Given:
[tex]f(x)=4x^3-5x^2-3x+2[/tex]
[tex]g(x)=x-3[/tex]
To find:
The remainder when f(x) is divided by g(x).
Solution:
According to remainder theorem, if f(x) is divides by (x-c), then remainder is f(c).
Using remainder theorem, if [tex]f(x)=4x^3-5x^2-3x+2[/tex] is divides by [tex]g(x)=x-3[/tex], then remainder is f(3).
Substitute x=3 in f(x).
[tex]f(3)=4(3)^3-5(3)^2-3(3)+2[/tex]
[tex]f(3)=4(27)-5(9)-9+2[/tex]
[tex]f(3)=108-45-7[/tex]
[tex]f(3)=56[/tex]
Therefore, the required remainder is 56.
In a study of the effect of aluminum intake on the mental development of infants, a group of 54infants who had been born prematurely were given a special aluminum depleted intravenous-feeding solution. At an adjusted age of 18 months,the neurologic development of the infants were measured using the Bayley Mental Development Index (BMDI), a unitless scale with higher scores indicating higher development. They had a sample mean BMDI of 97.4 and a sample standard deviation of 18.0.The (BMDI) is similar to an IQ score, with 100 being the average in the general population.
Assuming all relevant assumptions are met, carry out the appropriate testto determine if infants who receivedthealuminum depleted intravenous-feeding solution had a significantly differentaverage BMDI score thaninthe general population. Be sure to include all the stepsfor full credit.
Given:critical value= = 2.00
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
The no sufficient evidence to conclude that the average BMDI score is different from the general population
Step-by-step explanation:
From the question we are told that
The sample size is n = 54
The sample mean is [tex]\= x = 97.4[/tex]
The standard deviation is [tex]s = 18.0[/tex]
The population mean is [tex]\mu = 100[/tex]
The critical value is [tex]t_{critical } = 2.0[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu}{\frac{s}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 97.4 - 100}{\frac{ 18}{\sqrt{54} } }[/tex]
=> [tex]t =-1.062[/tex]
Comparing the obtained t statistics with the critical value we see that
The critical value is not within the region of rejection (i.e -1.062 to 1.062 )
Hence the decision rule is
Fail to reject the null hypothesis
The conclusion is
The no sufficient evidence to conclude that the average BMDI score is different from the general population
Question 16 (1 point)
Solve for X using Special Rights
X
13
y
1412
7
С
14
772
Answer:
d
Step-by-step explanation:
Find the point P that is 2/5 of the way from A to B on the directed line segment AB if A (-8, -2) and B (6, 19).
The location of the point P that is 2/5 of the way from A to B on the directed line segment AB if A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).
How to determine the location of a point within a line segment
By geometry we know that a line segment is generated from two distinct points set on a plane. The location of the point P within the line segment can be found by means of the following vectorial formula:
P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)], 0 < k < 1 (1)
Where:
A(x, y) - Initial pointB(x, y) - Final pointk - Distance factorIf we know that A(x, y) = (- 8, - 2), B(x, y) = (6, 19) and k = 2/5, then the location of the point P is:
P(x, y) = (- 8, -2) + (2/5) · [(6, 19) - (- 8, -2)]
P(x, y) = (- 8, -2) + (2/5) · (14, 21)
P(x, y) = (- 12/5, 32/5)
The location of the point P that is 2/5 of the way from A to B on the directed line segment AB if A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).
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answer quick 50 points
Answer: The 1/10, 0.22, then 1/4.
Second Picture: 9.8, Pie^2, then 99
Answer:
The 1/10, 0.22, then 1/4.
Second Picture: 9.8, Pie^2, then 99
PLEASE HEELP
Match the inverse, converse, contrapositive, and biconditional with their sentences.
Conditional Statement: If two angles are congruent, then they have the same measure.
Question 1 options:
converse
biconditional
inverse
contrapositive
1.
If two angles have the same measure, then they are congruent.
2.
If two angles are not congruent, then they do not have the same measure.
3.
If two angles do not have the same measure, then they are not congruent.
