Using the GREAT decision-making model, one could consider telling the driver not to drive after drink, getting out of the car and looking for another, or riding in the same car while ignoring the situation.
What options do we have in this situation?The options we have in this situation are:
Complain to the driver and tell him not to drive after drink.Get out of the car and look for another.Go in the same car ignoring the situation.What are the pros and cons of these options?Option 1:
Pro: The driver can understand my concern and go to his house to avoid an accident.Con: The driver doesn't understand my concern, he gets angry and we start arguing.Option 2:
Pro: I'm going to be safe in another car.Con: While I wait for another car they can rob me.Option 3:
Pro: I'm going to get home.Con: It is an irresponsible action that puts the lives of several people at risk.Learn more about GREAT decision making model in: https://brainly.com/question/18066206
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For the following exercises, evaluate the function at the indicated values:
f(−3); f (2); f(−a); −f(a); f (a + h).
6 f (x) = 2∣3 x − 1∣
Answer:
The evaluated function for the indicated values is given below.
The value of f(-3) is 20 .
The value of f(2) is 10 .
The value of f(-a) is [tex]$2|-3 a-1|$[/tex].
The value of -f(a) is [tex]$-2|3 a-1|$[/tex].
The value of f(a+h) is [tex]$2|3 a+3 h-1|$[/tex].
Step-by-step explanation:
A function [tex]$f(x)=2|3 x-1|$[/tex] is given.
It is required to evaluate the function at [tex]$f(-3) ; f(2) ; f(-a) ;-f(a) ; f(a+h)$[/tex].
To evaluate the function, substitute the indicated values in the given function to determine the output values and simplify the expression.
Step 1 of 5
The given function is [tex]$f(x)=2|3 x-1|$[/tex].
To evaluate the function at f(-3), substitute -3 in the given function [tex]f(x)=2|3 x-1|$\\ $f(-3)=2|3(-3)-1|$\\ $f(-3)=2|-9-1|$\\ $f(-3)=2|-10|$\\ $f(-3)=2(10)$\\ $f(-3)=20$[/tex]
Step 2 of 5
To evaluate the function at $f(2)$, substitute 2 in the given function.
[tex]f(x)=2|3 x-1|$\\ $f(2)=2|3(2)-1|$\\ $f(2)=2|6-1|$\\ $f(2)=2(5)$\\ $f(2)=10$[/tex]
Step 3 of 5
To evaluate the function at f(-a), substitute -a in the given function.
[tex]$$\begin{aligned}&f(x)=2|3 x-1| \\&f(-a)=2|3(-a)-1| \\&f(-a)=2|-3 a-1|\end{aligned}$$[/tex]
Step 4 of 5
To evaluate the function at -f(a), substitute a in the given function.
[tex]f(x)=2|3 x-1|$\\ $-f(a)=-2|3(a)-1|$\\ $-f(a)=-2|3 a-1|$[/tex]
Step 5 of 5
To evaluate the function at f(a+h), substitute a+h in the given function. [tex]$f(x)=2|3 x-1|$[/tex]
[tex]$$\begin{aligned}&f(a+h)=2|3(a+h)-1| \\&f(a+h)=2|3 a+3 h-1|\end{aligned}$$[/tex]
Question 9(Multiple Choice Worth 5 points)
(05.02 LC)
Which of the following possibilities will form a triangle?
O Side 15 cm, side = 6 cm, side = 8 cm
=
O Side 15 cm, side = 6 cm, side = 9 cm
Side = 16 cm, side = 9 cm, side = 6 cm
Side = 16 cm, side = 9 cm, side = 8 cm
Answer:
D. 16, 9, 8
Step-by-step explanation:
sum of any two sides of triangles must be greater than the third side
only the fourth option follows this rule
Simplify by factoring or distributing:
1.) 2(x + 3) =
2.) 2(x + 3 + y) =
3.) −5 (2x − 3) =
4.) –5(–8w + p) =
5.) 20 + 32w =
6.) 84 + 36z =
7.) (2x - 6)(5x + 7) =
8.) (y - 10)(4y + 2) =
The following equation simplified by factoring or distributing:
2x + 62x + 6 + 2y-10x + 1540w - 5p4(5 + 8w)12(7 + 3z)12(7 + 3z)4y² - 38y - 20Factorization1.) 2(x + 3)
= 2x + 6
2.) 2(x + 3 + y)
= 2x + 6 + 2y
3.) −5 (2x − 3)
= -10x + 15
4.) –5(–8w + p)
= 40w - 5p
5.) 20 + 32w
= 4(5 + 8w)
6.) 84 + 36z
= 12(7 + 3z)
7.) (2x - 6)(5x + 7)
= 10x² + 14x - 30x - 42
= 10x² - 16x - 42
8.) (y - 10)(4y + 2)
= 4y² + 2y - 40y - 20
= 4y² - 38y - 20
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ASAP
Match the function with the graph.
y=√x+4
b, y=√z-1
Cy=√√x-1+4
d.y=√x+1
Using translation concepts, the function is given by:
C. [tex]y = \sqrt{x - 1} + 4[/tex].
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The graphed function is the square root function shifted one unit to the right(x -> x - 1), and four units up(y -> y + 4), hence the function is:
C. [tex]y = \sqrt{x - 1} + 4[/tex].
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There are 20 boys and 18 girls in a class.
Find the percentage of
(i) boys in the class
(ii) girls in the class
Answer:
Step-by-step explanation:
Total Students = 20 + 18 = 38 students
For boys percentage = 20/38 * 100
Boys percentage = 52.6%
For girls percentage = 18/38 * 100
Girls percentage = 47.3%
Answer:
(i) 52.631578947368 %
(ii) 47.368421052632 %
Step-by-step explanation:
there are :
20 boys
18 girls
Total number of students 38
========================
(i) the percentage of boys in the class
[tex]=\frac{20}{38} \times100 = 52.631578947368 \ \%[/tex]
(ii) the percentage of girls in the class
[tex]=\frac{18}{38} \times100 = 47.368421052632 \ \%[/tex]
A rectangular tank has its width exactly half its length. That the height of the tank is 3M and the length is 8m. What is the volume of the tank in M3?
Answer:
Volume = 96m^3
Step-by-step explanation:
If the length of the tank is 8 meters, then the width must be 4 meters, because the question said the width was half the length. Since the height, 3 meters, was also given, we can find the volume.
Vol = L × w × h
We multiply together the length, width and height.
Vol = 8 × 4 × 3
= 96
The volume is 96 meters^3
The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 9,
6, 18, 2, 13, 3, 5. Using the given data, find the mean, median, and mode for this sample.
OA. mean: none, median: 6, mode: 8
B. mean: 6, median: 8, mode: none
C. mean: 8, median: 6, mode: none
OD. mean: 18, median: 8, mode: 6
Reset Selection
e
Answer:
C
Step-by-step explanation:
Mean: 9+6+18+2+13+3+5= 56/7 = 8
Median: 2,3,5,6,9,13,18 the middle number is 6
mode:none
What is the leading coefficient of the polynomial? 5x² + 8x³ +4 - 6x² – 3x5
Answer:
In polynomial function f(x) = 5x² + 2x³ + 4 the leading coefficient is 5.
The leading coefficient of a polynomial is the coefficient of the leading term 5x².
Step-by-step explanation:
Find the Area-Rectangle
a = x +3
b = 2x - 1
Answer:
2x^2 + 5x - 3
Step-by-step explanation:
Area = length (a) * width (b)
(x + 3) * (2x - 1)
2x^2 + 6x - x - 3 (combine like terms)
2x^2 + 5x - 3
Brainliest, please :)
¿Cual es el volumen del cilindro si su area lateral es 55,8cm2?
Based on the lateral area of the cylinder, the volume of the cylinder can be calculated to be 139.5 cm³.
What is the volume of the cylinder?When given the lateral surface area of a cylinder, you can find the volume as:
= Area of lateral surface x (radius / 2)
Solving gives:
= 55.8 x (5 / 2)
= 55.8 x 2.5
= 139.5 cm³.
Missing part of the question:
Radius of the cylinder is 5cm.
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please help please and thank you
Answer:
B or the second option
Step-by-step explanation:
We can label the diagram parts A-E to fully represent the situation in the question.
A: Julie's ascent up the mountain (moving/increasing)
B: Julie drinking hot chocolate (stationary/constant)
C: Julie's descent down the mountain (moving/decreasing)
D: Julie rests (stationary/constant)
E: Julie's final descent down the mountain (moving/decreasing)
PLS HELPPPP MEEEEE EASY POINTS
Reflecting over y=x maps (x,y) onto (y,x).
So, the answer is A. (-8, 3).
Answer:
Step-by-step explanation:
Place the indicated product in the proper location on the grid. (x + 2)(x - 2)
The product of the polynomials, (x + 2)(x - 2) = x² - 4.
How to Find the Product of Polynomials?Given the following expression, (x + 2)(x - 2), to find the product, apply the distributive property as shown below:
(x + 2)(x - 2)
x(x - 2) + 2(x - 2)
x² - 2x + 2x - 4
Combine like terms together
x² - 4
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Many states use a sequence of three letters followed by a sequence of three digits as their standard license-plate pattern. Given that each three-letter three-digit arrangement is equally likely, what is the probability that a ran- domly chosen license plate contains at least one palindrome (a three-letter arrangement or a three-digit arrangement that reads the same left-to-right as it does right-to-left)?
Answer:
Step-by-step explanation:
There are 26 letters, so there are 26
3
possible 3-letter sequences.
the number of these which are palindromes can be computed as follows:
26 choices for the first letter
26 choices for the second letter
1 choice for the third letter ( it has to agree with the first)
number of ways =26
2
Probability of a letter palindrome =26
2
/26
3
=1/26
there are 10 digits, so there are 10
3
sequences of digits.
Reasoning as above, the number of digit-palindromes is (10)(10)(1)=10
2
so the probability of a digit-palindrome is 10
2
/10
3
=1/10
The events
D - digit palindrome
L - letter palindrome
are independent but not mutually exclusive.
So, P(LorD)=P(L)+P(D)−P(LandD)
P(LorD)=P(L)+P(D)−P(L)P(D)
=1/26+1/10−(1/26)(1/10)
=10/260+26/260−1/260
=35/360=7/52
GIVING BRAINLEST!
A cup of apple juice requires spoons of sugar. If David prepares 18 cups of juice, then how much
spoons of sugar is required?
90
72
8
2
Answer:
I think it is 72
Step-by-step explanation:
but the question doesn't make sense because it should tell the number of spoons per 1 cup of sugar, perhaps it was a copy-paste mistake?
The completed construction of regular hexagon is shown below explain why act is a 30-60-90 triangle
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg and length of the hypotenuse is twice the length of the shorter leg.
How to explain the reasonACF is a 30º-60º-90º triangle because of the following reasons;
Based on a theorem, in a 30°-60°-90° triangle, it is said that the length of the longer leg is √3 times the length of the shorter leg and length of the hypotenuse is twice the length of the shorter leg,
1 → short leg = 1
2 → hypotenuse = 2
√3 → long leg = √3
Using the Pythagorean theorem., we have that
a² + b² = c²
1² + b² = 2²
b² = 2² - 1²
b² = 4 - 1
b² = 3
√b² = √3
b = √3
Thus, in a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg and length of the hypotenuse is twice the length of the shorter leg.
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The speed of light is 186,282 miles per second write the place name and the value of each eight in this number
Place name of eights are ten thousands place & tens place & 80000, 80 are the values respectively.
The expanded form of a number is splitting of numbers based on place value. The place are ones, tens, hundreds, thousands, ten thousand etc
that is, the number represented by the sum of each digit multiplied by its place value is called the expanded form of a number.
Example : Expanded form of 4567 is 4000+500+60+7. where 4 is in thousands place, 5 is in hundreds place, 6 is in tens place and 7 is in ones place.
Given that, The speed of light is 186,282 miles per second.
The number is 186282.
Expanding the number, we get,
186282 = 100000+80000+6000+200+80+2
Here in the number 186282, eight present in the ten thousands place and in the tens place.
Since one eight is in ten thousands place, so the value is 80000
And the another eight is in the tens place, so the value is 80.
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Find the measure of the exterior angle.
Answer:
The exterior angle is 77
Step-by-step explanation:
The measure of the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
2x+11 = x +44
First we need to find x
Subtract x from each side
2x+11-x = x+44
x +11 = 44
Subtract 11 from each side
x+11-11 = 44-11
x =33
Now we can find the exterior angle
2x+11 = 2(33)+11 = 66+11 = 77
The exterior angle is 77
Type the correct answer in each box. Use numerals instead of words. The domain of this function is {-12, -6, 3, 15}. Complete the table based on the given domain. x y -6 5 15 15
The complete table is
x -12 -6 3 15
y -6 5 15 15
How to complete the table?The domain is given as:
Domain = {-12, -6, 3, 15}.
The incomplete table is given as
x
y -6 5 15 15
Enter the domain in the x values
x -12 -6 3 15
y -6 5 15 15
Hence, the complete table is
x -12 -6 3 15
y -6 5 15 15
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Consider functions f and g
Using successive approximation, what is the approximate solution to the equation f(x)= g(x)? Use the graph as a starting point
PLEASE THIS HAS A TIME LIMIT AND GIVE PROOF BECAUSE I REALLY NEED TO GET THIS RIGHT :((
25 POINTS AND WILL MARK BRAINLIEST
Answer:
1)D 2) Can't see the function
A spherical ball for a machine was made with a radius of 2 centimeters. if the ball has a mass of 278.1 grams, which material was used to make the ball?
The spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams and will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.
Thus, we can say that Terbium is the material used to make the spherical ball.
The density of an object is given as the ratio of its mass and its volume.
Density = Mass/Volume.
In the question, we are informed that a spherical ball for a machine was made with a radius of 2 centimeters.
Thus, the volume of the spherical ball, using the formula for the volume of a sphere, V = (4/3)πr³, where r is its radius, can be calculated as:
V = (4/3)π(2)³ cm³ = 32π/3 cm³ = 33.51032 cm³.
The mass of the ball is given to be 278.1 grams.
Thus, its density = 278.1/33.51032 grams per cm³ = 8.2989355 grams per cm³.
We know that the density of Terbium is 8.23 grams per cm³.
Thus, the spherical ball for the machine with a radius of 2 centimeters, has a mass of 278.1 grams, will have a density of 8.29 grams per cm³, which is identical to the density of Terbium's 8.23 grams per cm³.
Thus, we can say that Terbium is the material used to make the spherical ball.
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Answer: copper
Step-by-step explanation:
Please Help Asap!!! I would really appreciate it
Using the given exponential function, it is found that the colony would have 852 bacteria after 10 days.
What is the exponential function?The exponential function for the colonies' size is given as follows:
[tex]F = I(1 + r)^t[/tex]
In which:
I is the initial amount.r is the growth rate.t is the number of time periods.The parameters are given as follows:
I = 55, r = 0.73, t = 5, as 10/2 = 5.
Hence the amount will be given by:
[tex]F = 55(1 + 0.73)^5 = 852[/tex]
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Can someone help me out if question 37. triangle is a SSS, SAS or ASA? ASAP, gotta have an answer fast pls
Answer:
ASA Postulate
Step-by-step explanation:
The two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle. (Angle, Common Side, Angle)
Help me pls my mom wants me to finish soon
Answer:
B
Step-by-step explanation:
NEED HELP ASAP!
Please see the attachment below.
The angle ∠14 and angle ∠16 are the supplementary angles. Then the measure of angle ∠16 will be 188° – 5x.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The line l and the line m are parallel to each other.
The angle ∠7 = 4x – 3 and angle ∠14 = 5x – 8.
Then the measure of angle ∠16 will be
The angle ∠14 and angle ∠16 are the supplementary angles. Then we have
∠14 + ∠16 = 180°
5x – 8 + ∠16 = 180°
∠16 = 180° – 5x + 8
∠16 = 188° – 5x
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please help
are these functions or not?
Answer:
1. Function
2. Not a function
3. Function
4. Not a function
Step-by-step explanation:
A function just means that for each input it outputs only 1 output. This output isn't necessarily unique. So for example if you're just given: f(2) = 3 and f(1) = 3, this is a function since each input only outputs 1 value, even though the output isn't unique, but if you're given: f(3) = 2, f(2) = 1, f(3) = 3. that's not a function since f(3) outputs both 2 and 3.
Anyways now that you hopefully understand this, let's look at each image.
Relation 1: (Function)
So for each input (the domain) it's only pointing to one output (range), even if multiple input (the domain) are pointing to the same output (the range), it's still a function.
Relation 2: (Not a function)
This is not a function, since if you look at the input 7 (the range), you'll see it outputs two things (range). It outputs -6 and -7. So this is not a function
Relation 3: (Function)
This is a function since each x-value (input) has only one y-value (output). So it's a function
Relation 4: (Not a functio)
This is not a function, since there are multiply coordinates with the same x-coordinate (input) and different y-coordinates (output). The x-coordinate 2 has the output b, y, and m, and since no value is given for these variables, it can be assumed they're different values, thus it's not a function.
picture says all 20 charecters needed
Answers:
Lower bound = 41.3
Upper bound = 41.5
===========================================================
Explanation:
49.15 is the smallest f can be while 49.24 is the largest it can be. Well technically we could have something like 49.2499 or 49.24999 and so on. We slowly approach 49.25 but never actually get there
So the variable f is between 49.15 and 49.25 inclusive of the first value but excluding the second value. We can write it as [tex]49.15 \le f < 49.25[/tex]
For similar reasoning, [tex]7.75 \le g < 7.85[/tex]
-----------------
If we wanted to subtract those variables and get the smallest result possible, then we need to pick values that are closest together. It might help to set up a number line.
This means we'd go for f = 49.15 and g = 7.85
The lower bound for f-g is f-g = 49.15-7.85 = 41.3
In contrast, the upper bound is when the two variables are spaced as far apart as possible. The upper bound is f-g = 49.25 - 7.75 = 41.5
Answer:
See below
Step-by-step explanation:
49.2 could be 49.15 <= f < 49.25
7.8 could be 7.75 <= f < 7.85
Lower bound of f- g would then be 49.15 - 7.85 > 41.3
upper bound 49.25 - 7.75 < 41.5
41.3 < f-g < 41.5
22
Select the correct answer.
Consider functions fand g.
f(x) = ^x4 + 9x^2 - 3
g(x) = (1/2) ^x-2
Using a table of values, what are the approximate solutions to the equation f(x) = g() to the nearest quarter of a unit?
OA -0.5 and
OB.
I-0.25 and
OC
OD. I
0.5
1.5
-0.25 and ≈ 2.5
I ~ -1 and I ~ 0.75
Reset
Next
The approximate solution of the system of equations is x = 0.75
How to determine the approximate solutions?The functions are given as:
f(x) = x^4 + 9x^2 - 3
g(x) = (1/2)^x - 2
Calculate the values of the function from -1 to 1
x f(x) g(x)
-1 7 8
-0.75 2.38 6.72
-0.5 -0.69 5.66
-0.25 -2.43 4.76
0 -3 4
0.25 2.43 3.36
0.5 -0.69 2.83
0.75 2.38 2.38
1 7 2
From the above table, we have:
f(0.75) = g(0.75) = 2.38
Hence, the approximate solution of the system of equations is x = 0.75
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Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
7 is multipled by the difference of a number and 1.
The algebraic expression of the given sentence is: 7(x - 1).
How to Write an Algebraic Expression?Let the unknown number be represented as x.
The word "difference" means subtraction which is "-". Multiplied means times.
We would have the following:
"Difference of x and 1" is: x - 1
x - 1 multiplied by 7 would be: 7(x - 1)
Therefore, the algebraic expression is: 7(x - 1).
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Jeremy left the house in the morning and the temperature outside was 2 degrees Celcius. Once he returned at night, the temperature was -7 degrees Celcius.
How much did the temperature decrease by?
Answer:
The temperature decreased by 9 degrees.
Step-by-step explanation:
Since the temperature in the morning was 2*C & at night, the temperature was -7*C, the temperature had to decrease using this equation => ||-7 + 2|| = x, with -2 being the temperature loss added as well. All we have to do is 7+2 = x & 9 = x, with x being the temperature drop.
Answer:
9 degrees Celcius
Step-by-step explanation:
The difference between 2 and -7 is 9.