7 Which of the following is a true statement? OA. A probability near indicates an unlikely event ОВ. A probability near O indicates a likely event OC. A probability near 1 indicates a likely event OD A probability near 1 indicates an unlikely event.
Answers
Okay, here we have this:
Considering the provided information, we are going to analyze which of the statements is true, so we obtain:
A) A probability of 1/2=0.5=50% does not indicate that the event is likely or unlikely. So the option is wrong.
B) A probability of 0=0% does not indicate that the event is likely. So the option is wrong.
C) A probability of 1=100% indicate that the event is likely. So this is the correct option.
B) A probability of 1=100% does not indicate that the event is unlikely. So the option is wrong.
Finally we obtain that the correct answer is the option C.
Related Questions
write a quadratic function whose graph satisfies a.o.s is x=2 and range is y is greater than or equal to -9 and explain how. please, i've been stuck for hours and i have a math test tomorrow
Answers
The a.o.s of the quadratic function is:
[tex]x=2[/tex]And the range is:
[tex]\text{Ran}_f=\lbrack-9,\infty)[/tex]Then, the vertex of the parabola should be:
[tex]V=(2,-9)[/tex]And it opens upwards. Then, using the vertex form of the quadratic function:
[tex]f(x)=(x-2)^2-9[/tex]Find LCM for 125 and 175
Answers
We will find LCM for the numbers 125 and 175
So, factorize both numbers will give:
[tex]undefined[/tex]b. Use the graph to determine the equation that models the number of calories Jenny burns within a certain number of minutes.
Answers
The equation of a line in slope-intercept form, is:
[tex]y=mx+b[/tex]From the graph, we can see that the y-intercept is equal to 0, and since the rate of burning calories is 6.5 calories per minute, that value corresponds to the slope of the line. Therefore, if y represents the number of calories and x represents the time measured in minutes, then:
[tex]y=6.5x[/tex]difference in the number of colonies projected afunrestricted growth? ShoursRoom temperature growthf(t) = 20.52e^0.0195tProjected number of colonies after 5 hours:
Answers
1) Considering the function below:
[tex]f(t)=20.52e^{0.0195t}[/tex]This question is really about evaluating that function when t=5. So when we do that, we'll find the projected number of colonies.
2) So let's do it, considering that "e" is an irrational number and we're going to approximate the final answer:
[tex]\begin{gathered} f(5)=20.52e^{0.0195(5)} \\ f(5)=20.52e^{1.1024} \\ f(5)=22.62\approx23 \end{gathered}[/tex]Since colonies are given as whole numbers, we rounded it off to the nearest whole number.
3) Hence, the answer is approximately 23 colonies
Is the number of miles driven proportional to the amount of time? How do you know? 250 200 150 Miles 100 What does the point (2, 100) mean in the context of the situation? Hours What does the point (5,250) mean in the context of the situation? d. What does the point (1,50) mean in the context of the situation?
Answers
a) Looking at the question, for us to determine whether the number of miles driven proportional to the amount of time, we need to check if there are any constant of proportionality which can also be refered to slope.
From the data,
Let M represent miles
t represent the time
We know that:
at t = 1, M = 50
at t = 2, M = 100
at t = 3, M = 150
at t = 4, M = 200
k = M2-M1/t2-t1
k = 100-50/2-1 = 150-100/3-2 = 200-150/4-3
k = 50/1
k = 50
We can say that k = M/t
50 = M/t
M = 50
From the expression derived, it can be seen that the number of miles is directly proportional to the time taken. This shows that the number of miles driven is proportional to the amount of time.
b) the point (2, 100) in the context of the situation means that the total amount of time covered to drive for 100 miles is 2 minutes.
c) the point (5, 250) in the context of the situation means that the total amount of time covered to drive for 250 miles is 5 minutes.
d) the point (1, 50) in the context of the situation means that the total amount of time covered to drive for 50 miles is 1 minutes.
complete the two-way table that shows the time during the year that people take vacations based on their age
Answers
Given a two-way table as shown in the following picture:
As shown in the table, we need to find the variables from x to w
So, we can deduce the following relations:
From the first column:
[tex]\begin{gathered} x+2=18 \\ x=18-2=16 \end{gathered}[/tex]And, from the fourth column:
[tex]\begin{gathered} z+20=50 \\ z=50-20=30 \end{gathered}[/tex]And, from the first row:
[tex]x+6+y=z[/tex]Substitute with x and z to find y
[tex]\begin{gathered} 16+6+y=30 \\ 22+y=30 \\ y=30-22=8 \end{gathered}[/tex]And
[tex]\begin{gathered} 2+v+8=20 \\ v+10=20 \\ v=20-10=10 \end{gathered}[/tex]u = w = 16
mr yonaki's first year of college was back in 2001 when college inflation was at 390% last year in 2020, college tuition inflation was at 1,180%, we think of the years as our x-values and the percent of inflation as our y-values, find the average rate of change in college tuition from 2001 to 2020.
Answers
To solve this problem, we will calculate the average rate of change as follows. Given two points (a,f(a)) and (b,f(b)). The average rate of change would be
[tex]\frac{f(b)-f(a)}{b-a}[/tex]In our case, we are given the points (2001,390%) and (2020, 1180%). So, in this case we have
f(2001)=390% and f(2020)=1180%. So, the average rate of change would be
[tex]\frac{1180-390}{2020-2001}=\frac{790}{19}=41.578947[/tex]This means that the average rate of change is approximately 41.58% per year.
Determine of the given equations are parrell perpendicular or neither. 3x+2y=6 and y= -3/2x+5
Answers
When two lines are parallel their slope is equal, when they're perpendicular the slopes are opposite reciprocal from each other.
To solve the problem we need to look for the slope of each line. To do that we will rewrite the expressions on it's slope-intercept form. This is done by isolating the "y" variable on the left side. The second equation already is in this form, therefore:
[tex]\begin{gathered} 3x+2y=6 \\ 2y+3x-3x=6-3x \\ 2y=6-3x \\ \frac{2y}{2}=\frac{6-3x}{2} \\ y=-\frac{3}{2}x+3 \end{gathered}[/tex]The slope of the line is the number multiplying "x" on the right side. The number on both lines is equal, this means that they are parallel.
Theodore needs to mix a 20% saline solution with a 60% saline solution to create 200 milliliters of a 34% solution. how many millimeters of each solution must Theodore use?
Answers
130 ml of solution 1 and 70 ml of solution 2
Explanation
Step 1
Let
Volume of solution 1 ( 20% saline solution)=x
Volume of solution 2( 60 % saline solution)=y
Step 2
replace
Theodore needs to mix a 20% saline solution with a 60% saline solution to create 200 milliliters of a 34% solution
the volume of salt ( in solution 1)= 0.2 *volume of the solution 1
the volume of salt ( in solution 2)= 0.6 *volume of the solution 1
the volume of salt ( in mix)= 0.34 *volume of mix
replace,
[tex]\begin{gathered} 0.2x+0.6y=0.34*200\text{ } \\ 0.2x+0.6y=68\text{ Equation(1)} \end{gathered}[/tex]Also
volume os solution 1 + volume of solution 2 = volume of mix
replace,
[tex]x+y=200\text{ Equation (2)}[/tex]Step 3
use equatino (1) and (2) to find x and y
a) isolate x form equation (2)
[tex]\begin{gathered} x+y=200 \\ x=200-y\text{ Equation (3)} \end{gathered}[/tex]b) replace equation (3) in equation (1)
[tex]\begin{gathered} 0.2(200-y)+0.6y=68 \\ 4-0.2y+0.6y=68 \\ 0.4y=68-40 \\ 0.4y=28 \\ y=\frac{28}{0.} \\ y=70 \end{gathered}[/tex]c) replace the valur of y =70in equation (3) to find x
[tex]\begin{gathered} x=200-y \\ x=200-70 \\ x=130 \end{gathered}[/tex]please can you help me find the derivative of the equation
Answers
The given function is
[tex]f(x)=\frac{x+1}{2x^2+2x+3}[/tex]To find its derivative we should use the rule of division
[tex]\frac{d}{dx}(\frac{u}{v})=\frac{u^{\prime}v-uv^{\prime}}{v^2}[/tex]Let
[tex]\begin{gathered} u=x+1 \\ v=2x^2+2x+3 \end{gathered}[/tex]Let us find u' and v' first
[tex]\begin{gathered} u^{\prime}=(1)x^{1-1}+0 \\ u^{\prime}=(1)x^0 \\ u^{\prime}=(1)(1) \\ u^{\prime}=1 \end{gathered}[/tex][tex]\begin{gathered} v^{\prime}=2(2)x^{2-1}+2(1)x^{1-1}+0 \\ v^{\prime}=4x^1+2x^0 \\ v^{\prime}=4x+2 \end{gathered}[/tex]Substitute them in the rule above
[tex]f^{\prime}(x)=\frac{1(2x^2+2x+3)-(x+1)(4x+2)}{(2x^2+2x+3)^2}[/tex]Simplify the numerator
[tex]\begin{gathered} f^{\prime}(x)=\frac{2x^2+2x+3-\lbrack x(4x)+x(2)+1(4x)+1(2)\rbrack}{(2x^2+2x+3)^2} \\ f^{\prime}(x)=\frac{2x^2+2x+3-\lbrack4x^2+2x+4x+2\rbrack}{(2x^2+2x+3)^2} \\ f^{\prime}(x)=\frac{2x^2+2x+3-4x^2-2x-4x-2}{(2x^2+2x+3)^2} \end{gathered}[/tex]Add the like terms in the denominator
[tex]\begin{gathered} f^{\prime}(x)=\frac{(2x^2-4x^2)+(2x-2x-4x)+(3-2)}{(2x^2+2x+3)} \\ f^{\prime}(x)=\frac{-2x^2-4x+1}{(2x^2+2x+3)^2} \end{gathered}[/tex]Can I have help finding each of the missing variables please?
