Answer:
7
Step-by-step explanation:
For each Polynomial:
a. Do the arithmetic
b. Write what the resulting degree is
c. Write the end behavior (of the resulting polynomial)
1. ( 6x3 + 3x2 − 4 ) + ( 2x4 − 3x2 + 12x3 )
2. ( 10 + 4x − 3x3 ) − ( 5x3 + 8 )
3. ( x + 4 )( 2x − 5 )
4. ( x + 2 )( 3x2 + 4x + 1 )
a. The polynomials are given as follows:
1. 2x^4 + 18x³ - 4.
2. -8x³ + 4x + 2.
3. 2x² - x - 10
4. 3x³ + 10x² + 9x + 2.
b. The resulting degrees are given as follows:
1. 4.
2. 3.
3. 2.
4. 3.
c. The end behavior of each polynomial is given as follows:
1. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> ∞.
2. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> -∞.
3. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> ∞.
4. As x -> -∞, f(x) -> -∞, as x -> ∞, f(x) -> ∞.
How to obtain the polynomials?The polynomials are obtained doing the operations and then combining the like terms.
Hence:
(6x³ + 3x² - 4) + (2x^4 - 3x² + 12x³)
2x^4 + (6 + 12)x³ + (3 - 3)x² - 4.
2x^4 + 18x³ - 4.
(10 + 4x - 3x³) - (5x³ + 8)
10 + 4x - 3x³ - 5x³ - 8
-8x³ + 4x + 2.
(x + 2)(2x - 5)
2x² - 5x + 4x - 10
2x² - x - 10
(x + 2)(3x² + 4x + 1)
3x³ + 4x² + x + 6x² + 8x + 2
3x³ + 10x² + 9x + 2.
What are the resulting degrees and the end behavior?The degree of a polynomial is given by the highest exponent in it's equation.
The end behavior of a polynomial is calculated as the result of elevating negative infinity and then positive infinity to the highest exponent of the polynomial, considering the leading coefficient.
More can be learned about polynomials at https://brainly.com/question/24737967
#SPJ1
according to the united states census bureau, the average single-family home constructed in 2016 was 2,412 square feet. carmen wondered if families in her area still want a smaller home in comparison to the average. she randomly selected 53 people and asked what the ideal square footage of a home is for them. from the responses, she calculated the sample mean equals 1,230 square feet with a sample standard deviation of 56 square feet. calculate the value of the test statistic.
The correct hypothesis relation is is H₀ : μ ≥ 2,412. and Ha : μ < 2,412
According to the United States Census Bureau, the average area = 2, 412 square feet
Then the null hypothesis is
H₀ :μ ( mean ) area is greater than or equal to 2,412
H₀ : μ ≥ 2,412.
But, according to Jane, in her area, still families want a small home comparison to average.
Alternative hypothesis is that, mean area is less than 2,412 .
Ha : μ < 2,412.
Therefore, H₀ : μ ≥ 2,412. and Ha : μ < 2,412
To learn more about Alternative hypothesis click here:
brainly.com/question/27335001
#SPJ4
let s 5 {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s. must there be two integers whose sum is 15? why?
The given set have two integers whose sum is 15 because if we selcet the element from the given set then there sum is equal to 15.
In the given question, let s = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s.
We have to check there be two integers whose sum is 15.
As we know that,
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The letter Z or the chalkboard Z is frequently used to represent the set of integers in mathematical terminology.
There are total 10 elements.
We have to choose two element from the given set which sum is equal to 15.
If we choose 3 and 12 then there sum is 15.
Similarly, if select (5,10), (6,9), (7,8) the sum of all these selection is 15.
So the given set have two integers whose sum is 15.
To learn more about integers link is here
brainly.com/question/15276410
#SPJ4
Write an algebraic expression for: 9 less than the quotient of z and 8.
The algebraic expression for "9 less than the quotient of z and 8" exists 9 - z / 8.
What is meant by algebraic expression?Using variables, constants, and algebraic operations, an expression can be described as an algebraic expression in mathematics (addition, subtraction, etc.). Terms are used to construct expressions.
Similar to this, when we describe an algebraic expression in English and it has a variable, we are doing so (an expression with a variable).
A mathematical expression made composed of integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).
