Answer:
15 2/3, or 47/3
Step-by-step explanation:
I'm going to assume, correctly or not, that you actually meant f(x) = 2x^2 - (1/3)x + 5. Double check on this right now, please.
If I'm right, then evaluate f(x) at x = 0 and x = 8:
f(0) = 5
and
f(8) = 2(8)^2 - (1/3)(8) + 5 = 128 - 8/3 + 5 = 133 - (2 2/3), or: 130 1/3
Then the average rate of change of f(x) = 2x^2 - (1/3)x + 5 over the interval [0,8] is:
130 1/3 - 5 125 1/3
a. r. c. = ------------------- = ---------------- = 15 2/3, or 47/3
8 - 0 8
The average rate of change of the function [tex]f(x)=2x-\frac{1}{3} x+5[/tex] over the interval [tex]x = 0[/tex] to [tex]x = 6[/tex] will be [tex]\frac{5}{12}[/tex] .
What is average rate of change of the function ?Average rate of change of the function is a rate of change of the function, on an average, over the given interval. i.e. values of [tex]x[/tex] and [tex]y[/tex] .
Using slope formula we find Average rate of change of the function.
i.e. [tex]f(x)=\frac{f(x_{2} )-f(x_{1} )}{x_{2}-x_{1}}[/tex]
We have,
[tex]f(x)=2x-\frac{1}{3} x+5[/tex]
[tex]x_{1} = 0[/tex] to [tex]x_{2}= 6[/tex]
So,
First find [tex]f(x_{1})[/tex],
[tex]f(x_{1})=2x-\frac{1}{3} x+5[/tex]
[tex]f(0)=2*0-\frac{1}{3} *0+5[/tex]
[tex]f(x_{1})=5[/tex]
Now, find [tex]f(x_{2})[/tex],
[tex]f(x_{1})=2x-\frac{1}{3} x+5[/tex]
[tex]f(2)=2x*2-\frac{1}{3} *2+5[/tex]
[tex]f(2)=4-\frac{2}{3}+5=9-\frac{3}{2}[/tex]
[tex]f(x_{2})=\frac{15}{2}[/tex]
Now, putting values of [tex]f(x_{1})[/tex] and [tex]f(x_{2})[/tex] in given formula of [tex]f(x)[/tex],
i.e.
[tex]f(x)=\frac{f(x_{2} )-f(x_{1} )}{x_{2}-x_{1}}[/tex]
[tex]f(x)=\frac{\frac{15}{2}-5 }{6-0}[/tex]
[tex]f(x)=\frac{\frac{15-10}{2} }{6}[/tex]
[tex]f(x)=\frac{5} {12}[/tex]
So, the average rate of change of the function is [tex]\frac{5}{12}[/tex], which is find out using the slope formula.
Hence, we can say that the average rate of change of the function [tex]f(x)=2x-\frac{1}{3} x+5[/tex] over the interval [tex]x = 0[/tex] to [tex]x = 6[/tex] will be [tex]\frac{5}{12}[/tex] .
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you score a 65% on your ap statistics exam and a 78% on your economics exam. the AP statistics scores were normally distributed with an average of 60% and a standard deviation of 6%. the economics scires were also normally distributed with an average of 75% and the standard deviation of 2.5%. In which class did you perform better relative to the class average? be sure to justify your answer
Answer:
You performed better relative to the class average in your economics class.
Step-by-step explanation:
There are two classes.
AP statistics class and Economic class
Using the z score formula,
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
In the AP statistics class, you scored a percentage of 65%. The class average was 60%
x is the raw score = 65%
μ is the population mean = 60%
σ is the population standard deviation = 6%
z = (x-μ)/σ
z = (65 - 60)/6
z = 5/6
z = 0.8333333333
In the Economics classes, you scored a percentage of 78% with a class average of 75%
x is the raw score = 78%
μ is the population mean = 75%
σ is the population standard deviation = 2.5%
z = (x-μ)/σ
z = (78 - 75)/2.5
z = 3/2.5
z = 1.2
Comparing the z score of both exams taken from different classes,we can see that your z score was higher in the Economics class compared to the A.P statistics class.
Therefore, you performed better relative to the class average in your economics class.
Find the height of a rectangular prism if the surface are is 288 square centimetres and the base has a length of 4 centimetres and a width of 9 centimetres.
The height of a rectangular prism is 8.3 cm.
What is Surface Area?The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface.
We have,
Surface Area = 288 square cm
Base length = 4 cm and width = 9 cm
So, SA of rectangular prism
288 = 2(lw+ wh + lh)
144 = (36 + 9h + 4h)
13h = 144- 36
13h = 108
h = 8.30 cm
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what’s 1 2/3 + 5 3/8
PLEASE HELP ASAP A group of 8th and 9th graders were surveyed about whether they use social media to communicate with their friends. The results are shown below in the conditional relative frequency table by row. A 4-column table with 3 rows. The first column has no label with entries 8th grade, 9th grade, total. The second column is labeled do not use with entries 0.06, 0.19, 0.38. The third column is labeled use with entries 0.84, 0.81, 0.62. The fourth column is labeled total with entries 1.00, 1.00, 1.00. Which conclusions can be drawn from the results of the survey? Check all that apply. There is no association between using social media and grade level. The probability a student uses social media, given that he or she is in 9th grade, is 81%. A student who is more likely to not use social media is in 8th grade. An 8th grader is more likely to use social media than not. Knowing a student’s grade level does not help determine if he or she uses social media.
Options A, B, D, and E are correct answers such that the probability of the usage of social media by 8th and 9th-grade students is given.
A. There is no association between using social media and grade level.
B. The probability a student uses social media, given that he or she is in 9th grade, is 81%.
D. An 8th grader is more likely to use social media than not.
E. Knowing a student’s grade level does not help determine if he or she uses social media.
What is Probability?Probability is the ratio of the favorable outcomes to the total outcomes.
Given that, a group of 8th and 9th graders were surveyed about whether they use social media to communicate with their friends.
We can see that, there is no relationship between the usage of social media and grade level so, we can say that there is no association between using social media and grade level.
Probability of using social media by a 9th grader is-
P(9) = 0.81 / 1 x 100 = 81%
Probability of using social media by a 8th grader is-
P(8) = 0.84 / 1 x 100 = 84%
We cannot define the usage of social media depending on the grade level.
Thus, Options A, B, D, and E are correct answers.
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The table is attached
Y = 3x + 9 complete a table of values
Answer: u have to cross out 3x and change into a positive and u try to find the other side of da equation. I hope dis helps :3
Step-by-step explanation:
When trying to find solutions to the system of equations x+y=3 2x+2y=6 you take several correct steps that lead to the expression 0=0. Which statement is true?
Answer:
They are the same equations. (I don't know what you mean by "true.")
Step-by-step explanation:
If you divide 2x + 2y = 6 by 2, it turns into x + y = 3. This means that the graphs of the lines are the same, or there are infinite solutions.
I am really sorry if this is wrong because I am not really sure what you meant by "Which statement is true?"
I NEED HELP PLZ I FORGOT HOW TO DO THIS PLZ EXPLAIN HOW U GOT UR ANSWER HELPP
Answer:
5
Step-by-step explanation:
Using the formula of a trapezoid, we can solve this!
Formula is A=1/2(b1+b2)h.
A=1/2(2+8)1
A=1/2(10)1
A=1/2(10)
The area would be 5 cubic in2.
Please tell me if im wrong! im just a student .m.
Answer:
5 units²
Step-by-step explanation:
a for a trapezoid = [tex]\frac{a+b}{2} *h[/tex]
[tex]\frac{8+2}{2} *1[/tex] = [tex]\frac{10}{2} * 1[/tex] = 5*1 = 5
The area is 5 units²
-2x2-x-1=0
our answer...
Answer:
_______________________________________
→ x = - 1 ± i√7 ;
4
_______________________________________
Or: Write as:
_______________________________________
→ x = -1 + i√7 ; -1 − i√7 ;
4 4
_______________________________________
Step-by-step explanation:
_______________________________________
Given:
-2x² − x − 1 = 0 ;
Solve for " x " .
