/4
10x+4=3/2x-5/8
37/8=-17/2x
37/8 (2)=-17/2x(2)
37/4=-17x
37/68=-x
-37/68=x
Lee washes the outsides of houses. It takes him 40 minutes to power wash a one-story home, and he uses 180 gallons of water. Power washing a two-story home takes less than 90 minutes, and he uses a maximum of 5,000 gallons of water per week. Lee works no more than 40 hours each week, and his truck holds 500 gallons of water. He charges $90 to wash a one-story home and $150 to wash a two-story home. Lee wants to maximize his weekly washing income washing houses. Let x represent the number of one-story houses and y represent the number of two-story houses.
What are the constraints for the problem?
Answers
Answer:
40x + 90y <2400
18x + 30y < 500
Step-by-step explanation:
Lee washes houses. It takes him 40 minutes to wash a one-story home, and he uses 18 gallons of water. Power washing a two-story home takes less than 90 minutes, and he uses 30 gallons of water. Lee works no more than 40 hours each week, and his truck holds 500 gallons of water. He charges $90 to wash a one-story home and $150 to wash a two-story home. Lee wants to maximize his income washing one- and two-story houses. Let x represent the number of one-story houses and y represent the number of two-story houses. What are the constraints for the problem
Let
x=one story houses
y=two story houses
The constraints are the following:
1. Lee works no more than 40 hours each week.
40 hours=40 × 60 minutes
=2400 minutes
2. Lee's truck holds 500 gallons of water.
it takes Lee 40 minutes and 18 gallons of water to wash a one-story house.
it takes Lee 90 minutes and 30 gallons of water to wash a two-story house.
First constraint:
40*x + 90*y < 2400
40x + 90y <2400
Second constraint:
18*x + 30*y < 500
18x + 30y < 500
Answer:
It’s D
Step-by-step explanation:
solve the following equation: x2-5=7
Answers
Answer:
x= 6
Step-by-step explanation:
Step 1: Write equation
2x - 5 = 7
Step 2: Solve for x
Add 5 to both sides: 2x = 12
Divide both sides by 2: x= 6
Step 3: Check
Plug in x to verify if it's a solution.
2(6) - 5 = 7
12 - 5 = 7
7 = 7
please help 15pts and will give brainlist!!
Answers
Answer:
1st ans
(x+15)=135(alternate angle)
x=135-15
x=120
2nd ans
(8x-4)=92(corresponding angle)
8x=92+4
x=96/8
x=12
3rd ans
(x+1)=51(vertically opposite angle)
x=51-1
x=50
Melissa drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Melissa drove home, there was notraffic and the trip only took 5 hours. If her average rate was 21 miles per hour faster on the trip home, how far away does Melissa live from the mountains?Do not do any rounding.
Answers
Let
x ----> average rate on the trip home
y ----> average rate on the trip to the mountains
Remember that
The rate or speed is equal to dividing the distance by the time
speed=d/t
d=t*speed
on the trip home
d=5x -----> equation 1
on the trip to the mountains
d=8y ----> equation 2
we know that
her average rate was 21 miles per hour faster on the trip home
x=y+21 -----> equation 3
therefore
substitute equation 3 in equation 1
d=5(y+21) -----> equation 4
Equate equation 2 and equation 4 (because the distance is the same)
8y=5(y+21)
solve for y
8y=5y+105
8y-5y=105
3y=105
y=35
Find out the distance
d=8y
d=8(35)=280
The answer is 280 mileswhich is an equivalent expression for 6 times d raised to the negative fourth power all over quantity 21 times d raised to the seventh power end quantity?
