Answer:
[tex]n \geq 42[/tex]
Step-by-step explanation:
Data provided
P = 0.6
The calculation of sample size is shown below:-
Here the sampling distribution of proportion will be approximately normal, then follow the rule which is here below:-
[tex]np\geq 10\ and\ np (1 - p)\geq 10[/tex]
Now we will consider condition 2
[tex]np(1 - p)\geq \ 10[/tex]
[tex]n(0.6) (1 - 0.6) \geq \ 10[/tex]
[tex]n(0.6) (0.4) \geq\ 10[/tex]
[tex]n\geq \frac{10}{0.24}[/tex]
[tex]n \geq 41.66667[/tex]
or
[tex]n \geq 42[/tex]
Therefore for computing the required sample size we simply solve the above equation.
If f(x) = 5x – 2 and g(x) = 2x + 1, find (f - g)(x).
A. 3 - 3x
B. 3x-3
C. 7x-1
D. 7x-3
Answer:
The difference of the functions is (f-g)(x) = 3x - 3
Step-by-step explanation:
In the problem, we are asked to find the difference of the two functions, f(x) and g(x). When we see (f-g)(x), this means that we are going to subtract g(x) from f(x).
f(x) = 5x - 2
g(x) = 2x + 1
(f-g)(x) = (5x - 2) - (2x + 1)
Distribute the negative to (2x + 1)
(f-g)(x) = 5x - 2 - 2x - 1
Combine like terms. Make sure your answer is in standard form.
(f-g)(x) = 3x - 3
So, the answer to the equation is (f-g)(x) = 3x - 3
PLEASE HELP!!! A LOT OF POINTS AND BRAINLIEST TO CORRECT ANSWERS!!!
1. Find the area of the region enclosed by the graph of [tex]$x^2 + y^2 = 2x - 6y + 6$[/tex].
2. The line [tex]x=4[/tex] is an axis of symmetry of the graph of [tex]$y = ax^2 + bx + c.$[/tex] Find [tex]$\frac{b}{a}$.[/tex].
3. The graph of [tex]$y = ax^2 + bx + c$[/tex] is shown below. Find [tex]$a \cdot b \cdot c$[/tex]. (The distance between the grid lines is one unit, picture of graph attached.)
4. Geometrically speaking, a parabola is defined as the set of points that are the same distance from a given point and a given line. The point is called the focus of the parabola and the line is called the directrix of the parabola. Suppose [tex]$\mathcal{P}$[/tex] is a parabola with focus [tex]$(4,3)$[/tex] and directrix [tex]$y=1$[/tex]. The point [tex]$(8,6)$[/tex] is on [tex]$\mathcal{P}$[/tex] because [tex]$(8,6)$[/tex] is 5 units away from both the focus and the directrix. If we write the equation whose graph is [tex]$\mathcal{P}$[/tex] in the form [tex]$y=ax^2 + bx + c$[/tex], then what is [tex]$a+b+c$[/tex]?
5. (This is a Writing Problem - please please please explain and answer the question thoroughly!) A quadratic of the form [tex]$-2x^2 + bx + c$[/tex] has roots of [tex]$x = 3 + \sqrt{5}$[/tex] and [tex]$x = 3 - \sqrt{5}.$[/tex] The graph of [tex]$y = -2x^2 + bx + c$[/tex] is a parabola. Find the vertex of this parabola.
If you do manage to answer every single one of these correctly, THANK YOU SO MUCH and please know you are very much appreciated! :)
Answer:
1. [tex]Area=16\,\pi=50.265[/tex]
2.- [tex]\frac{b}{a} =-8[/tex]
3. [tex]y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]
4. [tex]a+b+c=\frac{17}{4}[/tex]
5. the vertex is located at: (3, 10)
Step-by-step explanation:
1. If we rewrite the formula of the conic given by completing squares, we can find what conic we are dealing with:
[tex](x^2-2x)+(y^2+6y)=6\\\,\,\,\,\,\,+1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+9\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+10\\(x-1)^2+(y+3)^2=16\\(x-1)^2+(y+3)^2=4^2[/tex]
which corresponds to a circle of radius 4, and we know what the formula is for a circle of radius R, then:
[tex]Area=\pi\,R^2=\pi\,4^2=16\,\pi=50.265[/tex]
2.
If x=4 is the axis of symmetry of the parabola
[tex]y=ax^2+bx+c[/tex]
then recall the formula to obtain the position of the x-value of the vertex:
[tex]x_{vertex}=-\frac{b}{2a} \\4=-\frac{b}{2a}\\4\,(-2)=\frac{b}{a} \\\frac{b}{a} =-8[/tex]
3.
From the graph attached, we see that the vertex of the parabola is at the point: (-3, -2) on the plane, so we can write the general formula for a parabola in vertex form:
[tex]y-y_{vertex}=a\,(x-x_{vertex})^2\\y-(-2)=a\,(x-(-3))^2\\y+2=a(x+3)^2[/tex]
and now find the value of the parameter "a" by requesting the parabola to go through another obvious point, let's say the zero given by (-1, 0) at the crossing of the x-axis:
[tex]y+2=a\,(x+3)^2\\0+2=a(-1+3)^2\\2=a\,2^2\\a=\frac{1}{2}[/tex]
So the equation of the parabola becomes:
[tex]y+2=\frac{1}{2} (x+3)^2\\y+2=\frac{1}{2} (x^2+6x+9)\\y+2=\frac{1}{2} x^2+3x+\frac{9}{2} \\y=\frac{1}{2} x^2+3x+\frac{9}{2} -2\\y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]
4.
From the location of the focus of the parabola as (4, 3) and the directrix as y=1, we conclude that we have a parabola with dominant vertical axis of symmetry, displaced from the origin of coordinates, and responding to the following type of formula:
[tex](x-h)^2=4\,p\,(y-k)[/tex]
with focus at: [tex](h,k+p)[/tex]
directrix given by the horizontal line [tex]y=k-p[/tex]
and symmetry axis given by the vertical line [tex]x=h[/tex]
Since we are given that the focus is at (4, 3), we know that [tex]h=4[/tex], and that [tex]k+p=3[/tex]
Now given that the directrix is: y = 1, then:
[tex]y=k-p\\1=k-p[/tex]
Now combining both equations with these unknowns:
[tex]k+p=3\\k=3-p[/tex]
[tex]1=k-p\\k=1+p[/tex]
then :
[tex]1+p=3-p\\2p=3-1\\2p=2\\p=1[/tex]
and we now can solve for k:
[tex]k=1+p=1+1=2[/tex]
Then we have the three parameters needed to write the equation for this parabola:
[tex](x-h)^2=4\,p\,(y-k)\\(x-4)^2=4\,(1)\,(y-2)\\x^2-8x+16=4y-8\\4y=x^2-8x+16+8\\4y=x^2-8x+24\\y=\frac{1}{4} x^2-2x+6[/tex]
therefore: [tex]a=\frac{1}{4} , \,\,\,b=-2,\,\,and\,\,\,c=6[/tex]
Then [tex]a+b+c=\frac{17}{4}[/tex]
5.
The vertex of a parabola can easily found because they give you the roots of the quadratic function, which are located equidistant from the symmetry axis. So we know that is one root is at [tex]x=3+\sqrt{5}[/tex]and the other root is at [tex]x=3-\sqrt{5}[/tex]
then the x position of the vertex must be located at x = 3 (equidistant from and in the middle of both solutions. Then we can use the formula for the x of the vertex to find b:
[tex]x_{vertex}=-\frac{b}{2a}\\3=-\frac{b}{2\,(-2)}\\ b=12[/tex]
Now, all we need is to find c, which we can do by using the rest of the quadratic formula for the solutions [tex]x=3+\sqrt{5}[/tex] and [tex]x=3-\sqrt{5}[/tex] :
[tex]x=-\frac{b}{2a} +/-\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex]
Therefore the amount [tex]\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex], should give us [tex]\sqrt{5}[/tex]
which means that:
[tex]\sqrt{5}=\frac{\sqrt{b^2-4\,a\,c} }{2\,a} \\5=\frac{b^2-4ac}{4 a^2} \\5\,(4\,(-2)^2)=(12)^2-4\,(-2)\,c\\80=144+8\,c\\8\,c=80-144\\8\,c=-64\\c=-8[/tex]
Ten the quadratic expression is:
[tex]y=-2x^2+12\,x-8[/tex]
and the y value for the vertex is:
[tex]y=-2(3)^2+12\,(3)-8=-18+36-8=10[/tex]
so the vertex is located at: (3, 10)
Find the perimeter and total area ? Use 3.14 in
Answer:
Perimeter is when you add up all of the sides, and the area is when you multiply length times width.
What is the m ZACB?
10°
50°
90°
180°
Answer:
50 deg
Step-by-step explanation:
In an right triangle, the acute angles are complementary. That means their measures have a sum of 90 deg.
m<C + m<B = 90
7x - 20 + 4x = 90
11x = 110
x = 10
m<ACB= 7x - 20
m<ACB = 7(10) - 20
m<ACB = 70 - 20
m<ACB = 50
Answer: m<ACB = 50 deg
this circle is centered at the origin (0,0) the radius is 4, what is the equation?
Answer:
x^2 +y^2 = 16
Step-by-step explanation:
The equation of a circle is given by
(x-h) ^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x-0) ^2 + (y-0)^2 = 4^2
x^2 +y^2 = 16
which inequality represents the statement? the number of new cars(C) a ship carries cant exceed 975.
A. c<975
B. c>975
C. c<(—under<)975
D. c>(—under>)975
"can't exceed 975" means this is the largest value possible for C. So we could have C = 975 or smaller. We write this as [tex]C \le 975[/tex] which is read as "C is less than or equal to 975".
Answer: Choice C. [tex]C \le 975[/tex]Answer:
5
Step-by-step explanation:
Q12.
A woman applies for a new job that pays £8.50 a week more (after tax).
She will work 5 days a week and drive to work, as she does in her job now.
The new job is 6 miles further from her house.
Her car travels 8.5 miles per litre of petrol
Petrol costs £1.26 per litre
Will the woman be better off with the new job after she takes the petrol into consideration?
Explain your answer. Include calculations to support your decision.
Decision (yes/no)
8.5x1.295.70
Explanation and supporting calculations
CA
Answer:
Step-by-step explanation:
1l ........8.5 miles
x l .......6 miles
-----------------------
x=6*1/8.5
x=0.70 l
2*0.7=1.4 l petrol/day ( to work and come back home)
5*1.4=7 l/week ( 5 days works in a week)
7*1.26=8.82 L /week
8.82>8.5
The petrol costs more
So the answer is NO
The first four terms of a sequence are shown below 9,5,1,-3
Which of the following functions best defines this sequence?
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1
B. f(1)=9, f(n+1)=f(n)+4 for n> or equal to 1
C. f(1)=9, f(n+1)=f(n)-5 for n> or equal to 1
D. f(1)=9, f(n+1)=f(n)+5 for n> or equal to 1
Answer:
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1
Step-by-step explanation:
Given the sequence:
9, 5, 1, -3We can easily calculate the difference of terms:
-3- 1= 1- 5= 5-9= -4As the difference of terms is same and equal to -4, it is the AP (arithmetic progression)
This sequence can be defined In the form of function as:
f(1)= 9, as the first term is 9f(n+1)= f(n)- 4, as it is decreasing function with the difference of -4n ≥ 1, as we count from the first term onAll the above matches the first answer choice:
A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1The function h(x)=12/x-1 is one to one. Algebraically find it’s inverse, h^-1(x).
Answer:
Step-by-step explanation:
hello,
I assume that you mean
[tex]h(x)=\dfrac{12}{x-1}[/tex]
so first of all let's take x real different from 1 , as this is not allowed to divide by 0
[tex](hoh^{-1})(x)=x=h(h^{-1}(x))=\dfrac{12}{h^{-1}(x)-1} \ \ \ so\\h^{-1}(x)-1=\dfrac{12}{x} \\\\h^{-1}(x)=1+\dfrac{12}{x}[/tex]
and this is defined for x real different from 0
hope this helps
Use the addition method to solve the system of linear equations for x. (Enter an exact number.)
3x - 2y = 8
2x + y = 3
Answer:
work is shown and pictured
find P (3) if p(x)=-×^3-2x^2+7
Answer:
-38.
Step-by-step explanation:
p(x) = -x^3 - 2x^2 + 7
p(3) = -(3^3) - 2(3^2) + 7
p(3) = -27 - 2(9) + 7
p(3) = -27 - 18 + 7
p(3) = -45 + 7
p(3) = -38
Hope this helps!
Answer:
p(3) = -38
Step-by-step explanation:
p(x) = -x³ - 2x² + 7
p(3) = -3³ - 2(3)² + 7
p(3) = -27 - 2(9) + 7
p(3) = - 27 - 18 + 7
p(3) = -38
Which feature of a database displays data in a certain sequence, such as alphabetical order? Chart Filter Search Sort
Answer:
data bar
Step-by-step explanation:
Answer:
chart
Step-by-step explanation:
W
5. 26.5 liter air dan 8.25 liter jus oren dicampurkan bersama. Semua campuran itu
dibotolkan dengan saiz setiap botol adalah 1.25 liter. Berapa botolkah diperlukan
untuk mengisi semua campuran jus oren tersebut?
A. 25
B. 26
C.27
D. 28
Answer: D, 28 bottles.
Step-by-step explanation:
This can be translated to:
26.5 liters of water and 8.25 liters of orange juice are mixed together. All that mixture is bottled in bottles of 1.25 liters. How many bottles are needed to fill all the orange juice mixture?
the total mass of mixture that we have is:
26.5 L + 8.25 L = 34.75 L.
if we want to divide it into groups of 1.25 L, we have:
N = 34.75/1.25 = 27.8
So we have 27.8 groups of 1.25L this means that we need 27.8 bottles.
But we can not have a 0.8 of a bottle, so we must round it up to 28 bottles.
Then the correct option is D:
Which statement best interprets the factor (r+7) in this context?
Answer:
the height of the cylinder is 7 units greater than the radius
Step-by-step explanation:
When you match the forms of the equations ...
[tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]
you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...
the height of the cylinder is 7 units greater than the radius.
A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by the x-axis and the base of the house is at the origin. There are two trees on the property. One tree is 8 feet from the base of the house and is 14 feet tall. The other tree is 16 feet from the base of the house and is 9 feet tall. What is the distance from the base of the house to the closest treetop? Round your answer to the nearest tenth.
Answer:
15.81
Step-by-step explanation:
Sorry for the delay
I NEED HELP PLEASE, THANKS! :)
please see the attached picture for full solution..
Hope it helps..
Good luck on your assignment...
The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute.
Answer:show the table so I can help
Step-by-step explanation:
Determine the intercepts of the line. -5x+9y=-18−5x+9y=−18minus, 5, x, plus, 9, y, equals, minus, 18 xxx-intercept: \Big((left parenthesis ,,comma \Big))right parenthesis yyy-intercept: \Big((left parenthesis ,,comma \Big))
Answer:
(3.6, 0), (0, -2)
Step-by-step explanation:
To find the y-intercept, set x=0:
-5·0 +9y = -18
y = -18/9 = -2
To find the x-intercept, set y=0:
-5x +9·0 = -18
x = -18/-5 = 3.6
The intercepts are ...
x-intercept: 3.6
y-intercept: -2
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers that are 6 or even on the cards are 2, 4, and 6.
3 cards out of a total of 6 cards.
3/6 = 1/2
Answer:
1/2 chance
Step-by-step explanation:
There are 3 numbers that fit the rule, 2, 4, and 6. 3/6 chance of picking one or 1/2, simplified.
x = 16 18 34 can someone explain please?
Answer:
x = 16
Step-by-step explanation:
(whole secant) x (external part) = (tangent)^2
(x+2) * 2 = 6^2
2(x+2) = 36
Divide each side by 2
x+2 = 18
Subtract 2
x+2-2 = 18-2
x = 16
Answer:
x = 16
Step-by-step explanation:
According to tangent-secant Theorem:
(Tangent)² = (External Part of the secant)(Whole Secant)
(6)² = (2)(2+x)
36 = 4+2x
Subtracting 4 from both sides
36-4 = 2x
=> 2x = 32
Dividing both sides by 2
=> x = 16-4(-11+4n)-3(-2n+9) simplify to create an equivalent expression
chose 1 answer
-10n-35, -18n+17, -10n-17, or -10n+17
Answer:
the last one is correct
Step-by-step explanation:
hello,
-4(-11+4n)-3(-2n+9) = 44 - 16n + 6n - 27 = -10n + 17
hope this helps
How do you calculate the y-intercept of a line written in Standard Form?
Answer:
y-int = C/B
Step-by-step explanation:
Ax + By = C
y-int = C/B
Answer:
I hope this helps.
Step-by-step explanation:
Select all the correct answers.
Which three pieces of information contribute the most to your credit score?
the number of bank accounts you have
the amount of debt you have
your payment history
your ability to make a down payment on a credit purchase
the number of loans you have
W
Answer:
B) the amount of debt you have
C) your payment history
E) the number of loans you have
Step-by-step explanation:
To determine the three pieces of information that contribute the most to your credit score, we have to find the factors that affect credit score calculation.
The major factors that affect a person's credit score calculation include : Payment history:
This is the most important factor that affect your credit score. Lenders want to be sure that you have a reputation back your debt and on time when you apply for new credit.
Amount of Debt :
This is the amount of overall debt you carry. It is the ratio of your credit card balances to your credit limit. Too much debt can hurt your credit score
Credit History:
This is a borrower's track record for repaying debts and how old it is. Opening new accounts within a short time will affect your credit score.
Account Mix: having a diverse portfolio of credit accounts could tell how well you manage different credits.
Credit Inquiries:
Several applications involving inquiries into your credit check within a short duration can affect your credit score.
Therefore the three pieces of information that would contribute the most to your credit score:
B) the amount of debt you have
C) your payment history
E) the number of loans you have
What is the explicit rule for the geometric sequence?
600, 300, 150, 75, ...
Answer:
Step-by-step explanation:
Hello, this is a geometric sequence so we are looking for a multiplicative factor.
[tex]a_0=600\\\\a_1=a_0 \cdot \boxed{\dfrac{1}{2}} = 300 = 600 \cdot \boxed{\dfrac{1}{2}}\\\\a_2=a_1 \cdot \boxed{\dfrac{1}{2}} = 150= 300 \cdot \boxed{\dfrac{1}{2}}\\\\a_3=a_2 \cdot \boxed{\dfrac{1}{2}} = 75 = 150 \cdot \boxed{\dfrac{1}{2}}[/tex]
So, the explicit formula is for n
[tex]\boxed{a_n=a_0\cdot \left(\dfrac{1}{2}\right)^n=600\cdot \left(\dfrac{1}{2}\right)^n}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The explicit rule is aₙ = a₀(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.
What is geometric series?The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.
The nth term of a geometric progression is expressed as
Tₙ = arⁿ⁻¹
Where a is the first term, r is the common ratio.
We have been given that geometric sequence as:
600, 300, 150, 75, ...
To determine the explicit rule for the geometric sequence, we have to find the common ratio.
Here the first term (a₀) is 600
So the common ratio = 300/600 = 150/300 = 75/150 = 1/2
Thus, the explicit formula for n would be:
aₙ = a(1/2)ⁿ = 600(1/2)ⁿ
Therefore, the explicit rule is aₙ = a(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.
Learn more about the geometric series here:
brainly.com/question/21087466
#SPJ2
Sample data for the arrival delay times (in minutes) of airlines flights is given below. Determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped Click the icon to view the data set. Is the requirement of a normal distribution satisfied? A. No, because the histogram of the data is not bell shaped, there is more than one outlier, and line points in the normal quantile plot do not lie reasonably close to a straight line.B. Yes, because the histogram of the data is bell shaped, there are less than two outliers, and the line points in the normal quantile plot lie reasonably close to a straight line.C. Yes, because the histogram of the data is not bell shaped, there is more than one outlier, and line points in the normal quantile plot do not lie reasonably close to a straight line.D. No, because the histogram of the data is bell shaped, there are less than two outliers, and the the points in the normal quantile plot do not lie reasonably close to a straight
Answer:
(Option A) . No, because the histogram of the data is not bell shaped, there is more than one outlier, and line points in the normal quantile plot do not lie reasonably close to a straight line.
Step-by-step explanation:
After plotting the histogram, you will see that the data does not represent the normal distribution because the histogram is not bell shaped and there are two outliers.
Find [g ° h](x) and [h ° g](x) , if they exist. g(x)=x+6 and h(x)=3x2 YALL PLEASE I NEED HELP :((
Answer:
a) [g ° h](x) = 3x² +6
b) [h ° g](x) =3 x²+36x+108
Step-by-step explanation:
Explanation:-
a)
Given g(x) = x+6 and h(x) = 3x²
Given [g ° h](x) = g(h(x))
= g(3x²) (∵ h(x) =3x²)
= (3x²)+6 (∵ g(x) =x+6)
∴ [g ° h](x) = 3x² +6
b)
Given [h ° g](x) = h (g(x))
= h(x+6) (∵ g(x) =x+6)
= 3 (x+6)² (∵ h(x) =3x²)
= 3 (x²+2(6)x+36) (∵ (a + b)² = a²+2ab+b²)
= 3 (x²+12x+36)
= 3 x²+36x+108)
∴ [h ° g](x) =3 x²+36x+108
Need Help ASAP!!!
Which of the following is a key property of the linear parent function?
O A. It is in quadrants I and III.
B. It does not go through the origin.
C. It has a slope of zero.
O D. It is a curved line.
Answer:
The answer is:
A. It is in the quadrants I and III.
Step-by-step explanation:
I am not sure if this is correct, but I tried my best :)
I hope this helped~
What percent of this grid is unshaded?
The grid has 10 columns and 10 rows making 100 equal sized squares 5 rows are
unshaded. The sixth row has 6 squares unshaded.
Answer:
56%
Step-by-step explanation:
We have a grid with 10 columns and 10 rows making 100 equal sized squares, they tell us that 5 rows are unshaded. Therefore half is unshaded, like so:
5 rows = 50 squares
They also tell us that the sixth row has 6 squares unshaded, which means that in total they would be:
50 + 6 = 56 squares
Knowing that the total is 100, the percentage would be:
56/100 = 0.56, that is, 56% are unshaded
If f(x)=8x and g(x)=2x+1, what is (f×g)(x)
Answer:
(f * g)(x) has a final product of 16x² + 8x.
Step-by-step explanation:
When you see (f * g)(x), this means that we are going to be multiply f(x) and g(x) together.
f(x)=8x
g(x)=2x+1
Now, we multiply these terms together.
(8x)(2x + 1)
Use the foil method to multiply.
16x² + 8x
So, the product of these terms is 16x² + 8x.
Lee watches TV for 2 hours per day. During that time, the TV consumes 150 watts per hour. Electricity costs (12 cents)/(1 kilowatt-hour). How much does Lee's TV cost to operate for a month of 30 days?
Answer:
$1.08
Step-by-step explanation:
30 days × (2 hrs/day) × (150 W) × (1 kW / 1000 W) × (0.12 $/kWh) = $1.08