The rate of change of a function is the increase or decrease that a function experiences as the independent variable changes from one value to another.
The corresponding equation of the average rate of change is:
[tex]TVM(x_1,x_2)=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]In this case, x1 is 3 and x2 is 3
Remember that according to the notation of the limits, they take the values of 2 and 3.
Now, we solve f(3) and f(2)
[tex]\begin{gathered} f(3)=3^2-2\cdot(3)+4 \\ f(3)=9-6+4 \\ f(3)=7 \end{gathered}[/tex][tex]\begin{gathered} f(2)=2^2+2\cdot(2)+4 \\ f(2)=4-4+4 \\ f(2)=4 \end{gathered}[/tex]This way now we can replace the values in the TVM equation and I will solve this.
[tex]\begin{gathered} TVM(3,2)=\frac{7-4}{3-1_{}} \\ TVM(3,2)=\frac{3}{1}=3 \end{gathered}[/tex]In conclusion, the average rate of change of the function
Which fraction and decimal forms match the long division problem? 9) 7.000 6 37 70 63 TO 63 7 O A. 7 9 and 0.7 B. 9 and 0.777 7 O C. c. and 0.7 D. 9 and 0.7 7.
The given fraction is
[tex]\frac{5}{8}[/tex]So, this means, that five is being divided by eight.
So this is best described by option (a) where, five pounds of oats are being divided equally among 8 horses.
Got to put this in a equation for each line
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
equation of the line:
we must analyze the lines to find the solution.
line l:
y = 4
line p:
x = - 4
line m:
point 1 (0 , 4)
point 2 (2, 0)
slope:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\frac{0-4}{2-0}=\frac{-4}{2}=-2[/tex]Slope-intercept form of the line
y = mx + b
y = -2x + 5
line n:
point 1 (5, 4)
point 2 (0 , -1)
slope:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\frac{-1-4}{0-5}=\frac{-5}{-5}=1[/tex]Slope-intercept form of the line
y = mx + b
y = 1x + (-1) = x - 1
The answer is:
line l: y = 4
line m: y = -2x + 5
line n: y = x - 1
line p: x = -4
the question is in the picture. Is B one of the right answers? Is B the only right answer?
To answer this question we first need to notice that the sequence of dots increases by a factor of 3 in each drawing. This means that this is a geometric sequence with common ratio 3.
We know that the nth term of a geometric sequence is given by:
[tex]a_n=a_1r^{n-1}[/tex]where a1 is the first term and r is the common ratio. In this case a1=3 and r=3, hence the nth term is:
[tex]a_n=3(3)^{n-1}[/tex]Now, if we add the first 15 stages, this means that we are adding the first 15 terms of the sequence, then our sum will be of the form:
[tex]\begin{gathered} a_1+a_2+a_3+a_4+\cdot\cdot\cdot+a_{15}_{} \\ =3(3)^{1-1}+3(3)^{2-1}+3(3)^{3-1}+3(3)^{4-1}+\cdot\cdot\cdot+3(3)^{15-1} \\ =3(3)^0+3(3)^1+3(3)^2+3(3)^3+\cdot\cdot\cdot+3(3)^{14} \\ =3(3^0+3^1+3^2+3^3+\cdot\cdot\cdot+3^{14}) \\ =3(1^{}+3^1+3^2+3^3+\cdot\cdot\cdot+3^{14}) \end{gathered}[/tex]Then we notice that option a is a correct expression for the sum of the first 15 stages.
We also know that the sum of the first nth terms of a geometric sequence is given by:
[tex]\frac{a_1(1-r^n)}{1-r}[/tex]plugging the values we know, we have that:
[tex]3\frac{(1-3^{15})}{1-3}[/tex]Therefore option d is also a correct expression for the sum of the first 15 stages.
f(x)=x²-12x + 3 find vertex
The function f(x)=x²-12x + 3 is a quadratic function, the vertex is given as x = -b/2a
f(x)=x²-12x + 3
a = 1, b=-12, c=3
x = -(-12)/2(1)
x = 12/2
x = 6
to get the y-coordinate, substitute x = 6 into f(x)
f(6) = 6²-12(6) + 3
= 36-72+3
=-33
the coordinate of the vertex is (6, -33)
what is the greatest common factors of these numbers? 12 3
Answer:
The GCF of 12 and 3 is 3.
Step-by-step explanation:
The answer is 3 because you have to find the common factors of each and see which one they both have in common, and are the biggest:
The factors of 12 are:
1, 2, 3, 4, 6, and 12.
The factors of 3 are:
1, and 3
Thus, the GCF is 3.
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complete the sentence to make it true 0.5 is 1/100 of?
to find 0.5 is 1/100 of what ?
[tex]50\times\frac{1}{100}=0.5[/tex]the answer is 50.
Use the general multiplication rule to solve for the given probability model. For events A and B, calculate P(A∩B) given the following information: P(B)=0.70 and P(A I B)=0.45
21, 16, 11, 6 , ...The next 3. Terms would be ?And is an = an-1 - 5 a recursive or explicit?
Answer:
Step by step solution:
This is an arithmetic sequence a, a+d, a+2d, a+3d, ..., where a is the initial term and d the common difference.
For 21, 16, 11, 6, ....
The initial term a = 21 and the common difference is d = 5, then the next 3 terms are
21, 16, 11, 6, 1, -4, -9. This representation is explicit
The mean number of employee sick days used per week at a company is 6.4 with a standard deviation of 1.5 days. What proportion of weeks would you expect to have more than 7 employee sick days used?
Given the z-score formula,
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \text{Where x =7} \\ \mu=6.4\text{ and} \\ \sigma=1.5 \\ z=\frac{7-6.4}{1.5}=\frac{0.6}{1.5}=0.4 \end{gathered}[/tex]Given the z-score of 0.4
Question 3(Multiple Choice Worth 1 points)(02.01 LC)Which of the following tables represents a function?Ox 11 22y 3-34-4Ox2-2-2y 1 2340X 3 -3 2-2y 2 25 5x 4 477y 9876
In a function, every x-value must be associated with only one y-value.
In the first table, we can see that the x-value x = 1 has two different y-values associated, y = 3 and y = -3. Then, this table doesn't represent a function.
Similarly, in the second table, x = 2 and x = -2 each have two y-values associated, and in the fourth table, x = 4 and x = 4 each have two y-values associated. Therefore, they are not functions.
On the other hand, in the third table, there is only one y-value associated with each x-value. In consequence, it is a function.
Simplify. Assume that all variables result in nonzero denominators.
The value of the given expression is (5p+3)/ p
A fraction is a portion of a larger total. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator. A suitable fraction has a numerator that is less than the denominator.
Given (6p/p+1) – (p-3/9) + (6/p+1)
We have to simplify the given expression
(6p/p+1) – (p-3/9) + (6/p+1)
(6p2 – (p-3)(p+1) + 6p)/p(p+1)
(6p2 – (p2-3p + p - 3) + 6p)/p(p+1)
(6p2 – p2n + 3p - p + 3 + 6p)/p(p+1)
(5p2 + 8p + 3)/p(p+1)
(5p+3)(p+1)/ p(p+1)
(5p+3)/ p
Therefore the value of the given expression is (5p+3)/ p
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f(x)=3x+4 Evaluate f(2)=
We will look at how to evaluate a function for one of the value from a defined domain.
Domain is a set of values over which the function is defined. These are set of values of ( x ) that serves as an input to the function.
Function expresses an input -> output relationship usually expressed as an amalgam of different mathematical expressions. The function evaluates the output for every set value of ( x ) from the domain. The mathematical expressions ( relationships ) are given in terms of the input variable(s).
We are given the following function as follows:
[tex]f\text{ ( x ) = 3x + 4}[/tex]The above functions isd efined for all the real values. Hence, the domain of the above function is defined as:
[tex]\text{\textcolor{#FF7968}{Domain:}}\text{ x :-> ( -}\infty\text{ , }\infty\text{ )}[/tex]We will evaluate the above function for one of the values from the domain. We will plug in the value of input ( x = 2 ) into the function. Then we will evaluate the function f ( x ) as follows:
[tex]\begin{gathered} f(2)\text{ = 3}\cdot(2)\text{ + 4} \\ f(2)\text{ = 6 + 4} \\ \textcolor{#FF7968}{f(2)}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{10} \end{gathered}[/tex]Hence, the function is evaluated for the input value of ( x = 2 ) and the ouput is:
[tex]\textcolor{#FF7968}{10}[/tex]I solved part C I just need help with part D
1) Gathering the data
8% sales tax
2 DVDs' price: $21.60 (after taxation)
2) To find out how much for the DVDs without the sales tax, let's write this equation.
P for the price without tax, 1.08 the sales tax factor, $21.60 the full price
p (1.08) =21.60 Let's divide both sides by 1.08
p= 21.60 /1.08
p= 20
3) So the price without tax, is $20
What is the range of the function shown on the graph?уO642-6X-4- 226826-8OA -00
SOLUTION
Looking at the graph, the range is from - 6 on the y-axis and from there going upwards the y-axis. That is y at - 6 to infinity.
So, the range is
[tex]-6So, the correct answer is option B.
Solve: 2(1 - 5k) = 2k + 38
k=-3
1) Let's solve for k, the following expression:
2(1 - 5k) = 2k + 38 Distribute the factor 2
2 -10k = 2k +38 Subtract 2 from both sides and 2k
-10k -2k = 38 -2
-12k = 36 Divide by -1
12k=-36 Divide both sides by 12
k= -3
2) So k is equal to -3 in this equation.
You pick a card at random. Without putting the first card back, you pick a second card at random. 7 8 9 What is the probability of picking an 8 and then picking a prime number? Simplify your answer and write it as a fraction or whole number.
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]To quality for a police academy, applicants are given a lest of physical fitness. The scores are normally distributed with a mean of 64 and a standard deviation of 9. If only the top 20% of the applicants are selected, find the cutoff score.
ANSWER
[tex]71.56[/tex]EXPLANATION
Parameters given:
Mean, μ = 64
Standard deviation, σ = 9
To find the cutoff score, we want to find the score that has a corresponding z-score which represents the top 20% of the data.
To do this, first, we have to subtract 20% from 100%:
[tex]\begin{gathered} 100-20 \\ \Rightarrow80\% \end{gathered}[/tex]Now, we have to use the standard normal table to find the z score that corresponds to the closest value to 80% (0.80) on the standard normal table i.e. P(x > 80).
From the table, we see that the z-score that corresponds to 0.80 (0.79955 from the table) is 0.84.
Now, using the formula for z-score, find the cutoff score:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x = cutoff score
Solving for x, we have that:
[tex]\begin{gathered} 0.84=\frac{x-64}{9} \\ \Rightarrow0.84\cdot9=x-64 \\ \Rightarrow x-64=7.56 \\ \Rightarrow x=64+7.56 \\ x=71.56 \end{gathered}[/tex]That is the cutoff score.
a scratching post for a cat is in the shape of a cylinder. if you have had to find the amount of carpeting needed to completely cover the post which formula would you useC=2πRSA=2πRH+2πR^2V= πr^2h
The scratching post is in the shape of a cylinder.
To cover the scratching post with a carpet, the surface of the post has to be covered.
This means that the amount of carpeting to be used will be equal to the total surface area of the pole.
The total surface area of the pole is calculated using the formula:
[tex]SA=2πrh+2πr^2[/tex]where r is the radius of the pole and h is the height of the pole.
The SECOND FORMULA is correct.
Find the slope, m of the line that passes through the points 3 83 - .) and (1) 6. -5 16' 6 Enter your answer as a fraction in simplest form in the box.
Given:
The points on the line are,
[tex](\frac{3}{8},-\frac{1}{4})\text{ and (-}\frac{5}{16},\frac{1}{6})[/tex]The slope of the line is calculated as,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(\frac{3}{8},-\frac{1}{4}) \\ (x_2,y_2)=\text{(-}\frac{5}{16},\frac{1}{6}) \\ m=\frac{\frac{1}{6}-(-\frac{1}{4})}{-\frac{5}{16}-\frac{3}{8}} \\ m=\frac{\frac{2}{6\times2}+\frac{3}{4\times3}}{-\frac{5}{16}-\frac{3\times2}{8\times2}} \\ m=\frac{\frac{2+3}{12}}{\frac{-5-6}{16}} \\ m=\frac{5}{12}\times\frac{16}{-11} \\ m=-\frac{20}{33} \end{gathered}[/tex]Answer: slope is -20/33
y < 2x33y<--2-2Which graph represents the system of inequalities?Choose 1 answer:y42А→ 224
Graphing the inequalities:
From the options provided, the correct one is C
Answer:
C
Solve, then identify whether it is an identity or a contradiction. 4(2-3t)+6t= -6t+8
To solve the given equation, we first apply the distributive property of multiplication and reduce like terms:
[tex]\begin{gathered} 4(2-3t)+6t=-6t+8, \\ 8-12t+6t=-6t+8, \\ 8-6t=-6t+8. \end{gathered}[/tex]Now, we notice that the left and the right side of the equation are equal for any choice of t.
Answer: Identity.
Part A: On one day, the exchange rate model might be B = 0.60A with the parameter k = 0.60.
Under these conditions, an American tourist exchanging US$ 11 would receive £
Round to the nearest hundredth, if necessary.
Part B: Under those same conditions, an English tourist exchanging £ 11 would receive US$
Round to the nearest hundredth, if necessary.
The amount of money each tourist will get:
Part A: The American tourist exchanging US$ 11 would receive £6.60.
Part B: The English tourist exchanging £ 11 would receive US$ 18.33.
We are given a relation in terms of algebraic expression:
B = 0.60A
We need to find the money of tourists after exchanging.
Part A:
The American tourist exchanged US$ 11.
substitute the value A = 11 in the given expression, we will get:
B = 0.60 * 11 = 6.60
So, the American tourist will get £6.60.
Part B:
The English tourist exchanged £ 11.
substitute the value B = 11 in the given expression, we will get:
11 = 0.60A
A = 11 / 6.60
A = 18.33333
A = 18.33
So, the English tourist will get US$ 18.33.
Thus, the amount of money each tourist will get:
Part A: The American tourist exchanging US$ 11 would receive £6.60.
Part B: The English tourist exchanging £ 11 would receive US$ 18.33.
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The inequality 2c−3<9 represents the amount of money a student can spend on c candy bars. Select the values that best complete the sentence. The solution to the inequality is , and it represents that the student can buy a maximum of whole candy bars.
Answer:
Step-by-step explanation:
1. 2c-3<9
2. 2c<9+3
3. 2c<12
4. c<6
5. c can be: 5,4,3,2,1,0,-1,-2,-3 and so on(infinite solutions)
6. The solution to the inequality is 5, and it represents that the student can buy a maximum of 5 whole candy bars.
can u help me with this question
You have a case in which you have the probability of obtaining six different results: 1, 2, 3, 4, 5 and 6
The probaility of getting a specific number is given by the formula:
p = 1/n = 1/6
where n is tha number of different cases, which is 6.
To calculate the probability of getting two results, you have to multiply the probability of one result with the probaility of the other one.
The probability of getting a 4 is:
1/6
The probability of getting a 3 is:
1/6
Then, the probaility of getting the two previous results is:
P = (1/6)(1/6) = 1/36
Write an equation for the line that passes through the point (2,2) and is perpendicular to -8x+y=8. Use slope-intercept form.
Ok, first of all, let's put the equation of the line in the slope-intercept form:
-8x+y=8
y=8x+8
The slope of this line is m=8.
The slope of a perpendicular line is the negative reciprocal of the slope of the first line, so:
m2=-1/8
Now let's calculate the equation of the perpendicular linbe, using the given point, (2,2):
y-y1=m*(x-x1)
y-2 = -1/8(x-2)
y-2=-1/8x + 2/8
y=-1/8x +2/8 +16/8
y=-1/8x + 18/8
y= -1/8x + 9/4
The equation will be y= -1/8x + 9/4
Mrs. Hamilton is trying to plan a party for her math classes and receive two quotes. The Hypotenuse Hall
charges $100 for a damage deposit and $6 per per person for snacks. The Pi Place charges only $20 for a
damage deposit but $10 per person for snacks. Mrs. Hamilton needs your help!
The hypotenuse hall will be cheaper .
Both places charge $200 for 20 people .
The linear system of equation gives C = 20 + 10 n
Where ,
C = total cost
N = number of cost
What is linear system of equation?A system of linear equations in mathematics is a grouping of one or more linear equations that share the same variables. A collection of one or more linear equations involving the same variables is known in mathematics as a system of linear equations (or linear system). A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display significantly simpler traits and properties. A line equation is referred to as a linear equation. Or, for example, y + 0.5x 3.5 = 0 and more. The linear equation in each case is the same (remember this!) When two or more linear equations cooperate, this is known as a system of linear equations.
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A) If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is: B) If half of the passengers are men, find the probability that the mean height of the men is less than 74 in. C) When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? D) When considering the comfort and safety of passengers, why are women ignored in this case?
Hello there. To solve this question, we'll have to remember some properties about probabilities.
Selecting male passengers randomly from the 400 passengers set, we want to find the probability that he can fit through the 74 in doorway without bending.
First, calling x the height of the random selected man, the probability of him fitting is P(x <= 74), and of him not fitting is P(x > 74)
To find P(x <= 74), we calculate the z-score by the formula:
[tex]z=\frac{x-\mu}{\sigma}=\frac{74-69}{2.8}=\frac{5}{2.8}\approx1.78[/tex]Looking for a table of z-scores for a normally distributed set, we say that the probability is around 95 or 96%. Using the under 8 approximation, P(x <= 74) = 0.96246 or 96.25%.
part (b)
We now have that the sample size is 200, since we had 400 passengers on the flight.
Making the new standard deviation as:
[tex]s=\frac{\sigma}{\sqrt[]{\text{sample}}}=\frac{2.8}{\sqrt[]{200}}=0.198[/tex]From the Central limit theorem, the z-score will then be:
z = (74 - 69)/0.198 = 25.25
-9x² - 4 + 6x + 11x² - 7x
ANSWER
2x² - x - 4
EXPLANATION
To solve this we have to add like terms:
[tex]-9x^2-4+6x+11x^2-7x[/tex]Like terms are those that have x with the same power:
[tex](-9x^2+11x^2)+(6x-7x)-4=2x^2-x-4[/tex]Solving a percent mixture problem using a linear equationLaurIn the lab, Chris has two solutions that contain alcohol and is mixing them with each other. He uses 200 milliliters less of Solution A than Solution B. Solution Ais 12% alcohol and Solution B is 18% alcohol. How many milliliters of Solution B does he use, if the resulting mixture has 126 milliliters of pure alcohol?
Step 1: Let solution A be A
Let solution B be B
If he uses 200 milliliters less of A than B, then
[tex]undefined[/tex]The circumference of a circle is 13π in. What is the area, in square inches? Express your answer in terms of pie.
The circumference (C) of a circle with radius r is:
[tex]C=2\pi r[/tex]Given the measure of the circumference (13π in), first, let's substitute it in the equation find r:
[tex]\begin{gathered} 13\pi=2\pi r \\ \text{ Dividing both sides by 2}\pi\text{:} \\ \frac{13\pi}{2\pi}=\frac{2\pi}{2\pi}r \\ \frac{13}{2}=r \\ r=\frac{13}{2}\text{ in} \end{gathered}[/tex]The area (A) of a circumference with radius r is:
[tex]A=\pi r^2[/tex]Knowing r, substitute it to find A:
[tex]\begin{gathered} A=\pi r^2 \\ A=\pi *(\frac{13}{2})^2 \\ A=42.25\text{ in}^2 \end{gathered}[/tex]Answer: Area = 42.25 in².