Let the given expression be "9 less than the quotient of z and 8".
simplifying the expression, we get
= 9 - z / 8
To learn more about algebraic expression refer to:
https://brainly.com/question/2164351
#SPJ4
From the sum of 3x +4y -3xy and 5x +3y -2xy subtract the sum of 2x +y – 3xy and 10x -9y -8xy.pls sent fast dont spam
Answer:
The answer is (-4x + 15y - 6xy)
Step-by-step explanation:
(3x + 4y - 3xy + 5x + 3y - 2xy)
= 8x + 7y - 5xy
(2x + y - 3xy + 10x - 9y - 8xy)
= 12x - 8y - 11xy
Now,
(8x + 7y - 5xy) - (12x - 8y - 11xy)
8x + 7y - 5xy - 12x + 8y + 11xy
= -4x + 15y - 6xy
Thus, The answer is (-4x + 15y - 6xy)
suppose you have calculated a two-way anova where the interaction was not significant. how should you next proceed?
The connection test is performed prior to making any ends in view of the tests for the primary impacts. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.
Before drawing any conclusions based on the tests for the main effects, the interaction test is carried out. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.
There may be an interaction if the plot's lines don't line up in the same direction. A collaboration demonstrates that the method for the Y information at the levels of the main X variable are different at each level of the second X variable. The interaction's strength increases with the number of nonparallel lines.
To learn more about Interaction test here
https://brainly.com/question/29633075
#SPJ4
A particular fungal cell weighs 0.0009 gram. If this weight, in grams, is written in scientific notation as 9 x 10^q , what is the value of q?
Answer:
q = -4
Step-by-step explanation:
0.0009 = 9 × 10^(-4)
q = -4
A= (a, b} B = {1,2,3} Select the expression that is an element of AxBxB. O (1,2,3) (a, a,1) (,22 (2.1.1)
The expression that has the element of A*B*B is Option A - (b,2,3)
Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
The "elements" of a set are the objects that make up the collection. Sets are equal if and only if they have the same elements, therefore a = A denotes that 'a' is one of A's elements. For sets, repetition and order are irrelevant.
Given, A={a.b} and B=[1,2,3]
Since the required expression was supposed to have the element of A*B*B the correct option would be A since it has elements b from A, 2 from B, and 3 from B, fulfilling all the required elements.
To learn more about discrete maths visit: brainly.com/question/27793609
#SPJ4
5x-3(x-2)-x show your work
Answer: x+6
Step-by-step explanation:
5x-3(x-2)-x .......................... Question
5x-3x+6-x ........................... Distribute
1x+6 ..................................... Combine like terms
x+6 ...................................... Multiply by 1
Answer: x+6
Step-by-step explanation:
5x-3(x-2)-x
5x -3x +6 -x
x + 6
Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
Answer: h = 92
Step-by-step explanation:
148 - 180 = 32
32 + 56 = 88
88 - 180 = 92
Challenge in the first week of July, a record 1,120 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more
people went to the pool than in the second week. In the fourth week, 254 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool
over these four weeks?
The percent decrease of people who went to the pool is%
C
Answer:
20%
Step-by-step explanation:
You want to know the percentage change from 1120 to a final number that is 100 less, 130 more, and 254 less.
Percentage changeThe percentage change is given by ...
percent change = change/(original amount) × 100%
Here, the total amount of change is the sum of the given changes:
-100 +130 -254 = -224
Then the percentage change is ...
-224/1120 × 100% = -20%
The percent decrease is 20%.
<95141404393>
Find the general solution of the given differential equation.
(x + 1) dy/dx + (x + 2)y = 2xe?x
y=
Give the largest interval I over which the general solution is defined. (Think about the implications of any singular points.)
(??, ?)
(0, 1)
(?1, ?)
(0, ?)
(??, 1)
The general solution of the given differential equation is y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2) and the largest interval is (-infinity, -2) U (-1, infinity).
The general solution of the mentioned differential equation will be calculated as follows -
Firstly rewriting the differential equation in standard form:
(x+1) dy/dx + (x+2)y = 2x[tex] {e}^{(xy)} [/tex]
Calculating the integrating factor to make the LHS as a total derivative:
As known, formula for integrating factor is:
mu = [tex] {e}^{(integral of (x+2)/(x+1) dx)} [/tex]
= [tex] {e}^{(ln(x+1) + ln(x+2))} [/tex]
= (x+1)(x+2)
Now multiplying both sides of the equation by the integrating factor:
(x+1)(x+2) × (x+1) dy/dx + (x+1)(x+2) × (x+2)y = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)
LHS will be a total derivative. Rearrange the equation for the same -
d/dx((x+1)(x+2)y) = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)
Integrating both sides of the equation:
(x+1)(x+2)y = integral of 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2) dx
= 2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C
Now find the equation for y:
y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2)
Equation for y is the general solution of the differential equation where constant C is the arbitrary constant of integration.
The general solution is not defined at the position x=-1 and x=-2. Hence, the largest interval over which the general solution is defined is (-infinity, -2) U (-1, infinity).
Learn more about integration -
https://brainly.com/question/27419605
#SPJ4
In 200920092009, Usain Bolt set the world record for sprinting 100 \text{ m}100 m100, start text, space, m, end text in approximately 9\dfrac359
5
3
9, start fraction, 3, divided by, 5, end fraction seconds.
Find his average speed in meters per second.
Average speed of Usain Bolt is 10.41 m/s.
What is Speed?The distance travelled by an object in relation to the amount of time it takes to travel that distance can be used to define speed. In plainer terms, it is a gauge of how quickly an object moves.
Average speed = (Total distance travelled)/(Total time required)
SI unit of speed is m/s.
Distance Travelled by Usain Bolt = 100m
Time required to travel this distance = [tex]9\frac{3}{5}[/tex] = 48 ⁄ (5 sec)
Average speed = (Total distance travelled)/ (Total time required)
Average speed = 100/ (48/5)
= 500/48
= 10.41 m/s
Therefore, average speed of Usain Bolt is 10.41 m/s.
To know more about speed, visit the link:
https://brainly.com/question/4931057
#SPJ1
Select all the statements that are true for the graph shown. Submarines descent graph of a diagonal line on a coordinate plane going down and to the right with Time in seconds on the x-axis and Height above Sea Level in feet on the y-axis. The line begins at the origin and passes through point 4 comma negative 12.
The relationship is proportional.
The rate of change is −32
The rate of change is −83
The relationship is linear.
The correct option for the graph shown are-
The relationship is proportional.The relationship is linear.Explain the term proportional relation?Relationships across two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, each variable is consistently equal to the other's constant value.The question's line traverses the origin and (4,-12).
The line's rate of change is;
m = -12 - 0 / 4 - 0
m = -3
The slope of the line or its rate of change is -3.
The line's equation is provided by;
y - 0 = -3(x - 0)
y = -3x
This relationship is linear as a result.
The relationship is proportionate if we take any value of x because there will only ever be one value of y.
Therefore, the following claims are accurate:
The relationship is proportional.The relationship is linear.To know more about the proportional relation, here
https://brainly.com/question/2598881
#SPJ4
Which of the following are the roots of the quadratic equation 3x^2 + 7x + 2 = 0?
Step-by-step explanation:
The figure shows two lines cut by a transversal. What value of x shows that the lines are parallel? Show your work.
Answer:
5x + 10× - 30= 180 degree
15x =150
x= 10
If you wanted to shingle the roof and each package of shingles covered an area of 5.6 m² , what would be the minimum number of packages of shingles needed to do the job?
HINT:you only need to cover the top of the roof. You need to find the side length of each roof side first.
The minimum number of packages of shingles that would be needed to do the job would be = 0.285 package.
What is an area of an object?An area of an object is defined as the total area that is being covered by the shape of that object.
This given object has the total of five sides with two triangles, and three rectangles.
The top part of the object is what is needed to be roofed therefore the area of the 2 rectangles should be determined as follows.
Area of rectangle =2( l ×w)
l = 14cm
w = X cm ( this is calculated using the Pythagorean theorem)
w² = 4.1² + 4²
w² = 16.81 + 16
w² = 32.81
w = √ 32.81
w = 5.7cm
Area of rectangle = 2× (14 × 5.7)
= 2× 79.8 = 159.6 cm²= 1.596m²
If 1 package of shingles = 5.6 m²
X package = 1.596m²
make X package the subject of formula = 1.596× 1/5.6
= 0.285 package.
Learn more about triangle here:
https://brainly.com/question/28470545
#SPJ1
it is commonly believed that average body temperature for humans is 98.6 degrees f. a study was done in which a group of healthy adults had their temperature measured 1 to 4 times daily for 3 days. this resulted in 175 temperature measurements. the sample mean temperature was 98.2 degrees f, with a sample standard deviation of 0.7 degrees f. construct a 95% confidence interval for the mean body temperature of humans. show all work. round the margin of error and interval bounds to 2 decimal places.
The 95% confidence interval estimate of the population mean is 98.10< μ < 98.30.
Given that
sample mean = ~x = 95.2
sample standard deviation = s = 0.7
sample size = n = 175
Degrees of freedom = d.f = n - 1 = 175 - 1 = 174
αt /2,d.f = 1.974.
The explanation for step 1
At 95% confidence level
α= 1-0.95% =1-0.95 =0.05
α /2=0.05/ 2= 0.025
αt /2,d.f = t0.025,174 = 1.974
αt /2,d.f = 1.974
The explanation of Step 2
Margin of error = E = t/2,df x (s /Vn ) = 1.974 x ( 0.7/ V175) = 0.10
Margin of error = E = 0.10
The 95% confidence interval estimate of the population mean is,
~x- E < μ < ~x + E
98.2 - 0.10< μ < 98.2 + 0.10
98.10< μ < 98.30
Margin of error = E = 0.10
To learn more about confidence interval
https://brainly.com/question/24131141
#SPJ4
Katherine is working two summer jobs, lifeguarding and walking dogs. She can work
no more than 14 hours altogether between both jobs in a given week. Write an
inequality that would represent the possible values for the number of hours
lifeguarding, I, and the number of hours walking dogs, d, that Katherine can work in
a given week.
Answer: l +d ≤ 14
Step-by-step explanation:
how much do national football league players weigh on aerage in a random sample of 50 nfl players the average weight is 244.4 pounds
This statistic is based on an average of all players in the NFL. The average weight of a random sample of 50 NFL players may be slightly different.
This statistic is based on an average of all players in the NFL. It is not possible to accurately estimate the average weight of a random sample of 50 NFL players without actually measuring the weight of each individual player. The average weight of a random sample of 50 NFL players may be slightly different due to the randomness of the sample and individual player physical characteristics.
In order to accurately determine the average weight of a random sample of 50 NFL players, the weight of each individual player must be measured. The sample size of 50 players is relatively small, and the results may be significantly affected by the inclusion or exclusion of a single player. Additionally, the average weight of the sample may vary due to individual player physical characteristics such as height, body composition, and muscle mass. Furthermore, the average weight could be affected by the age and experience level of the players in the sample. All of these factors should be taken into consideration when attempting to determine the average weight of a random sample of NFL players.
Learn more about statistic here
https://brainly.com/question/14128303
#SPJ4
the area of a square flowerbed is 1.21 square yards. what is the length of each side? write your answer as a decimal if necessary.
The length of each side of the given square is 3.306 yards.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.
It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.
In geometry, a square is a flat shape with four equal sides and four right angles (90°).
A square is a unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).
So, we have the area of the square as:
1.21 yards²
Area formula of square: A = s²
Now, calculate to find the length of the square as follows:
A = s²
1.21 = s²
s = 4/1.21
s = 3.306
Therefore, the length of each side of the given square is 3.306 yards.
Know more about a square here:
https://brainly.com/question/25092270
#SPJ4
In a hurry, will give 40 points.
Answer:
A: 74.9
B: 51.4
C: 53.7
Sorry I don't have enough time for the rest
Step-by-step explanation:
all angles should add up to 180
Estimate 64.5 divided by 12.3 using rounding 60 divided by 10
64.5 divided by 12.3 using rounding 60 divided by 10 gives 5.33.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
The given numbers are,
64.5 and 12.3.
When 64.5 is divided by 12.3.
The 64.5 can be rounded as 64
And 12.3 can be written after rounded as 12
Now divide 64 by 12.
64 / 12 = 5.333
The value of 64.5 divided by 12.3 is 5.33.
To learn more about Mathematical operations on :
https://brainly.com/question/22469627
#SPJ1
Can someone please help me to convert 2,8hours to hours, minutes and seconds ?
convert 2.8hours to hours, minutes and seconds is 2.8 hours = 2 hours 48 minutes 0 seconds
The conversion of 2.8 hours into hours, minutes and seconds is relatively simple. To begin, we must first convert 2.8 hours into minutes. To do this, we multiply 2.8 by 60, which equals 168 minutes. Now, we need to convert those minutes into hours and seconds. To do this, we divide the 168 minutes by 60, which gives us 2 hours. We then take the remainder, which is 48 minutes, and divide it by 60, which gives us 0 seconds. Therefore, 2.8 hours is equivalent to 2 hours 48 minutes 0 seconds.
Learn more about minutes here
https://brainly.com/question/13624026
#SPJ4
How do you solve 2/x = 7/9?
Answer:
2x=9+7
2x=16
x= 2/16
x=8
Step-by-step explanation:
Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x=98.13, y=100.6, r=0.904, P-value=0.000, ŷ=14.68+0.88x, where x represents the IQ score of the twin born first. Find the best predicted value of ModifyingAbove y with caret given that the twin born first has an IQ of 104? Use a significance level of 0.05.
The predicted value of the twin born first has an IQ of 104 is 106.2..
We have given that,
sample size n = 10
x = 98.13
y = 100.6
r = 0.904
p-value = 0.000
y'= 14.68 + 0.88x
significance level = 0.05
and we have to find predicted value of the twin born first has an IQ of 104.
We know that x represents the IQ score of the twin born first.
Therefore value of x is 104.
Hence the predicted value P will be,
P = 14.68 + 0.88(104)
= 14.68 + 91.52
P = 106.2
Therefore the best predicted value of the twin born first has an IQ of 104 is 106.2.
The positive predicted value is the probability that a test gives result for a true statistic. The negative predictive value is the probability that a test gives a false result for a false statistic.
To know more about predicted value here
https://brainly.com/question/19756249
#SPJ4
Find the gradient vector field of f. f(x, y) =xe9xy
The gradient vector field of function f(x,y) is given as follows:
grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.
The gradient vector field of a function
Suppose that a function defined as follows:
f(x,y).
The gradient function is defined considering the partial derivatives of function f(x,y), as follows:
grad(f(x,y)) = fx(x,y) i + fy(x,y) j.
The gradient of a function is a vector field. It is obtained by applying the vector operator V to the scalar function f(x, y). Such a vector field is called a gradient (or conservative) vector field.
In which:
fx(x,y) is the partial derivative of f relative to variable x.
fy(x,y) is the partial derivative of f relative to variable y.
The function in this problem is defined as follows:
f(x,y) = xe^(9xy).
The partial derivative relative to x as follows:
fx(x,y) = e^(9xy) + 9xye^(9xy) = (1 + 9xy)e^(9xy).
The partial derivative relative to y as follows:
fy(x,y) = 9x²e^(9xy).
Hence the gradient vector field of the function is defined as follows:
grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.
To learn more about Gradient Function visit:
brainly.com/question/13646769
#SPJ4
the+population+of+a+town+is+2500+and+is+decreasing+at+a+rate+of+3%+per+year+5+years
2,092.1 is the population of the town after 5 years, and P(t)=2500*(1-0.035)^t is the exponential function.
What is the exponential decay function?In mathematics, exponential decay defines the process of diminishing an amount by a consistent percentage rate over a period of time.
It can be stated by the formula y=a(1-b)x wherein y is the total form and is the initial money, b is the decay factor, and x is the quantity of time that has passed.
So, we got:
r = 3.5%/100% = 0.035
We have our exponential function:
P(t) = 2500*(1 - 0.035)^t
The number after 5 years is provided by substituting t = 5, we will get:
P(5) = 2500*(1 - 0.035)^5 = 2,092.1
Therefore, 2,092.1 is the population of the town after 5 years, and P(t) = 2500*(1 - 0.035)^t is the exponential function.
Know more about the exponential decay function here:
https://brainly.com/question/2046253
#SPJ4
Correct question:
The population of the town is 2500 and is decreasing at a rate of 3.5% per year. Write an exponential decay function to find the population of the town after 5 years
$32.75. Find the total cost if the tax is 9.25% and you want to leave an 18% tip.
Answer:About 155 results (0.47 seconds)
Tax and Tip - Illustrative Math Taskshttps://tasks.illustrativemathematics.org
Step-by-step explanation:
this may help
Type the correct answer in each box. Use numerals instead of words.
Multiply the expressions.
Answer:
[tex]$\frac{x^{2}+12x-27}{x^{2}-x-6}$[/tex]
Step-by-step explanation:
See picture below :)
