To find the PDF of Z=X+Y, we can use the convolution of probability density functions. Let fX(x) and fY(y) be the PDFs of X and Y, respectively. Then, the PDF of Z is:
fZ(z) = ∫fX(x)fY(z−x)dx
Since X and Y are exponentially distributed, we have:
fX(x) = λe^−λx for x > 0
fY(y) = μe^−μy for y > 0
Substituting these expressions into the convolution formula, we obtain:
fZ(z) = ∫λe^−λx μe^−μ(z−x) dx
= λμe^−μz ∫e^−(λ−μ)x dx
= λμe^−μz / (λ−μ) [1−e^(−(λ−μ)z)]
Thus, the PDF of Z is:
fZ(z) = { λμe^−μz / (λ−μ) [1−e^(−(λ−μ)z)] } for z > 0
To find the PDF of U=X−Y, we can use the change of variables technique. Let g(u,v) be the joint PDF of U and V=X. Then, we have:
g(u,v) = fX(v)fY(v−u)
Substituting the expressions for fX and fY, we get:
g(u,v) = λμe^−λve^−μ(v−u) for u < v
The PDF of U is obtained by integrating out V:
fU(u) = ∫g(u,v)dv
= ∫_u^∞ λμe^−λve^−μ(v−u) dv
= λμe^−μu ∫_0^∞ e^−(λ+μ)v dv
= λμe^−μu / (λ+μ) for all u
Therefore, the PDF of U is:
fU(u) = { λμe^−μu / (λ+μ) } for all u
To know more about PDF of U, visit:
https://brainly.com/question/31730410
#SPJ11
What is 4x5 ratio in pixels?
The 4:5 ratio in terms of pixels is nothing but the measure of 1080×1350 pixels in an image of the video.
A colon separates two numbers that represent the width-to-height proportion of an image or video. This proportion or ratio is referred to as the aspect ratio. In terms of height and width, it shows how wide the size is. It makes sure the videos or images are presented without stretching or resolution loss.
The resolution in pixels for the aspect ratio 4x5 or 4:5 is 864 x 1080 or 1080 x 1350 pixels. This establishes how many pixels are present in an image's or video's width and height. The most popular pixel ratio is this one.
To know more about pixels:
https://brainly.com/question/28430816
#SPJ4
rewrite the following ratios in simplest form
Answer:
in Step-by-step explanation
Step-by-step explanation:
9)
60/40 = divide both side by 10
6/4 = divide both side by 2
3/2
10)
28/63 = divide both side by 7
4/9
11)
45/120 = divide both side by 15
3/8
Convert this equation into standard form
The standard form of the given equation is expressed as; 3x + y = -1
How to write a Linear Equation is standard form?The standard form for linear equations in two variables is expressed as; Ax + By = C
We are given the equation as;
y - 5 = -3(x + 2)
Expanding the bracket gives us;
y - 5 = -3x - 6
Add 3x to both sides to get;
y - 5 + 3x = -6
Add 5 to both sides to get;
3x + y = -1
Read more about Linear equation in standard form at; https://brainly.com/question/1958920
#SPJ1
What are the values for the coefficients and constant term of 0 2 3x² 5x?
The expression's coefficients have values of 3 and -5, and the constant term has a value of 2.
The formula is 0 = 2 + 3x² - 5x.
We obtain = 3x² - 5x + 2 = 0 by arranging the equation in the form of the general equation ax2 + bx + c = 0.
The leading coefficient is a, the intermediate term's coefficient is b, and the constant term is c.
We may locate the equation's roots or the parabola's vertex by knowing the values of a, b, and c.
After comparing the equation to the general equation, the coefficient and constant term values are as follows.
A = 3
B = -5
C = 2
So, now both the polynomial and the coefficients are available.
To know more about polynomial, visit,
https://brainly.com/question/2833285
#SPJ4
How to solve
-y - 10=6x
5x + y= -10
Using the system by elimination
The area of a rectangle is 14 1/2 sq cm and one side is 4 1/2 cm. how long is the other side?
Answer:
6cm*4.5cm = 27cm²
5cm*5cm = 25cm²
The first has a greater area - by 2 square centimeters.
Step-by-step explanation:
Answer:5 1/2
Step-by-step explanation:
4 1/2+4 1/2=9
14 1/2 -9=5 1/2
Which proportion could you use to find SR?
In triangle ABC and triangle PQR , DC IS PROPORTION TO SR.
What are triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.
This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.
In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.
The vertex is the intersection of two straight lines. The triangle therefore has three vertices.
Hence, In triangle ABC and triangle PQR , DC IS PROPORTION TO SR.
learn more about triangles click here:
brainly.com/question/1058720
#SPJ1
y = what to 48 from 180
When 27x^2 z^4/-3x^2z is completely simplified, the exponent on the variable z is ___.
Therefore , the solution to the given problem of expression comes out to be 5 is the exponent of the variable z.
Definition of the expressionMath allows for the conceivable operations of multiplication, division, addition, and subtraction. The structure of the expression is as follows: Calculator, expression, and a number or variable A mathematical expression is made up of variables, numbers, and operations (such as addition, subtraction, multiplication, or division, etc.). You can contrast two statements or expressions.
Here,
The following expression (27x2)z/3x2)(z6) can be simplified as follows:
If your base is the same, you can subtract the exponents using the properties of powers.
Then:
=(27x^2)z/(-3x^2)(z^6)
=-9z/z^6 You can see that x2-2=x0=1
=-9/z^5 (Thereafter, z6-1=z5)
Consequently, the response is: 5 is the exponent of the variable z.
Therefore , the solution to the given problem of expression comes out to be 5 is the exponent of the variable z.
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ1
A bakery sells different packages of muffins. The number of muffins, , and the price in dollars, , of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
The bakery is considering adding a new package of muffins. Which of these combinations would make the relation NOT a function? Select TWO that apply.
A relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.
What are combinations?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
You can choose the components of combos in any order.
Permutations and combinations can be mixed up.
So, given is the ordered pair:
(x, y) = (1, 2); (2, 3); (4, 5); (6, 7); (12, 13)
All of the x-values in a relation must be distinct for it to be a function (i.e. no repetition)
The x values of choices (b) and (d) already exist in the ordered pair, namely (6,7) and (d), from the list of alternatives given (4,5)
Accordingly, (b) and (d) would prevent the relation from being a function.
Therefore, a relation could be a function or it could not. Since b. (6, 8) and d. (4, 3), the connection would no longer be a function.
Know more about combinations here:
https://brainly.com/question/11732255
#SPJ1
Correct question:
A bakery sells different packages of muffins. The number of muffins, x, and the price in dollars, y, of their packages of muffins are given in the ordered pairs below. The set of ordered pairs is a relation that is also a function.
{(1,2),(2,3),(4,5),(6,7),(12,13)}
The bakery is considering adding a new package of muffins. which ordered pairs would make the relation NOT a function? Choose all that are correct.
a. (10,13)
b. (6,8)
c. (8,12)
d. (4,3)
e. (24,18)
Find the equation of the line passing through the given point and perpendicular to the given line
Answer:
5x + y = 34
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x - 5y = 8 ( subtract x from both sides )
- 5y = - x + 8 ( divide through by - 5 )
y = [tex]\frac{1}{5}[/tex] x - [tex]\frac{8}{5}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{5}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{5} }[/tex] = - 5 , then
y = - 5x + c ← is the partial equation
to find c substitute (5, 9 ) into the partial equation
9 = - 25 + c ⇒ c = 9 + 25 = 34
y = - 5x + 34 ← equation of perpendicular line in slope- intercept form
add 5x to both sides
5x + y = 34 ← equation in standard form
How do you find the center of enlargement of a triangle?
To find the center of enlargement, draw line segments between corresponding vertices of pre-image and image triangles, the point where they intersect is the center of enlargement, check that all the line segments intersect at the same point, or use the coordinates of the triangle and the scale factor.
