If a pair of linear equations in two variables have no solution then the pair of lines are inconsistent or parallel lines.
Solutions of a pair of linear equations:
Depending on the number of variables and type of equations there are 3 types of solutions to an equation.
1. Unique Solution (One solution):
When there is only one variable then the linear equation will have a Unique Solution or One solution. In the case of pair of linear equations, the linear equation will have a unique solution when the straight lines are intersected at a single point.
2. No solution:
When the given pair of linear equations is inconsistent equations the linear equation will have no solutions in common or we can say that the given lines are non-intersected lines. Usually, a pair of parallel lines will have no solutions.
3. Infinite Solutions (Many solutions):
When the given lines are overlapped on each other or coincident with each other the given lines will have Infinite Solutions. These intersected lines.
Therefore,
If a pair of linear equations in two variables have no solution then the pair of lines are inconsistent or parallel lines.
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Question 5(Multiple Choice Worth 2 points)
(Translating Algebraic Inequalities MC)
Wyatt had to climb the stairs to ride the waterslide. The top of the waterslide was more than 56 feet from the ground. Which graph represents this inequalit
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The graph representing the inequality x ≥ 12 is with a closed and shaded circle to the left.
What is inequality ?
An inequality is an expression that shows the non-equal comparison of the two or more numbers and variables. A number line can be used to represent numbers put on regular intervals. A number line is sometimes used to represent an inequality.
The height of the water slide is = 56 feet
The graph representing the inequality x ≥ 12 is shown on the number line begining from 12 with a closed and shaded circle.
Therefore, The graph representing the inequality x ≥ 12 is with a closed and shaded circle to the left.
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assign ballradius with ballheight divided by 2.0. do not use the fraction 1.0 / 2.0; instead, divide ballheight directly by 2.0.
The C++ or Python code for the given problem is float ballRadius = ballHeight / 2.0;
To assign the value of ballRadius with ballHeight divided by 2.0, you can write the following code in a programming language such as C++ or Python:
float ballRadius;
float ballHeight = [some value];
ballRadius = ballHeight / 2.0;
This code uses the division operator (/) to divide ballHeight by 2.0, which results in a floating-point value. This value is then assigned to the variable ballRadius. By dividing ballHeight directly by 2.0, we are not using the fraction 1.0 / 2.0.
In detail, the operation ballHeight / 2.0 performs floating-point division, which means that the result will be a floating-point value with decimal places. The value of ballHeight is divided by 2.0, which is a floating-point constant. The result of this division is assigned to the variable ballRadius, which is also a floating-point value.
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find the following limit or state that it does not exist. x-9
The limit of the function [tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ] is equal to 18.
[tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ]
Substitute the limit x tends to 9 in the function we have,
= ( 9² - 81 ) / ( 9 - 9 )
= ( 81 - 81 ) / 0
= 0 /0
0 /0 form is not defined term.
Simplify the function before substituting the limit we have,
[tex]\lim_{x \to9}[/tex] [( x² - 81 ) / ( x - 9 ) ]
= [tex]\lim_{x \to9}[/tex] [ ( x ² - 9² ) / ( x - 9 ) ]
= [tex]\lim_{x \to9}[/tex] [ ( x - 9 ) ( x + 9 ) / ( x - 9 ) ]
= [tex]\lim_{x \to9}[/tex] ( x + 9 )
= 9 + 9
= 18
Therefore, the value of the limit for the function [tex]\lim_{x \to9}[/tex] [( x² - 81 ) /( x - 9) ] is equal to 18.
The given question is incomplete, I answer the question in general according to my knowledge:
Find the following limit or state that it does not exist.
[tex]\lim_{x \to9} \frac{(x^{2} - 81)}{(x - 9)}[/tex].
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What conditions must be met for the results of an ANOVA test to be reliable?
The conditions that must be met for the results of an ANOVA test to be reliable are Independence , Random Sampling , Large Sample Size and Normality .
The ANOVA (Analysis of Variance) is defined as a statistical method that is used to determine if there are significant differences among the means of two or more groups.
For the results of an ANOVA test to be reliable, the conditions that must be met are :
(i) Independence: The observations within each group should be independent of each other.
(ii) Normality: The data within each group should be approximately normally distributed.
(iii) Random Sampling: The samples within each group should be selected randomly from the population.
(iv) Large Sample Size: The sample size within each group should be large enough to provide a robust estimate of the population mean.
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Can someone PLEASE help me? I don’t understand. Could you please show work?
Answer:
Step-by-step explanation:
Angle ABD plus angle DBC = 90. That's what that little square in the corner there means...a right angle which is 90 degrees. Using substitution,
3x + 15 + 2x = 90 and
5x + 15 = 90 and
5x = 75 so
x = 15. Now we need to plug in 15 for x in 2x to get 2(15) which is 30. Second choice down.
Aya sells stuffed animals at a craft fair. She charges $13 for the small ones and $12 for the large ones. She sold $350 worth of animals. After the show, she noticed that she sold 27 stuffed animals. How many were small and how many were large?
Let's call the number of small stuffed animals sold "x" and the number of large stuffed animals sold "y".
We know that:
x + y = 27 (the total number of stuffed animals sold)
13x + 12y = 350 (the total amount of money Aya earned)
We can use these two equations to solve for x and y. To do this, we'll use substitution:
x + y = 27
x = 27 - y
Now, we'll substitute this expression for x into the second equation:
13(27 - y) + 12y = 350
351 - 13y + 12y = 350
351 = 350
This equation is true for all y, which means that we cannot solve for y using these two equations. We need more information to determine the number of small and large stuffed animals sold.
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x + y = 27 (the total amount of stuffed creatures sold) (the total number of stuffed animals sold)
These two formulae can be used to find the answers to x and y. We'll use replacement to accomplish this:
x + y = 27
x = 27 - y
We will now change x in the second equation to the following expression:
13(27 - y) + 12y = 350
351 - 13y + 12y = 350
351 = 350
from largest to smallest, the correct order is:group of answer choicessample, sampling frame, population.
Population - - > Sampling Frame - - > Sample - - > Individual being surveyed is the order from largest to smallest.
The population is the largest as they include all units or subject of interest in a particular study or experiment.
Next is the sampling frame which is the list or compilation of all subjects which can form part of a sample. It is a compilation of all elements in the population from which the sample can be drawn.
The sample is a subset of the population of population, usually selected at random and it is representative of the population.
The individual surveyed represents a single subject or observation from the chosen sample.
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In a survey of youths, it was found that 85% like to do farming in their village, 60% like to go for foreign employment.If 5% of them did not like both of them then,
1)Show that above information in a Venn diagram.
2)What percent of use who like to do farming in their village only?
3) What percent of youths like foreign employment only?
4) What percent of you like both of the jobs?
On solving the provided question, we can say that by percentage the proportion of pupils who participate in either cricket or volleyball.
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions.
In a study conducted at a school, 300 students preferred volleyball, 250 preferred cricket, and 110 preferred playing both sports. Calculate the following using a Venn diagram: a. the number of pupils who play cricket exclusively.
b. the proportion of pupils who participate in either cricket or volleyball.
After their SEE, a survey found that 120 students desired to be both an engineer and a doctor, while 190 students wanted to be both. Draw a Venn-diagram and count the number of students who said they wanted to be neither of them if 300 students were surveyed.
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East West Distributing is in the process of trying to determine where they should schedule next year's production of a popular line of kitchen utensils that they distribute. Manufacturers form in four different countries have submitted bids to East West. However, a pending trade in bill in Congress will greatly affect the cost to East West due to proposed tariffs, favorable trading status, etc. After a careful analysis, East West has determined the following cost breakdown for the four manufacturers (in $1,000's) on whether or not the trade bill passes: Bill Passes country A 260, country B 320, country C 240, country D 275 Bill Fails country A 210, country B 160, country C 240, country D 210 a. If East West estimates that there is a 40% chance of the bill passing, which country should they choose for manufacturing? b. Over what range of values for the "bill passing" will the solution in part (a) remain optimal?
