2. Compare the function ƒ(x) = –x^2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maximum (vertex)?
Answers
Answer:
g(x)
Step-by-step explanation:
The vertex of g(x) as shwon in the graph is located in the point wich coordinates are (3.5,6.25) approximatively
We need to khow the coordinates of f(x) vertex
Here is a way without derivating:f(x) = -x² + 4x -5
let a be the leading factor, b the factor of x and c the constant:
a= -1b= 4c= -5The coordinates of a vertex are: ([tex]\frac{-b}{2a}[/tex] , f([tex]\frac{-b}{2a}[/tex]) )
-b/2a = -4/ (-1*2) = 4/2 = 2
f(2)= -2²+4*2-4 = -4+4-4 = -4
obviosly f(x) has a minimum wich less than g(x)'s maximum
Answer:
Step-by-step explanation:
g(x) i think
Related Questions
Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answers
Answer:
The answer is below
Step-by-step explanation:
Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
Given:
Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645
The margin of error (E) is given by:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]
The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)
The 90% confidence interval is from 7.3442 to 9.9278
a warehouse had 3 shelves long enough to hold 8 boxes and high enough to hold 4 boxes. all the shelves are full how many boxes are on the shelves all together?
Answers
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I think. I just multiplies the 3 numbers. Hope this helps (:
Answer:
8*4*3=96 boxes in total
Step-by-step explanation:
I just multiplies the 3 numbers.
The area of a square is 64n36. What is the length of one side of the square?
Answers
Answer:
8n6
step by step explanation.
find the values of x and y that make k ll j and m ll n
Answers
Answer:
x = 80
y = 130
Step-by-step explanation:
The 2 angles are supplementary. so, x-30 + x+50 = 180.
We solve and get 2x = 180-20
x = 80
y = x+50, because of parallel rules.
y = 130
Answer:
x = 80
y = 130
Step-by-step explanation:edge 2020
Given p(x) = x4 + x3 - 13x2 - 25x - 12
1. What is the remainder when p(x) is divided by X - 4?
2. Describe the relationship between the linear expression and the polynomial?
How do we describe the relationship?
Answers
When a number is divided by a number it results in a quotient and a remainder
E.g. 9 / 4 = 2 remainder 1
9 is the dividend
4 is the divisor
2 is the quotient
1 is the remainder
Same way when a polynomial is divided by a linear expression
E.g.
Ax^2 + bx + c / (x-b) = (x+a) + r
Which can be rearranged to
ax^2 + bx + c = (x+a)(x-b) + r
When x = - a or b, only the remainder is left since either (x+a)(x-b) is 0.
If x = - a or b is substituted into the polynomial and the value is 0 then there is no remainder,
This would suggest (x+a) or (x-b) are factors of the polynomial.
Now apply this logic to these questions
1. Let’s assume (x-4) is a factor, this would mean that when x=4 is substituted into the polynomial the answer would be 0.
This is the case, therefore the remainder is 0.
2. Having seen the logic above (applied using the remainder and factor theorem) the linear expression is a factor of the polynomial.
simplify (3+3 / x(x+1) )(x-3 / x(x-1) )
Answers
Answer:
I think it is [tex]\frac{6x-18}{x^{4} }[/tex]
Step-by-step explanation:
5/12 +( 5/12 + 3/4 ) =
Answers
Answer:
Proper: 15/4
Improper: 3 3/4
Step-by-step explanation:
Well to solve the following question,
5/12 + (5/12 + 3/4)
We solve the part in the parenthesis first,
5/12 + 3/4 = 14/4
Simplified -> 7/2
5/12 + 7/2
= 45/12
Simplified -> 15/4
Thus,
the answer is 15/4 or 3 3/4.
Hope this helps :)
Answer:
19/12= [tex]1 \frac{7}{12}[/tex]Step-by-step explanation:
[tex]\frac{5}{12}+\left(\frac{5}{12}+\frac{3}{4}\right)\\\\=\frac{5}{12}+\frac{5}{12}+\frac{3}{4}\\\\\mathrm{Add\:similar\:elements:}\:\frac{5}{12}+\frac{5}{12}=2\times \frac{5}{12}\\=2\times \frac{5}{12}+\frac{3}{4}\\\\=\frac{5\times \:2}{12}\\\\=\frac{10}{12}\\\\=\frac{10}{12}\\\\=\frac{5}{6}+\frac{3}{4}\\L.C.M =12\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{5}{6}=\frac{5\cdot \:2}{6\times \:2}=\frac{10}{12}\\\\\frac{3}{4}=\frac{3\times \:3}{4\times \:3}=\frac{9}{12}\\[/tex]
[tex]\\=\frac{10}{12}+\frac{9}{12}\\\mathrm{Since\:the\:denominators\:are\:equal\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{10+9}{12}\\\\=\frac{19}{12}[/tex]
24=3(n-5) solve for n
Answers
Answer:
n = 13
Step-by-step explanation:
24 = 3 (n-5)
3n - 15 = 24
3n = 24 +15
3n = 39
n = 39/3
n = 13
Answer:
[tex]\boxed{\sf n=13}[/tex]
Step-by-step explanation:
[tex]\sf 24=3(n-5)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]\sf 24=3n-15[/tex]
[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]
[tex]\sf 24+15=3n-15+15[/tex]
[tex]\sf 39=3n[/tex]
[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]
[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]
[tex]\sf 13=n[/tex]
WHY CAN'T ANYONE HELP ME :( Solve the formula for the specified variable. tex]D=\frac{1}{4}fk for f.
Answers
Answer:
4d/k or [tex]\frac{4d}{k}[/tex]
Step-by-step explanation:
first multiply both sides by four
you will have 4d=fk
then divide by k
4d/k=f
A random sample of 61 Foreign Language movies made in the last 10 years has a mean length of 135.7 minutes with a standard deviation of 13.7 minutes. Construct a 95% confidence interval.
Answers
Answer:
95% confidensce interval of the mean (two-tail) = [132.2, 139.2]
Step-by-step explanation:
Given:
N = size of sample = 61
m = sample mean = 135.7
s = sample standard deviation 13.7
Need 95% confidence interval
Solution.
alpha (95% confidence interval) = 0.05
(1-alpha/2) = 0.975 [two sided]
Equation for confidence interval of the mean
= m +/- t(1-alpha/2,N-1) * s / sqrt(N)
= 135.7 +/- 2.0003 * 13.7 / sqrt(60)
= [132.16, 139.24]
f(x)= x^2– 3x + 9
g(x) = 3x^3+ 2x^2– 4x – 9
Find (f - g)(x).
Answers
Answer:
[tex]\large \boxed{\sf \ \ -3x^3-x^2+x+18 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex](f-g)(x)=f(x)-g(x)=x^2-3x+9-(3x^3+2x^2-4x-9)\\\\=x^2-3x+9-3x^3-2x^2+4x+9\\\\=\boxed{-3x^3-x^2+x+18}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the measure of the indicated angle to the nearest degree. Thanks.
Answers
Answer:
θ ≈ 40°
Step-by-step explanation:
Since, sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
In the picture attached,
Measures of adjacent side and opposite side of the triangle have been given. Therefore, tangent rule will be applied in the given triangle.
tanθ = [tex]\frac{19}{23}[/tex]
θ = [tex]\text{tan}^{-1}(\frac{19}{23})[/tex]
θ = 39.56
θ ≈ 40°
A sample of bacteria is growing at an hourly rate of 10% compounded continuously. The sample began with 4 bacteria. How many bacteria will be in the sample after 18 hours?
Answers
Answer:
24
Step-by-step explanation:
The computation of the number of bacteria in the sample after 18 hours is shown below:
We assume the following things
P = 4 = beginning number of bacteria
rate = r = 0.1
Now
We applied the following formula
[tex]A = Pe^{rt}[/tex]
[tex]= 4\times e^{18\times0.1}[/tex]
[tex]=4e^{1.8}[/tex]
[tex]= 4\times6.049647464[/tex]
= 24
We simply applied the above formula to determine the number of bacteria after the 18 hours
PLEASEEEEE HELPPOO
For Individual or Group Explorations
Maximizing the Total Profit
Payles at The Christmas Store very periodically with a high ef 550.000 in December
the Christmas Stove also comes the Powe, where profits reach a high of $80,000
in Aurust and a few of $20,000 in February Assume that the profit function for
Crm Store
Save
40
20
10
1 2 3 4 5 6 7 8 9 10 11 12
Month
a) Write the profit function for The Christmas Store as a function of the month
and sketch its graph
b)
Write the profit function for The Pool Store as a function of the month and
sketch its graph.
are are length
Write the total profit as a function of the month and sketch its graph. What is
the period?
are inside the
est enth of a
Use the maximum feature of a graphing calculator to find the owner's maxi-
mum total profit and the month in which it occurs.
Find the owner's minimum total profit and the month in which it occurs.
We know that y -a sin x + bcos x is a sine function. However, the sum of
two arbitrary sine or cosine functions is not necessarily a sine function. Find an
example in which the graph of the sum of two sine functions does not look like
a sine curve.
Explain.
is tangent to one
Answers
Answer:
what
Step-by-step explanation:
a hardware store ordered cartons of hammers at 100$ per carton and cartons wrenches at 150$ per carton if there were a total of 25 cartons in this order And the total cost of the order was 3,000$ how many cartons of hammers were ordered
Answers
Answer:
15 cartons of Hammers were ordered
Step-by-step explanation:
Cost per carton of Hammer = $100
Cost per carton of Wrenches = $150
Total Carton = 25
Total Cost = $3,000
Required
Determine the numbers of Hammer and Wrenches
Represent the hammers with H and the wrenches with W
So;
[tex]H + W = 25[/tex]
and
[tex]100H + 150W = 3000[/tex]
Make W the subject of formula in the first equation:
[tex]H + W = 25[/tex]
[tex]W = 25 - H[/tex]
Substitute 25 - H for W in the second equation
[tex]100H + 150(25 - H) = 3000[/tex]
[tex]100H + 3750 - 150H = 3000[/tex]
Collect Like Terms
[tex]100H - 150H = 3000 - 3750[/tex]
[tex]-50H = -750[/tex]
Divide both sides by -50
[tex]\frac{-50H}{=50} = \frac{-750}{-50}[/tex]
[tex]H = \frac{-750}{-50}[/tex]
[tex]H = 15[/tex]
Hence, 15 cartons of Hammers were ordered
What is the missing term that makes these ratios equivalent? 1.5:3, 31.5:____
Answers
=========================================
Work Shown:
1.5/3 = 31.5/x
1.5x = 3*31.5 cross multiply
1.5x = 94.5
x = 94.5/1.5 dividing both sides by 1.5
x = 63
-----------
An alternative equation to solve is
1.5/31.5 = 3/x
1.5x = 31.5*3
1.5x = 94.5
The remainder of the steps are the same as in the previous section above.
Need help finding the length
Answers
Answer:
27
Step-by-step explanation:
First, we need to find x. We are given the perimeter, which is 2l + 2w, so from there, we have an equation of 2(4x-1) + 2(3x+2) = 100. By working through it, we get that x = 7. We're asked to find WX, so plug 7 into 4x - 1 and get 27.
Answer:
27 unitsStep-by-step explanation:
Perimeter of rectangle is 2(l) + 2(w).
The perimeter is given 100 units.
2(4x-1) + 2(3x+2) = 100
Solve for x.
8x-2+6x+4=100
14x+2=100
14x=98
x=7
Plug x as 7 for the side WX.
4(7) - 1
28-1
= 27
what are the coordinates of point b on ac such that ab=2/5ac
Answers
Answer:
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]
= [tex]-\frac{36}{7}[/tex]
y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]
= [tex]\frac{40}{7}[/tex]
Therefore, coordinates of pint B will be,
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
A bicycle tire has a radius of 5 inches. To the nearest inch, how far does the tire travel when it makes 8 revolutions?
Answers
Answer:
251 inches
Step-by-step explanation:
c = 2πr
c = 2(3.14)(5) = 31.4
31.4 x 8 rev. = 251 inches
Two jokers are added to a $52$ card deck and the entire stack of $54$ cards is shuffled randomly. What is the expected number of cards that will be strictly between the two jokers?
Answers
Answer:
52/3.
Step-by-step explanation:
There are (54·53)/2 = 1431 ways the 2 jokers can be placed in the 54-card deck. We can consider those to see how the number of cards between them might work out.
Suppose we let J represent a joker, and - represent any other card. The numbers of interest can be found as follows:
For jokers: JJ---... there are 0 cards between. This will be the case also for ...
-JJ---...
--JJ---...
and so on, down to ...
...---JJ
The first of these adjacent jokers can be in any of 53 positions. So, the probability of 0 cards between is 53/1431.
__
For jokers: J-J---..., there is 1 card between. The first of these jokers can be in any of 52 positions, so the probability of 1 card between is 52/1431.
__
Continuing in like fashion, we find the probability of n cards between is (53-n)/1431. So, the expected number of cards between is ...
[tex]E(n)=\sum\limits_{n=0}^{53}{\dfrac{n(53-n)}{1431}}=\dfrac{53}{1431}\sum\limits_{n=0}^{53}{n}-\dfrac{1}{1431}\sum\limits_{n=0}^{53}{n^2}\\\\=\dfrac{53(53\cdot 54)}{1431(2)}-\dfrac{1(53)(54)(107)}{1431(6)}=53-\dfrac{107}{3}\\\\\boxed{E(n)=\dfrac{52}{3}}[/tex]
10=12-x what would match this equation
Answers
Answer:
x=2
Step-by-step explanation:
12-10=2
Answer:
x=2
Step-by-step explanation:
10=12-x
Subtract 12 from each side
10-12 = 12-12-x
-2 =-x
Multiply by -1
2 = x
What is the best way to remember the 6 trigonometric ratios?
Answers
Answer:
SOHCAHTOA
Step-by-step explanation:
Usually, in American schools, the term "SOHCAHTOA" is used to remember them. "SOH" is sine opposite hypotenuse, "CAH" is cosine adjacent hypotenuse, and "TOA" is tangent opposite adjacent. There is also Csc which is hypotenuse/opposite, Sec which is hypotenuse/adjacent, and Cot is adjacent/opposite.
Answer: SOHCAHTOA
Step-by-step explanation:
The pneumonic I learned is SOH-CAH-TOA. it says that Sin = opposite/hypotenuse. Cos = adjacent/hypotenuse. Tan = opposite/adjacent.
Hope it helps <3
Classify the polynomial 2x^3+6x^2-4 by the number of terms. binomial. trinomial. cubic. quadratic.
Answers
Answer:
monomial
Step-by-step explanation:
Hi any help is appreciated. Just wanna graduate:))
Answers
Answer: C
Step-by-step explanation:
h · k(x) = 2(3x - 5)(-2x + 1)
= (6x - 10)(-2x + 1)
= -12x² + 6x + 20x - 10
= -12x² + 26x - 10
Answer:
C
Step-by-step explanation:
h(x) × k(x)
= 2(3x - 5)(- 2x + 1) ← expand factors using FOIL
= 2(- 6x² + 3x + 10x - 5)
= 2(- 6x² + 13x - 5) ← distribute parenthesis by 2
= - 12x² + 26x - 10 → C
NEED HELP THANKLSSSS
Answers
Answer:
Side length: 3 cm.
Surface area: 54 cm squared.
Step-by-step explanation:
The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.
So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.
There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.
Hope this helps!
Write 3 expressions containing exponents so that each expression equals 81
Answers
Answer:
9x9= 81
3x3x3x3=81
81 to the first power.
Step-by-step explanation:
I hope this helps in any way:)
in the life of a car engine, calculatedin miles, is normally distributed, with a mean of 17,000 miels and a standard deviation of 16,500 miles, what should be the guarantee period if the company wants less than 2% of the engines to fail while under warranty g
Answers
Answer:
the guarantee period should be less than 136010 miles
Step-by-step explanation:
From the given information;
Let consider Y to be the life of a car engine
with a mean μ = 170000
and a standard deviation σ = 16500
The objective is to determine what should be the guarantee period T if the company wants less than 2% of the engines to fail.
i.e
P(Y < T ) < 0.02
For the variable of z ; we have:
[tex]z = \dfrac{x - \mu }{\sigma}[/tex]
[tex]z = \dfrac{x - 170000 }{16500}[/tex]
Now;
[tex]P(Y < T ) = P( Z < \dfrac{T- 170000}{16500})[/tex]
[tex]P( Z < \dfrac{T- 170000}{16500})< 0.02[/tex]
From Z table ;
At P(Z < -2.06) ≅ 0.0197 which is close to 0.02
[tex]\dfrac{T- 170000}{16500}<- 2.06[/tex]
[tex]{T- 170000}<- 2.06({16500})[/tex]
[tex]{T- 170000}< - 33990[/tex]
[tex]{T}< - 33990+ 170000[/tex]
[tex]{T}<136010[/tex]
Thus; the guarantee period should be less than 136010 miles
An unbiased coin is tossed 14 times. In how many ways can the coin land tails either exactly 9 times or exactly 3 times?
Answers
Answer
[tex]P= 0.144[/tex] ways
the coin can land tails either exactly 8 times or exactly 5 times in
[tex]0.144[/tex] ways
Step by step explanation:
THis is a binomial distribution
Binomial distribution gives summary of the number of trials as well as observations as each trial has the same probability of attaining one particular value.
P(9)=(14,9).(0.5)⁹.(0.5)¹⁴⁻⁹
p(3)=(14,3).(0.5)⁹.(0.5)¹⁴⁻³
p=(9)+p(3)
p=C(14,9)(0.5)¹⁴ + C(14,3). (0.5)¹⁴
P= (0.5)¹⁴ [C(14,9) + C(14,3)]
P= (0.5)¹⁴ [2002 * 364]
P= 1/16384 * (2002 +364)
P= 91091/2048
P= 0.144
Hence,the coin can land tails either exactly 8 times or exactly 5 times in
[tex] 0.144[/tex] ways
Given that 243√3 =3^a, find the value of a
Answers
Answer:
a=11/5 OR 5.5
Step-by-step explanation:
Ifx + iy = 1
1+i/
1-i
prove that, x² + y² = 1
Answers
HI MATE