If X and Y are independent and identically distributed uniform random variables on (0, 1), then the joint density of
(a) U = X + Y, V = X/Y is u/v² for v > 1 and 0 ≤ u ≤ 1.
(b) U = X, V = X/Y is 1/v for v > 1 and 0 ≤ u ≤ 1.
(c) U = X + Y, V = X/(X+Y) is v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.
In probability theory, joint density is a mathematical function that describes the probability distribution of two or more random variables. It represents the probability of occurrence of different values of those variables in a particular region of space. In this problem, we have to calculate the joint density of U and V, where U and V are functions of X and Y.
(a) For U = X + Y and V = X/Y, we can find the joint density as follows:
First, we need to find the distribution of U and V separately. Since X and Y are independent and identically distributed uniform random variables on (0, 1), their individual probability density functions are f(x) = 1 for 0 ≤ x ≤ 1.
To find the density of U, we can use the convolution formula, which states that the density of the sum of two independent random variables is the convolution of their individual densities. Thus,
fU(u) = ∫ fX(u - y)fY(y) dy
= ∫ 1 dy
= u for 0 ≤ u ≤ 1.
Next, to find the density of V, we need to transform X and Y using the change of variables formula. Let Z = X/Y, then
fV(v) = fZ(z)|dz/dv|
= fX(vz)/(z²) |z|
= 1/(v²) for v > 1.
Therefore, the joint density of U and V is given by the product of their individual densities:
fUV(u,v) = fU(u) fV(v)
= u/v² for v > 1 and 0 ≤ u ≤ 1.
(b) For U = X and V = X/Y, we can similarly find the joint density as:
fUV(u,v) = fX(u) fV(v)
= 1/v for v > 1 and 0 ≤ u ≤ 1.
(c) For U = X + Y and V = X/(X+Y), we can use the same method as in (a) to find the individual densities of U and V:
fU(u) = u for 0 ≤ u ≤ 1,
fV(v) = v/(1+v)² for v > 0.
Then, the joint density of U and V is given by:
fUV(u,v) = fU(u) fV(v) |du/dx|
= v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.
To know more about density here.
https://brainly.com/question/29775886
#SPJ4
100 POINTS BRAINLIEST A business buys equipment with $300 cash and puts $425 on credit. What is the value of this asset?
A. $725
C. $425
B. $300
D. $125
Answer: A) $725
Step-by-step explanation:
The value of the asset that the business bought with $300 cash and $425 on credit is $725. The total amount that the business spent on the equipment is equal to the sum of the cash and the credit, which is $300 + $425 = $725.
SOMEONE PLEASE HELP ASAP!!!! Solve the triangle round to the nearest tenth.
Answer:
s = 13.6
m∠T = 35.7°
m∠U = 61.3°
Step-by-step explanation:
• Solving for side s:
To find the length of side s, we have to use the cosine rule:
[tex]\boxed{a^2 = b^2 + c^2 - 2bc \ cosA}[/tex],
where:
a = unknown sideb, c = adjacent sidesA = angle opposite to the unknown side.In this case, the unknown side is s, and the sides adjacent to it have lengths of 8 and 2. The angle opposite to s is ∠S = 83°. Therefore,
[tex]s^2 = 8^2 + 12^2 -2(8)(12) \cdot cos(83^{\circ})[/tex]
⇒ [tex]s = \sqrt{8^2 + 12^2 -2(8)(12)\cdot cos(83^{\circ})}[/tex]
⇒ [tex]s = \bf 13.6[/tex]
• Solving for m∠T:
In order to find m∠T, we can use the sine rule:
[tex]\boxed{\frac{sinA}{a}= \frac{sinB}{b} =\frac{sinC}{c}}[/tex],
which means that the ratios of the sines of angles and their opposite sides are equal for a triangle.
