Answers
Answer:
C and A
Step-by-step explanation:
For the triangle to be isosceles then the legs are congruent, that is
XZ = XY , substitute values
5x - 1 = 3x + 5 ( subtract 3x from both sides )
2x - 1 = 5 ( add 1 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3 → C
(10)
The diagonals of a square bisect each other
Calculate PR using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2-y_{1})^2 }[/tex]
with (x₁, y₁ ) = P(0, 0) and (x₂, y₂ ) = R(6, - 8)
PR = [tex]\sqrt{(6-0)^2}+(-8-0)^2[/tex]
= [tex]\sqrt{6^2+(-8)^2}[/tex]
= [tex]\sqrt{36+64}[/tex]
= [tex]\sqrt{100}[/tex]
= 10
Then
PT = 0.5 × 10 = 5 → A
Related Questions
Add f(x)=2x^3 and g(x) = log(x+4) + 100
Answers
The sum of the given function is 2x^3 + log(x+4) + 100
Sum of functionsGiven the following functions
f(x)=2x^3 and;
g(x) = log(x+4) + 100
Take the sum of the functions
f(x) + g(x) = 2x^3 + log(x+4) + 100
Hence the sum of the given function is 2x^3 + log(x+4) + 100
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PLSS HELP IMMEDIATELY!!! i’ll give brainiest if u don’t leave a link!
Answers
Answer:
Step-by-step explanation:
B i took that same quiz
Help this is clever 8.4 I need this by 7
Answers
Answer:
Just do 8.4 times 7
Step-by-step explanation:
8.4 times 7 = 58.8
The random variable x is known to be uniformly distributed
between 10 and 20.
a. Compute P( 10 ≤ x ≤ 15)
Answers
The random variable x is uniformly distributed between 10 and 20. To compute the probability of 10 ≤ x ≤ 15, Hence, the probability of 10 ≤ x ≤ 15 is 0.5.
Since x is uniformly distributed between 10 and 20, the probability density function (PDF) of x is a constant within this range. The PDF is given by the reciprocal of the range, which in this case is 1/10.
To find the probability of 10 ≤ x ≤ 15, we need to calculate the area under the PDF curve between 10 and 15. Since the PDF is constant, the area under the curve corresponds to the proportion of the total range that falls within this interval.
The width of the interval 10 ≤ x ≤ 15 is 15 - 10 = 5. The total range of x is 20 - 10 = 10. Therefore, the proportion of the total range that falls within the interval is 5/10 = 0.5.
Hence, the probability of 10 ≤ x ≤ 15 is 0.5. This means that there is a 50% chance that a randomly chosen value of x will fall within the interval from 10 to 15.
It is important to note that in a uniform distribution, the probability of any subinterval within the range is proportional to the width of that subinterval. In this case, since the subinterval 10 ≤ x ≤ 15 has a width of 5 out of the total range of 10, the probability is 0.5 or 50%.
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!!PLS HELP I WILL GIVE BRAINLEST!!
A family-sized box of cereal with dimensions 3x9x12 inches costs $6, while the regular size with
dimensions 2 x 8 x 9 inches costs $4.50. What is the diference in price per cubic inch?
Answers
they amount of money are not the same
reason why;
the reason why its not the same is because 2x8x9=144 and 3x9x12=324 and the amount of money spent is different
The difference in price per cubic inch between the two sizes of cereal boxes is $0.0128.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The volume of the family-sized box of cereal is:
= 3 x 9 x 12
= 324 cubic inches
The volume of the regular-sized box of cereal is:
= 2 x 8 x 9
= 144 cubic inches
The price per cubic inch of the family-sized box is:
= 6 / 324
= 0.0185 dollars per cubic inch
The price per cubic inch of the regular-sized box is:
= 4.50 / 144
= 0.0313 dollars per cubic inch
The difference in price per cubic inch is:
= 0.0313 - 0.0185
= 0.0128 dollars per cubic inch
Therefore,
The difference in price per cubic inch between the two sizes of cereal boxes is $0.0128.
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find the height of a cone when its diameter is 8 inches and the volume is 100 cubic inches
Answers
Answer:
[tex]\frac{75}{4\pi }[/tex] inches or approximately 5.97 inches
Step-by-step explanation:
Use the cone volume formula: V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
The diameter is 8 inches, so the radius will be 4 inches.
Plug in the radius and volume, and solve for h
V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
100 = [tex]\pi[/tex](4²)([tex]\frac{h}{3}[/tex])
100 = 16[tex]\pi[/tex][tex]\frac{h}{3}[/tex]
Divide each side by 16[tex]\pi[/tex]
[tex]\frac{25}{4\pi }[/tex] = [tex]\frac{h}{3}[/tex]
Cross multiply and solve for h:
4[tex]\pi[/tex]h = 75
h = [tex]\frac{75}{4\pi }[/tex]
So, the cone's height is [tex]\frac{75}{4\pi }[/tex] or approximately 5.97 inches
This is the equation: f(x)=x^2
e) Is f(x) symmetric? If so, what is the equation of the line of symmetry?
f) Does f(x) have a maximum or minimum? If so, at what point?
g) What are the x-intercept(s) of f(x)?
Answers
Answer:
e) yes, symmetric around the y-axis
f) minimum at (0,0)
g) x-intercept at 0
Step-by-step explanation:
Using the order of operations, what should be done first when evaluating this expression?
Negative one-half divided by 2 (9 + 3) minus 4 minus three-fourths (8)
Divide Negative one-half divided by 2.
Add 9 + 3.
Multiply Negative three-fourths (8).
Subtract 3 minus 4.
Answers
Answer:
You add (9+3)
Step-by-step explanation:
because PEMDAS evaluates the parenthesis first,
Answer:
It' B
Step-by-step explanation:
I got a 100 on the test
1. GASOLINE The table gives the cost of a gallon of gasoline at two stations. How much more does gasoline cost at Gas For Less than at Cut-Rate? Cut-Rate 2.x + 3.5 Gas for less V12
Answers
Answer:
GASOLINE The table gives the cost of a
gallon of gasoline at two stations.
How much more does gasoline cost at
Gas For Less than at Cut-Rate?
Step-by-step explanation:
Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable.
x^2(dw/dx)=sqrt(w)(3x+2)
w(x)= ? (Use C as the arbitrary constant)
Answers
The general solution of the given equation, x^2(dw/dx) = sqrt(w)(3x+2), expressed explicitly as a function of the independent variable, is w(x) = (1/27)((9x^2 + 6x + C)^3), where C is an arbitrary constant.
To solve the given equation, we can separate the variables and integrate.
First, rewrite the equation as
(1/sqrt(w))dw = (3x+2)/x^2 dx.
Integrate both sides with respect to their respective variables:
∫(1/sqrt(w))dw = ∫(3x+2)/x^2 dx.
The integral of (1/sqrt(w)) with respect to w is 2√w, and the integral of (3x+2)/x^2 with respect to x can be found using partial fractions or another suitable method.
After integrating and simplifying, we obtain:
2√w = (1/27)(9x^2 + 6x + C),
where C is the arbitrary constant.
To find the explicit solution, isolate w by squaring both sides:
w(x) = (1/27)((9x^2 + 6x + C)^3),
where w(x) is the function expressing the solution explicitly in terms of the independent variable x, and C is the arbitrary constant.
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Joseph orders some pizza for himself and his friends. The cost of each pizza is £12.50, and the delivery charge is £1.50. If Joseph orders 11 pizzas, how much does Joseph pay in total?
Answers
Answer:
£139
Step-by-step explanation:
£12.50 * 11 = 137.50
137.50 + 1.50 = £139
Answer:
137.5 + 1.50 = £139
Step-by-step explanation:
Please Give brainliest
Three less than the product of 5 and a number equals 7
Answers
5x-3=7
5x=10
x=2
Marcus wants to use a model to determine the difference − 8 − 3 ( + 3 ) -8-3+3. He starts with 8 negative counters. He wants to add 3 positive counters to the model without changing the value. How can he do that?
A. add 3 positive counters
B. add 3 positive counters and take away 3 negative counters
C. add 3 negative counters
D. add 3 positive counters and 3 negative counters
Answers
Without changing the value, Marcus can add 3 positive counters and 3 negative counters. Option d is correct.
To determine the difference -8 - 3 (+3), Marcus wants to use a model with counters. He starts with 8 negative counters, and in order to add 3 positive counters without changing the value, he can add 3 positive counters and 3 negative counters.
By adding 3 positive counters, he is increasing the value by 3. However, since he wants to maintain the same value, he also needs to add 3 negative counters. This ensures that the net change in value remains zero.
So, by adding 3 positive counters and 3 negative counters to the model, Marcus can represent the difference -8 - 3 (+3) without changing the overall value. Therefore, d is correct.
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In physics, we can find the amount of force needed to push or pull an object by multiplying the object’s mass by the object’s acceleration. The units of force are called Newtons.
force = mass × acceleration
F = ma
Find the amount of force it takes to push Jeff’s race car if the mass of the race car is 750 kg and the acceleration is 2.5 StartFraction m Over s squared EndFraction
The amount of force needed to push Jeff’s race car is
Newtons.
ALSO I DONT KNOW IF THIS IS MATH OR SCIENCE SO IMA PUT IT AS MATH
Answers
Answer:
1875
Step-by-step explanation:
750 x 2.5 = 1,875
2) The equation y = 18x represents the relationship between 2, the number of hours biked, and
y, the distance traveled,
Which ordered pairs represent a number of hours and the corresponding
distance in the given equation? Choose ALL that apply.
(2,36)
(3,54)
(5,23)
(23,5)
(36,2)
(54,3)
Answers
Answer:(2,36)and (3,54)
Step-by-step explanation:
Answer:
(2, 36) and (3, 54)
Step-by-step explanation:
I just answer the question from iready and I got it correct.
let be the line spanned by -1 2 3 in . find a basis of the orthogonal complement
Answers
The required basis of the orthogonal complement is {(2, 1, 0), (3, 0, 1)}.
Given that the line spanned by (-1, 2, 3) in R3.
To find the basis of the orthogonal complement, we need to find the vector which is orthogonal to (-1, 2, 3).
Let x = (x1, x2, x3) be a vector in the orthogonal complement of the given line.
Then we have: (-1, 2, 3)·x = 0-1x1 + 2x2 + 3x3 = 0x1 = 2x2 + 3x3
Thus, every vector x in the orthogonal complement has the form x = (2x2 + 3x3, x2, x3) = x2(2, 1, 0) + x3(3, 0, 1)
Therefore, the set { (2, 1, 0), (3, 0, 1) } is a basis of the orthogonal complement of the line spanned by (-1, 2, 3) in R3.
This is because both these vectors are linearly independent, and every vector in the orthogonal complement of the given line can be written as a linear combination of these two vectors.
Hence, the required basis of the orthogonal complement is {(2, 1, 0), (3, 0, 1)}.
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CONTAINER SPECIFICATIONS: • Each container must hold exactly one litre of liquid. Each container must have a minimum surface area. The surface area of each container must include the lid. The length of the rectangular base must be twice the breadth. The triangular container must have an equilateral base. TASK 1 Rectangular base container: CONTAINER A Sketch a rectangular base container with dimensions to hold exactly one litre of liquid. Clearly show your dimensions on your diagram. 1. Calculate the volume of this container in terms of above dimensions. 2. Calculate the surface area of the container in terms of above dimensions. 3. Calculate the value of the dimensions for this container for the surface area to be a minimum?
Answers
1. Volume of the Container: 1000 = l * b * h
2. Surface Area = 2(lw + lh + bh)
3. For the rectangular base container, the dimensions for the surface area to be a minimum will be the ones that satisfy the condition: l = 2b
1. Rectangular Base Container:
To sketch a rectangular base container that holds exactly one liter of liquid, we can assume the length of the rectangular base as 'l' and the breadth as 'b'. According to the given specifications, the length of the rectangular base must be twice the breadth.
Sketch:
--------------------
| |
| |
| |
| l |
| |
| |
----------------------
bVolume of the Container:
The volume of a rectangular prism is calculated by multiplying the length, breadth, and height. In this case, the height will represent the depth of the container.
Volume = l * b * h
Since we want the container to hold exactly one liter of liquid, which is equivalent to 1000 cubic centimeters, we have:
1000 = l * b * h
2. Surface Area of the Container:
The surface area of a rectangular prism can be calculated using the formula:
Surface Area = 2(lw + lh + bh)
In our case, the lid of the container is also included in the surface area calculation.
Dimensions for Minimum Surface Area:
3. To determine the dimensions for the container's surface area to be a minimum, we can use calculus and find the critical points. In this case, we need to minimize the surface area formula by differentiating it with respect to one variable, setting it equal to zero, and solving for that variable.
For the rectangular base container, the dimensions for the surface area to be a minimum will be the ones that satisfy the condition:
l = 2b
Substituting this value into the surface area formula, we can find the minimum surface area for a given volume of one liter.
By solving the equation for the surface area with respect to 'b' and substituting the result into the volume equation, we can find the exact dimensions of the container to satisfy the given conditions.
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which inequality represents the sentence below?
two more thwn a numbre is less than 14
Answers
Answer:
the answer is B
I hope it helps have a great day
Answer:
2 + n < 14
Step-by-step explanation:
Hey!
==================================================================
Let's work this word by word.
"Two more than a number is less than 14"
--------------------------------------------------------------------------------------------------------------
"Two more than"
⇒ 2 +
"A number"
⇒ 2 + n
"Is less than"
⇒2 + n <
"14"
⇒2 + n < 14
==================================================================
Hope I Helped, Feel free to ask any questions to clarify :)
Have a great day!
More Love, More Peace, Less Hate.
-Aadi x
Which of the following expressions represents the solution to x – 3 > -4?
a. x > -7
b. x > -1
c. x < 12
d. x > 12
Answers
Step-by-step explanation:
x - 3 > -4
= x > -4+3
= x > -1 _ Answer
Which of the following distances is a circumference? a.the distance around the face of a cube. b.the distance around a text book. c.the distance around a nickel. d.the distance around one of the hawaiian islands.
Answers
Answer:
c
Step-by-step explanation:
circumference = perimeter around circle
The answer is c. Use the formula for circumference.
What is the midpoint of line segment RS with endpoints R(5, -10) and S(3, 6)?
Answers
Answer:
(4, -2)
Step-by-step explanation:
The midpoint of two points is found by averaging the X coordinates and averaging the Y coordinates to create a new pair.
X: (5+3)/2 = 4
Y: (-10+6)/2 = -2
Answer:
(4,-2)
Step-by-step explanation:
add the x and divide by two. do the same with the y. this is the same as finding the average
A different math class took the same test with these five test scores: 92, 92,92,52,52 Find the standard deviation and the variance for this class.
Answers
The standard deviation for the given test scores is 20, and the variance is 400
We have,
To find the standard deviation and variance for the given test scores, we can follow these steps:
Calculate the mean (average) of the test scores:
Mean (μ) = (92 + 92 + 92 + 52 + 52) / 5 = 80
Calculate the deviation of each test score from the mean:
Deviation = Test score - Mean
For the given test scores:
Deviations = (92 - 80), (92 - 80), (92 - 80), (52 - 80), (52 - 80)
= 12, 12, 12, -28, -28
Square each deviation:
Squared Deviations = Deviation²
Squared Deviations = 12², 12², 12², (-28)², (-28)²
= 144, 144, 144, 784, 784
Calculate the variance:
Variance = (Sum of Squared Deviations) / (Number of Scores)
Variance = (144 + 144 + 144 + 784 + 784) / 5
= 2000 / 5
= 400
Calculate the standard deviation:
Standard Deviation = √Variance
Standard Deviation = √400
= 20
Therefore,
The standard deviation for the given test scores is 20, and the variance is 400.
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Evaluate 2m if
m = 7.2
Answers
2M= 2 x 7.2
2M= 14.4
Let f(t) be the number of units produced by a company t years after opening in 2005. what is the correct interpretation of f(6) = 44,500?
a. six years from now, 44500 units will be produced
b. in 2009, 44500 units are produced
c. in 2006, 44500 units are produced
d. in 2011, 44500 units are produced
Answers
The correct interpretation of `f(6) = 44,500` is that in the year 2011, a company that opened in 2005 will produce 44,500 units of products is the answer.
Given, `f(t)` be the number of units produced by a company `t` years after opening in 2005.
According to the question, `f(6) = 44,500`. It means six years after the company opened, which is in the year 2011, the company will produce 44,500 units of products.
The statement "six years from now, 44,500 units will be produced" (option a) is not correct because the year is not specified. The company will produce 44,500 units of products in the year 2011, not six years from the present.
The statement "in 2009, 44,500 units are produced" (option b) is not correct because in the year 2009, the company will only have been open for four years, and not enough information is provided to calculate the number of units produced.
The statement "in 2006, 44,500 units are produced" (option c) is not correct because in the year 2006, the company will have only been open for one year, and not enough information is provided to calculate the number of units produced.
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the ratio of the angle measures in a triangle is 2:3:10 . what is the measure of each angle?
Answers
The measure of each angle in the triangle is 24 degrees, 36 degrees, and 120 degrees.
Let's denote the three angles of the triangle as A, B, and C. According to the given ratio of 2:3:10, we can assign the values 2x, 3x, and 10x to angles A, B, and C, respectively, where x is a common factor.
The sum of the angle measures in a triangle is always 180 degrees. Therefore, we can set up the following equation:
2x + 3x + 10x = 180
Simplifying the equation, we get:
15x = 180
Dividing both sides by 15, we find:
x = 12
Now we can substitute x back into the expressions for each angle:
Angle A = 2x = 2(12) = 24 degrees
Angle B = 3x = 3(12) = 36 degrees
Angle C = 10x = 10(12) = 120 degrees
Therefore, the measure of each angle in the triangle is 24 degrees, 36 degrees, and 120 degrees.
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ANSWER ISN'T DECIMALS ANSWER ASAP!
Answers
Answer:
972 cubic feet
Step-by-step explanation:
12 by 9 by 7.5
+
1.5 by 9 by 12
Answer:
891 ft³
Step-by-step explanation:
First I'll find the volume of the rectangular prism. (l * w * h)
12 * 9 * 7.5
Multiply 12 by 9 to get 108.
108 * 7.5
Now, multiply 108 by 7.5 to get 810. (756 + 54 = 810)
810
Now for the triangular prism. (1/2(l * w * h))
1/2(12 * 9 * 1.5) (I figured the height was 1.5 since the height of the rectangular prism was 7.5; the entire figure's height was 9)
Multiply 12 by 9 to get 108.
1/2(108 * 1.5)
Multiply 108 by 1.5 to get 162. (108 + 54 = 162)
1/2(162)
Multiply 162 by 1/2 to get 81. (162/2)
81
Now add that to 810 to get 891.
810 + 81
891 ft³
The volume of the garage is 891 ft³.
Which of the following sets of vectors in R3 are linearly de- pendent? (a) (4, -1,2). (-4, 10, 2) (b) (-3.0.4). (5. -1,2), (1,1.3) (c) (8,-1,3), (4,0,1) (d) (-2, 0, 1), (3, 2, 5), (6.-1.1), (7,0, -2) 11 ofrector in p4 are linear de
Answers
The set of vectors (b) (-3,0,4), (5,-1,2), (1,1,3) are linearly dependent. The other given sets of vectors in R3 are linearly independent.
Let's review the given sets of vectors in R₃ to determine which ones are linearly dependent.
(a) (4.-1,2), (-4, 10, 2).
To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to
0.a(4,-1,2) + b(-4,10,2) = (0,0,0).
The system of equations can be written as;
4a - 4b = 0-1a + 10b = 00a + 2b = 0.
Clearly, a = b = 0 is the only solution.
So, the set is linearly independent.
(b) (-3,0,4), (5,-1,2), (1, 1,3)
To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to
0.a(-3,0,4) + b(5,-1,2) + c(1,1,3) = (0,0,0).
The system of equations can be written as;
-3a + 5b + c = 00a - b + c = 00a + 2b + 3c = 0
Clearly, a = 2, b = 1, and c = -2 is a solution.
So, the set is linearly dependent.
(c) (8.-1.3). (4,0,1).
To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to
0.a(8,-1,3) + b(4,0,1) = (0,0,0).
The system of equations can be written as;
8a + 4b = 01a + 0b = 0-3a + b = 0.
Clearly, a = b = 0 is the only solution.
So, the set is linearly independent.
(d) (-2.0, 1), (3, 2, 5), (6,-1, 1), (7,0.-2).
To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to
0.a(-2,0,1) + b(3,2,5) + c(6,-1,1) + d(7,0,-2) = (0,0,0)
The system of equations can be written as;
-2a + 3b + 6c + 7d = 00a + 2b - c = 00a + 5b + c - 2d = 0
Clearly, a = b = c = d = 0 is the only solution.
So, the set is linearly independent.
Therefore, The set of vectors (b) (-3,0,4), (5,-1,2), (1,1,3) are linearly dependent. The other given sets of vectors in R₃ are linearly independent.
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Can someone help me with this. Will Mark brainliest. Need answer and explanation/work. Thank you.
Answers
Answer:
[tex]14/50\\[/tex]
Step-by-step explanation:
The equation for sine is sine = opposite/ hypotenuse
The opposite of W is 14 and the hypotenuse the the side across the 90° angle, which is 50.
So, when you set up the equation it should be [tex]14/50[/tex].
Given the joint density f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere, show that the random variables X and Y are uncorrelated but not independent.
Answers
The joint density f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere, the variables X and Y are uncorrelated but not independent.
The problem requires the determination of whether the random variables X and Y are independent and uncorrelated. For that, the expectation of the product of X and Y is needed. Evaluating E(XY). For the two variables X and Y, their joint density is given as:
f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere
To evaluate the expectation of XY, multiply the variables X and Y as follows: E(XY) = ∫∫xy f(x,y) dy dx.
We evaluate the above equation over the range of the variables.
Since the domain of the density function is given by -y < x < y and 0 < y < 1, E(XY) = ∫∫xy f(x,y) dy dx = ∫0¹ ∫-[tex]y^{y}[/tex] xy dy dx
The above equation can be simplified as:
E(XY) = ∫0¹ (1/3)*y³ dy = 1/12
Hence the covariance between X and Y is given by: Cov (X, Y) = E(XY) - E(X)E(Y) = E(XY) = 1/12.
The variance of X is calculated as follows: E(X) = ∫∫xf(x, y) dy dx
For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere.
Thus, E(X) = ∫∫x f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex] x dy dx= 0.
Hence, Var(X) = E(X²) - [E(X)]² = E(X²) - 0² = E(X²).
The variance of X² is calculated as follows:
E(X²) = ∫∫x² f(x, y) dy dx. For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere.
Thus, E(X²) = ∫∫x² f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex] x² dy dx= 1/3
Hence, Var(X) = E(X²) - [E(X)] ² = 1/3 - 0 = 1/3
The variance of Y² is calculated as follows: E(Y²) = ∫∫y² f(x, y) dy dx
For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere. Thus, E(Y²) = ∫∫y² f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex]y² dy dx= 1/3
Hence Var(Y) = E(Y²) - [E(Y)]² = 1/3 - [E(Y)]²
The covariance between X and Y is given by: Cov (X, Y) = E(XY) - E(X)E(Y) = 1/12 - 0 = 1/12.
We can evaluate the correlation between X and Y as: Corr (X, Y) = Cov (X, Y) / √Var (X) Var(Y)= (1/12) / [(1/3) * (1/3)] = 1/4
Thus, the variables X and Y are uncorrelated but not independent.
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The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.8 grams with a standard deviation of 0.17 grams. For parts (a) through (c), enter your responses as a decimal with 4 decimal places. a) What is the probability that a randomly chosen mouse has a mass of less than 20.7 grams? b) What is the probability that a randomly chosen mouse has a mass of more than 21.02 grams? c What proportion of mice have a mass between 20.65 and 20.95 grams? d) 10% of all mice have a mass of less than grams.
Answers
a. Using the z-score, the probability of a randomly chosen mouse having a mass of less than 20.7 grams is approximately 0.2794.
b. The probability that a randomly chosen mouse has a mass more than 21.02g is 0.0985
c. The probability of a mouse having a mass between 20.65 and 20.95 grams is approximately 0.6474.
d. About 10% of all mice have a mass of less than 20.5649 grams.
What is the probability that a randomly chosen mouse has a mass of less than 20.7g?a) To find the probability that a randomly chosen mouse has a mass of less than 20.7 grams, we can use the normal distribution.
First, we need to standardize the value of 20.7 grams using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
The z-score for the data is;
z = (20.7 - 20.8) / 0.17 = -0.5882
P = 0.2794
b) To find the probability that a randomly chosen mouse has a mass of more than 21.02 grams, we also need to standardize the value:
z = (21.02 - 20.8) / 0.17 = 1.2941
P = 0.0985
Using the standard normal distribution table or a calculator, we find that the probability corresponding to this z-value is approximately 0.0985.
c) To find the proportion of mice that have a mass between 20.65 and 20.95 grams, we can standardize both values:
For 20.65 grams:
z₁ = (20.65 - 20.8) / 0.17 = -0.8824
For 20.95 grams:
z₂ = (20.95 - 20.8) / 0.17 = 0.8824
Using the standard normal distribution table or a calculator, we can find the probabilities corresponding to these z-values. The probability of a mouse having a mass between 20.65 and 20.95 grams is approximately 0.6474.
d) To find the mass of mice that corresponds to the 10th percentile, we need to find the z-score associated with the 10th percentile. We can use the standard normal distribution table or a calculator to find this value.
The z-score associated with the 10th percentile is approximately -1.2816.
Next, we can use the z-score formula to find the corresponding mass value:
z = (x - μ) / σ
-1.2816 = (x - 20.8) / 0.17
Solving for x, we get:
x = -1.2816 * 0.17 + 20.8 ≈ 20.5649 grams
Therefore, 10% of all mice have a mass of less than 20.5649 grams.
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