The pros and cons regarding the methods of the polynomial include:
Graphing the related system eliminates the need to rewrite the equation in order to set it equal to 0. It is simpler because you can graph each side of the equation separately.
It can be difficult to locate the system's intersection point at times. You may need to zoom in or learn how to resize the window. Using the related function allows you to find the points by focusing on the x-axis.
What is a polynomial?A polynomial is an expression made up of variables, constants, and exponents that are combined using mathematical operations such as addition, subtraction, multiplication, and division.
The formula is ax² + bx + c = 0, where a and b are coefficients, c is a constant, and the polynomial degree is 2. A trinomial equation is a polynomial with three variable terms. It is also known as a cubic equation. To be a polynomial term, an expression must contain no square roots of variables, no fractional or negative powers on variables, and no variables in the denominators of any fractions.
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A travel agent is interested in the average price of a hotel room during the summer in a resort community. The agent randomly selects 18 hotels from the community and determines the price of a regular room with a king size bed. The average price of the room for the sample was $135 with a standard deviation of $25. Assume the prices are normally distributed. Construct an interval to estimate the true average price of a regular room with a king size bed in the resort community with 99% confidence. Round the endpoints to two decimal places, if necessary.
The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 ).
What is the confidence interval of an average?One method of determining the actual population mean is by using a confidence interval for the mean. A confidence interval provides a lower estimate and an upper estimate rather than just the mean.
A confidence interval expresses the degree of uncertainty surrounding a given statistic. A margin of error is frequently used with confidence intervals. It reveals the degree to which you may be certain that the findings of a poll or survey correspond to what you would anticipate discovering if it were possible to poll the complete population. Levels of confidence are inextricably linked to confidence intervals.
x = mean;
99% confidence interval for μ is
(x - t * S) /√n < μ <( x + t * S) /√n;
(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;
14.74< μ< 48.89;
99% CI is ( 14.74, 48.89 ) ;
critical value at 0.01 significance level with 17 df = 2.898
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The average score of all golfers for a particular course has a mean of 80 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 81. Round to four decimal places.
The probability that the average score of golfers exceeded = 0.0228
What is standard deviation?A measurement of a data set's deviation from the mean is referred to as "standard deviation.". A low standard deviation means that the data are grouped around the mean, whereas a large standard deviation says that the data are more spread out.
According to the given information
We are given that,
[tex]& \mu=80 \\[/tex]
[tex]& \sigma=3.5 \\[/tex]
[tex]& n=49 \\& \mu \bar{x}=\mu=80 \\[/tex]
[tex]& \sigma \bar{x}=\sigma / \sqrt{n}=3.5 / \sqrt{ } 49=0.5 \\& P(\bar{x} > 81)=1-P(\bar{x} < 81) \\& =1-P[(\bar{x}-\mu \bar{x}) / \sigma \bar{x} < (81-80) / 0.5] \[/tex]
[tex]& =1-P(z < 2) \\&[/tex]
Using standard normal table
[tex]& =1-0.9772 \\& =0.0228[/tex]
Probability [tex]$=0.0228$[/tex]
The probability that the average score of golfers exceeded = 0.0228
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Hello can you help me with this question
Part A: Without using a graphing calculator, which equation could be represented by the accompanying graph?
A) y= x^2-2
B) y =2^-x
C) y= -2^x
D) y= 2^x
Answer:
Step-by-step explanation:
A
what is the measure of AB in O below?
The measure of AB in the figure is C. 100 degree
How to find the measure of ABThe measure of AB in the figure is the length of arc, this is given by the formula
given angle / 360 * 2πr
However, the measure in degree is equal to the angle given which is 100 degree.
The size or the measure of the angle is same at any point within same lines that formed the angel AB.
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Consider r (x) = StartFraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline EndFraction, where a, b, c, and d are positive integers and b < d. What value does r(x) approach as x approachesInfinity?
0
StartFraction a Over c EndFraction
StartFraction b Over d EndFraction
Infinity
The value of r(x) approaches as x approaches Infinity is; 0
How to find the limit of a function?Limit is defined as the value that a function approaches for the given input value.
We have been given a function;
r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction
We can rewrite this function as;
r(x) = (axᵇ + 8)/(cx^d)
where a, b, c, and d are positive integers and b < d.
We need to find the value of r(x) approach as x approaches Infinity.
This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]
Now, we find the value of limit for given function;
[tex]\lim_{x \to \infty} \frac{ax^b + 8 }{cx^d}[/tex]
This simplifies to;
[tex]\lim_{x \to \infty} \frac{8 }{cx^d}[/tex] (since d > b)
Thus;
[tex]\lim_{x \to \infty} r(x) = 0[/tex]
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There is 14 feet of fencing available to enclose a rectangular region. For what
The maximum area is 12.25 square feet
How to determine the maximum areaFrom the question, we have the following parameters that can be used in our computation:
Perimeter = 14 feet
This means that
P = 2(l + w)
So, we have
2(l + w) = 14
Divide by 2
l + w = 7
Make l the subject
l = 7 - w
The area is calculated as
A = lw
So, we have
A = (7 - w)w
Expand
A = 7w - w²
Differentiate and set to 0
7 - 2w = 0
So, we have
w = 3.5
Substitute w = 3.5 in A = (7 - w)w
A = (7 - 3.5) * 3.5
Evaluate
A = 12.25
Hence, the area is 12.25 square feet
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Complete question
There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum
Monique wants to rent online movies. Movies Plus charges a one-time free of $20 plus $5 per movie. Movies-To-Go charges $7 per movie. Write and solve an equation to determine m, the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same.
__; m = __ movies
The number of movies rented when the cost for Movies Plus and Movies-To-Go is the same is 10.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let the no. of movies be 'm' and the total cost is 'C'
Movies Plus charges a one-time fee of $20 plus $5 per movie
which is, C = 5m + 20.
Movies-To-Go charges $7 per movie
which is, C = 7m.
Now, the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same will be when we equate both equations.
∴ 7m = 5m + 20.
2m = 20.
m = 10.
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There are two investment options:
• Option 1: An initial investment of $5 that increases by 50% every year.
.
• Option 2: An initial investment of $0.01 that doubles every year.
Part A:
Write an equation for each option to model the value A of the account after x years
Part B:
Explain which investment will eventually have the greatest value.
Option 1: An initial investment of $5 that increases by 50% every year
as after 20 years, it amounts to a greater value.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
The given situations can be modeled as a geometric sequence.
Option A :
a₁ = 5, r = 1.5.
We know Sₙ = a₁(rⁿ - 1)/(r -1).
Sₙ = 5(1.5ⁿ - 1)/(1.5 - 1).
Sₙ = 5(1.5ⁿ - 1)/(0.5).
Let us see for n = 20, 20th year.
S₂₀ = 5(1.5²⁰ - 1)/(0.5).
S₂₀ = 5(3324.25)/(0.5).
S₂₀ = 33242.5.
Option B :
a₁ = 0.01 and r = 2.
Sₙ = 0.01(2ⁿ - 1)/(1).
S₂₀ = 0.01(2²⁰ - 1)/(1).
S₂₀ = 10,485.75
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What is the surface area of the cube shown below?
Answer:
150 in^2
Step-by-step explanation:
It is a cube...it has six equal sides
the surface area of one side is 5 x 5 = 25 in^2
there are six .... so 6 x 25 = 15o in^2
Edited: should be in^2 not cm^2 as originally posted...wrong units
Answer:
150
Step-by-step explanation:
To find the surface area of a cube, you do 6a^2. That would mean it is 150.
Stem and leaf plots
And box
Pls help I have no idea what this is
Answer:
13
Step-by-step explanation:
The box plot ends at 13.
Box plots show the average score of the data. It shows the minimum, median and maximum. The line inside the box is the median. The minimum, in this case is 0 and the max is 13.
Factorise fully the following:
4x² + 28x³
Answer: 4x^2(7x+1)
Step-by-step explanation: Divide by the common divisible of 4x^2 and you will get your answer/.
Answer:4x^2(1+7x)
Step-by-step explanation:
4x^2(1+7x)
2 1/2 divided by 1 3/4
Answer:
10/7 or 1 3/7
Step-by-step explanation:
1. change from mixed fraction to improper fraction, 5/2 and 7/4
2. instead of the dividing the fractions as is, multiply the reciprocal which would be 5/2 multiplied by 4/7. Then you cross multiply. 2 into 2, 1 and 2 into 4, 2. So now you're left with 5 and 2/7 since 5/1 is basically 1.
3. simplify to just 10/7
Answer:
10/7 or 1 3/7
I took a test with that question.
Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean?
The minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean is 40.
What is the confidence interval?In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter.
We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.
α = (1 - 0.90)/2 = 0.05.
Now, we have to find z in the Ztable as such z has a p-value of 1 - α.
So it is z with a pvalue of 1 - 0.05 = 0.95 = 1.96.
Now, find the margin of error M as such,
M = z×(sigma/√n).
5 = 1.96×(16/√n).
5√n = 31.36.
n = 39.9.
