Cumulative Exam
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The polynomial function f(x) is a fourth degree polynomial. Which of the following could be the complete list of the
roots of f(x)?
3.4.5.6
3, 4, 5, 6
3.4.4+/6, 5+ √6
Answers
Answer:
the answer is 3,4,5,6
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The polynomial function is solved and the roots are = 3 , 4 , 5 and 6
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the polynomial equation be represented as A
Now , the value of A is
A = a fourth degree polynomial can have at most four roots.
Therefore, the first option with five roots is not possible. The third option has two roots that are not integers, which is also not possible since the question asks for a complete list of the roots.
Hence , the number of roots = 4 which is { 3 , 4 , 5 , 6 }
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Related Questions
what is the slope of the line that passes thru (7,-6) and (6,-6)
Answers
The slope of the straight line passing through the two given points is undefined which means the line is parallel to the y-axis.
Let us consider the two points A(x₁,y₁) and B(x₂,y₂) be the two points (7,-6) and (6,-6) on the cartesian coordinates.
Let the slope of the line joining A (7,-6) and B(6,-6) be m.
We know that the slope of a line is given by:
\(m=\frac{y_2-y_1}{x_2-x_1}\)
Slope of the line
= (6-7) / (-6+6)
= -1 / 0
= undefined
Since the slope is undefined we can say that the straight line is parallel to the y axis.
we know that tan 90° = ∞
So any line parallel to this line will have the same slope as the y axis.
Hence the slope of the given line is undefined or infinity.
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Find two numbers which have a sum of 132 and that can be written as the simplified
ratio 3:8
Answers
Answer:
96 and 36
Step-by-step explanation:
3+8 = 11
132/11 = 12
so:
12 x 3 = 36
12 x 8 = 96
A manufacturer produces soda cans and a quality control worker randomly selects two cans from the assembly line for testing. Past statistics show that 12% of the cans are defective. What is the probability that the two selected cans are defective if the quality control worker selects the two cans from a batch of 50 cans?
Answers
Answer:
6 cans will be defective
Step-by-step explanation:
do 50x0.12
A certain lottery has 28 numbers. In how many different ways can 5 of the numbers be selected? (Assume that order of selection is not important.)
Answers
After answering the provided question, we can conclude that As a result, expression there are 98,280 different ways to choose 5 numbers from a set of 28 where order is irrelevant.
what is expression ?An expression in mathematics is a collection of characterizations, digits, and huge corporations that resemble a significant correlation or regimen. A real number, a flexible, or a combination of the two can be used as an expression. Mathematical operators include addition, multiplication and division, rapid spread, separation, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
The combination formula gives the number of ways to choose 5 numbers from a set of 28 where order is irrelevant:
(k!(n-k)!) = nCk
where n represents the total number of items in the set (28 in this case), and k represents the number of items to be chosen (5 in this case).
When we plug in the values, we get:
\(28C5 28!/(5!(285)!) (28x27x26x25x24)/(5x4x3x2x1) = 98, 280\)
As a result, there are 98,280 different ways to choose 5 numbers from a set of 28 where order is irrelevant.
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The complete question is
: A certain lottery has 26 numbers.
In how many different ways can 5 of the numbers be selcted?
(assume that order of selection is not important)
26! 26x25x24x23x22x21
____ -----------------= 1,578,720
(26-5)!5! 105
Hi, can you help me answer this question please, thank you!
Answers
SOLUTION
3To calculate the test statistics, we use the following steps:
Step 1: We write out the parameters
\(\begin{gathered} sample\text{ mean (}\bar{\text{x}}\text{)}=0.9 \\ \text{standard deviation(s)=}0.58 \\ \operatorname{mean}(\mu)=0.8 \\ n=32 \end{gathered}\)Step 2: Write out the formula for the test statistics (t)
\(t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt[]{n}}}\)step 3: Find t
\(\begin{gathered} t=\frac{0.9-0.8}{\frac{0.58}{\sqrt[]{32}}} \\ t=\frac{0.1}{0.1025} \\ t=0.97532 \\ t\approx0.98 \end{gathered}\)Hence, the test statistic is approximately 0.98 to two decimal places.
The square below has 9X. Find the area of the square remaining after a circle of radius is 6X is removed from the square in other words find the area of the shaded region in factored form 
Answers
The area of the shaded region in factored form is 9x^2(9 - 4π)
How to find the area of the shaded region in factored formFrom the question, we have the following parameters that can be used in our computation:
Square length = 9x
Radius of circle = 6x
The area of the square is given by (side length)^2.
Since the square has 9x as a side length, its area is:
Area 1 = (9x)^2 = 81x^2
For the circle, we have
Area 2 = π(6x)^2
Area 2 = 36πx^2
The area of the shaded region is the area of the original square minus the area of the circle, which is:
Shaded = 81x^2 - 36πx^2
Factorize
Shaded = 9x^2(9 - 4π)
Hence, the area is 9x^2(9 - 4π)
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PLEASEEEE HELPPPP IM BEING TIMED WILL GIVE BRAINLIEST AND POINTS
Choose the correct classification of 5x + 3x4 − 7x3. (5 points)
Third degree polynomial
Fourth degree trinomial
Sixth degree polynomial
First degree binomial
Answers
Answer:
fourth degree trinomial
Step-by-step explanation:
fourth degree trinomial
Pairs of shorts had a mark_up of 17%which includes profit and GST at a price of k29. 25.Find the cost price.
Answers
The cost price of the shorts is K22.50.
To find the cost price of the shorts, we need to reverse calculate the original price before the markup and taxes were applied.
Let's assume the cost price of the shorts is represented by C.
The markup of 17% is applied to the cost price, which means the selling price (including the markup) is 117% of the cost price.
117% of the cost price C can be calculated as (117/100) * C.
GST (Goods and Services Tax) is also included in the selling price. GST is typically calculated as a percentage of the selling price. In this case, the selling price of the shorts including GST is K29.25.
Since the GST is included in the selling price, we can subtract it from the selling price to obtain the selling price before GST.
Let's assume the GST rate is R% (as a decimal), then the selling price before GST can be calculated as:
Selling price before GST = Selling price - (Selling price × R)
In this case, the selling price before GST is K29.25, and the GST rate is 17% (0.17 as a decimal). Substituting these values into the equation, we have:
K29.25 = Selling price - (Selling price × 0.17)
Simplifying the equation
K29.25 = Selling price × (1 - 0.17)
K29.25 = Selling price × 0.83
Selling price = K29.25 / 0.83
Now we can substitute the selling price in terms of the cost price:
K29.25 / 0.83 = (117/100) × C
Simplifying the equation:
C = (K29.25 / 0.83) × (100/117)
Calculating the cost price C:
C = K22.50
Therefore, the cost price of the shorts is K22.50.
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eon checked a book out of the library, but forgot to return it and owes
1.50 in fines. If a book is 1 day overdue, the fine is 10 cents, 2 days
verdue, 20 cents, 3 days overdue, 30 cents, and so on. How many days
verdue is Keon's book?
Answers
Answer:
15 days
Step-by-step explanation:
It seems that the fines are 10x cents for every x days overdue. Therefore, 10x = 150 (150 because $1.50 is 150 cents) so x = 15 days.
write an equation in slope intercept form that passes through the given point and is perpendicular to the graph of given equation (1,-2) y=5x+4
Answers
The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.
To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.
The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.
To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.
The negative reciprocal of 5 is -1/5.
Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Substituting the values:
y - (-2) = (-1/5)(x - 1)
Simplifying:
y + 2 = (-1/5)(x - 1)
To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:
y + 2 = (-1/5)x + 1/5
Subtracting 2 from both sides:
y = (-1/5)x + 1/5 - 2
Combining the constants:
y = (-1/5)x - 9/5
Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.
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A direct mail appeal for contributions from a university’s alumni and supporters is considered to be too costly if less than 28%
28
%
of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 165
165
people on the alumni and supporters mailing lists. They receive monetary contributions from 36
36
people. Does this evidence demonstrate that the direct mail campaign is not cost effective? Use a 0.05
0.05
level of significance.
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
Answers
The test statistic is given as follows:
z = -1.77.
As the test statistic is less than the critical value for the left-tailed test, this evidence demonstrates that the direct mail campaign is not cost effective.
How to obtain the test statistic?
The equation for the test statistic is given as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
In which:
\(\overline{p}\) is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The parameters for this problem are given as follows:
\(p = 0.28, n = 165, \overline{p} = 0.2182\)
The critical value for a left tailed test with a significance value of 0.05 is given as follows:
z = -1.645.
The test statistic is then given as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
\(z = \frac{0.2182 - 0.28}{\sqrt{\frac{0.28(0.72))}{165}}}\)
z = -1.77.
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of Hypothesis Testing
Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1079 adults, 86% said that they have a cell phone. Find the value of the test statistic.
The value of the test statistic is.
Answers
If the sample test exists 1079 then the value of the test statistics exists -7.88.
What is meant by test statistic?A statistical test's result, or test statistic, is a numerical value. It describes how distant the observed data is from the null hypothesis, which states that there is no link between the variables or distinction between the sample groups.
The test statistic indicates how dissimilar two or more groups are from the population mean as a whole or how different a linear slope is from the slope implied by the null hypothesis. Various statistical tests employ various test statistics.
Given:
Sample size, n = 1079
Probability of success, p = 0 . 86
The hypotheses are:
\(&H_0\) : p = 0.94
\(&H_a\) : p < 0.94
where:
\($\hat{p}\) = proportion of the sample
p = proportion of the population
n = sample size
The values of the variables exists:
\(&\hat{p}\) = 86 % = 0.86
p = 94 % = 0.94
n = 1074
Substitute the values into the formula and solve for the test statistics:
\($z &=\frac{0.86-0.94}{\sqrt{\frac{0.93(1-0.94)}{1079}}} \\\)
simplifying the above equation, we get
\($z=\frac{-0.08}{\sqrt{\frac{0.93(1-0.94)}{1079}}}$\)
z = -11.12457
Therefore, the value of the test statistics is -7.88.
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Fine the slope of the line that passes through the given point (-1,9) and (2,8)
Answers
Step-by-step explanation:
please mark me as brainlest
in a recent year, 34.1% of all registered doctors were female. If there were 56,600 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number.
Answers
324309
doctors were registered that year.
Explanation:
The questions says, "18.1% of all registered doctors are females"
(Consider, total number of registered doctors as
x
)
that's,
18.1
%
of
x
are female.
and
18.1
%
of
x
is
58
,
700
.
Mathematically,
18.1
100
⋅
x
=
58700
x
=
58700
⋅
100
18.1
x
=
324309
doctors were registered that year.
Buddy and Michael get into a
snow fight with some boys on the
way home from school. It seems
as though Buddy can throw 4
times as many snowballs as the
boys can. If Buddy throws 1200
snowballs, how many did the boys
throw? Write an equation and
solve.
Answers
Answer:
1500
Step-by-step explanation:
1200/4=300
1200+300=1500
Answer:
This means the boys throw 300 snowballs while Buddy throws 1200 snowballs
Step-by-step explanation:
Equations
Let's call
x = number of snowballs the other boys throw.
4x = number of snowballs Buddy throws.
We know Buddy throws 1200 snowballs, thus
4x = 1200
Divide by 4:
x = 1200/4
x = 300
This means the boys throw 300 snowballs while Buddy throws 1200 snowballs
PLEASE HELP ASAP
Add.
7215+523+91315
Answers
Answer:
99,053
Step-by-step explanation:
It seems that recently something invented which called the calculator I'm gonna use it to answer ur question dude.
There u go have a great day ❤
PLEASE HELP I WILL MAKE YOU BRAINLIEST IF IT LETS ME
NO FAKE LINKS OR YOU WILL BE REPORTED
Answers
Answer:
The top left graph
Step-by-step explanation:
All the others are wrong
Answer:
the first one (top left)
go over however many numbers on the left side of the coordinate and up whatever is on the right its always x first y second
Step-by-step explanation:
HELP!!!! Write an exponential function to describe the given sequence of numbers.
Answers
Answer:
y = 5^(x+1)
Step-by-step explanation:
y = 5^(x+1)
x = 1 for the initial step
A bakery did a survey among 100 customers to
find their food preferences. The customers were asked about their preferences for cupcakes
or brownies. Out of the total 72 people who liked cupcakes, 37 also liked brownies. There were 59 people who liked brownies.
Part A: Summarize the data by writing the values that the letters A to l in the table below represent.
Part B: What percentage of the survey respondents did not like either cupcakes or brownies?
Part C: Do the survey results reveal a greater dislike for brownies or cupcakes? Justify your answer.
Answers
Answer:
Answer:
put 37, 22,59,35,6,41,72,28,100 in chart < That is for the ppl who cant click on the brainly site but it still shows alitttle
For the ppl who can click on brainly:
Part A:
Like Cupcakes
Do Not Like Cupcakes
Total
Like Brownies
37
22
59
Do Not Like Brownies
35
6
41
Total
72
28
100
Part b: 6
Part c: You really have to figure out how to word this 37- 72=35 35-41=6
hope it helps
Which number has exactly 3 factors?
2-4-6-8
Answers
Answer:
4
Step-by-step explanation:
the factors are 1,2,4
Factors:
2 - 1,2
4 - 1,2,4
6 - 1,2,3,6
8 - 1,2,4,8
A line goes through the points (4, 5) and (2, -6). Write the equation of the line in slope- intercept form. Did I get the correct answer? Y= 11/2x - 17
Answers
Given:
A line passing through the points (4,5) and (2,-6).
The objective is to find the equation of line in slope-intercept form.
Explanation:
Consider the given points as
\(\begin{gathered} (x_1,y_1)=(4,5) \\ (x_2,y_2)=(2,-6) \end{gathered}\)The slope of the line can be calculated as,
\(m=\frac{y_2-y_1}{x_2-x_1}\text{ . . . . . . .(1)}\)To find slope m:
On plugging the gven vales in rquation of slope,
\(\begin{gathered} m=\frac{-6-5}{2-4} \\ m=\frac{-11}{-2} \\ m=\frac{11}{2} \end{gathered}\)The general equation of straight line is,
\(y-y_1=m(x-x_1).......(2)_{}\)To find equation:
On plugging the values in the above equation.
\(\begin{gathered} y-5=\frac{11}{2}(x-4) \\ y-5=\frac{11}{2}x-4(\frac{11}{2}) \\ y=\frac{11}{2}x-22+5 \\ y=\frac{11}{2}x-17 \end{gathered}\)Hence, the equation of straight linne is y = (11/2)x - 17.
So the answer is correct.
What is 9 divided by 0.17
Answers
Answer:
52.94
Step-by-step explanation:
Answer: It's 52.9411765
• En un vuelo con 200 pasajeros que se
dirigía a Miami, algunos pasajeros (clase
económica) pagaron $200.00 y otros
(primera clase) $250.00 por sus boletos
de avión. Si los ingresos por concepto de
venta de boletos en ese vuelo fueron de
$44,000.00, ¿cuántos boletos se
vendieron de cada categoría?
Answers
Answer:
1356545986--&_67ghtyojioftu?fuñt?fufldtuñf
determine the x-intercepts of the quadratic function f(x)= 2x^2 - 6x + 1give exact answers
Answers
Given the quadratic equation:
\(2x^2-6x+1\)The x-intercepts are the values of (x) which make the equation equal to zero
Or, the x-intercepts are the values of intersection with the x-axis
So, we will equate the equation to zero then solve it for (x):
\(\begin{gathered} 2x^2-6x+1=0 \\ \end{gathered}\)As we will not be able to factor the equation, we will use the general formula:
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)From the equation:
\(a=2,b=-6,c=1\)substitute with the values of {a, b, c} into the general formula:
\(\begin{gathered} x=\frac{6\pm\sqrt[]{(-6)^2-4\cdot2\cdot1}}{2\cdot2}=\frac{6\pm\sqrt[]{28}}{4} \\ \\ x=\frac{6+\sqrt[]{28}}{4}=\frac{6+2\sqrt[]{7}}{4}=\frac{3}{2}+\frac{1}{2}\sqrt[]{7} \\ or \\ x=\frac{6-\sqrt[]{28}}{4}=\frac{6-2\sqrt[]{7}}{4}=\frac{3}{2}-\frac{1}{2}\sqrt[]{7} \end{gathered}\)So, the x-intercepts are:
\(x=\mleft\lbrace\frac{3}{2}-\frac{1}{2}\sqrt[]{7},\frac{3}{2}+\frac{1}{2}\sqrt[]{7}\mright\rbrace\)Writing the Equation of a Parallel Line
Try it
CIE
What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (-5, 1)? Check all
that apply.
y = -x-1
2x + 5y = -5
y=-x-3
2x + 5y = -15
y-1= (x + 5)
Intro
Answers
Answer: math waaays can really help you
Step-by-step explanation:
math
Solve the simultaneous equations using elimination method= x+2y-3z=0 3x+3y-z = 5 x-2y = 2z=1
Answers
Answer:
[1;1;1]
Step-by-step explanation:
try this option; all the details are in the attachment.
you sailed 0.032 units to the left and found treasure at 0.248 units find where the ship started
Answers
n an
1 6
2 11
3 16
4 21
Which recursive formula describes this sequence?
a1 = 1 and an = 5n-1 +1
a1 = 6 and an = an-1 + 5
a1 = 6 and an = a1 + 6
a1 = 1 and an = a6 + 1
Answers
Answer:
(b) a1 = 6, a(n) = a(n -1) +5
Step-by-step explanation:
It helps to recognize the form of a recursive definition for an arithmetic sequence. It looks like ...
\(a_1=\text{(first term)},\ a_n=a_{n-1}+d\qquad\text{for common difference $d$}\)
Only one of the offered answer choices has this form. That is the correct choice.
Which expression is equal to (x+2)(x−4)(x−4)(x+4)?
x+2x+4
x−2x+4
x−2x−4
x+4x+2
Answers
Answer:Since the expression on each side of the equation has the same denominator, the numerators must be equal.
x
2
=
16
Take the square root of both sides of the equation to eliminate the exponent on the left side.
x
=
±
√
16
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps...
x
=
4
,
−
4
Exclude the solutions that do not make
x
2
x
−
4
=
16
x
−
4
true.
x
=
−
4
Step-by-step explanation:
FASTEST GETS MOST POINTS
a tuxedo rental service charges $150 flat fee for a suit plus $50 per additinal day. The total cost of the tuxedo is $300. How many days was the tuxedo rental for?
Answers
The tuxedo was rented for 4 days.
Let's start by assigning variables to the unknowns. Let "x" be the number of additional days rented, and "d" be the total number of days rented (including the first day).
From the given information, we know that the flat fee for the rental is $150, so the cost of the additional days is the total cost minus the flat fee, which is $300 - $150 = $150. We also know that the cost for each additional day is $50. Therefore, we can set up the equation:
$150 + $50x = $300
Subtracting $150 from both sides, we get:
$50x = $150
Dividing both sides by $50, we get:
x = 3
So the tuxedo was rented for 3 additional days, making the total number of days rented:
d = 1 + 3 = 4
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