________________
First, let us multiply BOTH sides of the equation by "-1" ;
to get rid of that "negative sign" in the coefficient: " -2" ;
→ as follows:
________________
-1 * {-2x² − x − 1 } = 0 *{-1} ;
_________________
Rewrite the value: "x" on the "left-hand side" of the question; as: "1x" ;
since "any value" ; multipled by "1" ; results in that same individual value:
_________________
-1 * {-2x² − 1x − 1 } = 0 *{-1} ;
________________
Note the "distributive property" of multiplication:
________________
a(b + c) = ab + ac ;
________________
Likewise, from the "left-hand side" of the equation:
-1 * {-2x² − 1x − 1 } = {-1 * -2x²} + {-1 * -1x} + {-1* -1 } ;
= 2x² + 1x + 1 ;
_______________________________________
Rewrite the "left-hand side" of the equation:
2x² + 1x + 1 ;
Now, the "right-hand side of the equation:
" { 0 * -1 } = 0 " .
Now, rewrite the entire equation:
2x² + 1x + 1 = 0 ;
________________
Note: This equation is written in "quadratic format" ;
that is: " ax² + bx + c " ; [a ≠ 0] ;
→ in which:
a = 2 ; b = 1 ; c = 1 ;
________________
→ which means we can solve for the value(s) for "x" ; by using the
"quadratic equation formula" ;
→ that is:
________________
→ x = -b ± √(b² − 4ac) ;
2a
________________
So; to solve for the values for "x" ; we substitute our known values for:
"a" ; "b" ; and "c" ; and solve:
________________
→ x = -1 ± √(1² − 4*2 *1) ;
4
_________________________
→ x = -1 ± √(1 − 8) ;
4
_________________________
→ x = -1 ± √(-7) ;
4
_________________________
Note: "√(-7)" ; is the square root of a negative number.
Note that we use the lower case letter, " i " ;
as a symbol to represent the imaginary number: " √(-1) " .
This is an "imaginary number" ; since one cannot take the "square root" of a "number lower than zero."
So, we write: √-7 ; as: " i * 7 " ; or, just: " i √7 " ; since:
"i = √-1" ; and since: " √-7" would "factor out" to: "√7 * √-1 " .
_________________________
Note: In the mainstream U.S.A. , the concept of " i " as the "imaginary number" — " √-1 " ; is usually introduced in the second year college-prep algebra class (after "first year high school algebra" in 9th grade; and after "geometry" in 10th grade).
_________________________
So; we have:
→ x = -1 ± √(-7) ;
4
___________
We can rewrite this as:
____________
→ x = -1 ± i√7 ;
4
_____________
We can leave our answer written like that.
We have two (2) solutions—so we can also write out both solutions for the value of x:
_____________
→ x = -1 + i√7 ; -1 + i√7 ;
4 4
_____________________________________________
Hope this explanation is helpful to you!
Best of luck— and best wishes!
_____________________________________________
What is 1/2 + 2/3? Im stupid so I don't know what this is. idk I'm dumb
Answer:
=7/6 pls mark me as brainlist
Step-by-step explanation:
1/2+2/3
=find lcm = 6
=1x3/2x3 +2x2/3x2
3/6+4/6
=7/6
Answer:
1/2 + 2/3 = 1 1/6
Step-by-step explanation:+
1/2 + 2/3 = ?
Find the common denominator.
3/6 + 4/6 = 7/6
Turn your improper fraction into a mixed number.
1 1/6
can you please help me fill this out thanks
Answer: [tex]\sqrt{2}[/tex]
Step-by-step explanation:
In a 45 45 90 triangle the two sides are 1 wile the hypothenuse is [tex]\sqrt{2}[/tex]
Write the equation of a line that passes through the point (4, 2) and is parallel to the line graphed below.
Answer:
Step-by-step explanation:
(-2, 2) (2, -3)
(-3 - 2)/(2 + 2)
-5/4 the slope
y - 2 = -5/4(x + 2)
y - 2 = -5/4x - 5/2
y- 4/2 = -5/4x - 5/2
y = -5/4x - 1/2
f(x) = (x-6)(x + 5)
What are the zeros of the quadratic?
Answer:
x=6 x=-5
Step-by-step explanation:
f(x) = (x-6)(x + 5)
To find the zeros, set the function equal to zero
0 = (x-6)(x + 5)
Using the zero product of property
0 = x-6 0=x+5
x=6 x=-5
What is the area of triangle DEF? Triangle D E F has a base of 42 centimeters and a height of 28 centimeters. The other sides have lengths of 35 centimeters.
Answer:
The area of triangle DEF is 588 cm²
Step-by-step explanation:
Given;
triangle DEF with base, b = 42 centimeters
triangle DEF with height, h = 28 centimeters
triangle DEF other side length, L = 35 centimeters
Area of a triangle is half of the product of the triangle base and height.
Represented in formula as;
A = ¹/₂bh
where;
b is the base of the triangle
h is the height of the triangle
A = ¹/₂ x 42 x 28
A = 588 cm²
Therefore the area of triangle DEF is 588 cm²
Answer:
588
Step-by-step explanation:
What is the sum of the numbers
Answer:
B 4i sqrt(2)
Step-by-step explanation:
sqrt(-2) = sqrt(-1) * sqrt(2) = i sqrt(2)
sqrt(-18) = sqrt(-1) sqrt(2) sqrt(9) = 3i sqrt(2)
Add them together
i sqrt(2) + 3i sqrt(2)
4i sqrt(2)
Answer:
B.) [tex]4\sqrt{2}i[/tex]
Step-by-step explanation:
Simplify both radicals from negative form (the square root of -1 is i ):
[tex]\sqrt{-1*2} +\sqrt{-1*18} \\\\\sqrt{2}i+\sqrt{18}i[/tex]
Simplify [tex]\sqrt{18}[/tex] :
[tex]\sqrt{9*2}\\\\\sqrt{9}*\sqrt{2}\\\\ 3\sqrt{2}i[/tex]
Add:
[tex]1\sqrt{2}i+3\sqrt{2}i\\\\4\sqrt{2}i[/tex]
:Done
give that a load of mass 20kg is acted upon by a force of 60N calculate the acceleration of the load
Answer:
[tex]3m/s^2[/tex]
Step-by-step explanation:
the information that we have is:
mass: [tex]m=20kg[/tex]
force applied: [tex]F=60N[/tex]
since we need to find the acceleration, we can use Newton's second law of motion:
[tex]F=ma[/tex]
Where [tex]F[/tex] is the force applied to a mass [tex]m[/tex] which creates an acceleration [tex]a[/tex].
we solve this equation for the acceleration:
[tex]a=\frac{F}{m}[/tex]
and we substitute the known values:
[tex]a=\frac{60N}{20kg} \\\\a=3m/s^2[/tex]
the acceleration of the load is: [tex]3m/s^2[/tex]
What is 0.83¯¯¯¯ expressed as a fraction in simplest form?
Enter your answer in the box.
Answer: 5/6
Step-by-step explanation:
Answer:
the answer is
100÷83
Step-by-step explanation:
hope this helps
The function f(x) = (x - 4)(x-2) is shown.
What is the range of the function?
1:01
all real numbers less than or equal to 3
all real numbers less than or equal to - 1
all real numbers greater than or equal to 3
all real numbers greater than or equal to -1
6+
4
2
10.-
-6
-4
8
10
X
-2
-2
-4
-6
-10
Save and Exit
Next
Submit
Mark this and return
Answer:
the range for f(x) = (x-4) (x-2) is [-1,∞)
Step-by-step explanation:
all real numbers greater than or equal to -1
The range of the function is all real numbers greater than or equal to -1
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = ( x - 4 ) ( x - 2 ) be equation (1)
On simplifying , we get
f ( x ) = x ( x - 2 ) - 4 ( x - 2 )
f ( x ) = x² - 2x - 4x + 8
f ( x ) = x² - 6x + 8
Now , the range of the function is set of possible y values
The vertex of the parabola is at ( 3 , -1 )
So , the range of the function is f ( x ) ≥ -1 and the interval is [ -1 , ∝ ]
Hence , the range of the function is f ( x ) ≥ -1
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I'm a surgery 9 out of 15 students named math as their favorite subject. Express this rate as a decimal
WILL LIST BRANLIEST
Answer:
0.6
Step-by-step explanation:
9÷15=0.6
find the surface area of the prism
Answer: C
Step-by-step explanation:
Length: 6in
Width: 8in
Height: 9in
[tex]A=2(wl+hl+hw)\\A=2[(8in)(6in)+(9in)(6in)+(9in)(8in)]\\A=2(48in^2+54in^2+72in^2)\\A=2(174in^2)\\A=348in^2[/tex]
If Nick used 56 feet of fence to enclose a square garden.How long,in feet was each side of Nicks garden?
Answer:
Each side is 14 ft.
Step-by-step explanation:
If there are 4 equal sides, you divide 56 by 4. That equals 14.
what is the area of the following circle
Answer: 25 pi
Step-by-step explanation:
A group of friends is addressing wedding invitations. Casey can address 20 envelopes in one hour, Anne can address 44 envelopes in two hours, and Paula can address 68 envelopes in three hours. About how long will it take them to address 400 envelopes?
Answer:
Time taken = 6.2 hours
Step-by-step explanation:
Firstly, we will calculate the rate of each person per hour. Then we combine the rates and afterward divide the number of envelope they could address by the combined rate.
Casey can address 20 envelopes at the rate of 20 per hour.
Casey rate = 20 envelope per hr
Anne can address 44 envelope in 2 hours
Anne rate = 22 envelope per hr
Paula can address 68 envelope in 3 hours
Paula rate = 68/3 envelope per hr
Time it will take them to address 400 envelope can be solved below
Add their rate = 20 + 22 + 68/3 = 42 + 68/3 = (126 + 68)/3 = 194/3
Time = 400 ÷ 194/3 = 400 × 3/194 = 1200/194 = 6.1855670103
Time taken = 6.2 hours
Identify domain and range of each function.y=3•5^x
Answer:
Domain- {IR} all real numbers or {infinity,infinity}
Range-{0,infinity}
Step-by-step explanation:
plug into calculator
The cost to rent a dvd has decreased 25% per year over the past several years if the current cost is $2 write an exponential equation describing this situation, what did it cost to rent a DVD 5 years ago
Answer:
y = x(0.75)^t
the cost to rent a dvd 5 years ago is $8.43
Step-by-step explanation:
Let x represent the cost to rent a dvd 5 years ago;
And y the cost to rent a dvd t years after.
The cost to rent a dvd has decreased 25% per year, this can be written as an exponential function;
y = x(100% -25%)^t
y = x(1-0.25)^t
y = x(0.75)^t .....1
if the current cost is $2;
t = 5 years
y = $2
Substituting the values into equation 1;
2 = x(0.75)^5
2 = x(0.2373046875)
x = 2/(0.2373046875)
x = 8.427983539094
x = $8.43
Solve y = x + 6 for x.
A. x = y + 6
B. x = -y + 6
C. x = y - 6
D. x = -y - 6
Answer:
B: x = -y+6
Step-by-step explanation:
Since y = x+6:
Bring x and y to their opposite sides:
x = -y+6
I hope this helps and plz mark me brainliest!!
What is the answer to this
Answer:
im pretty sure it's c
Step-by-step explanation:
Answer:
its C
Step-by-step explanation:
Which describes the error and solve for surface area.
There different ways to think about 1 3/8- 1/1/8. Select three ways to find it
Answer:
1. 1 3/8- 1 /1/8
2. 11/8- 9/8
3. 1 3/8- 9/8
Step-by-step explanation:
A brand of uncooked spaghetti comes in a box that is a rectangular prism with the length of 8 inches width of 2 inches and the height of 1 1/2 inches what is the surface area
Answer:
176
Step-by-step explanation:
Can anyone help me fix the mistakes i made? I will give you brainiest if you do and the teacher tells me its correct.
Answers:
#1: infinite solutions; #2: no solutions
Step-by-step explanations:
Steps for #1
3(2x+7)=13+4(x+2)+2x
6x+21=13+4x+8+2x
6x+21=21+6x
6x=6x
x=x
After completing the steps to find the value of x using Order of Operations, we see that in the end, the answer we have is x=x. We can easily conclude that x is equal to any number because the final answer in this exercise is always whatever the value of x is. For example, if x=4, our final answer would be 4.
Steps for #2
5(6x+8)=9x-10+21x
30x+40=30x-10
40=-10
Here, we see that once we've completed the steps using the Order of Operations, we come out with the answer 40=-10, which is not true on any terms. Therefore we can simply conclude that the answer for #2 is "no solutions."
If you have any trouble figuring out how I got my answers, please refer back to the steps I used to get the answers.
Thank you!
