The answer is (a) MX + MY. Whether or not X and Y are independent, we cannot simplify (a) or (b) further.
The mean of X + Y is:
E(X + Y) = E(X) + E(Y)
So the answer is not (a) or (b).
(c) is incorrect because the formula given is only true if X and Y are independent, but no such assumption is given in the problem.
(d) is also incorrect because we cannot simply divide the means by the standard deviations to get the standard normal variables, especially when the variables X and Y have different means.
Therefore, the answer is (a) MX + MY.
Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
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What is the value of k such that (x³ + x² - 9x - 36) + (x + 4) has a rernainder
of zero? Show your work.
Answer:x^3+x^2-8x-32
Step-by-step explanation:
Multiplying a number by which of the following would result in a smallest number?
O 10-1
O 10⁰
O 10¹
102
Simplify the following as much as possible
A. csc x
B. sec x
C. sin x
D. cos x
Answer:
[tex]\textsf{C.} \quad \sin x[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}[/tex]
Rewrite the numerator and denominator of the given rational expression using the following trigonometric identities:
[tex]\boxed{\boxed{\begin{array}{c}\underline{\sf Trigonometric\;Identities}\\\\\boxed{\sec^2 x=\dfrac{1}{\cos^2x}} \qquad \boxed{\csc^2 x=\dfrac{1}{\sin^2 x}}\qquad \boxed{\csc x=\dfrac{1}{\sin x}}\\\\\end{array}}}[/tex]
Therefore:
[tex]=\dfrac{\dfrac{1}{\cos^2x} \cdot \dfrac{1}{\sin x}}{\dfrac{1}{\cos^2x}+\dfrac{1}{\sin^2x}}[/tex]
Multiply the fractions in the numerator, and make the denominators of the fractions in the denominator the same:
[tex]=\dfrac{\dfrac{1}{\sin x\cos^2x}}{\dfrac{\sin^2x}{\sin^2x\cos^2x}+\dfrac{\cos^2x}{\sin^2x\cos^2x}}[/tex]
[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}\right)}[/tex]
[tex]\textsf{Apply the trigonometric identity}\;\;\boxed{\sin^2x + \cos^2 x = 1}:[/tex]
[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{1}{\sin^2x\cos^2x}\right)}[/tex]
[tex]\textsf{Apply\:the\:fraction\:rule}\;\;\boxed{\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{ad}{bc}}:[/tex]
[tex]=\dfrac{\sin^2x\cos^2x}{\sin x\cos^2x}[/tex]
Cancel the common factor cos²x:
[tex]=\dfrac{\sin^2x}{\sin x}[/tex]
Simplify:
[tex]= \sin x[/tex]
Therefore:
[tex]\large\textsf{$\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}=$}\;\boxed{\boxed{\sin x}}[/tex]
How many 7 digit telephone numbers can be formed from the digits 0,1,2,...,9, where each telephone number begins with digit 2?
Answer: A lot
Step-by-step explanation:
A roller-coaster car is at the top of a hill. The car and its passengers have a combined mass of 1,088 kilograms. If the hill is 62 meters tall, how much potential energy does the car have?
PE=mgh
67,456 J
330,534.4 J
1,159.8 J
661,068.8 J
Answer:
661,068.8j
Step-by-step explanation:
The car has 661068.8 J of potential energy at a height of 62 m having a mass of 1088 grams.
What is potential energy?Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases.
We know, The gravitational constant is 9.8 m/s².
From the given information, m = 1088 grams, h = 62 meters.
Therefore, The amount of potential energy the car has is,
PE = mgh.
PE = 1088×9.8×62 J.
PE = 661068.8 J.
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A mailer for posters is a triangular prism as shown. Determine the lateral surface area of the mailer. Draw a net if necessary.
The lateral surface area of the mailer is 234 In²
How to determine the lateral areaIt is important to note that the formula for the lateral area of a triangular prism is expressed as;
A = (a + b+ c) h
Given that the parameters are enumerated as;
A is the lateral area of the triangular prisma is the base sideb is the base sidec is the base sideNow, substitute the values into the equation, we have;
Lateral area, A = (4 + 4 + 5) 18
Add the values
Lateral area = (13)(18)
Multiply the values
Lateral area = 234 In²
Hence, the value is 234 In²
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2) Find the sum of the first 15 terms of the sequence *
(2/7) + (4/7) + (8/7) + ...
Answer:32768/7
Step-by-step explanation:
double every term
12 (long division) 924
The solution is, 12 (long division) 924 = 77.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
given that,
12 (long division) 924
so, we get,
12 | 924 | 77
84
----------------
84
84
-----------------
0
Hence, The solution is, 12 (long division) 924 = 77.
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need help asap. pls somebody help.
Answer:
D
Step-by-step explanation:
why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.
x²
-x²
-x -x
x x x x (clearly that means 4x)
-1 -1 -1
1 1
so, we see it is D.
Does 0% percent on battery health of capacity mean your iphone will never turn on again or it will?
Answer asap for brainlist
Answer:
It will turn on again, just charge it. All phones come with a charger.
question 4 i need help with
Answer:
$3.25 per hotdog
Step-by-step explanation:
This question can be written as a system of equations:
x = price of hotdogs
y = price of drinks
First family:
4x + 4y = 18
Second family
5x + 3y = 20
Multiply each equation so that one of the variables can cancel out:
-3(4x + 4y = 18)
4(5x + 3y = 20)
First equation:
-12x - 12y = -54
Second equation
20x + 12y = 80
Add the equations together
-12x - 12y = -54
20x + 12y = 80
8x = 26
Divide
x = $3.25
Insert the x into one of the original equations to find y:
4(3.25) + 4y = 18
13 + 4y = 18
4y = 5
y = $1.25
A circular walkway is to be built around a monument, with the monument as the center. The distance from the monument to any point on the inner boundary of the walkway is 30 feet.
The equation of the inner boundary of the circular walkway around the monument is x² + y² = 900.
The equation of the outer boundary of the circular walkway around the monument is x² + y² = 1369.
What is the equation of a circle?A circle is a conic section whenever the plane cuts the cone parallel to its base. Every point of the circumference lies at the same distance from its center. The equation of a circle is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.
a.
According to the diagram, the radius of the inner boundary is 30 feet and the center is (0, 0).
Substitute h = 0, k = 0, and r = 30 into the equation of circle (x-h)² + (y-k)² = r².
(x-0)² + (y-0)² = 30²
x² + y² = 900
Therefore, the obtained answer is x² + y² = 900.
b.
According to the diagram, the radius of the outer boundary is 37 feet (30 feet + 7 feet) and the center is (0, 0).
Substitute h = 0, k = 0, and r = 37 into the equation of circle (x-h)² + (y-k)² = r².
(x-0)² + (y-0)² = 37²
x² + y² = 1369
Therefore, the obtained answer is x² + y² = 1369.
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The complete question is mentioned in the image below.
The sum of two numbers is 17 and their product is 60 what are the two numbers?
Answer:
12 and 5
Step-by-step explanation:
12+5=17
12x5=60
Answer:
Step-by-step explanation:
5 12 step by step
How to find the vertex of the function y = 2x^2 + 4
The vertex of the given function is (0,4)
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
identify the coefficients a and b of the quadratic function
y =ax² +bx+c-------(1)
a=2, b=0
x-coordinate of the vertex is x= -b/2a = -(0)/(2(2)) = 0
Substitute x=0 into given equation to get y-coordinate of the vertex
y= 2(0)² + 4 = 0+4 = 4
Vertex= (x,y) = (0,4)
The vertex of the given function is (0,4)
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Steve invests $2,100 in an account that earns 6.9% interest, compounded continuously. What is the value of the account after 13 years? Round your answer to the nearest hundredth.
The amount after 13 years with a compound interest of 6.9 % is given by the equation A = $ 5,149.69
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount after compound interest be represented as A
Now , the equation will be
The principal amount P = $ 2,100
The rate of interest r = 6.9 %
The number of years b = 13 years
when compounded continuously ,
The compound interest amount A = Pe^rt
Substituting the values in the equation , we get
A = 2,100.00 ( 2.71828 ) ^ ( 0.069 ) ( 13 )
A = 2,100 ( 2.71828 )^( 0.897 )
On further simplification , we get
A = $ 5,149.69
Hence , the amount after 13 years is $ 5,149.69
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Write this ratio as fraction in lowest terms. 8.64 to 37.76
The ratio 8.64 : 37.76 as a fraction will be 27/118.
What precisely is ratio?
Ratios and proportions are typically described using fractions. When a fraction is presented as a:b, a ratio is shown, whereas a percentage suggests that two ratios are equal. In this case, a and b can be any two numbers. The ratio and proportion are two essential notions that serve as a foundation for understanding other concepts in mathematics and science.
In our daily lives, we apply the notion of ratio and proportion, such as in business when dealing with money or in cooking.
As a consequence, when b is greater than zero, the ratio specifies the connection between two variables, such as a:b. The 2:4 ratio, for example, is written as 2:4 = 1:2.
Now,
Given ratio is 8.64 : 37.76
we can write this as 8.64/37.76
=864/3776
=432/1888
=216/944
=54/236
=27/118
Hence,
The ratio 8.64 : 37.76, as a fraction will be 27/118.
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Solve the equation for all real solutions in simplest form.
2q² +11q+13= 0
On average the number of drum sets sold in Ohio each year is equivalent to eight times the average number sold yearly in Vermont. If, on average, there are 79,992
drum sets sold each year in Ohio, how many are sold in Vermont?
Given the letters H A M I L T O N in a game of scrabble:
a) How many ways can you arrange all of the letters if the arrangement must end in a vowel [vowel: a,e,i,o,u]
b) How many arrangements are there if you can only use five letters?
The number of ways to arrange all the letters if the arrangement must end in a vowel is; 25,200.
The number of arrangement using only five letters is; 6720.
What is the number of ways to arrange the letters as described?Since there are 5 options for the last letter, and there a 7 letters left to make an arrangement of 7.
Hence, The number of ways can you arrange all of the letters if the arrangement must end in a vowel is; 5 × 7!
= 5 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 25,200.
b). The number of arrangements if one can only use five letters is; ⁸P₅
= 6720.
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Select all the expressions that have a value of 13.5 when s = 1.5
Answer:
Given that s = 1.5, the expressions that have a value of 13.5 are:
(1) 5s + 8 = 5 × 1.5 + 8 = 13.5
(2) 2s^2 + 9 = 2 × 1.5^2 + 9 = 13.5
Note: The value of any other expression will depend on the specific formula and the value of other variables used in the expression.
Find the value of the variables. If the answer is not an integer, express it in simplest radical form.
60
20
Please help
The values of x and y would be [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].
What are trigonometric ratios?
Trigonometric ratios are mathematical functions that describe the relationship between the angles and sides of a right triangle. The three main trigonometric ratios are the sine, cosine, and tangent.
In the given figure, by using trigonometric ratios, we can find x
tan60° = 20/x
√3 = 20/x
x = 20/√3
=> [tex]x=\frac{20 \sqrt{3}}{3}[/tex]
Now by using the ratio sin60°
sin60° = 20/y
√3/2 = 20/y
y = 40/√3
[tex]y=\frac{40\sqrt{3}}{3}[/tex]
Hence, the values of x and y would be [tex]x=\frac{20 \sqrt{3}}{3}[/tex] and [tex]y=\frac{40\sqrt{3}}{3}[/tex].
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Use the discriminant to describe the solutions as one real, two real, or two
imaginary solutions.
4. x2 − 15x + 12 = 0 5. 3x2 − 6x + 4 = 0
The Equation x² − 15x + 12 = 0 have two Real solution and 3x² − 6x + 4 = 0 have Imaginary solution.
What is solution to the Equation?The discriminant, denoted by the equation b² - 4ac, can be used to ascertain if the solutions are real, repetitive, or complex:
1) If the discriminant is smaller than 0, there are two imaginary roots to the problem (s).
2) The equation has one repeating real solution if the discriminant equals zero (s).
Given:
x² − 15x + 12 = 0
Solving the Quadratic Equation
x² − 15x + 12 = 0
D = b² - 4ac
D = (-15)² - 4(1)(12)
D = 225 - 48
D = 177 >0
So, the Equation will have two Real solution.
b) 3x² − 6x + 4 = 0
Solving the Quadratic Equation
3x² − 6x + 4 = 0
D = b² - 4ac
D = (-6)² - 4(3)(4)
D = 36 - 48
D = -12 >0
So, the Equation will have Imaginary solution.
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Find the GCF of the terms of each polynomial 15x^2+18 and -18y^4+6y^3+24y^2
The GCF of the polynomials are
1. for 15x²+18 , the GCF is 3
2. for -18y⁴+6y³+24y² ,the GCF is 6y²
What is GCF?The GCF stands for the “greatest common factor”. The GCF is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.
The GCF is the highest factor that can be used to divide through 2 or more terms
1. For 15x²+18, 3 is a factor of 15 and 18 and it's the greatest factor, therefore the GCF is 3
2. For -18y⁴+6y³+24y², between 18,6 and 24, 6 is the greatest factor Ang between y⁴ ,y³, y², y² is the greatest factor. Therefore the GCF of the expression is 6y².
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Suki wants to pour 25 milliliters
of water, 35 milliliters of oil,
and 45 milliliters of syrup into
the same beaker for a science
experiment. The beaker holds up to 100 milliliters. Will the beaker hold all three liquids? Explain why or why not.
The Nutty Professor sells cashews for $7.70 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 30 pound mixture that sells for $6.08 per pound?
Round answers to the nearest pound.
The mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.
What is Mixture?A physical combination of two or more unrelated substances is referred to as a mixture. For instance, water and salt are two different substances that, when combined, form a combination.
According to question:Let's call the amount of cashews used in pounds "x". The amount of Brazil nuts used in pounds can be calculated as 30 - x.
We know that the total cost of the mixture is $6.08 per pound * 30 pounds = $182.40.
The cost of the cashews in the mixture is $7.70 per pound * x pounds =$7.70x.
The cost of the Brazil nuts in the mixture is $5.00 per pound * (30 - x) pounds = $150 - $5.00x.
The total cost of the cashews and Brazil nuts in the mixture must equal $182.40, so we can set up the equation:
$7.70x + ($150 - $5.00x) = $182.40
Expanding and simplifying the equation:
$2.70x = $32.40
Dividing both sides by 2.70:
$x = 12
So, the mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.
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Find the distance the point P(3, 1, 7), is to the plane through the three points
Q(5, 0, 3), R(0, -1, 7), and S(7, 5, 0).
To find the distance from a point P to a plane defined by three points Q, R, and S, we can use the following formula:
distance = |(A * x + B * y + C * z + D) / √(A^2 + B^2 + C^2)|
where (A, B, C) are the coefficients of the normal vector of the plane, (x, y, z) are the coordinates of the point P, and D is the constant in the equation of the plane.
To find the coefficients of the normal vector, we can use the cross product of two vectors lying in the plane, say, QR and RS.
Let's first find the vectors QR and RS:
QR = (5 - 0, 0 - (-1), 3 - 7) = (5, 1, -4)
RS = (7 - 0, 5 - (-1), 0 - 7) = (7, 6, -7)
Next, we find the cross product of QR and RS:
cross product of QR and RS = (B, C, A) = (7, -30, 15)
So, the normal vector of the plane is (15, -30, 7).
Now we substitute the values for the coefficients and the coordinates of the point P into the formula:
distance = |(15 * 3 + (-30) * 1 + 7 * 7 + D) / √(15^2 + (-30)^2 + 7^2)|
To find the value of D, we can use any of the three points on the plane and substitute their coordinates into the equation of the plane in the form Ax + By + Cz + D = 0.
Let's use the point Q:
15 * 5 + (-30) * 0 + 7 * 3 + D = 0
Expanding and solving for D, we get:
75 + 21 + D = 0
D = -96
Finally, substituting the values back into the formula for distance, we get:
distance = |(15 * 3 + (-30) * 1 + 7 * 7 + -96) / √(15^2 + (-30)^2 + 7^2)|
distance = |(-24 + -30 + 49 - 96) / √(15^2 + (-30)^2 + 7^2)|
distance = |(-101) / √(15^2 + (-30)^2 + 7^2)|
distance = |(-101) / √(15^2 + (-30)^2 + 7^2)|
distance = |(-101) / √(225 + 900 + 49)|
distance = |(-101) / √1274|
distance = |(-101) / 35.6|
distance = 2.85
So, the distance between the point P and the plane is approximately 2.85.
Accountants often use the median when studying salaries for various businesses. What is the median of the following salary list: 32019, 21955,27507, 43715,38850,25963
The median of the following salary list is 29763.
What is a median?The median is the average in the centre of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. For a small data collection, calculate the number of data points (n) and organize them in ascending order.
The middle score in the group is called the median. Begin by sorting all of the data sets from lowest to highest before calculating the median. The median in an odd-numbered set will be the value that falls exactly in the center of the list. You must determine the average of the two middle integers in a set of even numbers.
Arrange in ascending order
21955, 25963, 27507, 32019, 38850, 43715
Take the two mid terms
27507 and 32019
Median = [tex]\dfrac{27507 + 32019}{2}[/tex]
Median = 29763
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what formula is used to determine the percentage change in quantity demanded
Answer:
slope
Step-by-step explanation:
Step-by-step explanation:
always find the quantity of 100%.
then
1% = 100%/100
then calculate the absolute quantity change.
then divide the quantity change by 1% to see how many % fit into it.
and that is your answer.
so, if the original quantity is q1, the new quantity is q2, then the % of quantity change is
|q1 - q2| / (q1/100)
or
100 × |q1 - q2| / q1
where || means the absolute value.
write a number or expression in each empty box to create a true equation 15 + 10 = _____ (3 + 2)
Answer:
5(3-2)
Step-by-step explanation:
15-10
5×3-5×2
select the equivalent expression.
Answer:
Step-by-step explanation: Option A is correct.
