The average rate of change of the function is: 0
What is average rate of change?You should know that average rate of change is also referred to as the slope of the function
At point where x = -8, the value of f(-8) = -10 and
At x = -1, the value of f(-1) = -10
We have to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ -1.
When x₁ = -8, f(x₁) = f(-8) = -10 also
when x₂ = -1, f(x₂) = f(-1) = -10
This implies that
Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]
= [f(-1) - f(-8) ] / [-1-(-8)]
= [-10 - (-10)] / [-1+8]
= [-10 + 10] / 7
= 0 / 7
= 0
In conclusion, 0 is the average rate of change which is also the slope of the function
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2 Would the percent change be greater than or less than 50%
if the plants had grown to 8 inches instead of 9? Lesson 13
Answer: Less than
Step-by-step explanation:
The percent change is exactly what it sounds like, the percent that changed. and 1/9 is less that 4.5/9 (half of 9) so it is less than
The number of crimes that occurred in a certain city per 1000 people had decreased from 46.1 in 1920 to 45.3 in 1940. Find the average rate of change in the number of crimes per 1000 people that occurred from 1920 to 1940.
Answer:
-0.04 = decrease of 4%
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$\dfrac{f(b)-f(a)}{b-a}$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}[/tex]
Given interval:
1920 ≤ x ≤ 1940Therefore:
a = 1920b = 1940Given values:
f(a) = f(1920) = 46.1f(b) = f(1940) = 45.3Substitute the values into the formula:
[tex]\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(1940)-f(1920)}{1940-1920}\\\\&=\dfrac{45.3-46.1}{1940-1920}\\\\&=\dfrac{-0.8}{20}\\\\&=-0.04\end{aligned}[/tex]
Therefore, the average rate of change was -0.04 which is a decrease of 4%.
Gavin has a deck that measures 6 feet by 3 feet. He wants to increase each dimension by equal lengths so that its area is tripled. By how much should he increase each dimension?
You are treating two of your friends to the movies tonight. Your parent gives you $70.
Tickets are $7 each. At the candy counter, you are buying snacks and drinks for your
friends as they find seats. Snacks are $2 each, and drinks are $2.25. You are trying to
decide what combination of snacks and drinks are possible given the money remaining.
You can only carry 4 drinks on a tray by yourself.
a. Write a system of inequalities for this situation, using x for the number of
snacks and y for bottles of water purchased.
b. Graph the system and find the vertices.
c. Indicate on the graph what combinations of snacks and drinks are possible.
Explain your reasoning in-depth.
d. Does every point within the feasible region represent a valid solution in this
context? Why or why not?
e. Denote one combination that is possible and one that is not. Explain your
reasoning.
f. Prove each of your answers to part (e) algebraically.
Please tell me each one of these answers! Thx
a. The system of inequalities for this situation can be represented as:
x (number of snacks) ≥ 0
y (number of bottles of water) ≥ 0
2x + 2.25y ≤ 70 (total amount of money remaining)
y ≤ 4 (maximum number of bottles of water that can be carried on a tray)
7x + 7y ≤ 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)
b. To graph the system, we can start by plotting the inequality 2x + 2.25y ≤ 70. This represents all the points that satisfy the inequality and forms a boundary line for the feasible region. The line will be a boundary line because it is less than or equal to 70.
We can plot the inequality y ≤ 4 as a horizontal line at y = 4. This represents the maximum number of bottles of water that can be carried.
Finally, we can plot the inequality 7x + 7y ≤ 70 as a boundary line. This represents the total cost of tickets and snacks/drinks that cannot exceed the amount given.
The feasible region will be the area between these lines, above the x-axis and y-axis, and below the line y=4.
The vertices of this feasible region will be the intersection points of the three lines, which are (10,0), (0,10) and (8,4)
c. The combinations of snacks and drinks that are possible are the ones that fall within the feasible region. Any point within the feasible region represents a valid solution in this context, because it satisfies all the constraints and is within the budget.
d. Every point within the feasible region represents a valid solution in this context, because it satisfies all the constraints and is within the budget.
e. One possible combination is (8,4) which is 8 snacks and 4 bottles of water, this combination is possible because it's within the feasible region and satisfies all the constraints. One combination that is not possible is (12,3), it's not possible because it's not within the feasible region and doesn't satisfy the constraint y ≤ 4.
f. To prove that the combination (8,4) is possible, we substitute these values into the system of inequalities:
2(8) + 2.25(4) = 35 ≤ 70 (total amount of money remaining)
4 ≤ 4 (maximum number of bottles of water that can be carried)
7(8) + 7(4) = 56 ≤ 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)
To prove that the combination (12,3) is not possible, we substitute these values into the system of inequalities:
2(12) + 2.25(3) = 30.5 > 70 (total amount of money remaining)
3 > 4 (maximum number of bottles of water that can be carried)
7(12) + 7(3) = 63 > 70 (total cost of tickets and snacks/drinks cannot exceed the amount given)
As all the inequalities are not satisfied, the combination (12,3) is not possible.
What is system of inequalities?A system of inequalities is a set of two or more inequalities that must be satisfied simultaneously. It is a way to represent a set of constraints using mathematical equations. These constraints can be related to a problem in a specific area, such as finance, engineering, or operations research. The solution set of a system of inequalities is the common set of solutions that satisfy all the inequalities in the system. The solutions can be represented graphically as a region in a coordinate plane called the feasible region, which is the set of all possible solutions.
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Loren and Julie have different part time jobs after school. They are both paid at a constant rate of dollars per he
The table below show Loren and Julie's total income (amount earned) for working a given amount of time.
Loren
Hours 2 4 6 8 10 12 14 16 18
Dollars 18 36 54 72 90 108 ? ? 162
Julie
Hours 3 6 9 12 15 18 21 24 27
Dollars 36 ? 108 144 180 216 ? 288 324
How much money would Julie eam for working 16 hours?
Since Julie earns a constant rate of $12 per hour, for working 16 hours based on mathematical operations, she will earn $192.
What are mathematical operations?The basic mathematical operations involve addition, subtraction, division, and multiplication.
These operations combine parts of the mathematical operations with their assigned operands and the equation symbol (=) to solve mathematical problems.
In this situation, we employ division and multiplication operations to solve the requirement.
Loren and Julie's Total Income Table
LorenHours 2 4 6 8 10 12 14 16 18
Dollars 18 36 54 72 90 108 ? ? 162
Loren's Constant Rate of Pay (Hourly Rate) = $9 ($162/18)
JulieHours 3 6 9 12 15 18 21 24 27
Dollars 36 ? 108 144 180 216 ? 288 324
Julie's Constant Rate of Pay (Hourly Rate) = $12 ($324/27)
Total hours worked = 16
Total earnings = $192 ($12 x 16)
Thus, when Julie works 16 hours, she earns $192.
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√2x + 4 - √x = 2
please solve the solution and show how
Answer: x = 0, 16
Step-by-step explanation:
First square both sides
(sqrt2x+4 - sqrtx)^2 = 4
now distribute the inside using the (a-b)^2 = a^2 -2ab + b^2 property to get
2x+4 - (2sqrt 2x^2 +4x) + X = 4
3x=2sqrt 2x^2 +4x
9x^2 = 4(2x^2+4x)
9x^2 = 8x^2+16x=0
x^2-16x=0
x(x-16)=0
x=0, 16
For what values of m does the graph of y = mx²-5x-2 have no x-intercepts?
25
8
Om>
Om<-
25
8
25
Om 8
Om>
25
The values of m in the graph of y = mx²-5x-2 have no x-intercepts are
m< 25/8.
What is the x-intercept?A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.
Given a function y = mx²-5x-2 for not having the x-intercepts means that at any value of m function can not have the value zero or in other words function would not have any roots.
Thus for not having any root b² - 4ac < 0
For our function
a = m
b = -5
c = -2
substituting the values in the general formula
(-5)² - 4 * m * -2 < 0
25 + 8m< 0
m < 25/ 8
Therefore, The values of m are m 25/8 on the graph of y = mx2-5x-2, which has no x-intercepts.
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can someone look at this please? it’s due in like five minutes
The inequality equations for the rides High-Bounce, Climb-A-Thon, and Twirl-O-Coaster are 55<h<7, h<60, and h>=58 respectively.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.
Let the unknown height be h.
For the ride High-Bounce, the height requirement is between 55 and 72 inches tall.
This can be written in the inequality form as 55<h<72.
For the ride Climb-A-Thon, the height requirement is under 60 inches tall.
This can be written in the inequality form as h<60.
For the ride Twirl-O-Coaster, the height requirement is 58 inches minimum.
This can be written in the inequality form as h>=58.
The representations of these inequalities on number lines is given below.
Therefore, the inequalities are - 55<h<7, h<60, h>=58.
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Raymond wants to know the costs of buying different numbers of songs for his MP3 player. The cost of each song is the same.
• Let s represent the possible number of songs Raymond could buy.
• Let d represent the amount of money, in dollars, Raymond would need to buy the songs.
Fill in the table for all missing values of s and d.
Number of songs, s
Amount of money ($), d
2
2.58
5.16
7
11
21.93
The table for all missing values of s and d should be completed as follows;
Number of songs, s Amount of money ($), d
2 2.58
4 5.16
7 9.03
11 14.19
17 21.93
How to fill in the table for all missing values of s and d?In order to have a proportional relationship and equivalent ratios, the variables s and d must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = d/s
Constant of proportionality (k) = 2.58/2
Constant of proportionality (k) = 1.29.
When the amount of money (d) is 5.16, the number of songs (s) is given by;
s = d/k
s = 5.16/1.29
s = 4 songs.
When the number of songs (s) is 7, the amount of money (d) is given by;
d = ks
d = 1.29(7)
d = $9.03.
When the number of songs (s) is 11, the amount of money (d) is given by;
d = ks
d = 1.29(11)
d = $14.19.
When the amount of money (d) is 21.93, the number of songs (s) is given by;
s = d/k
s = 21.93/1.29
s = 17 songs.
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The probability that it is Monday and that a student is absent is 3/100. Because there are 5 school days in a week, the probability that a randomly selected day of the school week is Monday is 1/5.
What is the probability that a student is absent given that today is Monday?
Enter your answer as a fraction in simplest form, formatted like this: 3/14
The probability that the student is absent is 3/20
What is Probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The probability that the student will be absent and it will be on Monday is 3 /100.
The probability that it will be Monday is 1/5
Therefore the probability that the student will be absent any day is 3/100÷1/5 = 3/20
Since it is certain that it is Monday , the probability that it is Monday is 1.
Therefore, the probability that the student is absent on that Monday is 1 × 3/20 = 3/20
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A new manufacturing process requires 45 minutes to produce a piece of furniture. If the old process took 1 hour and 20 minutes what is the percent of change in production time and is it a percent increase or a percent decrease? Round your answer to the nearest hundredth.
There is a percent decrease of about 43.75%
What is Percentage?Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of whole is always taken as 100. They are used like fractions and decimals i.e ways to describe parts of a whole. While using percentages, the whole is considered to be made up of a hundred equal parts. The symbol % is used to show that a number is a percentage
New Process = 45 mins
Old Process = 1 hour and 20 minutes (80mins)
Increase/Decrease = Old Process - New Process
Increase/Decrease = 80 - 45
Increase/Decrease = 35
Therefore there is reduction in the manufacturing process;
% decrease = (35/80) x 100
% decrease = 43.75%
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Please can someone help me
Answer:
reciprocal
Step-by-step explanation:
Reciprocal just means to turn it upside down.
N - 3 = -1
Answers
-2
3
2
-4
Answer:2
Step-by-step explanation:
N minus 3 equals negative 1
add 3 to both sides leaving the equation N = -1 +3 or N=3-1
3-1 equals 2
In regression analysis, the error term e is a random variable with a mean or expected value of
1
x
0
u
You are given the following information about y and x.
Explanatory Variable Response Variable
3 5
1 3
4 4
3 6
5 8
a) The least squares estimate of the slope or b₁ equals
b) The least squares estimate of the intercept or b₀ equal
c) The point estimate of y when x=2 is
a) The least squares estimate of the slope (b₁) can be calculated using the formula:
b₁ = (n∑(xy) - (∑x)(∑y)) / (n∑(x^2) - (∑x)^2)
Where n is the number of observations, x and y are the explanatory and response variables, respectively.
b₁ = (5*(35+13+44+36+58) - (3+1+4+3+5)(5+3+4+6+8)) / (5*(3^2+1^2+4^2+3^2+5^2) - (3+1+4+3+5)^2) = 0.8
b) The least squares estimate of the intercept (b₀) can be calculated using the formula:
b₀ = (∑y - b₁*(∑x))/n
b₀ = (5+3+4+6+8-0.8*(3+1+4+3+5))/5 = 3.4
c) The point estimate of y when x=2 can be calculated using the equation of the line:
y = b₀ + b₁x
y = 3.4 + 0.82 = 4.8
So the point estimate of y when x=2 is 4.8
What are random variable?In probability and statistics, a random variable is a variable whose possible values are numerical outcomes of a random event. It is a function that maps outcomes of a random experiment to a real number. It can be discrete, meaning it can take on only a countable number of values, or it can be continuous, meaning it can take on any value within a given range. The probability distribution of a random variable describes the likelihood of different outcomes occurring. It can be used to calculate expected values, variances, and other measures of statistical dispersion.
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Find the value of x and explain please
Answer:
Step-by-step explanation:
All triangle's angles have a sum of 180 degrees.
56 + 61 = 117
180 - 117 = 63
x = 63
What is the product of the complex numbers below?
(3-2)(1+7i) please help
Answer:
6125555566/6661234567
Pls, answer the question below.
Answer:
B. 3⁻⁴; E. 1/3⁴.
Step-by-step explanation:
1. rule is:
cᵃ:cᵇ=cᵃ⁻ᵇ;
2. according to the rule above:
3⁻⁸:3⁻⁴=3⁻⁸⁺⁴=3⁻⁴, then
3. correct answer is 'B'; 'E'.
The same number goes into each box to make the two ratios below equivalent.
4 0
36
Which number goes into both boxes?
6
09
12
18
27
Answer:
12
Step-by-step explanation:
4 / 12 = 12 / 36 so answer : 12
That was just by looking.....here is mathematical way :
4/ x = x/36 cross multiply
144 = x^2
x = 12
on interval 0<= x <= 2pi, where are the x-int of y=cos(2x)
Answer: If you're on the test, the answer should be B
Step-by-step explanation:
Answer:
[tex]\left(\frac{\pi}{4}, 0 \right), \left(\frac{3\pi}{4}, 0 \right), \left(\frac{5\pi}{4}, 0 \right), \left(\frac{7\pi}{4}, 0 \right)[/tex]
Step-by-step explanation:
The [tex]x[/tex]-intercepts are when [tex]y=0[/tex].
[tex]0 \leq x \leq 2\pi \implies 0 \leq 2x \leq 4\pi \\ \\ \cos 2x=0 \implies 2x=\frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \frac{7\pi}{2} \\ \\ \implies x=\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4} \\ \\ \therefore \left(\frac{\pi}{4}, 0 \right), \left(\frac{3\pi}{4}, 0 \right), \left(\frac{5\pi}{4}, 0 \right), \left(\frac{7\pi}{4}, 0 \right)[/tex]
9c-10(4c-2) I need help asap
Answer:
-31c + 20
Step-by-step explanation:
distribute
9c + -10 × 4c, -10 × -2
9c - 40c + 20
-31c + 20
Answer:
-31c+20
Step-by-step explanation:
You multiply the equation in the parenthesis by negative ten and then subtract it all from 9c
what is -6.15/-8.2 show work
The solution to the expression -6.15/-8.2 is 0.75
How to evaluate the expression?From the question, we have the following parameters that can be used in our computation:
-6.15/-8.2
Next, we cancel out the negative sign
So, we have the following representation
-6.15/-8.2 = 6.15/8.2
Using a calculator, we have the following result
So, we have the following representation
-6.15/-8.2 = 0.75
Hence, the solution is 0.75
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3. An aspirin manufacturer fills bottles by weight rather than by count. Since each bottle should contain 100 tablets, the average weight per tablet should be 5 grains. Each of 100 tablets taken from a very large lot is weighed, resulting in a sample average weight per tablet of 4.87 grains and a sample standard deviation of 0.35 grain. Does this information provide strong evidence for concluding that the company is not filling its bottles as advertised? Test the appropriate hypotheses using by first computing the P-value and then comparing it to the specified significance level.
As the p-value of the test, of 0.0002, is less than the significance level of 0.05, the information provide strong evidence for concluding that the company is not filling its bottles as advertised.
What are the hypothesis tested?At the null hypothesis, it is tested if the tablets are filled as advertised, that is, the mean is of 5 grains, hence:
[tex]H_0: \mu = 5[/tex]
At the alternative hypothesis, it is tested if the tablets are not filled as advertised, that is, if the mean is less than 5 grains, hence:
[tex]H_1: \mu < 5[/tex]
What is the test statistic?The equation for the test statistic is defined as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the parameters are given as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of these parameters for this problem are given as follows:
[tex]\overline{x} = 4.87, \mu = 5, s = 0.35, n = 100[/tex]
Hence the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{4.87 - 5}{\frac{0.35}{\sqrt{100}}}[/tex]
t = -3.71.
What is the p-value?Using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with 100 - 1 = 99 df, the p-value of the test is of:
0.0002.
Hence the information provide strong evidence for concluding that the company is not filling its bottles as advertised.
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What is this expression in simplified form?
2/135*6 - 3√15*6
A. 9x³√10
OB. 8³/30
C. 119³√15
D. 3x³√15
4
Answer: The expression in simplified form is D. 3x³√15
To simplify the expression, we can first simplify the fractions.
2/1356 can be simplified to 12/225.
Then, we can use the distributive property to simplify the expression further.
12/225 - 3√156 = 12/225 - 18√15
The last step is to combine the terms,
12/225 - 18√15 = (-6/75) - (6√15) = -6/5 * (1/5 - √15) = -6 * (- √15/5) = 3 * √15 * 6
Therefore, the simplified form of the expression is D. 3x³√15
Step-by-step explanation:
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then graph the equation.
y=8.4 when x=1.2
The equation of variation is y = ________.
(Simplify your answer.)
The equation of the variation is y =7x.
What is the equation?When we are discussing about the idea of variation then on specie is changing with respect to the other. If the change is such that the both variables are increasing at the same time then we could say that we have a direct variation.
Now, we know that;
y=8.4 when x=1.2
Given that;
y α x
If we add k;
y = kx
8.4 = k 1.2
x = 8.4/1.2
x = 7
Then the equation is;
y =7x
This is the equation that has been used to produce the graph in the image attached to the answer given here.
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Allea, Iniko, and Loki played a game. Allea scored 2/5 of the points, and Loki scored 1/3 of the points. What part did Iniko score. Who had the highest score?
Answer:
Iniko's part is 4/15
Allea had the highest score
Step-by-step explanation:
Use the LCD 15 and convert the fractions:
Allea: 2/5 = 6/15
Loki: 1/3 = 5/15
Iniko score = 15/15 - 6/15 - 5/15 = 4/15
How to you solve this?
The sum of the sequence ∑₀⁵⁰⁰(2i - 312) is 94500
What is the sum of a sequence?The sum of a sequence is the sum of terms of the sequence.
How to evaluate the sum of the sequence?Given the sum ∑₀⁵⁰⁰(2i - 312).
To evaluate the sum, we expand the brackets.
So, we have that
∑₀⁵⁰⁰(2i - 312) = ∑₀⁵⁰⁰2i - ∑₀⁵⁰⁰312
= 2∑₀⁵⁰⁰i - ∑₀⁵⁰⁰312
Now, ∑₀⁵⁰⁰i is the sum of natural numbers
So, ∑₀⁵⁰⁰i = n(n + 1)/2 where n = 500
Also, ∑₀⁵⁰⁰312 = 312n where n = 500
Thus substituting these into the equation for the sum, we have that
∑₀⁵⁰⁰(2i - 312) = 2∑₀⁵⁰⁰i - ∑₀⁵⁰⁰312
= 2n(n + 1)/2 - 312n
Given that n = 500, substituting n = 500 into the equation, we have that
∑₀⁵⁰⁰(2i - 312) = n(n + 1) - 312n
= 500(500 + 1) - 312 × 500
= 500(501) - 312 × 500
= 250500 - 156000
= 94500
So, the sum is 94500
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A plumber wants to cut a piece of pipe 4 meters long into two pieces so that one piece is 2/3 as long as the other. Find the length of each piece.
simplify 5a-10a. please i need the answer asap.
Answer:
-5a
Step-by-step explanation:
Think of it as 5-10 since both of them have "a"
5-10=-5
-5a
Answer:
-5a
Step-by-step explanation:
AlgebraAlgebra are algebraic expressions that can be used as variables and is subjected to BODMAS rule just like numerical expressions.
Example: 5b + 9b = 14b
SolutionGiven from the question:
5a - 10a = -5a
3. A 12 -foot-tall statue stands in the park and casts a shadow that is 18 feet long. How long is the shadow of a 3 -foot-tall child who stands next to the statue?
6.5 ft.
72 ft.
4.5 ft.
2 ft.
please help with math
Answer:
B. 15, 20, ...
Step-by-step explanation:
You want to know which sequence of numbers has the steepest graph.
SlopeThe slope (steepness) of the graph is the ratio of the change in y to the change in x. Here, we presume the x-values for each of these sets of points are 1, 2, 3, 4, ....
That means the slope will be the difference of adjacent y-values. Subtracting the first from the second, we get ...
8 -4 = 4
20 -15 = 5
52 -50 = 2
7 -4 = 3
The sequence in which the values differ by 5 has the largest difference, so will have the steepest graph:
15, 20, 25, 30, ...