Answers
The equivalent expression for 6 times d raised to the negative fourth power all over quantity 21 times d raised to the seventh power end quantity is \(\frac{2}{7} d^{-11}\)
To find the equivalent expression, follow these steps:
The numerator is 6 times d raised to the negative fourth power, which can be written as 6×\(d^{-4}\). The denominator is 21 times d raised to the seventh power, which can be written as 21×\(d^{7}\). So, the given expression= \(\frac{6d^{-4}}{21d^7}\).To find the equivalent expression, the given expression should be simplified. The numerator has the number 6 and the denominator has the number 21. The ratio 6/21 can be simplified to 2/7.Next, we can use the properties of exponents to simplify the expression further. The numerator has \(d^{-4}\) and the denominator has \(d^{7}\). This can be simplified as \(d^{-4-7} =d^{-11}\) Thus, the equivalent expression for \(\frac{6d^{-4}}{21d^7}\) is \(\frac{2}{7}d^{-11}\).So the equivalent expression is \(\frac{2}{7} d^{-11}\).
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Part B: Starting from the origin, explain how to plot the following three points accurately: (2, −2) (−2, 1.5) (−1, fraction 2 over 4) HELP PLEASEEEE
Answers
1. (2,-2). From the origin, go 2 units to the right and two units down
2) (-2,1.5) From the origin, go 2 units to the left and 1.5 units up
3) (-1,\(\frac{2}{4}\)) From the origin, go 1 unit to the left and half a unit up
!!!!!!!!!!!!!!!!!!!!!!!!!HELP!!!!!!!!!!!!!!! Find the slope of the line.
Answers
Answer:
3/1
Step-by-step explanation:
Make sure you know a few concepts first:
The point where the line crosses the y-axis (or vertical axis) is called the y-intercept.Slope is commonly taught using \(\frac{rise}{run}\) as I will teach it here.First, find the y-intercept of the line. This line crosses the y-axis as (0,0), so that is the y -intercept.Find another point on the line, preferably where it crosses a whole-number coordinate (just for simplicity… you can use any point on the line). We will use the point (1,3). Counting in your head, count vertically from (0,0) until you are horizontal to the point (1,3) we chose earlier. Put the distance it took to reach that point on the top (numerator) of the fraction. Because it takes 3 counts to be horizontal, your fraction should look like \(\frac{3}{run}\).Count horizontally until you reach the point (1,3). Put the number of units on the bottom (denominator) of the fraction. The number was 1 unit, so your finished fraction which is the slope is \(\frac{3}{1}\).Alternatively
Use the formula for slope from two points… \(\frac{x_{1} -y_1}{x_2-x_1}\)Find two points on the line. We will use (0,0) and (1,3). Designate one point as 1 and the other as 2. We will choose (0,0) to be 1 and (1,3) to be 2.Plug in the points following the “key” you created: Let x₁ be the x coordinate from ordered pair 1, let y₁ be the y coordinate point from ordered pair 1, etc. Following this pattern, you should be set up like this: \(\frac{3-0}{1-0}\)Subtract to get \(\frac{3}{1}\) as your slope.find the critical value za/2 that corresponds to a 80 confidence level
Answers
the critical value zα/2 that corresponds to an 80% confidence level is approximately 1.2816.
To find the critical value zα/2 that corresponds to an 80% confidence level, we need to determine the value of α/2.
A confidence level of 80% implies that the remaining area under the standard normal distribution curve is (1 - 0.80) = 0.20.
Since the standard normal distribution is symmetric, we divide this remaining area equally between the two tails, resulting in
α/2 = 0.10.
To find the corresponding critical value, we look up the z-score that corresponds to an area of 0.10 in the standard normal distribution table (also known as the z-table) or use a statistical calculator.
The critical value zα/2 for α/2 = 0.10 is approximately 1.2816.
Therefore, the critical value zα/2 that corresponds to an 80% confidence level is approximately 1.2816.
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Simplifying Perfect Roots
Quiz Active
4
5 6
7
8
9
Which expression is equivalent to $/32x10-15?
25-10
2x1²23
65-10
6x²3
10
Answers
Answer: 10
Step-by-step explanation:
5x+3y=-9 in slope intercept
Answers
The slope-intercept form of the equation 5x + 3y = -9 is y = (-5/3)x - 3.