4.
Two angles are congruent if and only if they have the same measure.
Answer:
First, let's define each case:
A conditional statement is:
If P then Q.
P = hypothesis
Q = conclussion.
Converse: If Q then P.
Biconditional: P if and only if Q.
Inverse: If not P, then not Q.
Contrapositive: If not Q, then not P.
Our statement is:
"If two angles are congruent, then they have the same measure."
P = two angles are congruent.
Q = they have the same measure.
Now let's look at the options:
1) If two angles have the same measure, then they are congruent.
or: if Q then P, this is converse.
2) If two angles are not congruent, then they do not have the same measure.
or: If not P, then not Q, this is inverse.
3) If two angles do not have the same measure, then they are not congruent.
or: If not Q, then not P, this is the contrapositive.
4) Two angles are congruent if and only if they have the same measure.
or: P if and only if Q, this is biconditional.
Can someone please help me with this?
Answer:
I'm gonna say b
Step-by-step explanation:
b should be the answer
DUE IN 10 MINS HELP AS SOON AS POSSIBLE ASAP ILL GIVE BRAINLIEST!!
Answer:
m = -3
Step-by-step explanation:
First, find two clear points:
(1, -2) (0, 1)
Then, use the slope formula:
m = y2 - y1
x2 - x1
m = 1 - (-2)
0 - 1
= 3 = -3
-1
m = -3
This means that the rise-over-run is -3 over 1, or 3 over -1.
Which means three down and 1 to the right, or 3 up and 1 to the left.
Slope is the steepness of the line.
B. Solve the following Polynomials:
1. u³ + 64
Answer:
(4 + u)(16 – 4u + u2)
Step-by-step explanation:
64 + u3.
= 43 + u3.
= (4 + u)(42 – 4.u + u2).
= (4 + u)(16 – 4u + u2).
A jet travels 500 miles in 5 hours . At this rate ,how far could the jet fly in 9 hours ? What is the rate of speed of the jet?
Answer:
900 miles it will fly in 9 hours
Step-by-step explanation:
the rate of the speed of the jet is 100 miles per hour because if the jet traveled 500 miles in 5 hours that means it's been flying at 100 miles per hour.
What is the critical value for a chi-square test with 13 degrees of freedom at the 1 percent level of significance
Answer: 27.688
Step-by-step explanation:
The critical chi-square value [tex]\chi^2_{(df,\alpha)}[/tex] depends on significance level ([tex]\alpha[/tex]) and degrees of freedom (df) .
Given significance level: ([tex]\alpha[/tex]) = 1% = 0.01
Degrees of freedom (df)= 13
From the chi-square table, the critical chi-square value for df = 13 and [tex]\alpha =0.01[/tex]
is [tex]\chi^2_{(df,\alpha)}=27.688[/tex]
Hence, the required critical value = 27.688
What is the difference between the largest prime number less than 50 and the smallest com posite number greater than 10?
O 35
O 36
O 37
O 38
Answer:
prime numbers are those which can't be dividend for 2 and composites are the reverse of prime numbers so largest prime number <50 is 49 and smallest composite number >10 is 12 know we have got the numbers then by subtracting 12 from 49 we get 37
Answer:
37
Step-by-step explanation:
37
Show every subsequence of a subsequence of a given sequence is itselfa subsequence of the given sequence. Hint: Define subsequences asin (3) of Definition 11.1 g
Answer: Suppose that [tex]S_{n}[/tex], [tex]K_{n}[/tex] and [tex]A_{n}[/tex] are all sequences, also suppose that [tex]A_{n}[/tex] ⊂ [tex]K_{n}[/tex] ⊂ [tex]S_{n}[/tex] ∀ [tex]n[/tex] ∈ [tex]Z^{+}[/tex]. This implies that [tex]A_{n}[/tex] ⊂ [tex]S_{n}[/tex] as required.
Step-by-step explanation:
If you suppose that [tex]S_{n}[/tex], [tex]K_{n}[/tex] and [tex]A_{n}[/tex] are all representing three sequences respectively, and you also suppose that [tex]A_{n}[/tex] is a subset (in other words subsequence) of [tex]K_{n}[/tex] and [tex]K_{n}[/tex] is a subset (in other words subsequence) of [tex]S_{n}[/tex], where n takes its values from the set of positive integers. We can safely say that [tex]A_{n}[/tex] is a subsequence of [tex]S_{n}[/tex] and this can demosnstrated mathematically as follows:
Suppose that [tex]S_{n}[/tex], [tex]K_{n}[/tex] and [tex]A_{n}[/tex] are all sequences, also suppose that [tex]A_{n}[/tex] ⊂ [tex]K_{n}[/tex] ⊂ [tex]S_{n}[/tex] ∀ [tex]n[/tex] ∈ [tex]Z^{+}[/tex]. This implies that [tex]A_{n}[/tex] ⊂ [tex]S_{n}[/tex] as required.
A producer plans an outdoor concert for the weekend. The cost of the concert is $8,000 which includes advertising, security, printing, tickets, etc. The producer plans to profit $15,000 if all goes well. However, it it rains, the concert will be canceled. The chance of rain is 0.3 according to the weather report. Find the producer’s expected profit.
Answer: $8,100
Step-by-step explanation:
If it does not rain, the producer stands to make a profit of $15,000.
If it rains, the producer will lose the $8,000 they invested.
The chance of rain is 0.3 which means the chance it does not rain is 0.7.
Producer's expected profit is the weighted average of these outcomes;
= (15,000 * 0.7) + ( -8,000 * 0.3)
= 10,500 + ( - 2,400)
= $8,100
Prove the following statement directly from the definitions. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r
Answer:
- Integers, b ≠ 0 and d ≠ 0.
- r - s = (ad - bc)/bd.
- products and differences of integers are integers.
- zero product property
- quotient.
Step-by-step explanation:
Rational numbers are integers that can take the form of numerator divided by a denominator, that is to say in the form of 'a/b;. So, we are given from the question or problem to prove and fill in the gap the correct information or data:
For the first part of the question:
The missing data in the gap = Integers; b ≠ 0 and d ≠ 0. That is to say the denominators can not be zero or say that the denominators are non zero. This is one of the properties or let us say one of the ways of identifying a Rational number.
For the second part:
The missing data in the gap = a/b - c/d = (ad - bc)/bd. This is the representation in a simplified form.
For the third part:
The missing data or information = products and differences of integers are integers.
For the fourth part:
The missing data or information: zero product property, that is to say the product of the numerators is not equal to zero, or it is non zero.
For the fifth part:
The missing data or information: quotient. r - s is a quotient of two integers.
4p+2q=62
8p−q=59
Multiply 4p+2q=62 by 2, then subtract 8p−q=59 from the result.
Multiply 8p−q=59 by 2, then add the result to 4p+2q=62.
Do both strategies work for solving the system? If so why?
Answer:
3/2 and 6/9
Step-by-step explanation:
the teacher said i was right
Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 4, y = 16.
Answer:
The answer is "[tex]\bold{\frac{1024}{3}}[/tex]".
Step-by-step explanation:
[tex]= \int\limits^{4}_{-4} \int\limits^{4}_{0} \int\limits^{16}_{x^2} dy\ dx \ dz \\\\= 2 \int\limits^{4}_{0} \int\limits^{4}_{0} \int\limits^{16}_{x^2} dy\ dx \ dz \\\\ = 2 \int\limits^{4}_{0} \int\limits^{4}_{0} (16-x^2) dx \ dz \\\\= 2 \int\limits^{4}_{0} \int\limits^{4}_{0} 16x -\frac{x^3}{3} dx \ dz \\\\= 2 (16x -\frac{x^3}{3})^4_{0} \ dz \\\\= 2 (4) (16x -\frac{64}{3}) \\\\=8(\frac{2}{3} \times 64) \\\\=(\frac{16\times 64}{3} ) \\\\= \frac{1024}{3}[/tex]
The volume of the given solid is [tex]\frac{1024}{3}[/tex] cubic units.