Answers
We have the parallel lines:
Angles c and b are vertical angles, and the same is true for a and 54°. The definition of two vertical angles is that they are equal. Then:
[tex]\begin{gathered} a=54^{\circ} \\ c=b \end{gathered}[/tex]Additionally, c and a are consecutive exterior angles, which are equal by definition. We conclude that:
[tex]\begin{gathered} c=a\Rightarrow c=54^{\circ} \\ \Rightarrow b=54^{\circ} \end{gathered}[/tex]Find the mean for the scores: 3,860; 5,300; 8,540; 4,400; 5,350.The mean for the scores is
Answers
ANSWER
5,490
EXPLANATION
The mean is the sum of all the scores, divided by the number of scores. In this case, we have 5 scores,
[tex]\bar{x}=\frac{3,860+5,300+8,540+4,400+5,350}{5}=\frac{27,450}{5}=5,490[/tex]Hence, the mean is 5,490.
What is the slope (round your answer to one decimal place)?
Answers
Difference quotient formula
[tex]\frac{f(x+h)-f(x)}{h}[/tex]To find the estimation of the slope of f(x) at x = 7, we can use the difference quotient. Substituting with the function f(x) provided, h = 0.001, and x = 7, we get:
[tex]\begin{gathered} f\mleft(x\mright)=9.2x^2-6.4x \\ f(7)=9.2\cdot7^2-6.4\cdot7=406 \\ f\mleft(x+h\mright)=9.2\mleft(x+h\mright)^2-6.4\mleft(x+h\mright) \\ f(7+0.001)=9.2(7.001)^2-6.4(7.001)=406.1224 \\ m=\frac{f(7+0.001)-f(7)}{0.001} \\ m=\frac{406.1224-406}{0.001} \\ m\approx122.4 \end{gathered}[/tex]Equation of the tangent line
[tex]y-y_1=m(x-x_1)[/tex]The tangent line is tangent to the point (x₁, y₁) which also passes through f(x). And m is the slope of the tangent line.
Given that f(7) = 406, then the tangent point is (7, 406). Using this point and m = 122.4, we get:
[tex]\begin{gathered} y-406=122.4(x-7) \\ y-406=122.4x-122.4(7) \\ y-406=122.4x-856.8 \\ y=122.4x-856.8+406 \\ y=122.4x-450.8\text{ (which is in the mx + b format)} \end{gathered}[/tex]I don't know how to ask a question here so can I just send you a picture?
Answers
the circle is in the third quadrant and its coordinate of the centre is,
Q(-4,-5)
now after the translation of the circle into first quadrant,
its coordinate of the centre will be Q' (4,5)
thus, the equation of the translation is,
Q(x,y) ---> Q' (-x , - y)
thus, the correct answer is option C
(x,y) ----> (-x, -y))
Which table contains only points that lie on the line represented by y = 6x - 6
Answers
Given the equation:
y = 6x - 6
Let's find the table that contains only points that lie on the line represented by the equation.
To find the correct table, input the given values of x and evaluate to find y. If the values of the calculated y corresponds with the given value of y, the table is correct.
