Answer:
(f + g)(x) = 3x² + x + 1
Step-by-step explanation:
[tex]\displaystyle{(f+g)(x) = f(x)+g(x)}[/tex]
Substitute f(x) = 3x² - 1 and g(x) = x + 2 in:
[tex]\displaystyle{f(x)+g(x) = (3x^2-1)+(x+2)}\\\\\displaystyle{f(x)+g(x)=3x^2-1+x+2}\\\\\displaystyle{f(x)+g(x) = 3x^2+x+1}\\\\\displaystyle{\therefore (f+g)(x) = 3x^2+x+1}[/tex]
Idil invested $150 in an account paying an interest rate of 5.785% compounded annually. Sophie invested $150 in an account paying an interest rate of 5.625% compounded continuously. To the nearest hundredth of a year, how much longer would it take for Sophie's money to triple than for Idil's money to triple?
there is no difference in the values of Time for Idil or Sophie in that their amount will be tripled.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
Given, Idil invested $150 in an account paying an interest rate of 5.785% compounded annually. Sophie invested $150 in an account paying an interest rate of 5.625% compounded continuously.
From the general formula of compound interest:
Final value A = (1 + r/n)^nt,
where P is the principal balance
r is the interest rate
n is the number of times interest is compounded annually
t is the number of years,
For Idil,
P = 150, r = 5.782, A = 3*p = 450, and n = 1
Thus,
450 = 150 (1 + 5.785%)^t
3 = (1.05785)^t
t = 19.535 years
The time required to get a total amount of $450.00 with compounded interest on a principal of $150.00 at an interest rate of 5.785% per year and compounded 1 time per year is 19.535 years.
(about 19 years 6 months)
For Sophie,
P = 150, r = 5.625, A = 3*p = 450
First, convert R as a percent to r as a decimal
r = R/100
r = 5.625/100
r = 0.05625 per year,
Then, solve the equation for t
t = ln(A/P) / r
t = ln(450.00/150.00) / 0.05625
t = 19.531 years
The time required to get a total amount of $450.00 with compounded interest on a principal of $150.00 at an interest rate of 5.625% per year and compounded continuously is 19.531 years.
(about 19 years 6 months)
therefore, there is no difference in the values of Time for Idil or Sophie.
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guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).
The value of the limit that exists at the given numbers is approximately 0.5.
First of all at x = 3.1, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.1} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]\frac{(3.1)^2-3(3.1)}{(3.1)^2-9}[/tex] = [tex]\frac{0.31}{0.61}[/tex] ≅ 0.508197
At x = 3.05, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.05} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(3.05)^2-3(3.05)}{(3.05)^2-9}=\frac{0.1525}{0.3025}$[/tex] ≅ 0.504132
At x = 3.01, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.01} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(3.01)^2-3(3.01)}{(3.01)^2-9}=\frac{0.0301}{0.0601}$[/tex] ≅ 0.500832
At x = 3.001, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.001} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(3.001)^2-3(3.001)}{(3.001)^2-9} $[/tex]= [tex]$\frac{3.001 \times 10^{-3}}{6.001 \times 10^{-3}}$[/tex] ≅0.500083
At x = 3.0001, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 3.0001} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(3.0001)^2-3(3.0001)}{(3.0001)^2-9} $[/tex]= [tex]$\frac{3.001 \times 10^{-4}}{6.001 \times 10^{-4}}$[/tex] ≅ 0.500008
At x = 2.9, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.9} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.9)^2-3(2.9)}{(2.9)^2-9} $[/tex]= [tex]$\frac{-0.29}{-0.59}$[/tex] = 0.491525
At x = 2.95, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.95} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.95)^2-3(2.95)}{(2.95)^2-9} $[/tex]= [tex]$\frac{-0.1475}{-0.2975}$[/tex] = 0.495798
At x = 2.99, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.99} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.99)^2-3(2.99)}{(2.99)^2-9} $[/tex]= [tex]$\frac{-0.0299}{-0.0599}$[/tex] = 0.499165
At x = 2.999, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.999} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.999)^2-3(2.999)}{(2.999)^2-9} $[/tex]= [tex]$\frac{-2.999 \times 10^{-3}}{-5.999 \times 10^{-3}}$[/tex] = 0.499917
At x = 2.9999, the value of [tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9} $$[/tex] will be
[tex]$$\lim _{x \rightarrow 2.9999} \frac{x^2-3 x}{x^2-9} $$[/tex] = [tex]\frac{x^2-3 (x) }{x^2-9}$$[/tex] = [tex]$\frac{(2.9999)^2-3(2.9999)}{(2.9999)^2-9} $[/tex]= [tex]$\frac{-2.999 \times 10^{-4}}{-5.999 \times 10^{-4}}$[/tex] = 0.499992
From above all, we can see that the limit is approximately equal to and tends towards 0.5. So 0.5 will be our answer.
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Your question was incomplete, your most probable question was:
Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).
[tex]$$\lim _{x \rightarrow 3} \frac{x^2-3 x}{x^2-9}[/tex], x = 3.1, 3.05, 3.01, 3.001, 3.0001, 2.9, 2.95, 2.99, 2.999, 2.9999
пер 15. If it took Lex from 10:00 a.m. to 11:45 a.m. to walk 14 blocks, what was his average speed in blocks per hour? Enter your answer with numbers and decimals only
His average speed in blocks per hour is 18.66 blocks per hour
What was his average speed in blocks per hour?From the question, we have the following parameters that can be used in our computation:
It took Lex from 10:00 a.m. to 11:45 a.m. to walk 14 blocks
This means that
Blocks = 14
Time = 45 minutes = 3/4 hour
The speed is then calculated as
Speed = 14/(3/4)
Evaluate
Speed = 18.66
Hence, the speed is 18.66 blocks per hour
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Ellen is playing a video game in wich she captures butterflies/ There are 3 butterflies onscreen, but the number of butterflies doubles every minute. After 4 minutes, she was able to capture 7 of the butterflies.
Write an expression for the number of butterflies after 4 minutes. Use a power of 2 in your answer
The expression for the number of butterflies after 4 minutes 3([tex]2^4[/tex]) - 7.
What is Sequence?A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.
An ordered list of numbers is a sequence. The three dots indicate that the established pattern should move forward.
Given:
Initially we have 3 butterflies
After one minute = 3(2)
= 6 butterflies
After two minutes = 3(2)(2)
= 3(2²) butterflies
After three minutes = 3(2³) butterflies
After four minutes = 3([tex]2^4[/tex]) butterflies
as, she captured 7 butterflies
Then, after 4 min the number of butterflies on screen
= 3([tex]2^4[/tex]) - 7
= 3(16) - 7
= 48-7
= 41
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in order to determine cash flows from operating activities, firms may use a method in which every item on the income statement is adjusted from accrual accounting to cash accounting.
In order to determine cash flows from operating activities, firms may use a method in which every item on the income statement is adjusted from accrual accounting to cash accounting which is called Modified cash basis.
What is Modified cash basis?This is referred to as an accounting method that combines elements of the two primary bookkeeping practices known as cash and accrual accounting.
In this scenario, different adjustments are made so as to get the accurate value of the income generated by the company or organization.
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How much money should be invested at 8% compounded quarterly so that it will be worth $5000 in 5 years?
Answer: $25,000
Step-by-step explanation:
You invest $10,000 annually. If you divide 10,000 by 4, you get 25,000. It's $25,000 quarterly.
juanita is evaluating four television brands using four criteria: price, quality, screen size, and features. Juanita assigns 20% importance to price, 30% importance to quality, 30% importance to screen size, and 20% importance to features. She rates the TV brands as follows:Samsung:Price (20%): 5Quality (30%): 8Screen Size (30%): 8Features (20%):9Sony: Price (20%): 4Quality (30%): 8Screen Size (30%): 8Features (20%): 9LG:Price (20%): 8Quality (30%): 6Screen Size (30%): 6Features (20%): 5Vizio:Price (20%): 9Quality (30%): 5Screen Size (30%): 4Features (20%): 4Based on the multi-attribute model, which television brand does Juanita prefer?
Junita prefers Samsung Television brand with score of 7.6. A multi-attribute model is a way of evaluating products or services based on multiple attributes or characteristics.
In this scenario, Juanita is evaluating four television brands based on four criteria: price, quality, screen size, and features. She assigns a weight to each criteria, indicating its importance to her, with price having 20% importance, quality having 30% importance, screen size having 30% importance, and features having 20% importance. She then rates each brand on each criteria and calculates an overall score for each brand using the weights and ratings. Based on her evaluations, Juanita prefers the Samsung brand as it has the highest overall score.
Based on the multi-attribute model, Juanita prefers the Samsung television brand. Here's the calculation:
Samsung: [tex]5 *0.20 + 8 * 0.30 + 8 *0.30 + 9 * 0.20 = 1 + 2.4 + 2.4 + 1.8 = 7.6[/tex]
Sony: [tex]4 * 0.20 + 8 * 0.30 + 8 * 0.30 + 9 * 0.20 = 0.8 + 2.4 + 2.4 + 1.8 = 7.4[/tex]
LG: [tex]8 *0.20 + 6 *0.30 + 6 * 0.30 + 5 * 0.20 = 1.6 + 1.8 + 1.8 + 1 = 6.2[/tex]
Vizio: [tex]9 * 0.20 + 5 * 0.30 + 4 * 0.30 + 4 * 0.20 = 1.8 + 1.5 + 1.2 + 0.8 = 5.3[/tex]
Juanita prefers the Samsung television brand with a score of 7.6 compared to the other brands.
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9. If the arc measure of MN = 87°, what is the measure of
The complete question:
If the arc measure of MN = 87°, what is the measure of angle ∠MON ?
Solution:
In the given circle, the required measure of the angle ∠MON is given as 87°.
What is an angle ?
An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
Here,
For the given circle, the measure of arc MN is given in the form of an angle of 87° which consists of an angle MNO,
So the measure of the section is equal to MON i.e. ∠MON = 87°
Thus, the required measure of the angle ∠MON is given as 87°.
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A cart wheel is to be made out of a circular disk of wood surrounded by a strip of rubber. The wood costs $2.50 per square foot and the rubber costs $3.60 per foot. If the wheel has a 1.5-foot radius, what is the total cost of the materials needed to construct the wheel? Show or explain how you got your answer.
The total cost of the materials used to construct the wheel is $51.57
What is the total cost?The total cost of the materials used to construct the wheel is the sum of the total cost of the wood and the rubber.
Total cost = total cost of the wood + total cost of the rubber
Total cost of the wood = (area of the wood used x cost per square foot) + (circumference of the wheel x cost of the rubber)
Area of the wood = πr²
Where :
π = pi = 3.14
R = radius
3.14 x 1.5² = 7.065 ft²
Total cost of the wood = $17.66
Circumference of the wood = 2πr
2 x 3.14 x 1.5 = 9.42 feet
Total cost of the rubber = 9.42 x 3.60 = $33.91
Total cost of the materials = $33.91 + $17.66 = $51.57
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7/22 as a decimal rounded to the nearest tenth
Answer:0.3
Step-by-step explanation:
6) Jack jogged 2- 5/10 miles on a path in the park. What is this distance written as a decimal?
The distance covered by the jack is 1.5 miles.
What are arithmetic operations?The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.
Given Jack jogged 2 - 5/10 miles on a path in the park.
2 - 5/10 miles
convert 5/10 in decimal form,
5/10 = 0.5
subtract 0.5 from the equation,
so 2 - 5/10 miles = 2 - 0.5 = 1.5 miles
2 - 5/10 miles = 1.5 miles
Hence distance in decimal is 1.5 miles.
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b) A (-3,-5), B (2,-5), C (2, 2) are three of the four vertices of a rectangle ABCD and D is the vertex opposite to B. Plot these vertices in graph paper and find: (i) the coordinates of the vertex D (ii) the area of the rectangle ABCD.
Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys 6 flights from Boston to Salt Lake City to determine the number of babies on the flights. R determines the amount of safety equipment reeded by the result of that study. Select the things that were wrong with the way the survey was conducted. Conducting the survey on a holiday weekend will not produce representative results The survey uses systematic sampling. The survey was conducted using six similar flights. The survey would not be a true representation of the entire population of air travelers. Choosing 6 flights represents a stratified sample. Select the ways that you would improve the survey if it were to be repeated. Ask travelers to fill out a questionnaire Conduct the survey at the entrance to the airport. Conduct the survey during different times of the year. Conduct the survey on different days of the week. Conduct the survey using flights to and from various locations
Survey was wrong: holiday, systematic sample, 6 similar flights. To improve: questionnaire, various times/locations, entrance, different days.
The problems with the survey conducted by the airline are:
1) Conducting the survey on a holiday weekend is not representative of the entire population of air travelers;
2) The survey uses systematic sampling which may not accurately reflect the entire population;
3) The survey was only conducted on 6 similar flights and does not represent the entire population of air travelers.
To improve the survey, the following steps can be taken:
1) Ask travelers to fill out a questionnaire;
2) Conduct the survey at the entrance to the airport;
3) Conduct the survey during different times of the year;
4) Use various days of the week to conduct the survey;
5) Conduct the survey using flights to and from various locations.
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Please HELP ASAP
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 20 N acts on a certain object, the acceleration of the object is 5 /ms2. If the force is changed to 16 N, what will be the acceleration of the object? /ms2
Step-by-step explanation:
Since force doesn't depend on mass and varies directly, you can set up a proportion. group the F's together and the acceleration together, as so
[tex] \frac{20}{16} = \frac{5}{x} [/tex]
Next, cross m multiply
[tex]20x = (16)(5)[/tex]
[tex]20x = 80[/tex]
Lastly, divide by 20
[tex]x = 4m {s}^{2} [/tex]
The acceleration of the object when force is 16N is 4m/s².
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, The force acting on the object varies directly with the object's acceleration.
Therefore, F ∝ a.
F = ka.
20 = 5k.
k = 4.
Now,
16 = 4a.
a = 4.
So, The acceleration is 4m/s²
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Examine the figure below, what is a = ?
The value of a in the circle is 6.
How to solve for variable in a circle?Using circle theorem, angles on the circumference from opposite end of a diameter are 90 degrees.
Therefore, the value of angle L is 90 degrees.
Recall the diameter of the circle is MK.
Hence, let's find the value of a as follows:
15a = 90
divide both sides of the equation by 15
15a / 15 = 90 / 15
a = 6
Therefore, the value of a is 6
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given two independent random variables such that x has a mean of 50 and a standard deviation of 8 and that y has a mean of 100 and a standard deviation of 6, find the mean and standard deviation of the variable x 50.
The standard deviation is 19.21 while the mean is 20.785.
a) Because E(Y) = 12, var(Y) = 9.
then, for 2Y+20
E(2Y+20)=2E(Y)+20=24+20=44
Var(2Y+20)=4(9)=36.
The average deviation is six.
b)E(X) = 80 var(X) = 144
so, for 3X
E(3X)=3(80)=240
Var(3X)=9Var(X)=9(144)=1296
The average deviation is 36.
c)0.25x+y
E(0.25x+y)=0.25E(x)+E(y)=0.25(80)+12=32
Var(0.25x+y)=0.0625 var(x)+var(y) +2(0.25)Cov(x,y)
Cov(x,y)=0 since x and y are independent.
Var(0.25x+y)=18
Standard deviation = 4.24 d) x – 5 y
E(x-5y)=E(x)-5E(y)=80-5(12)=20
Var(x-5y)=var(x)+25var(y)-2(5)Cov(x,y)
Because X and Y are unrelated, Cov(x,y) = 0
Var(x-5y)=369
The standard deviation is 19.21, while the mean is 20.785
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There are 6 onion bagels and 18 plain bagels in a box of 24 bagels. What is the ratio of the number of onion bagels to the number of plain bagels in the box?
Consider the following table.
Defects in batchProbability
2. 0.35
3. 0.23
4. 0.20
5. 0.09
6. 0.07
7. 0.06
Find the standard deviation of this variable.
2.27
3.48
1.51
4.50
The standard deviation of the variable "Defects in batch" is approximately 0.47.
The closest answer in the options is (C) 1.51.
What is standard deviation?The standard deviation is described as a measure of the amount of variation or dispersion of a set of values.
Standard Deviation is given as = √(sum(p(x - μ)^2) / n)
Where μ = sum(xp)
= 2 * 0.35 + 3 * 0.23 + 4 * 0.20 + 5 * 0.09 + 6 * 0.07 + 7 * 0.06
= 2.49
substituting the values into the standard deviation formula, we have :
SD = √(sum(p(x - μ)^2) / n)
= √((0.35 * (2 - 2.49)^2 + 0.23 * (3 - 2.49)^2 + 0.20 * (4 - 2.49)^2 + 0.09 * (5 - 2.49)^2 + 0.07 * (6 - 2.49)^2 + 0.06 * (7 - 2.49)^2) / 6)
= √(1.32 / 6)
= √(0.22)
= 0.47
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The standard deviation of this variable is given as follows:
1.51.
How to obtain the standard deviation?Before obtaining the standard deviation, we must obtain the expected value, which is given by the sum of each value multiplied by it's respective probability, hence:
E(X) = 2 x 0.35 + 3 x 0.23 + 4 x 0.20 + 5 x 0.09 + 6 x 0.07 + 7 x 0.06
E(X) = 3.48.
Then we obtain the sum of the differences squared between each observation and the mean, multiplied by it's respective probabilities, hence:
(2-3.48)² x 0.35 + (3-3.48)² x 0.23 + (4-3.48)² x 0.20 + (5-3.48)² x 0.09 + (6-3.48)² x 0.07 + (7-3.48)² x 0.06 = 2.2696.
The standard deviation is the square root of this sum, hence:
S(X) = sqrt(2.2696)
S(X) = 1.51.
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Round to the indicated place: 9,83(9),038
The number 9,839,038 after indicated rounding off gives the number 9,839,000.
What is Rounding Off?Rounding off of a number is defined as the simplification of the number by keeping the value of the number same but is made closer to the next number.
Rounding can be done for whole numbers as well as decimals.
Given is a whole number 9,839,038.
We have to round it to the place shown where the digit is 9.
Look at the next digit right to 9.
It is 0, which is less than 5.
So replace all the digits next to 9 by 0.
We get the number 9,839,000.
Hence the rounded number is 9,839,000.
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1) The original price of a radio is $78.50 and was discounted 12% off. What is the sale price? not in college don't know why it says I am lol
Answer:$69.08
Step-by-step explanation:
2
In order to calculate marginal cost, producers must compare the difference in the cost of producing orie unit to the cost
of
O purchasing a unit.
O distributing that unit.
31:27
O producing the next unit.
O producing a different unit.
The solution is Marginal cost is (1200 - 1000) / (30 - 20) = 12.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
In order to calculate marginal cost, producers must compare the difference of producing one unit to the cost of producing the next unit
Marginal cost is the change in total cost as a result of increasing output produced by one unit.
For example, if the total cost of producing 20 units of a good is 1000 and the total cost of producing 30units is 1200.
Marginal cost is (1200 - 1000) / (30 - 20) = 12
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F(–5, 5) and G(–7, –7) are the endpoints of a line segment. What is the midpoint M of that line segment?
Answer:
-6, -1
Step-by-step explanation:
midpoint M of the line segment
M = (x1 + x2) / 2 , (y1 + y2) / 2
= (-5-7) / 2, (5-7) / 2
= -12 / 2, -2 / 2
= -6 , -1
What will be congruence criterion
Yes, By SAS congruency criteria both ΔDEF and ΔHIG are congruent.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
In the given figure,
⇒ DE = IH
⇒ EG = FI
⇒ ∠E = ∠I
Now, In ΔDEF and ΔHIG;
⇒ DE = IH (Given)
⇒ ∠E = ∠I (Given)
Since, EG = FI
Hence, We get;
⇒ GF + FI = FG + EG
⇒ GI = FE
So, In ΔDEF and ΔHIG;
⇒ EF = GI (Common side)
Thus, By SAS congruency criteria both ΔDEF and ΔHIG are congruent.
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A sales representative must visit four cities. Omaha, Dallas, Wichita and Oklahoma City. There are direct air connections between each of the cities. Use the multiplication rule of counting to determine the number of differenct choices the sales representative has for the order in which to visit the cities. Use the multiplciation rule of counting to determine the number of possible sequences of the cities. There are four choices for the first city, three choices for the second city, two choices for the third city and one choice for the fourth city.
The sales representative has 24 possible sequences of cities to visit.
The multiplication rule of counting states that if there are n choices for the first event, m choices for the second event, p choices for the third event, and q choices for the fourth event, then there are a total of n x m x p x q possible sequences of choices. Applying this to the situation of the sales representative visiting four cities, we can say that there are 4 x 3 x 2 x 1 = 24 possible sequences of the cities.
To break this down further, the sales representative has 4 choices for the first city, Omaha, Dallas, Wichita, and Oklahoma City. Once the first city has been chosen, there are then 3 choices for the second city, Omaha, Dallas, and Wichita. From these 3 choices, there are then 2 choices for the third city, Omaha and Dallas. And then finally, there is 1 choice for the fourth city, Omaha. Multiplying these numbers together gives us 4 x 3 x 2 x 1 = 24 possible sequences of cities.
Therefore, the sales representative has 24 possible sequences of cities to visit.
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i need help with question 23 please i need it quick
The measure of the angle ∠FEB will be 70°.
An infinitely long row of evenly spaced dots that extends in both directions makes up a line. Its length is the only dimension it has. An illustration of a line is a horizontal mark made on a piece of paper. A figure made by two rays that intersect at the same endpoint is referred to as an angle.\
Given that the angle ∠EFB is 35° and BD is the angle bisector of ∠EFD. The measure of the angle ∠FEB will be;-
∠FEB = 2 x ∠EFB
∠FEB = 2 x 35
∠FEB = 70°
Therefore, the value of the angle ∠FEB will be 70°.
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The difference between 5/2 of a number and 17 is 48
The numerical form of the statement is (5/2)n - 17 = 48.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, 'n' be the unknown number,
So, the statement The difference between 5/2 of a number and 17 is 48
can be written as,
(5/2)n - 17 = 48.
5n - 34 = 96.
5n = 96 + 34.
5n = 130.
n = 130/5.
n = 26.
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There are a total of 39 students in fourth grade at school this year. Today, some of the fourth graders have gone on a field trip to be exact 3/4 of the women went and 2/3 of the men went. This leaves 11 fourth graders at the school. How many women and how many men are in fourth grade at your school this year?
Solving a system of equations we wll see that there are are 24 women, and the other 15 students are men in foruth grade.
How many women and men are in fourth grade?We know that there are 39 students in fourth grade, we know that:
3/4 of the women went
2/3 of the men went
And this leaves 11 students at the school, then we can write the equation:
(3/4)*W + (2/3)*M + 11 = 39
Where W and M are the number of women and men respectively.
(3/4)*W + (2/3)*M = 39 - 11 = 28
(3/4)*W + (2/3)*M = 28
And we also know that the total number is 39, then:
M + W = 39
So we can write the system of equations:
(3/4)*W + (2/3)*M = 28
M + W = 39
M = 39 - W
REplacing that on the other equation we get:
(3/4)*W + (2/3)*(39 - W) = 28
(3/4)*W - (2/3)*w + 26 = 28
(3/4)*W - (2/3)*W = 28 - 26 = 2
(9/12)*W - (8/12)*W = 2
(1/12)*W = 2
W = 2*12 = 24
There are 24 women, and the other 15 students are men.
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One popular model had a front wheel with a 52 in. diameter and one spoke on the back wheel measuring 9 in
Determine the diameter of the back wheel.
The diameter of the back wheel is 18 in.
What is a diameter?A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle.
Given that, a model had a front wheel with a 52 in. diameter and one spoke on the back wheel measuring 9 in, we need to find the diameter of the back wheel.
Since, the spoke in a wheel will act as a radius of the wheel,
Radius = diameter / 2
Also, it is given that, the one spoke on the back wheel measuring 9 in,
Therefore, the diameter of the back wheel = 9 × 2
= 18 in
Hence, the diameter of the back wheel is 18 in.
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Un rectángulo está inscrito en un círculo de radio igual a 3 centímetros. Exprese el área A del rectángu- lo como una función de la longitud de uno de sus lados.
Therefore , the solution of the given problem of rectangle comes out to be A= b* √6²-b².
Describe the rectangle.In the Euclidean plane, a rectangle is merely a cube with four right angles. It is sometimes referred to as an equiangular quadrilateral or a quadrant that seems to have equal angles. The parallelogram also has the option of a straight angle. Four of a square's sides are all the same length. Rectangular quadrilaterals have four equal sides and four 90° vertices. It is sometimes referred as an "equirectangular square" as a result. A rectangle is also referred to as a parallelogram due to the identical and parallel lengths of its opposite sides.
Here,
radio= 3 cm
Al estar un rectángulo inscrito en un círculo, el diámetro del círculo corresponderá a la diagonal del rectángulo
Siendo b la base del rectángulo y a la altura, se tiene que:
6²= a²+b²
a²= √6²-b²
Nota: Se empleó el teorema de Pitágoras
El área del rectángulo está dado por:
A= base* altura
A= b*a
Reemplazando a:
A= b* √6²-b²
Therefore , the solution of the given problem of rectangle comes out to be A= b* √6²-b².
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Which equation below does not show equivalent expressions when y = 2
The equation below that does not show equivalent expressions when y = 2, is 5y + 25 = 5 ( y + 4 ).
option C.
Which equation does not follow the equivalent expression?
The equation below that does not show equivalent expressions when y = 2, is determined by solving for y in all the given equation.
y + 4y = y ( 1 + 4 )
y + 4y = y + 4y
5y = 5y
y = y
y + y + y = 3y
3y = 3y
y = y
5y + 25 = 5 ( y + 4 )
5y + 25 = 5y + 20
5y + 5 = 5y
5 ( y + 1 ) = 5y
y + 1 = y
2 (y + 2 ) = 2y + 4
2y + 4 = 2y + 4
2y = 2y
y = y
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