Answers
Answer:
Option D. \(g(x)=5(0.8)^{x}+2\)
Step-by-step explanation:
Main concepts
Concept 1: identifying horizontal asymptote
Concept 2: assuring decreasing exponential function
Concept 1. identifying horizontal asymptote
Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis. A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number. Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units. Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.
Concept 2. assuring decreasing exponential function
Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".
If "b" is between 0 and 1 (a "small" number), the function will decrease.If "b" is larger than 1 (a "big" number), the function will increase.Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.
To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.
Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.
Related Questions
Use the formula A = bh, where A is the area, b is base length, and H is the height of the parallelogram, to solve this problem.
Mr.Bill orders a parallelogram-shaped window for one of the rooms in the house he is building. The window has an area of 1440 square inches. The height of the window is 32 inches.
What is the length of the base of the window?
Enter your answer in the box.
___ in.
Answers
Answer:
45 in
(1440 / 32)
(a) Complete the table of values for y = 2x + 4.
Please help ❤️ 15 points awarded :)
Answers
Answer:
your first answer is incorrect it is y= 2
y=6
y=8
Cells B1, C1, and D1 contain the values Seat1Row1, Seat2Row1, and Seat3Row1. If cells B1, C1, and D1 were selected, and autofill
used to fill E1, F1, and G1, what would be the auto-filled values?
Seat1Row2, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row3, Seat4Row4
Seat 1Row1, Seat2Row2, Seat3Row2
Seat 2Row2, Seat3Row2, Seat4Row2
Answers
In the event that cells B1, C1, and D1 were highlighted and then used to fill E1, F1, and G1, the values we would see are A. Seat1Row2, Seat2Row2, Seat3Row2.
What values would be in E1, F1, and G1?When using a spreadsheet, you can autofill succeeding cells if you highlight the preceding ones and then drag the cursor.
If Seat1Row1, Seat2Row1, and Seat3Row1 are in the cells B1, C1, and D1, then the spreadsheet would take note of the "1s" at the end of the values.
When it is then used to autofill the next cells, it would make this a 2 such that we see Seat1Row2, Seat2Row2, Seat3Row2.
If cells H1, I1, and J1 are filled, we would then see Seat1Row3, Seat2Row3, Seat3Row3.
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On Monday Mrs.Smith rode her favorite horse, Wild Racer, 1 3/4 mi.
On Tuesday she rode 1 9/15 mi; on Wednesday, 1 4/5 mi;
on Thursday 1 3/5 mi.
On which days did Mrs.Smith ride Wild Racer the same distance?
Answers
Answer: On Tuesday and Thursday
Step-by-step explanation:
On Tuesday, Mrs. Smith rode her favorite horse for 1 9/15 miles. Taking it to its simplest form by dividing it by 3 would yield a mixed fraction of 1 3/5 which is the same as the distance that the horse was ridden on Thursday.
Another method is to convert them back into their original improper fractions.
Tuesday; Thursday
= 1 9/15 = 1 3/5
= (15 * 1 + 9) / 15 = (5 * 1 + 3)/5
= 24/15 = 8/5
= 8/5
Notice how again they are the same at their simplest forms.
Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards, and 20 are selected without replacement for functional testing. a. If 20 cards are defective, what is the probability that at least 1 defective card is in the sample
Answers
Answer:
The probability that at least 1 defective card is in the sample is \(0.9644\)
Step-by-step explanation:
Here
N = 140
and n = 20
We will use the below given formula
P(at least 1 defective) = 1 - P( 0 defectives)
P( 0 defectives) =
\(= \frac{^{20}C_0 * ^{120}C_{20}}{ ^{140}C_{20}}\\= 0.0356 1-0.0356 \\= 0.9644\)
i need you to show your work
Answers
\(5\dfrac 23 + 4\dfrac 12\\\\\\=5+ \dfrac 23 + 4 + \dfrac 12\\\\\\=9 + \dfrac 23 + \dfrac 12\\\\\\=9+ \dfrac 76 \\\\\\=\dfrac{61}6\\\\\\=10\dfrac 16\)
Answer:
\( \displaystyle{5 \frac{2}{3} + 4 \frac{1}{2} }\)
\(\displaystyle{ \frac{17}{3} + \frac{9}{2} }\)
\(\displaystyle{ \frac{17 \times 2 + 9 \times 3}{6} }\)
\(\displaystyle{ \frac{34 + 27}{6} }\)
\(\displaystyle{ \frac{61}{6} }\)
\(\displaystyle{10 \frac{1}{6} }\)
A biologist wants to estimate how many fish are in a lake. The biologist takes a sample of 10 fish from the lake and tags all 10 fish. The biologist then releases the fish back into the lake. The nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. Using this information, estimate the number of fish in the lake.
Answers
If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.
How to find the estimated number?Let x represent the estimated number of fish in the lake
Hence,
x /10 = 7/2
Cross multiply
2x = 10 × 7
2x = 70
Divide both side by 2x
x =70/2
x = 35 fish
Therefore 35 is the number of fish.
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which of the following is most likely the next step in the series
Answers
Answer:
A.
Step-by-step explanation:
Let's think of this as a clock. We can see that the 2 lines start in the same place, around 3 o'clock. Next, one of the line segments shifts down to around 6 o'clock. Next, it shifts to about 9 o'clock. Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.
We can also just use a regular circle, with one of the line segments moving 90 degrees each time.
Hope this helps! :)
Four times a number, added to 8, is 32
Answers
Answer: 6
Step 1: Subtract 8.
32 - 8 = 24
Step 2: Divide by 4, since the question is asking for 4 times the number.
24 ÷ 4 = 6
Answer = 6
How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
Answers
For example, suppose you have the Cartesian equation of a line in the form:
y = mx + b
and the equation of a plane in the form:
ax + by + cz + d = 0
To check if the line belongs to the plane, you can substitute a point (x, y) on the line into the equation of the plane and solve for z. If the resulting value of z satisfies the equation of the plane, then the line belongs to the plane.
Here's an example:
Suppose the Cartesian equation of the line is y = 2x + 1, and the equation of the plane is 2x + 3y + 4z + 5 = 0.
If we substitute a point on the line, such as (1, 3), into the equation of the plane, we get:
2(1) + 3(3) + 4z + 5 = 0
Solving for z, we find that z = -1.5.
Since the resulting value of z satisfies the equation of the plane, the line belongs to the plane.
If the resulting value of z does not satisfy the equation of the plane, then the line does not belong to the plane.
\( 3 {x}^{2} - 15x = 15\)
Answers
\(3x^2-15x= 15\\\\x^2 -5x = 5\\\\x^2-5x-5=0\\\\\Delta = 25+20\\\\\Delta = 45\\\\\\x = \dfrac{5\pm \sqrt{\Delta}}{2}\\\\\\x = \dfrac{5\pm \sqrt{45}}{2}\\\\\\x = \dfrac{5\pm 3\sqrt{5}}{2}\\\\\\\)
x + y = -50
y = 4x
Answer (x,y)
Answers
Answer:
x = -10 ; y = -40
Step-by-step explanation:
Note:
y = 4x.
Plug in 4x for y in the first equation:
x + y = -50
x + (4x) = -50
Solve for x. First, simplify, then isolate the variable, x.
x + 4x = -50
5x = -50
Divide 5 from both sides of the equation.
(5x)/5 = (-50)/5
x = -50/5
x = -10
Plug in -10 for x in one of the equations:
y = 4x
y = 4(-10)
y = -40
x = -10 ; y = -40 is your answer.
~
150, 60, 24,...
Find the 9th term.
Answers
Divided by 2.5
150, 60, 24, 9.6, 3.84, 1.536, 0.6144, .24576, 0.098304
The 9th term is 0.098304
A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t)= −4.9t^2+11t+7. How many seconds does it take to reach maximum height? Enter the answer with at least 3 decimal places.
Answers
Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.
To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = \(-4.9t^2 + 11t + 7.\)
The vertex of a parabola in the form y = \(ax^2 + bx\) + c is given by the formula t = -b / (2a).
Comparing the equation h(t) = \(-4.9t^2 + 11t + 7\) to the standard form, we have:
a = -4.9
b = 11
Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:
t = -11 / (2 * -4.9)
t = -11 / -9.8
t ≈ 1.122
Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.
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NO LINKS!!! NOT MULTIPLE CHOICE!!!!!
1. Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition.
a. -5, 2, 1; f(3) = 32
f(x) = ___________
b. -3i, -3i, 2; f(1) = 30
f(x) = ___________
b.
Answers
Answer:
\(\textsf{a)} \quad f(x)=2x^3+4x^2-26x+20\)
\(\textsf{b)} \quad f(x)=-3x^3+6x^2-27x+54\)
Step-by-step explanation:
Factor TheoremIf f(x) is a polynomial, and f(c) = 0, then (x – c) is a factor of f(x).
