An object was dropped off the top of a building. The function f(x) = -16x2 + 36represents the height of the object above the ground, in feet, X seconds after beingdropped. Find and interpret the given function values and determine an appropriatedomain for the function.
Answers
f(x) = -16x^2 + 36
Where:
f(x) = height of the object
x = seconds after being dropped.
f(-1) = -16 (-1)^2 + 36
f(-1) = -16 (1) + 36
f(-1) = 20
-1 seconds after the object was dropped, the object was 20 ft above the ground.
This interpretation does not make sense, because seconds can't be negative.
f(0.5) = -16 (0.5)^2 + 36
f(0.5) = -16 (0.25) +36
f(0.5) = -4 + 36
f(0.5) = 32
0.5 seconds after the object was dropped, the object was 32 ft above the ground.
This interpretation makes sense in the context of the problem.
f(2) = -16 (2)^2 + 36
f(2) = -16 (4) +36
f(2) = -64+36
f(2) = -28
2 seconds after the object was dropped, the object was -28 ft above the ground.
This interpretation does not make sense in the context of the problem, because the height can't be negative.
Based on the observation, the domain of the function is real numbers in a <- x <-b , possible values of x where f(x) is true.
before the object is released x=0
next, calculate x when f(x)=0 ( after the object hits the ground)
0= -16x^2+36
16x^2 = 36
x^2 = 36/16
x^2 = 2.25
x = √2.25
x = 1.5
0 ≤ x ≤ 1.5
Related Questions
The sum of two numbers is 83. The difference of the 2 numbers is 13. What is the product of the two numbers?A.1632B.1650C.1666D.1680
Answers
Answer:
Let the first number be
[tex]=x[/tex]Let the second number be
[tex]=y[/tex]The sum of two numbers is 83 can be represented below as
[tex]x+y=83\ldots\ldots(1)[/tex]The difference of the 2 numbers is 13 can be represented below as
[tex]x-y=13\ldots\ldots\text{.}(2)[/tex]Step 1:
From equation (1) make x the subject of the formula to to give equation (3)
[tex]\begin{gathered} x+y=83\ldots\ldots(1) \\ x=83-y\ldots\text{.}(3) \end{gathered}[/tex]Step 2:
Substitute equation (3) in equation (2)
[tex]\begin{gathered} x-y=13\ldots\ldots\text{.}(2) \\ x=83-y\ldots\text{.}(3) \\ 83-y-y=13 \\ 83-2y=13 \\ \text{collect similar terms,} \\ -2y=13-83 \\ -2y=-70 \\ \text{divide both sides by -2} \\ \frac{-2y}{-2}=\frac{-70}{-2} \\ y=35 \end{gathered}[/tex]Step 3:
Substitute y= 35 in equation (3)
[tex]\begin{gathered} x=83-y\ldots\text{.}(3) \\ x=83-35 \\ x=48 \end{gathered}[/tex]Hence,
The product of the two numbers will be calculated as
[tex]\begin{gathered} =x\times y \\ =35\times48 \\ =1680 \end{gathered}[/tex]Hence,
The final answer is = 1680
OPTION D is the final answer
Find the simple interest owed for the following loan. Principal = 2775 Rate = 7.5% Time = 5 1/2 years
Answers
We would apply the simple interest formula which is xpressed as
I = PRT/100
Where
I represents interest
P represents principal or amount borrowed
T represents time in years
R represents rate.
From the information given,
P = 2775
R = 7.5
T = 5 1/2 = 5.5
I = (2775 * 7.5 * 5.5)/100
I = 1144.6875
Rounding to the nearest cent,
I = 1144.69
Write the first 4 terms of the sequence defined by the given rule. f(n)=n^3-1
Answers
How to tell if a sequence is linear, exponential, quadratic or absolute value as simply as possible without graphing (8th grade algebra) examples will be greatly appreciated
Answers
We will have the following:
We will be able to tel apart sequences as follows:
Linear sequence: We have that linear sequences follow the form:
[tex]y=mx+b[/tex]Here "x" represents the iteration value for the sequence, "m" the ratio (slope) and "b" a value that modifies the "position" of the sequence. This sequences grows in a linear manner.
Example:
[tex]\begin{cases}y_{}=2x+2 \\ \\ y_1=4 \\ y_2=6 \\ y_3=8 \\ \ldots\end{cases}[/tex]Exponential sequence: We have that exponential sequences follow the form:
[tex]y=a_1(r)^{x-1}[/tex]Here "a1" is the first term of the sequence, "r" is the ratio and "x" the iteration of the sequence.
We obtain the ratio as follows:
[tex]r=\frac{y_n}{y_{n-1}}[/tex]Example:
[tex]\begin{cases}y=1(5)^{x-1}_{} \\ \\ y_1=1 \\ y_2=5 \\ y_3=25 \\ \\ \ldots\end{cases}[/tex]The ratio for this case:
[tex]r=\frac{y_3}{y_2}\Rightarrow r=\frac{25}{5}\Rightarrow r=5[/tex]Quadratic sequence: A quadratic sequence follows the general form
Which expressions are equivalent to (1/3x−4x−5/3x)−(−1/3x−3) ? Select all correct expressions. Responses −3+5x negaive 3 minus 5 x −2x+3−3x negative 2 x plus 3 minus 3 x −5x+3 negative 5 x plus 3 2x−3+3x 2 x minus 3 plus 3 x
Answers
The equivalent expression for the given expression (1/3x - 4x - 5/3x) - (- 1/3x - 3) is 3 - 7x / 3
Given,
The expression;
(1/3x - 4x - 5/3x) - (- 1/3x - 3)
We have to solve this and find the equivalent expression;
Here,
(1/3x - 4x - 5/3x) - (- 1/3x - 3)
= 1/3x - 4x - 5/3x + 1/3x + 3
= 3 - 4x - 5/3x
= 3 - (12x - 5x) / 3
= 3 - 7x / 3
That is,
The equivalent expression for the given expression (1/3x - 4x - 5/3x) - (- 1/3x - 3) is 3 - 7x / 3
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what is the rate change of the equation?Y=8x+20Remember Y=MX+B
Answers
The general equation of the line : y = m * x + b
where m is the slope , b is y -intercept
Given the function :
[tex]y=8x+20[/tex]The rate of change of the equation = the slope of the function
So, by comparing the given equation to the general from
The slope = m = 8
So, the rate of change = 8
can you help me to find midpoint
Answers
First, locate the given points.
Then, draw the line that connects them
Next, add the two x-coordinates of the endpoints and divide by 2. In this case, (1 + 4)/2 = 5/2 = 2.5
Then, draw a line perpendicular to the x-axis that passes through x = 2.5, until it intersects the other line. The intersecting point is the midpoint.
In this case, the coordinates of the midpoint are (2.5, 0.5), as can be seen in the figure
What is the factored form of the expression 18x +12y -30?
Answers
Let's begin by listing out the information given to us:
[tex]18x+12y-30[/tex]Factoring means we will use the common factor of the elements to break down the expression into a simpler form:
[tex]6(3x+2y-5)[/tex]Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters asdimes. Write a system of equations that could be used to determine the number ofdimes and the number of quarters that Sophie has. Define the variables that you useto write the system.
Answers
d = 2q .........................................................................(1)
0.1d + 0.25q = 4.20 ................................................(2)
Explanation:Let d be the number of dimes, and q be the number of quarters Sophie has.
Since she has twice as many quarters as dimes, and they are worth $4.20, we have:
d = 2q .........................................................................(1)
Also, because:
1 dime = $0.1
1 quarter = $0.25
0.1d + 0.25q = 4.20 ..................................................(2)
Equation (1) and (2) can be solved to determine the number of dimes and quarters
You are choosing between two health clubs. Club A offers membership for a fee
of $20 plus a monthly fee of $25. Club B offers membership for a fee of $25
plus a monthly fee of $24. After how many months will the total cost of each
health club be the same? What will be the total cost for each club?
Answers
Let:
x = Number of months
y1 = Total cost for Club A
y2 = Total cost for Club B
a = Fee of Club A per month
b = Fee of Club B per month
c = Initial fee of Club A
d = Initial fee of Club B
so:
[tex]\begin{gathered} y1=ax+c \\ y1=25x+20 \\ -------- \\ y2=bx+d \\ y2=24x+25 \end{gathered}[/tex]So, the total cost will be the same for:
[tex]\begin{gathered} y1=y2 \\ 25x+20=24x+25 \\ solve_{\text{ }}for_{\text{ }}x\colon \\ 25x-24x=25-20 \\ x=5 \end{gathered}[/tex]The cost will be the same for the month number 5. And the total cost will be:
[tex]\begin{gathered} y1(5)=25(5)+20=145 \\ y2(5)=24(5)+25=145 \end{gathered}[/tex]$145
Find the Z-score for which 5% of the distributions area lies between-z and z
Answers
The equation that will represent this situation will be:
[tex]\begin{gathered} P(-z\le x\le z)=P(x\le z)-(1-P(x\le z))=0.05 \\ \end{gathered}[/tex]Thus:
[tex]\begin{gathered} P(x\le z)-1+P(x\le z)=0.05 \\ 2\cdot P(x\le z)-1=0.05 \\ 2\cdot P(x\le z)=0.05+1 \\ 2\cdot P(x\le z)=1.05 \\ P(x\le z)=\frac{1.05}{2} \\ P(x\le z)=0.525 \end{gathered}[/tex]If we check in a standard normal table. the z-score that corresponds to a probability of 0.525 is 0.063.
Answer: z-score is 0.063.
Writing and evaluating a function modeling continuous exponential growth or decay given two outputs
Answers
Explanation
The model has the form
[tex]y=ae^{-kt}[/tex]Where a=initial amount
y= final amount
K= growth rate constant
t= time
When 140 kg of substance is left after 7 hours, the formula can be remodeled to be.
[tex]\begin{gathered} 140=400e^{-7k} \\ e^{-7k}=\frac{140}{400} \\ e^{-7k}=\frac{7}{20} \\ \ln (e^{-7k})=\ln (\frac{7}{20}) \\ -7k=\ln (\frac{7}{20}) \\ k=\frac{\ln(\frac{7}{20})}{-7} \\ \therefore k=\frac{\ln (\frac{20}{7})}{7} \end{gathered}[/tex]Therefore, the first solution is
[tex]y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}[/tex]For part b we have 16 hours.
[tex]\begin{gathered} y=400e^{-\ln (\frac{20}{7})\frac{t}{7}}=400e^{-\ln (\frac{20}{7})\frac{16}{7}} \\ y=36.302\approx36\operatorname{kg}\text{ (To the nearest whole number)} \end{gathered}[/tex]Thus, the answer is 36kg
A contractor bought 10.8 ft² of sheet metal. He has used 3.5 ft² so far and has $219 worth of sheetmetal remaining. The equation 10.8x - 3.5x = 219 represents how much sheet metal is remainingand the cost of the remaining amount. How much does sheet metal cost per square foot?
Answers
The first step to do is to combine 10.8x - 3.5x and that is equal to 7.3x.
[tex]7.3x=219[/tex]The next step is to divide both sides by 7.3 to solve for x.
[tex]\begin{gathered} \frac{7.3x}{7.3}=\frac{219}{7.3} \\ x=30 \end{gathered}[/tex]Therefore, the remaining sheet metal is 7.3 ft² and the cost per square foot of sheet metal is $30.
24. A rocket is launched into the air. Its height in feet, after x seconds, is given by the equation The starting height of the rocket is h(x)=-16x’ +300x + 20 The maximum height is The rocket hits the ground after seconds.
Answers
Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that
[tex]h(0)=-16(0)^2+300(0)^{}+20^{}=20^{}[/tex]So the first answer is that the start heigth of the rocket is 20.
Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so
[tex]h^{\prime}(x)=-32x^{}+300[/tex]now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when
[tex]\begin{gathered} -32x\text{ + 300 =0} \\ 300\text{ = 32x} \\ \frac{300}{32}=x \end{gathered}[/tex]to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so
[tex]h^{\doubleprime}(x)\text{ = -32}[/tex]now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.
Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then
[tex]-16x^2+300x+20=0^{}[/tex]we can solve this with the quadratic equation to solve this kind of equations. This equation is
so we have that
[tex]\begin{gathered} x\text{ = }\frac{-300\text{ }\pm\sqrt[]{300^2\text{ -4(-16)20}}}{2(-16)} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{90000\text{ + 1280}}}{-32} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{91280}}{-32} \end{gathered}[/tex]the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is
[tex]x\text{ = }\frac{75\text{ }\pm\sqrt[]{5705}}{8}[/tex]Well we just need to do the analise of the function h, so for the first question we need to know what is the value of h when x=0, so if we evaluate we see that
[tex]h(0)=-16(0)^2+300(0)^{}+20^{}=20^{}[/tex]So the first answer is that the start heigth of the rocket is 20.
Now for the second we need to do the derivate and see the critical ponit to know the maximum, we are going to calculate first the derivate, so
[tex]h^{\prime}(x)=-32x^{}+300[/tex]now we need to find the critical ponits so for this, we are going to see when h'(x) = 0, this meand when the derivate is equal to zero, so h'(x) = 0 when
[tex]\begin{gathered} -32x\text{ + 300 =0} \\ 300\text{ = 32x} \\ \frac{300}{32}=x \end{gathered}[/tex]to see if this critical poni is a maximum we need to calculate the secon derivate and see that the second derivate valued in 300/32 is smaller than 0, so
[tex]h^{\doubleprime}(x)\text{ = -32}[/tex]now when x= 300/32 we have that h''(x) is -32 because the second derivate is constant, in this case h''(300/32) < 0, because of this the answer is that 300/32 is the maximum, bur 300/32 = 75/8.
Now for the third question, we need to see the roots of h, so we need to see when h is zero, so for wich values of x we have that h(x) = 0, then
[tex]-16x^2+300x+20=0^{}[/tex]we can solve this with the quadratic equation to solve this kind of equations. This equation is
so we have that
[tex]\begin{gathered} x\text{ = }\frac{-300\text{ }\pm\sqrt[]{300^2\text{ -4(-16)20}}}{2(-16)} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{90000\text{ + 1280}}}{-32} \\ x\text{ = }\frac{-300\text{ }\pm\sqrt[]{91280}}{-32} \end{gathered}[/tex]the answer is x = (-300 - v/ 91280)/(-32) or x = (-300 + v/ 91280)/(-32) and this is equal to x = (300 + v/ 91280)/(32) or x = (300 - v/ 91280)/(32) if you prefer. We can also write the answer in a simpler way: x = (75 + v/ 5705)/(8) or x = (75 - v/ 5705)/(8), this is
[tex]x\text{ = }\frac{75\text{ }\pm\sqrt[]{5705}}{8}[/tex]In a right triangle, the side opposite angle β has a length of 16.4 cm. The hypotenuse of the triangle has a length of 25.1 cm. What is the approximate value of sin(β)?
Answers
Given
Length of hypotenuse= 25.1 cm
length of BC = 16.4 cm
Find
Value of
[tex]sin\beta[/tex]Explanation
As , we know
[tex]sin\beta=\frac{opposite}{hypotenuse}[/tex]now, put values
[tex]sin\beta=\frac{16.4}{25.1}=0.653[/tex]Final Answer
Value of
[tex]sin\beta=0.653\text{ approx}[/tex]which expression is equivalent to 5^-2 x 5^5
Answers
Given the expression:
[tex]5^{-2}\ast5^5[/tex]To find the equivalent expression, let's simplify the expression using power rule.
[tex]a^m\ast a^n=a^{m+n}[/tex]Since they have the same base, we are to add the exponents.
We have:
[tex]5^{-2}\text{ }\ast5^5=5^{-2+5}=5^3[/tex]Therefore, the eqivalent expression is 5³
ANSWER:
[tex]5^3[/tex]We a
copy and complete each problem
/20 = 11/55
Answers
Answer:
[tex]\frac{4}{20}[/tex] = [tex]\frac{11}{55}[/tex]
Step-by-step explanation:
[tex]\frac{x}{20}[/tex] = [tex]\frac{11}{55}[/tex] cross multiply and solve for x
55x = 11(22)
55x = 220 Divide both sides by 55
x = 4
make a conjecture about each value or geometric relationship.
The relationship between the angles of a triangle with all sides congruent.
Answers
Congruence of all sides implies congruence of all angles. All of the angles line up.
What is geometric conjecture?
According to Thurston's geometrization conjecture in mathematics, each of a select group of three-dimensional topological spaces has a distinctive geometric structure that can be connected to it.
How do the angles of a triangle with congruent sides relate to one another?
We refer to a triangle as being equilateral when its three sides are congruent. We add a slash mark to the sides that are congruent. An equilateral triangle always has 60° angles.Learn more about congruent
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Simplify the problem and use the chart to find the answer.
Answers
When an exponent is a fraction, the number of the numerator is the exponent and the number of the denominator is the radical number:
Then, in this case:
Since
[tex]\sqrt[2]{x^3}=\sqrt[]{x^3}[/tex](when the number of the radical is 2 we can write it without the 2), then
[tex]\sqrt[2]{x^3}=\sqrt[]{x^3}[/tex]Then
Answer: III
The diameter of a planet at its equator is 5790 kilometers.Estimate using scientific notation:
Answers
Explanation
Step 1
divide the number by 1000
remember:
[tex]1000=10^3[/tex][tex]\frac{5790}{1000}=5.79[/tex]Step 2
input the value of cubic ten instead of 100
[tex]\begin{gathered} 5790=5.79\cdot1000 \\ 5.79\cdot1000=5.79\cdot10^3 \end{gathered}[/tex]then, the answer is
[tex]5.79x10^3\text{ kilometers}[/tex]
In triangle HIJ,△HIJ, overline{HI}cong overline{JH} HI ≅ JH and text{m}angle H = 118^{\circ}.m∠H=118 ∘ . Find \text{m}\angle J.m∠J.
Answers
The measure of angle J in the isosceles triangle is given as follows:
m<J = 31º.
What is an isosceles triangle?An isosceles triangle is a triangle in which:
Two of the angles have equal measures.Two of the sides have equal measures.In the context of this problem, the angles are given as follows:
118º. (angle H).x: angle J.x: angle I.Angles J and I are equal as the triangle is isosceles and the congruent angles are acute, that is, they cannot have measures above 90º.
The sum of the measures of the internal angles of a triangle is of 180º, hence we can solve for x as follows:
x + x + 118º = 180º
2x = 62º
x = 62º/2
x = 31º.
Hence the measure of angle J is of 31 degrees.
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If a square has a perimeter of 28 inches, what is its area in square inches?
Answers
Remember that
The formula to calculate the perimeter of a square is
[tex]P=4*b[/tex]where
b is the length side of the square
we have
P=28 in
substitute in the formula
[tex]\begin{gathered} 28=4*b \\ sol\text{ve for b} \\ b=\frac{28}{4}=7\text{ in} \end{gathered}[/tex]The area of a square is
[tex]A=b^2[/tex]substitute the value of b
[tex]\begin{gathered} A=7^2 \\ A=49\text{ in}^2 \end{gathered}[/tex]The area is 49 square inchesoption CIf you are given odds of 5 to 6 in favor of winning a bet, what is the probability of winning the bet?
Answers
5 to 6 odds means that, out of 11 possible outcomes, odds are that there will be 5 of one kind of outcome and 6 of another kind of outcome.
In this case, you are given 5 to 6 odds, which means that out of 11 possible outcomes you will win a bet 5 times, and lose it 6.
In fraction, it will look like this:
[tex]\frac{11}{11}\text{ \lparen these are all the possible outcomes, which equals 1\rparen = }\frac{5}{11}(the\text{ outcomes in which you win, which equals .4545, so 45.45\%\rparen + }\frac{6}{11}\text{ \lparen the outcomes in which you lose, which equals 0.5454, so 54.54\% \rparen}[/tex]Because of that, the probability of winning the bet is 45.45%, and in a fraction, it is 5/11, which means you will win in 5 out of 11 scenarios.
It takes Evelyn, traveling at 36 mph, 20 minutes longer to go a certain distance than it takes Sarah traveling at 60 mph. Find the distance
traveled.
Answers
The distance travelled by both Evelyn and Sarah is 30 miles.
Given,
The speed travelled by Evelyn = 30 mph
Time taken by Evelyn to cover a distance = 20 minutes
Speed travelled by Sarah = 60 mph
We have to find the distance travelled by both of them.
Speed = distance / time
Then,
Distance = speed x time
Lets take x as the distance.
Then,
36 × (x + 20) = 60x
36x + 720 = 60x
60x - 36x = 720
24x = 720
x = 720/24
x = 30
That is,
The distance travelled by both Evelyn and Sarah is 30 miles.
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Cilantro earns $17.43 per hour. If Cilantro works 27 hours in a week, what will Cilantro's earnings be for the week?
Answers
Let be "x" Cilantro's earnings (in dollars) for the week.
According to the explained in the exercise, Cilantro makes $17.43 per hour and works a total of 27 hours per week.
With that information, you can set up the following proportion:
[tex]\frac{$17.43\text{dollars}$}{1\text{hour}}=\frac{x}{27\text{hours}}[/tex]In order to find the value of "x", you need to solve for it. You can apply the Multiplication property of equality and multiply both sides of the equation by 27 hours.
Therefore, you get this result:
[tex]\begin{gathered} (27\text{hours)(}\frac{$17.43\text{dollars}$}{1\text{hour}})=(\frac{x}{27\text{hours}})(27\text{hours)} \\ x=470.61\text{dollars} \end{gathered}[/tex]Then, Cilantro's earnings for the week will be $470.61
The population of the county, which follows the exponential growth model,
increased from 491,675 in 2000 to 782,341 in 2010.Write the exponential growth function.
Answers
Step 1
Given; The population of the county, which follows the exponential growth model,
increased from 491,675 in 2000 to 782,341 in 2010.
Write the exponential growth function.
Step 2
The exponential function is given as;
[tex][/tex]what are the lenghths of the legs in the triangle?give your answer in simplest radical form or rounded to the nearest hundredth.
Answers
Here, we are given a 45°-45°-90° triangle.
Let's find the length of the legs.
A 45°-45°-90° triangle is an isosceles triangle, and the two legs of an isosceles triangle are of equal lengths.
To find the length of each leg apply the formula:
[tex]c=a\sqrt[]{2}[/tex]Where;
c = 12
Thus, we have:
[tex]12=a\sqrt[]{2}[/tex]Solve for a:
Divide both sides by √2
[tex]\begin{gathered} \frac{12}{\sqrt[]{2}}=\frac{a\sqrt[]{2}}{\sqrt[]{2}} \\ \\ \frac{12}{\sqrt[]{2}}=a \\ \\ a=\frac{12}{\sqrt[]{2}} \\ \\ \text{Simplify the denominator:} \\ a=\frac{12}{\sqrt[]{2}}\ast\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ \\ a=\frac{12\sqrt[]{2}}{2} \\ \\ a=6\sqrt[]{2} \end{gathered}[/tex]Therefore, the length of each leg in radical form is 6√2
ANSWER:
[tex]6\text{ }\sqrt[]{2}[/tex]Please help me with this question I have a test next week and I really have to study this is 11th grade algebra 2
Answers
ANSWER:
(a)
(b) P(x < 4) = 0.29
(c) P(x= 6) = 0.17
(d) P(x ≥ 5) = 0.34
STEP-BY-STEP EXPLANATION:
The probability in each case would be the specific amount divided by the total amount, therefore, we calculate the total amount and the probability in each case, like this:
[tex]\begin{gathered} 5+10+2+9+33+12+15+3+1\:=\:90 \\ \\ P(0)=\frac{5}{90}=0.06 \\ \\ P(1)=\frac{10}{90}=0.11 \\ \\ P(2)=\frac{2}{90}=0.02 \\ \\ P(3)=\frac{9}{90}=0.1 \\ \\ P(4)=\frac{33}{90}=0.37 \\ \\ P(5)=\frac{12}{90}=0.13 \\ \\ P(6)=\frac{15}{90}=0.17 \\ \\ P(7)=\frac{3}{90}=0.03 \\ \\ P(8)=\frac{1}{90}=0.01 \end{gathered}[/tex]Therefore, the table would look like this:
With this we calculate the probability in each case:
[tex]\begin{gathered} P\left(x<4\right)=P\left(x=0\right)+P\left(x=1\right)+P\left(x=2\right)+P\left(x=3\right)=0.06+0.11+0.02+0.10=0.29 \\ \\ P(x=6)=0.17 \\ \\ P(x\ge5)=P\left(x=5\right)+P\left(x=6\right)+P\left(x=7\right)+P\left(x=8\right)=0.13+0.17+0.03+0.01=0.34 \end{gathered}[/tex]State the domain using an appropriate notation and evaluate f(2)
Answers
The domain of a function or coordinates of a function are the input values of the function "x" for which the function exists.
For instance, given the coordinates of the function {(-7, 2), (0, -2), (2, 5), (8, 1)}, the corresponding value of the x-coordinates are the domain. Therefore the domain of the given coordinate points are given as;
[tex]\text{Domain}=\mleft\lbrace-7,0,2,8\mright\rbrace[/tex]Get the value of f(2).
To get the value of f(2), we will find the y-value of the coordinate with a domain of 2. From the given coordinates, we can see that the coordinate that has a domain of 2 is (2, 5) and the corresponding y-value of the coordinate is 5. Hence f(2) = 5
Calculating a rate of change
What is the vertical change form Point A to Point B?
What is the horizontal change from Point A to Point B ?
What is the rate of change shown on the graph? Give the answer as a decimal rounded to the nearest tenth, if necessary?
Answers
Hello there. To solve this question, we'll have to remember some properties about rate of change.
Given the points A and B from a line, we want to determine the vertical change and the horizontal change between the points and then, using these values, determine the rate of change of the function (the line passing through them).
For this, we first find the coordinates of the points.
[tex]A=(2,1)\text{ and }B=(4,2)[/tex]The vertical change is the difference between the y-coordinates of the points, hence
[tex]y(B)-y(A)=2-1=1[/tex]The horizontal change is given by the difference between the x-coordinates of the points, therefore
[tex]x(B)-x(A)=4-2=2[/tex]The rate of change of this function is, finally, given by the ratio between the vertical (rise) and horizontal (run) changes of the function:
[tex]\dfrac{1}{2}=0.5[/tex]This is the rate of change of this function.