To rewrite the equation 5x + 3y = -9 in slope-intercept form, which is in the form y = mx + b, where m represents the slope and b represents the y-intercept, we need to solve for y.
Let's start by isolating y:
5x + 3y = -9
Subtract 5x from both sides:
3y = -5x - 9
Divide both sides by 3 to isolate y:
y = (-5/3)x - 3
Now, we have the equation in slope-intercept form. The slope of the line is -5/3, which means that for every unit increase in x, y decreases by 5/3 units. The y-intercept is -3, which means that the line intersects the y-axis at the point (0, -3).
Therefore, the slope-intercept form of the equation 5x + 3y = -9 is y = (-5/3)x - 3.
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What is the measure of angle onp? 50° 65° 80° 130°
Answers
Answer:
80
Step-by-step explanation:
edge 2023
Solve for x in the diagram below?
Answers
Answer:
x = 35
Step-by-step explanation:
the 3 angles lie on a straight line and sum to 180° , that is
40 + 2x + 30 + 40 = 180
110 + 2x = 180 ( subtract 110 from both sides )
2x = 70 ( divide both sides by 2 )
x = 35
A pet toy company performed an experiment to see how
many toys dogs might play with. Each of the 60 dogs
involved was put in a room with its owner and 4 different
toys.
The researchers recorded how many toys each of the 60
dogs used.
Fill in the blanks to complete the probability
distribution.
Do not round your answers.
Toys used
Frequency
Probability .05
0
3
1 2
2
0.25
3
3 4
21 12
9
0.35 0.2 0.15
Answers
The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
What is the probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
To fill in the blanks, we need to use the given information to complete the probability distribution table.
We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.
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Evaluate r(x)=−x−7 when x=−2,0, and 5.
Answers
Answer:
-5, -7, and -12
Step-by-step explanation:
A function is defined as a relation between a set of inputs having one output each.
The values of the function r(x) at x = -2, 0 and 5 are -5, -7, and -12.
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
A function r(x)
r(x) = x - 7
The value of r(x) at x = -2:
r(-2) = - ( -2) - 7
r(-2) = 2 - 7 = -5
The value of r(x) at x = 0:
r(0) = -0 - 7 = -7
The value of r(x) at x = -2:
r(5) = -5 - 7 = -12
We see that,
Domain = -2, 0, and 5.
Range = -5, -7, and -12.
Thus,
The values of the function r(x) at x = -2, 0 and 5 are -5, -7, and -12.
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5. For what value of 'a' the differential equation 4ydx + axdy=0 is exact? A. 1 B. -4 C. 4
D. None of these
Answers
To determine the value of 'a' that makes the given differential equation exact, we need to check if the partial derivatives satisfy a certain condition.
The given differential equation is 4ydx + axdy = 0. For a differential equation to be exact, the partial derivatives of the coefficients with respect to x and y must satisfy the condition ∂(∂M/∂y)/∂(∂N/∂x) = ∂(∂M/∂x)/∂(∂N/∂y), where M = 4y and N = ax.
Calculating the partial derivatives, we have:
∂M/∂y = 4
∂N/∂x = a
∂(∂M/∂y)/∂(∂N/∂x) = ∂(4)/∂(a) = 0
Since the condition is not satisfied for any value of 'a', we can conclude that there is no value of 'a' that makes the differential equation exact. Therefore, the correct answer is D. None of these.
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what is inverse tangent derivative?
Answers
Answer:
(tan-1x)' = 1/(1 + x2)
Step-by-step explanation:
The differentiation of tan inverse x is the process of finding the derivative of tan inverse x with respect to x.
Work out the volume of this sphere?
Answers
Answer:
434.9
Step-by-step explanation:
\(\frac{4}{3}\) × π (4.7)²
434.893
Answer:
434.893
Step-by-step explanation:
hope this helps