The side opposite to ∠T is US = 8. Therefore:
[tex]{\frac{sinT}{8} = \frac{sin(83^{\circ})}{13.6}}[/tex]
⇒ [tex]sinT= \frac{sin(83^{\circ})}{13.6} \times 8[/tex]
⇒ [tex]T = sin^{-1}( \frac{sin(83^{\circ})}{13.6} \times 8)[/tex]
⇒ [tex]T = \bf 35.7^{\circ}[/tex]
• Solving for m∠U:
Now that we know the values of two angles of the triangle, we can calculate the third angle using the fact that the angles in a triangle add up to 180°:
∠U + ∠S ∠T = 180°
⇒ ∠U + 83° + 35.7° = 180°
⇒ ∠U = 180° - 83° - 35.7°
⇒ ∠U = 61.3°
Assuming that b is positive, solve the following equation for b.
b
S
- 1
b≈
(2x-6)dx=13 Round your final answer to 4 decimal places.
(Give the positive answer only.)
The value of b is given as follows:
b = 8.4.
How to obtain the value of b?The value of b is obtained solving the definite integral in this problem.
The integral of the function 2x - 6 is given as follows:
x² - 6x.
At x = b, the numeric value of the integral is given as follows:
b² - 6b.
At x = -1, the numeric value of the integral is given as follows:
(-1)² - 6(-1) = 1 + 6 = 7.
Applying the Fundamental Theorem of Calculus, the equation to obtain the value of b is given as follows:
b² - 6b - 7 = 13.
b² - 6b - 20 = 0.
Which is a quadratic function with the coefficients given as follows:
a = 1, b = -6 and c = -20.
The discriminant is given as follows:
D = b² - 4ac
D = (-6)² - 4(1)(-20)
D = 116.
Hence the positive solution is given as follows:
b = (-b + sqrt(D))/2a
b = (6 + sqrt(116))/2
b = 8.4.
More can be learned about definite integrals at https://brainly.com/question/22008756
#SPJ1
Based on previous sales, Ron predicted sales of 80 pen sets. He actually sold 100 pen sets. Find the error and absolute error for the pen sets. A 5-column table with 3 rows. Column 1 is labeled Item with entries folders, erasers, pen sets. Column 2 is labeled Approximate Value with entries 25, 220, 80. Column 3 is labeled Exact value with entries 30, 200, 100. Column 4 is labeled Error with entries negative 5, 20, a. Column 5 is labeled Absolute Error with entries 5, 20, b.
The error is 20 and absolute error for the pen sets is also 20. Absolute error is the difference between a quantity's observed or inferred value and its actual value.
What is a absolute error statement?Absolute error is the difference between such a quantity's observed or assumed value and its real value. Because it doesn't indicate the error's magnitude, the absolute inaccuracy is insufficient.
What are absolute and relative error?The difference between a quantity's measured value and its actual value is known as absolute error. The difference between the measurement's absolute error and the quantity's actual value is referred to as relative error.
To know more about absolute error visit;
https://brainly.com/question/11599357
#SPJ1
Answer:
15%
Step-by-step explanation:
flip edge
HELP ASAP TIMED!! hurry
Answer:
3rd choice (x + 8)² + (y - 11)² = 4
Step-by-step explanation:
(x - -8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
Step-by-step explanation:
(x - h)² + (y - k)² = r²
h = -8
k = 11
r = 2
(x + 8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
The answer is C. (x+8)² + (y-11)² = 4
13 Show that the equation (p+1)x² + (2p+3)x+ (p+2)=0 has real roots for all real values of p.
The equation (p+1)x² + (2p+3)x+ (p+2)=0 has real roots for all real values of p at x = -1, -2
What is a polynomial?A polynomial equation is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.
Given that:
(p+1)x² + (2p+3)x + (p+2) = 0
Open brackets;
px² + x² + 2px + 3x + p + 2 = 0
Move all terms not containing p to the right side of the equation.
px² + 2px + p = −x² − 3x − 2
Factor p out of px² + 2px + p.
p(x² + 2x + 1) = −x² − 3x − 2
Factor using the perfect square rule.
p(x+1)² = −x² − 3x − 2
Divide each term in p( x + 1 )² = −x² − 3x − 2 by (x + 1)² and simplify.
[tex]p= - \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}[/tex]
Set [tex]p= - \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}[/tex] to be equal to zero;
[tex]- \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}=0[/tex]
Solve for x;
-x² - 3x - 2 = 0
Factor the left side of the equation.
-(x + 1) (x + 2) = 0
x = -1
x = -2
The final solution is all the values that make -(x + 1) (x + 2) = 0 true
x = -1, - 2
Exclude the solutions that do not make [tex]- \dfrac{x^2}{(x+1)^2}-\dfrac{3x}{(x+1)^2}-\dfrac{2}{(x+1)^2}=0[/tex] true.
Therefore, x = -2
Learn more about solving polynomial equations here:
https://brainly.com/question/2833285
#SPJ1
What is the quotient and remainder, written as partial fractions, of
15x²+52x +43
3x²+5x-8
The quotient and remainder, written as partial fractions, of 15x²+52x+43/3x²+5x-8 would be A/(3x + 8) + B/(x - 1) where A is -8/3 and B is 1.
What in mathematics is a partial fraction?
The fractions that are utilized to break down a rational expression are called partial fractions.
Any component of an algebraic expression that is divided into a sum of two or more rational expressions is referred to as a partial fraction.
15x²+ 52x + 43/3x²+5x-8
15x²+52x +43/3x² + ( 8 -3)x - 8
15x²+52x +43/3x² + 8x -3x - 8
15x²+52x +43/3x(x - 1) +8(x - 1 )
15x²+52x +43/(3x + 8)(x -1 )
A/(3x + 8) + B/(x - 1)
To find the value of A;
3x + 8 = 0
x = -8/3
To find the value of B;
x - 1 = 0
x = 1
Learn more about Partial fractions
brainly.com/question/30404141
#SPJ1
Mrs. Hamada has 15 paintbrushes and wants to put the same number into each of 5 water cups. Complete the equation below to show how many paintbrushes will be in each cup.
Answer:
3 paintbrushes
Step-by-step explanation:
15 divided by 5 is 3.
So, Mrs. Hamada will put 3 paintbrushes in each cup.
Please help!! Number 7
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
Solving For #7
We will use the Angle Bisector Theorem
The angle bisector theorem states that in a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.
In the figure provided in #7 we see that QS bisects ∠Q forming two smaller triangles ΔPQS and ΔQRS
According to the angle bisector theorem:
[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\[/tex]
Given
[tex]QR = 12.6\\PQ = 7\\RS = x\\PS = 5\\\\[/tex]
[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\\\\\\rightarrow \dfrac{12.6}{7} = \dfrac{x}{5}[/tex]
If we multiply by [tex]5[/tex] both sides of the equation we can get rid of the denominator 5 on the right side:
[tex]\rightarrow \dfrac{12.6}{7} \times 5 = x\\\\9 = x\\\\\boxed{x = 9}[/tex]
Find dy/dx by implicit different iation xy^2= 4.
The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).
What is differentiation by parts?By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.
Given function is xy²= 4. The given expression will be different as below,
dy / dx ( xy² ) - 4 = 0
2xy( dy / dx) + y² = 0
dy / dx = -y / 2x
Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).
To know more about differentiation follow
https://brainly.com/question/16644382
#SPJ9
This is a number sequence
2,3,5,9,17,33,65
what are the next two terms?
The next two terms of the number sequence 2,3,5,9,17,33,65 are given as follows:
129, 257.
How to obtain the next two terms of the number sequence?This is a recursive number sequence, as each term is obtained multiplying the previous term by 2 and then subtracting one.
Then the term after 65 is given as follows:
65 x 2 - 1 = 130 - 1 = 129.
The term after 129 is given as follows:
2 x 129 - 1 = 257.
Then the next two terms are 129 and 257.
More can be learned about number sequences at https://brainly.com/question/29633561
#SPJ1
Which inequality's solution is graphed here?
x
A
B
X+2≤0
D
X-2≤0
CX-220
x+220
-10-9-8-7-6-5-4-3
E x = 0
-2 -1 0
1 2 3
4
5
6 7 8 9 10
The complete question:
Which inequality's solution is graphed here?
A) x + 8 < 5
B) x - 5 < 8
C) x + 5 < 8
D) x - 8 < 5
The given graph represents on the number line is represented by inequality x - 5 < 8. So option B is correct.
What is a number line?Real numbers are represented by a straight line known as a number line. The distance between the dots on the line, which correlates to the magnitude of the numbers, is how the numbers are typically represented. Positive or negative numerals can be used, and they are normally marked at regular intervals.
Given that,
A graph,
which has values less than 13,
In form of inequality it can be written as,
x < 13
And inequality x - 5 < 8,
can be written as x < 13
Hence, the option b is correct inequality.
To learn more about Number lines check:
brainly.com/question/24644930
#SPJ1
Two draws are made at random without replacement from a box containing the following five tickets:
1 2 3 4 3
What is the probability that the sum of the tickets is 5?
in %
The probability that the sum of the ticket is 5, expressed as a percentage is 30%
What is the probability that an event will occur?The probability that an event will occur can be found by the ratio of the number of times the event occurs to the number of all possible events.
The five tickets in the box = 1, 2, 3, 4, 3
The tickets that sum to 5 are; 1 and 4, 2 and 3
The probability that the first ticket picked is 1 = 1/5
The probability that the next ticket picked is a 4 = 1/(5-1) = 1/4
Therefore, the probability of picking a 1 and 4 = (1/5) × (1/4) = 1/20
Similarly, the probability of picking a 4 and then a 1 is 1/20
The probability of picking tickets with numbers 1 and 4 in either order therefore = 2 × 1/20 = 1/10
The probability that the first ticket drawn is 2 = 1/5
The probability that the next ticket picked is a 3 = 2/(5-1) = 1/2
Therefore, the probability to draw a 2 and 3 = (1/5) × (1/2) = 1/10
The probability that the first ticket picked is 3 = 2/5
The probability that the next ticket picked is a 2 = 1/(5-1) = 1/4
Therefore, the probability of picking a 3 and 2 = (2/5) × (1/4) = 2/20 = 1/10
The probability of picking a 2 and a 3 in either order is therefore;
1/10 + 1/10 = 2/10 = 1/5
The probability that the sum of the ticket is 5, is the sum of the probabilities of picking a 1 and a 4 and the probability of picking a 2 and a 3, which is; 1/10 + 1/5 = 3/10 = 0.3
The probability that the sum of the ticket is 5, therefore is 0.3 × 100 % = 30%Learn more on probabilities here: https://brainly.com/question/17082285
#SPJ1
Everyone should have free Internet access to education, news, jobs, and more.
The graph plots education and news on the x-axis and other goods and services on the y-axis.
Draw the economy's PPF before the Internet and label it PPF0.
Draw the PPF after the arrival of the Internet if the effect on education and news is greater than on other goods and services. Label it PPF1.
From the provided graph, Due to the greater impact of the internet on education and news, PPF on the x-axis (education and news axis) moves more than the shift on the y-axis.
What is graphs?Mathematicians use graphs to lοgically convey facts or values using visual representations or charts. A graph pοint will typically reflect a relationship between two or more things. Nοdes, or vertices, and edges make form a graph, a nοn-linear data structure. Glue together the nodes, often referred tο as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representatiοns of expοnential growth. a lοgarithmic graph in the shape of a triangle.
Assume that in the "οld PPF," which existed befοre the internet, equal amounts of news, educatiοn, and other commodities and services are generated.
Due to the greater impact οf the internet on education and news, PPF on the x-axis (education and news axis) moves mοre than the shift on the y-axis.
To know more about graphs visit:
brainly.com/question/11950136
#SPJ1
Hey what is 10(4/24 - 9) - 7.45
Answer
[tex] - 95.783[/tex]
O Points: 0 of 1
Sav
Write the following phrase as an algebraic expression and simplify if possible. Let x represent the unknown number.
Two times the sum of a number and five
The required simplified expression for "Two times the sum of a number and five" is 2x + 10.
What is an algebraic expression?An algebraic expression is defined as when the expression is formed with help of variables such as x, y z, and so on. in the format of x + y + z or in any mathematical operation.
Here,
The phrase "Two times the sum of a number and five" can be written as
= 2(x + 5)
This is an algebraic expression that represents the value of two times the sum of the unknown number (represented by "x") and five.
We can simplify this expression by distributing the 2
= 2(x + 5) = 2x + 10
Therefore, the simplified expression for "Two times the sum of a number and five" is 2x + 10.
Learn more about algebraic expression here:
https://brainly.com/question/17510671
#SPJ9
plsss help i really need it
A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.
First, we need to know the conversion rate between the two units (pounds lb and kilograms kg)
1 pound = 0.45359237 kilogramsNow, we can convert 90 pounds.
90 × 0.45359237 = 40.8233133 kgSo, 90lb ≈ 41kg
(If you were to round)
prove that sin51 + sin81 - cos21 = 0
Answer:
Step-by-step explanation:
To prove that sin(51) + sin(81) - cos(21) = 0, we can use the trigonometric identity:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
We can rewrite 51 and 81 as the sum of two angles:
51 = 45 + 6
81 = 90 - 9
Using the above identity, we can write:
sin(51) = sin(45 + 6) = sin(45)cos(6) + cos(45)sin(6) = (2/2)sin(6) + (2/2)cos(6) = sin(6) + cos(6)
and
sin(81) = sin(90 - 9) = sin(90)cos(9) - cos(90)sin(9) = 0 + (-1)sin(9) = -sin(9)
Finally,
sin(51) + sin(81) - cos(21) = sin(6) + cos(6) - sin(9) - cos(21) = (sin(6) + cos(6)) - (sin(9) + cos(21))
We know that sin(90 - x) = cos(x) and cos(90 - x) = sin(x), so we can rewrite the right-hand side as:
(sin(6) + cos(6)) - (cos(90 - 9) + sin(90 - 21)) = (sin(6) + cos(6)) - (cos(9) + sin(69))
We also know that sin(180 - x) = -sin(x) and cos(180 - x) = -cos(x), so we can rewrite the right-hand side as:
(sin(6) + cos(6)) - (cos(9) + -sin(111)) = (sin(6) + cos(6)) - (-sin(111) + cos(9))
Since sin(6) + cos(6) = sin(6 + 90) = sin(96) and -sin(111) + cos(9) = sin(69 - 180) = -sin(111), we can simplify the expression further to:
sin(6) + cos(6) - (-sin(111)) + cos(9) = sin(96) + cos(9)
Since sin(x + y) = sin(x)cos(y) + cos(x)sin(y), we can write:
sin(96) + cos(9) = sin(60)cos(36) + cos(60)sin(36) = (2/2)sin(36) + (√3/2)cos(36) = sin(36) + (√3/2)cos(36)
Finally, since sin(2x) = 2sin(x)cos(x), we can write:
sin(36) + (√3/2)cos(36) = 2sin(18)cos(18) + (√3/2)cos(36) = 2(√2/2)(√2/2) + (√3/2)(√2/2) = (√2 + √6)/2 + (√6/2) = (√2 + √6)
So, sin(51) + sin(81) - cos(21) = (√2 + √6) ≠ 0.
Therefore, we have shown that sin(51) + sin(81) - cos(21) ≠ 0, and the statement "sin(51) + sin(81) - cos(21) = 0" is false.
What is the value of x? enter your answer in the box. X = cm a bow tie shape polygon made of two bow ties that share a vertex. The shape is created by two segments intersecting forming two triangles with vertical angles. An alternate interior angle of the triangles are marked congruent to each other. The larger triangle is on the left and the smaller triangle is on the right. In the larger triangle, the left side of the triangle is 32 centimeters. The south side of the triangle is 40 centimeters. On the smaller triangle, the right side of the triangle is 4 centimeters. The north side of the triangle is labeled x.
By proving the two triangles as similar triangles , the value of x in the triangles is x = 5 cm .
By using the proportions, for the two triangles which are similar because they contain three equal angles ;
The One angle due to connected by the vertex (oppose by the vertex), another angle as marked with the tick, and
the third angle one has to be same because of the sum of the three internal angles of a triangle must equal 180 degrees.
So , the proportions of the sides are written as :
⇒ 4/32 = x/40 ;
Cross multiplying , and solving for "x" ,
we get ;
⇒ x = (4 × 40)/32 ;
⇒ x = 5 .
Learn more about Similar Triangles here
https://brainly.com/question/14926756
#SPJ4
The given question is incomplete , the complete question is
What is the value of x in the polygon given below ?
20% discount on $365 purchase
Answer:
To find the amount of the discount, we need to multiply the purchase price by 20% or 0.20.
Discount = $365 × 0.20 = $73
So, the discount on a $365 purchase is $73.
The price after the discount would be $365 - $73 = $292.
To calculate the discount on a $365 purchase with a 20% discount, you can follow these steps:
1. Calculate the discount amount:
Discount = 20% x $365 = $73
2. Subtract the discount from the original price:
Final price = $365 - $73 = $292
Therefore, the final price of the $365 purchase with a 20% discount is $292.
In the diagram below, AD EB, m/ABD = 115° and m/D = 27°.
Find m < ABE
The value of angle ABE is 52°
What are interior angle of a triangle ?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.
The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.
The sum of interior angle in a triangle is 180°
Angle EBD = 180-(90+27)
= 180-117
= 63°
angle ABE + EBD = ABD
ABE = ABD - EBD
ABE = 115-63
= 52°
Therefore the value of angle ABE is 52°
learn more about interior angle of triangle from
https://brainly.com/question/25215131
#SPJ1
convert the following measurement
The value of expression after change its measurement as;
⇒ 3.4 × 10⁻⁴ kg . m²/ s²
What is Measurement unit?A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Given that;
The expression is,
⇒ 3.4 × 10⁵ g . cm² / s²
Now, We know that;
⇒ 1 cm = 1/1000 m
⇒ 1 cm = 1/10³ m
⇒ 1 g = 1/1000 kg
⇒ 1 g = 1/10³ kg
Hence, We get;
⇒ 3.4 × 10⁵ g . cm² / s²
⇒ 3.4 × 10⁵ (1/10³) kg . (1/10³)² m²/ s²
⇒ 3.4 × 10⁵ × 10⁻³ × 10⁻⁶ kg . m²/ s²
⇒ 3.4 × 10⁻⁴ kg . m²/ s²
Learn more about the measurement unit visit:
https://brainly.com/question/777464
#SPJ1
Given the function: calculate the following values.
The values of f(-1) , f(0) and f(2) are 0, 8 , 16 .
What is a function ?
Function can be defined in which it relates an input to output.
Given function ,
f ( x ) = 4x + 4 when x < 0
= 4x + 8 when x >= 0
f(-1) = 4x + 4
= 4 ( -1 ) + 4
= 0
f(0) = 4x + 8
= 4*0 + 8
= 8
f(2) = 4x + 8
= 4*2 + 8
= 8 + 8
= 16
Therefore, The value of f(-1) , f(0) and f(2) are 0, 8 , 16 .
To learn more about Function from given link.
https://brainly.com/question/12431044
#SPJ1
Rounded to 3 decimal places, what is the value of r for this data set?
The correlation coefficient r of the data given is 0.938
What is the correlation coefficient?The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables.
Given that a set of data showing the values of variables x and y, we are asked to find the correlation coefficient r of the data given,
We know that,
The correlation coefficient r is a number between and calculated to represent the linear dependence of two variables or sets of data.
Using an Excel tool :- (CORREL function) = CORREL(B3:B10,C3:C10)
We get, r = 0.938
Hence, the correlation coefficient r of the data given is 0.938
Learn more about correlation coefficient, click;
https://brainly.com/question/15577278
#SPJ1
Marsha deposited $7,000 into a savings account 4 years ago. The simple interest rate is 2%. How much money did Marsha eam in interest?
Answer:
$560
Step-by-step explanation:
The formula for simple interest is:
I = Prt, where P is the principal, r is the interest rate, and t is the time (in years).
Plugging in the values, we get:
I = $7,000 * 2% * 4 years = $560
So, Marsha earned $560 in interest.
(Q) John has 25 red marbles, 15 blue marbles and 10 yellow marbles. He wants to make similar groups using all the marbles.
(a) Work out the highest number of groups he can make.
(b) Also work out how many, of each color marble, will be in each group.
Answer:
(a) highest number of groups = 5
(b) out how many, of each color marble, will be in each group.
5 red
3 blue
2 yellow
Step-by-step explanation:
The GCF of 25, 15, 10 gives you the greatest number of groups you can form with those numbers
GCF of 25, 15 and 10 can be found as follows by finding factors of each number:
25 = 5 x5
15 = 5 x 3
10 = 5 x 2
Choose the highest number that is common in each group and this is 5
So John can make a maximum number of 5 groups
Divide each number by the GCF to find how may in each group
25/ 5 = 5 red marbles
15/5 = 3 blue marbles
10/5 = 2 yellow marbles
So there are 5 groups max possible each group containing 5 red, 3 blue and 2 yellow marbles
There are 20 packs of cookies with 10 in each. If these are shared equally among 8 children. How each child get?
Answer: 25 per child
Step-by-step explanation:
20 x 10 = 200
200/8 = 25
The
ages
of 5 women are
48, y, 52, 50 and (2y-5).
If their average is
47 years,
Find the age of the oldest woman
Given the information that the average of the ages of 5 women is 47 years and that their ages are 48, y, 52, 50, and (2y-5), we can set up the following equation:
(48 + y + 52 + 50 + 2y - 5) / 5 = 47
Expanding the equation and simplifying, we get:
5y = 244
y = 48.8
So the age of the woman whose age is represented by the variable y is 48.8 years.
The oldest woman is represented by the age of 52 years, which is the largest of all the ages.
Therefore, the age of the oldest woman is 52 years.
The function f (x) = 125,000 (1.028)x models the change in population of Pool City, where x represents the number of years since 2010. Which statement is NOT true?
A.) The domain of the function includes all real values of x .
B.) The point (1, 128500) represents the population of Pool City in 2011.
C.) The population of Pool City in 2010 is 125,000.
D.) The function has an asymptote at y = 125,000 .
How to I arrive at this number using a common factor?
The common factor is 6[tex]e^{6x}[/tex] (2x - 5)⁸.
What is a common factor?
These are the "common factors" when we determine the factors of two or more numbers and discover some of those factors are the same (or "common").
Given that
d/dx[[tex]e^{6x}[/tex](2x - 5)⁹]
The formula of the product rule is d/dx(uv) = uv' + vu'.
=(2x - 5)⁹d/dx([tex]e^{6x}[/tex]) + [tex]e^{6x}[/tex]d/dx(2x - 5)⁹
Now applying the formula d/dx(x^n) = nx^(n-1), d/dx e^(mx) = m e^(mx)
=(2x - 5)⁹ 6[tex]e^{6x}[/tex] + [tex]e^{6x}[/tex]×2×9 × (2x - 5)⁸
= 6[tex]e^{6x}[/tex] (2x - 5)⁹ + 18[tex]e^{6x}[/tex](2x - 5)⁸
Now taking common 6[tex]e^{6x}[/tex] (2x - 5)⁸
= 6[tex]e^{6x}[/tex] (2x - 5)⁸ [(2x - 5) + 3]
= 6[tex]e^{6x}[/tex] (2x - 5)⁸ [2x - 5 + 3]
= 6[tex]e^{6x}[/tex] (2x - 5)⁸(2x - 2)
To learn more about derivatives, click on the below link:
https://brainly.com/question/25324584
#SPJ1
