Ue the factor Theorem to determine if
the given binomial i a factor of f(x)
f(x)=2x^3x^2-9x-6;x-1
By using factor theorem it is obtained that,
x - 1 is not a factor f(x) =[tex]2x^5-9x-6[/tex]
What is factor theorem?
At first, it is important to know about remainder theorem
Remainder theorem states that if f(x) is divided by (x - a), then the remainder is f(a)
If the remainder is zero, then f(a) is a factor of f(x)
Factor theorem states that if f(a) = 0, then (x - a) is a factor of f(x).
Here,
[tex]f(x)=2x^5-9x-6[/tex]
Divisor = x - 1
x - 1 = 0
x = 1
By remainder theorem,
Remainder = f(1)
f(1) =
[tex]2(1)^5 - 9(1) - 6\\2 - 9 -6\\-13[/tex]
Which is not equal to zero
x - 1 is not a factor f(x) [By factor theorem]
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Question 6
Write an equation in point-slope form for the line that passes through the given points.
(4,-6), (6,-4)
1) The USA Today claims that 44% of adults who access the Internet read the international news online. You want to check the accuracy of their claim by surveying a random sample of 120 adults who access the Internet and asking them if they read the international news online. Fifty-two adults responded "yes. " Use a 95% confidence interval to test the newspaper's claim
The accuracy of the USA Today claim about the access the internet read the international news online by adults is 0.089.
We have provided in question that,
adults who access the internet read the international news online is 44% i.e 0.44
this provides the interval ( .344, .522)
Using the estimation formula (E) or margin error
= Z-value √(p (1-p)/n
where, p --> Sample proportion of sucess
1-p = q ----> sample proportion of failure
n ---> sample size
Now, a random sample of 120 adults is considered for survay.
i.e., n= 120 and 52 adults out of 130 are responded "yes" for reading international news online.
so, p = 52/120 = 0.433 and 1-p = q = 1-0.433
= 0.567
Confidence interval to test the newspaper's claim is 95% . Thus, the Z-value for 95% confidence interval is 1.96..
putting the value in above formula we get,
E = 1.96 √0.433×0.567/120 = 1.96√0.2455/120
= 1.96√0.00204 = 1.96× 0.0452 = 0.0889 ~ 0.089
So, accuracy is 0.089 to support the claim of newspaper.
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Xavier earns $20 each time he walks someone's dog. He walks his neighbor's dog each day. He also earned an additional $10 for running with the dog one day.
Part B: Write an algebraic expression from your written description used in Part A. Let d stand for the number of days.
The numbers i am using is $20 and $10 so just use those numbers and do the rest please because i don't know.
The figure shows lines r, n, and p intersecting to form angles 1, 2, 3, 4, 5, and 6. All 3 lines lie in the same plane. Based on the figure, which of the individual statements would provide enough information to conclude that line r is perpendicular to line p ? Select all that apply. M∠4 + M∠5 = 60° M∠3 = M∠6 M∠6 = 90° M∠1 + M∠6 = 90° M∠5 + M∠4 = 90° M∠2 = 90°
The individual statements which would provide enough information to conclude that line r is perpendicular to line p are m∠3 = m∠6, m∠6 = 90°, and m∠5 + m∠4 = 90°. Option B, option C, and option E are correct.
First, let us understand the angle formed by intersecting lines:
The types of angles formed by intersecting lines are adjacent angles, vertical angles, etc.
We are given;
The figure shows lines r, n, and p intersecting to form angles 1, 2, 3, 4, 5, and 6.
All 3 lines lie in the same plane.
If line r is perpendicular to line p, then;
m∠1 + m∠2 = m∠5 + m∠4 = 90° (Vertical angles)
m∠3 = m∠6 = 90° (Vertical angles)
Thus, the individual statements which would provide enough information to conclude that line r is perpendicular to line p are m∠3 = m∠6, m∠6 = 90°, and m∠5 + m∠4 = 90°. Option B, option C, and option E are correct.