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Which answer describes the type of sequence? 1, 6, 7, 13, ...
O arithmetic
O geometric
O neither arithmetic nor geometric
A series that is neither mathematical nor geometric is described by the provided sequence. Which is the proper response would be a choice (B).
What exactly is an algebraic sequence?A grouping of numbers in a specific order is known as an arithmetic sequence.
The following question gives the sequence as follows: 1, 6, 7, 13,...
We must determine the kind of the current sequence.
According to the question, we have 1, 6, 7, 13,...
For verification as an arithmetic series:
The usual deviation between 1 and 6 is given by d = 6 - 1 = 5.
Commonly, 6 and 7 differ by 1 when d = 7 - 6
It is not an arithmetic sequence since the common difference between subsequent terms is not the same.
In order to verify it as a geometric sequence:
r = 6/1 = 6 is a common ratio between 1 and 6.
r = 7/6 is a common ratio between 6 and 7.
It is not a geometric sequence since the common ratio between subsequent terms is not the same.
A series that is neither mathematical nor geometric is described by the provided sequence.
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MULTIPLE CHOICE PRACTICE
9. For the function defined by the equation y=2 x²-10, which of the following represents the output when the input is -3 ?
(1) 6
(3) -10
(2) 8
(4) -28
10. If a function is defined by the equation y=-5 x+1 and the domain is the set {-2,0,2,4\}, which set below represents the range of the function?
(1) {11,12,13,14}
(3) {-10,-1,9,19}
(2) {-19,-9,1,10}
(4) {51,53,55,57}
11. A function is given by the set: {(-6,2),(-4,7),(0,5),(2,-4),(5,2),(7,5)}. Which of the following gives a pair of inputs that have the same output?
(1) -6and -4
(3) -4 and 2
(2) 5 and 7
(4) 0 and 7
Answer:
answer for no.10 is {11,12,13,14}
Step-by-step explanation:
According to question domain and equation is given. At first we have to write equation as f(y)=5x+1 and at the place of y we have to write the given domain respectively then we can get the answers
Which statement correctly describes the relationship between the graph of f(x) and the graph of g(x)=f(x)−4?
Answer:
the range of the graph would move down by 4 units.
Step-by-step explanation:
f(x) is the original/basis equation
g(x) is the translation equation
-4 does not have any x's attached to it, so it would affect the range, or the y of the equation
for example:
f(x) = 2x + 8
if you subtracted 4 from that it would be:
f(x) = 2x - 4, so the range would be affected
Round off 878 to the nearest 10
Answer:
880 is the answer
Step-by-step explanation:
hope this helps
a) Work out the minimum number of dogs that could have a mass of more than 24 kg
b) Work out the maximum number of dogs that could have a mass of more than 24 kg}.
Mass(kg) Frequency
0≤x<10 2
10≤x<20 7
20≤x<30 12
30≤x<40 6
a) The minimum number of hikers who could have walker between 6 and 17 miles is of: 9.
b) The maximum number of hikers who could have walker between 6 and 17 miles is of: 19.
What is shown by the frequency table?The frequency table shows the number of times that each range was observed in this problem.
For the minimum number of hikers walking between 6 and 17 miles, we have that:
All the 2 hikers in the interval 5 < x < 10 walked less than 6 miles.All the 8 hikers in the interval 15 < 20 < 20 walked more than 17 miles.Hence the minimum number is of 9, all of which walked between 10 and 15 miles, which is between 6 and 17.
For the maximum number of hikers walking between 6 and 17 miles, we have that:
All the 2 hikers in the interval 5 < x < 10 walked more than 6 miles.All the 8 hikers in the interval 15 < 20 < 20 walked less than 17 miles.Hence the maximum number is of:
2 + 9 + 8 = 19.
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Select all the points of intersection between the graphs of the functions f(x)=(x+5)(x-2)and g(x)=(2x + 1)(x-2)
Select all that apply
a: (-5,0)
b: (-1/2,0)
c: (-2, -12)
d: (2,0)
e: (4, 18)
f: (5, 30)
The point of intersection between the function f(x) and g(x) is x = 4 then, g(x)=18 where option E (4,18) is correct answer.
What is a function?
A function is defined as a relation between a set of inputs having one output each.
We have,
f(x) = ( x + 5 ) ( x - 2 )
g(x) = ( 2x + 1 ) ( x - 2 )
To find the points of intersection between the two functions we must equal the function.
f(x) = g(x)
( x + 5 ) ( x - 2 ) = ( 2x + 1 ) ( x - 2 )
( x - 2 ) gets canceled
x + 5 = 2x + 1
5 - 1 = 2x - x
4 = x
x = 4
This means that at x =4 the function f(x) and g(x) intersect.
we can see that at x = 4 both the functions have the same value.
f(x) = ( x + 5 ) ( x - 2 ) = ( 4 + 5 ) ( 4 - 2 ) = 9 x 2
f(x) = 18
g(x) = ( 2x + 1 ) ( x - 2 ) = ( 2 x 4 + 1 ) ( 4 - 2 ) = ( 8 + 1 ) ( 4 - 2 )
= 9 x 2
g(x) = 18
Thus the point of intersection between the function f(x) and g(x) is x = 4 then, g(x) =18 where option E (4,18) is correct answer.
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Find the sum of the arithmetic series where n = 50, a = 9, and t50 = 331.
Solution
Given series is [tex]$5+11+17+\ldots .+95$.[/tex]
Thus,
[tex]$\mathrm{a}=5, \mathrm{~d}=11-5=6,1=95$$$\begin{aligned}& \mathrm{n}=\frac{1-a}{d}+1 \\& =\frac{95-5}{6}+1 \\& =\frac{90}{6}+1=15+1=16\end{aligned}[/tex]
Therefore, [tex]$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+1)$$$\begin{aligned}& =\frac{16}{2}(5+95) \\& =8(100) \\& =800\end{aligned}$$[/tex]
What is arithmetic series?
The total of the terms in an arithmetic sequence with a predetermined number of terms is known as an arithmetic series. Here is a straightforward formula for calculating the sum: Formula 1: If the sum of an arithmetic series of terms is represented by S n, then The first and last terms' values, as well as the total number of terms, are needed for this formula.
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A box of chocolates contains 24 chocolates. Ten of the chocolates have cherry centers. All chocolates appear the same.
Two chocolates are selected. Find the probability of each of the following. (Round your answers to four decimal places.)
(a) both have cherry centers
(b) one has a cherry center and one does not
The probability of selecting chocolate such that:
(a) both have cherry centers: 0.1630
(b) one has a cherry center and one does not: 0.507
In this question, we have been given a box of chocolates contains 24 chocolates.
n(S) = 24
Ten of the chocolates with cherry centers.
n(A) = 10
So, the number of chocolates with no cherry centers are:
n(B) = 14
We need to find the probability of selecting chocolate such that
(a) both have cherry centers
P = (10/24)(9/23)
P = 90/552
P = 15/92
P = 0.1630
(b) one has a cherry center and one does not
P = 2*(10/24)(14/23)
P = 0.507
Therefore, the probability of selecting chocolate:
(a) both have cherry centers
P = 0.1630
(b) one has a cherry center and one does not
P = 0.507
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what is the perimeter of a rhombus when the diagonals are 42cm and 40cm
Answer:
Step-by-step explanation:
P = 4 a
a = √p^2 + q^2 / 2
P = 2√p^2 + q^2 = 2 x √42^2 + 40^2 = 116cm
∴ the perimeter of a rhombus when the diagonals are 42cm and 40cm is 116cm
find the volume of the Rectangular prism given below the length is is 10 cm the width is 3.2 cm and the height is 1.5 cm
Answer:
44.8
Step-by-step explanation:
Volume = Length * Height * Width
Volume = 10 * 1.5 * 3.2
Volume = 44.8cm
what level of confidence (as a ) would accompany each of the following intervals? (Round your answers for parts (a), (b), and (c) to the nearest Integer and your answer for part(a) tsample proportion 1.96(b) sample proportion 1.645to sample proportion 2.576(d) sample proportion 3.0 S
The level of confidence as a would accompany each of the given intervals are a. 95%, b. 90%, c. 99%
what level of confidence?Instead of being expressed as a percentage, the confidence level is expressed as a proportion using the confidence coefficient. For instance, the confidence coefficient would be. 99 if you had a confidence level of 99%. In general, the greater the coefficient, the more confident you can be in the accuracy of your findings.
What are the 3 common confidence level?The most typical levels of confidence are 90%, 95%, and 99%. A summary of the values corresponding to these typical confidence levels can be seen in the following table. The "confidence coefficient" is simply the confidence level presented as a proportion .
for a:
Z1=a/2=1.96
1-a/2=0.975
a=0.05
so,
(1-a)x100
=95%
Hence, the level of confidence is 95%
for b:
Z1=a/2=1.645
1-a/2=0.95
a=10
so,
(1-a)x100
=90%
Hence, the level of confidence is 90%
for c:
Z1=a/2=2.576
1-a/2=0.995
a=0.01
so,
(1-a)x100
=99%
Hence, the level of confidence is 99%
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if 25% of tolla's sallary is birr 135.75, what is the amount of his full salary?
If 25% of Tolla's salary is Birr 135.75, then the full amount of his salary is 4 times this amount, since 25% is one quarter of the total amount.
Therefore, the full amount of Tolla's salary is 4 * Birr 135.75 = Birr 543.
This is the amount of Tolla's full salary.
LOL
An approximate solution to an equation is found using this iterative process.
Xₙ₊₁= (Xₙ)³ - 1 / 4 and x₁= -1
a)
(i) Work out the value of x₂
(ii) Work out the value of x₃
b) Work out the solution to 6 decimal places.
a) The values are given as follows:
i) x1: -0.5.ii) x2: -0.280125.b) The solution of the equation is of: -0.25410169644.
How to obtain the solution to the equation?The equation in this problem is given as follows:
y = (x³ - 1)/4.
The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.
Then the values are given as follows:
x1 = -1 -> attributed.x2 = ((-1)³ - 1)/4 = -0.5.x3 = ((-0.5)³ - 1)/4 = -0.28125.x4 = ((-0.281255)³ - 1)/4 = -0.25556212524.x5 = ((-0.25556212524)³ - 1)/4 = -0.25417281837x6 = ((-0.25417281837)³ - 1)/4 = -0.25410513385x7 = ((-0.25410513385)³ - 1)/4 = -0.25410185521.x8 = ((-0.25410185521)³ - 1)/4 = -0.25410169644. -> difference less than six decimal places.More can be learned about iterative solution methods at https://brainly.com/question/13718918
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Joe flew his small airplane 1000 km in 4 hours flying with the wind. He flew 700 km against
the wind in 7 hours. Find the rate at which he flew in still air and the rate of the wind.
Answer:
To solve this problem, we can set up the following system of equations:
Let x be the rate at which Joe flew in still air and y be the rate of the wind.
1000 km / 4 hours = x + y
700 km / 7 hours = x - y
Solving this system of equations using the elimination method, we get:
x + y = 250
x - y = 100
Adding these two equations together, we get 2x = 350, so x = 175 km/hour.
Subtracting the second equation from the first equation, we get 2y = 150, so y = 75 km/hour.
Therefore, the rate at which Joe flew in still air is 175 km/hour and the rate of the wind is 75 km/hour.
Step-by-step explanation:
Which relationships would most likely be causal? Check all that apply.
O a positive correlation between depth under water and pressure
a negative correlation between total distance run and the runner's height
a positive correlation between a puppy's age and weight
a negative correlation between temperature and snowboards sold
a positive correlation between the price of milk and the price of socks
The correlation of two pairs of data values tells about the degree of movement that can occur. The correct option is A, C, and D.
What is correlation?The degree of movement that can occur in one of the data values when another data value is increased or decreased is indicated by the correlation of two pairs of data values.
A.) There is a positive relationship between depth under water and pressure.
Because water pressure increases with depth, this is a casual relationship that can be observed while swimming in a deep swimming pool.
C.) A positive relationship between the age and weight of a puppy.
This is a casual relationship because the puppy's weight and size both increase as it grows.
D.) A negative relationship between temperature and the number of snowboards sold
This is a casual relationship because as the weather warms up, fewer people prefer to go snowboarding.
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help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
Connor is driving to a concert and needs to pay for parking. There is an automatic fee
of $8 just to enter the parking lot, and when he leaves the lot. he will have to pay an
additional $2 for every hour he had his car in the lot. How much total money would
Connor have to pay for parking if he left his car in the lot for y hours? How much
vould Connor have to pay if he left his car in the lot for t hours?
The solution is
a) The amount Connor has to pay for parking if he left his car for y hours is given by the equation A = 8 + 2y where y is the number of hours
b) The amount Connor has to pay for parking if he left his car for t hours is given by the equation B = 8 + 2t where t is the number of hours
What is an 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.
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 data ,
Let the first equation be represented as A
Let the second equation be represented as B
Now , the value of A is
The automatic fee for parking = $ 8
The additional fee for parking every hour = $ 2
So , for x number of hour , the additional parking fee = 2x
And , the total parking fee including x hours = automatic fee for parking + additional parking fee
Substituting the values in the equation , we get
The total parking fee including x hours = 8 + 2x
Now , when x = y hours
The total parking fee including y hours A = 8 + 2y
And , when x = t hours
The total parking fee including t hours B = 8 + 2t
Hence , the equations are A = 8 + 2y and B = 8 + 2t where y and t are number of hours
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