Given f (x) = 17 minus x squared, what is the average rate of change in f(x) over the interval [1, 5]? –6 Negative one-half One-fourth 1
Answers
The average rate of change of the function is equal to - 6.
What is the average rate of change of a function in a given interval?
Mathematically speaking, the average rate of change of a function continuous in a given interval can be determined by using secant line slope formula, which is defined below:
r = [f(b) - f(a)] / (b - a)
Where:
Lower end of the intervalUpper end of the intervalIf we know that f(x) = 17 - x², a = 1 and b = 5, then the average rate of change is:
r = [17 - 5² - 17 + 1²] / (5 - 1)
r = - 24 / 4
r = - 6
The average rate of change of the function is equal to - 6.
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Answer:
-6 is A on edge 2023
Step-by-step explanation:
mhm
Related Questions
Whats the InversE of Y=3x+2
Answers
Head lengths of brushtail possums follow a nearly normal distribution with mean 92.6 mm and standard deviation 3.6 mm.
a) What percent of possums have heads less than 95.4 mm?
b) What percent of possums have heads more than 85.8 mm?
c) What percent of possums have heads between 85.8 and 95.4 mm?
d) What is the maximum head length of the shortest 10% of possum heads?
Answers
a) Approximately 77.94% of possums have heads less than 95.4 mm.
b) Approximately 96.93% of possums have heads more than 85.8 mm.
c) Approximately 74.93% of possums have heads between 85.8 and 95.4 mm.
d) The maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.
a) We can use the normal distribution to answer this question. Let X be the head length of a brushtail possum. Then X has a normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm. We want to find P(X < 95.4 mm).
Using the standard normal distribution table or a calculator, we can find the z-score corresponding to a head length of 95.4 mm:
\(z = \frac{(95.4 - 92.6)}{3.6} = 0.78\)
Then, using the standard normal distribution table, we can find the probability that a standard normal variable is less than 0.78:
P(Z < 0.78) = 0.7794
Therefore, approximately 77.94% of possums have heads less than 95.4 mm.
b) Again, using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find P(X > 85.8 mm).
Finding the corresponding z-score:
\(z = \frac{(85.8 - 92.6)}{3.6} = -1.89\)
Using the standard normal distribution table, we find:
P(Z > -1.89) = P(Z < 1.89) = 0.9693
Therefore, approximately 96.93% of possums have heads more than 85.8 mm.
c) To find the percentage of possums with heads between 85.8 and 95.4 mm, we can subtract the probability of heads less than 85.8 mm from the probability of heads less than 95.4 mm:
P(85.8 < X < 95.4) = P(X < 95.4) - P(X < 85.8)
Using the same calculations as in parts (a) and (b), we get:
P(85.8 < X < 95.4) = 0.7794 - 0.0301 = 0.7493
Therefore, approximately 74.93% of possums have heads between 85.8 and 95.4 mm.
d) We want to find the maximum head length of the shortest 10% of possum heads. This is equivalent to finding the 10th percentile of the distribution. Using the normal distribution with mean μ = 92.6 mm and standard deviation σ = 3.6 mm, we want to find the head length x such that P(X < x) = 0.1.
Using the standard normal distribution table or a calculator, we can find the z-score corresponding to the 10th percentile:
P(Z < z) = 0.1
z = -1.28
Then, we can find the corresponding head length x:
x = μ + zσ = 92.6 + (-1.28)(3.6) = 87.68
Therefore, the maximum head length of the shortest 10% of possum heads is approximately 87.68 mm.
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Bob rides his bike he records his time and distance each time he stops for water how many miles will Bob have traveled if you stopped after 180 minutes continue in the same pattern enter your answer in the first response parks and to the equation represents the relationship between Bob’s distance and the time he stops for water in the second response box use D for the distance you travel in t for the time in minutes
Answers
The equation represents of Bob’s distance is D = 1/4t
How to determine the equation represents of Bob’s distanceThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The table of values
On the table of values, we can see that
The distance multiplied by 4 gives the time
Mathematically, this is represented as
4 * D = t
Divide by 4
D = 1/4t
Hence, the equation is D = 1/4t
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IM TIMED What is 3.71 simplified!!!!!!!
Answers
Answer:
if its asking for the tenths place its 3.7
if its asking for the ones place its 4
Step-by-step explanation:
HELP MEEEEE THIS IS DUE IN 2 HOURSSS
Answers
The bacteria took 1 hour and 40 minutes to fill the initial
bottle. Explain how it only took 10 minutes to fill 3
additional empty bottles.
