Answers
The average rate of change f(x) on the interval -6 ≤ x ≥ 2 is; 5
What is the Average Rate of Change of the function?
Average rate of change is a measure of how much the function changed per unit, on average, over that interval. This is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Now, the formula for the average rate of change over the interval (a, b) is;
f'(x) = [f(b) - f(a)]/(b - a)
Now, we are given the interval as -6 ≤ x ≥ 2.
From the given polynomial graph, we see that;
f(2) = 0 and f(-6) = 40
Thus;
f'(x) = [f(-6) - f(0)]/(2 - (-6))
f'(x) = (40 - 0)/8
f'(x) = 5
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Related Questions
Assume that a sample is used to estimate a population mean μ
. Find the margin of error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95%.
Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.
M.E. =
Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
Answers
The margin error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95% is 0.04694
We would utilize the t distribution in the estimation of the margin of error because the population standard deviation is unknown (and the sample size is less than 30).
Error margin = t-critical * standard deviation/square root sample size
It is given in the above question that,
Standard deviation is given as = 8.6
And, the Sample size which is given is = 22
Also, the confidence level which given is = 95%
Then the alpha will be = 100% - 95%
= 5% = 0.05
Now, the critical value, t would be = alpha / 2
= 0.05 /2 = 0.025
Also, the sample we'll consider will be = given sample size - 1 = 22 -1 = 21
To find the margin error, we'll put all the values in the formula
Error margin = t-critical * standard deviation/square root sample size
= [tex]\frac{0.025 * 8.6}{\sqrt{21} }[/tex]
= 0.215 / 4.58
= 0.04694
Hence, the margin error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95% is 0.04694
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Given the recursive formula below, what are the first 4 terms of the sequence? A) 17, –6, –3, 0B) 17, 13, 9, 5C) 17, 19, 21, 23D) 17, 15, 13, 11
Answers
Explanation
Step 1
we have the recursive formula
[tex]f(x)=\begin{cases}f(1)=17 \\ f(n)=f(n-1)-2\text{ if n }>1\end{cases}[/tex]A recursive formula is a formula that defines each term of a sequence using the preceding term(s), we can see in the formula that the new term ( f(n)) equals the previous term minus 2
so
[tex]\begin{gathered} f(1)=17 \\ hence \\ f(n)=f(n-1)-2 \\ \text{for n=2} \\ f(2)=f(2-1)-2 \\ f(2)=f(1)-2 \\ f(2)=17-2=15 \\ so,\text{ the second term is 15} \end{gathered}[/tex]and so on,
Now for n=3
[tex]\begin{gathered} f(n)=f(n-1)-2 \\ f(3)=f(3-1)-2 \\ f(3)=f(2)-2 \\ f(3)=15-2=13 \\ so,the\text{ second third terms i s13} \end{gathered}[/tex]for n=4
[tex]\begin{gathered} f(n)=f(n-1)-2 \\ f(4)=f(4-1)-2 \\ f(4)=f(3)-2 \\ f(4)=13-2=11 \\ \text{hence, the fourth term is 11} \end{gathered}[/tex]so, the answer is
D) 17,15,13,11
I hope this helps you
A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Which diagram best represents this information?
Answers
The diagram which best represents the hiking track of the hiker is attached below.
As time increases, speed is constant, i.e., 214 miles per hour
So, the distance increases with an increase in time.
Speed = Distance/Time
Let, Distance = D and Time = T,
214 = D / T
D = 214T
Let, D = Y coordinate, Time = X coordinate
y = 214 x→→Equation of the line passing through the origin and slope 214.
For the given situation, the equation is a linear equation and the equation will be on the y-axis.
Hence, a diagram that represents this information is:
Correct question :
A hiker began hiking from the 0-mile mark of a trail. The hiker walked at a steady rate of 214 miles per hour. Draw the diagram which best represents this information?
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juans dog Stan's two feet and 3 inches tall Peters dog stands 9 in tall how much taller is juans dog than Peters dog
Answers
To answer this question, we need to transform all the values into one type of measure. In this case, we can work with inches. Then, we have:
[tex]2ft\cdot\frac{12in}{1ft}=24in[/tex]Then, we have that in two feet we have 24 inches. Then, we have:
Juan's dog: 24 inches + 3 inches ---> 27 inches tall.
Peter's dog: 9 inches tall.
Now, how much taller is Juan's dog than Peter's dog is:
[tex]\frac{\text{Juan's dog}}{\text{Peter's dog}}=\frac{27in}{9in}=3[/tex]Therefore, Juan's dog is 3 times taller than Peter's dog.
In a large school, it was found that 80% of students are taking a math class, 75% of student are taking an English class, and 67% of students are taking both. Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary. Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
Answers
The probability that a randomly selected student is taking a math class or an English class is 0.88
And the probability that a randomly selected student is taking neither a math class nor an English class 0.12
In this question, we have been given in a large school, it was found that 80% of students are taking a math class, 75% of student are taking an English class, and 67% of students are taking both.
Let A represents math class, B represents English class
P(A) = 0.80
P(B) = 0.75
P(A ∩ B) = 0.67
We need to find the probability that a randomly selected student is taking a math class or an English class.
P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A U B) = 0.80 + 0.75 - 0.67
P(A U B) = 0.88
Also, we need to find the probability that a randomly selected student is taking neither a math class nor an English class.
P(~(A U B) ) = 1 - P(A U B)
P(~(A U B) ) = 1 - 0.88
P(~(A U B) ) = 0.12
Therefore, the probability that a randomly selected student is taking a math class or an English class is 0.88
And the probability that a randomly selected student is taking neither a math class nor an English class 0.12
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Solve the equation below and find the variation constant, Find y when x=18, if y varies directly as x, and y=50 when x=13.
Answers
Answer:
• k=50/13
,• y=69.231 (to the nearest 1000th)
Explanation:
If y varies directly as x, the equation of variation is:
[tex]y=kx,\text{ k=variation constant}[/tex]When x=13 and y=50
[tex]\begin{gathered} 50=13k \\ k=\frac{50}{13} \end{gathered}[/tex]Substituting k into the equation above, we have:
[tex]y=\frac{50}{13}x[/tex]Therefore, when x=18
[tex]\begin{gathered} y=\frac{50}{13}\times18 \\ y\approx69.231 \end{gathered}[/tex]Question
Solve.
−6.6x=−4
What is the solution to the equation?
Enter your answer as a simplified fraction in the box.
Answers
The solution to the equation would be 20/33 as a simplified fraction.
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of that variable would give a true mathematical statement.
We have been given an equation as; −6.6x=−4
Thus we need to solve the equation to find the solution.
-6.6x = -4
Then Divide both sides by -6.6.
x = -4/(-6.6)
x = 40/66
x = 20/33
Hence, the solution to the equation would be 20/33 as a simplified fraction.
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[tex](a - \frac{95 }{5} )^{2} - \frac{36}{25} m^{2} [/tex]
Please Evaluate
Answers
Line c has an equation of y = -5x + 3. Parallel to line c is line d, which passes through the
point (2, -6). What is the equation of line d?
Answers
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient so equation of line d is y = -5x + c.
Substitute (2,-6) into the equation to find c.
-6 = -5(2) + c
c = 4
Hence equation of line d is y = -5x + 4.
7. Which state had a population of eight
hundred four thousand, one hundred
ninety-four?
Answers
Answer:
I read it's south Dakota but not sure of it.
I found it from this picture
Independent Practice7. The original quantity is 10 and the new quantityis 13. What is the percent change? Is it anincrease or decrease?8. The original quantity is 5 and the new quantityis 3. What is the percent change? Is it an increaseor decrease?7%1310100%100%poP.P Р-P%.The percent increase is%The percent decrease is
Answers
The percentage increase or decrease can be calculated by :
[tex]\%change=\frac{New-Orig}{Orig}\times100[/tex]7. New = 13, Orig = 10
% change = [(13 - 10)/10] x 100 = 30% (Increase)
8. New = 3, Orig = 5
% change = [(3 - 5)/5] x 100 = -40% or 40% (decrease)
Match each compound inequality on the left to the graph that represents its solution on the right. 4x + 3 > 15 or -6x > 12 -5 0 1 - 8x > - 24 and -10 < 2x - 6 -7 1 - 29 < 9x - 2 < 16 6 4
Answers
The first compound inequality 4x+3>15 or -6x≥12 matches the third graph, i.e x>3 or x≥-2.