Over the 0.33 and 0.375 range of values for the "bill passing" will country C remain optimal.
a. To calculate the estimated costs for each country, we must divide the cost by the likelihood of the bill being approved or rejected. Each country's expected cost is computed as follows:
Country A: 0.4 * 260 + 0.6 * 210 = 244
Country B: 0.4 * 320 + 0.6 * 160 = 256
Country C: 0.4 * 240 + 0.6 * 240 = 240
Country D: 0.4 * 275 + 0.6 * 210 = 250
Since country C has the lowest expected cost of $240,000, East West should choose this country for manufacturing.
b. Part a solution will continue to stay optimal as long as the estimated cost for country C is less than the estimated cost for the other countries. This means that if the "bill passing" range is such that country C still has the lowest estimated cost, the solution will remain optimal. To evaluate this range, we can find the "break-even points," which are the points at which the expected costs for country C equal the expected costs for countries A and D. The following is how these break-even points are calculated:
BE (country A) = (210 - 240) / (260 - 210) = 0.375
BE (country D) = (210 - 240) / (275 - 210) = 0.33
This means that as long as the probability of the bill passing is between 0.33 and 0.375, the solution of choosing country C will remain optimal.
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A juice container haped like a cylinder ha a bae area of 100cm² and can hold 1500cm³ of juice. The height of the juice container id
The height of the juice container with a base area of 100cm² is 15 cm
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2
The base area of a cylinder is given by:
base area = π*r²
base area = 100 cm^2
100 = π * r^2
r^2 = 100 / π
r = √(100 / π)
The volume of a cylinder is given by:
volume = π*r²*h
1500 = π * [√(100 / π)]^2 * h
1500 = π* (100 / π) * h
1500 = 100h
Clearing the variable (h) height we have:
h = 1500 / 100
h = 15 cm
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ALGEBRA II
Find the angle measured to the nearest degree
The measure of the angle X for the trigonometric ratio of sine X equal to 0.7547 is 49° to the nearest degree.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
For the sine of X equal to 0.7547, we can make x the subject by finding the sine inverse of 0.7547 as follows:
sin X = 0.7547
X = sin⁻¹(0.7547)
X = 48.9992
Therefore, the measure of the angle X for the trigonometric ratio of sine X equal to 0.7547 is 49° to the nearest degree.
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Please help me with this math problem
a) The experimental probability of both choosing a ball that is odd and drawing a car that is either a K or J is given as follows: 29/60.
b) The theoretical probability of both choosing a ball that is odd and drawing a car that is either a K or J is given as follows: 4/9.
c) With a small number of trials, it is not surprising when the experimental probability is much greater than the theoretical probability.
How to calculate a probability?A probability is calculated via the division of the number of desired outcomes by the number of total outcomes.
An experimental probability, as the name says, is calculated considering previous experiments.
Out of 60 outcomes, the desired outcomes and their absolute frequencies are given as follows:
1K -> odd and K -> 8.3K -> odd and K -> 4.1J -> odd and J -> 10.3J -> odd and J -> 7.Hence the experimental probability is obtained as follows:
(8 + 4 + 10 + 7)/60 = 29/60.
For the theoretical probability, we have that:
2 out of 3 letter are K and J.2 out of 3 numbers are odd.Hence it is given as follows:
p = 2/3 x 2/3
p = 4/9.
For a small number of trials, there usually are differences between the experimental and the theoretical probabilities, but these probabilities get closer as the number of trials increase.
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consider the system of equations 2x −5y =1 4x −10y =3 how many solutions does this system have? explain.
Solutions for the system of equations 2x −5y =1 , 4x −10y =3 has no solution as ( 2 /4 ) = (-5/-10) ≠ (1/3) .
Simplify the system of equations to get the solution of the system :
2x - 5y = 1
⇒ 2x = 1 + 5y
⇒ x = ( 1+ 5y ) / 2 __(1)
4x -10y = 3
⇒ 2 ( 2x - 5y ) = 3
⇒2x - 5y = 3/2 ___(2)
Standard form of the system of equations are :
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Substitute the value of x from (1) into (2) we get,
2 ( 1 + 5y )/2 - 5y = 3/2
⇒1 + 5y -5y = 3/2
⇒1 = 3/2
⇒2 = 3 which is not true.
System of the equation has no solution.
Here, ( a₁ /a₂ ) = (b₁ /b₂) ≠ (c₁ /c₂ ) that is ( 2 /4 ) = (-5/-10) ≠ (1/3) .
Therefore, the system of equations has no solution.
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Cheese burgers= x
Hamburgers= y
y-x= 62
x+y = 588
add both equations
2y=650
y=650/2
y= 325 ---------- hamburgers
cheese burgers
The total number of Cheeseburgers will be 263.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
Cheese burgers= x
Hamburgers= y
y-x= 62
x+y = 588
we add both the equations we get 2y = 650
y=650/2
y= 325
x = 588-325= 263
Hence, The total number of Cheeseburgers will be 263.
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The lateral height of a cone is 8 inches and the area of the base of the cone is 49π in². It requires 2.5 minutes to paint the cone.
The area of the base is doubled.
How long will it take to paint this cone if it can be painted at the same rate? Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
min
It will take the painter a total of 5 minutes to paint this cone
How long will it take to paint this cone ?Since the area of the base of the cone is doubled,
the new base area = 2 * 49π in² = 98π in².
The radius of the original cone can be found by using the formula for the area of a circle:
49π = πr^2
r = 7 in
The height of the new cone can be calculated using the same lateral height as the original cone:
h = 8 in
Using the formula for the volume of a cone, we can calculate the volume of the new cone:
V = (1/3)πr^2h = (1/3)π(7^2)(8) = (1/3)π(392)
The surface area of the original cone can be found using:
A = πr^2 + πrs
where s is the slant height of the cone.
s = √(r^2 + h^2) = √(7^2 + 8^2) = √(49 + 64) = √(113)
So, we have
A = πr^2 + πrs = π(7^2) + π(7)(√(113)) = 49π + 7π(√(113))
The surface area of the new cone can be found using the same formula:
A = πr^2 + πrs = π(7^2 * 2^2) + π(7 * 2)(√(113)) = 98π + 14π(√(113))
When the equations are compared, we have
2 * (49π + 7π(√(113))) = 98π + 14π(√(113))
i.e. the new cone has twice the surface area of the original cone
It will take 2.5 * 2 = 5 minutes to paint this cone.
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80 percent of students finished their assignment on time. if 30 turned theirs in late, how many total students were in the class?
Answer:
150
Step-by-step explanation:
80% on time so 20% late, 30 late
30/20% = 150
1. Given two systems of equations, determine if they have the same solution.
System A System B
−12x+9y=7 −12x+9y=7
9x−12y=6 −9x+5y=9
a.Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3
and subtracting from the first equation in system A.
b.Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3 and adding to the first equation in system A.
c.Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 3
and adding to the first equation in system A.
d. No, they don't have the same solution.
2. What number must you multiply the second equation by so that the sum of the x-coefficients is zero?
7x−y=55
x+3y=33
A.-1/3
B. 1/3
C.-7
D.7
3. Which system of linear equations will yield the same solution as the system below?
x−y=3
2x−3y=−1
A. 2x−2y=−6
2x−3y=−1
B.2x−2y=6
2x−3y=−1
C.−2x+2y=3
2x−3y=−1
D.3x+3y=9
2x−3y=−1
4. A system of equations is shown below.
Equation A: 5x+9y=12
Equation B: 4x−3y=8
Which method eliminates one of the variables?
A. Multiply equation A by 4/5 and add the result to equation B.
B. Multiply equation B by 3 and add the result to equation A.
C. Multiply equation A by −1/3, and add the result to equation B.
D. Multiply equation B by 5/4, and add the result to equation A.
The solution to the equations are given below.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
1. System A System B
−12x+9y=7 −12x+9y=7
9x−12y=6 −9x+5y=9
Solving system A
x= -46/21 and y= -15/7
and, solving system B
x= -46/21 and y= -15/7
We can say that
Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3 and adding to the first equation in system A.
2. -7 should be multiply the second equation by so that the sum of the x-coefficients is zero.
3. x−y=3
2x−3y=−1
Solving the above equation gives
x= 10 and y= 7.
The equation yields the same solution as above is
2x−2y=6
2x−3y=−1
4. Equation A: 5x+9y=12
Equation B: 4x−3y=8
Now, solving both equations we can proceed as Multiply equation B by 3 and add the result to equation A.
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Answer:
To determine which system of equations would have the same solution, we evaluate each system of equations.
System 1 4x − 5y = 2, 3x − y = 8
x = 38/11
y = 26/11
System 2 4x − 5y = 2, 3x − 2y = 1
x = 1/7
y = -2/7
System 3 4x − 5y = 2, 3x − 8y = 4
x = -4/17
y = -10/17
System 4 4x − 5y = 2, 10x − 9y = 4
x = 1/7
y = -2/7
Therefore, the correct answer is option 3. System 2 and system 4 are equal, because the second equation in system 4 is obtained by adding the first equation in system 2 to two times the second equation in system 2.
4x− 5y = 2 2( 3x − 2y = 1)
----------------------- 10x - 9y = 4
Step-by-step explanation:
Give me a brainilest please...
write a in the form without finding t and n.
tangential acceleration a in the form without finding t and n is |a|= T+ t N
The tangential acceleration is a measure of the rate of change in the magnitude of the velocity vector, i.e. speed, and the normal acceleration are a measure of the rate of change of the direction of the velocity vector.
r(t)=(cost+ t sin t )i +( sin t−t cost)j
first find the particle's velocity.
[tex]v=dr/dt\\=(−sint+sint+tcost)i^+(cost−cost+tsint)j^\\\\ \\=(tcost)i^+(tsint)j^[/tex]
find the speed.
|v|=[tex]\sqrt{t^{2} cos^{2}t+ t^{2} sin^{2}t }[/tex]
= √t^2
=t
When t>0 , |t| simply becomes t .
We know that a T= [tex]\frac{d}{dt}[/tex]|v|
, which we can use to find that [tex]\frac{d}{dt}[/tex](t)=1
Now that we know a T , we can use it to find a N
a=(cost−t sin t ) i+(sin t +t cos t)j
|a|^2=t^2+1
a N=√(t^2+1) -1
= t
By substituting this back into the original definition, we find that
|a|=(1)T+(t)N=T+ t N
a in the form without finding t and n is |a|= T+ t N
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The dot plot represents the distribution of wages earned during a one-week period by 12 collage students.
From the line dot plot of 12 college students wages,
The Mean is $118.25
The Median is $118.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
From the dot plot.
Weekly wages = 112, 113, 116, 116, 116, 118, 118, 119, 119, 124, 124, 124.
Now,
Mean = Sum of all the values / Number of values
= (112 + 113 + 116 + 116 + 116 + 118 + 118 + 119 +119 + 124 +124 +124) / 12
= 118.25
Median = Mid value from the wages.
= 118
Thus,
The Mean is $118.25
The Median is $118.
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Sales tax is __________ the price
Sales tax is added to the price.
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
The statement is about sales tax
As a general rule
sales tax are added to the price of the item that is being bought
So, the complete statement is Sales tax is added to the price.
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How heavy is 150 pounds? How much does 150 pounds weigh in kilograms? 150 lb to kg conversion.
The conversion of 150 pounds weight in kilograms 68.039.
What is meant by weight?
The gravitational force that pulls a body toward the earth or another celestial body; it is equal to the mass multiplied by the local gravitational acceleration.Weight, which is expressed in newtons, is a unit of measurement for the gravitational force acting on an object. The weight of a bird with a mass of 15 g changes with the strength of the gravitational force acting on it, and would differ significantly if it were measured, for instance, on the Moon rather than on Earth.On Earth compared to the Moon, an object would weigh differently as a result of gravity. The following is an explanation of the weight formula: Weight is calculated as mass multiplied by gravity. W = mg is the formula for this.To learn more about weight refer to
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Does a school has provided a teacher with a budget to purchase math notebooks hacker rank solution?
A teacher may receive funding from the school to buy arithmetic amount notebooks for the pupils in their class. Materials like notebooks, pens, calculators, and other essential items can be purchased with this money.
A teacher may receive funding from the school to buy arithmetic notebooks for the pupils in their class. Materials like notebooks, pens, calculators, and other essential items can be purchased with this money. It is crucial to provide each student with enough math notebooks so that they have enough supplies to work with. These notebooks can be used by the students to keep track of key information, practise equations and other mathematical ideas, and stay organised and study-focused. To make sure that kids have the resources they need to excel in the classroom, provide the instructor a budget to buy math notebooks.
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a fair coin is tossed 14 times. what is the probability that exactly 3 heads occur?
If a fair coin is tossed 14 times then the probability that exactly three head occur is 0.023 .
The Binomial Probability formula is used to find the Probability of getting exactly 3 heads in 14 tosses of a fair coin .
The formula is:
⇒ P(X=k) = ⁿCₓ × pˣ × (1-p)ⁿ⁻ˣ ;
where,
⇒ P(X=k) is the probability of getting exactly "x" heads in n tosses of coin ;
⇒ n (number of tosses) = 14
⇒ k (number of heads) = 3
⇒ p (probability of getting heads in a single toss) = 0.5 for a fair coin
Substituting in the values, we get:
⇒ P(X = 3) = ¹⁴C₃ * (0.5)³ * (1 - 0.5)¹¹
⇒ P(X = 3) = ¹⁴C₃ * (0.5)³ * (0.5)¹¹
On simplifying further ,
we get ;
⇒ 0.02221679 ≈ 0.023 .
Therefore , the probability of getting exactly 3 heads 0.023 .
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What advantage does the involvement of citizen scientists have in measuring biodiversity? Explain your answer.
Answer: citizen scientists are already providing large amounts of data for monitoring biodiversity, but they could do much more, according to a new study published in the journal Biological Conservation, which suggests that citizen science has the potential to contribute much more to regional and global assessments of biodiversity. Citizen scientists are regular people who provide data or input to science, for example by monitoring species in their community or examining satellite imagery for evidence of deforestation or land use change.
Step-by-step explanation:
which of these statements do you think is true?
(a) Exactly one of these statements is false
(b) Exactly two of these statements are false
(c) Exactly three of these statements are false
(d) Exactly four of these statements are false
answer:
a. (a)
b. (b)
c. (c)
d. (d)
All the given options are paradoxical, and it's not possible to determine their truth value as they depend on their own veracity.
The statement "Exactly one of these statements is false" can be referred to as the liar paradox. It is a classic example of self-referential statements, where the truth of the statement depends on its own veracity.
In this paradox, if the statement is true, then it must be false, and if the statement is false, then it must be true. Hence, this statement creates a paradox and it's impossible to determine its truth value.
In the case of options (b), (c), and (d), it's also not possible to determine their truth value as they too depend on the truth value of the other statements, which are paradoxical.
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A conical cup has a 10-cm diameter and is 12 cm deep. How much can this cup hold? (Continuation) Water in the cup is 6 cm deep. What percentage of the cup is filled? (Continuation)Dana takes a paper cone of the given dimensions,cuts it along a straight line from the rim to the vertex, then flattens the paper out on a table. Find the radius, the arc length, and the central angle of the resulting circular sector.
The radius, the arc length, and the central angle of the resulting circular sector is 13 cm
What is Radius?
A radius of a circle or sphere is any of the line segments connecting its center to its perimeter, and it is also their length in more recent usage. The term is derived from the Latin radius, which means both ray and spoke of a chariot wheel.
1) volume of the cone = 1/3[tex]\pi[/tex][tex]r^{2}[/tex]h
r = radius
h = height or depth
given, D = 10 cm
so r = 5 cm
v = 1/3*22/7*5*5*12
v = 100[tex]\pi[/tex]
2) for up to 6cm height
volume = ?
here in this triangle
triangle ΔAOC and ΔEDC are similar (have some shape as all three angle of both Δ are same
when two figure are similar the ratios of the length of their corresponding sides are equal
here, ΔAOC and ΔEDC
so r = 2.5cm
so volume when cup is 6cm deep
v1 = 1/3[tex]\pi r^{2} h[/tex]
v1 = 1/3 *[tex]\pi[/tex]*2.5*2.5*6
v1 = 12.5[tex]\pi[/tex]
length = [tex]r^{2}+h^{2}[/tex] pythogonus theorem
length = 13cm
arc length = angle (in radius)*radius
2*[tex]\pi[/tex]*5
=10[tex]\pi[/tex]
centre angle = 10[tex]\pi[/tex]/13 radiance
= 10 * 180 Degree/13
=138.46 degree
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select the correct answer .
Which piecewise function is shown on the graph?
A piecewise function which is shown on the graph include the following: A. piecewise function A.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
Based on the graph shown above, we can evaluate the piecewise function based on the following domains (input values or independent values);
For the domain x ≤ -2, the value of y (y-value) is equal to 5. Additionally, for the domain -2 < x < 1,we can logically deduce that the function is a polynomial, which implies that it must have this ordered pair (0, -5):
For -2 < x < 1, when x is equal to 0 and y is equal to -5;
y = x² ± 5
For the domain x ≥ 1, we know that, when y is equal to 0, x would lie between 3 and 4;
y = 2^{x - 2} - 3
When y = 0, the value of x is given by:
0 = 2^{x - 2} - 3
2^{x - 2} = 3
x = 3.584.
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What are the missing reasons in the proof?
Given: ABCD with diagonal BD
Prove: ABD = CDB
Statements
1. AD || BC
2. ADB=CBD
3. AB || CD
4. ABD=CDB
5. DB=DB
6. ABD=CDB
Reasons
1. Definition of parallelogram
2. Alternate Interior Angles Theorem
3.
4.
5.
6.
All the missing reasons are given below.
What do you mean by parallelogram?A parallelogram is a two-dimensional shape with four sides and opposite sides that are parallel and equal in length. It can be defined as a quadrilateral with two pairs of parallel sides. In other words, opposite sides of a parallelogram are parallel and equal in length. The opposite angles of a parallelogram are equal and its diagonals bisect each other. A rectangle and a rhombus are both examples of parallelograms. The properties of parallelograms are important in geometry, trigonometry, and linear algebra.
The missing reasons for steps 3 and 4 are:
Definition of parallelogram (AB || CD and AD || BC implies that ABCD is a parallelogram)Converse of the alternate interior angles theorem (if a quadrilateral is a parallelogram, then its opposite sides are congruent)So the complete proof would be:
Given: ABCD with diagonal BD
Prove: ABD = CDB
Statements:
AD || BCADB=CBDAB || CDABD=CDBDB=DBABD=CDBReasons:
Definition of parallelogramAlternate interior angles theoremDefinition of parallelogram (AB || CD and AD || BC implies that ABCD is a parallelogram)Converse of the alternate interior angles theorem (if a quadrilateral is a parallelogram, then its opposite sides are congruent)Reflexive property of equalityTransitive property of equality (ABD=CDB and CDB=DB imply that ABD=DB)To know more about angles visit:
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Raven just purchased a gumball machine. Each compartment has the
dimensions of 8 inches by 6 inches by 15 inches. Assuming the vending
machine uses Gumballs that are approximately spherical and 1 inch in
diameter, how many gumballs did she order if each machine has 3
compartments and she ordered 25 machines? (Hint: Packing spheres in a
rectangular prism usually take up 190% of the volume of the spheres.)
Round your answer to the nearest whole number.
O A. 2171
B. 10,856
C. 32,568
D. 54,280
*
10 points
Answer:
The answer is C. 32,568. Assuming that the gumballs are 1 inch in diameter and packed in a rectangular prism, each compartment can hold approximately 190% of the volume of the spheres. Therefore, each compartment can hold approximately 7,560 gumballs. Since there are 3 compartments per machine and 25 machines, the total number of gumballs that Raven ordered is 32,568.
Step-by-step explanation:
How much time do executives spend each day reading and sending e-mail. A survey was conducted by Accountemps (reported in USA Today, March 12, 2001). The responses (in minutes) were recorded. Can we infer from these data that the mean amount of time spent by all executives reading and sending e-mail daily differs from 60 minutes?
The survey data collected by Account employees provides valuable insight into the amount of time executives spend on e-mails.
A survey was conducted by Account employees in 2001 to determine the amount of time executives spend each day reading and sending e-mails.
The results were recorded in minutes and analyzed to determine if the mean amount of time spent by all executives reading and sending e-mail daily differs from 60 minutes.
The survey data collected from the executives can be used to calculate the mean and standard deviation of the time spent on e-mails.
If the mean is significantly different from 60 minutes, it would suggest that the executives on average spend more or less time on e-mails compared to 60 minutes.
By conducting a statistical test, we can determine if the mean is significantly different from 60 minutes and make inferences about the e-mail habits of executives.
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