Answers
Answer:
The bacteria took 1 hour and 40 minutes to fill the first bottle and it took only 10 minutes to fill 3 more. This is because of the amount of bacteria, for the first bottle there were only a few so it took them time to grow and multiply but once there were a lot the process starts to get faster. Think of it like this if you have 1 bacteria it will multiply into 2 bacteria. The 2 will multiply into 4, then 8, 16, 32, 62, 124 and so on. Do you notice how the numbers are getting bigger every time? Each number is being multiplied by 2 so the growth rate speeds up very quickly, which is why it took the bacteria 1 hour and 40 minutes to fill the first bottle and only 10 minutes to fill the other 3.
(I'm not sure but this is my theory)
Answer:
The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes. Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full
Step-by-step explanation:
Edge 2020
The whale shark feeds for 7.5 hours each day. Graph the function that represents the amount f of food (in pounds) filtered by the whale shark as a function of the number d of days.
Answers
Answer:
step by step answer at least
Rewrite the equation by completing the square.
x^{2}+10x+21 = 0
(x+__)^2=__
Answers
Answer:
Step-by-step explanation:
x²+10x+21=0
x²+10x+(10/2)²-(10/2)²+21=0
x²+10x+25-25+21=0
(x+5)²-4=0
(x+5)²=4
(x+y)²=(x+y)(x+y)=x(x+y)+y(x+y)=x²+xy+xy+y²=x²+2xy+y²
(x+y)²=x²+2xy+y²
coefficient of x=2y
y²=[(coefficient of x)/2]²=(2y/2)²=y²
Is there an option for no solution?
can u guys help me with this
Answers
Answer:
1. 50
2. 18
Step-by-step explanation:
Answer:
1st paper
18
2nd paper
50
When an object is weighed on a scale, the number displayed may vary from the object’s actual weight by at most 0.4 pounds. The scale says the object weighs 125.8 pounds. Part A: Write an absolute value inequality that describes the range of the actual weight of the object. Use the variable w to represent the actual weight of the object. Part B: Solve the absolute value inequality for w. Express your answer as a compound inequality.
Answers
The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.
Part A: The absolute value inequality that describes the range of the actual weight of the object is:
|w - 125.8| ≤ 0.4
Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:
w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4
Solving the first inequality:
w - 125.8 ≤ 0.4
Add 125.8 to both sides:
w ≤ 126.2
Solving the second inequality:
-(w - 125.8) ≤ 0.4
Multiply by -1 and distribute the negative sign:
-w + 125.8 ≤ 0.4
Subtract 125.8 from both sides:
-w ≤ -125.4
Divide by -1 (note that the inequality direction flips):
w ≥ 125.4
Combining the solutions, we have:
125.4 ≤ w ≤ 126.2
The object is 125.4 ≤ w ≤ 126.2.
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solve for x using the quadratic formula -2x^2+2x+9=0
Answers
12. Find all x- and y-intercepts, state the multiplicity of each zero and tell if the graph crosses or
bounces, and state the end behavior Then graph each polynomial by hand,
P(x)=x^2(x-3)^2(x+2)
P(x)=x^4-4x^2
Answers
Step-by-step explanation:
12a. To
find x intercepts, set each factor equal to zero
\( {x}^{2} = 0\)
\(x = 0\)
\((x - 3) {}^{2} = 0\)
\(x = 3\)
\(x + 2 = 0\)
\(x = - 2\)
So the x intercepts are( 0,-2,3.)
The multiplicity of 0 and 3 is 2,
The multiplicity of -2 is 1.
The y intercepts are
\(0 {}^{2} (0 - 3) {}^{2} (0 + 2) = 0\)
The y intercept is 0.
End Behavior: Since this is a positve 5th root function, as x increases, f(x) increases while as x decreases, f(x) decreases.
The First picture shows the graph of the function. Notice ried the zeroes that have a multiplicity of 2 have a parabolic reflection after thre function reaches their zero.
The zero that have a multiplicity of 1 have just passes through the graph.
12b. We have
\( {x}^{4} - 4 {x}^{2} \)
We can easily find y intercept, which is 0.
To find x intercept,
Factor
\( {x}^{2} ( {x}^{2} - 4)\)
\( {x}^{2} (x + 2)(x - 2) = 0\)
\(x = 0\)
\(x = 2\)
\(x = - 2\)
So the x intercepts are (0,2,-2).
The multiplicity of 0 is 2 while 2 and -2 is 1.
End Behavior: Since this is a positve quartic function, as x increases or decreases , f(x) increases
Look at the second graph,
Answer:
\(P(x)=x^2(x-3)^2(x+2)\)
y-intercept is when x = 0:
\(\implies P(0)=0^2(0-3)^2(0+2)=0\)
Therefore, y-intercept is at (0, 0)
x-intercept(s) is when P(x) = 0
\(\implies x^2(x-3)^2(x+2)=0\)
\(\implies x^2=0\implies x=0\)
\(\implies (x-3)^2=0\implies x=3\)
\(\implies (x+2)=0\implies x=-2\)
Therefore, x-intercepts are:
(0, 0) with multiplicity 2 → bounces(3, 0) with multiplicity 2 → bounces(-2, 0) with multiplicity 1 → crosses x-axisEnd-behavior:
As the lead coefficient is positive and the lead degree is odd,
\(P(x) \rightarrow - \infty \textsf{ as }x\rightarrow - \infty\)
\(P(x) \rightarrow + \infty \textsf{ as }x\rightarrow +\infty\)
-------------------------------------------------------------------------------
\(P(x)=x^4-4x^2\)
y-intercept is when x = 0:
\(\implies P(0)=(0)^4-4(0)^2=0\)
Therefore, y-intercept is at (0, 0)
x-intercept(s) is when P(x) = 0
\(\implies x^4-4x^2=0\)
\(\implies x^2(x^2-4)=0\)
\(\implies x^2(x-2)(x+2)=0\)
\(\implies x^2=0 \implies x=0\)
\(\implies (x-2)=0 \implies x=2\)
\(\implies (x+2)=0 \implies x=-2\)
Therefore, x-intercepts are:
(0, 0) with multiplicity 1 → crosses x-axis(2, 0) with multiplicity 1 → crosses x-axis(-2, 0) with multiplicity 1 → crosses x-axisEnd-behavior:
As the lead coefficient is positive and the lead degree is even,
\(P(x) \rightarrow + \infty \textsf{ as }x\rightarrow - \infty\)
\(P(x) \rightarrow + \infty \textsf{ as }x\rightarrow +\infty\)
Kelly needs 1/8 cups of sugar to make 1/4 of her cookie recipe. How much sugar does she need to make the entire recipe?
Answers
Answer:
1/2 cup of sugar
Step-by-step explanation:
She needs to multiply 1/8 cup of sugar by 4 to make the entire recipe since 18 cup of sugar is only good for a fourth of the recipe.
Solve the following inequality.
m-2
<-2 OR 4m +3 > 15
3
m < [?] OR m > [ ]
![Solve the following inequality.m-2<-2 OR 4m +3 > 153m < [?] OR m > [ ]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/abNmG52bMg54z6GqVRlK7voVWMhB0vuQ.png)
Answers
Solving the inequality given algebraically, the solution of the inequality for the value of m is:
m < -4 OR m > 3
Given the following inequality,
\(\frac{m - 2}{3} < -2 \\\)
or
4m + 3 > 15
Let's solve algebraically for the value of m in both inequality statements given.
\(\frac{m - 2}{3} < -2 \\\)
Multiply both sides by 3\(\frac{m - 2}{3} \times 3 < -2 \times 3\\\\m - 2 < -6\)
Add 2 to both sides\(m - 2 + 2 < -6 + 2\\\\m < -4\)
Or
4m + 3 > 15
Subtract 3 from each side4m + 3 - 3 > 15 - 3
4m > 12
Divide both sides by 4\(\frac{4m}{4} > \frac{12}{4} \\\\\)
m > 3
Therefore, solving the inequality given algebraically, the solution of the inequality for the value of m is:
m < -4 OR m > 3
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The demand for a product is given by D(x)=130e^(−0.025x), where x is the number of units sold each week and 0≤x≤90. Step 1 of 2: Find the number of units sold that will yield maximum revenue. Round your answer to the nearest whole unit.Step 2 of 2:Find the price per unit that will yield maximum revenue. Round your answer to the nearest cent.
Answers
(a) 40 unit have to be the number of units sold that will yield maximum revenue.
(b) The price per unit that will yield maximum revenue, will be $1.195.
