Answers
n=2→an=a2 (second term) = 4 (on the graph for n=2)→Second term = 4
ratio=(Second term)/(First term)=a2/a1=4/16
Simplifying the fraction dividing the numerator (4) by 4 and the denominator (16) by 4:
ratio=(4/4)/(16/4)→ratio=1/4
Answer: Option A. First term = 16, ratio = 1/4
Related Questions
Which of the following functions has the largest value when x = 3? c(x) = 3x2 + 5x + 22 j(x) = 12x a(x) = 9x
Answers
To determine the function which has the largest value at x=3,
We will calculate the value of each function by substituting the value of x=3 in each of the given function.
Let us consider the first function,
[tex] c(x)=3x^{2}+5x+22 [/tex]
[tex] c(3)=3\times 3^{2}+5 \times 3+22 [/tex]
[tex] c(3)=27+15+22 [/tex]
[tex] c(3)=64 [/tex]
Let us consider the second function,
[tex] j(x)=12x [/tex]
[tex] j(x)=12 \times 3 =36 [/tex]
Let us consider the third function,
[tex] a(x)=9x [/tex]
[tex] a(x)=9 \times 3=27 [/tex]
Therefore, the function c(x) has the largest value at x=3.
The answer is 3
To determine which function has the largest value when x = 3, we need to substitute x with 3 into each function and calculate their values.
c(x) = 3x2 + 5x + 22 => c(3) = 3(3)2 + 5(3) + 22 = 27 + 15 + 22 = 64
j(x) = 12x => j(3) = 12(3) = 36
a(x) = 9x => a(3) = 9(3) = 27
The function c(x) has the largest value of 64 when x = 3.
ralph is a electrician he charges an initial fee of 24$ , plus 24 per hour. If ralph earned 144$ on the job , how long did the job take.
Answers
Describe a reasonable sample space to model this experiment. (b) let n be the number of sample points that are inside the unit circle. find e(n). (c) use this to construct a random variable p with e(p) = π. this random variable will give your estimate of π.
Answers
TTTT
HTTT
THTT
TTHT
TTTH
HHTT
HTHT
HTTH
TTHH
THHT
THTH
HHHT
THHH
HTHH
HHTH
HHHH
B) ω= 1+4+6+4+1= 16 = number of sample space, which is = to n.
C) the random variable should 3.14 approximately or 22/7
Now that you have 3x=42, you need to isolate the variable so that you have an equation of the form "x= some number." what is the value of x (i.e., the amount you must pay)?
Answers
3x/3=42/3 that leaves you with the isolated variable
x=14
To solve the equation 3x = 42, divide both sides by 3, which results in x = 14. This means you would pay $14. The process is similar to isolating a variable in quadratic equations, where different methods may be employed.
Given the equation 3x = 42, we need to isolate the variable x to find its value. This is accomplished by dividing both sides of the equation by 3, which is the coefficient of x. Therefore, the equation becomes x = 42 / 3.
By performing this simple division, we find that x equals 14. So, if x represents the amount you must pay, then you would pay $14.
The process of isolating the variable is essential for solving not only simple equations but also more complex ones, such as quadratic equations which take the form ax² + bx + c = 0.
When dealing with quadratic equations, you can employ the quadratic formula or other methods like factoring or completing the square, depending on the nature of the coefficients and the terms present in the equation.
A tank initially contains 40 ounces of salt mixed in 100 gallons of water. a solution containing 4 oz of salt per gallon is then pumped into the tank at a rate of 5 gal/min. the stirred mixture flows out of the tank at the same rate. how much salt is in the tank after 20 minutes ?