In this question we must use the triple integral formula in rectangular coordinates to determine the volume of the solid ([tex]V[/tex]):
[tex]V = \iiint dy\,dx\,dz[/tex] (1)
The solid is constrained by the following intervals:
[tex]y \in [x^{2}, 16][/tex], [tex]x \in [-4, 4][/tex], [tex]z\in [0, 4][/tex]
Then, the triple integral is now described:
[tex]V = \int\limits_{0}^{4}\int\limits_{-4}^{4}\int\limits_{x^{2}}^{16} dy\,dx\,dz[/tex]
Now we proceed to integrate thrice to obtain the volume:
[tex]V = \int \limits_{0}^{4}\int \limits_{-4}^{4} (16-x^{2})\,dx\,dz[/tex]
[tex]V = \int\limits_{0}^{4} \left(16\cdot x - \frac{x^{3}}{3}\right)\left|\limits_{-4}^{4} dz[/tex]
[tex]V = \frac{256}{3} \int\limits_{0}^{4} dz = \frac{1024}{3}[/tex]
The volume of the given solid is [tex]\frac{1024}{3}[/tex] cubic units.
We kindly invite to check this question on triple integrals: https://brainly.com/question/19484372
15. To receive a B in his English class, Nicolas must have an average score of at least 84 on five
tests. He scored 90,91, 79, and 81 on his first four tests. What is the score range he can receive
on his last test and still receive a B in the class?
Answer:
(90+91+79+81+x)/5=84and 341+x=84*5and341+x=420and x=420-341 finally x=79
Please help!! Will give brainliest if correct!
If triangle RST is an equilateral triangle, find x and y.
A. x = 70, y = 35
B. x = 80, y = 40
C. x = 120, y = 30
D. x = 120, y = 40
Answer:
C.
Step-by-step explanation:
let f(x) = 2x - 1, g(x) = x²- 2 x+ 1. find (f• g ) (x)
Answer:
f•g(x) = f(x)•g(x)
f•g(x) = (2x-1) (x²-2x+1)
= 2x³-4x²+2x-x²+2x-1
= 2x³-5x²+4x-1
A researcher is exploring the notion that there is an economy of scale in raising children. While having one child might add to a family's financial stress, the second or third one might not be as "expensive" since they would already be sharing one roof, could share clothing, etc. The researcher has access to a large community of parents where 15% have one child under 18 in their home, 65% of parents have two children, and 20% of parents have three or more children. Rounded to the nearest whole number, the probability that any given family who is selected has two or more children at home is ________ %?
Answer:
The probability that any given family who is selected has two or more children at home is 85%.
Step-by-step explanation:
The information provided is as follows:
Number of Children Probability
1 0.15
2 0.65
> 3 0.20
Compute the probability that any given family who is selected has two or more children at home as follows:
P (At least 2 Children) = P (2 children) + P (More than 3 children)
= 0.65 + 0.20
= 0.85
Thus, the probability that any given family who is selected has two or more children at home is 85%.
An Airliner has a capacity for 300 passengers. If the company overbook a flight with 320 passengers, What is the probability that it will not be enough seats to accommodate all passengers. Assume that the probability that a randomly selected passenger shows up to the airport is 0.96. Find the probability using the normal distribution as an approximation to the binomial distribution.
Answer:
The probability is [tex]P(X >300 ) = 0.97219 [/tex]
Step-by-step explanation:
From the question we are told that
The capacity of an Airliner is k = 300 passengers
The sample size n = 320 passengers
The probability the a randomly selected passenger shows up on to the airport
[tex]p = 0.96[/tex]
Generally the mean is mathematically represented as
[tex]\mu = n* p[/tex]
=> [tex]\mu = 320 * 0.96[/tex]
=> [tex]\mu = 307.2[/tex]
Generally the standard deviation is
[tex]\sigma = \sqrt{n * p * (1 -p ) }[/tex]
=> [tex]\sigma = \sqrt{320 * 0.96 * (1 -0.96 ) }[/tex]
=> [tex]\sigma =3.50 [/tex]
Applying Normal approximation of binomial distribution
Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as
[tex]P(X > k ) = P( \frac{ X -\mu }{\sigma } > \frac{k - \mu}{\sigma } )[/tex]
Here [tex]\frac{ X -\mu }{\sigma } =Z (The \ standardized \ value \ of \ X )[/tex]
=>[tex]P(X >300 ) = P(Z > \frac{300 - 307.2}{3.50} )[/tex]
Now applying continuity correction we have
[tex]P(X >300 ) = P(Z > \frac{[300+0.5] - 307.2}{3.50} )[/tex]
=> [tex]P(X >300 ) = P(Z > \frac{[300.5] - 307.2}{3.50} )[/tex]
=> [tex]P(X >300 ) = P(Z > -1.914 )[/tex]
From the z-table
[tex]P(Z > -1.914 ) = 0.97219[/tex]
So
[tex]P(X >300 ) = 0.97219 [/tex]
suppose 123 people voted for danny if 55 of the votes from girls to votes for boys explain
Answer:
Suppose 123 people voted for Danny. If 55 of the votes were from girls, what would be the ratio of votes from girls to votes from boys? If 55 were girls then there were 123-55 = 68 boys. Thus the ratio would be 55 girls to 68 boys, or 55/68.
Answer:
60
Step-by-step explanation:
What is the answer to this question and please give an explanation. Please help me. Thank you.
Answer:
No, your classmate is not correct because the line isn't a line segment but a line and a line is never ending so their isn't a middle and their can't be those angles.
y+7=y–3 how many solutions does this equation have?
Answer:
No value
Step-by-step explanation:
Y has zero solutions
What is 4/5 divided 1/3
Lucas owed his friend 12$. He got some money from babysitting and was able to pay his friend back $8. What is his balance now?
~find an equation to match this word problem and solve~
Plz i need it right now thanksss
Answer:
balance $4
Step-by-step explanation:
12 - 8 = 4
Answer:
$4
Step-by-step explanation:
$ = 12 - 8
12 - 8 = $4
What number should be placed in the box to help complete the division calculation?
Long division setup showing an incomplete calculation. 17 is in the divisor, 2635 is in the dividend, and 1 hundreds and 5 tens is written in the quotient. 1700 is subtracted from 2635 to give 935. An unknown value represented by a box is being subtracted from 935.
Numerical Answers Expected!
Answer for Blank 1:
I WILL GIVE LOTS OF BRAINYS 20
PLEASE HELP I WILL DO ENEYTHING PLEASE
l. l. l_____. l. l__-__
l------- l l_____. l l. ____ l
l. l. l_____. l_____ l
Answer:
780
Step-by-step explanation:
17 is the divisor, while 2635 is the dividend. So that,
[tex]\frac{2635}{17}[/tex] = 155
The quotient = 155 = 1 hundreds, 5 tens and 5 units
Also,
2635 - 1700 = 935
Hence, let the unknown value be represented by x. Then;
935 - x
The answer of the subtraction should be equal to the quotient of the division.
935 - x = 155
935 - 155 = x
780 = x
Therefore the unknown value represented by a box is 780.
Answer:
780
Step-by-step explanation:
If jacks age is three years more than twice Trinas age, t, then which of the following represents the sum of their ages in terms of it
1. 2t+3
2. 2t +3t
3. 2t^2+3t
4. 3t+3
HELP ME ITS MY LAST PROBLEM ITS PRECAL HELP MEEEE
Step-by-step explanation:
LHS = (tan β + Sec β)(1 - sin β)
= ((sin β / cos β) + (1/cos β))(1-sin β)
= ((1+ sin β)*(1- sin β))/cos β
= (1 - sin^2 β) / cos β
= cos^2 β / cos β
= cos β
= RHS
Hence proved
simplify the expression and explain each step.
1. 4(3x + 2) -2
2. factor the expression completely 20b -16
please explain how to solve! will mark brainliest
Answer:
is the 3x a expression ill comment the awnser if is
Step-by-step explanation: