Answer:
The average rate of change of the function over the interval is 5.
Step-by-step explanation:
Average rate of change of a function:
The average rate of change of a function f(x) over an interval [a,b] is given by:
[tex]A = \frac{f(b)-f(a)}{b-a}[/tex]
Interval -3 less-than-or-equal-to x less-than-or-equal-to 3
This means that [tex]a = -3, b = 3[/tex]
[tex]f(x) = x^2 + 3x + 6[/tex]
So
[tex]f(b) = f(3) = (3)^2 + 3(3) + 6 = 9 + 9 + 6 = 24[/tex]
[tex]f(a) = f(-3) = (-3)^2 + 3(-3) + 6 = 9 - 9 + 6 = 6[/tex]
Average rate of change
[tex]A = \frac{f(b)-f(a)}{b-a} = \frac{24+6}{3-(-3)} = \frac{30}{6} = 5[/tex]
The average rate of change of the function over the interval is 5.
Suppose that of 2000 students, 1100 take math, 500 take science, and 300 students take both math and science. What is the probability that a student selected at random takes math or science?
Answer:
4/5
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
probability that a student selected at random takes math or science = probability a student takes maths + probability a student takes science
probability a student takes maths = number of maths students / total number of students
probability a student takes science = number of science students / total number of students
(500 / 2000) + (1100 / 2000) = 1600/2000 = 4/5
CAN SOMEONE PLEASE HELP ME I'M STUCK. PLEASE
I don't understand and know how to solve it.
Answer:
7/10
Step-by-step explanation:
red + green = 50 + 20 = 70 marbles
Total marbles = 50 + 30 + 20 = 100 marbles
P(red or green) = 70/100
P(red or green) = 7/10
The graph of f(x) = 2x2 + x – 15 passes through the point (0, –15) and one of its zeros is (2.5, 0). What is the other zero of the function?
Answer:
x=-3
Step-by-step explanation:
Given the numbers 24 and 18 as legs of a right triangle, what is the length of the hypotenuse? Round your answer to the nearest tenth (1 decimal place)
Help plz..And No links!! I repeat No links!!
A garden table and a bench cost 816 combined. The garden table costs 84 less than the bench. What is the cost of the bench?
Answer:
366
Step-by-step explanation:
A garden table and bench cost 816 when combined together
The garden table cost 84 less than the bench
Therefore the price of the bench can be calculated as follows
x + (x+84)= 816
2x+84= 816
2x= 816-84
2x= 732
Divide both sides by 2
x= 732/2
= 366
Hence the price of the bench is 366
help me please and thank you.
Answer:
$127
Step-by-step explanation:
Ur welcome :)
Someone help me with this ASAP pls . I need to know “how do we know that <3~=<6
Answer:
Alternate Interior Angles
Step-by-step explanation:
They are alternate interior angles. The reason this works is because 4 is opposite to 3, meaning that 4 is equivalent to the value of (180-Angle3)
Meanwhile 6 is equivalent to (180-Angle5). Angle 5 is the same value is Angle 4.
PLZ HELP!!!
Explain how you would solve this problem. (Use words!!)
4(x +3) = 3(x - 12)
Answer:
4(x+3)=3(x-12)
=4x + 12= 3x - 36
= 4x- 3x= -36 - 12
= x = -48
If equation is x + y = 3 and x - y = 7 then the value of x will be?
A) 0
B) -3
C)-2
D)2
Its on the topic Simultaneous equations
Answer:
x = 5
Step-by-step explanation:
Add the equations
x + y = 3
x - y = 7
––––––––
2x = 10
Divide both sides by2
x = 5
Note: for the equations in the question,
none of the given answers are correct.
Complete each statement by circling the correct answer based on the figure
below
M
a. One small triangle is what portion of the figure?
1 fourth
1 half
1 third
n
b. One square is what portion of the figure?
1 fourth
1 half
1 whole
ИИ
One rectangle that is not a square is what portion of the figure?
1 half
1 fourth 1 whole
Answer:
a. 1 fourth
b. 1 half
c. 1 whole
17.
Write the equation in standard form. Then factor the left side of the equation.
2x2 + 7x = 15
A. (2x – 5)(x + 3) = 0
B. (2x + 3)(x + 5) = 0
C. (2x – 3)(x + 5) = 0
D. (2x + 5)(x – 3) = 0
Answer:
C. (2x – 3)(x + 5) = 0
Step-by-step explanation:
The equation in standard form should be 2x^2 + 7x - 15 = 0
Factored the expression is (2x - 3)(x + 5).
In order to find the factored portion, you must look for factors of the front number (2) to use in the front of the parenthesis and factors of the last number (-15) to go in the end.
When we use the ones that we have above, it distributes to the overall end result.
(2x - 3)(x + 5)
2x^2 - 3x + 10x - 15
2x^2 + 7x - 15
Con someone help me with questions 3 and 4
Answer:
t = 13 hours
The values will be equal in 10 years.
Step-by-step explanation:
Three
There are two ways to do this problem. I'll do it the simplest way -- which will benefit you most if you are about to take a physics class.
Follow these observations.
The difference of speed of these two cars is 70 - 65 = 5 mphThe distance travelled by the first car before the second one starts is 65 miles in 1 hour. That comes about because Tom goes 65 miles before Michelle even starts. She starts exactly 1 hour after Tom and he has gone 65 miles in that time.She is going faster, but he is still moving. That's what makes the problem hard.Fortunately, you don't have to figure that out. You have all the information you need.Solution
Time it takes to Catch Tom = distance to be made up / difference in speed
Distance to be made up = 65 miles
Difference in speed = 5 mph
Time taken for michelle to catch Tom = t
t = 65/5
t = 13 hours.
Solution Two
The distance is the same when Michelle catches Tom
d = r*t
Michelle's rate = 70 mph
Michelle's time = t
Tom's rate = 65
Tom's Time = t + 1
70 * t = 65(t + 1)
70 * t = 65*t + 65
70*t - 65*t = 65
5t = 65
t = 65/5 = 13
In thirteen hours, Michelle will catch Tom
Four
One house increases by 10000 the other decreases by 5000. You could do it using the first method above, but in this case the second is actually easier.
Juan: 200000 + 10000*t
Tia : 350000 - 5000t
When will the be equal (at what price and when?).
200000 + 10000t =350000 - 5000t Divide by 1000
200 + 10t = 350 - 5t Add 5t to both sides
200 + 10t + 5t = 350 Combine
200 + 15t = 350 Subtract 200 from both sides
15t = 150 Divide by 15
t = 150/15
t = 10 years
How many times larger than
(15 + 10) is 8 x (15 + 10)?
Answer:
8 times larger
Step-by-step explanation:
(15+10) is the singular equation alone. Muiltiply it by 8, and it's 8 times larger then the initial singular expression. Therefore, the answer is 8 times larger.
Solve for f
-5f + 5 < 15
-------------------
A: f < 2
B: f < 8
C: f > -2
D: f = 3
Answer:
f>-2
Step-by-step explanation:
-5f+5<15
Isolate f
-5f<10
Isolate
-f<2
Because f is negative we have to flip the sign
f>-2
If this helps please mark as brainliest
cuanto es la mitad de 2 mas 2
Answer:
2+(2÷2)
2+1
3
La respuesta es 3 :)
Answer:
la mitad de dos mas dos es 2
Step-by-step explanation:
2+2= 4 la mitad de cuatro es 2
espero que ayude y diganme si me equivoque no entendi mucho la pregunta
porfavor denme brainslet o thanks me ayuda mucho que tengan un buen dia
Find the equation of the line that passes through (2,7) and (7,12)
Answer:
equation of the line that passes through (2,7) and (7,12) is y=x+5
HURRY PLEASE!!!!
Describe the transformation that was performed on parallelogram EFGH to create parallelogram E'F'G'H'. Show or explain how you got your answer.
Answer: 4'6 2'4
Step-by-step explanation:
A DVD has a diameter of 15 millimeters. Which equation would help you determine the circumference?
Answer:
Step-by-step explanation:
radius =diameter/2
=15/2
=7.5 mm
circumference=2πr
=2*3.14*7.5
=47.1 mm
The equation that can be used to determine the circumference of the DVD is π15.
What is the circumference of a circle?
The DVD has the shape of a circle. The circumference of a circle is the distance round the circle. The diameter of a circle is a straight line that touches two points on the circumference of a circle and also passes through the center.
The circumference of a circle = πD
Where:
d is the diameter
To learn more about how to determine the circumference of a circle, please check: https://brainly.com/question/14351152
please I need it urgent
Answer:
Step-by-step explanation:
Hope this helps u !!
Step-by-step explanation:
[tex] \frac{ {x}^{a + b} \times {x}^{b + c} \times {x}^{c + a} }{ {x}^{2a} \times {x}^{2b} \times {x}^{2c} } \\ \\ = \frac{ {x}^{a + b + b + c + c + a} }{ {x}^{2a + 2b + 2c} } \\ \\ (∵ {x}^{m} \times {x}^{n} = {x}^{m + n} ) \\ \\ = \frac{ {x}^{2a + 2b + 2c} }{ {x}^{2a + 2 b+ 2c} } \\ \\ = 1[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]
5,126 divided by 12 with remainder
Solve for X
Solve for X
Solve for X
Answer:
we know that 8+6x=30+4x+2
2x=24
x=12
pls mark as brainliest
Answer:
[tex]\bf x=12[/tex]Step-by-step explanation:
By applying the Exterior angle theorem.
[tex]\bf 30+4x+2+8+6x[/tex]
[tex]\bf 4x+30+2=8+6x[/tex]
[tex]\bf 4x+32=8+6x[/tex]
[tex]\bf 4x+32-32=8+6x-32[/tex]
[tex]\bf 4x=6x-24[/tex]
[tex]\bf 4x-6x=6x-24-6x[/tex]
[tex]\bf -2x=-24[/tex]
[tex]\bf \cfrac{-2x}{-2}=\cfrac{-24}{-2}[/tex]
[tex]\bf x=12[/tex]
___________________14cm and 31cm and 34cm equal
Answer:
if its addition then it will be 79cm
z = 3. & y = 6
Evaluate the
expression: Y - Z
Answer:
6-3=3
3 is the answer because they gave you the value of Y and Z then they asked you to subtract
48 POINTS!! ANSWER QUICK AND ASAP PLEASE!! EVERYBODY IT'S A IMPORTANT TEST.
There are four sixth graders and seven seventh graders in Elsa's chess club. Two members of the club will be chosen at random to attend a tournament with several other chess clubs. Elsa is using simulation to determine the experimental probability of randomly selecting two sixth graders. So, she places four red discs (to represent the sixth graders) and seven blue discs (to represent the seventh graders) in a bag. She randomly selects one disc from the bag, records the color, keeps the disc out, selects another disc and records it, and then returns both discs to the bag. Elsa does this twenty-five times. Her results are shown in the table below.
b, b b, r b, r b, b r, b
b, r b, b b, r b, r r, b
r, b r, r b, r r, b b, r
b, b r, r b, r r, r r, b
b, b r, r b, b r, r b, r
Based on the results of Elsa's simulation, the experimental probability of randomly selecting two sixth graders is [ INSERT AN ANSWER HERE ]
the theoretical probability of randomly selecting two sixth graders.
A. equal to
B. greater than
C. less than
Answer:
A.equal to
Step-by-step explanation:
thats the answer correct me if you want
the total of a number m and a number n
Answer:
m+n
Step-by-step explanation:
math pls pls help help no trolls i really need this grade
Answer:
The second one is 3 and the third one is 8
Step-by-step explanation:
Just trust me
Ravi is 8 years older than nastasha the sum of their ages is 42 find their ages
Answer: Natasha is 17 and Ravi is 25
Step-by-step explanation:
Let n = Natasha’s age and r = Ravi’s age
We can write an equation then substitute: 42=n+r
We know that Ravi is 8 years older than Natasha, so Ravi’s age is equal to n+8. We can substitute that in, so 42= n+(n+8)
Simplify:
42=n+(n+8)
42= 2n+8
42-8=2n+8-8 (subtract 8 from both sides to isolate n)
34=2n
34/2=2n/2 (divide both sides by two)
17=n
Natasha is 17, and Ravi is 8 years older. 17+8= 25, Ravi is 25. You can double check by adding 25 and 17 together, which brings you back to 42 :]
Averigua el número que cumple la siguiente condición: si se multiplica su sucesor por el número disminuido en 3 unidades se obtiene 77
Answer:
X=10
X=-8
Step-by-step explanation:
(x+1)*(x-3)=77
x²-3x+x-3=77
x²-2x-3=77
x²-2x-3-77=0
x²-2x-80=0
(x-10)*(x+8)=0
x-10 = 0
x=10
x+8=0
X=-8
The two possible numbers that satisfy the given equation model are -8 and 10.
What is a expression? What is a mathematical equation? What is Equation modelling ?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is the successor of a number, when multiplied by the number decreased by 3 units, 77 is obtained.
Assume the number to be [x]. Its successor would be [x + 1]. Then, we can write -
(x + 1)(x - 3) = 77
Refer to the graph attached. The [x] - intercepts the solution. We get -
x = - 8
x = 10
Therefore, the two possible numbers that satisfy the given equation model are -8 and 10.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ2
[Refer to question in english -
Find the number that meets the following condition: if its successor is multiplied by the number decreased by 3 units, 77 is obtained.]
SOMEONE PLEASE HELP ME WITH THIS ITS DUE TONIGHT
I NEED TO HAVE A SCORE OF 68 AND IM AT 32 RIGHT NOW IM SO CLOSE
You can transform ⨀X to ⨀X' by translating it and then performing a dilation centered at X'. Find the translation rule and the scale factor of the dilation.
Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number.
Answer:
The scale factor is 3 and the translation is (-8,2)
Step-by-step explanation:
(I'm not very good at translation/dilation but since you asked, I'm pretty sure this is the answer!)