1. Answer (a) Positive. The leading coefficient of the polynomial on the right is positive.
Answer (b) 3, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.
2. Answer (a) 2, Answer (b) 1
3. Answer (a) 3, Answer (b) 1 and 5
What is polynomial?A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can have constants and variables, and they usually have multiple terms that are separated by addition or subtraction.
1. The leading coefficient of a polynomial is the coefficient of the highest degree term. In the graph, the highest degree term is x3, and it is positive. Therefore, the leading coefficient of the polynomial on the right is positive.
The degree of a polynomial is the highest power of the variable in the equation. In the graph, the highest power of the variable is 3, so the minimum degree of the polynomial is 3.
2. The number of real zeros of a polynomial is the number of times the polynomial crosses the x-axis. In the graph, the polynomial crosses the x-axis twice, so it has 2 real zeros.
The number of imaginary zeros of a polynomial is the number of times the polynomial bounces off the x-axis. In the graph, the polynomial bounces off the x-axis once, so it has 1 imaginary zero.
3. The polynomial p(x) bounces off the x-axis at x=3 because the polynomial changes direction at this point.
The polynomial p(x) crosses the x-axis at x=1 and x=5 because the polynomial intersects the x-axis at these points.
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I need help on question 30 and 32.
Refer to the attached images.
What is the lowest common multiple of 8 and 12?
Answer:
2 hope that helps
Step-by-step explanation:
What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
cm³
Answer:
40 5/8
Step-by-step explanation:
6 1/2 × 2 1/2
13/2 × 5/2= 65/4
65/4 × 2 1/2
65/4 × 5/2 = 325/8
325/8= 40 5/8
Answer:
40 5/8
Step-by-step explanation:
6 1/2 × 2 1/2
13/2 × 5/2= 65/4
65/4 × 2 1/2
65/4 × 5/2 = 325/8
325/8= 40 5/8
Weathering and erosion are two processes that shape Earth’s surface. Which of the
following sets of factors cause both weathering and erosion?
a) acid rain, tree roots, waves
b) glaciers, waves, wind
c) moving water, plants, wind
d) acid rain, plants, ice
3. On a state math exam the scores were normally distributed with a mean of 72 and a standard deviation of 8. Use bell curve with standard deviations to help you complete the problem.
b. What percentage of students will score less than 72?
C. What percentage of students will score above 80?
The mean is 72, which is the center of the distribution, 50% of the students will score less than 72. The area to the right of z = 1, so approximately 15.87% of students will score above 80.
a) Since the mean is 72, and we want to know the percentage of students who scored less than 72, we need to find the area under the normal distribution curve to the left of the z-score that corresponds to 72. Since the standard deviation is 8, the z-score is:
z = (72 - 72) / 8 = 0
Using a standard normal distribution table or a calculator, we can find that the area to the left of z = 0 is 0.5. Therefore, 50% of students scored less than 72.
b) To find the percentage of students who scored above 80, we need to find the area under the normal distribution curve to the right of the z-score that corresponds to 80. The z-score is:
z = (80 - 72) / 8 = 1
Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 1 is 0.1587. Therefore, approximately 15.87% of students scored above 80.
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A bag has 2 blue cubes, 3 red cubes, and 5 green cubes. If you draw a cube and replace it in the bag 100 times, which of the following amounts would you expect to pull? Select all that apply. A) Pull more than 2 times as many green cubes as blue cubes B) Pull a green cube 50 times C) Pull a blue cube 20 times D) Pull more red cubes than green cubes E) Pull a blue cube 70 times
Pull a green cube 50 times; Pull a blue cube 70 times. The possible options are B and E.
Describe Probability?Probability refers to the likelihood or chance of an event occurring, expressed as a number between 0 and 1.
A probability of 0 indicates that an event is impossible, while a probability of 1 indicates that an event is certain to occur. For example, the probability of rolling a 7 on a fair six-sided die is 0, while the probability of rolling a 1, 2, 3, 4, 5, or 6 is 1/6.
Probabilities can also be expressed as percentages, with a probability of 0.5 (or 50%) indicating an even chance of an event occurring.
A) Pull more than 2 times as many green cubes as blue cubes:
Since there are only 2 blue cubes in the bag and 5 green cubes, it is highly unlikely that you would pull more than 2 times as many green cubes as blue cubes in 100 draws. Therefore, this option is unlikely.
B) Pull a green cube 50 times:
There are 5 green cubes in the bag, so it is possible to pull a green cube 50 times in 100 draws. Therefore, this option is possible.
C) Pull a blue cube 20 times:
There are only 2 blue cubes in the bag, so it is unlikely that you would pull a blue cube 20 times in 100 draws. Therefore, this option is unlikely.
D) Pull more red cubes than green cubes:
There are 3 red cubes and 5 green cubes in the bag, so it is possible to pull more red cubes than green cubes in 100 draws. Therefore, this option is possible.
E) Pull a blue cube 70 times:
Since there are only 2 blue cubes in the bag and you are drawing with replacement, it is highly unlikely that you would pull a blue cube 70 times in 100 draws. Therefore, this option is unlikely.
Therefore, options B and D are possible.
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9. The price of a Delta Air Lines ticket from New York to Orlando increased to $450. This is an 8% increase. What was the old fare to nearest cent?
Answer:
$416.66
Step-by-step explanation:
We take
450 divided by 108, then time 100 = $416.66
So, the old fare is $416.66
Simplificacion de 18/25
Answer:
Step-by-step explanation:
Ici, nous allons réduire la fraction 18/25 aux termes les plus bas et la convertir en un nombre fractionnaire, si nécessaire.
Dans la fraction 18/25, 18 est le numérateur et 25 est le dénominateur.
On commence par trouver le plus grand diviseur commun de 18 et 25, qui est 1. Ensuite, on divise 18 et 25 par le plus grand diviseur commun pour obtenir la plus petite expression, écrite comme suit :
(18 ÷ 1) / (25 ÷ 1)
= 18/25
Which of the following equations will reduce the graph shown below
The equation y = -1/2(x-3)² + 5 reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.
What is graph?In mathematics, a graph is a visual representation of a set of objects (called vertices or nodes) and the connections (called edges) between them.
The equation y = -1/2(x-3)² + 5 is a quadratic function in vertex form. The vertex of this parabola is at the point (3, 5), and the coefficient of the x² term is negative (-1/2), which tells us that the parabola opens downwards. This means that the graph of this equation reduces.
To see why this is the case, consider the behavior of the y-values as x moves away from the vertex. Since the leading coefficient is negative, the y-values will decrease as x moves to the left or right from the vertex. Additionally, the squared term inside the parentheses means that the graph will be symmetric around the x-coordinate of the vertex, which is 3 in this case.
Thus, as x moves away from the vertex to the left or right, the y-values decrease in a symmetric manner, resulting in a graph that reduces. This can be seen in the shape of the parabola as it curves downwards from the vertex.
Therefore, the equation y = -1/2(x-3)² + 5 reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.
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The list below represents the number of novels written
by each of Amir's 10 favorite authors.
1 3 3 4 5 7 8 10 12 23
What is the interquartile range of the number of novels
written by each of Amir's 10 favorite authors?
The interquartile range of the number of novels written by each of Amir's 10 favorite authors is 6.
What is the interquartile range ?
In statistics, the interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. Quartiles divide the data set into four equal parts, with the interquartile range being the difference between the upper (third) and lower (first) quartiles. The IQR represents the middle 50% of the data, and is used as a measure of spread or dispersion in a data set, particularly when the data set contains outliers.
To find the interquartile range (IQR), we need to first find the first quartile (Q1) and the third quartile (Q3).
To find Q1:
Arrange the data in order from smallest to largest: 1 3 3 4 5 7 8 10 12 23
Find the median of the lower half of the data (the first five numbers): (3+3)/2 = 3
This is the first quartile (Q1)
To find Q3:
Arrange the data in order from smallest to largest: 1 3 3 4 5 7 8 10 12 23
Find the median of the upper half of the data (the last five numbers): (8+10)/2 = 9
This is the third quartile (Q3)
Now we can calculate the IQR:
IQR = Q3 - Q1 = 9 - 3 = 6
Therefore, the interquartile range of the number of novels written by each of Amir's 10 favorite authors is 6.
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100 POINTS + BRAINLIEST!!
Answer:
(2x)(4x)= 8x^22x + 4x = 6x(x+1)+ 2x = 3x + 1(x+1)(2x) = 2x^2 + 2x3x + (2x) = 5x(3x)(2x) = 6x^2
Step-by-step explanation:
hope this helped
Find the mean of the data set. 3, 22, 0, 15, 9, 23
Answer:
12
Step-by-step explanation:
Mean = 3+22+0+15+9+23=72
72÷6 =12
Lyla invests $2,500 into a savings account
which earns 5% per year. In 15 years, how
much will Lyla's investment be worth if interest
is compounded semiannually (twice a year)?
Round to the nearest dollar.
Answer:
We can use the formula for compound interest to find the future value of Lyla's investment:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal (initial investment), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.
Substituting the given values, we get:
A = $2,500(1 + 0.05/2)^(2*15)
Simplifying, we get:
A = $2,500(1.025)^30
Using a calculator, we get:
A ≈ $5,016.35
Therefore, Lyla's investment will be worth approximately $5,016.35 in 15 years if interest is compounded semiannually. Rounded to the nearest dollar, the answer is $5,016.
how far is sam from the top of a temple?
The distance between Sam from the top of the temple is 56. 6 feet
How to determine the distanceTo determine the distance, we need to know that trigonometric identities are mathematical identities that is mostly used to prove that all the values of the functions of trigonometry are true.
The types of trigonometric identities are;
tangentsinecosinecotangentcosecantsecantFrom the information given, we can deduce that;
The angle of elevation, θ = 62 degrees
The opposite side of the angle that is the height of the temple is 50 feet
The distance is the hypotenuse side
Then, using sine identity, we have;
sin 62 = 50/d
d = 50/0. 8829
d = 56. 6 feet
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the absolute value functions with their vertices.
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f(x)= |x-51+
f(x) = -2|2|-
-
f(x)= |x-1| +4
f(x)=x+11-4
Vertex
(-1,-4)
(5, 1)
(0, -1)
(2, 4)
f(x) = |z|-
f(2)=|z-|+{
Absolute Value Function
Answer:
[tex]\boxed {\left(-1, -\dfrac{3}{7}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{1}{2}\left|x\:+\:1\right|-\frac{3}{7}}[/tex]
[tex]\boxed{\left(5,\:\frac{2}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\:\frac{3}{5}\left|x\:-\:5\right|+\:\frac{2}{3}}[/tex]
[tex]\boxed{\left(0,\:-\frac{4}{5}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{1}{2}\left|x\right|\:-\:\frac{4}{5}}[/tex]
[tex]\boxed{\left(\frac{2}{5},\:\frac{5}{3}\right)} \longrightarrow \boxed{f\left(x\right)\:=\frac{3}{2}\left|x-\frac{2}{5}\right|+\frac{5}{3}}[/tex]
Step-by-step explanation:
The vertex of an absolute function
y = f(x) = a|x - b| + c occurs at x - b = 0 or when x = b
Plugging this into the original equation will give the value for f(b) which will be f(b) = 0 + c which will be the y-value of the vertex
[tex]\text{Vertex of } f(x) = \dfrac{3}{5} |x - 5| + \dfrac{2}{3}\\\\ \longrightarrow x = 5, y = \dfrac{2}{3} \\\\\longrightarrow \left(5, \dfrac{2}{3} \right)[/tex]
You can do the others in a similar manner.
Here it is easier because the constant in f(x) corresponds to the y-coordinate of the vertex and they are different in the answer choices
The volume of a cuboid is 630cm3.
The length is 14cm and the width is 90mm.
Whatt is the height of the cuboid in cm.
Answer:
Height = 630 / (14 x 0.9) = 47.5 cm
The equation P=7h gives the amount of pay (P) you earn for working h hours. Identify the independent and dependent variables. How my do you earn after 8 hours of work?
Earn 56 units of currency after 8 hours of work.
What is independent variable?
The independent variable is the variable that you change and control in your experiment.
The independent variable is the number of hours worked, h. The dependent variable is the amount of pay earned, P.
To find how much you earn after 8 hours of work, we can simply substitute h = 8 into the equation and evaluate:
P = 7h
P = 7(8)
P = 56
So you would earn 56 units of currency after 8 hours of work.
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Lamonte was driving down a road and after 4 hours he had traveled 62 miles. At this speed, how many hours would it take Lamonte to drive 93 miles?
The time taken by the Lamonte would be 6 hours to drive 93 miles at a speed of 15.5 miles per hour.
How to calculate the time ?We can use the following formula to answer this question:
rate x time = distance
We know Lamonte drove 62 miles in four hours, so we can use that to calculate his speed:
62 miles = rate multiplied by 4 hours
When we solve for the rate, we get:
rate = 62 miles divided by 4 hours equals 15.5 miles per hour
We can now use this rate to calculate how long it would take Lamonte to drive 93 miles:
93 miles = time x rate
Substituting the recently discovered rate yields:
93 miles = 15.5 miles per hour multiplied by time
When we solve for time, we get:
time = 93 miles / 15.5 miles per hour = 6 hours
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20 POINTS ANSWER FOR BRAINLIST
Multiply. Final answer needs to be in Standard
Form. Two different methods need to be shown.
You can choose between Area Model, Distributive
Property and FOIL.
(3x − 4)(2x − 1)
Answer:
Method 1: Distributive Property
To multiply (3x - 4) and (2x - 1), we can use the distributive property:
(3x - 4)(2x - 1) = 3x(2x) + 3x(-1) - 4(2x) - 4(-1)
= 6x^2 - 3x - 8x + 4
= 6x^2 - 11x + 4
Therefore, the final answer in standard form is 6x^2 - 11x + 4.
Method 2: FOIL
To multiply (3x - 4) and (2x - 1), we can use the FOIL method:
(3x - 4)(2x - 1) = 3x(2x) + 3x(-1) - 4(2x) - 4(-1)
= 6x^2 - 3x - 8x + 4
= 6x^2 - 11x + 4
Therefore, the final answer in standard form is 6x^2 - 11x + 4.
the unit rate for this relationship is 1 gallon per 18.25 minutes
The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.
So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:
(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons
Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be approximately 6.58 gallons.
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The complete question is :
What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?
Roselli's Machine Manufacturing Co reported its sales as R120 000, a gross profit of R50 000, and current liabilities of R25 000. If the current ratio is 2,5 and the quick ratio is 1,75, what is the inventory turnover for the company?
Answer:
Step-by-step explanation:
To find the inventory turnover for Roselli's Machine Manufacturing Co, we need to use the formula:
Inventory turnover = Cost of goods sold / Average inventory
First, we need to find the cost of goods sold (COGS):
COGS = Sales - Gross profit
COGS = R120 000 - R50 000
COGS = R70 000
Next, we need to find the average inventory. We can use the quick ratio formula to find the current assets:
Quick ratio = (Current assets - Inventory) / Current liabilities
Rearranging the formula to solve for inventory, we get:
Inventory = Current assets - (Quick ratio x Current liabilities)
Plugging in the values we know, we get:
1.75 = (Current assets - Inventory) / R25 000
Current assets - Inventory = 1.75 x R25 000
Current assets - Inventory = R43 750
Inventory = Current assets - R43 750
Since the current ratio is 2.5, we know that:
Current assets / Current liabilities = 2.5
Solving for current assets, we get:
Current assets = 2.5 x R25 000
Current assets = R62 500
Substituting the values we found for inventory and COGS into the inventory turnover formula, we get:
Inventory turnover = COGS / Average inventory
Inventory turnover = R70 000 / [(R62 500 - R43 750) / 2]
Inventory turnover = R70 000 / (R18 750 / 2)
Inventory turnover = R70 000 / R9 375
Inventory turnover = 7.47
Therefore, the inventory turnover for Roselli's Machine Manufacturing Co is 7.47.
Natasha worked for part of the year before receiving a raise in her hourly rate of pay. The graph below shows the amount of money she has made this year and the hours she has worked since she received the raise. What was the initial amount of money Natasha made?
Answer:
Unfortunately, I cannot see the graph you are referring to since we are communicating through text. However, based on the information given, we can make some general observations.
We know that Natasha received a raise in her hourly rate of pay at some point during the year. Before the raise, she earned some initial hourly rate of pay. Let's call this initial rate of pay "x". Let's also assume that she worked for "h" hours before receiving the raise, and "k" hours after receiving the raise.
We can write an equation to represent the total amount of money she made this year:
Total amount of money = (initial hourly rate of pay x number of hours worked at the initial rate) + (new hourly rate of pay x number of hours worked at the new rate)
Using the variables we defined earlier, we can write:
Total amount of money = (x × h) + ((x + y) × k)
where y is the increase in her hourly rate of pay after the raise.
We also know that she earned a certain amount of money before the raise. Let's call this amount "M". This means that:
M = x × h
Solving for x, we get:
x = M/h
Substituting this expression for x into the first equation, we get:
Total amount of money = (M + yh) + ((M/h + y) × k)
We don't know the values of M, y, h, or k, so we cannot determine the initial hourly rate of pay x or the total amount of money Natasha made this year. However, we have set up an equation that can be used to solve for these values if we have more information.
Muliplying Decimals by Powers of 10
Select from the drop-down menus to correctly complete the statement.
The product of 0.014 and 100,000 is Choose
the right.
because the decimal point in 0.014 moves Choose places to
V
The required of 0.014 and 100,000 product is 1400.
What is Product?The object being sold is referred to as a product. A service or an object both qualify as products. It could take on a physical, virtual, or cyber shape. Every product has an expense associated with it, and each one has a price. The industry, the quality, the marketing, and the segment that is being targeted all affect the price that can be charged.
According to question:
We have to numbers
0.014 and 100000
Then;
0.014( 100000)
= 1400
Thus, required product is 1400.
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I need help solving this
The correct answer is sixteen (16).
A hiker hikes at a steady rate throughout the day on a mountain. Which student wrotr a correct equation to represent the linear relationship shown on the table between X, the number of hours hiked and y, the current altitude of the climber?
There is no table provided to reference, but the equation that represents a linear relationship between X and Y is:
y = mx + b
where m is the slope of the line and b is the y-intercept. The equation can also be written as:
y = b + mx
where b is the y-intercept and m is the slope. The equation represents a straight line on a graph, where the slope determines the steepness of the line, and the y-intercept is the point where the line crosses the y-axis. To write the equation for the table of X and Y values, we need to determine the slope and y-intercept from the given data.
What is the area of this trapezoid?
Answer:
8*7=56 + 8*3=24 = 80_squared
Step-by-step explanation:
Which of the following sets of numbers could not represent the three sides of
a triangle?
{14, 24, 37}
{15, 30, 43}
{9, 21, 32}
{10, 19, 26}
The triangle that would not represent the three sides of a triangles is: {9, 21, 32}
How do determine this triangleWe can determine this through the use of the triangle rule. The rule tells us that the sum of the two sides of the triangle have to be greater than that of the other side.
With this in mind, we have that for each of this
14 + 24 > 37
15 + 30 > 43
9 + 21 < 32
10 + 19 > 26
Hence the third option does not fulfill the rule
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component of optimi
1. Jaden wanted to begin a career in marketing. He had his heart set on a marketing program at a
private university. However, the private university did not admit Jaden to the school. After finding
out he was not accepted, Jaden chose to apply to a nearby state school that also had a highly rated
marketing program. Jaden is now a marketing manager.
Answer:
you need to learn yo stuff
Step-by-step explanation:
bye
4. The fence around a circular pool is 75 ft long.
Diameter:0ft
Radius:0ft
Is it radius diameter or circumference
The resultant values are as follows:
Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft
What is the circumference?The circumference of a circle or ellipse in geometry is its perimeter.
That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.
The curve length around any closed figure is more often referred to as the perimeter.
The length of a circle's outline is referred to as its circumference, and the length of a form with straight sides is referred to as its perimeter.
So, since the fence around the circular pool is given, then it will also be the value of the circumference of the pool.
Circumference = 75 ft
Radius:
2πr = 75
r = 75/2π = 75/(2×3.14) ≈ 11.937
radius = 11.94 ft
Diameter:
2r = 2×11 ≈ 23.87 ft
Therefore, the resultant values are as follows:
Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft
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Complete question:
The fence around a circular pool is 75 ft long. Find: Radius, Diameter, and Circumference.
A car salesman was able to sell a car for 12,500, earning a commission of 5%. How much was his commission.
Answer:
12,500 is 100%, or 1 in decimal terms. We calculate 5% by multiplying 12500 by 0.05.
This gives us a total of £625
Step-by-step explanation:
Brainliest pls