Answer:
Dear user,
Answer to your query is provided below
The value of f(10) using synthetic division is 396.
Explanation:
Cubic polynomials cannot be factorized by splitting the middle term. Quadratic polynomials can be factorized by splitting the middle term.
A cubic polynomial can have a maximum of three linear factors. To factorize a cubic polynomial, we first find a factor by hit and trial method or using factor theorem and reduce it into the product of a quadratic polynomial and a linear polynomial. The quadratic polynomial can then be factorized in linear factors.
The value of f(10) using synthetic division method is 396.
What is synthetic division?"The synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division."
The given function is:
f(x) = x³ – 7x² + 8x + 16
Therefore using synthetic division, we get:
(10) | (1) (- 7) (8) (16)
| (10) (30) (380)
|............................................
(396)
Therefore, f(10) = 396.
Learn more about synthetic division here: https://brainly.com/question/13164931
#SPJ3
Given the functions f(x) = 6x + 11 and g(x) = x^2 + 6, which of the following functions represents f[g(x)] correctly?
Answer:
6x^2+47
Step-by-step explanation:
You simple have to "plug" g(x) into f(x) for x.
f(x)=6x+11
f(g(x))=6(x^2+6)+11
f(g(x))=6x^2+36+11
f(g(x))=6x^2+47
Find the exact coordinates of point E.
Answer:
is the correct answer.
Step-by-step explanation:
We are given that co-ordinates of D is (-3,8) and F is (5,2).
For finding a point E on the line segment DF dividing it in a ratio 4:1, we can use segment formula.
[tex]x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}[/tex]
Where [tex](x,y)[/tex] is the co-ordinate of the point which
divides the line segment joining the points and in the ratio m:n.
As per the given values
[tex]x_{1} = -3\\x_{2} = 5\\y_{1} = 8\\y_{2} = 2[/tex]
Putting the given values in above formula :
x-co-ordinate of F:
[tex]x = \dfrac{5 \times 4 + (-3 \times 1)}{4+1}\\\Rightarrow \dfrac{17}{5}\\\Rightarrow x = 3.4[/tex]
y-co-ordinate of F:
[tex]y = \dfrac{4 \times 2 + 1 \times 8}{4+1}\\\Rightarrow \dfrac{16}{5}\\\Rightarrow y = 3.2[/tex]
So, answer is [tex]E(3.4,3.2)[/tex].
A county is in the shape of a rectangle that is 60 miles by 70 miles and has a population of 50,000. What is the average number of people living on each square mile of the county? Round your answer to the nearest whole number.
192
10
14
12
Answer:
The correct answer is:
12
Step-by-step explanation:
Length of county = 70 miles
breadth of county = 60 miles
area of county (rectangle) = Length × Breadth = 60 × 70 = 4,200 sqaure miles
population of county = 50,000
Therefore, to find the average number of people living on each square mile of the county, we will assume that the whole population is equally distributed in the county, hence the population per square mile is calculated thus:
Total area = 4,200 square miles
total population = 50,000
This means that:
4,200 square miles contains 50,000 people
4,200 sq. miles = 50,000 people
∴ 1 sq. mile = 50,000 ÷ 4,200 = 11.9 = 12 people (to the nearest whole number)
therefore number of people living per square mile = 12
Answer:
12
Step-by-step explanation:
Got it right on the test! <3
What is sin(40)?
O A. 0.40
O B. 0.77
O C. 0.64
O D. 0.83
Answer:
The answer is C.
Step-by-step explanation:
If you type into the calculator for sin(40), you will get approximately 0.64 if you round it to 2 decimal places :
[tex] \sin(40) = 0.6427876097[/tex]
[tex] \sin(40) ≈ 0.64[/tex]
You bought a sachet water machine from Indie Inc. The cost of the machine was GH¢35,000. At that time, you asked for the payment to be deferred, and a contract was written. Under the contract, you could delay paying for the sachet water machine if you purchased the material for packaging the water from Indie Inc. You will then pay for the machine in a lump sum at the end of 2 years, with interest at a rate of 2% per quarter-year. According to the contract, if you ceased buying the packaging material from Indie Inc. at any time prior to 2 years, the full payment due at the end of 2 years would automatically become due. One year later, you decided to buy the packaging material elsewhere and stopped buying from Indie Inc., whereupon Indie Inc., per the contract terms, asked for the full payment that is due at the end of 2 years to be paid immediately. You were unhappy about this, so Indie Inc. offered as an alternative to accept the GH¢35,000 with interest at 10% per semiannual period for the 12 months that you had been buying the packaging material from Indie Inc. Which of the alternatives should you accept? Explain.
Answer: The answer has been attached below
Step-by-step explanation:
From the attached calculation, the amount payable in the first payment is cheaper than the amount payable for the second payment.
If both alternatives were presented to me by Indie incorporation after purchasing a sachet water machine from them, I'll choose the first method of payment.
Kindly check the attached file for the calculation which prompted the decision taken.
In an agricultural study, the average amount of corn yield is normally distributed with a mean of 189.3 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 180 bushels of corn per acre?
Answer:
About 786 would be expected to yield more than 180 bushels of corn per acre
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 189.3, \sigma = 23.5[/tex]
Proportion of acres with more than 180 bushels of corn per acre:
This is 1 subtracted by the pvalue of Z when X = 180. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 189.3}{23.5}[/tex]
[tex]Z = -0.4[/tex]
[tex]Z = -0.4[/tex] has a pvalue of 0.3446.
1 - 0.3446 = 0.6554
Out of 1200:
0.6554*1200 = 786.48
About 786 would be expected to yield more than 180 bushels of corn per acre
What is another way to write the equation StartFraction 7 over 8 EndFraction x + three-fourths = negative 6?
Answer:
1/8 x + 3/4 = -6
Step-by-step explanation:
If you want to solve this as well:
1/8 x = -5 3/4
x = -42
Answer:
B
Step-by-step explanation:
The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1600 and the standard deviation is $100. What is the approximate percentage of buyers who paid more than $1900? What is the approximate percentage of buyers who paid less than $1400?What is the approximate percentage of buyers who paid between $1400 and $1600?What is the approximate percentage of buyers who paid between $1500 and $1700?What is the approximate percentage of buyers who paid between $1600 and $1700?What is the approximate percentage of buyers who paid between $1600 and $1900?
Answer:
(a) 0.14%
(b) 2.28%
(c) 48%
(d) 68%
(e) 34%
(f) 50%
Step-by-step explanation:
Let X be a random variable representing the prices paid for a particular model of HD television.
It is provided that X follows a normal distribution with mean, μ = $1600 and standard deviation, σ = $100.
(a)
Compute the probability of buyers who paid more than $1900 as follows:
[tex]P(X>1900)=P(\frac{X-\mu}{\sigma}>\frac{1900-1600}{100})[/tex]
[tex]=P(Z>3)\\=1-P(Z<3)\\=1-0.99865\\=0.00135\\\approx 0.0014[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid more than $1900 is 0.14%.
(b)
Compute the probability of buyers who paid less than $1400 as follows:
[tex]P(X<1400)=P(\frac{X-\mu}{\sigma}<\frac{1400-1600}{100})[/tex]
[tex]=P(Z<-2)\\=1-P(Z<2)\\=1-0.97725\\=0.02275\\\approx 0.0228[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid less than $1400 is 2.28%.
(c)
Compute the probability of buyers who paid between $1400 and $1600 as follows:
[tex]P(1400<X<1600)=P(\frac{1400-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1600-1600}{100})[/tex]
[tex]=P(-2<Z<0)\\=P(Z<0)-P(Z<-2)\\=0.50-0.0228\\=0.4772\\\approx 0.48[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1400 and $1600 is 48%.
(d)
Compute the probability of buyers who paid between $1500 and $1700 as follows:
[tex]P(1500<X<1700)=P(\frac{1500-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1700-1600}{100})[/tex]
[tex]=P(-1<Z<1)\\=P(Z<1)-P(Z<-1)\\=0.84134-0.15866\\=0.68268\\\approx 0.68[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1500 and $1700 is 68%.
(e)
Compute the probability of buyers who paid between $1600 and $1700 as follows:
[tex]P(1600<X<1700)=P(\frac{1600-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1700-1600}{100})[/tex]
[tex]=P(0<Z<1)\\=P(Z<1)-P(Z<0)\\=0.84134-0.50\\=0.34134\\\approx 0.34[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1600 and $1700 is 34%.
(f)
Compute the probability of buyers who paid between $1600 and $1900 as follows:
[tex]P(1600<X<1900)=P(\frac{1600-1600}{100}<\frac{X-\mu}{\sigma}<\frac{1900-1600}{100})[/tex]
[tex]=P(0<Z<3)\\=P(Z<3)-P(Z<0)\\=0.99865-0.50\\=0.49865\\\approx 0.50[/tex]
*Use a z-table.
Thus, the approximate percentage of buyers who paid between $1600 and $1900 is 50%.
Answer:
Step-by-step explanation:
Two dataset in descending order (8,x,4,1) and (9,y,5,2). If the median is equal, find (y-x)
Answer:
y-x = -1
Step-by-step explanation:
Given the two dataset;
(8,x,4,1) and (9,y,5,2)
Since they are already arranged in descending order;
The median for the first dataset is;
M1 = (x+4)/2
The median for the second dataset is;
M2 = (y+5)/2
The median is equal;
M1 = M2
(x+4)/2 = (y+5)/2
x+4 = y+5
Collecting the like terms;
4-5 = y-x
y-x = -1
In 2011, the industries with the most complaints to the Better Business Bureau were banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships (USA Today, April 16, 2012), The results for a sample of 200 complaints are contained in the DATAfile named B8B. Click on the datafile logo to reference the data. a. Construct a frequency distribution for the number of complaints by industry, Category Bank 26 Cable Car Cell 42 60 Collection 28 Total b. Using α = .01, conduct a hypothesis test to determine if the probability of a complaint is the same for the five industries. The test-statistic is p-value- What is your conclusion?c. Which industry has the most complaints?
Answer:
Step-by-step explanation:
Hello!
The variable of study is
X: number of complaints per industry (Categorized: Bank, Cable, Car, Cell, Collection
Considering this is a categorical variable, and the hypothesis is that all categories have the same probability, you have to apply a Chi-Square Goodness to Fit test.
Observed frequencies per category
1) Bank: 26
2) Cable: 44
3) Car: 42
4) Cell: 60
5) Collection: 28
Total= 200
Statistical hypotheses:
H₀: P₁=P₂=P₃=P₄=P₅=1/5
H₁: At least one of the proposed proportions is different.
α: 0.01
[tex]X^2= sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}[/tex]
For this test the formula for the expected frequencies is:
[tex]E_i= n * P_i[/tex]
So the expected values for each category is:
[tex]E_1= n * P_1= 200*1/5= 40[/tex]
[tex]E_2= n * P_2= 200*1/5= 40[/tex]
[tex]E_3= n * P_3= 200*1/5= 40[/tex]
[tex]E_4= n * P_4= 200*1/5= 40[/tex]
[tex]E_5= n * P_5= 200*1/5= 40[/tex]
[tex]X^2_{H_0}= \frac{(26-40)^2}{40} +\frac{(44-40)^2}{40} +\frac{(42-40)^2}{40} +\frac{(60-40)^2}{40} +\frac{(28-40)^2}{40} = 11.5[/tex]
This test is one tailed and so is its p-value, under a Chi-square with 4 degrees of freedom p-value: 0.021484.
The p-value is less than the significance level so the decision is to reject the null hypothesis.
c. The industry with most complaints is the cellular phone providers
I hope this helps!
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 5 − x 2 . What are the dimensions of such a rectangle with the greatest possible area?
Answer:
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola
y=5−x^2. What are the dimensions of such a rectangle with the greatest possible area?
Width =
Height =
Width =√10 and Height [tex]= \frac{10}{4}[/tex]
Step-by-step explanation:
Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1)
are (h,k) and (-h,k).
Hence, the area of the rectangle will be (h + h) × k
Therefore, A = h²k ..... (2).
Now, from equation (1) we can write k = 5 - h² ....... (3)
So, from equation (2), we can write
[tex]A =h^{2} [5-h^{2} ]=5h^{2} -h^{4}[/tex]
For, A to be greatest ,
[tex]\frac{dA}{dh} =0 = 10h-4h^{3}[/tex]
⇒ [tex]h[10-4h^{2} ]=0[/tex]
⇒ [tex]h^{2} =\frac{10}{4} {Since, h≠ 0}[/tex]
⇒ [tex]h = ±\frac{\sqrt{10} }{2}[/tex]
Therefore, from equation (3), k = 5 - h²
⇒ [tex]k=5-\frac{10}{4} =\frac{10}{4}[/tex]
Hence,
Width = 2h =√10 and
Height = [tex]k =\frac{10}{4}.[/tex]
Which of these leaders would most likely have
spoken these words?
Tecumseh
Thomas Jefferson
Andrew Jackson
Answer:andrew Jackson
Answer:
D
Step-by-step explanation:
thank the person above ☝☝☝
Edge 2021
The three hands of an accurate 12-hour clock make a total of _?_ complete revolutions around the clock’s face every 24 hours. (A) 72 (B) 733 (C) 1466 (D) 10 104
Answer:
(C) 1466
Step-by-step explanation:
The hour hand makes one revolution each 12 hours. So it makes 2 revolutions a day.
The minute hand makes one revolution each hour. So it makes 24 revoulutions a day.
The second hand makes one revolution each minute. So it makes 24*60 = 1440 revolutions a day.
In total:
2 + 24 + 1440 = 1466
The correct answer is C.
Please answer this correctly
Answer: The first one
Step-by-step explanation:
If you take a look at the light pink squares, you can count three on the top and three on the bottom. Therefore, when looking at it from the top, you’ll see the first one.
I hope you found my answer helpful! If you did, give it a five-star rating and a thanks! I would really appreciate it!
Even a brainliest if you feel like it! ;)
Answer:
the first image will b da answer
Step-by-step explanation:
happy to help ya :)
What’s the correct answer for this?
Answer:
20
Step-by-step explanation:
Since chord AB and DE are at equal length from the centre, they are equal in length.
AB = DE
3x-7 = 5(x-5)
3x-7 = 5x-25
-7+25 = 5x -3x
18 = 2x
Dividing both side by 2
x = 9
Now
AB = 3(9)-7
= 27 -7
= 20
Select the number line that matches the expression |8-1|
Answer:
B
Step-by-step explanation:
We start at point 8 and go to point 1
the ratio of bicycles to to cars is 2:7 respectively. If the total number of vehicles are 63, how many bicycles are there?
Answer:
49 cars and 14 bikes
Step-by-step explanation:
we know [tex]7^{2}[/tex] is 49. 7 × 7 = 49
to match that, 7 × 2 = 14
14 plus 49 is 63
Keri deposits $100 in an account every year on the same day. She makes
no other deposits or withdrawals. The account earns an annual rate of 4%
compounded annually. How much interest does it earn on the 2nd year?*
Answer:
$20.32 or $12.16 depending on the question below!
Step-by-step explanation:
$320.32
It's a bit ambiguous, the current Principal is $100 plus 2 $ additions of $100 or the current Principal is $0 plaus 2 years of $100 contributions. In this case it's $212.16
Rounded to three decimal places, the value of the irrational number e is?
Answer:
2.178
hope it helps!
Answer:
2.718
______________________________
The sum of two numbers is 82. One number is 38 more than the other. Find the numbers.
Answer: 22, 60
Step-by-step explanation:
x+ x + 38 = 82
2x + 38 = 82
2x = 82 - 38
x = 44 / 2 = 22
Answer: 22, 60
Step-by-step explanation:
We can use system of equations to solve this. Let's use 1 for one number and y for the second number.
Equation 1
x+y=82
Equation 2
x+38=y
Since we know what y is, we can substitute it into the first equation.
x+(x+38)=82
x+x+38=82
2x+38=82
2x=44
x=22
Now that we know x, we cna plug it into any equaiton to find y.
(22)+38=y
y=60
What is the answer to the series of equations
Answer:
[tex]71\frac{2}{3}[/tex]
Step-by-step explanation:
1st equation:
3 cups = 3x
3x = 75
x = 25, cup = 25
2d equation
25 + lemon* lemons= 25 + y²
25 + y² = 89
y²= 89 - 25
y²= 64
y = 8, lemon = 8
3d equation
3 circles = 3c
3c = 44
c = 44/3 = 14 2/3
4th equation
25 + 32 + 14 2/3 = 71 2/3
Answer: 427/3
Step-by-step explanation:
The 3 cups added together is equal to 75, therefore, we can establish that each cup is equal to 25.
Cup=25
With the second equation, we plug in 25 for the cup and solve for the circles.
25+ Ο×Ο= 89
Ο×Ο=64
Circle=8
For the third equation, we can find the amount for the ovals if we divide by 3.
Oval= 44/3
Now that we know the value of each picture, we can solve the fourth equation.
25+8×(44/3)=?
25+(352/3)=?
(75/3)+(352/3)=427/3
Which point on the number line represents the product of 4 and -2.
Answer:
A: -8
Step-by-step explanation:
4 * -2 is -8, and A is on that point.
Answer:
its a I literally just did it
Step-by-step explanation:
The cafe where you work just ran out of coffee and you are at the store to buy 1 and 1/2 pounds of coffee you have to put a can with 3/4 pound of coffee in to your shopping cart how many more pounds of coffee do you need
Answer:
3/4 lbs more
Step-by-step explanation:
1 1/2 - 3/4 = 3/4
You need 3/4 lbs more coffee to have 1 1/2 lbs
y = -x2 + 6x - 5 whats
the axis of symmetry.
Answer:
x=3
Step-by-step explanation:
graphed on desmos.com
What’s the correct answer for this?
Answer
D.
Explanation
mIH = 44
mIJ = 46
mJK = 77
ADDING THEM ALL TO FIND THE MEASURE OF m<HOK
<HOK = 44+46+77
<HOK = 167°
Angie bought 44 pencils and paid 66.00. She sold the pencils at a rate of 2 for $3.50
calculate her profit.
Answer:
Profit of $11.00
Step-by-step explanation:
44÷2=22
22×$3.50=$77
$77.00-$66.00=$11.00/profit
A study done by researchers at a university concluded that 70 70% of all student athletes in this country have been subjected to some form of hazing. The study is based on responses from 1 comma 900 1,900 athletes. What are the margin of error and 95% confidence interval for the study? The margin of error is nothing .
Answer:
The margin of error is 0.0206 = 2.06 percentage points.
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.6794, 0.7206).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1900, \pi = 0.7[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.7*0.3}{1900}} = 0.0206[/tex]
The margin of error is 0.0206 = 2.06 percentage points.
The lower limit of this interval is:
[tex]\pi - M = 0.7 - 0.0206 = 0.6794[/tex]
The upper limit of this interval is:
[tex]\pi + M = 0.7 + 0.0206 = 0.7206[/tex]
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.6794, 0.7206).
One apple and three oranges cost $5.10 and another 5 oranges and one Apple cost $7.50 what is the price of one apple and one orange
Answer:
$2.7
Step-by-step explanation:
Let the price of one apple be x
and the price of one orange y
Hence ;
One apple and 3 oranges would cost:
x + 3×y = $5.10----------------------------(1)
One apple and 5 oranges would cost;
x + 5×y = $7.50--------------------------(2)
Subtracting eqn (1) from (2), we have :
x-x + 5y -3y = 7.5- 5.1
2y = 2.4
y = $1.2
From eqn(1)
x + 3y = $5.10
x= $5.10-3($1.2) = $5.10-$3.6 = $1.5
Hence x=$1.5 and y= $1.2
We are required to find the cost of one apple and one orange, hence :
x+y = $1.5+$1.2= $2.7
You earn $15 every week .at this rate , how much will you earn in 5 weeks
Answer:
If you earn $15 every week then you will have earned $75 by the end of 5 weeks.
Step-by-step explanation:
If $15 is 1 week,
and you need to find how much money after 5 weeks,
you multiply by the same number on both sides
1 = 15
1*5 = 15*5
5 = 75
So after 5 weeks you get $75
One-fourth If a scale factor of 1/4 is used to make a reduction, what is the base of the reduced triangle? ______ cm
Answer:
8 cm
Step-by-step explanation:
1/4 of 32 cm is (32/4) cm = 8 cm
The base of the reduced triangle is 8 cm.
Answer:
8 cm
Step-by-step explanation:
I just got it right on edge :) ur welcome
