Find the equation for a polynomial f(x) that satisfies the following:
- Degree 5
• Root of multiplicity 2 at x = 3
- Root of multiplicity 1 at x = 1
• Root of multiplicity 2 at x = 3
- y-intercept of (0, -162)
Root x= 3 of multiplicity 2, it means we can factor it with : (x-3)²
Root x = 1, of multiplicity 1, it means we can factor this polynomial with : (x-1)
Root x = -3, of multiplicity 2, it means we can factor this polynomial with : (x+3)²
Finally we get this expression : (x-3)²(x+3)²(x-1)
This expression is a polynomial of degree 5 but what is the y intercept of it ?
Basically, we need to replace x by zero and the value of the expression will be the y intercept :
let x = 0
then ,
(0-3)²(0+3)²(0-1) = 9*9*(-1) = -81 #-162
We need an y intercept of value = -162
Thus we simply need to multiply by 2, and finally f(x) = 2(x-3)²(x+3)²(x-1)
satisfies all the required condition
Good Luck
What is the total holiday debt (no less than $500) that you are trying to pay off and what did you purchase
to accrue (accumulate) that debt?
on what interval (s) are f(x) = x3 2x²+x+6 decreasing?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
What is 1.231 rounded to the nearest hundredth?
1.23 would be your answer.
Have a great day! :)
please i need help on the question
Answer:
A
D
B
C
Step-by-step explanation:
We can simplify the expressions for easier comprehension:
A. 60.7 x 10^-1 = 6.07
B. 6.07 x 10^3 = 6,070
C. 0.67 x 10^4 = 6,700
D. 6.7 x 10^2 = 670
Now, we can order them in ascending order (least to greatest):
A
D
B
C
it took ken 2/8 hour to finish a puzzle ken told his mom how long it took with the fraction in simplest form how many hours did ken tell his mom
A certain hybrid car with a 16 gallon gas tank can travel 35 miles on battery alone and then it uses its gas. The car can then travel 45 miles per gallon of gas used. Assume the car starts with a full tank of gas. Fill in the missing values.
Answer:
X miles ( 35, 125, 265, 310)
m = 35 + 45x
755
Step-by-step explanation:
Hope this helps, btw have an awesome day
A box plot is shown
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ما تا ته
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Answer:
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Determine the five-statistical summary of the data. Drag the correct number to each variable in the summary.
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22 24 26
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Minimum:
Maximum:
Median:
First Quartile:
Third Quartile:
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ما تا ته
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The mean hourly wage for employees in goods-producing industries was $24.57, April 12, 2012 (Bureau of Labor Statistics). Suppose a sample of 30 employees from the manufacturing industry is taken, in April 2012, to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries.
a. State the null and alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries.
b. Suppose a sample of 30 employees from the manufacturing industry showed a sam- ple mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value.
c. With a = .05 as the level of significance, what is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.
Step-by-step explanation:
a. The null hypothesis is generally an exact value and the alternative hypothesis is the one we are trying to show. We are trying to show that the population mean is different from $24.57, so the hypotheses are as follows:
Null: The population mean hourly wage in the manufacturing industry is the same as the population mean hourly wage in the goods-producing industries
Alternative: The population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries
b.
Because we know the population standard deviation, we can use a z test
Plugging in the values:
Expected population mean: 24.57
Sample average: 23.89
Sample size: 30
Population standard deviation: 2.4, we get 0.1207 as our p-value.
c. Using a = 0.05, our p-value is greater than that, so we can not conclude the alternative hypothesis (The population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries)
d. Using a critical value calculator, we can find that for a two-tailed approach, the critical value would be 1.96. This would mean that the z score would have to be greater than 1.96 or less than -1.96 for the results to be significant. The population mean we would plug in here is 24.57, while the raw score would be 23.89 and the standard deviation would be 2.4. The z score we get is -0.283, which is not in the values specified (>1.96 or <-1.95) so we cannot conclude the alternative hypothesis
.872 to scientific notation
Answer:
8.72×10²
Step-by-step explanation:
8.72×10²=872Which of the following expressions is equivalent to log 5 - k log 2?
Select one answer
Answer:
C
Step-by-step explanation:
log5- klog2= log5-log2^k = log(5/2^k)
What is the equation for the line in slope-intercept form? 20 18+ Enter your answer in the box. 16+ 14+ 112+ NO+ 6 4 2 - 20-18 -16-14-12-10 -9 -6 -4 4 6 8 -20 -27 10 12 14 16 18 20 -4- -B -8 -10 -12+ -14H -16+ -18+ -20+
The slope of the line represents that the remainder of the goal decrease by 8 for each card sold.
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
The line passes through the point (1, 8) and (2, 16), hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-8=\frac{16-8}{2-1}(x-1)\\\\y=8x[/tex]
The equation of the line is given by y =8x
Find out more about linear equation at: https://brainly.com/question/14323743
Find out more on linear equation at: https://brainly.com/question/14323743
5. Find the value of x.
17x – 18
7x
if 17x-18=7x
then 17x-7x=18
10x=18
x=1.8
how much solutions does 2x = 2x + 1 have?
Answer:
no solution
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
Help help help help help help help help
Answer:
y=2
y=4
y=6
y=8
Step-by-step explanation:
please mark brainlist
The Kicking Cacti and the Sprinting Stingrays met in their town's annual kickball championship this year. They were so evenly matched that the game lasted 11 innings! The Stingrays had 3 pitchers, and each of them pitched for the same number of innings.
How long did each of the pitchers for the Stingrays pitch?
Answer:
11/3 = 3 2/3 innings
Step-by-step explanation:
3 pitchers = 11 innings
1 pitcher = x innings
in the first equation, divide both sides by 3 to get 1 pitcher on one side
1 pitcher = 11/3 innings = 3 2/3 innings
What is the slope of the line containing the points (17,92) and
(21, 44)?
Answer:
-9.6
Step-by-step explanation:
92-44/17-21
Answer:
-12
Step-by-step explanation:
Formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Identify the values:
[tex]y_2=44[/tex]
[tex]y_1=92[/tex]
[tex]x_2=21[/tex]
[tex]x_1=17[/tex]
Plugin the values; solve:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{44-92}{21-17}[/tex]
[tex]= \frac{-48}{4}[/tex]
[tex]\bold{m=-12}[/tex]
Therefore, the slope of the line containing the points (17,92) and
(21, 44) is -12.
What number must each side of the equation 3/5x= 12 be multipled by to produce the equivalent equation x = 20?
Answer:
1
Step-by-step explanation:
First, find out what the product would be if you multiply 20 with the fraction:
(3 * 20)/5 = 60/5 = 12
12 = 12 ∴ (3/5)(20) = 12
As 20 is your answer, you would need to only multiply 1 to obtain the correct balance for the equation.
Which of the following is a correct interpretation of the expression 3+(-7)
Thanks
[tex]\huge\underline\mathtt\colorbox{cyan}{3-7}[/tex]
Step-by-step explanation:
The correct interpretation of 3+(-7) is 3-7, simply
Answer:
The answer will be
3+(-7)
The sum of positive and negative is negative
So 3+(-7) is 3-7
= -4
Step-by-step explanation:
Hope it helps
Please Mark as brainliest
. In a study of air-bag effectiveness it was found that in 821 crashes of midsize cars equipped with air bags, 46 of the crashes resulted in hospitalization of the drivers (based on data from the highway Loss Data Institute). Using a 0.01 significance level, you need to test the claim that the air-bag hospitalization rate is lower than the 7.8% rate for crashes of mid-size cars equipped with automatic safety belts. What conclusion should you make
Answer:
P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584
0.00885... < 0.01
The test statistic of 46 is significant
There is sufficient evidence to reject H₀ and accept H₁
Air bags are more effective as protection than safety belts
Step-by-step explanation:
821 crashes
46 hospitalisations where car has air bags
7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts
α = 0.01 or 1% ← level of significance
One-tailed test
We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;
The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;
So we are testing if hospitalisations in cars with air bags is less than 0.078;
So, firstly:
Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags
X~B(821, 0.078)
Null hypothesis (H₀): p = 0.078
Alternative hypothesis (H₁): p < 0.078
According to the information, we reject H₀ if:
P(X ≤ 46 | X~B(821, 0.078)) < 0.01
To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;
If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:
[tex]P(X = r) = nCr * p^{r} * (1 - p)^{n - r}[/tex]
You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:
P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584
Now, we need to consider if the condition for rejecting H₀ is met and recognise that:
0.00885... < 0.01
There is sufficient evidence to reject H₀ and accept H₁.
To explain what this means:
The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;
In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.
You start at (5, 0). You move left 1 unit and up 1 unit. Where do you end?
Answer:
(4; 1)Step-by-step explanation:
Look at the picture.
(x, y)
left 1 unit: (5 - 1 = 4)
up 1 unit: (0 + 1 = 1)
5 cm is about 2 inch. Explain in a line graph to find out how many inch are in 50 cm.
Answer:
20 inches
Step-by-step explanation:
If that's centimeters on the x-axis and inches in the y-axis, then the slope is 2/5 and the y-intercept is 0.
[tex]y=\frac{2}{5}x[/tex]
The slope of 2/5 in this context means 2 inches per 5 centimeters. Then, either by solving the equation or by graphing the line, you can determine that there are about 20 inches in 50 centimeters.
Can the sum or multiplication of two palindromic numbers be another palindromic number?
Answer: No.
Step-by-step explanation:
If you multiply 1001 by 1001 it's not another palindromic number.
Solve the equation for d. 0.2(d-6)=0.3d+5-3+0.1d
Answer:
Step-by-step explanation:
0.2(d - 6) = 0.3d + 5 - 3 + 0.1d
0.2d - 1.2 = 0.4d + 2
- 0.2d = 3.2
d = - 16
Answer:
d = -16
Step-by-step explanation:
[tex]0.2(d-6)=0.3d+5-3+0.1d\\\rule{150}{0.5}\\0.2d - 1.2 = 0.3d+5-3+0.1d\\\\0.2d - 1.2 = 0.3d+0.1d+ 5-3\\\\0.2d - 1.2=0.4d + 2\\\\0.2d- 0.2d - 1.2 = 0.4d -0.2d + 2\\\\-1.2 = 0.2d + 2\\\\-1.2 -2 = 0.2d + 2 - 2\\\\-3.2 = 0.2d\\\\\frac{-3.2 = 0.2d}{0.2}\\\\-16 = d\\\\\boxed{d = -16}[/tex]
If answer is correct you will be marked as brainliest
What is the discriminant of the polynomial below?
4x^2+4x+1
A. 32
B. -12
C. -4
D. 0
Answer:
Discriminant is [tex] {b}^{2} - 4 \times a \times c [/tex]
[tex]16 - 4 \times 4 \times 1 = 0[/tex]
Laurie wants to join the basketball team. Her parents ask her to figure out how much it will cost. Laurie knows that she has to pay an activities fee of $42 plus a fixed amount for each tournament. Write a formula that describes how much it will cost to join the team. Let's let:
c=cost for each tournament
n=number of tournaments the team plays
t=total amount to join the team
The Formula:
t = cn + 42
i need help for my bro
What is the equation of a circle with center at (4,-6) and radius of 5?
Answer:
Since the centre of the circle is (−4,−5) and its radius =6
Then, the equation of the circle is
⇒(x−(−4))
2
+(y−(−5))
2
=6
2
⇒(x+4)
2
+(y+5)
2
=36
⇒x
2
+8x+16+y
2
+10y+25−36=0
⇒x
2
+y
2
+8x+10y+5=0
Step-by-step explanation:
Paki brainlilest na lng po salamaf
2. Write an equation in slope-intercept form for the line with a slope of -9 and a
y-intercept of 18.
Answer:
y = -9x + 18.
Step-by-step explanation:
The general form is y = mx + c , where m = the slope and c = y-intercept.
[tex]\huge\boxed{Hi \: there! :)}[/tex]
We are given the slope of the line: -9.
We are also given its y-intercept: 18.
Slope-Intercept Form:
[tex]\huge\sf\{y=mx+b[/tex]
Where
m is the slope and b is the y-intercept.
Plug in the values:
y=-9x+18
[tex]\huge\boxed{Therefore, \: our \: equation \: is: y=-9x+18}[/tex]~An Unknown Dreamer
Good luck!
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