Part aGiven information:
Degree: 3Zeros: -5, 2, 1Condition: f(3) = 32According to the factor theorem the polynomial in factored form is:
\(f(x)=a(x-(-5))(x-2)(x-1)\)
\(f(x)=a(x+5)(x-2)(x-1)\)
To find the value of the leading coefficient, a, apply the condition:
\(\begin{aligned}f(3)=a(3+5)(3-2)(3-1)&=32\\a(8)(1)(2)&=32\\16a&=32\\a&=2\end{aligned}\)
Therefore, the factored polynomial is:
\(f(x)=2(x+5)(x-2)(x-1)\)
Expand the polynomial:
\(f(x)=2(x^2+3x-10)(x-1)\)
\(f(x)=2(x^3-x^2+3x^2-3x-10x+10)\)
\(f(x)=2x^3+4x^2-26x+20\)
Part bGiven information:
Degree: 3Zeros: -3i, 3i, 2Condition: f(1) = 30According to the factor theorem the polynomial in factored form is:
\(f(x)=a(x-(-3i))(x-3i)(x-2)\)
\(f(x)=a(x+3i)(x-3i)(x-2)\)
To find the value of the leading coefficient, a, apply the condition:
\(\begin{aligned}f(1)=a(1+3i)(1-3i)(1-2)&=30\\a(1-9i^2)(-1)&=30\\a(1-9(-1))(-1)&=30\\-10a&=30\\a&=-3\end{aligned}\)
Therefore, the factored polynomial is:
\(f(x)=-3(x+3i)(x-3i)(x-2)\)
Expand the polynomial:
\(f(x)=-3(x^2-9i^2)(x-2)\)
\(f(x)=-3(x^2+9)(x-2)\)
\(f(x)=-3(x^3-2x^2+9x-18)\)
\(f(x)=-3x^3+6x^2-27x+54\)
It is felt that respondents are more likely to be honest when a randomized response survey is used. Subsequently, a substance-abuse prevention program at a university has designed and distributed the following questionnaire to all the employees and students: Flip a coin. If the coin comes up heads, answer Question a; if tails, answer Question b. All answers are anonymous. a. Do you carpool to the school
Answers
Answer:
hello your question is incomplete below is the complete question
answer : 18%
Step-by-step explanation:
x = percentage using illicit drugs
sample size = 5000
number of persons with a yes = 1200
also management knows that 30% uses carpool
∴P ( yes ) = P( H and yes to carpool ) + P( T and yes to illicit drug use )
1200 / 5000 = (0.5 * 0.3 ) + ( 0.5 * x )
0.24 = 0.15 + 0.5 x
hence x ( percentage using illicit drug ) = ( 0.24 - 0.15) / 0.5 = 0.18 = 18%
Simplify (2a^3a^4)^5. Show all work
Answers
Answer:
(2a^3a^4)^5 simplifies to 32a^35.
Step-by-step explanation:
To simplify (2a^3a^4)^5, we can use the properties of exponents which states that when we raise a power to another power, we can multiply the exponents. Therefore, we can rewrite the expression as:
(2a^3a^4)^5 = 2^5 * (a^3a^4)^5
Next, we can simplify the expression inside the parentheses by multiplying the exponents:
a^3a^4 = a^(3+4) = a^7
Substituting this into our expression, we get:
(2a^3a^4)^5 = 2^5 * (a^3a^4)^5 = 2^5 * a^35
Finally, we can simplify this expression by using the property of exponents that states that when we multiply two powers with the same base, we can add their exponents. Therefore, we can rewrite the expression as:
2^5 * a^35 = 32a^35
Therefore, (2a^3a^4)^5 simplifies to 32a^35.
You need to be at least 39.37 inches tall (about a meter ) to ride on a bumper car. Diego cousin is 35.75inches tall. How many more inches will he need to grow before Diego can take him on the bumper car ride. Explain or show your reasoning.
Answers
Answer:
3.62
Step-by-step explanation:
39.37 - 35.75 = 3.62
Quadrilateral MNPQ is rotated at 90 degrees counterclockwise about the origin and then rotated 270 degrees counterclockwise about the origin
Answers
After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.
When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.
The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.
Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.
The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.
It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.
The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.
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A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible two-topping pizzas (2 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with banana peppers and Kalamata olives. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
Using the combination formula, it is found that there is a \(\frac{1}{78}\) probability that the first winner randomly selects the card for the pizza topped with banana peppers and Kalamata olives.
The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
Researching the problem on the internet, it is found that 2 toppings will be chosen from a set of 13, hence:
\(C_{13,2} = \frac{13!}{2!11!} = 78\)
The pizza topped with banana peppers and Kalamata olives is one outcome, hence:
p = 1/78.
There is a \(\frac{1}{78}\) probability that the first winner randomly selects the card for the pizza topped with banana peppers and Kalamata olives.
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What is 15 2/3 divided by 1/3
Answers
Answer:
47
Step-by-step explanation:
You divide 3 by 1 and 2 by 3.
2. The diagram above shows a wooden structure in the form of a cone mounted on hemispherical base. The vertical height of the cone is 24cm and the base 7cm. Calculate correct to 3 significant figures the surface area of the structure. (Take π= 22/7)
Answers
The surface area of the wooden structure is approximately 1012 cm².
To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.
Surface Area of the Cone:
The surface area of a cone is given by the formula:
A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.
The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:
\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)
Using the given measurements:
\(s_{cone\) = √(7² + 24²) cm
\(s_{cone\) ≈ √(49 + 576) cm
\(s_{cone\) ≈ √625 cm
\(s_{cone\) ≈ 25 cm
Now, we can calculate the surface area of the cone:
\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)
\(A_{cone\) = (22/7) × 7 cm × 32 cm
\(A_{cone\) = 704 cm²
Surface Area of the Hemispherical Base:
The surface area of a hemisphere is given by the formula:
\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.
Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:
\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²
\(A_{hemisphere\) = (22/7) × 2 × 49 cm²
\(A_{hemisphere\) = 308 cm²
Total Surface Area:
To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:
Total Surface Area = \(A_{cone} + A_{hemisphere}\)
Total Surface Area = 704 cm² + 308 cm²
Total Surface Area = 1012 cm²
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plssss it’s due in 5 min answer plsss
Answers
Find the volume of the figure.
Answers
Answer:
7777.5 ft^3
Step-by-step explanation:
First, separate the solid into two, the triangular prism and the rectangular prism. Then, find the area of both solids.
\(A_{triangular prism}=BA *h\)
\(A_{triangular prism} = (\frac{1}{2} * 17 * 19) *15\)
\(A_{triangular prism}=161.5*15\)
\(A_{triangular prism}=2422.5ft^3\)
\(A_{rectangular prism} = l * w * h\)
\(A_{rectangular prism}=17*15*21\)
\(A_{rectangular prism}=5355ft^3\)
Finally, add together both values
\(A_{total}=A_{triangular prism}+A_{rectangular prism}\)
\(A_{total}=2422.5+5355\)
\(A_{total}=7777.5ft^3\)
Jangles Co. earned $1.80 per share. Assuming a closing price of $40, the PE ratio is: (Round to the nearest whole number.)
Multiple Choice
7
22
72
20
Answers
The required value of PE is given as 22. The correct option is (B).
How to calculate the PE ratio of a company?The PE ratio can be calculated by taking the ratio of the price of stock to the earning of the company per share.
The given question can be solved as,
The earning per share is $1.80.
And, the closing price i s $40.
Thus, the PE ratio can be calculated as follows,
PE = 40/1.80
= 22.2
Which is equivalent to 22, rounding to the nearest whole number.
Hence, the PE ratio is given as 22.
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Bookwork code: N84
Look at the poster below showing the price of pencils in a stationery shop.
Annabel wants to buy exactly 76 pencils. What is the lowest amount she can
pay?
Give your answer in pounds (£).
spar
..
Pencils for sale!
30p each
Pack of 10
pencils for £2
Answers
Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20
How is the lowest amount determined?The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.
Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.
If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).
If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].
Pencils for sale
30p each
Pack of 10 pencils for £2
Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.
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Which of the following is the equation of the function f(x) graphed above? A. ƒ(x) = x(x − 2)²(x − 1)(x + 1) B. f(x) = (x - 2) (x − 1)(x + 1) c. f(x)= x(x - 2)²(x − 1)(x + 1) + 1)² D. f(x) = (x - 2)²(x - 1)(x - 1)^ E
Answers
A ballroom dance couple has learned 8 different routines and is going to perform 6 of them at a local competition. How many different ways could they arrange their performance?
Answers
The ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.
To solve this problem
The idea of combinations can be used.
The number of ways to select k items from a set of n items is given by the formula for combinations:
C(n, k) = n! / (k! * (n - k)!)
In this case, n = 8 (the total number of routines they have learned) and k = 6 (the number of routines they will perform).
Using the formula, we can calculate:
C(8, 6) = 8! / (6! * (8 - 6)!)
= 8! / (6! * 2!)
The factorial function is represented in this case by the exclamation symbol (!).
The sum of all positive integers from 1 to n is the factorial of the number n.
Calculating the factorials involved:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
2! = 2 * 1 = 2
Plugging in these values:
C(8, 6) = 40,320 / (720 * 2)
= 40,320 / 1,440
= 28
Therefore, the ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.
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Which of these is not an equation?
Answers
Answer:
where r the pictures
Step-by-step explanation:
attach a picture by file explorer when your creating your question so we can see what you're talking about (if you didn't know)
The number of students in a chess club decreased from 26 to 15. What is the percent decrease? Round your answer to the nearest percent.
Answers
Answer:
42%
Step-by-step explanation:
26 - 15 = 11
Take your decrease and divide it by the original price:
11/26 = 0.4230
Multiply 0.4230 by 100 to find the percent:
42.3
Round your answer and you would get -
42%
Answer:
42%
Step-by-step explanation:
You divide 15 by 26 and get 0.5769 and it continues with other numbers. to the nearest percent is 58. Then you subtract it from 100 and get 42%.