(a) We have to find the number of units sold that will yield maximum revenue
Given demand function is
D(x)=130e^{-0.025x}
where is the number of units sold each week
Revenue function R(x) = xD(x)
R(x) = x∙130e^{-0.025x}
To find maximum revenue put,
R’(x) = 0
⇒d/dx(x∙130e^{-0.025x}) = 0
⇒130 d/dx(x∙e^{-0.025x}) = 0
⇒130[e^{-0.025x}+xe^{-0.025x} ∙(-0.025x)]=0
⇒130e^{-0.025x} ∙(1-0.025x)=0
⇒1 - 0.025x=0
⇒0.025x = 1
⇒x = 1/0.025
⇒x = 40units
R''(x) = 130d/d[x(e^{-0.025x}-0.025xe^{-0.025x} )]
R''(x) = 130[-0.025e^{-0.025x}-0.025e^{-0.025x}+0.00625xe^{-0.025x}]
R''(x)|x=40 = 130-0.025*40[0.050+0.00625*40]
R''(x)|x=40 = 130/e ∙(-0.025)
R''(x)|x=40 = (130*(-0.025))/e < 0
At x= 40 units, the revenue will maximize.
$0 units will yield maximum revenue.
(2) Now we have to find the price per unit that will yield maximum revenue.
D(x) = 130e-0.025x
D(40) = 130e^{-0.025*40}
D(40) = 130e^{-1}
D(40) = 130/e
D(40) = 47.82(in dollar)
Price per unit = d(40)/40
Price per unit = 47.82/40
Price per unit = $1.195
The price per unit that will yield maximum revenue, will be $1.195.
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If 20 – r = 15, what is the value of 3.r ?
Answers
Answer:
3r =15
Step-by-step explanation:
r=20-15
r=5
3r=3×5
3r=15
pls follow
Answer:
r = 5
Step-by-step explanation:
20 - r = 15
+ r + r
20 = 15 + r
-15 -15
5 = r
A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100. Construct a 95% confidence interval for mu 1minusmu 2.
Answers
Answer:
For the first city, the 95% confidence interval would be:
28,900 +/- 2300 x 3 = 28,900 +/-6900$
For the second city, the 95% confidence interval would be:
30,300 +/- 2100 x 3 = 30,300 +/- 6300$
Tiana is looking up her county's census data for a school project. Her county conducts a census every decade. She finds that the population was about 641,000 the year she was born, and that it had decreased to about 634,590 a decade later. Tiana reads that the population of the county is expected to continue decreasing each decade.
Write an exponential equation in the form y=a(b)x that can model the county population, y, x decades after Tiana was born.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How many decades after Tiana was born will the county population fall below 600,000?
decades
Answers
The exponential function that can model the county population, y, x decades after Tiana was born, is:
\(y = 641000(0.99)^x\)
The population will fall below 600,000 in 6.6 decades after Tiana was born.
What is an exponential function?The definition of the exponential function is presented as follows:
\(y = a(b)^x\)
In which the parameters of the exponential function are presented as follows:
a is the initial value.b is the rate of change.In the context of this problem, the values of these parameters are given as follows:
a = 641000, which is the initial population.b = 634590/641000 = 0.99.Hence the function is:
\(y = 641000(0.99)^x\)
The population will fall below 600,000 when y = 600000, hence:
\(y = 641000(0.99)^x\)
\(600000 = 641000(0.99)^x\)
\((0.99)^x = \frac{600000}{641000}\)
\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)
\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)
\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)
x = 6.6 decades.
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There are 6 times as many females as males on the maths course at university. What fraction of the course are male? Give your answer in its simplest form.
Answers
We can do it like this to create this equation in our problem.
M(males)
F(females)
M+F=total
6F+F=total
7F=total
F=(1/7)total
Which means that there are 7 from every student which leads to us bringing that there is 1 female and 6 male.
1 out of 7 is based as 1/7.
If this helps could you mark this as brainiest? Thanks, have a good day.
Mrs. Carissi purchased a new smartphone. The cost of the phone was $675 and the local tax rate is 6.2%.
Answers
Answer:
716.85
Step-by-step explanation:
6.2 / 100 = 0.062
0.062 x 675 = 41.85
41.85 + 675 = 716.85
The total cost of the phone including taxes is $716.85.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the cost of the phone was $675 and the local tax rate is 6.2%.
The total cost will be calculated as,
6.2 / 100 = 0.062
0.062 x 675 = 41.85
41.85 + 675 = 716.85
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The equation of the graphed line is x+2y=5. What is the x-intercept of the graph? A coordinate plane with a line passing through (negative 5, 5) and (5, 0).
Answer choices
A) 2
B) 2.5
C) 5
D) 5.5
Answers
Answer:
the answer is... a
Step-by-step explanation:
A boy walks 5km due north and then 4km due east. Find the bearing of his current position from the starting point, how far is the boy now from the starting point
Answers
the book if it has 275 pages?
Raju painted 51 m of a fence in 6 days. How much did he paint in the rest (I).
4 days?
Answers
Answer:
34m
Step-by-step explanation:
51m in 6days
in 1day
51÷6
8.5
in 4 days
8.5x4
34
simplify(x^5^2/ x^2)
Answers
Answer:
x^23
Step-by-step explanation:
Cancel the common factor of x^5^2 and x^2
Factor x^2 out of x^5^2
(x^2) (x^5^2-2) / (x^2)
cancel common factors
x^25-2 = x^23
Fill in the blank. In the triangle below, z = 52° V 35 ze Z X
Answers
The sum of the three internal angles of a triangle is equal to 180°. For the triangle in the picture we have a 52° angle, a 90° right angle and an unknown angle z. Their sum must be equal to 180° so we get the following equation:
\(\begin{gathered} 180^{\circ}=90^{\circ}+52^{\circ}+z \\ 180^{\operatorname{\circ}}=142^{\operatorname{\circ}}+z \end{gathered}\)We can substract 142° from both sides of this equation:
\(\begin{gathered} 180^{\operatorname{\circ}}-142^{\operatorname{\circ}}=142^{\operatorname{\circ}}+z-142^{\operatorname{\circ}} \\ z=180^{\operatorname{\circ}}-142^{\operatorname{\circ}} \\ z=38^{\circ} \end{gathered}\)AnswerThen the answer is 38.
What is the value of the expression?
Answers
9514 1404 393
Answer:
3
Step-by-step explanation:
This is basically a calculator problem, though you can do it in your head. Follow the order of operations.
\(\dfrac{\sqrt{144}}{\sqrt[5]{243}}-5+16\div\sqrt[3]{64}=\dfrac{12}{3}-5+\dfrac{16}{4}\\\\=4-5+4=\boxed{3}\)
Answer:
3
Step-by-step explanation:
(√144/ ^5√243/) - 5 + 16 ÷ (³√64) =
12/3 -5 +16÷ 4 =
4 - 5 + 16 ÷ 4 =
-1 + 4 =
3
a. Will he be able to make a right triangle with his fence? Why or why not?
Answers
Joel be not able to make a right triangle with his fence because the given dimensions are not satisfying for Pythagoras theorem.
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Dimensions of triangle he has to use for fencing are
15 feet, 8 feet, and 20 feet.
For making it a right triangle it must satisfy the "Pythagoras theorem" which states that
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
H²=B²+P²
20²=15²+18²
400=225+64
400≠289
No, it will not be able to make a right triangle.
Hence, Joel will be not able to make a right triangle with his fence because the given dimensions are not satisfying for pythagoras theorem.
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The complete question is given below:
Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 15 feet, 8 feet, and 20 feet long.
1. Will he be able to make a right triangle out of his fence? Why or why not?
Select the correct answer.
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x - 11)?
A. It is the graph of f(x) where the slope is increased by 11.
It is the graph of f(x) translated 11 units to the left.
It is the graph of f(x) translated 11 units up.
It is the graph of f(x) translated 11 units to the right.
B.
C.
OD.
Answers
The correct answer is C. It is the graph of f(x) translated 11 units to the left.
The correct answer is:
C. It is the graph of f(x) translated 11 units to the left.
When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.
In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.
The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.
Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.
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please answer fast...............................
Answers
The coordinate of point R after the rotation is determined as = ( - 4, 7).
option A.
What is the rotation of a figure?A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.
You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.
When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.
The initial coordinate of point R = ( 4, 7),
The new coordinate of point R after the rotation = ( - 4, 7)
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1. What percent of 60 is 15?
Answers
Answer:
25%
Step-by-step explanation:
Mental math approach: 15 is 1/4 of 60, and 1/4 is 25%. So, 15 is 25% of 60.
Answer:
25% or 1/4
Step-by-step explanation: