Answer:
In a nutshell, [tex]f(x)[/tex] is obtained by applying an horizontal translation on [tex]g(x)[/tex], followed by a vertical translation.
Step-by-step explanation:
Let be [tex]g(x) = x^{3}[/tex] the parent function, [tex]f(x)[/tex] is obtained by applying an horizontal translation on [tex]g(x)[/tex], followed by a vertical translation, that is:
[tex]f(x) = g(x-a)-b,\,a,b\in\mathbb{R}[/tex] (1)
If [tex]a > 0[/tex], then translation is rightwards.
If [tex]b > 0[/tex], then translation in downwars.
If [tex]a = 2[/tex] and [tex]b = 1[/tex], then the resulting function is:
[tex]f(x) = g(x-2)-1[/tex]
[tex]f(x) = (x-2)^{3}-1[/tex] (2)
In a nutshell, [tex]f(x)[/tex] is obtained by applying an horizontal translation on [tex]g(x)[/tex], followed by a vertical translation.
Carlos bought a video game that was 15% off. The game was originally $20. How much money DID HE SAVE by getting it on sale?
Answer:
Carlos saved 17 dollars.
Step-by-step explanation:
15% of $20.00 = $3.00
what is the slope of the line that passes through the points (2,-3) and (2,13)? write your answer in simplest form
Answer:
The slope is undefined because there is no change in x, making it a vertical line
Step-by-step explanation:
PLEASE HELP‼️
A
B
C
D
Answer:
D
Step-by-step explanation:
hope this helps >.<
what fraction is 15 minutes of 1 hour
Answer:
1/4
Step-by-step explanation:
Convert 1 hour to minutes
1 hour = 60 minutes
Then you can find the fraction
15/60
simplifies to 1/4
15 minutes is 1/4 of 60 minutes/1 hour
Can someone please help me?
Answer:
#25 is left, #27 is between, #28 is below, and #26 is first i think.
Step-by-step explanation:
Answer: #25 is left, #27 is between, #28 is below, and #26 is first i think.
Step-by-step explanation:
help me please
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A polynomial function has zeros at 5/2 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function in standard form that could represent this function
Answer:
-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7
Step-by-step explanation:
[tex](x-5/2)^{2}(x-3)(x-0)^4 =0\\(2x-5)^{2}(x-3)(x)^4 =0[/tex]
Expand and get
-75 x^4 + 85 x^5 - 32 x^6 + 4 x^7
The standard form will be [tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]
What will be the standard form of the given expression?The given expression is
[tex](x-\dfrac{5}{2})^2(x-1)^2(x-0)^4=0[/tex]
[tex](x^2-5x+\frac{25}{4} )(x^2-2x+1)(x^4)=0[/tex]
[tex](x^4-2x^3+x^2-5x^3+10x^2-5x+\dfrac{25x^2}{4} -\dfrac{50}{4} x+\dfrac{25}{4} ) x^4=0[/tex]
[tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]
Thus the standard form will be
[tex]X^4(x^4-7x^3+12x^2-\dfrac{35x}{2} +\dfrac{25x^2}{4} +\dfrac{25}{4} =0[/tex]
To know more about Polynomials follow
https://brainly.com/question/15702527
An exponential distribution is formed by the waiting times for a patient in the emergency room. The average waiting time for this distribution is 38 minutes. Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes? Round your answer to three decimal places.
Answer:
0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes
Step-by-step explanation:
To solve this question, we should understand the exponential distribution and conditional probability.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
The average waiting time for this distribution is 38 minutes.
This means that [tex]m = 38, \mu = \frac{1}{38} = 0.0263[/tex]
Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes?
Event A: Taking more than 37 minutes.
Event B: More than 37 + 41 = 78 minutes.
Probability of taking more than 37 minutes:
[tex]P(A) = P(X \leq 37) = 1 - e^{-0.0263*37} = 0.6221[/tex]
More than 37 minutes and more than 78 minutes:
The intersection is more than 78 minutes, so:
[tex]P(A \cap B) = P(X > 78) = e^{-0.0263*78} = 0.1286[/tex]
The probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1286}{0.6221} = 0.207[/tex]
0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes
4. Solve this equation for x. Please show work. 4√x + 3 + 3 = 15
Answer:
i don't know sorry b a b y g i r l
Step-by-step explanation:
Consider the factored form equation of parabola y = 2(x - 3) * (x + 1)
Answer:
a= x= 3, -1
b= x=1
c= (1, -8)
Step-by-by-step explanation:
For the show your work, you have to create the graph of the parabola. (attached image)
Josiah bought two pounds of strawberries for $9.60. What is the price, in dollars per ounce of strawberries? 1 pound = 1 pound= 16 ounces 16 ounces Before you try that problem, answer the question below. How many ounces of strawberries did Josiah buy?
Answer:
$0.30 per ounce
Step-by-step explanation:
16 ounces per pound
16 x 2 = 32 ounces per 2 pounds
9.60/32 = $0.30 per ounce
Mason is working two summer jobs, making $20 per hour lifeguarding and making $10 per hour landscaping. In a given week, he can work no more than 13 total hours and must earn at least $170. If xx represents the number of hours lifeguarding and yy represents the number of hours landscaping, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
[tex]x = 4\\y = 9[/tex] hours
Step-by-step explanation:
Given -
x represents the number of hours lifeguarding and y represents the number of hours landscaping
[tex]x+ y = 13[/tex] -----Eq ( 1 )
and
[tex]20 * x + 10 * y = 170[/tex] -----Eq ( 2 )
Substituting the value of [tex]x = 13-y[/tex] in equation 2, we get -
[tex]20* (13 - y) + 10 y = 170[/tex]
[tex]260 - 20 y + 10 y = 170\\10y = 90\\y = 9[/tex]
[tex]x = 13-9 = 4[/tex]
Jim’s family is choosing whether to go to a restaurant for lunch or for dinner. The cost of a salad is $7 at lunch and $9 at dinner. The cost of a steak is $10 at lunch and $12 at dinner. Each person will choose either a salad or a steak regardless of the mealtime. Jim calculates the food bill to be $41 if they go during lunch and $51 if they go during dinner.
1.Write a system of equations that could be used to solve the problem. Define your variables.
2.Solve by any algebraic method (elimination/substitution). Work must be shown! How many people will choose a salad?
Answer:
3
Step-by-step explanation:
edge
Answer:
C. 3
Explanation:
edge 2020
What is the Voter Registration Act and how does it affect Gerrymandering?
Answer:
United States federal law signed into law by President Bill Clinton on May 20, 1993, and which came into effect on January 1, 1995.
Step-by-step explanation:
Hope It Helps :)
A motorboat takes 3 hours to travel 108 kilometers going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Rate of the boat in still water:
Rate of the current:
Answer:
45; 9
Step-by-step explanation:
1) if the rate of the boat in still water is 'b' and the rate of the current is 'c', then it is possible to write the rate of the boat going upstream: b-c, downstream: b+c.
2) the basic formula is: D=r*t, where D - distance, r - rate/velocity, t - time;
3) according to the condition it takes 3 hours to travel 108 km upstream, it means according to the formula above 3(b-c)=108;
4) according to the condition it takes 2 hours to travel 108 km downstream, it means according to the formula above 2(b+c)=108;
5) if to make up the system of two equations, then:
[tex]\left \{ {{3(b-c)=108} \atop {2(b+c)=108}} \right. \ => \ \left \{ {{b=45} \atop {c=9}} \right.[/tex]
6) rate of the boat in still water: 45 km/h;
rate of the current: 9 km/h.
How do savings account differ from checking accounts
- they’re not offered at banks
- they typically pay interest
- the funds are easier to get
-you have to keep the money in for a long
Answer:
Savings accounts typically pay interest.
Step-by-step explanation:
What is the answer plz
Answer:
A = 180m²
Step-by-step explanation:
To find the area of the bottom rectangle subtract the height of the top rectangle. Hope that makes sense if you want a another just ask.
an electronics store is having a 20%-off on all cell phones. the original price of a cell phone is x dollars. which expression represents the sale price of a cell phone?
a. x - 0.2
b. x - 0.8
c. 0.2*x
d. 0.8*x
Answer: x*.2
Step-by-step explanation:
When you are trying to find the sale price you want to multiply the origanal price of the cellphone to the percentage you are getting off. Hope this helped!
PLEASE HELP WITH THE FOLLOWING. WILL GIVE BRAINLIEST. THANK YOU
Answer:
50.8°Step-by-step explanation:
First, we need to use the Pythagorean Theorem to find the third side. We will then use the law of cosines to find the angle.
2√15² = 2√6² + b²
60 = 24 + b²
Subtract 24
36 = b²
b = 6
Now, that we have all three sides, we will use the law of cosines to figure out the angle.
c² = a² + b² - 2abCosC°
Substitute the values in.
6² = 2√15² + 2√6² - 2(2√15)(2√6)CosC°
36 = 60 + 24 - 2(37.947331922)CosC°
36 = 60 + 24 - 75.894663844CosC°
36 = 84 - 75.894663844CosC°
Subtract 84
-48 = -75.9CosC°
0.63241106719 = CosC°
Arccos (0.63241106719) = 50.77176844°
The largest acute angle is approximately 50.8°
A traveling circus with thrill rides Charge 7$ For admission $1.50 For each ride you take. If you pay $29.50 total, how many rides did you take?
Answer:
15 rides
Step-by-step explanation:
29.50 - 7 = 22.50
22.50 / 1.50 = 15
Because of bad weather, the number of days next week that the captain of a charter fishing boat can leave port is uncertain. The following probability distribution for the number of days that the boat is able to leave port per week was determined based on historical data when the weather was poor: The number of days the boat can leave port per week Probability 0 0.20 1 0.05 2 0.05 3 0.05 4 0.15 5 0.10 6 0.15 7 0.25 Based on the probability distribution, what is the expected number of days per week the captain can leave port. Group of answer choices 3.55 4.00 3.50 4.05 2.85
Answer:
The expected number of days per week the captain can leave port is 4.05.
Step-by-step explanation:
We are given the following distribution:
[tex]P(X = 0) = 0.2[/tex]
[tex]P(X = 1) = 0.05[/tex]
[tex]P(X = 2) = 0.05[/tex]
[tex]P(X = 3) = 0.05[/tex]
[tex]P(X = 4) = 0.15[/tex]
[tex]P(X = 5) = 0.1[/tex]
[tex]P(X = 6) = 0.15[/tex]
[tex]P(X = 7) = 0.25[/tex]
What is the expected number of days per week the captain can leave port.
We multiply each outcome by its probability. So
[tex]E = 0*0.2 + 1*0.05 + 2*0.05 + 3*0.05 + 4*0.15 + 5*0.1 + 6*0.15 + 7*0.25 = 4.05[/tex]
The expected number of days per week the captain can leave port is 4.05.
What is the volume of a cube with a side length of 3t5units?
Cube V = s3
Answer:
V=a3=33=27
Step-by-step explanation:
sorry if its wrong
What is the average rate of change for f(x) = 2 ^ x + 10 over the interval 2 <= x <= 4
give brailist but help me fast
Answer:
76.7
Step-by-step explanation:
11.3(3) + 10.7(4) = __ + 42.8
Multiply values
33.9 + 42.8 = __ + 42.8
The missing value is 33.9!
42.8 + 33.9 = 76.7
Round 1526.04 to the nearest tenths
a taxi company currently has nine cabs in its fleet, and its total daily cost is 4,000. if the company added a 10th cab its daily total cost would be 4.200 or 420 per cab.
Answer:
4000÷9 the answer it gaves for one you add it to the 4000
what is the shape and direction of f(x)=(x+7)(x+11)
Given:
The function is
[tex]f(x)=(x+7)(x+11)[/tex]
To find:
The shape and direction of the given function.
Solution:
We have,
[tex]f(x)=(x+7)(x+11)[/tex]
It can be written as
[tex]f(x)=x^2+11x+7x+77[/tex]
[tex]f(x)=x^2+18x+77[/tex]
It is a quadratic function and the power of [tex]x[/tex] is 2 so the graph of this function is a vertical parabola.
The leading coefficient is positive so the parabola opens upward.
Therefore, the given function is a vertical parabola that opens upward.
Please!!!!! help!!!!!
Answer:
유퓨요ㅛㅜㅑㅑㅅ재 내 8 ㅓㅕ를펴 16 ㅐㅏ?
Step-by-step explanation:
I'm gonna send you a picture of it
Answer:
Of whaT?
But thanks for the free points
Rewrite 10x - 5y = -30 in slope-intercept form.
somebody help me wit dis
Answer:
y = 2x + 6
Step-by-step explanation:
10x - 5y = -30
-5y = -10x - 30
y = 2x + 6