Answer:
The given polynomial is p(x)=x
4
−2x
3
+3x
2
−ax+3a−7
Given that, the polynomial p(x) when divided by (x+1) leaves remainder 19
Therefore, p(−1)=19 (By Remainder theorem)
=>(−1)
4
−2×(−1)
3
+3(−1)
2
−(−1)a+3a−7=19
=>1+2+3+a+3a−7=19
=>4a−1=19
=>4a=20
=>a=5
The value of a is 5
Now,
p(x)=x
4
−2x
3
+3x
2
−5x+3×5−7
=x
4
−2x
3
+3x
2
−5x+15−7
=x
4
−2x
3
+3x
2
−5x+8
Remainder when the polynomial is divided by (x+2)
=p(−2) (By Remainder Theorem)
=−2
4
−2(−2)
3
+3(−2)
2
−5(−2)+8
=16+16+12+10+8
=62
Thus, the remainder of the polynomial p(x) when divided by (x+2) is 62
Step-by-step explanation:
The remainder when P(x) is divided by (x-3) is 8
What is the quotient remainder theorem?The quotient-remainder theorem says that when any integer n is divided by any positive integer d, the result is a quotient q and a nonnegative remainder r that is smaller than d.
Given here, P(x)=x⁴ - 2x³ - 3x² + 4
Now we know from the polynomial remainder theorem that the remainder on dividing by (x-a) is f(a)
Thus P(3)=8
Hence, The remainder is 8
Learn more about the remainder theorem here:
https://brainly.com/question/29046143
#SPJ2
A bacteria culture contains 1500 bacteria initially and doubles every hour. Find a function N that models the number of bacteria after t hours. Write out how many bacteria there will be for t = 0, 1, 2, etc. and think about how you are getting those values.
Answer: N(t) = (2^t)*1500
Step-by-step explanation:
Let's define the hour "zero" as the initial population.
So if N(t) is the number of bacteria after t hours, then:
N(0) = 1500.
Now, we know that the population doubles every hour, so we will have that after one hour, at t = 1
N(1) = 2*1500 = 3000
after two hours, at t = 2.
N(2) = 2*(2*1500) = (2^2)*1500
After three hours, at t = 3
N(3) = 2*(2^2)*1500 = (2^3)*1500
So we already can see the pattern, the number of bacteria after t hours will be:
N(t) = (2^t)*1500
solve for x, and explain how u did it :)
Answer:
71 I THINK
Step-by-step explanation:
since the angles on the base of an isosceles triangle equal each other you would wright 71=x as your equation. there is nothing else to solve so 71 is your answer
c) Parbati buys a mobile for Rs 6,300 and sells it to Laxmi at 15% profit. How much
does Laxmi pay for it?
Answer:
Rs. 7245
Step-by-step explanation:
Given parameters:
Cost price = Rs. 6300
Percentage profit = 15%
Unknown:
Selling price = ?
Solution:
If profit is made on a trade, the selling price is higher than the cost price.
Profit = Selling price - Cost price
To find the selling price simply;
Selling price =( 1 + [tex]\frac{15}{100}[/tex]) x cost price
Selling price = 1.15 x 6300 = Rs. 7245
solve the following formula for H. r=n/2(b+H)
Answer:
See below.
Step-by-step explanation:
What you wrote means:
[tex] r = \dfrac{n}{2}(b + H) [/tex]
If that is what you meant, then the answer is:
[tex] \dfrac{2r}{n} = b + H [/tex]
[tex] H = \dfrac{2r}{n} - b [/tex]
On the other hand, if this is what you meant:
[tex] r = \dfrac{n}{2(b + H)} [/tex]
then the answer is:
[tex] 2r(b + H) = n [/tex]
[tex] 2rb + 2rH = n [/tex]
[tex] 2rH = n - 2rb [/tex]
[tex] H = \dfrac{n - 2rb}{2r} [/tex]
Answer:
Step-by-step explanation:
[tex]\frac{n}{2}(b + H) = r\\\\b +H = r * \frac{2}{n}\\\\b + H = \frac{2r}{n}\\\\H = \frac{2r}{n} - b[/tex]
Please help I'm really stressed about this it's simple it's the last question on this assignment I'll mark brainliest plzzz help
The formula used to compute a confidence interval for the mean of a normal population when n is small is the following. x^^\_ +/-\(t text( critical value)\)s/sqrt(n) What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.) (a) 95% confidence, n = 17(b) 90% confidence, n = 12 (c) 99% confidence, n = 24 (d) 90% confidence, n = 24 (e) 80% confidence, n = 13 (f) 95% confidence, n = 10
Answer:
a) 2.120
b) 1.796
c) 2.807
d) 1.714
e) 1.356
f) 2.262
Step-by-step explanation:
The formula used to compute a confidence interval for the mean of a normal population when n is small is the following. x^^\_ +/-\(t text( critical value)\)s/sqrt(n) What is the appropriate t critical value for each of the following confidence levels and sample sizes? (Round your answers to two decimal places.)
(a) 95% confidence, n = 17
We find our degrees of freedom first
= n - 1
= 17 - 1
= 16
The t critical value using the t table =
2.120
(b) 90% confidence, n = 12
We find our degrees of freedom first
= n - 1
= 12 - 1
= 11
The t critical value using the t table =
1.796
(c) 99% confidence, n = 24
We find our degrees of freedom first
= n - 1
= 24 - 1
= 23
The t critical value using the t table = 2.807
(d) 90% confidence, n = 24
We find our degrees of freedom first
= n - 1
= 24 - 1
= 23
The t critical value using the t table =
1.714
(e) 80% confidence, n = 13
We find our degrees of freedom first
= n - 1
= 13- 1
= 12
The t critical value using the t table = 1.356
(f) 95% confidence, n = 10
We find our degrees of freedom first
= n - 1
= 10 - 1
= 9
The t critical value using the t table =
2.262
Help please!! Inverse of Matrix problem!!
Number 8 please!!
Step-by-step explanation:
Inverse of p matrix is in picture
i wish it will make u easy to do♥️✌️
I don’t get this question at all, pls help. I just need the function.
Suppose the average salary for a data scientist is $83,105 with a standard deviation of $10,503. What is the probability that the mean salary of 31 randomly selected data scientists is less than $80,000.
Answer:0.0499
Step-by-step explanation:
Let x be a random variable that represents the salary for a data scientist.
Given: Average salary for a data scientist [tex]\mu=\$83105[/tex]
standard deviation [tex]\sigma=\$10503[/tex]
Sample size : n= 31
The probability that the mean salary of 31 randomly selected data scientists is less than $80,000.
[tex]P(\overline{X}<80000)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{80000-83105}{\dfrac{10503}{\sqrt{31}}})\\\\=P(z<-1.646)\ \ \ [z=(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(z<1.646)\ \ \ [P(Z<-z)=1-P(Z<z)]\\\\=1-0.9501= 0.0499[/tex]
Hence, the required probability = 0.0499.
Help please!!!!
What is the absolute value of the number indicated on the number line below?
A. -2/3
B. -3/5
C. 3/5
D. 2/3
Answer:
b
Step-by-step explanation:
it is 3 out of 5 ticks over to the left
Does anyone know the simplest radical form for this question
Answer:
A.
Step-by-step explanation:
Simplify the radical by breaking up the radicand up into a product of known factors, assuming positive real numbers.
Answer:
A) 4[tex]\sqrt15\\[/tex]
Step-by-step explanation:
Start by factoring 240 to its prime factors
√240 = √10 · 24 =√2·5·2·2·2·3
look for pairs of numbers. There are 2 pairs of 2s, so take those out of the radical
= 2·2√5·3
= 4√15
At the time this question was written, one US Dollar equaled 0.88 Euros. What would 50 Euros equal in US Dollars? Round your answer to the nearest cent.
Answer:
$56.82 US dollars
Step-by-step explanation:
Set up a proportion where x is how many US dollars there are in 50 Euros:
[tex]\frac{1}{0.88}[/tex] = [tex]\frac{x}{50}[/tex]
Cross multiply and solve for x:
0.88x = 50
x = 56.82
So, 50 Euros is approximately equal to $56.82 US dollars
plsss helpppp 6x^2+4x-42
Answer:
Step-by-step explanation:
6x^2+4x-42
2(3x^2+2x-21)=0
3x^2+2x-21=0
3x^2+(9-7)x-21=0
3x^2+9x-7x-21=0
3x(X+3)-7(X+3)=0
(3X-7)(X+3)=0
So Answer is (3x-7)(X+3)
3−y÷ 3 5; y= 1 4
whats the answer to this
Answer:
2.6
Step-by-step explanation:
Divide the numbers, then subtract them
Please describe a situation where you would use Excel and please describe the growth mindset needed to learn and understand.
A growth mindset is an idea that people are born with certain characteristics and can't change. A growth mindset allows a person to believe they can change themselves, and that abilities and intelligence can be developed over time. A growth mindset helps you learn that mistakes are stepping stones and that you aren't defined as some characteristic (like "dumb").
Brainliest if you provide an explanation and/or get it right!
Q: Find the value of y if x = 3
Order the numbers from least to greatest
Answer:
2 then the square root of 7 then 9.5
Step-by-step explanation:
Answer:
Step-by-step explanation:
√7,2,9.5
√7=2.645
So
Order the numbers from least to greatest is
2,√7,9.5 is the answer
Find the mean monthly subscription fee? Round your answer to the nearest cent.
$8.78
$6.78
$5.78
Answer:
$6.78
Step-by-step explanation:
Add $10 +$6 +$2.75+$3+$5+$10+$10+$4+$12+$5 =$67.75
Now divide $67.75 by 10 which is the number of values you added up
$67.75/ 10 = 6.775
Now round to nearest cent = $6.78
Explain to me in words how you would find the slope of this line and explain how you got your answer
Answer: m= 5/3
Step-by-step explanation: the point were at (-1,2) (-4,-3)
m= y2-y1/ x2- x1
m= -3-2/ -4 (-1)
m= -5/-3
m= 5/3
( hope this helps)A commercial apple grower estimates from past records that if 50 trees are planted per acre, then each tree will yield an average of 70 pounds of apples per season. If, for each additional tree planted per acre (up to 30), the average yield is reduced by 1 pound, how many trees should be planted per acre to obtain the maximum yield per acre? What is the maximum yield?
Answer:
i) 60 trees
ii) 3600 apples
Step-by-step explanation:
50 trees per acre
Total pounds produced per acre ( ideally ) = 70 * 50 = 3500 pounds
Assumption :
lets assume the additional tree = X
Therefore the number of trees planted per acre = ( 50 + x ) where x ≤ 30
calculate average yield per tree = ( 70 - x )
Total yield per acre = number of trees * average yield per tree
= ( 50 + x ) * ( 70 - x )
Y(x) = 3500 + 20x - x^2
i) Number of trees that should be planted per acre to obtain maximum yield per acre
y'(x) = 20 - 2x = 0 hence X ( number of additional trees ) = 20 / 2 = 10
Number of trees that should be planted per acre = 50 + 10 = 60 trees
ii) Calculate maximum yield
where ; X = 10
number of trees planted per acre = ( 50 + x ) = 50 + 10 = 60
hence maximum yield = ( 50 + x ) * ( 70 - x ) = ( 60 ) * ( 60 ) = 3600 apples
PLZ HELP ASAP (This is not a text or an exam)
Answer:
x=4
Step-by-step explanation:
As the two angles are clearly congruent because of the bisector, we set them equal to each other:
7x=3x+16
4x=16
x=4
Therefore, the value of x is 4 and not 9
I need help someone ?
Answer:
1) y=4x+5, 2) y=-2x+2, 3)y= 4/3x+4
Step-by-step explanation:
1) y=4x+5
2) y=-2x+c
-4= -2(3)+c
-4=-6+c
+6 +6
2=c
y=-2x+2
3) 4-0/0--3
4/3= gradient
y= 4/3x+c
4= 4/3(0)+c
4=0+c
4=c
y= 4/3x+4
A new concert venue just opened in downtown Houston and they are in the process
of deciding how many tickets they can sell for each show. The venue has three levels,
two general admission that only have standing room, and one level with 150 seats.
The venue thinks each person will occupy 2.25 ft.
.
• The first level of standing room is a square with one side measuring 75ft.
The second level, also standing room, is a rectangle measuring 100' by 50' ft.
. The third level has 150 seats.
How many tickets can they sell for the first level?
Answer:
2500
Step-by-step explanation:
Dimensions of first level
Length = Breadth = 75 ft (since it is a square)
It is assumed that a person will occupy [tex]2.25\ \text{ft}^2[/tex]
Area of first level
[tex]75\times 75=5625\ \text{ft}^2[/tex]
When the area of the level is divided by the area of one person then we will get the number of people that can occupy the room or the number of tickets that can be sold.
[tex]\dfrac{5625}{2.25}=2500[/tex]
The number of tickets that can be sold for the first level is 2500.
Consider the figure, where segment M N is parallel to segment RP.
What is the value of x?
What are some important things I should put in my notes about ratios(In 6th grade so nothing to high up I wouldn't know about)
Answer:
some tips
Step-by-step explanation:
- Ratios can include fraction forms, ex; 5/3. using the word 'to', ex; 5 to 3, and using the colon symbol. 5:3. Do not put ratios in number order like least to greatest values, ever, because the order they come in matter. Make sure to always simplify if possible. ex; 5:25 = 1:5 . thats it, if you get any of the points down then you got it.
I need help with this I will give you 20 points
Mr. Smith provides music lessons online for a fee. He charges $15 per lesson plus an initial fee of $30. How many lessons could Jason sign up for if he wants to spend $120?
Wright an equation to represent how many lessons Jason could sign up for. Show all steps to solve the equation. Explain what your final answer means in context of the problem.
Answer:
2 lesson with a remainer of $30
Step-by-step explanation:
$15 + $30 = $45
$45 multipled by 3 would equal 135 witch is $15 over ,
but $45 multiplyed by 2 would equal $90 with a remainer of $30 (jason could buy some McDonlads with that money , lol)
What is the quotient of -3/8 and -1/3?
A. -1 1/8
B. -1/8
C. 1/8
D. 1 1/8
Answer:
d. 1 1/8
Step-by-step explanation:
-3 -1
---- ÷ -----
8. 3
Keep, Change, Flip.
-3/8 stays the same.
Division becomes multiplication.
-1/3 becomes -3/1
-3. -3. = 9
----- × ----- ------
8. 1. = 8
9/8 = 1 1/8
Answer:
D. 1 1/8
Step-by-step explanation:
the first term of GP where second term is 2 and sum of infinity is8 it will be
Answer:
a = 4
Step-by-step explanation: Given that
ar=2 where a is the first term and is the common ratio.
ar=2 ............1
Also give that a/1-r = 8 where a is the first term and r is the common ratio as well.
a/1-r = 8 ......... 2
From equation 1 make r the subject
ar=2
r= 2/a...........3
Put equation 3 into 2
a/1-2/a =8
a÷1-2/a
a = 8(1-2/a)
a= 8/1-16/a
a/1= 8a-16
a^2= 8a-16
Rewriting the above equation
a^2-8a+16=0
This will eventually be
a^2-8a+16=0
(a-4)^2= 0
a =4
A charity sells tickets for a fundraising dinner. Each adult's ticket cost $10 and each child's ticket cost $5. A total of $1050 was raised by selling 130 tickets. How many adult and child tickets were sold? Let x represent the number of adult tickets and y represent the number of child tickets.
Number of Adult Tickets Sold =
Number of Child Tickets Sold =
Answer:43
Step-by-step explanation: