Answer:
To differentiate the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x, we will use the chain rule and product rule.
First, we will take the derivative of both sides of the equation with respect to x:
d/dx [sin(y) + x^2y^3 - cos(x)] = d/dx [2y]
Next, we will differentiate each term on the left side of the equation:
cos(x) - 2xy^2 dx/dx + 3x^2y^2 + sin(y) dy/dx = 2 dy/dx
We can simplify this equation by moving all the terms involving dy/dx to the left side:
cos(x) - 2xy^2 - 2 dy/dx sin(y) = dy/dx [2 - sin(y)]
Now we can solve for dy/dx by isolating it on one side of the equation:
dy/dx [2 - sin(y)] = cos(x) - 2xy^2
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
Therefore, the derivative of the implicit function sin(y) + x^2y^3 - cos(x) = 2y with respect to x is:
dy/dx = (cos(x) - 2xy^2) / [2 - sin(y)]
We have 2 squares. One square is shaded 2/12 and the other shaded square in the diagram is 2/15 shaded. How much of the total diagram is shaded?
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
The correct answer is C. 0.3, which is equivalent to 3/10.
What are fractions?
A fraction is a mathematical representation of a quantity that expresses a part of a whole or a ratio between two quantities.
To find the total fraction of the diagram that is shaded, we need to add the fractions representing the shaded areas of the two squares.
Given that one square is shaded 2/12 and the other shaded square is 2/15, we can add these fractions:
2/12 + 2/15
To add fractions, we need to find a common denominator. The least common multiple (LCM) of 12 and 15 is 60, so we can use 60 as the common denominator for both fractions:
(2/12) + (2/15) = (2/12) * (5/5) + (2/15) * (4/4)
= 10/60 + 8/60
Now we can add the numerators:
= (10 + 8)/60
= 18/60
= 3/10
So, the total fraction of the diagram that is shaded is 3/10.
Hence, the correct answer is C. 0.3, which is equivalent to 3/10.
To learn more about fractions, Visit
https://brainly.com/question/78672
#SPJ1
What’s the greatest common factor of 42 and 50:(8 different answers)
Answer:
Step-by-step explanation:
The GCF of 42 and 50 is 2.
PLEASE HELP!!!! Luke is training for a long-distance bike race. On Tuesday, after riding for 1 hour, he has travelled 5 miles along a straight highway. After 3 hours, he has travelled 17 miles. Write the equation of the line that models Luke’s bike ride. What does the x represent? What does the y represent?
Answer: y=6x-1
Step-by-step explanation:
y=6x-1
x represents the time luke has been riding(hours) and the y represents the distance he has travelled (miles)
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving AC > EF, given BC = EF. Upload the entire proof below.
Given:
BC = EF
Prove:
AC > EF
STATMENT REASON
1. 1.
2. 2. Betweenness
3. AC > BC 3.
4. 4.
The given information and the transitive property of inequalities, we can prove that [tex]AC[/tex] is greater than [tex]EF[/tex] .
What is the transitive property of inequalities?Statement Reason
[tex]BC = EF[/tex] Given
Betweenness Given
[tex]AC > BC[/tex] Given
[tex]AC > EF[/tex] Transitive property [tex](3, 1)[/tex]
Explanation:
[tex]BC = EF[/tex] Given: Given statement that BC is equal to EF.
Betweenness Given: Given statement that states the concept of betweenness, where BC is between AC and EF.
AC > BC Given: Given statement that [tex]AC[/tex] is greater than BC.
[tex]AC > EF[/tex] Transitive property: Using the transitive property, we can conclude that [tex]AC[/tex] is greater than EF (based on statement 3 and 1).
Therefore, using the given information and the transitive property of inequalities, we can prove that AC is greater than [tex]EF[/tex] .
Learn more about transitive here:
https://brainly.com/question/2437149
#SPJ1
2 only can you solve associative, identity and inverse of this
The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.
Solving the associative, identity and inverse of this the setThe set 2Z is defined as follows:
2Z = {2n | n ∈ Z, a * b = a + b}
Associative element:
There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.
Let a, b, and c be arbitrary elements of 2Z:
a = 2n₁
b = 2n₂
c = 2n₃
Then we have:
a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)
(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)
Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.
Identity element:
There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.
Let e be an arbitrary element of 2Z:
e = 2n
Then we have:
ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z
ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z
Therefore, e = 2n is an identity element in 2Z.
Inverse element:
There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.
Let a be an arbitrary element of 2Z:
a = 2n
Then we need to find an element b in 2Z such that ab = ba = e = 2.
We have:
ab = ba = 2n*b = 2
Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.
Read more about set at
https://brainly.com/question/24462379
#SPJ1
Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity
The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
Describe Volume?In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).
In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.
For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.
In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.
The formula for calculating the volume of air passing through a filter is:
Volume = Filter Area x Airflow Velocity
Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:
Filter Area = Length x Width
Filter Area = 4 ft x 2 ft
Filter Area = 8 square feet
Now we can substitute the values into the formula:
Volume = Filter Area x Airflow Velocity
Volume = 8 sq ft x 100 ft/min
Volume = 800 cubic feet per minute (CFM)
Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
To know more about area visit:
https://brainly.com/question/7624796
#SPJ1
k^2+6k=0 solve the quadratic equation by factoring
Answer:
K = √-6k
i did the math and got this answer and it was right
1C. What do you do if you're collecting data and you're unable to survey everyone in a group because the group is
too large?
If the group is too large to survey everyone, you may consider using a sampling technique to select a representative subset of the group for the survey.
How to use Sampling Technique?Here are some common sampling techniques you could use:
Simple random sampling: randomly select individuals from the group to be surveyed.Stratified sampling: divide the group into subgroups based on certain criteria, and then randomly select individuals from each subgroup to be surveyed.Cluster sampling: divide the group into clusters, randomly select some of the clusters, and survey everyone in the selected clusters.Systematic sampling: select individuals from the group at regular intervals.When selecting a sampling technique, it's important to consider the size of the group, the available resources, and the research question. It's also important to ensure that the sampling technique is unbiased and representative of the group being studied.
Learn more about sampling technique here: https://brainly.com/question/17743025
#SPJ1
A four-sided shape with the top side labeled as 10.2 cm. The height is labeled 5 cm. A portion of the base from the perpendicular to a vertex is labeled 4 cm. The portion of the base from the perpendicular to the right vertex is 6.2 cm.
What is the area of the figure?
25.5 cm2
45.5 cm2
51 cm2
56.1 cm2
The area of the figure is 51 cm², which is option C.
What is area?In mathematics, area refers to the measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²) or square centimeters (cm²), and can be calculated for a variety of geometric shapes, including squares, rectangles, triangles, circles, and more complex shapes such as trapezoids or polygons.
To find the area of the figure, we need to identify the shape of the figure. From the given information, we know that the figure has a top side, a height, and a base. We are also told that the base is divided into two parts by a perpendicular, and one of the parts is labeled as 4 cm, while the other part from the perpendicular to the right vertex is 6.2 cm.
Based on this information, we can draw the figure as a trapezoid, where the top side is the shorter base, the height is the vertical distance between the two bases, and the longer base is the sum of the two parts of the base.
Using the given information, we can calculate the longer base:
longer base = 4 cm + 6.2 cm = 10.2 cm
Now we can use the formula for the area of a trapezoid to find the area of the figure:
A = (1/2)h(b₁ + b₂)
where h is the height, b₁ is the shorter base, and b₂ is the longer base.
Plugging in the given values, we get:
A = (1/2)(5 cm)(10.2 cm + 10.2 cm) = 51 cm²
Therefore, the area of the figure is 51 cm² , which is option C.
To know more about area visit:
https://brainly.com/question/25292087
#SPJ1
Complete Question:
A four-sided figure has one side labeled 10.2 cm, a height of 5 cm, and a portion of the base from the perpendicular to a vertex labeled 4 cm. The portion of the base from the perpendicular to the right vertex is labeled 6.2 cm. What is the area of the figure?
The thickness of a one-dollar bill is 1.1 × 10-4 meters. Each measurement below is the thickness of a stack of one-dollar bills. Drag each measurement to the correct dollar amount.
Thickness of 10 dollar bill is 1.1×10⁻³meters
Thickness of 1.25 × 10³ dollar bill is 1.375×10⁻¹meters
Thickness of 137 dollar bill is1.507 ×10⁻²meters
Define thicknessThickness is the measure of the distance between opposite surfaces of an object. In other words, it is the distance between two parallel planes that bound an object or material. Thickness is often used to describe the dimension of a flat or sheet-like object, such as paper, fabric, or metal, as well as the distance between the front and back surfaces of a three-dimensional object, such as a book or a wall. Thickness can be measured in units such as millimeters, inches, or micrometers.
The thickness of a one-dollar bill is 1.1 × 10⁻⁴ meters
Thickness of 10 dollar bill=10×1.1 × 10⁻⁴
=1.1×10⁻³meters
Thickness of 1.25 × 10³ dollar bill=1.25 × 10³ ×1.1 × 10⁻⁴
=1.375×10⁻¹meters
Thickness of 137 dollar bill=137 ×1.1 × 10⁻⁴
=1.507 ×10⁻²meters
To know more about millimeters, visit:
https://brainly.com/question/25862563
#SPJ1
Which expression represents the phrase The product of a number and ten decreased by eight.
A. n -8 x 10
B. 8n -10
C. 10xn8
D. 10n - 8
The statement "The product of a number and ten decreased by eight" is represented by the correct equation D. 10n - 8.
What is a number's product?A number's product is the outcome of multiplying it by another number.
What additional mathematical expressions are there?Addition, subtraction, multiplication, division, exponents, and square roots are some other examples of mathematical expressions.
What is an exponent?A mathematical action known as an exponent symbolizes the repeated multiplication of the same integer. It is represented by a tiny number above and to the right of a base number.
For instance, 23 signifies that the number 2 has been multiplied three times, for a result of 8.
The sentence "The product of a number and ten decreased by eight" is correctly expressed as D. 10n - 8.
With this formula, a number is multiplied by 10 first, and the result is then reduced by 8.
To know more about product of numbers visit:
brainly.com/question/3211849
#SPJ1
How long did Lizzie practice on Thursday and Friday altogether?
J
P
D
Lizzie's Drum Practice
P
S
P
D
P
S
S
Monday Tuesday Wednesday Thursday Friday
= 5 minutes
DONE
0
minutes
7 8
4
00
5
1 2
0
9
6
3
Answer:
Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
On Thursday, she practiced for 5 minutes according to the table.
On Friday, she practiced for 9 minutes according to the table.
Adding these two times together, we get:
5 minutes + 9 minutes = 14 minutes
Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
Julia drew s sketches of flowers. She split them evenly among her 3 pen pals. Write an expression that shows how many sketches each pen pal received.
Answer:
s/3
Step-by-step explanation:
since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.
Use the formula z = x-μ/σ
and the given information to find the missing piece of information
1. Given x = 75, μ = 80, o = 5, find z.
The missing piece of information z-score is -1.
Explain information
Information refers to data or knowledge that has been transmitted or received. It can be expressed in different forms, including numerical data, text, images, or sound. The information serves as a basis for understanding, analysis, and decision-making. It can be processed and analyzed using mathematical methods and tools such as statistics, probability, and data analysis. The effective management and utilization of information are essential for progress and innovation in many fields, including science, technology, and business.
According to the given information
Using the formula z = (x - μ) / σ, we can plug in the given values and calculate:
z = (75 - 80) / 5
z = -1
Therefore, the z-score is -1.
To know more about z-score visit
brainly.com/question/15016913
#SPJ1
Consider 8 = − 2/3x. 1 Which is the BEST first step to take when solving the given equation?
Amy and Zack each have 24 feet of fencing for their rectangular gardens. Amy makes her fence 6 feet long. Zack makes his fence 8 feet long. Whose garden has the better area? How much greater?
Answer:
The answer is Zack garden
Jasper's aunt gave him a big bin of 500 beads made out of assorted materials to use for the wind chimes he makes. Jasper takes out a handful of beads, looks at the types of beads, then puts them back. Here are the materials of the handful he selected: glass, clay, wood, glass, wood, clay, metal, clay, wood, glass, wood, clay, metal, wood, clay Based on the data, estimate how many glass beads are in the bin. If necessary, round your answer to the nearest whole number.
We can estimate that there are approximately 134 glass beads in the bin.
What is probability?
Probability is a measure of the likelihood of an event occurring.
To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.
There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:
4/15 ≈ 0.267
We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as:
0.267 x 500 ≈ 134
Therefore, we can estimate that there are approximately 134 glass beads in the bin.
To learn more about probability from the given link:
https://brainly.com/question/30034780
#SPJ1
If 4 < a < 5 and 2 < b < 4, find all possible values for each expression:
-2a + 3b
The potential values for the equation -2a + 3b, for given inequalities 4 < a < 5 and 2 < b < 4 are: (-8 + 3b), (-10 + 3b), (-2a + 6), and (-2a + 12), where 'a' and 'b' can take any value within their respective provided ranges.
What is "Inequalities" in mathematics?In mathematics, inequalities are mathematical expressions or statements that compare the relative magnitude of two or more numbers or quantities. They are used to depict connections such as "greater than," "less than," "greater than or equal to," "less than or equal to," and "not equal to" between numbers or mathematical expressions.
Some generally known types of inequalities in mathematics are:
Linear inequalitiesQuadratic inequalitiesRational inequalitiesExponential inequalities etc.For given problem,
Given that 4 < a < 5 and 2 < b < 4, we can consider the extreme values of 'a' and 'b' within these ranges to find the possible values of the expression.
When 'a' is at its Minimum, it equals 4: -2a + 3b = -2(4) + 3b = -8 + 3bWhen 'a' is at its Maximum, it equals 5:-2a + 3b = -2(5) + 3b = -10 + 3bWhen 'b' is at its Minimum, it equals 2:-2a + 3b = -2a + 3(2) = -2a + 6When 'b' is at its Maximum, it equals 4:-2a + 3b = -2a + 3(4) = -2a + 12So, the four potential values for the expression -2a + 3b, where 4 < a < 5 and 2 < b < 4, are:
-8 + 3b, -10 + 3b, -2a + 6, and -2a + 12
where 'a' and 'b' can take any value within their respective given ranges.
Learn more about Inequalities here:
https://brainly.com/question/30231190
#SPJ1
Answer: -4 and 4
Step-by-step explanation:
use the lowest value for a and the highest for b
What is a formula for the nth term of the given sequence? 18 , 21 , 24
Answer:
3n+15
Step-by-step explanation:
18, 21, 24
+3. +3
3n
18-3=15
3n+15
Find the critical value t
The answer of the given question based on the Critical value is , , the critical value to for the confidence level c = 0.99 and sample size n = 22 is 2.819.
What is Critical value?
In statistics, critical value is value that is used to determine whether to reject null hypothesis in hypothesis test. It is based on chosen level of significance, which is the maximum probability of making a Type I error (rejecting true null hypothesis). The critical value is determined by sampling distribution of the test statistic, which is often a t-statistic or z-statistic, depending on the test and the characteristics of the population being studied.
To find the critical value t for a 99% confidence level and a sample size of 22, we need to use a t-distribution table or a calculator.
Using a t-distribution table with 21 degrees of freedom (n-1), we find that critical value for a 99% confidence level is approximately 2.819.
Therefore, critical value for confidence level c = 0.99 and sample size n = 22 is 2.819 (rounded to nearest thousandth).
To know more about Null hypothesis visit:
brainly.com/question/30404845
#SPJ1
6. center (-2, 8), tangent to y = -4
The radius of the circle is 12, and the equation of the circle is:
(x + 2)² + (y - 8)² = 144
What is a circle?
It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
To find the equation of a circle that is tangent to a horizontal line at a given point, we can use the standard form of the equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
In this case, the center of the circle is (-2, 8), which gives us:
(x + 2)² + (y - 8)² = r²
To find the radius, we need to know where the circle intersects the y = -4 line. Since the circle is tangent to the line, the distance from the center of the circle to the line is equal to the radius.
The distance between a point (x, y) and a horizontal line y = k is given by |y - k|.
In this case, the distance between the center (-2, 8) and the line y = -4 is |8 - (-4)| = 12.
Therefore, the radius of the circle is 12, and the equation of the circle is:
(x + 2)² + (y - 8)² = 144
To learn more about the circle visit:
brainly.com/question/11833983
#SPJ1
Complete question:
What is the center at (-2, 8), tangent to the line y = -4?
The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, th
e area is increased by 67 square units. Find the length and breadth of the rectangle.
Answer:
length = 17; breadth = 9
Step-by-step explanation:
Let x = area of rectangle; a = length; b = breadth.
+) a × b = x (1)
+) (a - 5) × (b + 3) = x - 9 => x = ab + 3a - 5b - 15 + 9 (2)
+) (a + 3) × (b + 2) = x + 67 => x = ab + 2a + 3b + 6 - 67 (3)
Replace (1) into (2) & (3):
[tex]\left \{ {{3a - 5b=6} \atop {2a+3b=61}} \right. = > \left \{ {{a=17} \atop {b=9}} \right.[/tex]
Evaluate the expression without using a calculator. sin−1(cos(2)) sin^−1 (cos( − /2))
The value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
Describe Algebraic Expression?An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. These expressions can be used to represent mathematical relationships and patterns in a variety of contexts.
Algebraic expressions can include one or more variables, which are letters or symbols that represent unknown values or values that can vary. For example, in the expression 3x + 5, "x" is the variable.
To evaluate the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)), we first need to determine the value of cos(2) and cos(-π/2).
cos(2) cannot be evaluated directly since the range of cosine function is -1 to 1, and 2 is outside this range. Therefore, we can conclude that sin⁻¹(cos(2)) does not exist.
Next, we can evaluate cos(-π/2) using the unit circle, which is a circle of radius 1 centered at the origin of the coordinate plane. The angle -π/2 is located on the negative y-axis, where the cosine function is 0. Therefore, cos(-π/2) = 0.
Substituting this value into the expression, we get:
sin⁻¹(0) = 0
Therefore, the value of the expression sin⁻¹(cos(2)) sin⁻¹(cos(-π/2)) is 0.
To know more about function visit:
https://brainly.com/question/30954499
#SPJ1
Briana helps her mother make a quilt The quilt is 6 feet wide and 12 feet long
Briana and her mother will need to measure and cut the fabric for the quilt. They will need to decide on a pattern and color scheme for the quilt. They will need to sew the pieces of fabric together to create the quilt top. They will need to layer the quilt top with batting and backing fabric and then quilt the layers together. Finally, they will need to bind the edges of the quilt.
Look at the image provided below
The density of nitrogen in the space will be 3.13 kg/m³
What is density?Density is the ratio of mass to volume of a substance. It is measured in kg/m³.
The volume of the shade part = volume of the cone- volume of the hemisphere
volume of the hemisphere = 2/3 πr³
= 2/3 × 3.14 × 40³
= 401920/3
= 133973.33m³
volume of the cone = 1/3 πr²h
= 1/3 × 3.14 × 40²× 500
= 2512000/3
= 837333.33 m³
volume of the shaded part = 837333.33-133973.33 = 703360m³
The density of the space = 2200000/703360
= 3.13kg/m³.
learn more about density from
https://brainly.com/question/1354972
#SPJ1
4. The elevation at ground level is 0 feet. An elevator starts 80 feet below ground level. After
traveling for 20 seconds, the elevator is 30 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 20-second interval?
A. The elevator traveled upward at a rate
1 rate of 2½ feet per second.
B. The elevator traveled downward at a rate of 2 feet per second.
C. The elevator traveled upward at a rate of 4 feet per second.
D. The elevator traveled downward at a rate of 4 feet per second.
a
Answer:
[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]
A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.
Use the image to determine the direction and angle of rotation.
graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 3
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
360° counterclockwise rotation
The correct direction and angle of rotation between triangle ABC in quadrant 4 and polygon A' B' C' in quadrant 3 is: 90° clockwise rotation.
What is he concept of transformations in geometry?A transformation in geometry is a procedure that modifies the location, scale, or orientation of a shape. Translations, rotations, reflections, and dilations are examples of common transformations.
Rotations are transformations that involve rotating a shape around a fixed point called the center of rotation. The direction of rotation can be either clockwise or counterclockwise, and the angle of rotation is the amount of rotation in degrees.
A' is located to the left of A, which indicates a clockwise rotation.
B' is located below B, which also indicates a clockwise rotation.
C' is located to the right of C, which indicates a clockwise rotation as well.
The correct response is a 90° clockwise rotation since all of the relevant vertices of polygon A' B' C' are turned clockwise in relation to triangle ABC. I regret if the prior replies left you perplexed.
Learn more about polygon here:
https://brainly.com/question/28276384
#SPJ1
Answer:
(A) 90° clockwise rotation
Step-by-step explanation:
Took the test (FLVS) got it right. ;)
PLEASE HELP FAST 35 POINTS
calculate (p o q) (0)
0 is the value of (p o q) (0) in function .
What are functions in mathematics?
Function, in mathematics, a formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable).
Functions are ubiquitous in mathematics and essential in the natural sciences for formulating physical relationships. A function is a relationship between inputs, with each input associated with exactly one output. Each function has a domain and a codomain or scope.
P(0) = 0
Q(0) = - 1
(P o q)(0) = P(0) * Q(0)
= 0 * - 1
= 0
Learn more about Function
brainly.com/question/29452843
#SPJ1
content loaded
A department store manager has monitored the number of complaints received per week about poor service. The probabilities for numbers of complaints in a week, established by this review, are shown in the table. Answer Number of complaints 012 3 4 5 Probability 0.13 0.21 0.44 0.070. 0.06 0.09Save your answer What is the variance of complaints received per week? Please round your answer to the nearest hundredth Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.
200 word answer
To calculate the variance of complaints received per week, we first need to find the mean or expected value of the number of complaints. This can be calculated by multiplying the number of complaints in each category by its corresponding probability, and then adding up the results.
Expected value = (0 x 0.13) + (1 x 0.21) + (2 x 0.44) + (3 x 0.07) + (4 x 0.06) + (5 x 0.09) = 2.54
Next, we can use the following formula to calculate the variance:
Variance = Σ[(x - µ)²P(x)]
where Σ = sum, x = number of complaints, µ = expected value, and P(x) = probability.
Using this formula and the probabilities given in the table, we get:
Variance = (0 - 2.54)²(0.13) + (1 - 2.54)²(0.21) + (2 - 2.54)²(0.44) + (3 - 2.54)²(0.07) + (4 - 2.54)²(0.06) + (5 - 2.54)²(0.09) = 1.4856
Rounding this answer to the nearest hundredth, we get a variance of 1.49.
In conclusion, the variance of complaints received per week is 1.49, meaning that the number of complaints is quite spread out around the mean, which is 2.54. This could indicate that the department store has some variability in its service quality, as the number of complaints can vary widely from week to week.
8. You and 4 friends are going to an event, and you want to keep the cost below $100 per person. Write and solve an inequality to find the total cost, x.