The second compound inequality -8x>-24 and -10≤2x-6 matches the second graph, i.e x>3 or x≥-2.
The third compound inequality -29≤9x-2<16 matches the first graph, i.e -3≤x<2.
Given the expressions are:
a. 4x+3>15 or -6x≥12
simplify.
4x+3>15 or -6x≥12
4x>15-3 or x≥12/-6
4x>12 or x≥-2
x>3 or x≥-2
hence the graph is third.
b. -8x>-24 and -10≤2x-6
simplify.
-8x>-24 and -10≤2x-6
x>-24/-8 and -10+6≤2x
x>3 and -4≤2x
x>3 and -4/2≤x
x>3 and -2≤x
x>3 and x≥-2
hence the second graph matches.
c. -29≤9x-2<16
first take -29≤9x-2
simplify
-29+2≤9x
-27≤9x
-27/9≤x
-3≤x
now take 9x-2<16
simplify.
9x<16+2
9x<18
x<18/9
x<2
hence we get -3≤x<2
hence the first graph matches the given inequality.
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Use ''compound inequality'' in the main answer and ''graph'' in the explanation.
Fowler inc, just paid a dividend of 2.55 per share on its stock. The dividends are expected to grow by 3.9% per year indefinitely. If investers require a 10.4% return on this stock what will the price be in 3 years, what will the price be in 15 years?
Answers
When Fowler inc, just paid a dividend, the price in 15 years for the share is $72.36.
How to calculate the price?This will be illustrated as:
P0 = D1 / (Ke - g)
P0 = Current Price
D1 = Expected Dividend after 1 Year
Ke = COst of Equity
g = Growth Rate
Dividend for first year will be:
D1 = D0(1+g)
= $ 2.55 (1+0.039)
= $ 2.55(1.039)
= $ 2.6495
Current price will be:
P0 = D1 / (Ke - g)
= $ 2.6495 / (0.104-0.039)
= $ 2.6495 / 0.065
= $ 40.76
Price in 15 years will be
P15 = D16 / (Ke - g)
P15 = Price after 15 Years
D16 = Expected Div after 16 Years
Ke = COst of Equity
g = Growth Rate
D16 = D0(1+g)^16
= $ 2.55 (1+0.039)^16
= $ 2.55(1.039)^16
= $2.55 * 1.8444
= $ 4.7031
P15 = D16 / (Ke - g)
= $4.7031 / (0.104-0.039)
= $4.7031 / 0.065
= $72.36
The price is $72.36
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Cameron Benson is a dental assistant.
He earns $11.17 per hour and time
and a half for overtime. Last week
he worked 40 hours plus 7 hours of
overtime.
Answers
x2 + 7x + 12 = ** Show
Answers
x² + 7x + 12 = 0
Using the factorisation method
Find two numbers such that its product gives 12 and its sum gives 7
The two numbers are 3 and 4
Replace 7 in the equation by those two numbers and then factorise
That is;
x² + 3x + 4x + 12 = 0
x(x+3) + 4(x+3) = 0
(x+3)(x+4) = 0
Either x+3 = 0 or x+4 =0
Either x = -3 or x= -4
What is the proportional relationship between a and bA B8. 324 940 15 Write a equation describing the relationship between a and b
Answers
Explanation:
A proportional relationship means that the two variables are related by a constant called constant of proportionality:
[tex]a=kb[/tex]k is the constant of proportionality.
To find k we have to use the values of a and b from the table:
[tex]\begin{gathered} k=\frac{a}{b} \\ k=\frac{8}{3} \\ k=\frac{24}{9}=\frac{8}{3} \\ k=\frac{40}{15}=\frac{8}{3} \end{gathered}[/tex]Answers:
• equation: ,a = 8/3 b
,• constant of proportionality:, 8/3
A line that includes the point (1, 10) has a slope of 1. what is its equation in slope-intercept form?
Answers
Considering the definition of a line, the equation in slope-intercept of the line that passes through the point (1, 10) and has a slope of 1 is y=x+9.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Equation in slope-intercept form in this caseIn this case, you know:
The line has a slope of 1.The line passes through the point (1, 10).Substituting the value of the slope m, the line has a form: y=1x + b or what is the same y=x +b.
Replacing the value of the point in the expression of a linear equation, the value of the ordinate to the origin b can be obtained:
10= 1×1 + b
10= 1 + b
10 -1 = b
9= b
Finally, the equation of the line is y=x +9.
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5. The following stem-and-leaf plots compare the ages of 30 actors and 30 actresses at the time they won the Oscar award for Best Actor or Actress.ActorsStemsActresses2146667987532213001133444557788877654332210041112966515210601167480(a) What is the age of the youngest actor to win an Oscar? years(b) What is the age difference between the oldest and the youngest actress to win an Oscar? years(c) What is the oldest age shared by two actors to win an Oscar? years
Answers
Answer:
(a) 31 years
(b) 59 years
(c) 56 years
Step-by-step explanation:
In general, when reading a stem and leaf plot, we read firstly the number in the steam (middle) and then in the leaf.
Now, let's move on to the question:
(a) As we can see in the graph, the youngest actor has 31 years.
(b) The youngest actress is 21 years old and the oldest is 80.
So, the difference is 80 - 21 = 59 years.
(c) In this exercise, we have to look for actors who had the same age. That means, when evaluating the steam, we will have to find similar values in the leaf. The oldest age shared is 56 years.
When Mr. Jackson got in his car yesterday, the odometer read 187,198.9 km. When he got home, the reading was 187,399.4 km. How far did Mr. Jackson drive?
Answers
Answer:
200.5
Step-by-step explanation:
reading of odometer at beginning = 187,198.9 km
reading of odometer after reaching home = 187,399.4
distance travelled = 187,399.4 - 187,198.9 = 200.5 km
A travel agent arranged a payment plan for a client. It required a down payment of $150 and 15 monthly payments of $657. What was the total cost of the plan?
Answers
Answer:
$10,005
Step-by-step explanation:
We need to find the total cost of the plan and we already know that the client need to pay $150 for downpayment and 15 monthly payments of $657.
So all we need to find is the 15 monthly payments of $657. (Which we could found with multiplying $657 with 15)
$657×15 = $9,855
Now we just add it with the downpayment ($150) to find the total cost of the plan.
$9,855+$150 = $10,005
You could write the steps like this:
$150+($657×15)=$10 005
The graph of a function g is shown below.
Find g (-2)
Answers
Use the number line to determine if each number is a solution and type YES or NO . 0 = -10 = 8 = -9 =9 =5 =And don’t worry is just a practice:)
Answers
We need to know if the number given belongs to the set or no
0----- YES
-10------ NO
8 ------NO
-9 ----NO
9 ------NO
5 -----YES
a spinner contains the numbers 1 through 50. What is the probability that the spinner will land on a number that is not a multiple of 9? Give your answer in fraction form.
Answers
Answer:
[tex]\frac{9}{10}[/tex]
Step-by-step explanation:
multiplies of 9, 18,27,36, and 45. Every number has a change to be selected, but these 5. There are 50 numbers
[tex]\frac{50-5}{50}[/tex]
[tex]\frac{45}{50\\}[/tex]
[tex]\frac{9}{10}[/tex]
Use the point-slope form to find the equation of each altitude of SABC. (Recall ! a triangle is the perpendicular drawn from any vertex to the opposite side.) (b) A(4,3), B(0,7). C- (a) A(1, -2), B(3,4), C(-2,6)
Answers
The rule of the slope of a line has 2 points is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]A = (1, -2), B = (3, 4), C = (-2, 6)
We will take the altitude from A to the opposite side of BC
Then we will find the slope of BC first
x1 = 3 and y1 = 4. point B
x2 = -2 and y2 = 6. point C
We will substitute them in the rule above
[tex]\begin{gathered} m=\frac{6-4}{-2-3}=\frac{2}{-5} \\ m=-\frac{2}{5} \end{gathered}[/tex]The slope of BC = -2/5
Since the product of the slopes of the perpendicular line is -1, then if the slope of one is m, then the slope of the other will be -1/m, we reciprocal it and change its sign, then the slope of the altitude of BC should be 5/2
[tex]m_{\perp}=\frac{5}{2}[/tex]The form of the equation in point-slope is
y - y1 = m(x - x1)
m = 5/2
Since point A is lying on the altitude from A to BC, then
x1 = 1 and y1 = -2 point A
Substitute m and coordinates of point A in the form of the equation above
y - (-2) = 5/2 (x - 1)
[tex]y+2=\frac{5}{2}(x-1)[/tex]The equation of the altitude from A to BC is
y + 2 = 5/2 (x - 1)
please help tutor I will give you a good rating
Answers
Answer
Options A, D and E are correct.
The two functions are increasing.
The function for plan II has a greater unit rate.
The function for plan I has a greater y-intercept.
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
For the first plan, there's a one time investment of 15,000 dollars and subsequent monthly payments of 500 dollars.
y = 15,000 + 500x
y = 500x + 15,000
Slope = unit rate of increase = 500
y-intercept = 15,000
For the second plan, the function is just given as
y = 12,000 + 520x
y = 520x + 12,000
Slope = unit rate of increase = 520
y-intercept = 12,000
We can see that
The two functions are increasing.
The function for plan II has a greater unit rate.
The function for plan I has a greater y-intercept.
Hope this Helps!!!
Why the answer to 12am=4, for a is a=1/3m help please
Answers
We can solve the given expression for [tex]a=\frac{1}{3m}[/tex] by using the division method.
The given expression is [tex]12am=4[/tex].
We have to solve the given expression for [tex]a=\frac{1}{3m}[/tex].
Now we solving the expression.
[tex]12am=4[/tex]
We can easily solve the expression by seeing the value that we have to solve.
We using the division method to solve the given expression.
In the division method we divide the both side by same variable to find to value of particular variable.
For solving the expression for [tex]a[/tex] we eliminate [tex]12m[/tex].
We divide the given expression by [tex]12m[/tex] on both side
[tex]\frac{12am}{12m}=\frac{4}{12m}\\a=\frac{4}{3\times4m}\\a=\frac{1}{3m}[/tex]
Now we solve the given expression for [tex]a=\frac{1}{3m}[/tex].
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The wheels on noah’s bike have a circumference of about 5 feet how many time do the wheels rotated if noah rides 40 feet
Answers
Step by step
If the wheel is 5 feet around, we can divide the 40 feet by the 5 feet per rotation, = 8 rotations
Arc length s. Central Angle 36 feet. π/2 radiansFind the radius r of a circle with an arc length s and a central angle 0.
Answers
The formula for determining the length of an arc is expressed as
length of arc = #/360 * 2 * pi * radius
where
# represents the central angle
From the information given
length of arc = 36
We would convert from radians to degree
1 pi rad = 180 degrees
pi/2 rad = 180/2 = 90 degrees
Thus, # = 90 degrees
The equation becomes
36 = 90/360 * 2 * pi * radius
36 = 0.25 * 2 * 3.14 * radius
36 = 1.57 * radius
radius = 36/1.57
radius = 22.93 feet
a hybrid car can travel 45 miles on one gallon of gas. determine the amount of gas needed for a 500 miles trip
Answers
We have the following:
[tex]r=45\frac{m}{g}[/tex]now, for 500 miles
[tex]\frac{500m}{45\frac{m}{g}}=11.11g[/tex]therefore about 11.11 gallons of gas is needed
Answer: roughly 12 gallons or exactly 11.11111111111111111 etc
Step-by-step explanation:
The height of a sand dune (in centimeters) is represented by cm, where is measured in years since . Find and , and determine what each means in terms of the sand dune. Give the values of and below, including units.
Answers
The height of the sand dune after 13 years is 324 cm. The rate of change height of sand dunes is - 8t.
Given the equation is -
f(t)=1000-4t²
f(13) = 1000 - 4 (13)²
= 1000 - 676
= 324 cm
f'(t) = - 8t
f'(13) = - 8(13)
= -104cm
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Complete Question -
The height of a sand dune (in centimeters) is represented by f(t)=1000-4t2 cm, where t is measured in years since 1995. Find f(13) and f'(13), and determine what each means in terms of the sand dune. Give the values of f(13) and f'(13) below, including units.