(a) To find the product of -2x^3+x and x^3-3x-4, we can use the distributive property of multiplication:
(-2x^3 + x)(x^3 - 3x - 4)
= -2x^3(x^3) - 2x^3(-3x) - 2x^3(4) + x(x^3) - x(-3x) - x(4)
= -2x^6 + 6x^4 - x
= -2x^6 + 6x^4 - x
Therefore, the product of -2x^3+x and x^3-3x-4 is -2x^6 + 6x^4 - x.
(b) No, the product of 2x^3+x-5 and x^3-3x-4 is not equal to the product of x^3-3x-4 and -2x^3+x-5. This is because the order of the factors in a multiplication expression affects the outcome. When we expand both products using the distributive property, we get different expressions:
(2x^3 + x - 5)(x^3 - 3x - 4) = 2x^6 - 5x^3 - 3x^2 - 17x + 20
(x^3 - 3x - 4)(-2x^3 + x - 5) = -2x^6 + 11x^4 + 13x^3 - 3x^2 - x + 20
So the expanded expressions are not equal. Therefore, the two products are not equal.
Which of these equations does NOT have any solutions?
10
−
3
�
−
1
=
7
+
3
�
+
2
10−3x−1=7+3x+2
12
−
7
�
−
10
=
�
−
8
�
+
2
12−7x−10=x−8x+2
13
−
4
�
+
2
=
3
�
−
7
�
+
2
13−4x+2=3x−7x+2
15
−
2
�
−
2
=
10
�
+
3
�
+
2
15−2x−2=10x+3x+2
The equation does not have solution is 13−4x+2=3x−7x+2
What is an equation?An equation is a statement that equals two algebraic expressions with 'equal to' symbol (=).
consider the given equations,
10−3x−1=7+3x+2, x=0 is the solution for this equation.
12−7x−10=x−8x+2, all real values makes this equation true, so the solution is (-∞,∞)
13−4x+2=3x−7x+2 has no solution.
15−2x−2=10x+3x+2 , has solution [tex]x=\frac{11}{15}[/tex].
Hence, equation with no solution is 13−4x+2=3x−7x+2.
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What is the difference between qualitative forecasting techniques and quantitative forecasting techniques?
The difference between qualitative forecasting techniques and quantitative forecasting techniques is:
Quantitative projections frequently rely on historical information, like past sales and income numbers, production and financial reports, and website visitor statistics. You may use seasonal sales data, for instance, to estimate the production and labour requirements for the upcoming year based on the monthly or quarterly results from the previous year. Additionally, statistical modelling, trend analysis, or other information from authoritative sources like governmental organisations, professional groups, and academic institutions are used in quantitative forecasting.
Techniques for qualitative forecasting are derived from the knowledge and intuition of seasoned business professionals. These forecasting methods involve data interpretation together with the expert knowledge you've gained through years of work experience, so they go beyond simple guesswork. For instance, if you require qualitative data to predict sales for the year, you may calculate the influence of a new advertising campaign or promotion your business is preparing, consider the implications of emerging technology for customer behaviour, and consider current social fads and trends.
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Subtract 3 from 8, then subtract u from the result
Answer:
The result of 8 minus 3 is 5. Then, if you subtract u from 5, the result is 5 - u.
Answer: 5-u
Step-by-step explanation: Subtracting 3 from 8 is 5. Subtracting u from the result is 5-u.
What expression is equal to the length of segment ST in meters?
Check the picture below.
[tex]\sin(35^o )=\cfrac{\stackrel{opposite}{ST}}{\underset{hypotenuse}{34}}\implies 34\sin(35^o)=ST[/tex]
A blog refers to a website that contains a personal journal. According to one analyst, over a several year period, the number of blogs in existence followed a certain pattern. The analyst estimated that there were about 60,000 blogs in the first year, 120,000 in the second year, and 240,000 inthe third
. If the analyst was correct, how many blogs were there in the 5th year?
Answer:
960,000
Step-by-step explanation:
Every year, the number of blogs doubled.
The first year:60,000
The Second year: 120,000
The third year: 240,000
The fourth year: 480,000
The fifth year: 960,000
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members of a lacrosse team raised $1581.75 to go to a tournament. they rented a bus for $968.50 and budgeted $55.75 per player for meals. write and solve an equation which can be used to determine pp, the number of players the team can bring to the tournament.
Let pp be the number of players. We can write an equation to solve for the number of players.
1581.75 - 968.50 - (pp × 55.75) = 0
1581.75 - 968.50 - 55.75pp = 0
-55.75pp = -613.25
pp = 11
Therefore, the team can bring 11 players to the tournament. To find this, we subtracted the cost of the bus (968.50) and the cost of meals per player (55.75pp) from the total amount raised (1581.75).
We then divided both sides by -55.75 to solve for the number of players (pp) on the team.
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Find the geometric mean of √7 and √343.
Answer: 7 √7
Step-by-step explanation: If you find the greatest common factor of 343, you get 49 and 7 and 49 breaks down to 7 and 7. you now have 3 7's. You now group two of those sevens and bring it out of the radical, leaving one 7 under the radical. This gives you 7 √7.
if two numbers are randomly chosen without replacement from , what is the probability their sum is greater than their product? express your answer as a common fraction.
The probability their sum is greater than their product is 11/36.
For at least a single two numbers is 1 when they are randomly selected from the range of 1, 2, 3, 4, 5, and 6.
Success is defined as a measure of probability when there is a number of potential outcomes.
For instance, there is the chance of tossing a coin & obtaining heads is 1 in 2, and there is only one way to acquire a head and there are a total of 2 possible outcomes head or tail.
Now we can indicate this with P(heads)
12 P(at least 1 one) = 1 - P. (no ones)
P(no ones)=(5/6)*(5/6)
25/36 P(at least 1 one)=(1 - 25/36).
P(sum higher than product)=P(at least 1 one) = 11/36
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Write the terms of each sum.
3349/1260 is the amount, according to the provided document.
What does an sum total mean?The outcome of an addition is a total. For instance, adding 1, 2, 3, and 4 results in the printed number 10. (1) Addends—also known as summands—are the integers that are being added together.
(a)
[tex]\begin{aligned}& \text { D) } \sum_{j=1}^7 \frac{2}{j+2} \\& j=1 ; \frac{2}{1+2}=\frac{2}{3} \\& j=2 ; \frac{2}{2+2}=\frac{2}{4}=\frac{1}{2} \\& j=3 ; \frac{2}{3+2}=\frac{2}{5} \\& j=4 ; \frac{2}{4+2}=\frac{2}{6}=\frac{1}{3} \\& j=5 ; \frac{2}{5+2}=\frac{2}{7} \\& j=6 ; \frac{2}{6+2}=\frac{2}{8}=\frac{1}{4} . \\& j=7 ; \frac{2}{7+2}=\frac{2}{9} \\& \sum_{j=1}^7 \frac{2}{j+2}=\frac{2}{3}+\frac{1}{2}+\frac{2}{5}+\frac{1}{3}+\frac{2}{7}+\frac{1}{4}+\frac{2}{9} \\& =\frac{3349}{1260}\end{aligned}[/tex]
(b)
[tex]\begin{aligned}\frac{7}{2} \frac{8+0}{2} & =\frac{840}{1}+\frac{840}{2}+\frac{840}{3}+\frac{840}{4}+\frac{840}{5}+\frac{840}{6}+\frac{840}{7} \\& =840+420+280+210+168+140+120\end{aligned}[/tex]
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REALLY EASYY!! IF YOU ANSWER THIS YOU GET BRAINLIEST BUT MUST BE CORRECT!
The selling price of each item when matched with the correct problem is :
$18. 85$ 10. 18$ 20. 39$ 207. 20$ 79. 00$ 51. 45How to find the selling price ?Cost of CD : 14 . 50. Mark up : 30 % :
= 14. 50 x ( 1 + 30 % )
= $ 18. 85
Original price of a book : $ 18. 50, discount 45 %:
= 18. 50 x ( 1 - 45 % )
= $ 10. 18
Original price of shorts : $ 19. 99 , Tax 2%:
= 19. 99 x ( 1 + 2 %)
= $ 20. 39
Cost of MP3 Player : $ 129. 50. Mark up : 60 % :
= 129. 50 x ( 1 + 60 % )
= $207. 20
Original price of Concert tickets : $ 100. 00, discount 21 %:
= 100 x ( 1 - 21 % )
= $ 79
Original price of x - box game: $ 49. 95 , tax 3 %:
= 49. 95 x ( 1 + 3 % )
= $ 51. 45
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Find the next term in the series: 2, 5, 14, 41, x
I really need help with this question:
In a group of 14 children some are nine years old and the rest are eleven years old. When the ages of the 14 children are added together their total is 138 years. How many nine-year-old children are there?
Answer:
Therefore, there is 8 children that is 9 years old and 6 children that is 11 years old.
Step-by-step explanation:
Let x be the no. of 9 years old and y be the no. of 11 years old.
x+y= 14 (1)
9x+11y= 138 (2)
From (1) :
x=-y+14 (3)
sub (3) into (2) :
9(-y+14)+11y= 138
-9y+126+11y=138
2y= 138-126
y= 6 (4)
sub (4) into (1) :
x+6= 14
x= 8
Luke melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa.
There are 180 grams of cocoa in the resulting mixture.
When the 200 grams of dark chocolate and the 200 grams of milk chocolate are mixed together, the amount of cocoa in the mixture is found by adding the amount of cocoa in each type of chocolate.
First, the amount of cocoa in the dark chocolate is calculated by multiplying the total weight of the dark chocolate by its cocoa percentage:
200 grams(0.60) = 120 grams
Next, the amount of cocoa in the milk chocolate is calculated in the same manner:
200 grams(0.30) = 60 grams
Finally, the total amount of cocoa in the mixture is found by adding the amount of cocoa in each type of chocolate:
120 grams + 60 grams = 180 grams
Therefore, the total amount of cocoa in the resulting mixture is 180 grams.
The problem seems incomplete, it must have been...
"Luke melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa. How many grams of cocoa are in the resulting mixture?"
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Ethan starts an IRA (Individual Retirement Account) at the age of 34 to save for retirement. He deposits $400 each month. Upon retirement at the age of 65, his retirement savings is $709,165.25. Determine the amount of money Ethan deposited over the length of the investment and how much he made in interest upon retirement.
Ethan deposited amount $144,000 over 31 years and made a total of $565,165.25 in interest.
Ethan's total deposit amount to his IRA was $144,000 ($400 per month for 31 years). The total amount he had in his IRA upon retirement was $709,165.25. This means that he made a total of $565,165.25 ($709,165.25 - $144,000) in interest over the length of the investment. This amount was likely made up of a combination of capital gains, dividends, and other investment returns. It is important to note that the interest rate can vary depending on the type of investments chosen, so this amount may be higher or lower depending on the types of investments made.
1. Calculate the total number of months Ethan invested for: 31 years x 12 months = 372 months
2. Calculate the total amount deposited: $400 per month x 372 months = $148,800
3. Calculate the total amount upon retirement: $709,165.25
4. Calculate the total interest made: $709,165.25 - $148,800 = $565,165.25
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For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population. Thus, the population of such a type of organism satisfies a differential equation of the formdP/dt=aP2−bPwith a,b>0.Sketch a graph of dP/dt against P. Note when dP/dt is positive and negative.
The graph of dP/dt against P is a parabola, with the equation of the form [tex]y = ax^2 - bx[/tex] where a and b are positive parameters.
The graph has a vertex at [tex](b/2a, -b^2/4a)[/tex].
When P is less than b/2a, dP/dt will be positive, meaning the population is increasing. As P increases, dP/dt will reach a maximum at (b/2a, -b^2/4a) and then decrease, meaning the population is decreasing. When P is greater than [tex]b/2a, dP/dt[/tex] will be negative.
For example, if a = 4 and b = 1, the graph of dP/dt against P is [tex]y = 4x^2 - x[/tex], with the vertex at (0.5, -0.125). When P is less than 0.5, dP/dt will be positive, and when P is greater than 0.5, dP/dt will be negative.
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marty can go to one movie on either friday or saturday. he will be able to choose either comedy or an action movie. which list shows all possible outcomes of one move on one day?
There are the four possible combinations of day and movie genre that Marty can choose from.
OutcomesMarty has two options for the day of the week to go to the movie (Friday or Saturday) and two options for the movie genre (Comedy or Action).
Therefore, the list of all possible outcomes of one movie on one day is:
Friday ComedyFriday ActionSaturday ComedySaturday ActionThese are the four possible combinations of day and movie genre that Marty can choose from.
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Un auto recorre 50 km desde el punto o al punto P con dirección al Este y
¿Como se expresa la posicion del punto P? es urgente es de números
positivos y negativos
Assuming that "in an easterly direction" means that the displacement from O to P is in the positive direction, the position of point P can be expressed as +50 km.
What are the expressions of positive and negative numbers?Positive numbers are typically expressed with no sign or with a plus sign (+) in front of them. For example, +5 or 7. Negative numbers are expressed with a minus sign (-) in front of them. For example, -3 or -10.
These expressions are used to differentiate between values that are greater than zero (positive) and those that are less than zero (negative).
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if f(x) is the slope of a trail at a distance of x miles from the start of the trail, what does 9 7 f(x) dx represent? the elevation at x
The function f(x) is the sloping trail, it is the ratio of the change in the trail's height over the change in the trail's length.
It is the same as the rate of change of an evaluation of the trail, which is the derivative of a function that gives us the elevation. Thus, for a function F(x) that gives us the elevation, f(x)=F(x).
When we integrate a derivative, we can form a rate of change to total change. Thus integrating f(x) over an interval then the total change in elevation within that interval.
In this case, we will have to solve the integral:
[tex]\int\limits^9_7 {f(x)} \, dx[/tex]
The bounds of integration are 7 to 9, so this calculates the total change in elevation between 7 to 9, which is the total change in the elevation in the first seven miles of the trail.
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Describe the possible lengths of the third side of the triangle if the lengths of the other two sides are 6 meters and 9 meters.
The third side may be 6 or 9 metres long, or it may be between 9 and 15 miles long.
Depending on the lengths of the other two sides, the triangle's third side can have a variety of lengths. The third side's length could range from 9 to 15 metres if the first two sides are 6 and 9 miles, respectively. The reason for this is that the length of any two sides of a triangle must always be greater than the length of the third side; in this instance, the sum of the two sides is 15 metres, or 6 and 9 metres. As a result, the triangle's third side must be either less than or equal to 15 metres. A triangle can also have two equal sides, so the third side could also be equal to 6 or 9 metres. In conclusion, the third side of the triangle may be anywhere between 9 and 15 metres long, or it could be 6 or 9 metres long.
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rewrite this question without any fractions or decimals, ill give points if u help thx
Answer:
14x + 36 = 15
Step-by-step explanation:
To remove the fractions, multiply the entire equation by the LCM of 9 and 6.
LCM of 9 and 6 = 18
Multiply the entire equation by 18,
[tex]18*\dfrac{7}{9}x+*18*2=18*\dfrac{5}{6}[/tex]
2*7x + 36 = 3 *5
14x + 36 = 15
Let's consider what the question asks for:
--> equation without fractions:
To get rid of fractions, we must multiply a common multiple of 9 and 6 to get rid of the bottom denominator:
--> common multiple of 9 and 6: 54
Let's multiple:
[tex]\dfrac{7}{9}x+2=\dfrac{5}{6} \\\\54*(\dfrac{7}{9}x+2} )=54*\dfrac{5}{6} \\\\6*7x+108=9*5\\\\42x+108=45[/tex]
Answer: 42x + 108 = 45
Please help I’m so stuck
Answer:
(8x-7)<9
Use 1 to open the bracket
8x - 7 < 9
Add 7 to both sides
8x < 16
Divide both sides by 8
x < 2
Helpp
can you tell me how???
2 a) The letter A represents the value 0/3 on the number line.
2 b) The letter B represents the value 1/3 on the number line.
What is a number line?
A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
The number line is given.
The letter A represents the value of 0.
Find the value of 0/3.
Zero divided by anything yields the value 0.
Therefore, the value 0/3 is represented by letter A = 0.
Find the value of 1/3.
The decimal notation of fraction 1/3 is 0.33.
The value of 1/2 is 0.5.
This number should lie between 0 and 0.5.
Therefore, the value 1/3 is represented by letter B.
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2a) Which letter represents the better 0/3?
2b) Which letter represents the better 1/3?
Linear equation (graph)
need answer
A graph of the linear function with its points is shown in the image attached below.
How to complete the table?In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;
When the value of x = 0, the linear function is given by;
y - x = 4
y = x + 4
y = 0 + 4
y = 4
(x, y) = (0, 4).
When the value of x = 1, the linear function is given by;
y = x + 4
y = 1 + 4
y = 5
(x, y) = (1, 5).
When the value of x = 2, the linear function is given by;
y = x + 4
y = 2 + 4
y = 6
(x, y) = (2, 6).
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Kimberley's car can go 290 km on 21 L of gas. How far will her car go on 31 L of gas?
Answer:
428km
Step-by-step explanation:
21 L=290km
1 L=290/21
31 L=290/21×31=428km (to 3 s.f.)
solve the following systems of linear equations using substitution.
5x + y = -13 and -5x - 6y = -22
Answer:
x = -4, y = 7
Step-by-step explanation:
The two equations are:
5x + y = -13 ... (1)
-5x - 6y = -22 ...(2)
Isolate for x in (1)
5x + y = -13
5x = -13 -y
x = (-13-y)/5
Substitute this value of x into equation (1) -5x - 6y = -22
-5 · (-13-y)/5 -6y = -22
-1(-13-y) - 6y = -22
13 + y -6y = -22
y - 6y = -22 - 13
-5y = - 35
y = -35/-5 = 7
Substitute y = 7 in equation 1
5x + 7 = -13
5x = -13 - 7
5x = -20
x = 20/-5 = -4
Ans:
x = -4, y = 7
consider a standard deck of 52 cards. what is the probability of a card being black given it is a queen?
The probability of a card being black given it is a queen is P(A|B) = P(A ∩ B) / P(B) = (4/52) / (4/52) = 1. This means that if you draw a queen from a standard deck of 52 cards, it will be black with a probability of 100%.
The probability of a card being black given it is a queen can be determined using the formula P(A|B) = P(A ∩ B) / P(B). Where P(A) is the probability of a card being black and P(B) is the probability of a card being a queen.
To calculate this, we first need to calculate the probability of a card being a queen, which is 4/52 (there are 4 queens in a standard deck of 52 cards). The probability of a card being black is 26/52 (there are 26 black cards in a standard deck of 52 cards).
Using the formula, the probability of a card being black given it is a queen is P(A|B) = P(A ∩ B) / P(B) = (4/52) / (4/52) = 1. This means that if you draw a queen from a standard deck of 52 cards, it will be black with a probability of 100%.
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12 is no more of the product of a number w and 4
Answer:
Step-by-step explanation:
This statement is incorrect. 12 is a product of 3 and 4, or 12 = 3 * 4.
An automat machine make good pieces with a probability 0,96. Wich are the chances that the two piece is wrong?
To calculate the probability of getting two bad pieces in a row, we multiply the probabilities of each individual bad piece that is 0.96 and 0.04
0.04 * 0.04 = 0.0016
So the chances of getting two bad pieces are 0.0016, or 0.16%. This means that out of 100 tries, you would expect to get two bad pieces in a row 0.16 times.
It's vital to remember that independent events, like obtaining two terrible pieces, have probabilities that are determined by multiplying the individual possibilities.
This is based on the idea of the multiplication rule of probability, which states that the likelihood of two unrelated events occurring simultaneously is the sum of the probabilities of each event occurring separately.
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The cost, $C, of hiring a car for d days when on holiday is given by C = 20d + 50.
- Draw a graph of C against d for 0 ≤ d ≤ 7.
The graph of C against d for 0 ≤ d ≤ 7 is a straight line passing through (0, 50), (1, 70), ...
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given is an equation,
C = 20d + 50
We have to find the graph of the equation.
The points on the graph will be,
C(0) = 50
C(1) = 70
C(2) = 90
.........
The graph will be a straight line passing through (0, 50), (1, 70), (2, 90), ...
The graph is given below.
Hence the graph will be a straight line passing through (0, 50), (1, 70), ...
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Juliet's monthly entertainment expenses are $275.00 and account for 12% of her income. She would like to reduce her entertainment spending to 8% of her income.
The percentage of her income is 17.9%
What percent of her income is that amount?Percentage can be calculated by using the following rule:
Percentage = (fraction/total) x 100
Now, for this problem, the fraction of money used for expenses is 275$ while the total amount is 1536$
Substitute with these values in the above equation:
percentage = (275/1536) x 100 = 17.9%
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Correct question:
Juliet's budgets $275 each month for fixed expenses. What percent of her income is that amount if she nets $1536 each month?