Which of the following ordered pairs belongs to the graph of f(x)
- 3x + 9?
O (1, – 10)
O (-1, 12)
O (2, – 3)
O (-2, 13)
Answer:
The second choice, [tex](-1,\, 12)[/tex].
Step-by-step explanation:
Note, that the expression [tex]y = f(x)[/tex] is an equation. A point [tex](x,\, y)[/tex] is on the graph of [tex]y = f(x)\![/tex] if and only if the value of [tex]x[/tex] and [tex]y[/tex] satisfy this equation; that is: in other words, the [tex]y\![/tex]-coordinate of that point (the second number in the tuple) should be equal to [tex]f(x)[/tex], which is equal to [tex](-3\, x +9)[/tex] (evaluated where [tex]x\![/tex] is equal to the first number in the tuple.
For each tuple in the choices, calculate the value of [tex]f(x)[/tex] where [tex]x[/tex] is equal to the first number of each tuple. Compare the result to the second number in that tuple. That choice corresponds to a valid point on [tex]y = f(x)[/tex] only if these two numbers match.
First choice: [tex]x = 1[/tex], [tex]f(x) = f(1) = -3 + 9 = 6[/tex]. That's not the same as the second number, [tex]-10[/tex]. Therefore, this point isn't on the graph of [tex]y = f(x)[/tex].Second choice: [tex]x = -1[/tex], [tex]f(x) = f(-1) = (-3)\times (-1) + 9 = 3 + 9 = 12[/tex]. That matches the second number in the tuple. Therefore, this point is on the graph of [tex]y = f(x)[/tex].Third choice: [tex]x = 2[/tex], [tex]f(x) = f(2) = (-3)\times 2 + 9 = 3[/tex]. That's not the same as the second number, [tex](-3)[/tex]. Therefore, this point isn't on the graph of [tex]y = f(x)[/tex].Fourth choice: [tex]x = -2[/tex], [tex]f(x) = f(-2) = (-3)\times (-2) + 9 = 15[/tex]. That's not the same as the second number, [tex]13[/tex]. Therefore, this point isn't on the graph of [tex]y = f(x)[/tex].A king and his army will attempt to capture a fortress. The left and right flanks break off from the main group to attack the west and east guard towers. Suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. If both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. If, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. If both flanks fail, then the king's chance of capturing the fort drops to 20%. What is the chance the king will capture the fort
Answer:
Step-by-step explanation:
Let the probability of winning from left side be L and from right side by R .
Let the probability of winning by king be K .
Given information can be summarised as follows :
P(L) = .6
P(R) = .75
P K/(L∩R)=.98
P K/(L∩R')= .8
P K/(L'∩R) = .5
P K/(L∩R)' = .2
Probability of win by King can be summarised as follows .
P(k) = P(L∩R) x P K/(L∩R) + P(L∩R') x P K/(L∩R') + P(L'∩R) x P K/(L'∩R) + P(L∪R)' x P K/(L∪R)'
P(L∩R) = .6 X .75 = .45
P(L∪R) = P(L) +P(R) - P(L∩R)
= .6 +.75 - .45 = .90
P(L∪R)' = 1 - P(L∪R) = .10
P(L∩R') = P(L) - P(L∩R) = .6 - .45 = .15
P(L'∩R) = P(R) - P(L∩R) = .75 - .45 = .30
P(k) = P(L∩R) x P K/(L∩R) + P(L∩R') x P K/(L∩R') + P(L'∩R) x P K/(L'∩R) + P(L∪R)' x P K/(L∪R)'
= .45 x .98 + .15 x .8 + .30 x .5 + .1 x .2
= .441 + .12 + .15 + .02
= .73 approx .
What is the solution of the system of equations? y = –2x + 8 y = x – 4
Answer:
(4,0)
Step-by-step explanation:
So we have the system of equations:
[tex]y=-2x+8\\y=x-4[/tex]
To solve, we can use substitution.
Substitute the second equation into the first. So:
[tex]x-4=-2x+8[/tex]
Add 2x to both sides. The right cancels:
[tex]3x-4=8[/tex]
Add 4 to both sides:
[tex]3x=12[/tex]
Divide both sides by 3:
[tex]x=4[/tex]
Now, let's substitute this back into the second equation to find y:
[tex]y=x-4[/tex]
Substitute 4 for x:
[tex]y=4-4[/tex]
Subtract:
[tex]y=0[/tex]
So, our solution is (4,0).
And we're done!
GH =*
Help I’m trying to Gh, I need help bad
Answer:
11
Step-by-step explanation:
I just assumed D is the midpoint; and if D is the midpoint,
GD=DH, GD+DH=GH
5.5+5.5=11
Help me out 25 points
Answer: Can you give more details
Step-by-step explanation:
The ratio of a circle radius to its diameter is always 1 to 2. In math class, Russell uses his compass to draw a circle with a radius of 6 centimeters. What is the diameter of the circle Russell drew?
Answer:
The diameter is 12
Step-by-step explanation:
Since it is 1 to 2
The diameter is double the radius.
The radius is 6 and 6 times 2 is 12.
The diameter of the circle Russell drew is 12 centimeters.
A circle is a bounded figure with a point from the center to its circumference is equidistant.
A diameter is a straight line from one point on the circumference of the circle to another point on the circumference of the circle.
Radius is a line from the center of the circle to the circumference of the circle.
The ratio of radius to the diameter is 1 : 2. This means that the diameter is two times the length of the radius. If the radius is 6cm, the diameter = 6 x 2 = 12 cm.
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f(a) = 2a - 1
g(a) = 4a 1
Find f(a) + g(a)
6a + 2
O 6a-2
Oa+2
O 2a-2
Answer:
6a-2
Step-by-step explanation:
Fist wright the equation
2a+4a-1-1
add like terms
2a+4a=6a
-1+-1=-2
Combine
6a-2
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1.
A car dealer advertises a 8% markup over cost. Find the selling price of a car that costs the dealer $38,000.
Multiply the cost of the car by 1 + percent of markup:
38,000 x 1.08 = 41,040
The price is $41,040
Answer:
41040
Step-by-step explanation:
First find the markup
38000* 8%
38000*.08
3040
Add the markup to the original price
38000+3040
41040
You earn $106.25 for working 17 hours. What is
your hourly wage
Answer:YAY
Step-by-step explanation: :)
246/35 simplified to a whole number
Answer:
About 7
Step-by-step explanation:
245/35 = 7
So, 246/35 = 7.02, which is about 7.
Hope this helps!
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Carmen has taken out a loan for $800 to buy a car. She plans to pay back the loan at a rate of $40 per month. Ramona has borrowed $500 to buy a car, which she plans to pay back at a rate of $20 per month. How long will it take Carmen to pay back her loan?
Answer:
800 ÷ 40
=20
It will take Carmen 20 to pay back her loan
Answer:
20 Months
Step-by-step explanation:
800 / 40 = 20
simplify the following expression: -10x + 15 - 3x + 2 *
what is -20 and 3/4 as a decimal.
Answer:
20.75
Explanation:
20+3/4
= 20.75
= 2075
A paper sheet is cut 28 inches to the nearest inches. Find the maximum and minimum length of the patient possible.
Answer:
max: 28.5 inchesmin: 27.5 inchesStep-by-step explanation:
If the actual dimension were different from 28 inches by more than 1/2 inch, it would be reported as a different dimension. So, the minimum that will be reported as 28 is 27.5. The maximum that will be reported as 28 will be 28.4999999.... ≈ 28.5
The maximum and minimum length of the sheet are 28.5 inches and 27.5 inches, respectively.
Order the following from GREATEST to LEAST (descending order).
-32,-10, 161, -31,|- 301, 25
Answer: 161, 25,-10,-31,-32,-301
Step-by-step explanation:
Please help!!!!!
Turner treated his sister to lunch while visiting her in springdale. their lunch cost $400. and the sales tax in springdale is 11% if turner left an 18% tip on the $400, how much in total did he pay
Answer:
$516
Step-by-step explanation:
Price of lunch: $400
Sales tax: 11% of $400
Tip: 18% of $400
The sales tax and tip combined were 29% of $400 since 11% of $400 + 18% of $400 = 29% of $400.
We calculate the combined sales tax and tip:
29% of $400 =
= 0.29 * $400
= $116
The combined sales tax and tip were $116.
Now we add the combined sales tax and tip to the $400 price of dinner.
total = $400 + $116
total = $516
Please answer or i move down!!!!
Answer:
Since all views look like a circle, the solid would be a ball, which is also called a sphere.
The answer is Sphere
The geometrical name of the solid given is Sphere.
Name the parallel segment
1-4 pls I will mark you the brainiest
Answer:
Step-by-step explanation:
Ans 1: 250m/8.6s=29.07m/s(average velocity)
Ans 2: 0.12m/s*3s= 0.36m (it travelled 0.36m in 3 sec)
Ans 3: 467m/5.6/s= 83.4s (time Mychal was riding his bike)
Ans 4: 227 772.18m-200 000m= 27772.18m
finding per minute = 31.7/s*60
19902m/min
time on cruise control= 200 000m/19902/m
=105.15min
Abel was on cruise control for 105.15min
Which graph represents the line y=−3x+4?
The graph of equation y=−3x+4 has been drawn below.
How to plot a graph?
A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
After that, we need to substitute the values of x's and y's into the coordinate geometry.
Given a linear function y=−3x+4
In order to plot a graph, we need to assume one x value, and corresponding to that need to calculate the y value.
Lets say x = 0 than
y = -3(0) + 4
y = 4 ⇒ (0.4) will be the first coordinate of the line.
Now let's say y = 0 than
0 = -3x + 4
x = 1.33 ⇒ (1.33, 0) will be the second coordinate of the line.
So,
Draw a straight line by passing both points gives us an f the equation y=−3x+4.
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The graph of the equation y = -3x + 4 is shown in the figure attached with the answer.
We have the following equation of a straight line y = - 3x + 4.
We have to plot the equation of this straight line.
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to the question -
The equation of line = - 3x + 4
Now, comparing this line with the general equation of line - y = mx + c, we get -
m = -3
c = 4
Hence, the graph of the equation is shown in the figure attached with the answer.
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A college dormitory houses 200 students. Those who watch an hour or more of television on any day always watch for less than an hour the next day. One-fourth of those who watch television for less than an hour one day will watch an hour or more the next day. Half of the students watched television for an hour or more today. How many will watch television for an hour or more tomorrow, in 2 days, and in 40 days
Answer:
Tomorrow = 25 students
In 2 days = 44 students
In 40 days = 40 students
Step-by-step explanation:
Let A = watch more than an hour
B = watch less than an hour
First of all we need to make a transition matrix
[tex]P = \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix} \binom{A}{B}[/tex]
Also we are given,
X = [100, 100]
A B
Therefore,
[tex]XP=\begin{bmatrix}100 & 100\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix}[/tex]
= [25, 175]
Thus, 25 students will watch television for an hour or more tomorrow.
Now for 2 days,
[tex]XP^2=\begin{bmatrix}100 & 100\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix}[/tex]
= [43.75, 156.25]
Hence, 44 students will watch television for an hour or more in 2 days.
Now in 40 days,
[tex]XP^40=\begin{bmatrix}100 & 100\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix}^{40}[/tex]
But instead of multiplying the above matrix 40 times, we can we can find the long term division method.
Let
x = long term distribution of students watching television >1 hour
y = long term distribution of students watching television <1 hour
Therefore,
[tex]\begin{bmatrix}x & y\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix} = \begin{bmatrix}x & y\end{bmatrix}[/tex]
⇒ 0.25 y = x
And we know that x + y = 200
∴ 0.25 y + y = 200
∴ y = 160
And x = 40 ( ∵ x + y = 200)
Thus 40 students will watch televisions in the 40 days for an hour or more.
While hiking Sam ate 2/3 cup of nuts, Jordan ate 1/10 of a cup. How much more did Sam eat than Jordan.
Answer:
17/30
Step-by-step explanation:
2/3-1/10=
20/30-3/30=
17/30
You earn 5% commission on the first $2000 of sales and 8% commission on all sales over $2000. If you sold $7740, what is your total commission?
Answer:You earn 5% commission on the first $2000 of sales and 8% commission on all sales over $2000. If you sold $7740, what is your total ...
Step-by-step explanation:
PLEASE HELP!!!What are the possible rational roots of 2x^2-10x+8 according to the rational root theorem? (1 point)
[tex]\pm 8, \pm 4, \pm 2, \pm 1, \pm \frac{1}{2}[/tex]
================================================
Explanation:
The first coefficient is 2. The last term is 8.
To find the possible rational roots, we look at factors of 2 and 8
factors of 2 = 1, 2
factors of 8 = 1,2,4,8
Then you divide each factor of 8 over the factor of 2. More generally, we divide the factors of the last term over the factors of the first coefficient.
A table is recommended so you can keep everything organized. See the diagram below.
The table shows 8, 4, 2, 1 and 1/2 as the unique results in each cell.
The table only shows the positive results, but the negative results will basically be identical except for the negative sign of course. The plus minus is to account for things like saying "-2 is a factor of 8 since -2*(-4) = 8". I find its easier to just focus on the positive and then stick plus minus at the end when all is said and done.
This is why choice B is the answer.
-----------
Extra info:
Keep in mind this list is the possible rational roots and it does not mean they are all actual rational roots of the given polynomial. You'll need to plug each one into the polynomial to see if you get 0 as an output.
For instance, plugging x = 2 into y = 2x^2-10x+8 leads to y = -4 showing that x = 2 is not a root; however, x = 1 is a root because plugging x = 1 into y = 2x^2-10x+8 leads to y = 0. There's one other rational root for this polynomial.
answer asap................
Answer:
[tex] \sqrt{30} [/tex]
can not be simplified further.
Decimal = 5.477225575
State the requirements to perform a goodness of Fit test. Choose the correct answer below:
A. at least 80% of expected frequencies > 5
B. all expected frequencies > 5
C. at least 90% of expected frequencies > 5
D. at least 90% of expected frequencies >10 a
E. t least 80% of expected frequencies > 10
F. all expected frequencies > 1
Answer:
B. all expected frequencies > 5
Step-by-step explanation:
The expected number np(i) in any of the classes or cells should not be less than 5. So when the expected number np(i) in any class is less than 5 , we may combine this class with one or more other classes to meet this requirement.
It is clear that chi square will be small when all ni are close to their expected values npi. The chi square will become larger when the difference becomes larger. The chi square thus measures the amount of deviation ( or agreement ) between the observed and expected results.
Thus it is a good approximation if all the expected values npi are sufficiently large and hence chi square distribution confirms with the ( k-1) degrees of freedom.
Algebraic expression is what I NEED Your summer job pays $8.25 per hour and you must pay for a company shirt that costs $15. If your work x hours per week, how much will you make during the first week? NEEDED NOW!!!
Answer:
y=8.25x-15
Step-by-step explanation:
From the information provided, the algebraic expression will need to indicate that your earnings during the first week, y, would be equal to multiplying $8.25 for the number of hours, x, minus $15. According to that, the algebraic expression is:
y=8.25x-15
The ages in years of 21 people in a swimming pool are displayed in the stem-and-leaf plot. Determine the median age of
people in the pool.
ON
5 6 7 8 8 8
6 9
7
7
0 2 4
1 3
2 1
3 6
4 1 2
5
6 4 8
4
median =
years
Answer:
5 yearsStep-by-step explanation:
To get the median of the ages given
2, 4, 5, 6, 7, 8, 8, 8, 0, 3, 5, 9, 1, 4, 7, 6, 1, 2, 4, 4, 8
First we will need to rearrange the median ages in ascending order (from lowest to highest)
0, 1, 1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 8, 9
Next is to locate the middle value of the arranged data
(0, 1, 1, 2, 2, 3, 4, 4, 4, 4), 5, (5, 6, 6, 7, 7, 8, 8, 8, 8, 9)
The total values in both parenthesis are the same(10 in numbers) leaving 5 as the middle number.
Hence the median age of the people in the pool is 5years
an archer misses 60% of his shots how many shots must he make before he gets 100 hits?
Answer:
250
Step-by-step explanation:
60% is 3/5. Meaning, for every 5 shots taken, the archer only makes 3.
So, they would need to make 250 shots before they get 100.
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Rearrange the equation to isolate a . (a+bc)(d−e)=f
Answer:
a = cf - b(d-e)
c(d-e)
Step-by-step explanation:
Kindly check correct question as attached!
Solution
(a+b/c)(d-e) = f
a + b/c = f/d-e
a = [f/d-e] - [b/c]
Lcm = c(d-e)
a = cf - b(d-e)
c(d-e)
The equivalent value of the expression is a = [ f / ( d - e ) ] - ( b/c )
Given data ,
Let the equation be represented as A
Now , the value of A is
( a + b/c ) ( d - e ) = f
On simplifying the equation , we get
( a + b/c ) ( d - e ) = f
So , the left hand side of the equation is equated to the right hand side by the value of f
Divide by ( d - e ) on both sides , we get
a + b/c = f / ( d - e )
Subtracting b/c on both sides , we get
a = [ f / ( d - e ) ] - ( b/c )
a = [ f / ( d - e ) ] - ( b/c )
Therefore , the value of a = [ f / ( d - e ) ] - ( b/c )
Hence , the expression is a = [ f / ( d - e ) ] - ( b/c )
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