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-4(x-1)+6x=2(17-x) for X PLEASE HURRY
"-4(x-1)+6x=2(17-x)" for X
Exact Form: x= 15/2= 7-1/2
decimal form: X=7.5
Answer:
Step-by-step explanation:
1 ) multiply the number with the brackets (-4x -4 = 34 - 2x)
2) collect the like terms (-4x + 2x = 34 + 4)
3) -2x = 38
4) x = 38/-2
5) x = -19
A farmer determined the equation "y = -7/3x + 72.75" best fits his data when comparing the weight, y, in grams, of strawberries to the average daily mean temperature, x, in °F, each season. Which statement best describes the rate of change of the equation?
(Save me its mental abuse)
The rate of change, -7/3, in the equation means: the average weight of strawberry decrease by 7/3 grams at every 1°F increase in temperature.
How to Interpret the Rate of Change of an Equation?A linear equation is often expressed in the form of y = mx + b, which is the slope-intercept form, where the rate of change is the value of the variable "m" in the equation, and b is the starting or initial value.
Given the equation, y = -7/3x + 72.75, in slope-intercept form, where:
y = weight in grams of strawberries x = average daily mean temperatureTherefore:
-7/3 in the equation represents the rate of change.
72.75 represents the starting value or y-intercept.
The rate of change, -7/3, in the context of this situation as represented in the equation can be described as: 7/3 grams average weight that is decayed at every 1°F increase in temperature.
Therefore, the statement that best describes the rate of change is: There is 7/3 grams decrease in weight of the strawberry at every 1°F increase in temperature.
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Rochelle had 3/4 yard of twine each party favor requires 3/8 yard howmany party favors can Rochelle make
Rochelle can make 2 party favors with 3/4 yards of wine.
According to the question,
We have the following information:
Rochelle had 3/4 yard of wine. Each party favor requires 3/8 yard.
Now, we will find how many parts of a party can 1 yard of wine favor using division.
So, we have the following expression:
1 party = 3/8 yards
1 yard = 8/3 party
Now, Rochelle has 3/4 yards of wine in total. So, we can find the number of party favors using multiplication.
3/4 yards = (3/4)*8/3
3/4 yards = 2 parties
Hence, Rochelle can make 2 party favors with 3/4 yards of wine.
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A dealer sold 200 racquets. some were sold at rs 180 each and the rest at rs 330 each. the total receipts from these sales were rs 48000. how many racquests did the dealer sell at rs 180 each?
Answer:
120
Step-by-step explanation:
Number sold at rs180 = x
Number sold at rs330 = y
x + y = 200
180x + 330y = 48000
x = 200 - y
180(200 - y) + 330y = 48000
36000 - 180y + 330y = 48000
48000 - 36000 = 330y - 180y
12000 = 150y
12000/150 = y
y = 80
x = 200 - 80
x = 120
consider the following problem: a farmer with 750 ft of fenc- ing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. what is the largest possible total area of the four pens?
The largest possible total area of the four pens is 14,062.5 ft.²
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.
Diagrams illustrating the situation can be formed adjusting the width of the included diagram illustrating the general situation.
The expression for the total area is A=( 150- (2Y)/5 ) Y
Reasons:
The given parameter are;
Length of fencing available = 750 ft.
Area to be enclosed = Rectangular
Number of included pens with parallel fencing = Four
Let Y represent the width of the area and let X represent the breadth
Therefore, we have;
2·Y + 5·X = 750
Which gives;
X=(750/5)-(2Y/5)=150-(2Y/5)
The area is therefore;
A=Y [150-(2Y/5)] = 150Y-(2Y²/5)
Differentiate with respect to Y and equate to zero
dA/dY = 150- (4Y/5)=0
Y=(150*5)/4 = 187.5
The width of the maximum area, Y = 187.5 ft.
Which gives;
X=150- (2*187.5)/5 = 75
The breadth of the area, X = 75 ft.
The maximum area, = Y × X, which gives;
= 187.5 ft. × 75 ft. = 14,062.5 ft.²
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some times the lines "look" parallel or "look" non-parallel, therefore we cannot tell you by just looking at the lines of you are given the information that angle 4 measures 89 degrees and angle 3 measures 91 degrees, you would go ahead and say the lines are parallel.
A: true; this would be enough information to say that the lines are definitely parallel
False ; the lines are not parallel because angles 3 and 4 should be congruent
The sum of angles 3 and 4 is equal to 180 degrees, therefore: A: true; this would be enough information to say that the lines are definitely parallel.
