Answer:
\(\textsf{A)}\quad -2x^6+7x^4+3x^3-3x^2+11x+20\)
B) Yes → Commutative Law
Step-by-step explanation:
Part (A)
To find the product of the given quadratic expressions, place each expression in brackets then multiply them:
\(\implies (-2x^3+x-5)(x^3-3x-4)\)
Distribute the parentheses:
\(\implies -2x^3(x^3)-2x^3(-3x)-2x^3(-4)+x(x^3)+x(-3x)+x(-4)-5(x^3)-5(-3x)-5(-4)\)
Simplify:
\(\implies -2x^6+6x^4+8x^3+x^4-3x^2-4x-5x^3+15x+20\)
Group like terms:
\(\implies -2x^6+6x^4+x^4+8x^3-5x^3-3x^2-4x+15x+20\)
Combine like terms:
\(\implies -2x^6+7x^4+3x^3-3x^2+11x+20\)
Part (B)
According the to Commutative Law (for multiplication) changing the order or position of two numbers does not change the end result.
\(\textsf{Commutative Law}: \quad a \cdot b = b \cdot a\)
Therefore:
\((-2x^3+x-5)(x^3-3x-4)=(x^3-3x-4)(-2x^3+x-5)\)
a. Name the four components of a time series and give an example of each of the four components.
b. Discuss the advantages and disadvantages of using the moving average method.
The four components of a time series are: Trend, Seasonality, Cyclical, Irregular/Random.
Trend: The long-term movement or pattern in the data. It represents the underlying growth or decline in the series over time. Example: An increasing trend in monthly sales of a product. Seasonality: Regular and predictable variations that occur at specific time intervals, such as daily, weekly, or yearly patterns. Example: Higher sales of ice cream during summer months.
Cyclical: Medium-term fluctuations that are not predictable and can last for several years. They are often associated with economic cycles, such as periods of expansion and recession. Example: Fluctuations in housing prices due to changes in the real estate market. Irregular/Random: Unpredictable variations that cannot be attributed to any specific cause. They are often the result of chance events or unforeseen circumstances. Example: Sudden changes in sales due to unexpected weather conditions or natural disasters.
The moving average method has several advantages and disadvantages:
Advantages:
Smoothes out short-term fluctuations and highlights long-term trends.
Easy to understand and calculate.
Helps in identifying changes in the underlying pattern over time.
Provides a simple forecast that can be easily updated.
Disadvantages:
Ignores other components like seasonality and cyclical patterns.
Lagging effect: It may not respond quickly to sudden changes in the data.
May not be suitable for data with irregular or random fluctuations. Overall, the moving average method is a simple and useful technique for smoothing data, but it has limitations in capturing more complex patterns and making accurate forecasts.
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Seattle, Washington is known for being very rainy. One day last month, 8 inches of rain fell in 1 1/2 hours. What is the rate of rainfall expressed in feet per hour?
Answer:
0.44ft/hr
Step-by-step explanation:
Given parameters:
Quantity of rainfall = 8inches
1ft = 12inches
so;
\(\frac{8}{12}\) = 0.67ft
Time = \(\frac{3}{2}\)hr
Unknown:
Rate of rainfall expressed in ft/hr = ?
Solution:
The rate of the rainfall is given as;
Rate = \(\frac{Quantity}{time}\)
Rate = \(\frac{0.67ft}{\frac{3}{2} }\) = 0.44ft/hr
The difference in the medians is ___ times the IQR
Answer:
1/3
Step-by-step explanation:
You want the difference in medians in terms of the IQR.
IQRThe IQR is the difference of the numbers at the ends of the box.
top distribution: IQR = 12 -6 = 6
bottom distribution: IQR = 14 -8 = 6
MediansThe median of each distribution is the location of the line in the box.
top distribution: median = 11
bottom distribution: median = 9
DifferenceThe difference in medians is 11 -9 = 2. The ratio of that to the IQR is ...
2/6 = 1/3
The difference in medians is 1/3 times the IQR.
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Given: 4ABC, and BP is parallel to AC.
Prove: m21 + m22 + m23 = 180
Mathematical proofs are used to prove or disprove mathematical statements.
Mathematical theoremsThe theorems to use are:
The sum of angles on a straight line is 180 degreesAlternate angles are congruentThe proofFrom the question, we have: \(\triangle ABC\)
This means that, ABC is a triangle
Also, we have:
BP || AC
This means that lines BP and AC are parallel
So, the following angles are congruent by alternate angle theorem
\(\angle 5 \cong \angle 3\).\(\angle 4 \cong \angle 2\)The angles on a straight line add up to 180 degrees.
So, we have:
\(\angle 4 + \angle 1 + \angle 5 = 180\)
By substitution, the above equation becomes
\(\angle 2 + \angle 1 + \angle 3 = 180\)
Rewrite the equation as:
\(\angle 1 + \angle 2 + \angle 3 = 180\)
Hence, the statement that \(\angle 1 + \angle 2 + \angle 3 = 180\) has been proved
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The function v(t) = t^3-10t^2+24t, 0 < t < 8, is the velocity in m/sec of a particle moving along the x-axis.
The motion is in the positive direction 0 < t < 4 and 6 < t < 8
The motion is in the negative direction 4 < t < 6
b) Find the displacement over the given interval
c) Find the distance traveled over the given interval
b. The displacement over the interval is -8 meters.
c. Total distance traveled over the interval 0 is 40/3 meters.
To find the displacement over the given interval, we need to find the change in position of the particle. We can do this by integrating the velocity function over the intervals where the motion is in the positive and negative directions, and then adding these integrals together.
a) The velocity function is v(t) = t³ - 10t² + 24t, 0 < t < 8.
When 0 < t < 4, the particle is moving in the positive direction, so we integrate v(t) from 0 to 4:
∫₀⁴ (t³ - 10t² + 24t) dt = [t⁴/4 - 10t³/3 + 12t²]₀⁴= 16/3
When 6 < t < 8, the particle is also moving in the positive direction, so we integrate v(t) from 6 to 8:
∫₆⁸ (t³ - 10t² + 24t) dt = [t⁴/4 - 10t³/3 + 12t²]₆⁸ = -32/3
When 4 < t < 6, the particle is moving in the negative direction, so we integrate v(t) from 4 to 6:
∫₄⁶ (t³ - 10t² + 24t) dt = [t⁴/4 - 10t³/3 + 12t²]₄⁶ = -8
Therefore, the displacement over the interval 0 < t < 8 is:
Δx = 16/3 - 32/3 - 8 = -24/3 = -8 meters.
b) To find the distance traveled over the given interval, we need to add up the total distance traveled in the positive direction and the total distance traveled in the negative direction.
The total distance traveled in the positive direction is:
∫₀⁴ |t³ - 10t² + 24t| dt = ∫₀⁴ (t³ - 10t² + 24t) dt = 16/3
The total distance traveled in the negative direction is:
∫₄⁶ |t³ - 10t² + 24t| dt = ∫₄⁶ (10t² - t³ - 24t) dt = 8
The total distance traveled over the interval 0 < t < 8 is therefore:
d = 16/3 + 8 = 40/3 meters.
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can someone help me with this please?
Answer:
6. x=20;
7. x=38, y=104;
8. x=30
Step-by-step explanation:
The fraction mode below shows the steps a student performed to find a quotient. Which statement best interprets the quotient
Answer: i belive its C
Step-by-step explanation: May i have brainiest
Find a cubic and a quartic model for each set of values. Explain why one models the data better.
x
-2
-1
0
1
2
y
-65
-14
-4
2
90
Error while snipping.
The cubic model is y = -5x³ - 9x² - 3x - 4.
To find a cubic and quartic model for the given set of values, we can use polynomial regression. Polynomial regression is a type of regression analysis where the relationship between the independent variable (x) and the dependent variable (y) is modeled as an nth degree polynomial.
Let's start by finding the cubic model. The general equation for a cubic model is
y = ax³ + bx² + cx + d,
where a, b, c, and d are the coefficients we need to find.
To find the coefficients, we need to solve a system of equations using the given data points:
When x = -2, y = -65:
-65 = a(-2)³ + b(-2)² + c(-2) + d
When x = -1, y = -14:
-14 = a(-1)³ + b(-1)² + c(-1) + d
When x = 0, y = -4:
-4 = a(0)³ + b(0)² + c(0) + d
When x = 1, y = 2:
2 = a(1)³ + b(1)² + c(1) + d
When x = 2, y = 90:
90 = a(2)³ + b(2)² + c(2) + d
Simplifying these equations, we get:
-8a + 4b - 2c + d = -65
-a + b - c + d = -14
d = -4
a + b + c + d = 2
8a + 4b + 2c + d = 90
Solving this system of equations, we find:
a = -5
b = -9
c = -3
d = -4
Therefore, the cubic model is y = -5x³ - 9x² - 3x - 4.
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A household consists of a married couple, their twin three-year-old sons, and
their twin eight-year-old daughters. The couple's children had no income and
lived with their parents all of last year. How many exemptions can the couple
claim on last year's tax return if they file with the "Married filing jointly" status?
A. 5
B. 3
C. 6
D. 4
Answer:
6
Step-by-step explanation:
Mr. Tsu’s class volunteers at a farm one day per week. Each student is responsible for caring for two animals during every hour spent at the farm.
Part A: Complete the diagram to show how many animals are cared for by one student over various lengths of time.
Part B: Does the diagram represent a function? Explain why or why not.
Part A: Attached Image
Part B: Yes, you do the hours x2 because each kid has to care for two animals for one hour.
Are all isosceles triangles always similar?
No, not all isosceles triangles are always similar. Two triangles are considered similar if their corresponding angles are congruent and their corresponding sides are in proportion. While all equilateral triangles are also isosceles triangles, not all isosceles triangles have congruent angles and proportional sides.
Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. Triangles are three-sided polygons in geometry that can be divided into three groups based on their sides, such as:
Scalene triangle (All three sides are unequal)Isosceles triangle (Only two sides are equal)Equilateral triangle (All three sides are equal)For example, consider an isosceles triangle with base angles of 70 degrees and a third angle of 40 degrees, and another isosceles triangle with base angles of 80 degrees and a third angle of 20 degrees. These triangles have different angles and are therefore not similar, even though they are both isosceles triangles.
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Vicky is an airline attendant. Last week, she worked on flights on 3 small jets and 5 large jets, which could seat a total of 560 passengers. The week before, she was assigned to flights on 5 small jets and 2 large jets, which could seat a total of 338 passengers. How many seats were on each type of flight?
The number of the small seats is 30 while the number of the big seats is 94.
What is the number of seats on each of the flights?We know that from the question, Vicky is an airline attendant. Last week, she worked on flights on 3 small jets and 5 large jets, which could seat a total of 560 passengers. The week before, she was assigned to flights on 5 small jets and 2 large jets, which could seat a total of 338 passengers.
Now;
Let the number of small seats be x and the number of large seats be y
It follows that;
3x + 5y = 560 ----- (1)
5x + 2y = 338 ------(2)
If you multiply (1) by 5 and (2) by 3 we have;
15x + 25y = 2800 ------ (3)
15x + 6y = 1014 -----------(4)
19 y = 1786
y = 1786/19
= 94
Substitute y = 94 into (1)
3x + 5(94) = 560
x = 560 - 5(94)/3
x = 30
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A real estate agent receives a 3% commission on the sale price of a home.
How much does the real estate agent receive as a commission if the house sells for $232,000?
O $69,600.00
$6.960.00
$696.00
$69.60
multiply the percent by the money
Examine parallelogram ABCD below.
Determine which of the following values are correct. Select three that apply.
A
m2D = 105
B
m2A = 75°
C
m2 = 93°
D
m2B = 87°
E
x = 16
F
x = 19
Given that,
∠C = (6x-21)° and ∠A = (4x+11)°
To find,
Choose the correct option.
Solution,
For a parallelogram, the opposite angles are equal. ATQ,
(6x-21)° = (4x+11)°
Taking like terms together,
6x-4x = 21 + 11
2x = 32
x = 16
∠C = (6x-21)° = 6(16) -21 = 75°
So, ∠A = 75°
So, ∠A = ∠C = 75°. Hence, the correct option is (B).
what is the answer for 8 x 12.231
Answer: 97.848
Step-by-step explanation: you know calculators exist, right?
W+15x-9y+2z
Terms:
Coefficients:
In the problem given:
W + 15x - 9y + 2z
The term are single mathematical expressions that separate values.
In the expression, there is a + and -; these concludes 2 terms.
There are 3 coefficients next to each variable.
The coefficients are 15x, -9y, and 2z.
That means there are 3 coefficients.
Cheers
- ROR
\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)
\( \sf{W \rightarrow coefficient = 1} \)\( \sf{15x \rightarrow coefficient = 15} \)\( \sf{-9y\rightarrow coefficient = -9} \)\( \sf{2z\rightarrow coefficient = 2} \)
____________________________________
\( \large \tt Solution \: : \)
Term refers to each variable or constant separated by a mathematical operator.
Coefficient refers to the numberic part of variable or a constant number present in an expression.
\(\qquad \tt \rightarrow \: 12a - 10b + 6\)
\( \large\textsf{Terms :} \)
\( \texttt{W } \)\( \texttt{coefficient = 1} \)
\( \texttt{15x} \)\( \texttt{coefficient = 15} \)
\( \texttt{-9y} \)\( \texttt{coefficient = -9} \)
\( \texttt{ 2z} \)\( \texttt{coefficient= 2} \)
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
how does energy bulb works
hello My name es Liliana y arigato bye
Answer:
?????.... hii erica herrrr
Answer:
Hi Liliana i love your name! it's very pretty:) my name is Melody
Step-by-step explanation:
someone pleasee help
The table of values and the linear equations indicates
4. Andy is correct, the equation of the table of values is; y = 2·x + 4
5. The Three equations are the same
What is a linear equation in algebra?A linear equation is an equation that produces a straight line graph, when plotted on the coordinate plane and can be expressed in the form; y = m·x + c
Where;
m = The slope of the straight line graph of the equation
c = The y-intercept
4. The values in the table indicate that the difference between consecutive terms in the x-values and the first difference in the y-value is constant, therefore, the values represent a linear relationship.
The slope, m, of the linear relationship is constant and it can be found using any two pair of points as follows;
m = (4 - 2)/(0 - (-1)) = 2
The equation is therefore;
y - 2 = 2·(x - (-1)) = 2·(x + 1) = 2·x + 2
y = 2·x + 2 + 2 = 2·x + 4
The equation, y = 2·x + 4 is in the form y = m·x + c, therefore;
Andy is correct
5. The slope-intercept form of the equation of a straight line is; y = m·x + c
Therefore;
y + 1 = 2·x -3
y + 1 - 1 = 2·x - 3 - 1 (subtraction property)
y = 2·x - 4
The equation, y = 2·x - 4, is in the form, y = m·x + c
2·x - 3 = y + 1
2·x - 3 - 1 = y + 1 - 1 (subtraction property)
2·x - 4 = y
y = 2·x - 4 (symmetric property)
The equation, y = 2·x - 4 is in the form, y = m·x + c, which is the same as the first equation
2·y + 2 = 4·x - 6
2·y + 2 - 2 = 4·x - 6 - 2 (subtraction property of equality)
2·y = 4·x - 8
2·y ÷ 2 = (4·x - 8) ÷ 2 (division property)
y = 2·x - 4
The above equation is the same as the first two equations, therefore, the equations are the same
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what is the formula for elimintation
Answer:
The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.
Answer:
You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.
Step-by-step explanation:
3) -x + 5 = -11x + 25
Answer:
x=2
Step-by-step explanation:
-x+5=-11x+25
add +x on both sides -11x+x =-10x
-10x+25=5
subtract 25 on both sides
you get -10x=-20
x=2
8. Ryan covered a distance of 42 km in 3 hrs and a further distance of 44 km in 4 hrs. Find his average speed.
The average speed is 12.29 km/hr
How to calculate the average speed?The formula used to calculate average speed is
= distance/time
The first step is to calculate the total distance
Distance A + Distance B
= 42 + 44
= 86
The next step is to calculate the total time spent during the journey
= Time A + Time B
= 3 + 4
= 7
The average speed can be calculated as follows
Average speed= 86/7
= 12.29
Hence the average speed is 12.29 km/hr
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Alberto started out bench pressing 60 pounds. He then added 5 pounds every week. Determine whether the situation is linear or nonlinear, and proportional or nonproportional
Answer
linear
nonproportional
Step-by-step explanation:
Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.
At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.
Answer:
linear
nonproportional
what is the value of 10-¹
Answer:
100.
Step-by-step explanation:
it may be 100. im not sure though
Answer:
\(\frac{1}{10}\)
Step-by-step explanation:
\(10^{-1}\) = \(\frac{1}{10^{1} }\)= \(\frac{1}{10}\)
A line passes through the points (0, -2) and (3, 4). Find the slope of the line.
Find the equations of a line through these 2 points
(1,2) & (3,5)
2. (-2,0) & (0,8)
3. (4,-5) & (11,-5)
4. (6,2) & (9,3)
6. (6,2) & (10,3)
5. (7,5) & (6,11)
answer is 2.2 66 88862 u88272
7
Oliver makes a plan to be healthier, starting with exercising more often. He signs up for a karate class, thinking this will be a cool way to get active.After three weeks, Oliver finds himself dreading karate class. He would much rather stay home and play RPG with his friends. Since Oliver has already made the decision, what is the BEST path for him to take?
It a because i told the tese
This week Edward spent $30 for hot dogs and supplies. He eamed $18.
Did he make money or lose money this week? Explain.
In a class full of men and women,
3/5
of the class are women. What is the ratio of men to women in its simplest form?
Answer:
2 : 3
Step-by-step explanation:
Women are = 3/5
So, Men Must be = 2/5
Ratio of Men to Women:
=> 2/5 : 3/5
Multiplying both sides by 5
=> 2 : 3
Answer:
IT IS NOT 2/3 ORE 3/5
THE WRITE ANSWER IS 2:3
PLZ HELP!! I RLY NEED IT!! Josie selected 6 books from thr library. However, he can only check out 4 books at a time. How many possible selections can he make?
Answer:
4 selections
Step-by-step explanation:
We are told in the question that:
Josie selected 6 books from the library. However, he can only check out 4 books at a time.
The number of possible selections can he make is 4 selections. This is because, He can only take 4 books out of the library at a time. This is the standard.