Table A:
When x = 0, y = 6
Substitute 0 for x:
y = 6(0) - 6
y = 0 - 6
y = -6
This table is not correct
Table B:
When x = 2, y = 6
Substitute 2 for x:
y = 6(2) - 6
y = 12 - 6
y = 6
When x = -2, y = -18
Substitute -2 for x:
y = 6(-2) - 6
y = -12 - 6
y = -18
Since the value of x corresponds with the calculated value, this table (Table B) contains only points that lie on the line represented by the equation: y = 6x - 6
ANSWER:
Table B
I need help solving x+16=6
Answers
Answer : x = -10
Slove x + 16 = 6
Firstly, we need to combine values with like terms
Only 6 and 16 can be combined together
x + 16 = 6
Secondly, isolaate x
To isolate x, 16 will cross the equality sign and change to minus
x = 6 - 16
x = -10
Write a linear factorization of the function F(x)=x^4 + 49x^2
Answers
B) f(x) = x²(x+7i)(x-7i)
1) Let's start applying the factorization for that function
[tex]\begin{gathered} f(x)=x^4+49x^2 \\ f(x)=x^2(x^2+49) \\ \end{gathered}[/tex]2) Since the result of this quadratic incomplete equation: x² +49 is x1 = -7i and x_2= 7i let's rewrite it placing the factors, that zero the
[tex]f(x)=x^2(x\text{ +7i)(x-7i)}[/tex]Since distributing back we'll get to the original function.
Ivanna's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Ivanna $5.70 per pound, andtype B coffee costs $4.20 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a totalcost of $366.60. How many pounds of type A coffee were used?
Answers
Given:
Ivanna's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Ivanna $5.70 per pound, and type B coffee costs $4.20 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $366.60.
Required:
Find the type of coffee A was used.
Explanation:
The cost of type A coffee = $5.70
The cost of type B coffee = $4.20
Let the type of coffee A is used = a
Let the type of coffee B is used = b
This month's blend used twice as many pounds of type B coffee as type A.
[tex]b=2a[/tex]The total cost of the blend = $366.60
[tex]5.70a+4.20b=366.60[/tex]Substitute b =2a
[tex]\begin{gathered} 5.70a+4.20(2a)=366.60 \\ 5.70a+8.40a=366.60 \\ 14.10a=366.60 \\ a=\frac{366.60}{14.10} \\ a=26 \end{gathered}[/tex]Final Answer:
Thus 26 pounds of type A coffee is used.
Draw the graph for f(x)=x-1/x^2-x-6 and state:a. the x-intercept(s).b. the y-intercept.c. the equation(s) of any vertical asymptote(s).d. the equation of the horizontal asymptote.e. information about the behavior at the asymptote(s).f. the domain.g. the range.
Answers
ANSWER:
a. (1, 0)
b. (0, 1/6)
c. x = -2. x = 3
d. y = 0
e. The asymptotes have the form of a line and divide the function into 3 parts.
f.
[tex]\begin{equation*} \text{Domain: }\left(-\infty\:,\:-2\right)\cup\left(-2,\:3\right)\cup\left(3,\:\infty\:\right) \end{equation*}[/tex]g.
[tex]\text{Range}(-\infty,\infty)[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f\left(x\right)=\frac{x-1}{x^2-x-6}[/tex]The graph corresponding to the function is the following:
We determine in each case what the statement asks for, like this:
a. the x-intercept(s):
[tex]\begin{gathered} \text{ in this case y = 0, therefore:} \\ \\ \frac{x-1}{x^2-x-6}=0 \\ \\ x-1=0\cdot(x^2-x-6) \\ \\ x=1 \\ \\ \text{The x-intercept is \lparen1, 0\rparen} \end{gathered}[/tex]b. the y-intercept:
[tex]\begin{gathered} \text{ in this case x = 0, therefore } \\ \\ y=\frac{0-1}{0^2-0-6} \\ \\ y=\frac{-1}{-6} \\ \\ y=\frac{1}{6} \\ \\ \text{ The y-intercept is }\:\left(0,\frac{1}{6}\right) \end{gathered}[/tex]c. the equation(s) of any vertical asymptote(s). The horizontal asymptotes are the values that x cannot take since the function would be discontinuous for those values.
In this case, since it is a rational function, it would be when the denominator is 0, therefore, we solve the following:
[tex]\begin{gathered} x^2-x-6=0 \\ \\ (x-3)(x+2)=0 \\ \\ x-3=0\rightarrow x=3 \\ \\ x+2=0\operatorname{\rightarrow}x=-2 \\ \\ \text{ The equation\lparen s\rparen of any vertical asymptote are:} \\ \\ x=3,x=-2 \end{gathered}[/tex]d. the equation of the horizontal asymptote. If the degree of the denominator is greater than that of the numerator, the horizontal asymptote is the x-axis, that is:
[tex]y=0[/tex]e. information about the behavior at the asymptote(s).
In this case the behavior of the asymptotes are straight lines that represent values that the function cannot take or cannot reach, divide the function into 3 parts.
f and g.
In this case, the domain is the interval of values that x can take and the range is the interval of values that y can take.
Therefore:
[tex]\begin{gathered} \text{Domain: }\left(-\infty\:,\:-2\right)\cup\left(-2,\:3\right)\cup\left(3,\:\infty\:\right) \\ \\ \text{Range:}\:\left(-\infty\:,\:\infty\:\right) \end{gathered}[/tex]The temperature is 1\degree F1°F at dusk. It is 8 degrees colder at dawn. What is the temperature at dawn?
Answers
The temperature at dawn will be -7°F when the temperature at dusk is 1°F.
According to the question,
We have the following information:
The temperature is 1°F at dusk.
And it is 8° colder at dawn than the temperature at dusk.
So, in order to find the temperature at dawn, we will subtract 8 from the temperature at dusk.
So, we have the following expression:
1° - 8°
-7°F
(More to know: the units of temperature are always written with the measurement like any other physical quantity. Most commonly used units for temperature are °C and °F.)
Hence, the temperature at dawn is -7°F.
To know more about temperature here
https://brainly.com/question/11464844
#SPJ1
-1 + 8 = (-7) hope that helps
(:
A. Use the appropriate formula to determine the periodic depositB. How much of the financial goal comes from deposits and how much comes from interest?
Answers
For the given question, the formula to determine the periodic deposit will be:
[tex]A=\frac{P((1+\frac{r}{n})^{nt^{}}-1)}{\frac{r}{n}}[/tex]Given:
A= $1,000,000
r = 8.25% = 0.0825
Componded monthly, n = 12
time = t = 40 years
We will substitute with the given values and find the value of P
So,
[tex]\begin{gathered} 1000000=\frac{P\cdot((1+\frac{0.0825}{12})^{12\cdot40}-1)}{\frac{0.0825}{40}} \\ 1000000=P\cdot12,513.06881 \\ \\ P=\frac{1000000}{12513.06881}=79.916 \end{gathered}[/tex]Rounding to the nearest dollar
so, The periodic deposit = $80
Part (b): we will find the amount comes from the deposit and the amount comes from the interest
The amount of money comes from deposit = 80 * 12 * 40 = $38,400
The amount comes from the interest = 1000000 - 38400 = $961600
How to solve for the Y? And how do you graph it?5x-y=-3
Answers
Solve for y:
Multiply both sides by -1:
[tex]\begin{gathered} -1(5x-y)=-1(-3) \\ y-5x=3 \end{gathered}[/tex]Add 5x to both sides:
[tex]\begin{gathered} y-5x+5x=3+5x \\ y=5x+3 \end{gathered}[/tex]Now, in order to graph the equation we need to find at least two points. In this case, let's evaluate the function for -2,-1,0,1,2:
Please help me solve question 3 on my algebra homework
Answers
We are to find the equation of a line whose slope is undefined
Having x-intercept = 10
Since the slope of the line is undefined, then the line is a vertical line
Hence,
The equation will be in the form
[tex]x=a[/tex]Where a is the x value
Therefore,
The equation of a line whose slope is undefined and whose x-intercept = 10 is
[tex]x=10[/tex]Help me please is for tomorrow *cry*
Answers
Answer:
<KMU is a 140 degree angle
Step-by-step explanation:
Since the sum of all angles in a triangle are 180, we can add the 50 degrees and the 90 degrees and find the missing angle of KML
180 - (50+90) = KML
KML = 40
Since KML is 40, we subtract 40 from 180 to give us KMU
180 - 40 = KMU
KMU = 140
Good luck on your test :)
fifteen of your classmates can fit comfortably in a 9x9 feet area. Estimate how many people can stand 7 feet deep and 1 mile long on both sides of mitchell road watching the dutchtown middle school parade.
Answers
Explanation:
In a 9x9 feet area, an estimate of fifteen people can fit in, which means that
[tex]\begin{gathered} 9\times9=81 \\ \\ 15\text{ per }81\text{ square feet} \end{gathered}[/tex]Calculate the area for 7 feet by 1 mile
[tex]\begin{gathered} \text{Convert 1 mile into feet first} \\ 1\text{ mile }=5280\text{ feet} \\ \\ 7\times5280=36960\text{ square feet} \end{gathered}[/tex]Divide by 81, and multiply by 15
[tex]\begin{gathered} \text{Let }x\text{ be the estimate for the number of people who can fit in} \\ \frac{x}{36960}=\frac{15}{81} \\ x=36960\cdot\frac{15}{81} \\ x=6844.4444 \end{gathered}[/tex]Answer:
Rounding our answer to the nearest whole number, we can estimate that 6844 can stand to watch the school parade.
A) List the Steps of the operations for each number trick B) Simplify the expression (If possible)5(x+7)/3
Answers
a)
The expression given is:
[tex]\frac{5(x+7)}{3}[/tex]From this we can see that:
7 is added to a number, x
Then the whole thing is multiplied by 5 as shown by the parenthesis around it
Then the whole thing is divided by 3
So, the steps would be:
• Add 7 to the number
,• Multiply by 5
,• Divide by 3
b)
In order to simplify, we firsst distribute the 5:
[tex]\begin{gathered} \frac{5(x+7)}{3} \\ =\frac{5x+35}{3} \end{gathered}[/tex]This can be the final form, or we can divide the two terms by 3 and leave it added together:
[tex]\begin{gathered} \frac{5x+35}{3} \\ =\frac{5x}{3}+\frac{35}{3} \end{gathered}[/tex]solve for m: m/25 = 10/50
Answers
Answer
m/25 = 10/50
Multiply both sides by 50
50(m/25) = 50(10/50)
2m = 10
Divide through by 2
2m/2 = 10/2
m = 5
Joan attended school for 2 weeks longer than 3/4 of the year. How long did Joan attend school? (Assume 52 weeks in a year.)
Answers
Joan attended school for 41 weeks
What is Time?Time can be defined as the dimension based on the occurrence of a system . It can be measured in terms of seconds, minutes, hours, days, weeks, months, and years.
For example Joan attends school 2weeks more than 3/4 of a year
There are 52 weeks in a year
3/4of 52 weeks = 39weeks
Therefore the number of weeks Juan attended school in a year is( 39 +2)weeks
= 41 weeks
learn more about time from
https://brainly.com/question/17146782
#SPJ1
Only give answer, i will ask if i need any explanation Thank you
Answers
Giving the table, we are asked to convert the following into fraction, decimal and percentage.
(1) Fraction 3/50
Decimal form is 0.06
Percentage = 3/50 * 100 = 6%
(2) Decimal 4.78
Fraction
Rewrite as:
4 + 0.78
convert 0.78 to fraction: 39/50
= 4 + 39/50
= 4 39/50
Frcation = 239/50
Decimal = 478
(3) Percentage 113%
Fraction:
In order to covert a percent to ration, divide it by 100: a% = a/100
So, 113% = 113/100
Frcation = 1 13/100
Fraction = 113/100
Decimal = 1.13
The graph of a cosine function is drawn. One full cycle goes from x = 0 to x = 2 and the low point on that cycle is (1, — 5).Which of the following functions could have this graph?○ y = 5.cosmxy = 5. cos2xOy=-5 cos xxO y=-5-cos2x
Answers
Answer:
y=5 cos πx
Explanation:
In the graph of the cosine function:
One full cycle goes from x = 0 to x = 2, this means that the period of the graph is 2.
For the general cosine function:
[tex]f(x)=a\cos(bx+c)+d[/tex]The period is determined using the formula:
[tex]Period=\frac{2\pi}{b}[/tex]Thus, to have a period of 2, the value of b must be π.
The options that satisfy these properties are:
[tex]\begin{gathered} y=5\cos\pi x \\ y=-5\cos\pi x \end{gathered}[/tex]Next, the low point on that cycle is (1, — 5).
[tex]\begin{gathered} \text{ When }x=1:y=5\cos\pi x=5\cos\pi(1)=-5 \\ \text{When }x=1:y=-5\cos\pi x=-5\cos\pi(1)=5 \end{gathered}[/tex]The function of these two that contain (1, -5) is y=5 cos πx.
The function that could have this graph is y=5 cos πx.
