Answer:
A. $22,223
B. $20,000
C. $20,000
Explanation:
The annual return of the retired couple's investment is called the yield in percentage.
A. If they go for Treasury bills which has a yield of 9%, to attain a return of at least $2,000 their investment must exceed $20,000. 9% of 22,223 = $2,000.07
B. . If they go for Corporate bonds option which has a yield of 11%, to attain a return of at least $2,000; 11% of 20,000 = $2,200
C. . If they go for Junk bonds option which has a yield of 13%, to attain annual return of at least $2,000; 13% of $20,000= $2,600
someone could help me?
Answer:
[tex]B= 3.14 * 4^4 = 50.24cm^2\\h = 16cm\\V=B*h=50.24*16=803.84cm^3[/tex]
Step-by-step explanation:
The area of the base is the area of a circle with a radius equal to 4 cm. It means that the area can be calculated as:
[tex]B = 3.14 * r^2\\B= 3.14 * 4^4 = 50.24cm^2[/tex]
The height of the cylinder is shown in the picture, it is equal to 16 cm.
Finally, the volume of the cylinder can be calculated as:
[tex]V = B*h=50.24*16 = 803.84cm^3[/tex]
Where B is the base and h is the height of the cylinder.
What number is in between 10 and 16?
Answer:
13
Step-by-step explanation:
10 + 16 = 26
26 divided by 2 = 13
The middle number is 13
In a clinical trial, out of patients taking a prescription drug daily complained of flulike symptoms. Suppose that it is known that % of patients taking competing drugs complain of flulike symptoms. Is there sufficient evidence to conclude that more than % of this drug's users experience flulike symptoms as a side effect at the level of significance?
Answer:
Step-by-step explanation:
Hello!
Out of 846 patients taking a prescription drug daily, 18 complained of flulike symptoms.
It is known that the population proportion of patients that take the drug of the competition and complain of flulike is 1.8%
Be the variable of interest:
X: number of patients that complained of flulike symptoms after taking the prescription drug, out of 846.
sample proportion p'= 18/846= 0.02
You have to test if the population proportion of patients that experienced flulike symptoms as a side effect is greater than 1.8% (p>0.018)
Assuming that the patients for the clinical trial were randomly selected.
The expected value for this sample is np=846*0.02= 1658 (the expected value of successes is greater than 10) and the sample is less than 10% of the population, you can apply the test for the proportion:
The hypotheses are:
H₀: p ≤ 0.018
H₁: p > 0.018
α: 0.01
[tex]Z= \frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)
[tex]Z_{H_0}= \frac{0.02-0.018}{\sqrt{\frac{0.018*0.982}{846} } }= 0.437[/tex]
The p-value for this test is 0.331056
The decision rule is
If p-value ≤ α, reject the null hypothesis
If p-value > α, do not reject the null hypothesis
The p-value is greater than α, the decision is to reject the null hypothesis.
So at 1% significance level there is no significant evidence to reject the null hypothesis, you can conclude that the population proportion of patients that took the prescription drug daily and experienced flulike symptoms as a side effect is less or equal to 1.8%
I hope this helps!
An angle measures 125.6° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
The measure of each angle:
152.8° and 27.2°
Step-by-step explanation:
Supplementary angles sum 180°
then:
a + b = 180°
a - b = 125.6°
then:
a = 180 - b
a = 125.6 + b
180 - b = 125.6 + b
180 - 125.6 = b + b
54.4 = 2b
b = 54.4/2
b = 27.2°
a = 180 - b
a = 180 - 27.2
a = 152.8°
Check:
152.8 + 27.2 = 180°
Answers:
152.8° & 27.2°Step-by-step explanation:
Let x and y be the measures of each angle.
x + y = 180°
x - y = 125.6°
180 - 125.6 = 54.4
Now we divide 54.4 evenly to get y.
y = 27.2°
To get x, we substitute y into the equation.
x = 27.2 + 125.6
x = 152.8°
To check, we plug these in to see if they equal 180°.
27.2 + 152.8 = 180° ✅
I'm always happy to help :)Which graph shows the solution to the system of linear inequalities? y ≥ 2x + 1 y ≤ 2x – 2
The graph which shows the solution to the system of inequalities is attached in the picture below :
Given the inequalities :
y ≥ 2x + 1
y ≤ 2x - 2
From y ≥ 2x + 1 ;
Since the inequality sign is ≥, a solid line is used to draw the straight line graph of y ≥ 2x + 1
From :
y = mx + c
Where, m = slope ; c = intercept
Hence, a straight line graph with ;
Intercept, c = 1 (where the line crosses the y-intercept)
Slope, m = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality :
0 ≥ 2(0) + 1
0 ≥ 0 + 1
0 ≥ 1
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
From : y ≤ 2x - 2
Since the inequality sign is ≤, a solid line is used to draw the straight line graph of y ≤ 2x - 2
Graph the line y ≤ 2x - 2, with ;
Intercept, c = - 2
Slope = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality y ≤ 2x - 2:
0 ≤ 2(0) - 2
0 ≤ 0 - 2
0 ≤ - 2
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
Learn more : https://brainly.com/question/19670553
Answer:
Its graph B on edge 2022
Step-by-step explanation:
What is the y-value in the solution to this system of linear equations?
4x + 5y = -12
-2x + 3y = -16
-4.
-2
оооо
2
5
Answer:
y = -4
Step-by-step explanation:
4x + 5y = -12 ....eq1
-2x + 3y = -16 ...eq2
From eq1, solve for x:
4x + 5y = -12
4x = -12 - 5y
x = -12 - 5y/4
From eq2, substitute value of x:
-2(-12-5y/4) + 3y = -16
3y - 2 (-5y-12/4) = -16
3y - 2(-5y-12)/4 = -16
12y - 2(-5y - 12) = -16
4*3y - 4*2(-5y-12)/4 = 4*(-16)
12y - 2(-5y-12) = -64
12y + 10y + 24 = -64 (divide both sides by common factor 2)
6y + 5y + 12 = -32
11y = -32 - 12
11y = -44
Divide both sides by 11
11y/11 = -44/11
y = -4
The sum of Jason’s age and his brother’s age is 55. Jason is 7 years younger than his brother. How old is Jason?
Answer:
Jason is 24 years old
Step-by-step explanation:
Lets say that Jason's age is X, and his brother's age is Y.
We know that X + Y = 55.
We also know that (X + 7) = Y.
This means (X + 7) + Y = 62 (We got the 62 by adding 55 and 7)
Anyway if X+7= Y, and X+7 + Y = 62, then X+7 = 62/2, right?
We divide the 62 by 2 and we get 31.
Alright, so X+7 = 31.
substract both sides by 7.
We get X = 24
Sorry if this seemed longer or more complicated than it should've been, I don't know how to explain it better.
6th grade math , help me please :)
Answer:
a. 4.5 grams per cup
b. 3.2 ounces per week
c. 19.2 grams per cubic centimeters
d. $3.29 per gallon
Step-by-step explanation:
The unit rate is simply a ratio comparing 2 given quantities, whereby the denominator is 1.
The unit rate of the above given problems can be determined as shown below:
a. 18 grams of salt per 4 cups, to find the unit rate, calculate how many grams of salt you'd get in 1 cup by dividing 18 by 4
[tex] \frac{18}{4} = 4.5 [/tex]
Unit rate = 4.5 grams per cup
b. 19.2 ounces is gained by the baby in 6 weeks.
Unit rate is the amount of ounces gained in 1 week
Unit rate = [tex] \frac{19.2}{6} = 3.2 [/tex]
Unit rate = 3.2 ounces per week
c. Unit rate = [tex] \frac{76.8}{4} = 19.2 [/tex]
Unit rate = 19.2 grams per cubic centimeters
d. Unit rate = [tex] \frac{23.03}{7} = 3.23 [/tex]
Unit rate = $3.29 per gallon
6th grade math, help me pleasee.
Answer:
a) 12 ft/s (12 feet per second is the rate at which she runs)
b) the tables is completed as follows:
for column 1: 12
for column 2: 24
for column 3: 36
for column 4: 48
Step-by-step explanation:
Notice that since she did 60 feet in 5 seconds, then her speed (which is defined as distance divided by the time it took to cover that distance) is: 60/5 feet/second = 12 ft/s
Now this means that for every second she runs, she covers 12 feet
Then in the first second running she covered 12 ft, after 2 seconds running, she covered 24 ft, after 3 seconds running, she covered 36 ft, after 4 seconds running, she covered 48 ft. And these values complete the requested table.
A young Greek by the name of Zeno is riding his horse to his friends house which is two miles away. He travels half the distance in one hour. But his horse gets tired, and only travels half the remaining distance the second hour, and, again, only half the remaining distance in the third hour. How many miles did Zeno travel in those three hours?
Answer:
1.75 miles
Step-by-step explanation:
Zeno's friend's house is two miles away. He travels half the distance in one hour.
0.5 × 2 = 1
The second hour, his horse travels half the remaining distance.
0.5 × 1 = 0.5
The third hour, his horse travels half the remaining distance.
0.5 × 0.5 = 0.25
1 + 0.5 + 0.25 = 1.75
Zeno travels 1.75 miles in three hours.
Hope this helps.
H0:p=0.45 ; Ha:p>0.45
The p-value for this hypothesis test is 0.025.
The level of significance is α=0.05
Select the correct answer below:
a. There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 45%.
b. There is NOT sufficient evidence to conclude that the proportion of agenda-less meetings isgreater than 45%.
c. There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 55%.
d. There is NOT sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 55%.
Answer:
Option A is correct
Step-by-step explanation:
From the question we are told that
The Null Hypothesis is [tex]H_o : p = 0.45[/tex]
The alternative hypothesis [tex]H_a : p > 0.45[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The p-value is [tex]p-value = 0.025[/tex]
Now looking at the given data we see that the the p-value is less than [tex]\alpha[/tex]
Generally when this occurs in a hypothesis test we reject the null hypothesis which mean that the result which we obtain is statistically significant.
Hence the alternative hypothesis is correct, which means that,
There is sufficient evidence to conclude that the proportion of agenda-less meetings is greater than 45%. which is option A
[tex]\lim_{x\to \ 4} \frac{x-4}{\sqrt{x}-\sqrt{4} }[/tex] Please answer this one
Answer:
[tex]\large \boxed{\sf \ \ \lim_{x\to \ 4} \dfrac{x-4}{\sqrt{x}-\sqrt{4} }=4 \ \ }[/tex]
Step-by-step explanation:
Hello,
We need to find the following limit.
[tex]\displaystyle \lim_{x\to \ 4} \dfrac{x-4}{\sqrt{x}-\sqrt{4} }[/tex]
First of all, for any x real number different from 4 and positive, we can write
[tex]\dfrac{x-4}{\sqrt{x}-\sqrt{4}} = \dfrac{(x-4)(\sqrt{x}+\sqrt{4})} {(\sqrt{x}-\sqrt{4})(\sqrt{x}+\sqrt{4})}} ==\dfrac{(x-4)(\sqrt{x}+\sqrt{4})}{x-4}=\sqrt{x}+\sqrt{4}[/tex]
so the limit is
[tex]\sqrt{4}+\sqrt{4}=2+2=4[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A cylindrical can is to be made to hold 50 cm3 of oil. Determine the dimensions of the can that will minimize its surface area. What is the minimum surface area
Answer:
S(min) = 59,66 cm²
Step-by-step explanation:
The volume of a cylindrical can is:
V(c) = π*x²*h where x is radius of the base and h the height
V(c) = 50 cm³
50 = π*x²*h (1)
The surface area of the can (Sc) is Surface area of the base (Sb) plus surface lateral area (Sl)
S(b) = π*x²
And S(l) = 2*π*x*h
Then
S(c) = π*x² + 2*π*x*h
And surface area as a function of x is
From equation (1)
h = 50 /π*x² and plugging this value in the previous expression
S(x) = π*x² + 2*π*x*(50/π*x²)
S(x) = π*x² + 100/x
Taking derivatives on both sides of the equation
S´(x) = 2*π*x - 100/x²
S´(x) = 0 means 2*π*x - 100/x² = 0
π*x - 50/x² = 0
π*x³ - 50 = 0
π*x³ = 50
x³ = 50 / 3,14
x³ = 15,92
x = 2,51 cm
And h = 50 / π* (2,51)²
h = 2,53 cm
Then minimum surface area of the can is:
S(min) = 19,78 + 39,88
S(min) = 59,66 cm²
Simplify the expression:
2b – 5b + 7 + 3b
Answer:
7
Step-by-step explanation:
2b - 5b is -3b so it leaves the equation with -3b + 7 + 3b
-3b + 3b cancells out to 0 so it leaves the final answer to 7
A=63°
C = 7.75 inch
B = 47°
Oblique Triangle
13. Refer to the oblique triangle shown. What's the length of side a? Round to the nearest hundredth of an inch.
O A. 7.75 inches
O B. 7.35 inches
O C.4.72 inches
O D. 6.03 inches
Answer:
B. 7.35 inches
Step-by-step explanation:
In the triangle:
A=63° c = 7.75 inch B = 47°Now we know that:
[tex]\angle A+\angle B+\angle C=180^\circ$ (Sum of angles in a \triangle)\\63^\circ+47^\circ+\angle C=180^\circ\\\angle C=180^\circ-(63^\circ+47^\circ)\\\angle C=70^\circ[/tex]
Using the Law of Sines
[tex]\dfrac{a}{\sin A} =\dfrac{c}{\sin C}\\\\\dfrac{a}{\sin 63^\circ} =\dfrac{7.75}{\sin 70^\circ} \\\\a=\dfrac{7.75}{\sin 70^\circ} \times \sin 63^\circ\\\\a=7.35$ inches (to the nearest hundredth of an inch)[/tex]
Answer:
B. 7.35 inches
Step-by-step explanation:
just use the law of sines
The parabola y= x2 - 4 opens:
O up
O down
O right
O left
Answer:
it opens up
goes up 4 but doesn't move left or right
A transformation of KLM results in K'L'M'. Which transformation maps the pre-image to the image?
a. dilation
b.translation
c. reflection
d. rotation
Answer:
a. dilation.
Step-by-step explanation:
In this problem, the triangle has been neither reflected nor rotated. Although you could say the triangle has been translated, translation will preserve the lengths of the legs of the triangle.
Since all the angles are still congruent, we can say that the triangle has been dilated. It has been enlarged.
Hope this helps!
The dilation is a transformation that transfers the pre-image to the final image. The correct answer is A.
What is a transformation?When a point is relocated from its original place to a new location, it is changed. Different transformations include translation, rotation, reflection, and dilation.
As per the given figure, ΔKLM is transformed into ΔK'L'M'.
Here, the triangle hasn't been reflected or rotated.
Although we cannot claim the triangle has been translated, translation maintains the lengths of the triangle's legs.
We conclude that the triangle has been dilated because all of the angles are still congruent. It has grown in size.
Therefore, dilation is a transformation that transfers the pre-image to the final image.
To learn more about the transformations click here :
https://brainly.com/question/11352944
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In a cinema, there are eight seats in a row. Four of the seats in one row are occupied. What fraction of seats are available in that row?
Answer:
[tex] \frac{1}{2} [/tex]Step-by-step explanation:
Given,
There are 8 seats in a row.
There are 8 seats in a row.4 seats are occupied.
Available seats = 8 - 4 = 4 seats
Fraction of seats available:
[tex] \frac{number \: of \: seats \: available}{total \: number \: of \: seats} [/tex]
[tex] = \frac{4}{8} [/tex]
Reduce the fraction with GCF 4
[tex] = \frac{1}{2} [/tex]
Hope this helps..
Best regards!!
Answer:
Your correct answer is that there are 4 seats available. The fraction version is 1/2
Step-by-step explanation:
Since there are 8 in a row and 4 are taken, subtract 8 by 4.
8 - 4 = 4 seats that are available.
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.
r=0.543, n=25
a. Critical values: r = ±0.396, no significant linear correlation
b. Critical values: r = ±0.396, significant linear correlation
c. Critical values: r = ±0.487, significant linear correlation
d. Critical values: r = ±0.487, no significant linear correlation
Answer:
a. Critical values : r = ±0.396, no significant linear correlation.
Step-by-step explanation:
The critical value is 0.396 and test statistic is 0.543. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case test statistics value is greater than critical value then we should accept the null hypothesis.
The descriptive statistics listed below. These descriptive statistics were generated from a random sample of all USF students and contain information about the amount of time they exercise per week and the amount of student loan debt (in thousands of dollars) they expect upon graduating college.
Exercise Debt
N 200 200
Lo 95% CI 6.6061 11.380
Mean 7.5000 14.385
Up 95% Cl 8.4639 17.390
SD 6.0000 19.307
Minimum 0.0000 0.0000
Maximum 47.000 100.00
Which of the following graphical methods allows the individual data values to still be visible whil also allowing us to assess the shape of the exercise times?
A. Histogram.
B. Boxplot.
C. Stem and-Leaf Display.
D. All of these could do this.
Answer:
A. Histogram.
Step-by-step explanation:
Histogram is a graphical display in the form of bars. The numerical data is displayed through graph to understand easily. Skewness measure frequency distribution of histogram. The histogram is skewed in a way that its right side tail is greater than its left side tail. They are skewed to right. The histogram are positively skewed which means their most of data falls to right side. The mean of positively skewed histogram is greater than its median.
plsd its urgent i am begging u i will give u anything plsss brainliest and 50 pounts i am so sad and depressed currently and school work is not helping so if u can help i will appreciate it
Answer: 245 cu. cm.
Step-by-step explanation:
4/7-2/5=20/35-14/35=6/35
42 cm3 represents 6/35 of the total volume
how many 6/35's are in 35/35 ? (the total volume)
(35/35)/(6/35)=(35/35)*(35/6)=35/6=5 5/6
(5 5/6)*(42)=(35/6)*(42)=35*7=245 cm3 is the total volume
A population has a standard deviation of 50. A random sample of 100 items from this population is selected. The sample mean is determined to be 600. At 95% confidence, the margin of error is
Answer:
Margin of error is 9.8
Step-by-step explanation:
Using the formular for the margin of error
The margin of error = z* (sd/√n)
Where z is the z score for the desired confidence level = 1.96, sd is the population standard deviation = 50 and n is the sample size = 100
Thus
Margin of error = 1.96 (50/√100)
= 1.96 (50/10)
= 1.96 (5)
= 9.8
Margin of error is 9.8
The point (5, -2) is rotated 90° about the origin. Its image is:
Find the valuds to complete the table
Answer:
Where is the table
Step-by-step explanation:
I cant answer without it
Which of the following is represented by MN ?
A.
Radius of the circle
B.
Diameter of the circle
C.
A chord of the circle
D.
Circumference of the circle
Answer:
A
Step-by-step explanation:
That is the radius. Since its half of the diameter.
Answer:
A. Radius of the circle
Step-by-step explanation:
A line segment that has as endpoints the center of a circle and a point on the circle is called a radius.
Answer: A. Radius of the circle
Drag the labels to the correct locations
Answer:
Graph A
So it has two distinct real roots.
Graph B
It has one repeated real root
Graph C
So it has two complex roots.
Graph D
One real root and one complex root
Step-by-step explanation:
For graph A
The value of the roots is x= 1 and x= 3
And the minimum value = -3
It's a positive graph
So it has two distinct real roots.
For graph B
The value of the roots is x = 2 and x= 2
That is x= 2 twice
Has a maximum value of 0
It's an inverse graph
It has one repeated real root
For graph C
It's a positive graph but on the negative of x
Has a minimum value of 1
It didn't touch x at y = 0
And it's root will be negative
So it has two complex roots.
For Graph D
Value of the roots is x= 2 and x= -2
It's a positive graph
Minimum value of -4
One real root and one complex root
Please help. I’ll mark you as brainliest if correct!
Answer:
CDs: $30,000bonds: $90,000stocks: $50,000Step-by-step explanation:
You can let c, b, s represent the investments in CDs, bonds, and stocks, respectively.
c + b + s = 170000 . . . . . . total invested
0.0325c +0.038b +0.067s = 7745 . . . . . . . annual income
-c + b = 60000
You can solve this set of equations using any of a number of methods, including on-line calculators, graphing calculators, scientific calculators, Cramer's Rule, substitution, elimination, and more. The solution is ...
c = 30,000
b = 90,000
s = 50,000
Maricopa's Success invested $30,000 in CDs, $90,000 in bonds, and $50,000 in stocks.
A box contains 100 marbles, some of which are red and the rest blue. A sample of 10 marbles is taken randomly (with replacement) from the box and the statistic: number of red marbles in the sample is calculated. The probability model for this statistic is shown below. (Note: the probabilities should add to 1 - any difference from 1 is due to round-off errors.)
values probability
(%)
0 0.6047
1 4.0311
2 12.0932
3 21.4991
4 25.0823
5 20.0658
6 11.1477
7 4.2467
8 1.0617
9 0.1573
10 0.0105
a. Roughly, what is the shape of the probability model? Write the shape in a complete sentence
b. Calculate the center (mean) of the probability model. Use R as a calculator to calculate the mean. Write the mean in a complete sentence
c. Argue that 1.5 is a good guess for the standard deviation of the probability model. Write a brief answer
d. Suppose you repeat the experiment of sampling 10 randomly with replacement n times. Each time, you calculate the number of red marbles in your sample. Suppose you were to make a plot of the running means of the results, what would happen as n increases?
Step-by-step explanation:
a) The Roughly shape of the probability model is bell shaped or symmetric
( normal )
(b) Roughly, guess the center (mean) of the probability model
The mean is 5/10 =0.5
Because the symmetric distribution mean is middle bar and here we see using histogram 5/10 is mean .
(c) Argue that 1.5 is a good guess for the standard deviation of the probability model.
Yes 1.5 is very good guess because then it follow normal distribution it is exactly correct .
A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint. If a can of paint contains 75 ounces of white paint, how many ounces of blue paint are in the can?
Answer:
60 ounces
Step-by-step explanation:
A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint, that is, the white paint (w) to blue paint (b) ratio is 5:4. We can apply this ratio to different units such as ounces. This means that the mixture has 5 ounces of white paint to 4 ounces of blue paint. If a can of paint contains 75 ounces of white paint, the ounces of blue paint in the can are:
75 oz w × (4 oz b/5 oz w) = 60 oz b
Find factors of x³+12x²-19x= -20
Answer:
No Factors
Step-by-step explanation:
[tex]x^3-12x^2-19x+20 = 0\\Let \ p(x) = x^3-12x^2-19x+20[/tex]
Factors of 20 = ±1, ±2 , ±4 , ±5 , ±10 and ±20
±1, ±2 and ±3 are not the factors of given polynomial.
Putting x = 4 in the given polynomial
[tex]p(4) = (4)^3+12(4)^2-19(4)+20\\p(4) = 64+192-76+20\\p(4) = 200[/tex]
So, x = 4 is not a factor of p(x)
Putting x = -4 in the given equation
[tex]p(-4) = (-4)^3+12(-4)^2-19(4)+20\\p(-4) = -64+192-76+20\\p(-4) = 73[/tex]
So, x = -4 in the given equation
Putting x = 5 in the given equation
[tex]p(5) = (5)^3+12(5)^2-19(5)+20\\p(5) = 125+300-95+20\\p(5) = 350[/tex]
So, x = 5 is not a factor of p(x)
Putting x = -5 in the given equation
[tex]p(-5) = (-5)^3+12(-5)^2-19(-5)+20\\p(-5) = -125+300+95+20\\p(-5) = 290[/tex]
So, x = -5 is not a factor of p(x)
Putting x = 10 in the given equation
[tex]p(10) = (10)^3+12(10)^2-19(10)+20\\p(10) = 1000+1200-190+20\\p(10) = 2030[/tex]
So, x = 10 is not a factor of p(x)
Putting x = -10 in the given equation
[tex]p(-10) = (-10)^3+12(-10)^2-19(-10)+20\\p(-10) = -1000+1200+190+20\\p(-10) = 410[/tex]
So, x = -10 is not a factor of p(x)
Putting x = 20 in the given equation
[tex]p(20) = (20)^3+12(20)^2-19(20)+20\\p(20) = 8000+4800-380+20\\p(20) = 12440[/tex]
So, x = 20 is not a factor of p(x)
Putting x = -20 in the given equation
[tex]p(-20) = (-20)^3+12(-20)^2-19(-20)+20\\p(-20) = -8000+4800+380+20\\p(-20) = -2800[/tex]
So, x = -20 is not a factor of p(x)
From the above solution, we conclude that the given equation can not be factorized and thus, has no factors.
Answer:
[tex]\boxed{\mathrm{No \: factors}}[/tex]
Step-by-step explanation:
[tex]x^3 +12x^2 -19x= -20[/tex]
Add 20 on both sides.
[tex]x^3 +12x^2 -19x+20= 0[/tex]
Add 67x and 44 on both sides.
[tex]x^3 +12x^2 +48x+64= 67x + 44[/tex]
Factor left side of the equation.
[tex](x+4)(x+4)(x+4)= 67x + 44[/tex]
[tex](x+4)^3=67x+44[/tex]
Subtract 67x and 44 on both sides.
[tex](x+4)^3-67x-44=0[/tex]
Cannot be factored further.
This is a prime expression. A prime expression cannot be factored.
We cannot factor out x from the expression, there are no factors.