Answers
We are given the graph of a quadratic function. The general form of a quadratic function is the following:
\(y=a(x-h)^2+k\)Where the point:
\((h,k)\)Is the vertex of the parabola. From the graph we notice that the vertex is the point (0, 0), therefore, we have:
\((h,k)=(0,0)\)Replacing in the quadratic function we get:
\(y=ax^2\)To determine the value of "a" we notice that the point:
\((x,y)=(1,1)\)Is part of the parabola, therefore, we can substitute in the function the values x = 1 and y = 1:
\(\begin{gathered} 1=a(1)^2 \\ 1=a \end{gathered}\)Therefore, the value of "a" is 1 and the function of the parabola is:
\(y=x^2\)Now we are asked to determine f(x - 2).
We do this first by rewriting the equation as:
\(f(x)=x^2\)Now we will replace the value of "x" for "x - 2", we get:
\(f(x-2)=(x-2)^2\)Now, to determine the graph, we need to have into account that when we subtract a number "a" to the "x" value of a function what we are doing is moving the graph "a" units to the right. Therefore, the new graph must be:
Now, to determine the domain we need to have into account that a quadratic equation is a polynomial of grade 2 and the domain of any polynomial is the real numbers, therefore, the domain is:
\(\text{domf(x)}=\mleft\lbrace x\parallel x\in\R\mright\rbrace\)The rage in the values of the variable "y". We notice that "y" only takes positive values, therefore, the range is the real number that are greater or equal to zero, this is written as:
\(\text{ranf(x)}=\mleft\lbrace y\parallel y\ge0\mright\rbrace\)
Related Questions
It is estimated that only 68% of drivers wear their safety belt. Part A: What is the probability that exactly 3 drivers are wearing their safety belts if a police officer pulls over five drivers at random? (5 points) Part B: What is the probability the next driver wearing their safety belt that the police officer pulls over is the fifth driver? (5 points) (10 points)
Answers
Hence, there is a 0.68 percent probability that the fifth driver will be the one that police officer summons over while wearing a safety belt.
What does the name probability mean?The word "probability" derives from the Latin word "propitiate," which means "credibility, probability," from the noun probabilism in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.
Part A:
The likelihood that precisely 3 drivers are buckled up can be determined using the binomial probability formula:
P(X = 3) = (5 choose 3) × (0.68)³ × (0.32)²
Where (5 choose 3) = 10 is the number of ways to choose 3 drivers out of 5.
P(X = 3) = 10 × 0.68³ × 0.32²
P(X = 3) = 0.267
Consequently, there is a 0.267 percent chance that all 3 drivers are buckled up.
Part B:
The fifth driver will be pulled by by the police officer since 4 other drivers have already been stopped. We are looking for the likelihood that the motorist is wearing a safety belt.
Since 68% of drivers are safety belt wearers, there is a 0.68 percent chance that the following motorist will be as well.
Thus, there is a 0.68 percent chance that the next vehicle the police officer pulls over is driven by a person wearing a safety belt.
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Part A and Part C the same? Why or why not?
Answers
Answer:
is part 1 and part 3 the same, no
Step-by-step explanation:
Answer:yes
Step-by-step explanation:
fraction bears the same ratio to 1/27 as 3/7 does to 5/9.then the fraction is?
Answers
The fraction that bears the same ratio to 1/27 as 3/7 does to 5/9 is 27/35.
To find the fraction that bears the same ratio to 1/27 as 3/7 does to 5/9, we can set up a proportion.
Let's represent the unknown fraction as x. The ratio can be configured as follows:
x / (1/27) = (3/7) / (5/9)
To solve this proportion, we can cross-multiply:
(x * 5/9) = (3/7) * (1/27)
Simplifying the right side:
(x * 5/9) = 3/189
To eliminate the fraction on the left side, we can multiply both sides by the reciprocal of 5/9, which is 9/5:
(x * 5/9) * (9/5) = (3/189) * (9/5)
Simplifying further:
x = 27/35
Therefore, the fraction that bears the same ratio to 1/27 as 3/7 does to 5/9 is 27/35.
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Does anyone know this?
Answers
Answer: 65 degrees
( Im probally wrong and how is this college math?????)
Step-by-step explanation:
a + b=c make (a) the subject with working
Answers
Step-by-step explanation:
a= c-b pls let me know if it is correct or not
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Problem !. Draw the Logic Circuit for:
BD + BE + D'F
Problem 2. What is the boolean Expression of F5?
B
X
Y
Z
F5
Answers
The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.
To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.
Step 1: Apply De Morgan's laws
NOT (R AND NOT P) can be simplified as (NOT R) OR P.
Step 2: Distributive property
F5 = (P AND Q) OR ((NOT R) OR P)
Step 3: Apply associative property
F5 = (P AND Q) OR (P OR (NOT R))
Step 4: Apply absorption law
F5 = P OR (P OR (NOT R))
Step 5: Apply idempotent law
F5 = P OR (NOT R)
By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.
Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.
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The question probable may be:
Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:
F5 = (P AND Q) OR (R AND NOT P)
Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?
mr.hollins determines that he gives away $800 each month .if he gives away 16% his budget then how much is his overall budget
Answers
Answer:
$5000 hope this helped xoxo
Last month a nurse worked fourteen 10 hour shifts and two 12 hour shifts. At $21.00 per
hour. what was the nurse's monthly income before deductions?
Answers
Answer:
i think it’s $3,792
Step-by-step explanation:
11 • 10 = 110 and 12 • 4 = 48 so 110 + 48 = 158 and 158 • 24 = 3,792
What is the slope of the line?
y+3 = -4(2 + 7)
Answers
Answer:-4
Step-by-step explanation:
Find the measure of the following: m arcTR = m arcTL = m ∠L = m ∠R = m ∠RTV =
Answers
Applying the inscribed angle theorem, the missing measures are:
measure of arc TR = 106°
measure of arc TL = 74°
m∠L = 50°
m∠R = 37°
m∠RTV = 37°
The Inscribed Angle TheoremMeasure of an inscribed angle = half the measure of the arc it intercepts
Central angle = measure of intercepted arc
We are given the following:
LR and TV are diameters of the circle O.
m∠TOR = 106° (central angle)
Find measure of arc TR:
measure of arc TR = m∠TOR
measure of arc TR = 106°
Find measure of arc TL:
measure of arc TL = 180° - m∠TOR
measure of arc TL = 180° - 106°
measure of arc TL = 74°
Find m∠L:
m∠L = ½(measure of arc TR)
m∠L = ½(106°)
m∠L = 50°
Find m∠R:
m∠R = ½(measure of arc TL)
m∠R = ½(74°)
m∠R = 37°
Find m∠RTV:
m∠RTV = ½(measure of arc RV)
m∠RTV = ½(180 - 106)
m∠RTV = ½(74)
m∠RTV = 37°
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a rectangular window has a length of 81.47 cm and a width of 34.2 CM what is the least
Answers
Step-by-step explanation:
The least price measurement mean a value with the least number of significant figures.calculate the perimeter in this case as;
Perimeter of a rectangle = 2(l+w) where l is the length and w is the width
Perimeter= 2(81.47 + 34.2)
Perimeter=2(115.67)
Perimeter=231.34
Perimeter=231.30(4 significant figures)
There are only 6 blue pens, 5 green pens and 8 red pens in a box.
One pen is taken at random from the box.
Write down the probability that this pen is blue.
Answers
Answer:
0.316
Step-by-step explanation:
Probability = (number of outcomes)/(total number of outcomes)
In this case,
the total number of outcomes is 6+5+8 = 19, and
the number of outcomes for getting a blue pen = 6
Hence,
P(blue) = 6/19 = 0.31578947368 ≈ 0.316
Hope this helps and be sure to have a wonderful time ahead at Brainly! :D
Pls answer this fast
Answers
Answer: C
Step-by-step explanation:
1. divide 3 by 2 to find out how many pounds of blueberries she picked each day. 3/2 is 1.5
2. multiply 1.5 by 16 to convert to ounces. 1.5x16 is 24.
3. she picked 24 ounces of blueberries each day.
finding the volume for the figure 11ft 10ft 22ft 7ft 4ft 10ftIs it multiplying everything?
Answers
Jackie, this is the solution:
1. Calculate the volume of the big rectangular prism, this way:
Volume = 11 -* 10 * 22 cubic feet
2. Calculate the volume of the small prism, this way:
Volume = 7 * 4 * 10 cubic feet
3. Add up the two volumes, you get the answer and you can write it in the box
A fair 6-sided die is rolled five times. What is the probability that the sequence of rolls is 3,4,1,2,6
Answers
Answer:
Step-by-step explanation:
probability = number of favorable outcomes/total number of outcomes
To find compound probability multiply all the probabilities together.
p(3) = 1/6
p(4) = 1/6
p(1) = 1/6
p(2) = 1/6
p(6) = 1/6
Multiply all of them together.
1/6 x 1/6 x 1/6 x 1/6 x 1/6 = 1/7,776
or
\((\frac{1}{6} )^5 = \frac{1}{7,776}\)
Answer ASAP but only if you are SURE about it
Answers
Answer:
It's A, 6.86 × 10⁴
Step-by-step explanation:
In scientific notation, you have the base, and the 10. The 10 is represented next to an exponent, whereas the base is a whole number and a decimal. If the decimal is moved right, the exponent following the 10 becomes negative. Left, it becomes positive. In this instance, the decimal is being moved left, thus the exponent is positive.
Answer:
A
Step-by-step explanation:
All my work is provided in the attached Screenshot! :)
Use the table below to find d/dx[5f(x)-4x] x=2
![Use the table below to find d/dx[5f(x)-4x] x=2](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/ogIn5USQGVvHfvEkh7apF78xBv5N6p42.jpeg)
Answers
The value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
From the table:
At x=2,
f'(x) = 4
f(x) = 4x
= d/dx(5*4x - 4x)
= d/dx(20x - 4x)
= d/dx(16x)
= 16
Therefore the value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
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Show that each conditional statement in Exercise 11 is a tautology by applying a chain of logical identities as in Example 8. (Do not use truth tables.) a) (PA) P b) p (pv) c) p + ( pa) d) (p) - () e) (P+) - P f) (p)
Answers
a) (PA) P is a tautology because P is logically equivalent to P v F, and P v F is logically equivalent to P.
b) p (pv) is a tautology because p is logically equivalent to p v T, and p v T is logically equivalent to p.
c) p + ( pa) is a tautology because p is logically equivalent to p v F, and p v F is logically equivalent to p v (p v A).
d) (p) - () is a tautology because p is logically equivalent to p v T, and p v T is logically equivalent to p v F.
e) (P+) - P is a tautology because P+ is logically equivalent to P v T, and P v T is logically equivalent to P.
f) (p) is a tautology because p is logically equivalent to p v F, and p v F is logically equivalent to p.
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If (-2, y) lles on the graph of y = 3*, then y =
Answers
The value of y in the equation y = 3^x for the point (-2, y) is 1/9
How to determine the value of yFrom the question, we have the following parameters that can be used in our computation:
y = 3^x
The above function is an exponential function
Exponential functions are mathematical functions that involve a base raised to a power
Where the base is a constant greater than zero And not equal to one.Also, we have
(-2, y)
Substitute the known values in the above equation, so, we have the following representation
y = 3^-2
Evaluate
y = 1/9
Hence, the value of y is 1/9
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The weights of steers in a herd are distributed normally. The standard deviation is 200lbs and the mean steer weight is 900lbs. Find the probability that the weight of a randomly selected steer is between 1220 and 1320lbs. Round your answer to four decimal places.
Answers
Answer:
0.0369
Step-by-step explanation:
normalcdf (1220,1320,900,200) is 0.0369
please help !To convert 180 seconds to minutes, which proportion should you should use?
Answers
Answer:
The third option, 60 seconds/1 minute = 180 seconds/X
Step-by-step explanation:
Answer:
the third one. 60 seconds over 1 minute equals to 180 seconds over x.
Which of the following is an irrational number?
Answers
Answer:
A.
Step-by-step explanation:
An irrational number can’t be expressed as a fraction
work out the area of the triangle?
Answers
Answer:
Area = 30
Step-by-step explanation:
Formula for triangle: bh/2
12*5/2
60/2
= 30
which value of x makes this inequality true? x+9<4x
Answers
Answer:
Step-by-step explanation:
x+9
Let x, be 4
4+9=13
given condition,
x+9<4x
4+9<4(4)
13<16
The answer is:
x > 3Work/explanation:
Our inequality is:
\(\sf{x+9 < 4x}\)
Flip it
\(\sf{4x > x+9}\)
Solve
\(\sf{4x-x > 9}\)
Combine like terms
\(\sf{3x > 9}\)
Divide each side by 3
\(\sf{x > 3}\)
Hence, x > 3heheheheh hehehehehhehehehehehehheheh
Answers
Answer:
cscsc
Step-by-step explanation:
zcscc
Answer:
hehehehehehehehehehehehehehehehehehehehehehehehe
Step-by-step explanation:
lelelelelelelelelelelelelelelelelelelelelelelelelelelelelelelelelelele
Chicken Nuggets.
327.8 in scientific notation
Answers
Answer:
3.278 * 10 ^ 2
Step-by-step explanation:
To change a number to scientific notation you:
Move the decimal point to the left to make the number have 1 number before the decimal point.
From there you multiply by 10 to the power 2 the number of decimal points you moved.
So the answer is 3.278 * 10^2
HOPE IT HELPED
40 people attended the play. 15 were women, 10 were men, and 15 were children. what fraction were men?
Answers
Answer:
10/40 were men, or simplified the amount is 1/4 of the total is men
Write 35/9 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Answers
Answer:
3.88 (put a bar on top of '88')
Step-by-step explanation:
Which of the following best describes the graph shown below?
-4
+3
-2
+1
5
-4
-3
-2
-V
1
2
3
4
+-1
-2
+-3
+-4
Answers
Answer:
2 & 4Step-by-step explanation:
ODYSSEY
What are the steps to solving the inequality 3b + 8 ≥ 14?
Subtract 8 from both sides of the inequality. Divide both sides of the inequality by 3.
Subtract 8 from both sides of the inequality. Change the direction of the inequality. Divide both sides of the inequality by 3.
Divide both sides of the inequality by 3. Subtract 8 from both sides of the inequality.
Divide both sides of the inequality by 3. Change the direction of the inequality. Subtract 8 from both sides of the inequality.
Answers
Answer:Subtract 8 from both sides of the inequality. Divide both sides of the inequality by 3-- A
Step-by-step explanation:
Step 1
In solving 3b + 8 ≥ 14
we first subtract both sides by 8, which will give
3b+ 8 -8 ≥ 14-8
3b ≥ 6
Step 2
Then, divide both sides by 3----Since we are multiplying by a positive number, 3, the inequalities sign will not change but will still remain the same.
3b/3 ≥ 6/3
To give answer as b ≥ 2.
Answer:
A
Step-by-step explanation: