The intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a
Given that,
We have to find the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing.
We know that,
Take the function equation,
f(x)=ax² + bx + c
The derivative of the function of x is
f'(x)=ax+b
So, f(x) is increasing when f'(x) > 0
f(x) is decreasing when f'(x) < 0
Then we can say
f'(x) > 0 , when b > 0 and a < 0
2ax + b < 0
2ax < - b
x<-b/2a
Now,
f'(x) < 0 , when b < 0 and a > 0
2ax + b > 0
2ax > - b
x>-b/2a
Therefore, the intervals on which the function f(x) = ax² + bx + c (where "a" doesn't = 0) is increasing and decreasing is x>-b/2a and x<-b/2a.
To learn more about interval visit: https://brainly.com/question/11051767
#SPJ4
a statistician believes that the percent population growth rate of major cities has decreased compared to the last decade. to test his claim, he randomly selects major cities and compares the percent population growth between the years 2007 and 2017 to the percent population growth between the years 1997 and 2007. let d
Statisticians want to know if the hypothesized mean of the differences is less than zero for paired data. So, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd<0.Option(b)
What is a null hypothesis?A null hypothesis proposes that certain characteristics of a population or development process are the same regardless of whether they differ or not. There is a difference, according to the alternative hypothesis. A null hypothesis can be rejected with a certain degree of confidence through hypothesis testing.
The alternative hypothesis can be supported if the null hypothesis is rejected. A null hypothesis test is a basis for science's falsification principle.
Question:A statistician believes that the percent population growth rate of major cities has decreased compared to last decade. To test his claim, he randomly selects major cities and compares the percent population growth between the years 2007 and 2017 to the percent population growth between the years 1997 and 2007. Let d=percent growth rate from 2007 to 2017−percent growth rate from 1997 to 2007. Identify the correct null and alternative hypothesis for a hypothesis test.
H0:μd≠0
Ha:μd=0
H0:μd=0
Ha:μd<0
H0:μd=0
Ha:μd>0
H0:μd=0
Ha:μd≠0
To Learn more about null hypothesis:
https://brainly.com/question/19990568
#SPJ4
please help if you can I’m stuck
Answer:
• Area of parallelogram = 270 in.²
• Area of square = 225 in.²
• Area of composite figure = 495 in.²
Step-by-step explanation:
We are given a composite figure made up of a parallelogram and a square and told to find its area.
To do this, we are told first to find the area of the parallelogram. The formula for the area of a parallelogram is:
[tex]\boxed{\mathrm{Area \ of \ parallelogram = base \times height}}[/tex].
From the figure, we can see that, for the parallelogram, height = 18 in. and base = 15 in. (since opposite sides of a parallelogram are equal).
Using this information, we can calculate the area of the parallelogram:
Area = base × height
= 15 in. × 18 in.
= 270 in.²
Next, we have to find the area of the square using the formula:
[tex]\boxed{\mathrm{Area \ of \ square = side \times side}}[/tex].
From the figure, we can see that the length of a side of the square is 15 in.
Therefore, using the formula above, we can calculate the area of the square:
Area = side × side
= 15 in. × 15 in.
= 225 in.²
Now that we know the respective areas of the two shapes that make up the composite shape, we simply have to add the areas together:
Area of composite figure = 270 in² + 225 in²
= 495 in.²
when an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (mstr) is . a. sstr/k b. sstr/nt c. sstr/(k – 1) d. sstr/(nt – 1)
When data from k populations are utilized in an analysis of variance, the mean square between treatments (MSTR) = (C) SSTR/(k - 1).
What is an analysis of variance?A statistical method called analysis of variance (ANOVA) is used to examine variations in response variables (continuous random variables) evaluated under settings with discrete factors (classification variables, often with nominal levels).
Analysis of Variance is referred to as ANOVA.
Ronald Fisher created a statistical test in 1918, and it has been in use ever since.
Simply put, an ANOVA analysis determines if the means of three or more independent groups differ statistically.
The mean square between treatments (MSTR) equals SSTR/ when samples from k populations are used in an analysis of variance (k - 1).
Therefore, when data from k populations are utilized in an analysis of variance, the mean square between treatments (MSTR) = (C) SSTR/(k - 1).
Know more about an analysis of variance here:
https://brainly.com/question/25800044
#SPJ4
Correct question:
When an analysis of variance is performed on samples drawn from k populations, the mean square between treatments (MSTR) is _____.
a. sstr/k
b. sstr/nt
c. sstr/(k – 1)
d. sstr/(nt – 1)
In a tsunami, the wave speeds (in meters per second) can be modeled by s(d)=√9.8d, where d is the depth (in meters) of the water. Estimate the depth of the water when the wave speed is 200 meters per second
The depth of the water when the wave speed is 200 meters per second is 4081.63m
What is Speed?Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.
Given,
In a tsunami, the wave speeds (in meters per second) can be modeled by s(d)=√9.8d,
Where d is the depth
We need to find the depth when speed is 200 meters per second
s(d)=√9.8d,
200=√9.8d,
Square on both sides
40000=9.8d
Now divide both sides by 9.8
d=4081.63m
Hence, the depth of the water when the wave speed is 200 meters per second is 4081.63m
To learn more on Speed click:
https://brainly.com/question/28224010
#SPJ1
David pays a flat rate per day to rent his bike. The cost of David's bike rental plan, B(t), can be represented by which of the following functions?
A. B(t) = 5(0,6)^t
B. B(t) = 5(1 + 0.6)^t
C. B(t) = 0.6t + 5
D. B(t) = -0.6t + 5
The function that represents the cost of David's bike rental plan, B(t) is C. B(t) = 0.6t + 5
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the information, David pays a flat rate of $5 and and extra $0.6 per day to rent his bike. The cost of David's bike rental plan, B(t). Let the extra day be illustrated by t.
This will be:
B(t) = 5 + (0.6 × t)
B(t) = 5 + 0.6t
The correct option is C.
Learn more about equations on;
brainly.com/question/2972832
#SPJ1
Complete question
David pays a flat rate of $5 and and extra $0.6 per day to rent his bike. The cost of David's bike rental plan, B(t), can be represented by which of the following functions?
A. B(t) = 5(0,6)^t
B. B(t) = 5(1 + 0.6)^t
C. B(t) = 0.6t + 5
D. B(t) = -0.6t + 5
PLEASE HELP ASAPPP !!! WILL GIVE BRAINLIEST AND 5.0 STAR RATING
Answer: $13,000
Step-by-step explanation:
vera claimed the solution set on the number line represents the inequality . which error did vera make?
The error that Vera made is she used the wrong number in her inequality to claimed the solution set on the number line represents the inequality.
What is inequality?In mathematics, "inequality" refers to a connection between two expressions or values that are not equal to one another. The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in lieu of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in. An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
To know more about inequality,
https://brainly.com/question/15014103
#SPJ4
Round to 3 SF
70.782 please urgent
Answer:
70.8
Step-by-step explanation:
70.782 round the bold 7 to 8 because the number that follows it is >=5
70.8
Solve for x in the diagram below.
180-(45+15) = 120
4x+120=180
4x=60
x=15
endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. what is the probability that an endure all battery selected at random will last more than 550 hours? a) 0.1056 b) 0.1151 c) 0.8849 d) 0.8944 e) 0.1587 f) none of the above.
The probability that an Endure All battery selected at random will last more than 610 hours is 0.1056.
What is a normal distribution?
A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.
Here, we have
Normally distributed with a mean of 500 hours and a standard deviation of 40 hours.
We have to calculate the probability that an endure all battery selected at random will last more than 550 hours.
Given that μ = 500, σ = 40, for x > 550
z = 550-500/40
z = 1.25
From the normal distribution table, P(z > 1.25) = 1 - P(z < 1.25) = 1 - 0.8944 = 0.1056
Hence, The probability that an Endure All battery selected at random will last more than 610 hours is 0.1056.
To learn more about the normal distribution from the given link
https://brainly.com/question/4079902
#SPJ4
those who obtained the correct umbrella leave, while everyone else picks again randomly. this process continues until everyone has gotten his or her umbrella. what is the expected number of rounds needed?
The intercountry differences in participation rates in organ-donation programs is due to STATUS QUO BIAS.
Status quo bias can be defined as the emotional prejudice to the way things are and any change is considered a loss.
This status quo bias phenomenon often affect decision making in an individual. In some countries, organ donation is widely accepted by the people while it is not accepted in some other countries. The only reason for this is because of just the way things are done usually in those countries.
Another example of status quo bias will be saving money towards retirement. Everyone sees this as a The intercountry differences in participation rates in organ-donation programs is due to STATUS QUO BIAS.
Status quo bias can be defined as the emotional prejudice to the way things are and any change is considered a loss.
This status quo bias phenomenon often affect decision making in an individual. In some countries, organ donation is widely accepted by the people while it is not accepted in some other countries. The only reason for this is because of just the way things are done usually in those countries.
Another example of status quo bias will be saving money towards retirement. Everyone sees this as a norm.
To know more about status quo bias
https://brainly.com/question/14325636
#SPJ4
7. Solve 10x + 8 = 8x - (- 16) for x.
Answer:
Answer is 4.
x = 4
Step-by-step explanation:
write a question of interest for which a two-sided t test for the difference in populations means can be used to answer example
To determine whether the mean weight of two distinct turtle species is equal. It would take too much time and money to weigh each turtle because there are thousands of them in each group.
A two-sample t-test is used to determine whether or not genuine population means are equal.
The accompanying null hypothesis is usually used in a two-sample t-test:
[tex]H_0[/tex]: The two population averages are equivalent when 1 = 2.
The alternative hypothesis might have two tails, a left or right tail, or none at all:
Two-tailed [tex]H_1[/tex]: μ1 ≠ μ2 Neither of the two population means is equal.
(Left-tailed) [tex]H_1[/tex]: Population 1 mean is lower than population 2 mean by a factor of 1.
[tex]H_1[/tex] (right-tailed): Populations 1 and 2 have mean values that are higher than each other.
Learn more about t-tests at
https://brainly.com/question/15870238?referrer=searchResults
#SPJ4
Apply the distributive property to factor out the greatest common factor. 75+20=75+20=.
Using the distributive property, the greatest common factor of 75+20 is 5(15+4).
What is distributive property?The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.
For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.
So, the largest number that will split two values is the greatest common factor. Two values are available: 75 and 20.
Each has a set of numbers that when added together equal the total.
We must identify the most important quality or area where they most agree.
Each possesses the following elements:
75: 1,3,5,15,25, 75
20: 1, 2, 4, 5, 10, 20
Each has 5, making this the GCF.
As a result, we write the expression as 5(_+_).
We calculate the matching factor by multiplying each term by 5.
75/5= 15
20/5=4
5(15+4)
Therefore, using the distributive property, the greatest common factor of 75+20 is 5(15+4).
Know more about the distributive property here:
https://brainly.com/question/2807928
#SPJ4
Correct question:
Apply the distributive property to factor out the greatest common factor.
75 + 20 =
f two balls are drawn from a bag containing 2 white, 4 red and 5 black balls. what isthe chance thata. both the balls are redb. one is red and the other black ?
a) The probability of both balls drawn from the bag be red is 6/55
b) The probability of one ball red and other ball black is 4/11
Given,
Number of white balls in the bag = 2
Number of red balls in the bag = 4
Number of black balls in the bag = 5
Two balls are drawn from the bag.
Here,
a) Find the probability of both balls be red.
(²C₀ x ⁴C₂ x ⁵C₀) / ¹¹C₂
= (1 x 6 x 1)/ 55
= 6/55
That is,
The probability of both balls be red is 6/55
b) Find the probability of one ball red and other ball black
(²C₀ x ⁴C₁ x ⁵C₁) / ¹¹C₂
= (1 x 4 x 5) / 55
= 20/55
= 4/11
That is,
The probability of one ball red and other ball black is 4/11
Learn more about probability here;
https://brainly.com/question/23986809
#SPJ4
Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 12 and its height is 8?.
The possibile base and height of second triangle is option 4: 16 and 6.
We are given the height and base are inversely proportional for the triangle. Based on this, the area of triangle is given by the formula -
Area = 1/2 × base × height
Keep the values in formula to find the area of first triangle -
Area = 1/2 × 12 × 8
Area = 6 × 8
Area = 48
Now, option a in the choices is incorrect, because there is no variation seen in the two values. Trying the other three options to find the dimensions of same area.
Option 2: 60 and 36
Area = 1/2 × 60 × 36
Area = 30 × 36
Area = 1080
Option 3: 120 and 80
Area = 1/2 × 120 × 80
Area = 60 × 80
Area = 4800
Options 4: 16 and 6
Area = 1/2 × 16 × 6
Area = 8 × 6
Area = 48
Hence, option 4 16 and 6 are correct base and height.
Learn more about triangle -
https://brainly.com/question/17335144
#SPJ4
The complete question is attached in the figure.
What is -2x+2 (1-4x) = 52?
Answer:x=-5
Step-by-step explanation:
How do I find this? I am sturggling lol
The table is completed below
Distance (cm) weight (newtons)
20 28
55 77
100 140
1 1.4
The maximum data in the y axis is 140
The maximum data in the x axis is 100
How to find fill the blankThe blank is filled by finding proportional relationship, this is calcualted by
let the constant of proportionality be k
20k = 28
k = 20/28
k = 1.4
55k = 55 * 1.4 = 77
? * k = 140
? = 140/k = 140/1.4 = 100
1 * k = 1 * 1.4 = 1.4
How high each value can go is the highest value in each axis and the is 100 for x axis and 140 for y axis
Learn more about constant of proportionality at:
https://brainly.com/question/1835116
#SPJ1
what is 2(x-1) + 5 = x + 7
Answer:
x = 4
Step-by-step explanation:
Look what the attachment
x=4
Step-by-step explanation:
2x-2+5=x+7
2x+3=x+7
2x-x=7-3
x=4
PLEASE HELP ASAP
Part A: A 30-kilogram mass is moving across a horizontal surface at 5.0 m/s. The mass comes to
a stop over 6 seconds. What is the acceleration?
Part B: What is the magnitude of the force required to bring the object to a stop?
Answer:
Below
Step-by-step explanation:
acceleration = Δv / Δt = - 5/6 m/s^2
( negative sign shows it to be a deceleration)
F = ma
= 30 ( -5/6) = -25 N or 25 N in the direction opposite of the velocity ( like a frictional force)
Compare 0.3 and 0.8 using >,=, or <. Draw a model or number line to support your solution
0.8 is greater than 0.3 an image is attached to show the plotting on the number line.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
Given, are two decimals 0.3 and 0.8.
We know 0.3 lies between 0 and 0.5 and 0.8 lies between 0.5 and 1.
∴ 0.8 > 0.3.
The plotting of the numbers is attached in the image.
learn more about number line here :
https://brainly.com/question/13425491
#SPJ1
All of the following are steps in derivative classification EXCEPT:
Seek additional guidance to resolve uncertainty
Analyze material to be classified
Use authorized sources for guidance
Make recommendations for others to mark the new document
Option d). Making the initial determination for all the information requires protection among the unauthorized disclosure where the interest of security is not a derivative classification.
Derivative Classification is the incorporating, paraphrasing, restating, or producing in new shape data this is already categorized, and staining the newly evolved fabric constant with the class markings that practice to the supply data. Copying or duplicating present categorized data, which includes photocopying a document, isn't by-product class.
Derivative classifiers are accountable for preserving the safety and integrity of categorized data. These people should own information concerning the difficulty count number of the categorized data, in addition to class control and staining techniques. Typically, there are 4 classifications for data: public, internal-only, confidential, and restricted. Let's study examples for every of those.
Learn more about derivative classification visit: brainly.com/question/29546945
#SPJ4
Correct Question:
All of the following are steps in derivative classification EXCEPT:
a). Seek additional guidance to resolve uncertainty
b). Analyze material to be classified
c). Use authorized sources for guidance
d). Make recommendations for others to mark the new document
Some instructions for the time it take to roast a turkey are: "allow 20 minutes for every 450 g". How long will it to take to roast a turkey that weights 6.3 kg
Answer:
Step-by-step explanation:
6.3kg = 6300 g
450 * 14 = 6300
20 minutes for 450 g
so, 20 *14 = 280 minutes
Answer:
280 minutes
Step-by-step explanation:
To roast a turkey that weighs 6.3 kg, it will take 20 minutes for every 450 g of turkey, or a total of 20 minutes * (6.3 kg / 0.45 kg/450 g) = 280 minutes.
Which of the following PivotTable layouts displays all fields in separate columns and subtotal rows at the bottom of each group, similar to a table?
a. Compact
b. Outline
c. Tabular
d. Condense
The correct option is tabular
What is a pivot table and what is it used for?An interactive way to quickly summarize large amounts of data is with a pivot table. A Pivot Table can be used to thoroughly analyze numerical data and provide unexpected answers about your data. Querying vast amounts of data in a variety of user-friendly ways is one task that a pivot table is especially useful.
What is the main advantage of using a pivot table?Data are easily summarized in pivot tables. Pivot tables can be a huge help if you're looking for a quicker and easier way to summarize data. It will help any user create a brief summary from a large amount of disorganized data that is arranged in rows and columns.
From the above information
we can understand that
out of the 4 options
the PivotTable layouts displays all fields in separate columns and subtotal rows at the bottom of each group, similar to a table
is Tabular
hence the solution is Tabular
To learn more about pivot table click the following link :-
https://brainly.com/question/23501096
#SPJ1
I NEED HELP!! 100 points!!!!
Domain and range of G?
G = {( -8, 7 ), ( -9, 0 ), ( 3, 7 )}
Write answers as set notation
Answer:
domain {-9,-8,3}, range{0,7}
Step-by-step explanation:
domain is the set of all x values
range is the set of all y values
Oliver is buying equipment for his restaurant. He can buy two blenders for $396 or three blenders for $479. Find which deal has the best unit price per blender, then record the best unit price!
Hence, the deal of $[tex]479[/tex] is best unit price per blender.
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
Oliver is buying equipment for his restaurant. He can buy two blenders for $[tex]396[/tex] or three blenders for $[tex]479[/tex].
So,
Oliver buying two blenders at $[tex]396[/tex] so the cost of one blender is
i.e., [tex]\frac{396}{2}=198[/tex]$
Oliver buying two blenders at $[tex]479[/tex] so the cost of three blenders is
i.e., [tex]\frac{479}{3}=159[/tex]$
Hence, the deal of $[tex]479[/tex] is best unit price per blender.
To know more about the equation
https://brainly.com/question/12788590
#SPJ1
What is the value of x? Enter your answer as a decimal.
Triangle M N P with segment A B parallel to segment N P and A is between M and N and B is between M and P. M N equals 46.2 centimeters, A N equals 14 centimeters, M P equals 72.6 centimeters, and M B equals x.
The value of MB equal x which is equal to 50.6 as the two triangles are similar triangles.
Based on the given information, MNP has a segment AB which is parallel to NP. As AB and NP are parallel and MN is transverse. Therefore, ∠MAB ≅ ∠MNP. According to Angle – Angle property of similarity, triangle MNP and triangle MAB are similar triangle. If two pairs of corresponding angles are congruent in two triangles, then the triangles are similar. The corresponding sides of similar triangles will be in the same ratio. Hence,
MA/MN = MB/MP
MA = MN – AN = 46.2 – 14 = 32.2
Hence,
32.2/46.2 = x/72.6
x = 50.6
Learn more about Similar triangle:
https://brainly.com/question/14285697
#SPJ4
Which phrase describes the algebraic expression 3 x minus 4?
the sum of three times a number and four
four less than three times a number
the quotient of three times a number less four
the difference between four and three
Answer: four less than three times a number
Step-by-step explanation:
4 - 3x
x beside a number is times a number so example 4 - ( 3 multiply X)
sorry if it doesnt make sense
Answer:
yo
Step-by-step explanation:
the person above is right
um did it on edge
The school cafeteria manager surveys students to determine
which type of juice they prefer at breakfast. The manager
uses the computer to randomly select 250 students to
survey. What type of sampling is the manager using?
The type of sampling method that the manager used is called; Simple random sampling
What is the method of sampling that is used?There are different methods of sampling used in statistics and they are;
1. Simple random sampling
2. Systematic sampling
3. Stratified sampling
4. Cluster sampling
5. Convenience sampling.
Now, we are told that the manager uses the computer to randomly select 250 students to survey. This type of sampling method is known as simple random sampling because every single student of that school is chosen randomly, merely by chance. Each student has the same probability of being chosen to be a part of a sample.
Read more about Method of sampling at; https://brainly.com/question/9910540
#SPJ1
The radius of a circular disk is given as 27 cm with a maximum error in measurement of 0.2 cm.
1) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.)
2)What is the relative error? (Round your answer to four decimal places.)
3)What is the percentage error? (Round your answer to two decimal places.)
The maximum error in the calculated area of the disk is 33.93 square cm. The relative error is 0.0148. The percentage error is 1.48%.
a. The area [tex]$\mathrm{A}$[/tex] of a circle with radius [tex]$\mathrm{r}$[/tex] is given by the following formula from Geometry:
[tex]$A=\pi r^2$[/tex]
The question provides us the following information:
radius [tex]$r=27 \mathrm{~cm}$[/tex], maximum radius measurement error [tex]$\Delta r=0.2 \mathrm{~cm}$[/tex]
Using linear differentials we get the error in the calculation of the area of this disk [tex]$\Delta A$[/tex] from (1) as follows:
[tex]$\Delta A=2 \pi r \Delta r \Longrightarrow|\Delta A|=2 \pi r|\Delta r|$[/tex]
Using the information from (2) in (3) yields
[tex]$|\Delta A|=2 \pi(27)(0.2)=33.93 \mathrm{~cm}^2 \text {. }$$[/tex]
The maximum error in the calculated area of the disk is 33.93 square [tex]$\mathrm{cm}$[/tex].
b. The relative error is calculated using (1) and [tex]$r=27 \mathrm{~cm}$[/tex] as follows:
Relative Error [tex]$=\frac{|\Delta A|}{A}=\frac{33.93}{\pi\left(27^2\right)}=0.0148$[/tex].
The relative error is 0.0148.
c. The percentage error is the relative error in part b. above multiplied by [tex]$100 \%$[/tex] to give us
Percentage Error [tex]$=100 \% \times$[/tex] Relative Error [tex]$=100 \% \times 0.0148=1.48 \%$[/tex].
The percentage error is [tex]$1.48 \%$[/tex].
To learn more about percentage error visit: https://brainly.com/question/28746643
#SPJ4