Answers
[tex]A'(t)=\dfrac{5\text{ gal}}{1\text{ min}}\cdot\dfrac{4\text{ oz}}{1\text{ gal}}-\dfrac{5\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ oz}}{100+(5-5)t\text{ gal}}[/tex]
[tex]A'(t)+\dfrac{A(t)}{20}=20[/tex]
[tex]e^{t/20}A'(t)+e^{t/20}\dfrac{A(t)}{20}=20e^{t/20}[/tex]
[tex]\bigg(e^{t/20}A(t)\bigg)'=20e^{t/20}[/tex]
[tex]e^{t/20}A(t)=400e^{t/20}+C[/tex]
[tex]A(t)=400+Ce^{-t/20}[/tex]
Since [tex]A(0)=40[/tex], we get
[tex]40=400+C\implies C=-360[/tex]
so that the amount of salt at time [tex]t[/tex] is
[tex]A(t)=400-360e^{-t/20}[/tex]
After 20 minutes, the tank contains
[tex]A(20)=400-360e^{-20/20}\approx267.56\text{ oz}[/tex]
The amount of salt that is in the tank after 20 minutes is;
A(20) = 267.56 Oz
We are given;Initial amount of salt in tank; A(0) = 40 Ounces
A solution containing 4 oz salt per gallon is pumped into the tank at a rate of 5 gal/min.
This means rate in oz/min = 4/1 × 5/1 = 20 oz/min
Now, the rate at which the initial amount in the tank changes will be;A'(t) = 20 - [(A(t)/(100)) × 5/1]
A'(t) = 20 - A(t)/20
Rearranging gives;
A'(t) + A(t)/20 = 20
Since this is a linear equation, the integrating factor will be; [tex]e^{t/20}[/tex]Multiplying through by the integrating factor gives;
A'(t) [tex]e^{t/20}[/tex] + (A(t)/20) [tex]e^{t/20}[/tex] = 20[tex]e^{t/20}[/tex]
Thus, the solution will be;A(t) [tex]e^{t/20}[/tex] = 400[tex]e^{t/20}[/tex] + C
Divide through by [tex]e^{t/20}[/tex] to get;
A(t) = 400 + C [tex]e^{-t/20}[/tex]
At initial condition of A(0) = 40, we have;
40 = 400 + C
C = -360
Thus; at time (t), the amount of salt left is given by;
A(t) = 400 - 360 [tex]e^{-t/20}[/tex]
After 20 minutes;A(20) = 400 - 360 [tex]e^{-20/20}[/tex]
A(20) = 400 - 132.44
A(20) = 267.56 Oz
Read more at; https://brainly.com/question/17003995
How is the graph of y=^3√0.5x related to its parent function,y=^3√x ? A.It is horizontally stretched by a factor of 0.5 B. It is horizontally compressed by a factor of 0.5 C. It is translated left by 0.5 units D. It is translated right by 0.5 units
Answers
y = ^ 3√x
Applying the following transformation we have:
Expansions and horizontal compressions
The graph of y = f (bx):
If 0 <b <1, the graph of y = f (x) expands horizontally by the factor of 1 / b.
y = ^ 3√0.5x
Answer:
A.It is horizontally stretched by a factor of 1 / 0.5
find the slope of the line. -7 , - 1/7, 7, 7/1
Answers
point A(-2,2)
point B (5,3)
step 1 find the slope m
m=(y2-y1)/(x2-x1)------> m=(3-2)/(5+2)-----> m=1/7
the answer is
the slope m=1/7
by making (x₁,y₁) = (-2,2) and (x₂,y₂) = (5,3)
∴The slope = (3-2)/(5 - -2) = 1/7
Given that KJ = MN and that L is the midpoint of JN, prove JKL = NML.
Answers
1. KJ is congruent to MN ---> GIVEN (That means that you were told this is true when the problem was posed. Read the problem...everything before the word "prove" is given to you).
2. JL is congruent to LN --> You were told that L is the midpoint of JN. A midpoint divides a segment into two congruent parts. So, the fact that L is a midpoint means that JL and LN are congruent. Here we do not say given because you were given that L is the midpoint and you had to now what a midpoint does to get to the fact that JL and LN are congruent. So here we say DEFINITION OF A MIDPOINT
3. angle JKL is congruent to angle NLM --> GIVEN. Here the information was given to you in the diagram. These angles are both drawn with a red curved line. Since these are the same (both a single red curve) it means that the angles are congruent.
PROVING TRIANGLES CONGRUENT
We are asked to prove that triangle JKL and triangle NML are congruent. There are various ways to prove that two triangles are congruent. These are:
SSS (each side in one triangle is congruent to a side in the other triangle)
SAS (two sides and the angle between them in one triangle are congruent to two sides and the angle between them in the other triangle)
ASA (two angles and the side between them in one triangle are congruent to two angles and the side between them in the other triangle)
AAS Two angles and a side not between them in one triangle is congruent to two angles and a side not between them in the other triangle.
HL (the hypotenuse and a leg of a right triangle is congruent to the hypotenuse and a leg in another right triangle)
OUR TRIANGLES
Attached is a diagram for this problem. In it since KJ and MN are congruent I have marked each with a single hashmark. Since JL and LN are congruent I have marked each of these with two hashmarks. You will notice that both triangles have a side with one hashmark and another with two hashmarks Also, there is an angle congruent in each. However, the angle is not BETWEEN the sides so we cannot use SAS. None of the other methods of proving two triangles congruent work because what we have is two sides and an angles not between them. That would be SSA but SSA is NOT one of the ways of proving triangles congruent. The triangles we are given might be congruent but they also might not be.
The answers is D --> There is not enough information to prove the triangles congruent.
20 points Easy question
what is 5/20 simplify
Answers
To simplify this question, we can just divide both sides of the fraction by 5.
5 / 5 = 1
20 / 5 = 4
So, the fully simplified fraction would be 1/4.
Hope this helps!
The front wall of your shed is in the shape of a trapezoid. The bottom measures 22 feet, the top measures 20 feet, and the height is 10 feet. Calculate the area of the front wall of your shed.
Answers
A = (1/2)×(b₁ +b₂)×h
Substitute the given information and evaluate.
A = (1/2)×(22 ft +20 ft)×(10 ft)
A = (1/2)×(42 ft)×(10 ft)
A = (21 ft)×(10 ft)
A = 210 ft²
The area of the front wall of your shed is 210 ft².
Answer:
the answer on edge is D. 66^2
Step-by-step explanation:
Adam spent $3.42 on orange juice. It costs .12 per ounce. How many did Adam buy?
Answers
I would say that the answer is 28, but it still doesn't add up because when you multiply 12 by 28 you get $3.36 which isn't enough to meet his total, so I tried multiplying 12 by 29 and I got $3.48, which is six cents over his total. So I'm sorry if it is wrong I tried to help to my best ability.
I hope it helps, have a great day/night!!!
Adam bought 26.14 ounces of orange juice.
To solve the problem, we need to determine how many ounces of orange juice Adam bought with $3.42, given that the cost per ounce is $0.12. We can set up a simple proportion to find the answer.
First, we convert the cost of orange juice per ounce from a fraction to a decimal. The cost is $0.12 per ounce, which can also be written as [tex]$\frac{12}{100}$[/tex] dollars per ounce. Simplifying this fraction gives us [tex]$\frac{3}{25}$[/tex] dollars per ounce.
Next, we convert the total amount spent by Adam, $3.42, into a fraction. This is equivalent to [tex]$\frac{342}{100}$[/tex] dollars.
Now, we set up the equation to find the number of ounces (let's call it [tex]$x$[/tex]) that Adam bought:
[tex]\[ \frac{3}{25} \times x = \frac{342}{100} \][/tex]
To solve for [tex]$x$[/tex], we multiply both sides of the equation by the reciprocal of [tex]$\frac{3}{25}$[/tex], which is [tex]$\frac{25}{3}$[/tex]:
[tex]\[ x = \frac{342}{100} \times \frac{25}{3} \][/tex]
Multiplying the numerators and denominators separately, we get:
[tex]\[ x = \frac{342 \times 25}{100 \times 3} \][/tex]
Simplifying the right side of the equation by canceling out common factors (25 cancels with 100 to become 4, and 3 cancels with 342 to become 114), we have:
[tex]\[ x = \frac{114 \times 4}{4} \][/tex]
This simplifies to:
[tex]\[ x = 114 \][/tex]
However, we must remember that the original amount spent was $3.42, not $342. Therefore, we must divide our result by 100 to account for the cent conversion:
[tex]\[ x = \frac{114}{100} \][/tex]
[tex]\[ x = 1.14 \][/tex]
This result represents the number of ounces Adam bought in addition to the whole number of ounces he could buy with whole dollars. Since $3.00 would buy [tex]$\frac{3}{0.12}$[/tex] ounces, we need to add this to our 1.14 ounces to get the total:
[tex]\[ x_{total} = 1.14 + \frac{3}{\frac{12}{100}} \][/tex]
[tex]\[ x_{total} = 1.14 + \frac{3 \times 100}{12} \][/tex]
[tex]\[ x_{total} = 1.14 + \frac{300}{12} \][/tex]
[tex]\[ x_{total} = 1.14 + 25 \][/tex]
[tex]\[ x_{total} = 26.14 \][/tex]
Easy 20 points!
Which expression finds the length of side y in this right triangle?
Answers
The Last one is your answer
Answer:
The last one i did this before
Step-by-step explanation:
6 + 12 ÷ 3 – 2 × 2 =
Answers
HELP ASAP How do I find the answer to this
Answers
[tex] \frac{CD}{BD} = \frac{BD}{AD} [/tex]
Notice that we know for our problem that [tex]BD=h[/tex]. Also, we can find the length of AD by subtracting CD from AC:
[tex]AD=AC-CD[/tex]
[tex]AD=25-16[/tex]
[tex]AD=9[/tex]
Now we can replace the values in our proportion:
[tex] \frac{CD}{BD} = \frac{BD}{AD} [/tex]
[tex] \frac{16}{h} = \frac{h}{9} [/tex]
Solving for [tex]h[/tex]:
[tex]h^2=(16)(9)[/tex]
[tex]h^2=144[/tex]
[tex]h= \sqrt{144} [/tex]
[tex]h=12[/tex]
We can conclude that the correct answer is: B. 12
Triangle BCD:
BD=h
CD=16
Triangle ABD:
BD=h
AD=AC-CD=25-16→AD=9
Suppose <CBD is x and the <ABD is y
x+y=90°
The <BCD must be equal to y; and the <BAD must be equal to x, then the triangles ABD and BCD are similars, because they have two congruent angles (x and y), so theirs sides must be proportionals:
Opposite to angle x / opposite to angle y
Triangle ABD Triangle BCD
BD / AD = CD / BD
Replacing values:
h/9=16/h
Solving for h. Cross multiplication:
(h)(h)=(9)(16)
h^(1+1)=144
h^2=144
sqrt(h^2)=sqrt(144)
h=12
Answer: The value of h in the figure is 12
5:36, 2:9, 3:18 , 1:3 which ratio is the largest?
Answers
Short answer: 1:3
Why?
A fraction is at it's largest when it's closest to zero. The option 1:3 is the closest to zero, all the others are equal to 2:9
Hope this helped you! ♥
Hey can you please help me posted picture of question
Answers
So, vertical stretching of F(x) by a factor of 7 will be equal to 7 F(x).
Thus,
G(x) = 7 F(x)
G(x) = 7x²
So, option C gives the correct answer
The circumference of a circle is 28 pi inches. What is the length of the radius of this circle?
Answers
Answer:
The length of the radius of this circle is 14 inches.
Step-by-step explanation:
Circumference of the circle = [tex]28\pi[/tex]
Let's take the length of the radius of the circle as [tex]a[/tex]
Circumference of a circle = [tex]2\pi r[/tex]
Where,
r is the radius of the circle.
Therefore,
[tex]2\pi a=28\pi[/tex]
[tex]2a=28[/tex]
[tex]a=14[/tex]
Therefore, the length of the radius of this circle is 14 inches.
William made 1/2 gallon of lemonade to divide equally among 3 people. How much lemonade will each person?
a) 1/6 gallon
b)2/3 gallon
C) 1/5 gallon
d) 3/2 gallon
Answers
What is the total surface area of the cone? 90π cm2 65π cm2 120π cm2 115π cm2
Answers
The total surface area of a cone can be found using the formula A = πr(r + l), where A is the total surface area, r is the radius of the base, and l is the slant height. In this case, the correct answer is 115π cm².
Explanation:The total surface area of a cone can be found using the formula A = πr(r + l), where A is the total surface area, r is the radius of the base, and l is the slant height.
In this case, the correct answer is 115π cm². Let's calculate it:
Let's assume the radius of the cone is r.And let's assume the slant height of the cone is s.The total surface area of the cone is A = πr(r + s).We can substitute the given values into the formula: A = π(4)(4 + 7) = 115π cm².Therefore, the correct answer is 115π cm².
what percent of 28 is 21
Answers
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 28&100\\ 21&p \end{array}\implies \cfrac{28}{21}=\cfrac{100}{p}\implies p=\cfrac{21\cdot 100}{28}[/tex]
corey has 42 feet of fencing around his garden. The garden is rectangular in shape, and its length is equal to twice the width minus 3 feet. Define the variables, and write a system of equations to find the length and width of the garden
Answers
l= length
2w+2l=42
l=2w-3
w= 8
l= 13
The variables as length are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
As per the given total fencing = 42 feet
Let's say the length is L and the width is W.
As per the given,
L = 2W - 3
Perimeter = 2(length + width)
42 = 2(L + W)
21 = 2W - 3 + W
21 + 3 = 3W
W = 8 feet
And, L = 2(8) - 3 = 13 feet
Hence "The variables as lengths are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively".
For more about rectangles,
https://brainly.com/question/15019502
#SPJ2
Which has smallest value 0.79 or 0.425
Answers
PLEASE HELP ME ILL GIVE U A BRAINLIST a man who is 6 feet tall cats a shadow that is 15 feet long.A tree casts a similar shadow is 22 FT how tall is the tree?
Answers
Answer: 13
Here are the steps:
First we subtract 15 from 22 and then got 7
15 - 22 = 7
Finally we Add 7 + 6 = 13
Which is our final answer
I hope I helped
-Chris.
Yoshi is riding a bike-a-thon to raise money for his favorite charity The total distance of the bike-a-thon is 28.5 miles So far he has completed 1/10 of the bike-a-thon How many miles has Yoshi biked
Answers
Which expression is equivalent to 10x^6y^12/-5x^-2y^-6 ? Assume . –50x8y18 –2x8y18 –2x12y72 5x8y18
Answers
Answer:
Option B is correct, i.e. -2 x^8 y^18.
Step-by-step explanation:
To find the equivalent expression to (10)(x^6)(y^12) / (-5)(x^-2)(y^-6)
Step 1: simplify numerical terms
(10) / (-5) = -2
Step 2: simplify exponents of x-terms
(x^6) / (x^-2) = (x^6) * (x^2) = x^(6+2) = x^8
Step 3: simplify exponents of y-terms
(y^12) / (y^-6) = (y^12) * (y^6) = y^(12+6) = y^18
It means (10)(x^6)(y^12) / (-5)(x^-2)(y^-6) = -2 x^8 y^18
Hence, option B is correct, i.e. -2 x^8 y^18.
the length of johns patio is 5 feet less than 3 times the length of howards patio .johns patio has a length of 40 feet . what is the length of howards patio
Answers
The easiest way of solving this problem is by setting up and solving an equation.
Let the length of Howard's patio be represented by X. Now we can get the following expressions
3 times the length of Howard's patio would be 3X (multiply by three).
5 feet less than 3 times the length of Howard's patio would be 3X - 5 (just subtract five).
Now we've found an expression that represents the length of John's patio. Knowing this we can set up and solve an equation.
[tex]3x - 5 = 40[/tex]
First add 5 to both sides of the equation.
[tex]3x = 40 + 5[/tex]
[tex]3x = 45[/tex]
Finally divide both sides by 3.
[tex]x = \frac{45}{3} = 15[/tex]
Therefore, the length of Howard's patio is 15 feet. The answer is 15 feet.
~ Hope this helps you!
Can someone help me with this question, please?
Answers
The vertical stretch will make f look narrower than g, so the appropriate choice is ...
(B)
The average price of a gallon of milk at 5 supermarkets is $3.52. The prices at 4 of the supermarkets are $3.39, $3.82, $3.61, and $3.44, respectively. What is the price at the fifth supermarket?
Answers
Answer: B.)3.34
I did it on usatestprep
Step-by-step explanation:
Find the shaded area of the basketball court to the nearest foot.
Answers
Rectangle - 12*19 = 228Half a circle - [tex] \pi r^2 = \pi 6^2 = 36 \pi /2 = 18 \pi [/tex]
In the end there are 2 rectangles (2*228 = 456) and 1 full circle (18*2 = 36), which makes the shaded area 456ft and 36[tex] \pi [/tex]
Mitch's father needs 1 1\2 tons of gravel.He bought 1,750 pounds of gravel.How many more pounds of gravel does he need