How to Determine if Two Lines are Parallel?When two lines are intersected by a transversal, and the same-side interior angles are supplementary, that is are equal to 180 degrees, then we can state that the two lines are parallel to each other based on the converse of the same-side-interior angles theorem.
Given the following information:
Measure of angle 4 = 89°Measure of angle 3 = 91°Angle 4 and angle 3 are same-side-interior angles, thus:
89 + 91 = 180°
This means that, the sum of angle 4 and 3 are supplementary. Lines g and h are therefore parallel to each other.
In summary, our answer would be: A: true; this would be enough information to say that the lines are definitely parallel.
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Answer:
true
Step-by-step explanation:
An artist charges $980 for a portrait but gives 5% discount for cash. Calculate the cash Price of the portrait
Answer: $49
Step-by-step explanation: 5% of 980 = 0.05 × 980 = 49
Answer:
$931
Step-by-step explanation:
Discount = less money paid
100% - 5% = 95%
95% = 0.95
980 * 0.95 = 931
assuming that other factors are held constant, which of the following would tend to increase the likelihood of rejecting the null hypothesis? group of answer choices increase the sample variance decrease the sample size none of the other 3 options would increase the likelihood. increase the sample mean difference
Assuming that other factors are held constant, the sample means difference Increases. (option C)
The null hypothesis and the alternative hypothesis are the two types of hypotheses for a test.
Step 1: The null hypothesis is based on the assumption that there is no difference between the true mean (µ) and the compare value ([tex]m_{o}[/tex]). The alternative hypothesis is based on this assumption.
Step 2: Increasing the sample mean difference would probably make it more likely that the null hypothesis will be rejected, as long as other factors stay the same.
As a result, option C is the right one.
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(Complete question)
Assuming that other factors are held constant, which approach would tend to increase the likelihood of rejecting the null hypothesis?
a. Decrease the sample mean difference.
b. Increase the sample variance.
c. Increase the sample mean difference.
d. Decrease the sample size.
What is the slope of a line that is perpendicular to the line y=-3x
slope of a line that is perpendicular to the line y=-3x is 1/3
What is slope of line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.
y=-3x
tanθ=slope = y/x= -3
Slope(M) of this equation is -3
Let the slope of its perpendicular line is m
As we know that the product of the slopes of perpendicular lines is -1
so,
M*m =-1
-3 * m= -1
m=1/3
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True or false: The associative property is used on the following expression: 2 + 3 = 3 + 2.
if its false what is the answer
Answer: I believe this is True!
Step-by-step explanation:
I know what associative property and that seems like a example.
And if its false then answer should be false.
Try True, if not True then False!
1. an ecologist studying starfish populations collects the following data on randomly-selected 1-meter by 1-meter plots on a rocky coastline. --the number of starfish in the plot. --the total weight of starfish in the plot. --the percentage of area in the plot that is covered by barnacles (a popular food for starfish). --whether or not the plot is underwater midway between high and low tide. how many of these measurements can be treated as continuous random variables and how many as discrete random variables? a) three continuous, one discrete. b) two continuous, two discrete. c) one continuous, three discrete. d) two continuous, one discrete, and a fourth that cannot be treated as a random variable. e) one continuous, two discrete, and a fourth that cannot be treated as a random variable.
2 measurements can be treated as continuous random variables. 1 discrete random variable, and a fourth that cannot be treated as a random variable. (option d)
There are a few ways that a continuous random variable differs from a discrete variable: Due to the fact that it can contain an infinite number of values within a given interval, continuous random variables are typically uncountable. Measurements like height, weight, distance, and a plethora of other decimal values are examples of these variables. On the other hand, discrete random variables have values that can be counted, and the values of successive values are typically whole numbers.
In the above scenario, The number of starfish is a discrete variable, whereas the starfish's weight and percentage of the plot's area are continuous variables.
It is not a random variable whether the plot is in progress or halfway between high tide and low tide.
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Alexander Rothe ran the marathon in 1.2 X 10^5 seconds. Would it be more appropriate for the newspaper to say 1.2 x 10^5 seconds or would it be more appropriate to say 3 hours and 20 minutes?
10 points
1.2 x 10^5
3 hours and 20 minutes
Answer: 3 hours and 20 minutes
Step-by-step explanation:
The distribution of annual profit at a chain of stores was approximately normal with mean μ = $ 66 , 000 μ=$66,000mu, equals, dollar sign, 66, comma, 000 and standard deviation σ = $ 22 , 000 σ=$22,000sigma, equals, dollar sign, 22, comma, 000. The stores with profits in the top 5 % 5%5, percent each had a reward party for the employees to celebrate. What is closest to the minimum annual profit for a store that had a reward party?.
From the given mean and standard deviation the closest minimum annual profit, for a store that had a reward party is equal to $102,300.
As given in the question,
Given distribution of annual profit :
Approximately normal with mean μ = $66,000
Standard deviation σ = $22,000
Profits in the top 5 percent
Apply z-score formula :
z = ( x - μ) / σ
Top 5% mean 95% and more.
Using normal distribution table,
z -score corresponding to 95% or 0.95 is equal to 1.65.
Substitute all value in the formula we get,
1.65 = ( x - 66,000 ) / 22,000
⇒ x - 66,000 = 1.65 × 22,000
⇒ x = 36,300 + 66,000
⇒ x = 102,300
Therefore, from the given mean and standard deviation the closest minimum annual profit, for a store that had a reward party is equal to $102,300.
The complete question is :
The distribution of annual profit at a chain of stores was approximately normal with mean μ = $66,000, standard deviation σ = $22,000. The stores with profits in the top 5 percent each had a reward party for the employees to celebrate.
What is closest to the minimum annual profit for a store that had a reward party?
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the time it takes a woman to travel from her apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes. if she leaves home at 9:05 a.m., what is the probability that she will get to the station between 9:25 and 9:30 a.m.?
The probability that she will get the station between 9:25 and 9:30 is 1/2.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given: The time it takes a woman to travel from her apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes.
She leaves home at 9:05 a.m.
Let x be the random variable denoting that travel time of a women from apartment to bus stop.
Here x ≈ U (20, 30)
⇒ F(x) = (x - 20) / (30 - 20)
To find, she leaves home at 9:25 at reach bus stop at 9:25 to 9:30
⇔ P(20 < x < 25)
= (25 - 20) / (30 - 20)
= 5 / 20
= 1/2
Hence, the probability is 1/2.
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The area of the triangle below is 8.64 square inches. What is the length of the base?
Answer: The base is 4.8 sq inches.
Step-by-step explanation: The formula for a triangle is (B x H) x 1/2. Knowing this, we can double 8.64 to nullify the 1/2. This gives us 17.28. 17.28 divided by 3.6 gives us 4.8
Answer:
4.8
Step-by-step explanation:
The area of a triangle is half the base times the height.
[tex]0.5*b*3.6=8.64 \\ b = \frac{8.64}{0.5*3.6}[/tex]
Identify all values that make this equation true
x-3/x = -8/x+3
The values of x that makes the equation (x - 3)/x = - 8/(x + 3) true are x = - 9 and x = - 1.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The given equation is (x - 3)/x = - 8/(x + 3).
(x + 3)(x -3) = - 8x. (a² - b² = (a + b)(a - b))
x² - 9 = - 8x.
x² + 8x - 9 = 0.
x² + 9x - x - 9 = 0.
x(x + 9) - 1(x + 9) = 0.
(x + 9)(x + 1) = 0.
x + 9 = 0 Or x + 1 = 0.
x = - 9 Or x = - 1.
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A professor has 125 students in her classes at the beginning of the semester, but 16 students withdraw from her classes before Test #3. If she has 1 classes in total and each class has an equal number of students, how many students are in each class? Round your answer to the nearest ones (i.e., one student).
Answer:
Students in her classes At the beginning of the semester, but 13 students withdraw from her classes before Test three. So now she has 150 students. If she has one classes in total, in each class has an equal number of students. How many students are in each class round your answer to the nearest ones? Well, first of all, if she only has one class, then there's 150 students in that class is or class, this is the middle school math teacher signing out.
lazyuser30
The sum of 110 and a number
is five times that number
minus 10. What is the
number?
Answer: Let the number = x
5x+10 = 120
Or, 5x = 120 - 10
Or, 5x = 110
Or, x = 110/5
Or, x = 2
Step-by-step explanation:
Given the following formula, solve for a.
8 = a+b+c
O A.
a
OB. a
OC. a = s- bzc
OD.
28 b + c
-
28 b - c
-
a = s - btc
2
Answer:
a = -b - c + 8
Step-by-step explanation:
8 = a + b + c. Solve for a.
Subtract b from both sides
8 - b = a + c
Subtract c from both sides
8 - b - c = a
It is customary to rearrange so that the variable we solved for is on the left side
a = -b - c + 8
write a linear function f with f(5)=-1 and f(0)=-5
f(x)= ?
to get the equation of any straight line, we simply need two points off of it, let's use the provided ones
[tex]f(5)=-1\implies \underline{(\stackrel{x}{5}~~,~~\stackrel{y}{-1})}\hspace{5em}f(0)=-5\implies \underline{(\stackrel{x}{0}~~,~~\stackrel{y}{-5})} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{5}}} \implies \cfrac{-5 +1}{-5} \implies \cfrac{ -4 }{ -5 } \implies \cfrac{4 }{ 5 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{ \cfrac{4 }{ 5 }}(x-\stackrel{x_1}{5}) \implies y +1 = \cfrac{4 }{ 5 } ( x -5) \\\\\\ y-1=\cfrac{4 }{ 5 }x-4\implies {\Large \begin{array}{llll} y=\cfrac{4 }{ 5 }x-3 \end{array}}[/tex]
54 people can unload a ship in 5 hours. 54 people started unloading at 3pm. After 2 hours, 36 people had to leave. The remaining people kept working to finish unloading the ship. How many hours after 8pm did the remaining people each have to work?
Answer: 6 hours
to be honest i got 7 hours but i typed in 6 and it was correct so i cant really tell you how i got it right :/
[tex]-6=-3x^{2}-3x\\[/tex]
Your bank account has -$30, and you deposit $7 daily. How much money is your account after 5 days? Show you work with the Unit!
16 points
The amount in the account after the daily deposit for 5 days is $5
How to determine the amount in the account?The given parameters i the question are represented as follows
Initial balance = -$30
Daily deposit = $7
Number of days of deposit = 5
The equation that represents the amount in the account is represented as
Amount = Initial balance + Daily deposit * Number of days
Substitute the known values in the above equation So, we have the following equation
Amount = -30 + 7 * 5
Evaluate
Amount = 5
Hence, the amount is $5
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Tariq sold 2 kg, 4kg, 3 kg, and 4kg of almonds from Monday to
Thursday respectively. On Friday, he sold of the previous four days total
sold quantity.
a) How much almonds he sold on Friday?
b) How much almonds did he sell from Monday to Thursday?
Thi
a)
As per given information about selling of almonds from Monday to Thursday , answer of the following questions are as follow:
a. Amount of almonds sold on Friday as per given condition is equal to
13 kg.
b. Amount of almonds he sells from Monday to Thursday is equal to 13kg.
As given in the question,
Amount of almonds sold by Tariq from Monday to Thursday are as follow:
Monday = 2 kg
Tuesday = 4kg
Wednesday = 3 kg
Thursday = 4kg
a. Condition given:
Amount of almonds sold on Friday is equal to total sold quantity of previous four days that is Monday to Thursday
= (2 + 4 + 3 + 4) kg
= 13kg
b. Amount of almonds Tariq sell from Monday to Thursday is
= (2 + 4 + 3 + 4) kg
= 13kg
Therefore, as per given information about selling of almonds from Monday to Thursday , answer of the following questions are as follow:
a. Amount of almonds sold on Friday as per given condition is equal to
13 kg.
b. Amount of almonds he sells from Monday to Thursday is equal to 13kg.
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How do you find the Constant of Proportionality in a graph, table or in ordered pairs?
a.divide x by x
b.divide x by y
c.divide y by x
d.divide y by k
The constant of proportionality in a graph, table or ordered pairs is divide y by x
Ising a graph, the constant of proportionality is the constant value of the ratio obtained from two proportional quantities.
How to obtain a constant of proportionality?
The constant of proportionality is the slope of the graph of a straight line.
The slope of a graph of a straight line is determined by:
Slope = rise /run or increase in y/increase in x or decrease in y/decrease in x
In conclusion, rise in y/run in x determines the constant of proportionality.
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