Answers
Answer:
147cm³
Step-by-step explanation:
Bottom rectangular prism: 3x4x6=72
Top rectangular prism: 5x5x3=75
72+75=147cm³
Related Questions
Write 8:18 as a fraction in simplest form.
Ratio as a Fraction:
Fraction in Simplest Form:
Answers
Answer:
[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]
[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]
Step-by-step explanation:
Part 1: Writing a ratio as a fraction
A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,
Replace the colon with a divisor line or the divisor line with a colon (use the first portion to transform a ratio into a fraction and the second form to transform a fraction into a ratio).Therefore, 8:18 as a fraction is 8/18.
Part 2: Fraction in simplest form
To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.
8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.
Instead, if both numbers are even, divide by 2.
8/2 = 4
18/2 = 9
Check to see if the new numerator and denominator can reduce any further.
4/9 = 4/9
The fraction in simplest form is 4/9.
what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?
Answers
Answer:
Approximately 3.05
Step-by-step explanation:
Using "compatible numbers" we can simply round these numbers to integer values. Let's make 76.32 => 76 and 24.98 => 25
So from here let's do 76/25 to get 3 R 1/25
1/25 as a decimal is .04
So far, we have 3.04. Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98. So we should consider an extra value in our decimal.
Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.
Thus our number will be 3.04 + .01.
Making our quotient approximately 3.05.
Cheers.
* The American Diabetes Association estimates that 8.3% of people in the
United States have diabetes. Suppose that a medical lab has developed
a simple diagnostic test for diabetes that is 98% accurate for people who
have the disease and 95% accurate for people who do not have it. The
medical lab gives the test to a randomly selected person. What is the
probability that the diagnosis is correct? Explain each step.
Answers
Answer:
The probability that the diagnosis is correct is 0.95249.
Step-by-step explanation:
We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.
Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.
Let the probability that people in the United States have diabetes = P(D) = 0.083.
So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917
Also, let A = event that the diagnostic test is accurate
So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98
And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95
Now, the probability that the diagnosis is correct is given by;
Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')
= (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)
= 0.08134 + 0.87115
= 0.95249
Hence, the probability that the diagnosis is correct is 0.95249.
Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorates. When the average furfuryl ether content reaches 6 μg per liter, a typical consumer begins to taste an unpleasant chemical flavor. At α = .05, would the following sample of 12 randomly chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold? 8.92 6.99 5.54 5.73 6.38 5.51 6.45 7.50 8.48 5.56 6.90 6.46
Answers
Answer:
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
Step-by-step explanation:
We formulate our null and alternative hypotheses as
H0 u≤ 6 ug Ha : u > 6 ug
The significance level ∝ = 0.05
The test statistic used is
t = X` - u / s/ √n
which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.
The critical region t > t (0.05,11) = 1.796
We compute the t value from the data
Xi Xi²
8.92 79.5664
6.99 48.8601
5.54 30.6916
5.73 32.8329
6.38 40.7044
5.51 30.3601
6.45 41.6025
7.50 56.25
8.48 71.9104
5.56 30.9136
6.90 47.61
6.46 41.7316
80.42 553.0336
Now x` = ∑x/ n = 80.42/12 = 6.70
S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)
= 1/11 (553.034-538.948) = 1.2805
s= 1.1316
Putting the values in the test statistics
t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12
= 2.1698
The critical region t > t (0.05,11) = 1.796
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
A number is chosen at random from 1 to 10. Find
the probability of selecting 4 or a factor of 6.
Step by step.
Answers
Answer:
1/2
Step-by-step explanation:
The possible outcomes are
1,2,3,4,5,6,7,8,9,10
Factors of 6 are 1,2,3,6
or a 4
1,2,3,4,6 are the outcomes we want
There are 5 "good" outcomes
P( 4 or a factor of 6) = "good" outcomes/ total
= 5/10
=1/2
Answer:
[tex]\boxed{\frac{1}{2} }[/tex]
Step-by-step explanation:
There are total 10 outcomes.
[tex]1,2,3,4,5,6,7,8,9,10[/tex]
The probability of selecting 4 is 1 outcome out of total 10 outcomes.
Factors of 6 are [tex]1,2,3,6[/tex].
These are 4 outcomes out of total 10 outcomes.
The probability of selecting 4 or a factor of 6 is:
[tex]\displaystyle \frac{1}{10} +\frac{4}{10} =\frac{5}{10} =\frac{1}{2}[/tex]
find the value of each variable and the measure of each angle
Answers
Answer:
Left angle = 60°
Top angle = 120°
Right angle = 60°
Step-by-step explanation:
Use what you know about angle relationships to set up equations you can solve for each variable.
The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.
You have two variables, so you need at least two equations (I made three but only used two).
The work is in my attachment, comment of you have questions.
In Triangle A B C, what is the value of x? Triangle A B C. Angle A is (10 x minus 10) degrees, angle B is (8 x) degrees, angle C is (10 x + 8) degrees.
Answers
Answer:
6.5
Step-by-step explanation:
The sum of all angles in a triangle are 180 degrees.
=> 10x -10 + 8x + 10x + 8 = 180
=> 28x -2 = 180
=> 28x = 182
=> x = 6.5
So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees
Angle B = 8 x 6.5 = 52 degrees
Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.
55 + 52 + 73 = 55 + 125 = 180 degrees
Let a >= b.
show that gcd(a,b) = gcd(a-b, b)
Answers
let [tex] \gcd(a,b)= G[/tex] , $a\ge b$
$\therefore a=G\cdot m$ and $b=G\cdot n$
$a-b=Gm-Gn=G(m-n)$
Now, $\gcd(a-b,b)$ clearly is, $G$
Smoking by Race for Males Aged 18-24
Smoker Nonsmoker Row Total
(S) (N)
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
Calculate the probabilities given below (Round your answers to 4 decimal places.):
i. P(S) 0.3200
ii. P(W) 0.8500
iii. P(S | W) 0.2720
iv. P(S | B) 0.0300
v. P(S and W) 0.9062
vi. P(N and B) 0.1765
Answers
Answer:
(i) 0.32 (ii) 0.85
(iii) 0.3412 (iv) 0.20
(v) 0.29 (vi) 0.12
Step-by-step explanation:
The data provided is as follows:
Race Smoker (S) Nonsmoker (N) Row Total
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
(i)
Compute the value of P (S) as follows:
[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]
P (S) = 0.32.
(ii)
Compute the value of P (W) as follows:
[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]
P (W) = 0.85.
(iii)
Compute the value of P (S|W) as follows:
[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]
P (S|W) = 0.3412.
(iv)
Compute the value of P (S|B) as follows:
[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]
P (S|W) = 0.20.
(v)
Compute the value of P (S∩W) as follows:
[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]
P (S∩W) = 0.29.
(vi)
Compute the value of P (N∩B) as follows:
[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]
P (S∩W) = 0.12.
PLEASE HELP SOON! A 2011 study by the National Safety Council estimated that there are nearly 5.7 million traffic accidents year. At least 28% of them involved distracted drivers using a cell phones or texting. The data showed that 11% of drivers at any time are using cell phones. Car insurance companies base their policy rates on accident data that shows drivers have collisions approximately once every 19 years. That's a 5.26% chance per per year. Given.
A - Let dc= event that a randomly selected driver is using a cell phone. what is P(DC)? B - Let ta = event that a randomly selected driver has a traffic accident. what is P(ta) C - how can you determine if cell phone use while driving and traffic accidents are related? D - Give that the driver has an accident, what is the probability that the driver was distracted by a cell phone? Write this event with the correct conditional notation.
Answers
Answer:
(A) 0.11
(B) 0.0526
(C) Related
(D) 0.28
Step-by-step explanation:
The data provided is:
DC = event that a randomly selected driver is using a cell phone
TA = event that a randomly selected driver has a traffic accident
(A)
From the provided data:
P (DC) = 0.11
(B)
From the provided data:
P (TA) = 0.0526
(C)
To determine whether the events DC and TA are dependent, we need to show that:
[tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]
The value of P (DC ∩ TA) is,
[tex]P(DC\cap TA)=P(DC|TA)\time P(TA)[/tex]
[tex]=0.28\times 0.0526\\=0.014728[/tex]
Now compute the value of P (DC) × P (TA) as follows:
[tex]P (DC) \times P (TA)=0.11\times 0.0526=0.005786[/tex]
So, [tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]
Thus, cell phone use while driving and traffic accidents are related.
(D)
The probability that the driver was distracted by a cell phone given that the driver has an accident is:
P (DC | TA) = 0.28
A company has 8 mechanics and 6 electricians. If an employee is selected at random, what is the probability that they are an electrician
Answers
Answer:
[tex]Probability = \frac{3}{7}[/tex]
Step-by-step explanation:
Given
Electrician = 6
Mechanic = 8
Required
Determine the probability of selecting an electrician
First, we need the total number of employees;
[tex]Total = n(Electrician) + n(Mechanic)[/tex]
[tex]Total = 6 + 8[/tex]
[tex]Total = 14[/tex]
Next, is to determine the required probability using the following formula;
[tex]Probability = \frac{n(Electrician)}{Total}[/tex]
[tex]Probability = \frac{6}{14}[/tex]
Divide numerator and denominator by 2
[tex]Probability = \frac{3}{7}[/tex]
Hence, the probability of selecting an electrician is 3/7
This solid shape is made from 5 cubes. Which of the diagrams show the plan of the solid? Please help!
Answers
Answer:
A Maybe
Step-by-step explanation:
Cogntive identification
Unable to answer mathematically or analytically
The Plan of the solid shape is shown by : (A)
What is the Meaning of solid shape?A solid shape can be defined as a shape that possesses three dimensions. that is to say they are three dimensional shapes.
A solid shape has both length, width and height. They are more tangible and look physical than two dimensional shape.
solid shapes can take up space in the universe because they are more tangible and realistic.
In conclusion, the Plan of the solid shape is shown by : (A)
Learn more about solid shape: https://brainly.com/question/16717260
#SPJ2
What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)?
Answers
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Here is the equation
[tex]20+3\times(7+4)+5+2\times(7+9)[/tex]
In the order of operations parentheses go first so we get
[tex]20+3\times11+5+2\times16[/tex]
Next we do the multiplication
[tex]20+33+5+32\\[/tex]
And finally we add them all up
[tex]20+33+5+32=90\\[/tex]
Thus, 90 is the answer of [tex]20+3\times(7+4)+5+2\times(7+9)[/tex] or [tex]20+3(7+4)+5+2(7+9)[/tex]
A plane took off at a point that is 42 meters from the control tower. The flight path takes the plane over the control tower that is 98 meters high. After traveling 83 meters, which statement is most accurate?
A. The plane needs to be about 15 meters higher to clear the tower.
B. The plane clears the tower with about 27 meters to spare.
C. The plane clears the tower with about 15 meters to spare.
D. The plane needs to be about 27 meters higher to clear the tower.
Answers
Answer:
D. The plane needs to be about 27 meters higher to clear the tower.
Step-by-step explanation:
In this scenario a triangle is being formed. The base the plane's takeoff point to the tower base which is 42 meters (x).
The hypothenus is the distance travelled by the plane which is 83 meters (h)
The height of the tower is 98 Meters
We want to calculate the height of our triangle (y) so we can guage if the plane scaled the tower.
According to Pythagorean theorem
(x^2) + (y^2) = h^2
y = √ (h^2) - (x^2)
y = √ (83^2) - (42^2)
y= √(6889 - 1764)
y= 71.59 Meters
The height from the plane's position to the top of the tower will be
Height difference = 98 - 71.59 = 26.41 Meters
So the plane should go about 27 Meters higher to clear the tower
helppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
Brainliest!
Step-by-step explanation:
36x^-4y^2/5x^2y^-3z^-2
36y^5z^2/5x^6
make everything positive
STUCK Basic geometry A for senior year school
Answers
Answer:
(C) A reflection across a horizontal line and a horizontal translation
Step-by-step explanation:
We can see that, near the x-axis, these shapes are 3 y values away from the x-axis, meaning that if we reflect one over the x-axis we will be at the same y values as the other shape.
Reflecting these points shows that we’ve got the same shape, just skewed the one side. We can then translate this shape horizontally to get it to where we want it.
Hope this helped!
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.
1. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = (x - mu )?
2. What are the units of the corresponding z scores?
A. The z scores are measured with units of "beats per minute".
B. The z scores are measured with units of "minutes per beat".
C. The z scores are measured with units of "beats."
D. The z scores are numbers without units of measurement.
Answers
Answer:
D. The z scores are numbers without units of measurement.
Step-by-step explanation:
Z-scores are without units, or are pure numbers.
Determine the equation of the exponantial function with a common ratio of 2, a horizontal asymptote at y=4 and passin through the point (2,10).
Answers
Answer:
Step-by-step explanation:
Suppose the radius of a circle is 5 units. What is its circumference?
Answers
Answer:
C≈31.42
Step-by-step explanation:
C=2πr
C=2xπx5
C≈31.42
pls mark as brainliest
which expression is equivalent to x^-5/3
Answers
Answer:
B
Step-by-step explanation:
Since the power is negative, you automatically know it has to be a or b, because the only way it would be negative is if it was brought from the denominator to the numerator.
The answer is B, because the numerator of the power, is what is inside the square root, while the denominator is what is outside the square root.
plzz answer this fasttttttttt
Answers
Answer:
37°
This is because the square indicates a right angle.
53 - 90 = 37
We have,
∠AOB = 53°∠BOC = x°∠A0C = 90°Now,
AOB + ∠BOC = ∠A0C
⇒ 53° + x° = 90°
⇒ x° = 90° - 53°
⇒ x° = 37°
a function includes the points (4, -3) and (-9,4). what fraction in lowest terms represents the output value of this function for an input of zero
Answers
Answer:
-11/13
Step-by-step explanation:
The equation of the line through these points can be written using the 2-point form of the equation of a line:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (4 -(-3))/(-9-4)/(x -4) -3
y = (-7/13)x +28/13 -3
For x=0, the value of y is ...
y = 28/13 -39/13 = -11/13
The output for an input of 0 is -11/13.
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed?
Answers
Answer:
Speed of plane in still air is 270 mph
Wind speed is 30 mph
Step-by-step explanation:
Check the picture.
The speed of the plane in still air is 270 mph and the speed of the wind will be 30 mph.
What is the distance formula?The distance traveled by an object is the product of the speed of an object and the time taken.
Distance = speed x time
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind.
Let the speed of the plane be x
The speed of wind be y
Distance covered with the wind = (x + y)t
1200 = (x + y)4
(x + y) = 1200/4
(x + y)= 300 .....(a)
Distance covered against the wind = (x - y)t
1200 = (x - y)5
(x - y) = 1200/5
(x - y) = 240 .......(b)
By solving both the equation
(x + y)= 300
(x - y) = 240
Therefore the values will be x= 270mph and y = 30 mph
Learn more about the distance formula:
https://brainly.com/question/15172156
Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x
Answers
Answer:
[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]
Step-by-step explanation:
Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:
1) [tex]t = 2-x[/tex] Given
2) [tex]y = 5\cdot x +11[/tex] Given
3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties
4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property
5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property
6) [tex]y = -5\cdot (-x)+11[/tex] [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]
7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property
8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse
9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties
10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property
11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]
12) [tex]y = (-5)\cdot t +21[/tex] By 1)
13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result
14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition
15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition
16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property
17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property
18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result
In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].
A video rental store keeps a list of their top 15 movie rentals each week. This week the list includes 6 action, 4 comedies, 3 dramas, and 2 mysteries. The store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store. What is the probability that she selected 2 comedies and 1 action movie?
Answers
Answer:
32/1125Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome of event/Total outcome.
If a video rental store keeps a list of their top 15 movie rentals each week, the total outcome is 15.
If the list for the week includes 6 action, 4 comedies, 3 dramas, and 2 mysteries and the store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store, the probability that she selected 2 comedies and 1 action movie will be calculated as shown;
Probability of selecting 2 comedies = 4/15*4/15 = 16/225 (Note that the expected outcome in this case is 4).
Probability of selecting 1 action movie = 6/15 = 2/5
Hence, the probability that she selected 2 comedies and 1 action movie will be equivalent to 16/225*2/5 = 32/1125
Note that the rented movies will have to be returned hence reason for the replacement.
in a gp the sixth term is 8 times the third term, and the sum of the seventh and eighth term is 192. determine the common ratio
Answers
Answer:
common ratio = 2
Step-by-step explanation:
T6 = ar^5
T3 = ar²
T6 = 8 x T³
ar^5 = 8 x ar²
ar^5/ar² = 8
r³ = 8
r = ³√8
r = 2
In a recent year, a sample of grade 8 Washington State public school students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed. Question 9 (2.5 points) If 2000 students are randomly selected, how many would you expect to have a score between 250 and 305?
Answers
Answer:
The number is [tex]N =1147[/tex] students
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 281[/tex]
The standard deviation is [tex]\sigma = 34.4[/tex]
The sample size is n = 2000
percentage of the would you expect to have a score between 250 and 305 is mathematically represented as
[tex]P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )[/tex]
So
[tex]P(250 < X < 305 ) = P(-0.9012< Z<0.698 )[/tex]
[tex]P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)[/tex]
From the z table the value of [tex]P( z_2 < 0.698) = 0.75741[/tex]
and [tex]P(z_1 < -0.9012) = 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.75741 - 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.57[/tex]
The percentage is [tex]P(250 < X < 305 ) = 57\%[/tex]
The number of students that will get this score is
[tex]N = 2000 * 0.57[/tex]
[tex]N =1147[/tex]
In a school, there are 25% fewer 11th graders than 10th graders, and 20% more 11th graders than 12th graders. The total number of students in 10th, 11th, and 12th grades in the school is 190. How many 10th graders are there at the school?
Answers
Answer:
There are 80 10th graders in the school
Step-by-step explanation:
Let the number of 10th graders be x
There are 25% fewer 11th graders
That mean x - 25% of x
x -0.25x = 0.75x
There are 20% more 11th graders than 12th graders
So if number of 12th graders = y, then
0.75x = y + 20/100 * y = y + 0.2y = 1.2y
Since ;
0.75x = 1.2y
then y = 0.75x/1.2 = 0.625x
So let’s add all to give 190
x + 0.75x + 0.625x = 190
2.375x = 190
x = 190/2.375
x = 80
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want % confidence that the sample mean is within points of the population mean, and the population standard deviation is .
Answers
Answer: hello below is the complete question
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number
answer : 737 adults
Step-by-step explanation:
confidence interval = 90% = 0.9
( E ) = 4
standard deviation = 66
first we have to calculate the value of a
a = 1 - confidence interval
= 1 - 0.9 = 0.10 hence a / 2 = 0.05
next find the value of Z a/2 from table
Z[tex]_{0.05}[/tex] = 1.645
The number of Adults selected can be determined using this relation
N = [tex](Z_{a/2} * (s/E))^2[/tex]
= [tex](Z_{0.05} * ( 66/4))^2[/tex]
= 737
Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner 9University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:
x 1 2 3 4 5
y 14 18.9 14.4 19.6 20.0
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
(a) Draw a scatter diagram.
(b) Find the equation of the least-squares line, and plot the line on the scatter diagram of part (a).
(c) Find the correlation coefficient r. Find the coefficient of determination . What percentage of variation in y is explained by the variation in x and the least squares model?
Answers
Answer:
The answer and explanation are below
Step-by-step explanation:
i followed the data that was given in the question.
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
a.) please refer to the attachment for the scatter diagram. Y was plotted against X.
b. The equation is given as:
Y = b₁ + b₀X
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
b₁ = n∑xy - (∑x)(∑y)/n(∑x²) - (∑x)²
b₁ = 5 x 275 - 15 x 87.3/5 x 55 - (15²)
= 1375-1309.5/275-225
= 65.5/50
= 1.31
b₀ = 87.3/5 - 1.31(15/5)
= 87.3/5 - 1.31x3
= 13.53
the regression line is
Y = 13.53 + 1.31X
please refer to the attachment for the diagram for the regression line.
c. we are required to find r.
r = n∑XY - (∑X)(∑Y)/√n∑X²-(∑X)² × √n∑y²-(∑y)²
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
inserting these values:
r = 5 x 275-(15)(87.3)/√275-225 x √7848.85 - 7621.29
= 65.5/106.69
= 0.6139
Coefficient of determination = r²
r = 0.6139
r² = 0.3769 = 37.69%
Therefore 37.69% variation in y is explained by variation in x and the least square model.