You can follow these steps:
Identify the pre-image triangle. This is the original triangle that will be enlarged.Identify the image triangle. This is the enlarged version of the pre-image triangle.Draw a line segment between the corresponding vertices of the pre-image and image triangles.The point where these line segments intersect is the center of enlargement.To check that you have the correct center of enlargement, you can draw a line segment between any other corresponding vertices of the pre-image and image triangles and check that they intersect at the same point.Another way to find the center of enlargement is to use the coordinates of the triangle and the scale factor. The center of enlargement is the point that remains the same distance from all points on the image and the pre-image. The center of enlargement is the point that the coordinates of the image triangle obtained from the coordinates of the pre-image triangle by multiplying each coordinate by the same scale factor greater than 1.
It's important to note that, the center of enlargement is the same as the center of dilation.
In both ways, it's important to have the pre-image triangle and the image triangle to find the center of enlargement.
To learn more about the triangle, visit:
brainly.com/question/2773823
#SPJ4
Which set of numbers can represent the side lengths in inches of a right triangle?A. 8,12,15B. 10,24,26C. 12,20,25D. 15,18,20
The set B represent the side length in inches of a right triangle.
Now, According to the question:
Let's know:
What is Pythagoras Theorem?
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^2 + b^2 = c^2.[/tex]
Where a and b are the two legs of the triangle and c is the length of the hypotenuse [THE LONGEST SIDE].
We can square each leg on the triangle and take the sum, if that is equal to the square of the longest side, we have a right triangle. Let's check for all of these.
A) [tex]8^2+12^2=15^2[/tex]
64 + 144 = 225
208 ≠ 225
This is not a right triangle.
B) [tex]10^2+24^2=26^2[/tex]
100 + 576 = 676
676 = 676
This is a right triangle.
C) [tex]12^2 + 20^2=25^2[/tex]
144 + 400 = 625
544 ≠ 625
This is not a right triangle.
D) [tex]15^2+18^2=20^2[/tex]
225 + 324 = 400
549 ≠400
This is not a right triangle.
Hence, The set B represent the side length in inches of a right triangle.
Learn more about Right Triangle at:
https://brainly.com/question/22215992
#SPJ4
What is the area of a circle with a diameter of 5 m? use 3.14 for pi. round to the nearest tenth. responses a. 7.9 m² b. 15.7 m²c. 19.6 m² d. 78.5 m²
The area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².
What is circle ?
A circle is a two-dimensional geometric shape defined as the set of all points that are a fixed distance, called the radius, from a central point, called the center. A circle is the set of all points in a plane that are at a given distance from a given point, the center.
The area of a circle is given by the formula A = [tex]\pi r^{2}[/tex], where r is the radius of the circle. To find the area of a circle with a diameter of 5 m, we first need to find the radius. We can do this by dividing the diameter by 2:
r = 5 m / 2 = 2.5 m
Then we can substitute this value of r into the formula for the area of a circle:
A = [tex]\pi r^{2}[/tex] = π(2.5 m)^2 = 3.14 * 6.25 m^2 = 19.63 m²
So the area of a circle with a diameter of 5 m is 19.63 m², rounded to the nearest tenth, it would be 19.6 m². So the answer is c. 19.6 m².
To learn more about circle visit : brainly.com/question/29142813
#SPJ4
Answer:
The Area of a circle with a diameter of 5 m is 19.63 m² rounded to the Nearest tenth, it would be 19.6 m². the answer is c. 19.6 m².
Step-by-step explanation:
good luck to you
Create math problems with the words : each, time, and product (for multiplication)
On solving the provided question we can say that the value of multiplication is x^34.
What is the multiplication problems?A math problem is a problem or question that requires the application of mathematical concepts and skills to solve.It is an extension of repeated addition. The operation is symbolized by the multiplication sign "x" or an asterisk (*), a dot (•) or the letter "m" . .
For example, if we multiply 4 and 5, the product will be 20 (4x5 = 20).
In addition, multiplication can also be represented using the distributive property, which states that for any three numbers a, b and c, a(b+c) = ab + ac.
In Multiplication, order of numbers doesn't matter, meaning a x b = b x a.
It's also commutative, meaning the order of numbers doesn't change the result.
Multiplication is the foundation for many other mathematical concepts, including algebra and geometry. It's an essential operation in many fields such as science, engineering, and finance.
And answer for above question is given by,
If each of the 5 students in a class has 3 apples, the total number of apples among the students is 3 apples/student * 5 students = 15 apples.
To find the product of the number of apples and the number of students, we multiply the number of apples (15) by the number of students (5) which is 15*5 = 75
So the product of the number of apples and the number of students is 75.
To learn more about multiplication refer:
https://brainly.com/question/5992872
#SPJ1
A lighthouse sits at the edge of a cliff, as shown. A ship at sea level is meters from the base of the cliff. The angle of elevation from sea level to the base of the lighthouse is . The angle of elevation from sea level to the top of the lighthouse is . Find the height of the lighthouse from the top of the cliff. Do not round any intermediate computations. Round your answer to the nearest tenth. Note that the figure below is not drawn to scale.
There is no numbers provided, but this is how you solve it.
We can use the tangent function to solve for the height of the lighthouse.
Let h be the height of the lighthouse from the top of the cliff.
tan(angle of elevation from sea level to the top of the lighthouse) = (h+ height of lighthouse from sea level ) / distance from the base of the cliff
tan( angle of elevation from sea level to the top of the lighthouse) = (h+x) / distance from the base of the cliff
tan(angle of elevation from sea level to the base of the lighthouse) = (h) / distance from the base of the cliff
By dividing the first equation by the second equation
(h+x) / distance from the base of the cliff = tan( angle of elevation from sea level to the top of the lighthouse) / tan( angle of elevation from sea level to the base of the lighthouse)
(h+x) = (h) * (tan( angle of elevation from sea level to the top of the lighthouse) / tan( angle of elevation from sea level to the base of the lighthouse))
h = (x * tan( angle of elevation from sea level to the base of the lighthouse)) / ( tan( angle of elevation from sea level to the top of the lighthouse) - tan( angle of elevation from sea level to the base of the lighthouse))
After plugging in the values into the equation, we get:
h = (x * tan( )) / ( tan( ) - tan( ))
Round to the nearest tenth
h = (x * tan( )) /
Adam and Daniel are selling cheesecakes for a school fundraiser. Customers can buy pecan cheesecakes and chocolate marble cheesecakes. Adam sold 8 pecan cheesecakes and 6 chocolate marble cheesecakes for a total of $182. Daniel sold 7 pecan cheesecakes and 12 chocolate marble cheesecakes for a total of $274. What is the cost each of one pecan cheesecake and one chocolate marble cheesecake?
Using simultaneous equations, the cost of each pecan cheesecake and chocolate marble cheesecake is as follows:
Pecan Cheesecake = $10Chocolate Marble Cheesecake = $17.What are simultaneous equations?Simultaneous equations are a system of equations (two or more equations) solved concurrently or simultaneously.
Pecan Chocolate Total Revenue
Adam's sales 8 6 $182
Daniel's sales 7 12 $274
Let sales units of Pecan = p and sales units of chocolate = c
Equations:Equation 1: 8p + 6c = 182
Equation 2: 7P + 12C = 274
Multiply Equation 1 by 2:
Equation 3: 16p + 12c = 364
Subtract Equation 2 from Equation 3:
16p + 12c = 364
-
7P + 12C = 274
9p = 90
p = 10
= $10
Substitute, p = 10, in Equation 1:
8p + 6c = 182
8(10) + 6c = 182
80 + 6c = 182
6c = 102
c = 17
= $17
Check:
8p + 6c = 182
8(10) + 6(17) = 182
80 + 102 = 182
Thus, based on a system of equations, the pecan cheesecake costs $10 per unit while the chocolate marble cheesecake costs $17 per unit.
Learn more about simultaneous equations at https://brainly.com/question/148035
#SPJ1
Help me please I will make u the Brainlyest please help me. I will even you 30 points. someone just scammed me and took away 50 points and she/he did not answer my question. please help me. (I will report if you scam or pup something crazy.) habibadabanija scammed me.
The equivalent expression to 3/4 of 2 1/5 is 3/4 × 11/5
The number of miles Manny hiked before he stopped to climb a lookout tower is 1 3/5 miles.The writing area of the poster given the length and width gives them 9/8 square yards and 1 1/8 square yards.How to multiply fraction?Caleb:
Length of rope = 2 1/5 yards
Length used for dog leash = 3/4 of 2 1/5
= 3/4 × 11/5
Manny:
Distance hiked = 6 2/5 miles
Distance he stopped to climb a lookout tower = 1/4 of 6 2/5 miles
Number of miles Manny hiked before he stopped to climb a lookout tower = 1/4 of 6 2/5 miles
= 1/4 × 6 2/5
= 1/4 × 32/5
= 32/20
= 1 12/20
= 1 3/5 miles
Dante and friends:
Length of the poster = 1 1/2 yards
Width of the poster = 3/4 yard
Area of the poster = Length × width
= 1 1/2 yards × 3/4 yard
= 3/2 × 3/4
= 9/8
= 1 1/8 square yards
Therefore, the area of the poster can be calculated by multiplying length by width and written in square units.
Read more on fraction:
https://brainly.com/question/11562149
#SPJ1
1. The expression to illustrate the fact that Caleb has 2 1/5 yards and then used 3/4 of the rope is B. 3/4 × 11/5.
2. The number of miles that Manny hiked before he stopped is D. 1 3/5 miles.
3. The fraction of the writing area is D. 1 1/8 square yards.
How to compute the fractions?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Caleb has 2 1/5 yards and then used 3/4 of the rope. The expression to illustrate this will be:
= 3/4 × 2 1/5
= 3/4 × 11 / 5
The number of miles that Manny hiked before he stopped is;
= 1 /4 × 6 2/5
= 1/4 × 32/5
= 32 / 20
= 8 / 5
= 1 3/5 miles.
The fraction of the writing area is:
= 1 1/2 × 3/4
= 3/2 × 3/4
= 9/8
= 1 1/8 square yards.
Learn more about Fraction on:
brainly.com/question/78672
#SPJ1
Please help me with my work
Answer: 3k^2
Step-by-step explanation:
What kind of slope does y 10 have?
The slope of line y = 10 is zero.
We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.
It describes the steepness of a line.
The slope of x - axis.
m = 0
As for x-axis the change in y-coordinate is zero.
So, by definition of slope,
m = 0/(change in x coordinate)
m = 0
We know that the slopes of parallel lines are equal.
A line y = 10 is parallel to x-axis
So, the slope of line y = 10 is zero.
i.e., the line y = 10 has zero steepness.
Learn more about the slope here:
https://brainly.com/question/16180119
#SPJ4
What is 3 with an exponent of 0?
When a number has an exponent of 0, it means that the number is being multiplied by itself 0 times. In other words, it is multiplied by 1.
To determine this:
In the case of 3 with an exponent of 0, it would be represented as 3^0. To calculate the value, we would take 3 and multiply it by 0 times.
3 x 1 = 3
So, 3 with an exponent of 0 is equal to 3.
It is important to note that any number with an exponent of 0 will always equal 1, except for 0 which will always be 0. This is because any number multiplied by 1 is itself, and 0 multiplied by any number is always 0.
To learn more about the multiply, visit:
brainly.com/question/23536361
#SPJ4
A gym has soccer balls and basketballs. The ratio of soccer balls to basketballs is 3:2. The number of soccer balls at the gym is shown. How many basketballs does the gym have?
Answer: If the ratio of soccer balls to basketballs is 3:2, that means for every 3 soccer balls, there are 2 basketballs.
Let's say there are x soccer balls at the gym.
The ratio can be represented as 3x:2x
So the number of basketballs at the gym would be 2x.
So if you know the number of soccer balls at the gym, you can find the number of basketballs by multiplying the number of soccer balls by 2/3.
For example, if the gym has 18 soccer balls, the number of basketballs would be 2/3 * 18 = 12 basketballs
Step-by-step explanation:
What is the formula for area of a rectangle and triangle?
The area of a rectangle is found by multiplying the length and width.The area of a triangle is found by taking half the base multiplied by the height.
The formula for this is A = lw, where A is the area, l is the length, and w is the width. For example, if the length of the rectangle is 10 cm and the width is 5 cm, then the area of the rectangle is A = 10 * 5 = 50 cm2.
The area of a triangle is found by taking half the base multiplied by the height. The formula for this is A = 1/2bh, where A is the area, b is the base, and h is the height. For example, if the base of the triangle is 10 cm and the height is 5 cm, then the area of the triangle is A = 1/2 * 10 * 5 = 25 cm2.
Learn more about area of a rectangle and triangle here:
https://brainly.com/question/29117421
#SPJ4
Does anybody know what 5 1/3 minus 3 2/3 and 8 4/7 minus 7 5/7 is? And if possible try simplifying the answers.
Answer: 5 1/3 - 3 2/3 = 1 2/3. 8 4/7 - 7 5/7 = 6/7. Yes its simplified and 100% correct.
Step-by-step explanation:
Is 0 0 an infinite solution?
Since 0 = 0 for any value of x, the system of equations has infinite solutions.
What is infinite solution?
Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".
What is an infinite number?
There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.
The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.
Learn more about infinite solution
brainly.com/question/29093214
#SPJ4
Find the probability using the normal distribution. Use a graphing calculator and round the answer to four decimal places. P(0 < z < 2.18)- Find the area under the standard normal distribution curve to the left of z-1.34 and to the right ofz -2.13. Use a graphing calculator and round the answer to four decimal places. The area is
The probability of 0 < z < 2.18 is 0.9945, rounded to four decimal places.
1. To find the probability, we first need to calculate the area under the standard normal distribution curve to the left of z = 1.34 and to the right of z = 2.13.
2. To do this, we can use the graphing calculator to plot the standard normal distribution curve.
3. Then, we can calculate the area under the curve to the left of z = 1.34 by subtracting the area under the curve to the left of z = 2.13 from the total area under the curve.
4. Finally, we can round the answer to four decimal places to get the probability of 0.9945.
The probability of 0 < z < 2.18 is 0.9945, rounded to four decimal places.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
How many vectors are there in 3D Mcq?
There are three vectors in three-dimensional space, namely the X-axis, the Y-axis, and the Z-axis.
What is vector?Vector is a term used to describe a mathematical quantity that has both magnitude and direction, such as velocity, force, and acceleration. A vector can be represented by an arrow, with its length representing the magnitude and its direction indicating the direction. Vectors can be added together or scaled to create new vectors. Vector operations are essential in physics, engineering, and other fields of mathematics.
Each of these vectors has a magnitude and direction and can be used to represent any point in 3D space. All three axes intersect at the origin, which is the point (0,0,0). Vector algebra can be used to describe and calculate the relationships between these vectors in 3D space.
To know more about vector click-
https://brainly.com/question/15519257
#SPJ4
A spherical balloon has a radius of 15cm. Air is added to the balloon until it's surface area
increases by 500 cm². What would be the new diameter of the balloon after the air is added?
The new diameter of the sphere after the air is added is 32.6cm
What is surface area of a sphere?A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the centre.The Surface Area of Sphere is 4πr², where r is the radius of sphere.
The original surface area when air is not added. is :
A = 4×3.14×15²
A = 2826cm²
When air is added, the surface area increased by 500cm². Therefore the new surface area = 2826+500 =3326cm²
To find the new radius of the sphere
3326 = 4×3.14× r²
r² = 3326/12.56
r² = 265
r = √265
r = 16.3
the diameter of the balloon after the air is added = 2r = 2× 16.3 = 32.6 cm
learn more about surface area of a sphere from
https://brainly.com/question/1293273
#SPJ1
A system of linear equations with exactly one solution is a(n) __________ system.
Answer:
independent
Step-by-step explanation:
A system of linear equations with exactly one solution is a _independent system.
Which of the following ordered pairs is a solution to the inequality y is greater than one fourth times x plus 5? (12, 8) (11, 7) (8, 6) (4, 7)
The ordered pair that is a solution to the inequality:
y > (1/4)*x + 5
is (4, 7)
Which of the given ordered pairs is a solution for the inequality?Here we have the inequality:
y > (1/4)*x + 5
To check if an ordered pair is a solution, we just need to replace the values of the ordered pair on the inequality and see if it is true.
For example, for (12, 8)
We will get:
8 > (1/4)*12 + 5
8 > 3 + 5
8 > 8
This is false, so (12, 8) is not a solution.
The pair that is a solution is:
(4, 7)
7 > (1/4)*4 + 5
7 > 1 + 5
7 > 6
This is true.
Learn more about inequalities:
https://brainly.com/question/24372553
#SPJ1